LaTeX2e: An unofficial reference manual
1 About this document
2 Overview of LaTeX
3 Document classes
4 Fonts
5 Layout
6 Sectioning
7 Cross references
8 Environments
9 Line breaking
10 Page breaking
11 Footnotes
12 Definitions
13 Counters
14 Lengths
15 Making paragraphs
16 Math formulas
17 Modes
18 Page styles
19 Spaces
20 Boxes
21 Color
22 Graphics
23 Special insertions
24 Splitting the input
25 Front/back matter
26 Letters
27 Input/output
28 Command line interface
Appendix A Document templates
Index
LaTeX2e: An unofficial reference manual
1 About this document
2 Overview of LaTeX
  2.1 Starting and ending
  2.2 Output files
  2.3 TeX engines
  2.4 LaTeX command syntax
  2.5 Environment
  2.6 CTAN: The Comprehensive TeX Archive Network
3 Document classes
  3.1 Document class options
  3.2 Additional packages
  3.3 Class and package construction
    3.3.1 Class and package structure
    3.3.2 Class and package commands
4 Fonts
  4.1 'fontenc' package
    4.1.1 '\DeclareFontEncoding'
    4.1.2 '\DeclareTextAccent'
    4.1.3 '\DeclareTextAccentDefault'
    4.1.4 '\DeclareTextCommand' & '\ProvideTextCommand'
    4.1.5 '\DeclareTextCommandDefault' & '\ProvideTextCommandDefault '
    4.1.6 '\DeclareTextComposite'
    4.1.7 '\DeclareTextCompositeCommand'
    4.1.8 '\DeclareTextSymbol'
    4.1.9 '\DeclareTextSymbolDefault'
    4.1.10 '\LastDeclaredEncoding'
    4.1.11 '\UseTextSymbol' & '\UseTextAccent'
  4.2 Font styles
  4.3 Font sizes
  4.4 Low-level font commands
5 Layout
  5.1 '\onecolumn'
  5.2 '\twocolumn'
  5.3 '\flushbottom'
  5.4 '\raggedbottom'
  5.5 Page layout parameters
  5.6 '\baselineskip' & '\baselinestretch'
  5.7 Floats
    5.7.1 '\caption'
6 Sectioning
  6.1 '\part'
  6.2 '\chapter'
  6.3 '\section'
  6.4 '\subsection'
  6.5 '\subsubsection', '\paragraph', '\subparagraph'
  6.6 '\appendix'
  6.7 '\frontmatter', '\mainmatter', '\backmatter'
  6.8 '\@startsection', typesetting sectional unit headings
7 Cross references
  7.1 '\label'
  7.2 '\pageref'
  7.3 '\ref'
  7.4 'xr' package
8 Environments
  8.1 'abstract'
  8.2 'array'
  8.3 'center'
    8.3.1 '\centering'
  8.4 'description'
  8.5 'displaymath'
  8.6 'document'
    8.6.1 '\AtBeginDocument'
    8.6.2 '\AtEndDocument'
  8.7 'enumerate'
  8.8 'eqnarray'
  8.9 'equation'
  8.10 'figure'
  8.11 'filecontents'
  8.12 'flushleft'
    8.12.1 '\raggedright'
  8.13 'flushright'
    8.13.1 '\raggedleft'
  8.14 'itemize'
  8.15 'letter' environment: writing letters
  8.16 'list'
    8.16.1 '\item': An entry in a list
    8.16.2 'trivlist': A restricted form of 'list'
  8.17 'math'
  8.18 'minipage'
  8.19 'picture'
    8.19.1 '\put'
    8.19.2 '\multiput'
    8.19.3 '\qbezier'
    8.19.4 '\graphpaper'
    8.19.5 '\line'
    8.19.6 '\linethickness'
    8.19.7 '\thinlines'
    8.19.8 '\thicklines'
    8.19.9 '\circle'
    8.19.10 '\oval'
    8.19.11 '\shortstack'
    8.19.12 '\vector'
    8.19.13 '\makebox' (picture)
    8.19.14 '\framebox' (picture)
    8.19.15 '\frame'
    8.19.16 '\dashbox'
  8.20 'quotation' & 'quote'
  8.21 'tabbing'
  8.22 'table'
  8.23 'tabular'
    8.23.1 '\multicolumn'
    8.23.2 '\vline'
    8.23.3 '\cline'
    8.23.4 '\hline'
  8.24 'thebibliography'
    8.24.1 '\bibitem'
    8.24.2 '\cite'
    8.24.3 '\nocite'
    8.24.4 Using BibTeX
      8.24.4.1 BibTeX error messages
  8.25 'theorem'
  8.26 'titlepage'
  8.27 'verbatim'
    8.27.1 '\verb'
  8.28 'verse'
9 Line breaking
  9.1 '\\'
  9.2 '\obeycr' & '\restorecr'
  9.3 '\newline'
  9.4 '\-' (discretionary hyphen)
  9.5 '\discretionary' (generalized hyphenation point)
  9.6 '\fussy' & '\sloppy'
    9.6.1 'sloppypar'
  9.7 '\hyphenation'
  9.8 '\linebreak' & '\nolinebreak'
10 Page breaking
  10.1 '\clearpage' & '\cleardoublepage'
  10.2 '\newpage'
  10.3 '\enlargethispage'
  10.4 '\pagebreak' & '\nopagebreak'
11 Footnotes
  11.1 '\footnote'
  11.2 '\footnotemark'
  11.3 '\footnotetext'
  11.4 Footnotes in section headings
  11.5 Footnotes in a table
  11.6 Footnotes of footnotes
12 Definitions
  12.1 '\newcommand' & '\renewcommand'
    12.1.1 Control sequence, control word and control symbol
  12.2 '\providecommand'
  12.3 '\makeatletter' & '\makeatother'
  12.4 '\@ifstar'
  12.5 '\newcounter': Allocating a counter
  12.6 '\newlength'
  12.7 '\newsavebox'
  12.8 '\newenvironment' & '\renewenvironment'
  12.9 '\newtheorem'
  12.10 '\newfont'
  12.11 '\protect'
  12.12 '\ignorespaces & \ignorespacesafterend'
  12.13 xspace package
13 Counters
  13.1 '\alph \Alph \arabic \roman \Roman \fnsymbol': Printing counters
  13.2 '\usecounter'
  13.3 '\value'
  13.4 '\setcounter'
  13.5 '\addtocounter'
  13.6 '\refstepcounter'
  13.7 '\stepcounter'
  13.8 '\day' & '\month' & '\year'
14 Lengths
  14.1 Units of length
  14.2 '\setlength'
  14.3 '\addtolength'
  14.4 '\settodepth'
  14.5 '\settoheight'
  14.6 '\settowidth'
  14.7 '\stretch'
  14.8 Expressions
15 Making paragraphs
  15.1 '\par'
  15.2 '\indent' & '\noindent'
  15.3 '\parindent' & '\parskip'
  15.4 Marginal notes
16 Math formulas
  16.1 Subscripts & superscripts
  16.2 Math symbols
    16.2.1 Arrows
    16.2.2 '\boldmath' & '\unboldmath'
    16.2.3 Blackboard bold
    16.2.4 Calligraphic
    16.2.5 Delimiters
      16.2.5.1 '\left' & '\right'
      16.2.5.2 '\bigl', '\bigr', etc.
    16.2.6 Dots, horizontal or vertical
    16.2.7 Greek letters
  16.3 Math functions
  16.4 Math accents
  16.5 Over- and Underlining
  16.6 Spacing in math mode
    16.6.1 '\smash'
    16.6.2 '\phantom' & '\vphantom' & '\hphantom'
    16.6.3 '\mathstrut'
  16.7 Math styles
  16.8 Math miscellany
    16.8.1 Colon character ':' & '\colon'
    16.8.2 '\*'
    16.8.3 '\frac'
    16.8.4 '\sqrt'
    16.8.5 '\stackrel'
17 Modes
  17.1 '\ensuremath'
18 Page styles
  18.1 '\maketitle'
  18.2 '\pagenumbering'
  18.3 '\pagestyle'
  18.4 '\thispagestyle'
19 Spaces
  19.1 '\enspace' & '\quad' & '\qquad'
  19.2 '\hspace'
  19.3 '\hfill'
  19.4 '\hss'
  19.5 '\spacefactor'
    19.5.1 '\@'
    19.5.2 '\frenchspacing' & '\nonfrenchspacing'
    19.5.3 '\normalsfcodes'
  19.6 Backslash-space, '\ '
  19.7 '~'
  19.8 '\thinspace' & '\negthinspace'
  19.9 '\/'
  19.10 '\hrulefill' & '\dotfill'
  19.11 '\bigskip' & '\medskip' & '\smallskip'
  19.12 '\bigbreak' & '\medbreak' & '\smallbreak'
  19.13 '\strut'
  19.14 '\vspace'
  19.15 '\vfill'
  19.16 '\addvspace'
20 Boxes
  20.1 '\mbox' & '\makebox'
  20.2 '\fbox' & '\framebox'
  20.3 '\parbox'
  20.4 '\raisebox'
  20.5 '\sbox' & '\savebox'
  20.6 'lrbox'
  20.7 '\usebox'
21 Color
  21.1 'color' package options
  21.2 Color models
  21.3 Commands for color
    21.3.1 Define colors
    21.3.2 Colored text
    21.3.3 Colored boxes
    21.3.4 Colored pages
22 Graphics
  22.1 'graphics' package options
  22.2 'graphics' package configuration
    22.2.1 '\graphicspath'
    22.2.2 '\DeclareGraphicsExtensions'
    22.2.3 '\DeclareGraphicsRule'
  22.3 Commands for graphics
    22.3.1 '\includegraphics'
    22.3.2 '\rotatebox'
    22.3.3 '\scalebox'
    22.3.4 '\resizebox'
23 Special insertions
  23.1 Reserved characters
  23.2 Upper and lower case
  23.3 Symbols by font position
  23.4 Text symbols
  23.5 Accents
    23.5.1 '\accent'
  23.6 Additional Latin letters
  23.7 'inputenc' package
  23.8 '\rule'
  23.9 '\today'
24 Splitting the input
  24.1 '\endinput'
  24.2 '\include' & '\includeonly'
  24.3 '\input'
25 Front/back matter
  25.1 Table of contents, list of figures, list of tables
    25.1.1 '\@dottedtocline'
    25.1.2 '\addcontentsline'
    25.1.3 '\addtocontents'
    25.1.4 '\contentsline'
    25.1.5 '\nofiles'
    25.1.6 '\numberline'
  25.2 Indexes
    25.2.1 Produce the index manually
    25.2.2 '\index'
    25.2.3 'makeindex'
    25.2.4 '\printindex'
  25.3 Glossaries
    25.3.1 '\newglossaryentry'
    25.3.2 '\gls'
26 Letters
  26.1 '\address'
  26.2 '\cc'
  26.3 '\closing'
  26.4 '\encl'
  26.5 '\location'
  26.6 '\makelabels'
  26.7 '\name'
  26.8 '\opening'
  26.9 '\ps'
  26.10 '\signature'
  26.11 '\telephone'
27 Input/output
  27.1 '\openin' & '\openout'
  27.2 '\read'
  27.3 '\typein'
  27.4 '\typeout'
  27.5 '\write'
    27.5.1 '\write' and security
    27.5.2 '\message'
    27.5.3 '\wlog'
    27.5.4 '\write18'
28 Command line interface
  28.1 Command line options
  28.2 Command line input
  28.3 Jobname
  28.4 Recovering from errors
Appendix A Document templates
  A.1 'beamer' template
  A.2 'article' template
  A.3 'book' template
  A.4 Larger 'book' template
Index
LaTeX2e: An unofficial reference manual
***************************************

This document is an unofficial reference manual (version of January
2022) for LaTeX2e, a document preparation system.

1 About this document
*********************

This is an unofficial reference manual for the LaTeX2e document
preparation system, which is a macro package for the TeX typesetting
program (*note Overview::).

   This document's home page is <https://latexref.xyz>; it has separate
web pages for each topic.  Alternatively.
<https://latexref.xyz/dev/latex2e.html> has the entire document on a
single page.  For other output formats, the sources, and plenty more
information, see <https://latexref.xyz/dev/>.

   In this document, we will mostly just use 'LaTeX' rather than
'LaTeX2e', since the previous version of LaTeX (2.09) was frozen decades
ago.

   LaTeX is maintained by a group of volunteers
(<https://latex-project.org>).  The official documentation written by
the LaTeX project is available from their web site.  The present
document is completely unofficial and has not been written or reviewed
by the LaTeX maintainers.  Do not send bug reports or anything else
about this document to them.  Instead, please send all comments to
<latexrefman@tug.org>.

   This document is a reference, not a tutorial.  There is a vast array
of other information available about LaTeX, at all levels.  Here are a
few introductions.

<https://ctan.org/pkg/latex-doc-ptr>
     Two pages of recommended references to LaTeX documentation.

<https://ctan.org/pkg/first-latex-doc>
     Writing your first document, with a bit of both text and math.

<https://ctan.org/pkg/lshort>
     A longer introduction to LaTeX, translated to many languages.

<https://tug.org/begin.html>
     Introduction to the TeX system, including LaTeX, with further
     references.

2 Overview of LaTeX
*******************

LaTeX is a system for typesetting documents.  It was originally created
by Leslie Lamport in 1984, but has been maintained by a group of
volunteers for many years now (<https://latex-project.org>).  It is
widely used, particularly but not exclusively for mathematical and
technical documents.

   A LaTeX user writes an input file containing text to be typeset along
with interspersed commands.  The default encoding for the text is UTF-8
(as of 2018).  The commands specify, for example, how the text should be
formatted.

   LaTeX is implemented as a set of related so-called "macros" which use
Donald E. Knuth's TeX typesetting program or one of its derivatives,
collectively known as "engines".  Thus, the user produces output,
typically PDF, by giving the input file to a TeX engine.  (The following
sections describe all this in more detail.)

   The term LaTeX is also sometimes used to mean the language in which
the input document is marked up, that is, to mean the set of commands
available to a LaTeX user.

   The name LaTeX is short for "Lamport TeX".  It is pronounced LAH-teck
or LAY-teck, or sometimes LAY-tecks.  Inside a document, produce the
logo with '\LaTeX'.  Where use of the logo is not sensible, such as in
plain text, write it as 'LaTeX'.

2.1 Starting and ending
=======================

LaTeX files have a simple global structure, with a standard beginning
and ending.  This is a small example.

     \documentclass{article}
     \begin{document}
     Hello, \LaTeX\ world.
     \end{document}

Every LaTeX document has a '\begin{document}' line and an
'\end{document}' line.

Here, the 'article' is the "document class".  It is implemented in a
file 'article.cls'.  You can use any document class on your system.  A
few document classes are defined by LaTeX itself, and vast array of
others are widely available.  *Note Document classes::.

   You can include other LaTeX commands between the '\documentclass' and
the '\begin{document}' commands.  This area is called the "preamble".

   The '\begin{document}', '\end{document}' pair defines an
"environment"; the 'document' environment (and no others) is required in
all LaTeX documents (*note document::).  LaTeX make available to you
many environments that are documented here (*note Environments::).  Many
more are available to you from external packages, most importantly those
available at CTAN (*note CTAN::).

   The following sections discuss how to produce PDF or other output
from a LaTeX input file.

2.2 Output files
================

LaTeX produces a main output file and at least two auxiliary files.  The
main output file's name ends in either '.dvi' or '.pdf'.

'.dvi'
     If LaTeX is invoked with the system command 'latex' then it
     produces a DeVice Independent file, with extension '.dvi'.  You can
     view this file with a command such as 'xdvi', or convert it to a
     PostScript '.ps' file with 'dvips' or to a Portable Document Format
     '.pdf' file with 'dvipdfmx'.  The contents of the file can be
     dumped in human-readable form with 'dvitype'.  A vast array of
     other DVI utility programs are available
     (<https://mirror.ctan.org/dviware>).

'.pdf'
     If LaTeX is invoked via the system command 'pdflatex', among other
     commands (*note TeX engines::), then the main output is a Portable
     Document Format (PDF) file.  Typically this is a self-contained
     file, with all fonts and images included.

   LaTeX always produces at least two additional files.

'.log'
     This transcript file contains summary information such as a list of
     loaded packages.  It also includes diagnostic messages and perhaps
     additional information for any errors.

'.aux'
     Auxiliary information is used by LaTeX for things such as cross
     references.  For example, the first time that LaTeX finds a forward
     reference--a cross reference to something that has not yet appeared
     in the source--it will appear in the output as a doubled question
     mark '??'.  When the referred-to spot does eventually appear in the
     source then LaTeX writes its location information to this '.aux'
     file.  On the next invocation, LaTeX reads the location information
     from this file and uses it to resolve the reference, replacing the
     double question mark with the remembered location.

   LaTeX may produce yet more files, characterized by the filename
ending.  These include a '.lof' file that is used to make a list of
figures, a '.lot' file used to make a list of tables, and a '.toc' file
used to make a table of contents (*note Table of contents etc.::).  A
particular class may create others; the list is open-ended.

2.3 TeX engines
===============

LaTeX is a large set of commands that is executed by a TeX program
(*note Overview::).  Such a set of commands is called a "format", and is
embodied in a binary '.fmt' file, which can be read much more quickly
than the corresponding TeX source.

   This section gives a terse overview of the TeX programs that are
commonly available (see also *note Command line interface::).

'latex'
'pdflatex'
     In TeX Live (<https://tug.org/texlive>), if LaTeX is invoked via
     either the system command 'latex' or 'pdflatex', then the pdfTeX
     engine is run (<https://ctan.org/pkg/pdftex>).  When invoked as
     'latex', the main output is a '.dvi' file; as 'pdflatex', the main
     output is a '.pdf' file.

     pdfTeX incorporates the e-TeX extensions to Knuth's original
     program (<https://ctan.org/pkg/etex>), including additional
     programming features and bi-directional typesetting, and has plenty
     of extensions of its own.  e-TeX is available on its own as the
     system command 'etex', but this is plain TeX (and produces '.dvi').

     In other TeX distributions, 'latex' may invoke e-TeX rather than
     pdfTeX.  In any case, the e-TeX extensions can be assumed to be
     available in LaTeX.

'lualatex'
     If LaTeX is invoked via the system command 'lualatex', the LuaTeX
     engine is run (<https://ctan.org/pkg/luatex>).  This program allows
     code written in the scripting language Lua (<http://luatex.org>) to
     interact with TeX's typesetting.  LuaTeX handles UTF-8 Unicode
     input natively, can handle OpenType and TrueType fonts, and
     produces a '.pdf' file by default.  There is also 'dvilualatex' to
     produce a '.dvi' file.

'xelatex'
     If LaTeX is invoked with the system command 'xelatex', the XeTeX
     engine is run (<https://tug.org/xetex>).  Like LuaTeX, XeTeX
     natively supports UTF-8 Unicode and TrueType and OpenType fonts,
     though the implementation is completely different, mainly using
     external libraries instead of internal code.  XeTeX produces a
     '.pdf' file as output; it does not support DVI output.

     Internally, XeTeX creates an '.xdv' file, a variant of DVI, and
     translates that to PDF using the ('x')'dvipdfmx' program, but this
     process is automatic.  The '.xdv' file is only useful for
     debugging.

'platex'
'uplatex'
     These commands provide significant additional support for Japanese
     and other languages; the 'u' variant supports Unicode.  See
     <https://ctan.org/pkg/ptex> and <https://ctan.org/pkg/uptex>.

   As of 2019, there is a companion '-dev' command and format for all of
the above:

'dvilualatex-dev'
'latex-dev'
'lualatex-dev'
'pdflatex-dev'
'platex-dev'
'uplatex-dev'
'xelatex-dev'
     These are candidates for an upcoming LaTeX release.  The main
     purpose is to find and address compatibility problems before an
     official release.

     These '-dev' formats make it easy for anyone to help test documents
     and code: you can run, say, 'pdflatex-dev' instead of 'pdflatex',
     without changing anything else in your environment.  Indeed, it is
     easiest and most helpful to always run the '-dev' versions instead
     of bothering to switch back and forth.  During quiet times after a
     release, the commands will be equivalent.

     These are not daily snapshots or untested development code.  They
     undergo the same extensive regression testing by the LaTeX team
     before being released.

     For more information, see "The LaTeX release workflow and the LaTeX
     'dev' formats" by Frank Mittelbach, 'TUGboat' 40:2,
     <https://tug.org/TUGboat/tb40-2/tb125mitt-dev.pdf>.

2.4 LaTeX command syntax
========================

In the LaTeX input file, a command name starts with a backslash
character, '\'.  The name itself then consists of either (a) a string of
letters or (b) a single non-letter.

   LaTeX commands names are case sensitive so that '\pagebreak' differs
from '\Pagebreak' (the latter is not a standard command).  Most command
names are lowercase, but in any event you must enter all commands in the
same case as they are defined.

   A command may be followed by zero, one, or more arguments.  These
arguments may be either required or optional.  Required arguments are
contained in curly braces, '{...}'.  Optional arguments are contained in
square brackets, '[...]'.  Generally, but not universally, if the
command accepts an optional argument, it comes first, before any
required arguments.

   Inside of an optional argument, to use the character close square
bracket (']') hide it inside curly braces, as in '\item[closing bracket
{]}]'.  Similarly, if an optional argument comes last, with no required
argument after it, then to make the first character of the following
text be an open square bracket, hide it inside curly braces.

   LaTeX has the convention that some commands have a '*' form that is
related to the form without a '*', such as '\chapter' and '\chapter*'.
The exact difference in behavior varies from command to command.

   This manual describes all accepted options and '*'-forms for the
commands it covers (barring unintentional omissions, a.k.a. bugs).

   As of the 2020-10-01 release of LaTeX, the 'expl3' and 'xparse'
packages are part of the LaTeX2e format.  They provide a completely
different underlying programming language syntax.  We won't try to cover
them in this document; see the related package documentation and other
LaTeX manuals.

2.5 Environment
===============

Synopsis:

     \begin{ENVIRONMENT-NAME}
       ...
     \end{ENVIRONMENT-NAME}

   An "environment" is an area of LaTeX source, inside of which there is
a distinct behavior.  For instance, for poetry in LaTeX put the lines
between '\begin{verse}' and '\end{verse}'.

     \begin{verse}
       There once was a man from Nantucket \\
       ...
     \end{verse}

   *Note Environments::, for a list of environments.  Particularly
notable is that every LaTeX document must have a 'document' environment,
a '\begin{document} ... \end{document}' pair.

   The ENVIRONMENT-NAME at the beginning must exactly match that at the
end.  This includes the case where ENVIRONMENT-NAME ends in a
star ('*'); both the '\begin' and '\end' texts must include the star.

   Environments may have arguments, including optional arguments.  This
example produces a table.  The first argument is optional (and causes
the table to be aligned on its top row) while the second argument is
required (it specifies the formatting of columns).

     \begin{tabular}[t]{r|l}
       ... rows of table ...
     \end{tabular}

2.6 CTAN: The Comprehensive TeX Archive Network
===============================================

The Comprehensive TeX Archive Network, CTAN, is the TeX and LaTeX
community's repository of free material.  It is a set of Internet sites
around the world that offer material related to LaTeX for download.
Visit CTAN on the web at <https://ctan.org>.

   This material is organized into packages, discrete bundles that
typically offer some coherent functionality and are maintained by one
person or a small number of people.  For instance, many publishers have
a package that allows authors to format papers to that publisher's
specifications.

   In addition to the massive holdings, the 'ctan.org' web site offers
features such as search by name or by functionality.

   CTAN is not a single host, but instead is a set of hosts, one of
which is the so-called "master".  The master host actively manages the
material, for instance, by accepting uploads of new or updated packages.
For many years, it has been hosted by the German TeX group, DANTE e.V.

   Other sites around the world help out by mirroring, that is,
automatically syncing their collections with the master site and then in
turn making their copies publicly available.  This gives users close to
their location better access and relieves the load on the master site.
The list of mirrors is at <https://ctan.org/mirrors>.

3 Document classes
******************

The document's overall class is defined with this command, which is
normally the first command in a LaTeX source file.

     \documentclass[OPTIONS]{CLASS}

   The following document CLASS names are built into LaTeX.  (Many other
document classes are available as separate packages; *note Overview::.)

'article'
     For a journal article, a presentation, and miscellaneous general
     use.

'book'
     Full-length books, including chapters and possibly including front
     matter, such as a preface, and back matter, such as an appendix
     (*note Front/back matter::).

'letter'
     Mail, optionally including mailing labels (*note Letters::).

'report'
     For documents of length between an 'article' and a 'book', such as
     technical reports or theses, which may contain several chapters.

'slides'
     For slide presentations--rarely used nowadays.  The 'beamer'
     package is perhaps the most prevalent
     (<https://ctan.org/pkg/beamer>).  *Note beamer template::, for a
     small template for a beamer document.

   Standard OPTIONS are described in the next section.

3.1 Document class options
==========================

You can specify "global options" or "class options" to the
'\documentclass' command by enclosing them in square brackets.  To
specify more than one OPTION, separate them with a comma.

     \documentclass[OPTION1,OPTION2,...]{CLASS}

   Here is the list of the standard class options.

   All of the standard classes except 'slides' accept the following
options for selecting the typeface size (default is '10pt'):

     10pt  11pt  12pt

   All of the standard classes accept these options for selecting the
paper size (these show height by width):

'a4paper'
     210 by 297mm (about 8.25 by 11.75 inches)

'a5paper'
     148 by 210mm (about 5.8 by 8.3 inches)

'b5paper'
     176 by 250mm (about 6.9 by 9.8 inches)

'executivepaper'
     7.25 by 10.5 inches

'legalpaper'
     8.5 by 14 inches

'letterpaper'
     8.5 by 11 inches (the default)

   When using one of the engines pdfLaTeX, LuaLaTeX, or XeLaTeX (*note
TeX engines::), options other than 'letterpaper' set the print area but
you must also set the physical paper size.  One way to do that is to put
'\pdfpagewidth=\paperwidth' and '\pdfpageheight=\paperheight' in your
document's preamble.

   The 'geometry' package provides flexible ways of setting the print
area and physical page size.

   Miscellaneous other options:

'draft'
'final'
     Mark ('draft') or do not mark ('final') overfull boxes with a black
     box in the margin; default is 'final'.

'fleqn'
     Put displayed formulas flush left; default is centered.

'landscape'
     Selects landscape format; default is portrait.

'leqno'
     Put equation numbers on the left side of equations; default is the
     right side.

'openbib'
     Use "open" bibliography format.

'titlepage'
'notitlepage'
     Specifies whether there is a separate page for the title
     information and for the abstract also, if there is one.  The
     default for the 'report' class is 'titlepage', for the other
     classes it is 'notitlepage'.

   The following options are not available with the 'slides' class.

'onecolumn'
'twocolumn'
     Typeset in one or two columns; default is 'onecolumn'.

'oneside'
'twoside'
     Selects one- or two-sided layout; default is 'oneside', except that
     in the 'book' class the default is 'twoside'.

     For one-sided printing, the text is centered on the page.  For
     two-sided printing, the '\evensidemargin' ('\oddsidemargin')
     parameter determines the distance on even (odd) numbered pages
     between the left side of the page and the text's left margin, with
     '\oddsidemargin' being 40% of the difference between '\paperwidth'
     and '\textwidth', and '\evensidemargin' is the remainder.

'openright'
'openany'
     Determines if a chapter should start on a right-hand page; default
     is 'openright' for 'book', and 'openany' for 'report'.

   The 'slides' class offers the option 'clock' for printing the time at
the bottom of each note.

3.2 Additional packages
=======================

Load a package PKG, with the package options given in the
comma-separated list OPTIONS, as here.

     \usepackage[OPTIONS]{PKG}.

   To specify more than one package you can separate them with a comma,
as in '\usepackage{PKG1,PKG2,...}', or use multiple '\usepackage'
commands.

   Any options given in the '\documentclass' command that are unknown to
the selected document class are passed on to the packages loaded with
'\usepackage'.

3.3 Class and package construction
==================================

You can create new document classes and new packages.  For instance, if
your memos must satisfy some local requirements, such as a standard
header for each page, then you could create a new class 'smcmemo.cls'
and begin your documents with '\documentclass{smcmemo}'.

   What separates a package from a document class is that the commands
in a package are useful across classes while those in a document class
are specific to that class.  Thus, a command to set page headers is for
a package while a command to make the page headers say 'Memo from the
SMC Math Department' is for a class.

   Inside of a class or package file you can use the at-sign '@' as a
character in command names without having to surround the code
containing that command with '\makeatletter' and '\makeatother'.  *Note
\makeatletter & \makeatother::.  This allow you to create commands that
users will not accidentally redefine.  Another technique is to preface
class- or package-specific commands with some string to prevent your
class or package from interfering with others.  For instance, the class
'smcmemo' might have commands '\smc@tolist', '\smc@fromlist', etc.

3.3.1 Class and package structure
---------------------------------

A class file or package file typically has four parts.
  1. In the "identification part", the file says that it is a LaTeX
     package or class and describes itself, using the '\NeedsTeXFormat'
     and '\ProvidesClass' or '\ProvidesPackage' commands.

  2. The "preliminary declarations part" declares some commands and can
     also load other files.  Usually these commands will be those needed
     for the code used in the next part.  For example, an 'smcmemo'
     class might be called with an option to read in a file with a list
     of people for the to-head, as '\documentclass[mathto]{smcmemo}',
     and therefore needs to define a command
     '\newcommand{\setto}[1]{\def\@tolist{#1}}' used in that file.

  3. In the "handle options part" the class or package declares and
     processes its options.  Class options allow a user to start their
     document as '\documentclass[OPTION LIST]{CLASS NAME}', to modify
     the behavior of the class.  An example is when you declare
     '\documentclass[11pt]{article}' to set the default document font
     size.

  4. Finally, in the "more declarations part" the class or package
     usually does most of its work: declaring new variables, commands
     and fonts, and loading other files.

   Here is a starting class file, which should be saved as 'stub.cls'
where LaTeX can find it, for example in the same directory as the '.tex'
file.

     \NeedsTeXFormat{LaTeX2e}
     \ProvidesClass{stub}[2017/07/06 stub to start building classes from]
     \DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
     \ProcessOptions\relax
     \LoadClass{article}

It identifies itself, handles the class options via the default of
passing them all to the 'article' class, and then loads the 'article'
class to provide the basis for this class's code.

   For more, see the official guide for class and package writers, the
Class Guide, at
<https://www.latex-project.org/help/documentation/clsguide.pdf> (much of
the descriptions here derive from this document), or the tutorial
<https://www.tug.org/TUGboat/tb26-3/tb84heff.pdf>.

3.3.2 Class and package commands
--------------------------------

These are the commands designed to help writers of classes or packages.

'\AtBeginDvi{specials}'
     Save in a box register things that are written to the '.dvi' file
     at the beginning of the shipout of the first page of the document.

'\AtEndOfClass{CODE}'
'\AtEndOfPackage{CODE}'
     Hook to insert CODE to be executed when LaTeX finishes processing
     the current class or package.  You can use these hooks multiple
     times; the 'code' will be executed in the order that you called it.
     See also *note \AtBeginDocument::.

'\CheckCommand{CMD}[NUM][DEFAULT]{DEFINITION}'
'\CheckCommand*{CMD}[NUM][DEFAULT]{DEFINITION}'
     Like '\newcommand' (*note \newcommand & \renewcommand::) but does
     not define CMD; instead it checks that the current definition of
     CMD is exactly as given by DEFINITION and is or is not "long" as
     expected.  A long command is a command that accepts '\par' within
     an argument.  The CMD command is expected to be long with the
     unstarred version of '\CheckCommand'.  Raises an error when the
     check fails.  This allows you to check before you start redefining
     'cmd' yourself that no other package has already redefined this
     command.

'\ClassError{CLASS NAME}{ERROR TEXT}{HELP TEXT}'
'\PackageError{PACKAGE NAME}{ERROR TEXT}{HELP TEXT}'
'\ClassWarning{CLASS NAME}{WARNING TEXT}'
'\PackageWarning{PACKAGE NAME}{WARNING TEXT}'
'\ClassWarningNoLine{CLASS NAME}{WARNING TEXT}'
'\PackageWarningNoLine{PACKAGE NAME}{WARNING TEXT}'
'\ClassInfo{CLASS NAME}{INFO TEXT}'
'\PackageInfo{PACKAGE NAME}{INFO TEXT}'
'\ClassInfoNoLine{CLASS NAME}{INFO TEXT}'
'\PackageInfoNoLine{PACKAGE NAME}{INFO TEXT}'
     Produce an error message, or warning or informational messages.

     For '\ClassError' and '\PackageError' the message is ERROR TEXT,
     followed by TeX's '?' error prompt.  If the user then asks for help
     by typing 'h', they see the HELP TEXT.

     The four warning commands are similar except that they write
     WARNING TEXT on the screen with no error prompt.  The four info
     commands write INFO TEXT only in the transcript file.  The 'NoLine'
     versions do not show the number of the line generating the message,
     while the other versions do show that number.

     To format the messages, including the HELP TEXT: use '\protect' to
     stop a command from expanding, get a line break with
     '\MessageBreak', and get a space with '\space' when a space
     character does not allow it, like after a command.  Note that LaTeX
     appends a period to the messages.

'\CurrentOption'
     Expands to the name of the currently-being-processed option.  Can
     only be used within the CODE argument of either '\DeclareOption' or
     '\DeclareOption*'.

'\DeclareOption{OPTION}{CODE}'
'\DeclareOption*{CODE}'
     Make an option available to a user to invoke in their
     '\documentclass' command.  For example, the 'smcmemo' class could
     have an option '\documentclass[logo]{smcmemo}' allowing users to
     put the institutional logo on the first page.  The class file must
     contain '\DeclareOption{logo}{CODE}' (and later,
     '\ProcessOptions').

     If you request an option that has not been declared, by default
     this will produce a warning like 'Unused global option(s):
     [badoption].' Change this behavior with the starred version
     '\DeclareOption*{CODE}'.  For example, many classes extend an
     existing class, using a command such as '\LoadClass{article}', and
     for passing extra options to the underlying class use code such as
     this.

          \DeclareOption*{%
          \PassOptionsToClass{\CurrentOption}{article}%
          }

     Another example is that the class 'smcmemo' may allow users to keep
     lists of memo recipients in external files.  Then the user could
     invoke '\documentclass[math]{smcmemo}' and it will read the file
     'math.memo'.  This code handles the file if it exists and otherwise
     passes the option to the 'article' class.

          \DeclareOption*{\InputIfFileExists{\CurrentOption.memo}{}{%
              \PassOptionsToClass{\CurrentOption}{article}}}

'\DeclareRobustCommand{CMD}[NUM][DEFAULT]{DEFINITION}'
'\DeclareRobustCommand*{CMD}[NUM][DEFAULT]{DEFINITION}'
     Like '\newcommand' and '\newcommand*' (*note \newcommand &
     \renewcommand::) but these declare a robust command, even if some
     code within the DEFINITION is fragile.  (For a discussion of robust
     and fragile commands *note \protect::.)  Use this command to define
     new robust commands or to redefine existing commands and make them
     robust.  Unlike '\newcommand' these do not give an error if macro
     CMD already exists; instead, a log message is put into the
     transcript file if a command is redefined.

     Commands defined this way are a bit less efficient than those
     defined using '\newcommand' so unless the command's data is fragile
     and the command is used within a moving argument, use
     '\newcommand'.

     The 'etoolbox' package offers the commands '\newrobustcmd',
     '\newrobustcmd*', as well as the commands '\renewrobustcmd',
     '\renewrobustcmd*', and the commands '\providerobustcmd', and
     '\providerobustcmd*'.  These are similar to '\newcommand',
     '\newcommand*', '\renewcommand', '\renewcommand*',
     '\providecommand', and '\providecommand*', but define a robust CMD
     with two advantages as compared to '\DeclareRobustCommand':
       1. They use the low-level e-TeX protection mechanism rather than
          the higher level LaTeX '\protect' mechanism, so they do not
          incur the slight loss of performance mentioned above, and
       2. They make the same distinction between '\new...', '\renew...',
          and '\provide...', as the standard commands, so they do not
          just make a log message when you redefine CMD that already
          exists, in that case you need to use either '\renew...' or
          '\provide...' or you get an error.

'\IfFileExists{FILENAME}{TRUE CODE}{FALSE CODE}'
'\InputIfFileExists{FILENAME}{TRUE CODE}{FALSE CODE}'
     Execute TRUE CODE if LaTeX finds the file 'FILE NAME' or FALSE CODE
     otherwise.  In the first case it executing TRUE CODE and then
     inputs the file.  Thus the command

          \IfFileExists{img.pdf}{%
            \includegraphics{img.pdf}}{\typeout{!! img.pdf not found}

     will include the graphic 'img.pdf' if it is found and otherwise
     give a warning.

     This command looks for the file in all search paths that LaTeX
     uses, not only in the current directory.  To look only in the
     current directory do something like '\IfFileExists{./filename}{TRUE
     CODE}{FALSE CODE}'.  If you ask for a filename without a '.tex'
     extension then LaTeX will first look for the file by appending the
     '.tex'; for more on how LaTeX handles file extensions see *note
     \input::.

'\LoadClass[OPTIONS LIST]{CLASS NAME}[RELEASE DATE]'
'\LoadClassWithOptions{CLASS NAME}[RELEASE DATE]'
     Load a class, as with '\documentclass[OPTIONS LIST]{CLASS
     NAME}[RELEASE INFO]'.  An example is
     '\LoadClass[twoside]{article}'.

     The OPTIONS LIST, if present, is a comma-separated list.  The
     RELEASE DATE is optional.  If present it must have the form
     YYYY/MM/DD.

     If you request a RELEASE DATE and the date of the package installed
     on your system is earlier, then you get a warning on the screen and
     in the log like this.

          You have requested, on input line 4, version `2038/01/19' of
          document class article, but only version `2014/09/29 v1.4h
          Standard LaTeX document class' is available.

     The command version '\LoadClassWithOptions' uses the list of
     options for the current class.  This means it ignores any options
     passed to it via '\PassOptionsToClass'.  This is a convenience
     command that lets you build classes on existing ones, such as the
     standard 'article' class, without having to track which options
     were passed.

'\ExecuteOptions{OPTIONS-LIST}'
     For each option OPTION in the OPTIONS-LIST, in order, this command
     executes the command '\ds@OPTION'.  If this command is not defined
     then that option is silently ignored.

     It can be used to provide a default option list before
     '\ProcessOptions'.  For example, if in a class file you want the
     default to be 11pt fonts then you could specify
     '\ExecuteOptions{11pt}\ProcessOptions\relax'.

'\NeedsTeXFormat{FORMAT}[FORMAT DATE]'
     Specifies the format that this class must be run under.  Often
     issued as the first line of a class file, and most often used as:
     '\NeedsTeXFormat{LaTeX2e}'.  When a document using that class is
     processed, the format name given here must match the format that is
     actually being run (including that the FORMAT string is case
     sensitive).  If it does not match then execution stops with an
     error like 'This file needs format `LaTeX2e' but this is `xxx'.'

     To specify a version of the format that you know to have certain
     features, include the optional FORMAT DATE on which those features
     were implemented.  If present it must be in the form 'YYYY/MM/DD'.
     If the format version installed on your system is earlier than
     FORMAT DATE then you get a warning like this.

          You have requested release `2038/01/20' of LaTeX, but only
          release `2016/02/01' is available.

'\OptionNotUsed'
     Adds the current option to the list of unused options.  Can only be
     used within the CODE argument of either '\DeclareOption' or
     '\DeclareOption*'.

'\PassOptionsToClass{OPTION LIST}{CLASS NAME}'
'\PassOptionsToPackage{OPTION LIST}{PACKAGE NAME}'
     Adds the options in the comma-separated list OPTION LIST to the
     options used by any future '\RequirePackage' or '\usepackage'
     command for package PACKAGE NAME or the class CLASS NAME.

     The reason for these commands is: you may load a package any number
     of times with no options but if you want options then you may only
     supply them when you first load the package.  Loading a package
     with options more than once will get you an error like 'Option
     clash for package foo.' (LaTeX throws an error even if there is no
     conflict between the options.)

     If your own code is bringing in a package twice then you can
     collapse that to once, for example replacing the two
     '\RequirePackage[landscape]{geometry}' and
     '\RequirePackage[margins=1in]{geometry}' with the single command
     '\RequirePackage[landscape,margins=1in]{geometry}'.

     However, imagine that you are loading 'firstpkg' and inside that
     package it loads 'secondpkg', and you need the second package to be
     loaded with option 'draft'.  Then before doing the first package
     you must queue up the options for the second package, like this.

          \PassOptionsToPackage{draft}{secondpkg}
          \RequirePackage{firstpkg}

     (If 'firstpkg.sty' loads an option in conflict with what you want
     then you may have to alter its source.)

     These commands are useful for general users as well as class and
     package writers.  For instance, suppose a user wants to load the
     'graphicx' package with the option 'draft' and also wants to use a
     class 'foo' that loads the 'graphicx' package, but without that
     option.  The user could start their LaTeX file with
     '\PassOptionsToPackage{draft}{graphicx}\documentclass{foo}'.

'\ProcessOptions'
'\ProcessOptions*\@OPTIONS'
     Execute the code for each option that the user has invoked.
     Include it in the class file as '\ProcessOptions\relax' (because of
     the existence of the starred command).

     Options come in two types.  "Local options" have been specified for
     this particular package in the OPTIONS argument of
     '\PassOptionsToPackage{OPTIONS}', '\usepackage[OPTIONS]', or
     '\RequirePackage[OPTIONS]'.  "Global options" are those given by
     the class user in '\documentclass[OPTIONS]' (If an option is
     specified both locally and globally then it is local.)

     When '\ProcessOptions' is called for a package 'pkg.sty', the
     following happens:
       1. For each option OPTION so far declared with '\DeclareOption',
          it looks to see if that option is either a global or a local
          option for 'pkg'.  If so then it executes the declared code.
          This is done in the order in which these options were given in
          'pkg.sty'.
       2. For each remaining local option, it executes the command
          '\ds@'OPTION if it has been defined somewhere (other than by a
          '\DeclareOption'); otherwise, it executes the default option
          code given in '\DeclareOption*'.  If no default option code
          has been declared then it gives an error message.  This is
          done in the order in which these options were specified.

     When '\ProcessOptions' is called for a class it works in the same
     way except that all options are local, and the default CODE for
     '\DeclareOption*' is '\OptionNotUsed' rather than an error.

     The starred version '\ProcessOptions*' executes the options in the
     order specified in the calling commands, rather than in the order
     of declaration in the class or package.  For a package this means
     that the global options are processed first.

'\ProvidesClass{CLASS NAME}[RELEASE DATE BRIEF ADDITIONAL INFORMATION]'
'\ProvidesClass{CLASS NAME}[RELEASE DATE]'
'\ProvidesPackage{PACKAGE NAME}[RELEASE DATE BRIEF ADDITIONAL INFORMATION]'
'\ProvidesPackage{PACKAGE NAME}[RELEASE DATE]'
     Identifies the class or package, printing a message to the screen
     and the log file.

     When you load a class or package, for example with
     '\documentclass{smcmemo}' or '\usepackage{test}', LaTeX inputs a
     file.  If the name of the file does not match the class or package
     name declared in it then you get a warning.  Thus, if you invoke
     '\documentclass{smcmemo}', and the file 'smcmemo.cls' has the
     statement '\ProvidesClass{xxx}' then you get a warning like 'You
     have requested document class `smcmemo', but the document class
     provides 'xxx'.' This warning does not prevent LaTeX from
     processing the rest of the class file normally.

     If you include the optional argument then you must include a date,
     before any spaces, of the form 'YYYY/MM/DD'.  The rest of the
     optional argument is free-form, although it traditionally
     identifies the class, and is written to the screen during
     compilation and to the log file.  Thus, if your file 'smcmemo.cls'
     contains the line '\ProvidesClass{smcmemo}[2008/06/01 v1.0 SMC memo
     class]' and your document's first line is '\documentclass{smcmemo}'
     then you will see 'Document Class: smcmemo 2008/06/01 v1.0 SMC memo
     class'.

     The date in the optional argument allows class and package users to
     ask to be warned if the version of the class or package is earlier
     than RELEASE DATE.  For instance, a user could enter
     '\documentclass{smcmemo}[2018/10/12]' or
     '\usepackage{foo}[[2017/07/07]]' to require a class or package with
     certain features by specifying that it must be released no earlier
     than the given date.  (Although, in practice package users only
     rarely include a date, and class users almost never do.)

'\ProvidesFile{FILENAME}[ADDITIONAL INFORMATION]'
     Declare a file other than the main class and package files, such as
     configuration files or font definition files.  Put this command in
     that file and you get in the log a string like 'File: test.config
     2017/10/12 config file for test.cls' for FILENAME equal to
     'test.config' and ADDITIONAL INFORMATION equal to '2017/10/12
     config file for test.cls'.

'\RequirePackage[OPTION LIST]{PACKAGE NAME}[RELEASE DATE]'
'\RequirePackageWithOptions{PACKAGE NAME}[RELEASE DATE]'
     Load a package, like the command '\usepackage' (*note Additional
     packages::).  The LaTeX development team strongly recommends use of
     these commands over Plain TeX's '\input'; see the Class Guide.  An
     example is '\RequirePackage[landscape,margin=1in]{geometry}'.

     The OPTION LIST, if present, is a comma-separated list.  The
     RELEASE DATE, if present, must have the form YYYY/MM/DD.  If the
     release date of the package as installed on your system is earlier
     than RELEASE DATE then you get a warning like 'You have requested,
     on input line 9, version `2017/07/03' of package jhtest, but only
     version `2000/01/01' is available'.

     The '\RequirePackageWithOptions' version uses the list of options
     for the current class.  This means it ignores any options passed to
     it via '\PassOptionsToClass'.  This is a convenience command to
     allow easily building classes on existing ones without having to
     track which options were passed.

     The difference between '\usepackage' and '\RequirePackage' is
     small.  The '\usepackage' command is intended for the document file
     while '\RequirePackage' is intended for package and class files.
     Thus, using '\usepackage' before the '\documentclass' command
     causes LaTeX to give error like '\usepackage before
     \documentclass', but you can use '\RequirePackage' there.

4 Fonts
*******

LaTeX comes with powerful font capacities.  For one thing, its New Font
Selection Scheme allows you to work easily with the font families in
your document (for instance, see *note Font styles::).  And, LaTeX
documents can use most fonts that are available today, including
versions of Times Roman, Helvetica, Courier, etc.  (Note, though, that
many fonts do not have support for mathematics.)

   The first typeface in the TeX world was the Computer Modern family,
developed by Donald Knuth.  It is the default for LaTeX documents and is
still the most widely used.  But changing to another font often only
involves a few commands.  For instance, putting the following in your
preamble gives you a Palatino-like font, which is handsome and more
readable online than many other fonts, while still allowing you to
typeset mathematics.  (This example is from Michael Sharpe,
<https://math.ucsd.edu/~msharpe/RcntFnts.pdf>.)

     \usepackage[osf]{newpxtext} % osf for text, not math
     \usepackage{cabin} % sans serif
     \usepackage[varqu,varl]{inconsolata} % sans serif typewriter
     \usepackage[bigdelims,vvarbb]{newpxmath} % bb from STIX
     \usepackage[cal=boondoxo]{mathalfa} % mathcal

In addition, the 'xelatex' or 'lualatex' engines allow you to use any
fonts on your system that are in OpenType or TrueType format (*note TeX
engines::).

   The LaTeX Font Catalogue (<https://tug.org/FontCatalogue>) shows font
sample graphics and copy-and-pasteable source to use many fonts,
including many with support for mathematics.  It aims to cover all Latin
alphabet free fonts available for easy use with LaTeX.

   More information is also available from the TeX Users Group, at
<https://www.tug.org/fonts/>.

4.1 'fontenc' package
=====================

Synopsis:

     \usepackage[FONT_ENCODING]{fontenc}

   or

     \usepackage[FONT_ENCODING1, FONT_ENCODING2, ...]{fontenc}

   Specify the font encodings.  A font encoding is a mapping of the
character codes to the font glyphs that are used to typeset your output.

   This package only applies if you use the 'pdflatex' engine (*note TeX
engines::).  If you use the 'xelatex' or 'lualatex' engine then instead
use the 'fontspec' package.

   TeX's original font family, Computer Modern, has a limited character
set.  For instance, to make common accented characters you must use
'\accent' (*note \accent::) but this disables hyphenation.  TeX users
have agreed on a number of standards to access the larger sets of
characters provided by modern fonts.  If you are using 'pdflatex' then
put this in the preamble

     \usepackage[T1]{fontenc}

gives you support for the most widespread European languages, including
French, German, Italian, Polish, and others.  In particular, if you have
words with accented letters then LaTeX will hyphenate them and your
output can be copied and pasted.  (The optional second line allows you
to directly enter accented characters into your source file.)

   If you are using an encoding such as 'T1' and the characters appear
blurry or do not magnify well then your fonts may be bitmapped,
sometimes called raster or Type 3.  You want vector fonts.  Use a
package such as 'lmodern' or 'cm-super' to get a font that extends
LaTeX's default using vector fonts.

   For each FONT_ENCODING given as an option but not already declared,
this package loads the encoding definition files, named
'FONT_ENCODINGenc.def'.  It also sets '\encodingdefault' to be the last
encoding in the option list.

   These are the common values for FONT_ENCODING.

'OT1'
     The original encoding for TeX.  Limited to mostly English
     characters.

'OMS, OML'
     Math symbols and math letters encoding.

'T1'
     TeX text extended.  Sometimes called the Cork encoding for the
     Users Group meeting where it was developed.  Gives access to most
     European accented characters.  The most common option for this
     package.

'TS1'
     Text Companion encoding.

LaTeX's default is to load 'OML', 'T1', 'OT1', and then 'OMS', and set
the default to 'OT1'.

   Even if you do not use accented letters, you may need to specify a
font encoding if your font requires it.

   If you use 'T1' encoded fonts other than the default Computer Modern
family then you may need to load the package that selects your fonts
before loading 'fontenc', to prevent the system from loading any
'T1' encoded fonts from the default.

   The LaTeX team reserve encoding names starting with: 'T' for the
standard text encodings with 256 characters, 'TS' for symbols that
extend the corresponding T encodings, 'X' for test encodings, 'M' for
standard math encodings with 256 characters, 'A' for special
applications, 'OT' for standard text encodings with 128 characters, and
'OM' for standard math encodings with 128 characters ('O' stands for
'obsolete').

   This package provides a number of commands, detailed below.  Many of
them are encoding-specific, so if you have defined a command that works
for one encoding but the current encoding is different then the command
is not in effect.

4.1.1 '\DeclareFontEncoding'
----------------------------

Synopsis:

     \DeclareFontEncoding{ENCODING}{TEXT-SETTINGS}{MATH-SETTINGS}

   Declare the font encoding ENCODING.  It also saves the value of
ENCODING in '\LastDeclaredEncoding' (*note \LastDeclaredEncoding::).

   The file 't1enc.def' contains this line (followed by many others).

     \DeclareFontEncoding{T1}{}{}

   The TEXT-SETTINGS are the commands that LaTeX will run every time it
switches from one encoding to another with the '\selectfont' and
'\fontencoding' commands.  The MATH-SETTINGS are the commands that LaTeX
will use whenever the font is accessed as a math alphabet.

   LaTeX ignores any space characters inside TEXT-SETTINGS and
MATH-SETTINGS, to prevent unintended spaces in the output.

   If you invent an encoding you should pick a two or three letter name
starting with 'L' for 'local', or 'E' for 'experimental'.

   Note that output encoding files may be read several times by LaTeX so
using, e.g., '\newcommand' may cause an error.  In addition, such files
should contain '\ProvidesFile' line (*note Class and package
commands::).

   Note also that you should use the '\...Default' commands only in a
package, not in the encoding definition files, since those files should
only contain declarations specific to that encoding.

4.1.2 '\DeclareTextAccent'
--------------------------

Synopsis:

     \DeclareTextAccent{CMD}{ENCODING}{SLOT}

   Define an accent, to be put on top of other glyphs, in the encoding
ENCODING at the location SLOT.

   A "slot" is the number identifying a glyph within a font.

   This line from 't1enc.def' declares that to make a circumflex accent
as in '\^A', the system will put the accent in slot 2 over the 'A'
character, which is represented in ASCII as 65.  (This holds unless
there is a relevant 'DeclareTextComposite' or
'\DeclareTextCompositeCommand' declaration; *note
\DeclareTextComposite::.)

     \DeclareTextAccent{\^}{T1}{2}

   If CMD has already been defined then '\DeclareTextAccent' does not
give an error but it does log the redefinition in the transcript file.

4.1.3 '\DeclareTextAccentDefault'
---------------------------------

Synopsis:

     \DeclareTextAccentDefault{\CMD}{ENCODING}

   If there is an encoding-specific accent command \CMD but there is no
associated '\DeclareTextAccent' for that encoding then this command will
pick up the slack, by saying to use it as described for ENCODING.

   For example, to make the encoding 'OT1' be the default encoding for
the accent '\"', declare this.

     \DeclareTextAccentDefault{\"}{OT1}

If you issue a '\"' when the current encoding does not have a definition
for that accent then LaTeX will use the definition from 'OT1'

   That is, this command is equivalent to this call (*note
\UseTextSymbol & \UseTextAccent::).

     \DeclareTextCommandDefault[1]{\CMD}
        {\UseTextAccent{ENCODING}{\CMD}{#1}}

   Note that '\DeclareTextAccentDefault' works for any one-argument
'fontenc' command, not just the accent command.

4.1.4 '\DeclareTextCommand' & '\ProvideTextCommand'
---------------------------------------------------

Synopsis, one of:

     \DeclareTextCommand{\CMD}{ENCODING}{DEFN}
     \DeclareTextCommand{\CMD}{ENCODING}[NARGS]{DEFN}
     \DeclareTextCommand{\CMD}{ENCODING}[NARGS][OPTARGDEFAULT]{DEFN}

   or one of:

     \ProvideTextCommand{\CMD}{ENCODING}{DEFN}
     \ProvideTextCommand{\CMD}{ENCODING}[NARGS]{DEFN}
     \ProvideTextCommand{\CMD}{ENCODING}[NARGS][OPTARGDEFAULT]{DEFN}

   Define the command '\CMD', which will be specific to one encoding.
The command name CMD must be preceded by a backslash, '\'.  These
commands can only appear in the preamble.  Redefining \CMD does not
cause an error.  The defined command will be robust even if the code in
DEFN is fragile (*note \protect::).

   For example, the file 't1enc.def' contains this line.

     \DeclareTextCommand{\textperthousand}{T1}{\%\char 24 }

   With that, you can express parts per thousand.

     \usepackage[T1]{fontenc}  % in preamble
       ...
     Legal limit is \( 0.8 \)\textperthousand.

If you change the font encoding to 'OT1' then you get an error like
'LaTeX Error: Command \textperthousand unavailable in encoding OT1'.

   The '\ProvideTextCommand' variant does the same, except that it does
nothing if '\CMD' is already defined.  The '\DeclareTextSymbol' command
is faster than this one for simple slot-to-glyph association (*note
\DeclareTextSymbol::)

   The optional NARGS and OPTARGDEFAULT arguments play the same role
here as in '\newcommand' (*note \newcommand & \renewcommand::).
Briefly, NARGS is an integer from 0 to 9 specifying the number of
arguments that the defined command '\CMD' takes.  This number includes
any optional argument.  Omitting this argument is the same as specifying
0, meaning that '\CMD' will have no arguments.  And, if OPTARGDEFAULT is
present then the first argument of '\CMD' is optional, with default
value OPTARGDEFAULT (which may be the empty string).  If OPTARGDEFAULT
is not present then '\CMD' does not take an optional argument.

4.1.5 '\DeclareTextCommandDefault' & '\ProvideTextCommandDefault '
------------------------------------------------------------------

Synopsis:

     \DeclareTextCommandDefault{\CMD}{DEFN}

   or:

     \ProvideTextCommandDefault{\CMD}{DEFN}

   Give a default definition for '\CMD', for when that command is not
defined in the encoding currently in force.  This default should only
use encodings known to be available.

   This makes '\copyright' available.

     \DeclareTextCommandDefault{\copyright}{\textcircled{c}}

It uses only an encoding (OMS) that is always available.

   The '\DeclareTextCommandDefault' should not occur in the encoding
definition files since those files should declare only commands for use
when you select that encoding.  It should instead be in a package.

   As with the related non-default commands, the
'\ProvideTextCommandDefault' has exactly the same behavior as
'\DeclareTextCommandDefault' except that it does nothing if '\CMD' is
already defined (*note \DeclareTextCommand & \ProvideTextCommand::).
So, packages can use it to provide fallbacks that other packages can
improve upon.

4.1.6 '\DeclareTextComposite'
-----------------------------

Synopsis:

     \DeclareTextComposite{\CMD}{ENCODING}{SIMPLE_OBJECT}{SLOT}

   Access an accented glyph directly, that is, without having to put an
accent over a separate character.

   This line from 't1enc.def' means that '\^o' will cause LaTeX to
typeset lowercase 'o' by taking the character directly from slot 224 in
the font.

     \DeclareTextComposite{\^}{T1}{o}{244}

   *Note fontenc package::, for a list of common encodings.  The
SIMPLE_OBJECT should be a single character or a single command.  The
SLOT argument is usually a positive integer represented in decimal
(although octal or hexadecimal are possible).  Normally \CMD has already
been declared for this encoding, either with '\DeclareTextAccent' or
with a one-argument '\DeclareTextCommand'.  In 't1enc.def', the above
line follows the '\DeclareTextAccent{\^}{T1}{2}' command.

4.1.7 '\DeclareTextCompositeCommand'
------------------------------------

Synopsis:

     \DeclareTextCompositeCommand{\CMD}{ENCODING}{ARG}{CODE}

   A more general version of '\DeclareTextComposite' that runs arbitrary
code with '\CMD'.

   This allows accents on 'i' to act like accents on dotless i, '\i'.

     \DeclareTextCompositeCommand{\'}{OT1}{i}{\'\i}

   *Note fontenc package::, for a list of common encodings.  Normally
'\CMD' will have already been declared with '\DeclareTextAccent' or as a
one argument '\DeclareTextCommand'.

4.1.8 '\DeclareTextSymbol'
--------------------------

Synopsis:

     \DeclareTextSymbol{\CMD}{ENCODING}{SLOT}

   Define a symbol in the encoding ENCODING at the location SLOT.
Symbols defined in this way are for use in text, not mathematics.

   For example, this line from 't1enc.def' declares the number of the
glyph to use for «, the left guillemet.

     \DeclareTextSymbol{\guillemotleft}{T1}{19}

The command '\DeclareTextCommand{\guillemotleft}{T1}{\char 19}' has the
same effect but is slower (*note \DeclareTextCommand &
\ProvideTextCommand::).

   *Note fontenc package::, for a list of common encodings.  The SLOT
can be specified in decimal, or octal (as in ''023'), or hexadecimal (as
in '"13'), although decimal has the advantage that single quote or
double quote could be redefined by another package.

   If '\CMD' has already been defined then '\DeclareTextSymbol' does not
give an error but it does log the redefinition in the transcript file.

4.1.9 '\DeclareTextSymbolDefault'
---------------------------------

Synopsis:

     \DeclareTextSymbolDefault{\CMD}{ENCODING}

   If there is an encoding-specific symbol command '\CMD' but there is
no associated '\DeclareTextSymbol' for that encoding, then this command
will pick up the slack, by saying to get the symbol as described for
ENCODING.

   For example, to declare that if the current encoding has no meaning
for '\textdollar' then use the one from 'OT1', declare this.

     \DeclareTextSymbolDefault{\textdollar}{OT1}

   That is, this command is equivalent to this call (*note
\UseTextSymbol & \UseTextAccent::).

     \DeclareTextCommandDefault{\CMD}
        {\UseTextSymbol{ENCODING}{\CMD}}

   Note that '\DeclareTextSymbolDefault' can be used to define a default
for any zero-argument 'fontenc' command.

4.1.10 '\LastDeclaredEncoding'
------------------------------

Synopsis:

     \LastDeclaredEncoding

   Get the name of the most recently declared encoding.  The
'\DeclareFontEncoding' command stores the name so that it can be
retrieved with this command (*note \DeclareFontEncoding::).

   This relies on '\LastDeclaredEncoding' rather than give the name of
the encoding explicitly.

     \DeclareFontEncoding{JH1}{}{}
     \DeclareTextAccent{\'}{\LastDeclaredEncoding}{0}

4.1.11 '\UseTextSymbol' & '\UseTextAccent'
------------------------------------------

Synopsis:

     \UseTextSymbol{ENCODING}{\CMD}

   or:

     \UseTextAccent{ENCODING}{\CMD}{TEXT}

   Use a symbol or accent not from the current encoding.

   In general, to use a 'fontenc' command in an encoding where it is not
defined, and if the command has no arguments, then you can use it like
this:

     \UseTextSymbol{OT1}{\ss}

which is equivalent to this (note the outer braces form a group, so
LaTeX reverts back to the prior encoding after the '\ss'):

     {\fontencoding{OT1}\selectfont\ss}

   Similarly, to use a 'fontenc' command in an encoding where it is not
defined, and if the command has one argument, you can use it like this:

     \UseTextAccent{OT1}{\'}{a}

which is equivalent to this (again note the outer braces forming a
group):

     {fontencoding{OT1}\selectfont\'{\fontencoding{ENC_IN_USE}\selectfont a}}

Here, ENC_IN_USE is the encoding in force before this sequence of
commands, so that 'a' is typeset using the current encoding and only the
accent is taken from 'OT1'.

4.2 Font styles
===============

The following type style commands are supported by LaTeX.

   In the table below the listed commands, the '\text...' commands, are
used with an argument as in '\textit{TEXT}'.  This is the preferred
form.  But shown after it in parenthesis is the corresponding
"declaration form", which is often useful.  This form takes no
arguments, as in '{\itshape TEXT}'.  The scope of the declaration form
lasts until the next type style command or the end of the current group.
In addition, each has an environment form such as
'\begin{itshape}...\end{itshape}', which we'll describe further at the
end of the section.

   These commands, in any of the three forms, are cumulative; for
instance you can get bold sans serif by saying either of
'\sffamily\bfseries' or '\bfseries\sffamily'.

   One advantage of these commands is that they automatically insert
italic corrections if needed (*note \/::).  Specifically, they insert
the italic correction unless the following character is in the list
'\nocorrlist', which by default consists of period and comma.  To
suppress the automatic insertion of italic correction, use '\nocorr' at
the start or end of the command argument, such as '\textit{\nocorr
text}' or '\textsc{text \nocorr}'.

'\textrm (\rmfamily)'
     Roman.

'\textit (\itshape)'
     Italics.

'\textmd (\mdseries)'
     Medium weight (default).

'\textbf (\bfseries)'
     Boldface.

'\textup (\upshape)'
     Upright (default).

'\textsl (\slshape)'
     Slanted.

'\textsf (\sffamily)'
     Sans serif.

'\textsc (\scshape)'
     Small caps.

'\texttt (\ttfamily)'
     Typewriter.

'\textnormal (\normalfont)'
     Main document font.

   Although it also changes fonts, the '\emph{TEXT}' command is
semantic, for text to be emphasized, and should not be used as a
substitute for '\textit'.  For example, '\emph{START TEXT \emph{MIDDLE
TEXT} END TEXT}' will result in the START TEXT and END TEXT in italics,
but MIDDLE TEXT will be in roman.

   LaTeX also provides the following commands, which unconditionally
switch to the given style, that is, are _not_ cumulative.  They are used
as declarations: '{\CMD...}' instead of '\CMD{...}'.

   (The unconditional commands below are an older version of font
switching.  The earlier commands are an improvement in most
circumstances.  But sometimes an unconditional font switch is what is
needed.)

'\bf'
     Switch to bold face.

'\cal'
     Switch to calligraphic letters for math.

'\it'
     Italics.

'\rm'
     Roman.

'\sc'
     Small caps.

'\sf'
     Sans serif.

'\sl'
     Slanted (oblique).

'\tt'
     Typewriter (monospace, fixed-width).

   The '\em' command is the unconditional version of '\emph'.

   The following commands are for use in math mode.  They are not
cumulative, so '\mathbf{\mathit{SYMBOL}}' does not create a boldface and
italic SYMBOL; instead, it will just be in italics.  This is because
typically math symbols need consistent typographic treatment, regardless
of the surrounding environment.

'\mathrm'
     Roman, for use in math mode.

'\mathbf'
     Boldface, for use in math mode.

'\mathsf'
     Sans serif, for use in math mode.

'\mathtt'
     Typewriter, for use in math mode.

'\mathit'
'(\mit)'
     Italics, for use in math mode.

'\mathnormal'
     For use in math mode, e.g., inside another type style declaration.

'\mathcal'
     Calligraphic letters, for use in math mode.

   In addition, the command '\mathversion{bold}' can be used for
switching to bold letters and symbols in formulas.
'\mathversion{normal}' restores the default.

   Finally, the command '\oldstylenums{NUMERALS}' will typeset so-called
"old-style" numerals, which have differing heights and depths (and
sometimes widths) from the standard "lining" numerals, which all have
the same height as uppercase letters.  LaTeX's default fonts support
this, and will respect '\textbf' (but not other styles; there are no
italic old-style numerals in Computer Modern).  Many other fonts have
old-style numerals also; sometimes package options are provided to make
them the default.  FAQ entry: <https://www.texfaq.org/FAQ-osf>.

4.3 Font sizes
==============

The following standard type size commands are supported by LaTeX.  The
table shows the command name and the corresponding actual font size used
(in points) with the '10pt', '11pt', and '12pt' document size options,
respectively (*note Document class options::).

Command                     '10pt'    '11pt'    '12pt'
--------------------------------------------------------
'\tiny'                     5         6         6
'\scriptsize'               7         8         8
'\footnotesize'             8         9         10
'\small'                    9         10        10.95
'\normalsize' (default)     10        10.95     12
'\large'                    12        12        14.4
'\Large'                    14.4      14.4      17.28
'\LARGE'                    17.28     17.28     20.74
'\huge'                     20.74     20.74     24.88
'\Huge'                     24.88     24.88     24.88

   The commands are listed here in declaration (not environment) form,
since that is how they are typically used.  For example.

     \begin{quotation} \small
       The Tao that can be named is not the eternal Tao.
     \end{quotation}

Here, the scope of the '\small' lasts until the end of the 'quotation'
environment.  It would also end at the next type style command or the
end of the current group, so you could enclose it in curly braces
'{\small This text is typeset in the small font.}'.

   Trying to use these commands in math, as with '$\small mv^2/2$',
results in 'LaTeX Font Warning: Command \small invalid in math mode',
and the font size doesn't change.  To work with a too-large formula,
often the best option is to use the 'displaymath' environment (*note
Math formulas::), or one of the environments from the 'amsmath' package.
For inline mathematics, such as in a table of formulas, an alternative
is something like '{\small $mv^2/2$}'.  (Sometimes '\scriptsize' and
'\scriptstyle' are confused.  Both change the font size, but the latter
also changes a number of other aspects of how mathematics is typeset.
*Note Math styles::.)

   An "environment form" of each of these commands is also defined; for
instance, '\begin{tiny}...\end{tiny}'.  However, in practice this form
can easily lead to unwanted spaces at the beginning and/or end of the
environment without careful consideration, so it's generally less
error-prone to stick to the declaration form.

   (Aside: Technically, due to the way LaTeX defines '\begin' and
'\end', nearly every command that does not take an argument technically
has an environment form.  But in almost all cases, it would only cause
confusion to use it.  The reason for mentioning the environment form of
the font size declarations specifically is that this particular use is
not rare.)

4.4 Low-level font commands
===========================

These commands are primarily intended for writers of macros and
packages.  The commands listed here are only a subset of the available
ones.

'\fontencoding{ENCODING}'
     Select the font encoding, the encoding of the output font.  There
     are a large number of valid encodings.  The most common are 'OT1',
     Knuth's original encoding for Computer Modern (the default), and
     'T1', also known as the Cork encoding, which has support for the
     accented characters used by the most widespread European languages
     (German, French, Italian, Polish and others), which allows TeX to
     hyphenate words containing accented letters.  For more, see
     <https://ctan.org/pkg/encguide>.

'\fontfamily{FAMILY}'
     Select the font family.  The web page
     <https://tug.org/FontCatalogue/> provides one way to browse through
     many of the fonts easily used with LaTeX.  Here are examples of
     some common families.

     'pag'  Avant Garde
     'fvs'  Bitstream Vera Sans
     'pbk'  Bookman
     'bch'  Charter
     'ccr'  Computer Concrete
     'cmr'  Computer Modern
     'cmss' Computer Modern Sans Serif
     'cmtt' Computer Modern Typewriter
     'pcr'  Courier
     'phv'  Helvetica
     'fi4'  Inconsolata
     'lmr'  Latin Modern
     'lmss' Latin Modern Sans
     'lmtt' Latin Modern Typewriter
     'pnc'  New Century Schoolbook
     'ppl'  Palatino
     'ptm'  Times
     'uncl' Uncial
     'put'  Utopia
     'pzc'  Zapf Chancery

'\fontseries{SERIES}'
     Select the font series.  A "series" combines a "weight" and a
     "width".  Typically, a font supports only a few of the possible
     combinations.  Some common combined series values include:

     'm'  Medium (normal)
     'b'  Bold
     'c'  Condensed
     'bc' Bold condensed
     'bx' Bold extended

     The possible values for weight, individually, are:

     'ul' Ultra light
     'el' Extra light
     'l'  Light
     'sl' Semi light
     'm'  Medium (normal)
     'sb' Semi bold
     'b'  Bold
     'eb' Extra bold
     'ub' Ultra bold

     The possible values for width, individually, are (the meaning and
     relationship of these terms varies with individual typefaces):

     'uc' Ultra condensed
     'ec' Extra condensed
     'c'  Condensed
     'sc' Semi condensed
     'm'  Medium
     'sx' Semi expanded
     'x'  Expanded
     'ex' Extra expanded
     'ux' Ultra expanded

     When forming the SERIES string from the weight and width, drop the
     'm' that stands for medium weight or medium width, unless both
     weight and width are 'm', in which case use just one (''m'').

'\fontshape{SHAPE}'
     Select font shape.  Valid shapes are:

     'n'  Upright (normal)
     'it' Italic
     'sl' Slanted (oblique)
     'sc' Small caps
     'ui' Upright italics
     'ol' Outline

     The two last shapes are not available for most font families, and
     small caps are often missing as well.

'\fontsize{SIZE}{SKIP}'
     Set the font size and the line spacing.  The unit of both
     parameters defaults to points ('pt').  The line spacing is the
     nominal vertical space between lines, baseline to baseline.  It is
     stored in the parameter '\baselineskip'.  The default
     '\baselineskip' for the Computer Modern typeface is 1.2 times the
     '\fontsize'.  Changing '\baselineskip' directly is inadvisable
     since its value is reset every time a size change happens; instead
     use '\baselinestretch'.  (*note \baselineskip &
     \baselinestretch::).

'\linespread{FACTOR}'
     Equivalent to '\renewcommand{\baselinestretch}{FACTOR}', and
     therefore must be followed by '\selectfont' to have any effect.
     Best specified in the preamble.  *Note \baselineskip &
     \baselinestretch::, for using 'setspace' package instead.

'\selectfont'
     The effects of the font commands described above do not happen
     until '\selectfont' is called, as in
     '\fontfamily{FAMILYNAME}\selectfont'.  It is often useful to put
     this in a macro:
     '\newcommand*{\myfont}{\fontfamily{FAMILYNAME}\selectfont}'
     (*note \newcommand & \renewcommand::).

'\usefont{ENC}{FAMILY}{SERIES}{SHAPE}'
     The same as invoking '\fontencoding', '\fontfamily', '\fontseries'
     and '\fontshape' with the given parameters, followed by
     '\selectfont'.  For example:

          \usefont{ot1}{cmr}{m}{n}

5 Layout
********

Commands for controlling the general page layout.

5.1 '\onecolumn'
================

Synopsis:

     \onecolumn

   Start a new page and produce single-column output.  If the document
is given the class option 'onecolumn' then this is the default behavior
(*note Document class options::).  This command is fragile (*note
\protect::).

5.2 '\twocolumn'
================

Synopses:

     \twocolumn
     \twocolumn[PRELIM ONE COLUMN TEXT]

   Start a new page and produce two-column output.  If the document is
given the class option 'twocolumn' then this is the default (*note
Document class options::).  This command is fragile (*note \protect::).

   If the optional PRELIM ONE COLUMN TEXT argument is present, it is
typeset in one-column mode before the two-column typesetting starts.

   These parameters control typesetting in two-column output:

'\columnsep'
     The distance between columns.  The default is 35pt.  Change it with
     a command such as '\setlength{\columnsep}{40pt}'.  You must change
     it before the two column mode starts; in the preamble is a good
     place.

'\columnseprule'
     The width of the rule between columns.  The default is 0pt, meaning
     that there is no rule.  Otherwise, the rule appears halfway between
     the two columns.  Change it with a command such as
     '\setlength{\columnseprule}{0.4pt}', before the two-column mode
     starts.

'\columnwidth'
     The width of a single column.  In one-column mode this is equal to
     '\textwidth'.  In two-column mode by default LaTeX sets the width
     of each of the two columns, '\columnwidth', to be half of
     '\textwidth' minus '\columnsep'.

   In a two-column document, the starred environments 'table*' and
'figure*' are two columns wide, whereas the unstarred environments
'table' and 'figure' take up only one column (*note figure:: and *note
table::).  LaTeX places starred floats at the top of a page.  The
following parameters control float behavior of two-column output.

'\dbltopfraction'
     The maximum fraction at the top of a two-column page that may be
     occupied by two-column wide floats.  The default is 0.7, meaning
     that the height of a 'table*' or 'figure*' environment must not
     exceed '0.7\textheight'.  If the height of your starred float
     environment exceeds this then you can take one of the following
     actions to prevent it from floating all the way to the back of the
     document:

        * Use the '[tp]' location specifier to tell LaTeX to try to put
          the bulky float on a page by itself, as well as at the top of
          a page.

        * Use the '[t!]' location specifier to override the effect of
          '\dbltopfraction' for this particular float.

        * Increase the value of '\dbltopfraction' to a suitably large
          number, to avoid going to float pages so soon.

     You can redefine it, as with '\renewcommand{\dbltopfraction}{0.9}'.

'\dblfloatpagefraction'
     For a float page of two-column wide floats, this is the minimum
     fraction that must be occupied by floats, limiting the amount of
     blank space.  LaTeX's default is '0.5'.  Change it with
     '\renewcommand'.

'\dblfloatsep'
     On a float page of two-column wide floats, this length is the
     distance between floats, at both the top and bottom of the page.
     The default is '12pt plus2pt minus2pt' for a document set at '10pt'
     or '11pt', and '14pt plus2pt minus4pt' for a document set at
     '12pt'.

'\dbltextfloatsep'
     This length is the distance between a multi-column float at the top
     or bottom of a page and the main text.  The default is '20pt
     plus2pt minus4pt'.

'\dbltopnumber'
     On a float page of two-column wide floats, this counter gives the
     maximum number of floats allowed at the top of the page.  The LaTeX
     default is '2'.

   This example uses '\twocolumn''s optional argument of to create a
title that spans the two-column article:

     \documentclass[twocolumn]{article}
     \newcommand{\authormark}[1]{\textsuperscript{#1}}
     \begin{document}
     \twocolumn[{% inside this optional argument goes one-column text
       \centering
       \LARGE The Title \\[1.5em]
       \large Author One\authormark{1},
              Author Two\authormark{2},
              Author Three\authormark{1} \\[1em]
       \normalsize
       \begin{tabular}{p{.2\textwidth}@{\hspace{2em}}p{.2\textwidth}}
         \authormark{1}Department one  &\authormark{2}Department two \\
          School one                   &School two
       \end{tabular}\\[3em] % space below title part
       }]

     Two column text here.

5.3 '\flushbottom'
==================

Make all pages in the documents after this declaration have the same
height, by stretching the vertical space where necessary to fill out the
page.  This is most often used when making two-sided documents since the
differences in facing pages can be glaring.

   If TeX cannot satisfactorily stretch the vertical space in a page
then you get a message like 'Underfull \vbox (badness 10000) has
occurred while \output is active'.  If you get that, one option is to
change to '\raggedbottom' (*note \raggedbottom::).  Alternatively, you
can adjust the 'textheight' to make compatible pages, or you can add
some vertical stretch glue between lines or between paragraphs, as in
'\setlength{\parskip}{0ex plus0.1ex}'.  Your last option is to, in a
final editing stage, adjust the height of individual pages (*note
\enlargethispage::).

   The '\flushbottom' state is the default only if you select the
'twoside' document class option (*note Document class options::).

5.4 '\raggedbottom'
===================

Make all later pages the natural height of the material on that page; no
rubber vertical lengths will be stretched.  Thus, in a two-sided
document the facing pages may be different heights.  This command can go
at any point in the document body.  See *note \flushbottom::.

   This is the default unless you select the 'twoside' document class
option (*note Document class options::).

5.5 Page layout parameters
==========================

'\columnsep'
'\columnseprule'
'\columnwidth'
     The distance between the two columns, the width of a rule between
     the columns, and the width of the columns, when the document class
     option 'twocolumn' is in effect (*note Document class options::).
     *Note \twocolumn::.

'\headheight'
     Height of the box that contains the running head.  The default in
     the 'article', 'report', and 'book' classes is '12pt', at all type
     sizes.

'\headsep'
     Vertical distance between the bottom of the header line and the top
     of the main text.  The default in the 'article' and 'report'
     classes is '25pt'.  In the 'book' class the default is: if the
     document is set at 10pt then it is '0.25in', and at 11pt or 12pt it
     is '0.275in'.

'\footskip'
     Distance from the baseline of the last line of text to the baseline
     of the page footer.  The default in the 'article' and 'report'
     classes is '30pt'.  In the 'book' class the default is: when the
     type size is 10pt the default is '0.35in', while at 11pt it is
     '0.38in', and at 12pt it is '30pt'.

'\linewidth'
     Width of the current line, decreased for each nested 'list' (*note
     list::).  That is, the nominal value for '\linewidth' is to equal
     '\textwidth' but for each nested list the '\linewidth' is decreased
     by the sum of that list's '\leftmargin' and '\rightmargin' (*note
     itemize::).

'\marginparpush'
'\marginsep'
'\marginparwidth'
     The minimum vertical space between two marginal notes, the
     horizontal space between the text body and the marginal notes, and
     the horizontal width of the notes.

     Normally marginal notes appear on the outside of the page, but the
     declaration '\reversemarginpar' changes that (and
     '\normalmarginpar' changes it back).

     The defaults for '\marginparpush' in both 'book' and 'article'
     classes are: '7pt' if the document is set at 12pt, and '5pt' if the
     document is set at 11pt or 10pt.

     For '\marginsep', in 'article' class the default is '10pt' except
     if the document is set at 10pt and in two-column mode where the
     default is '11pt'.

     For '\marginsep' in 'book' class the default is '10pt' in
     two-column mode and '7pt' in one-column mode.

     For '\marginparwidth' in both 'book' and 'article' classes, in
     two-column mode the default is 60% of '\paperwidth - \textwidth',
     while in one-column mode it is 50% of that distance.

'\oddsidemargin'
'\evensidemargin'
     The '\oddsidemargin' length is the extra distance between the left
     side of the page and the text's left margin, on odd-numbered pages
     when the document class option 'twoside' is chosen and on all pages
     when 'oneside' is in effect.  When 'twoside' is in effect, on
     even-numbered pages the extra distance on the left is
     '\evensidemargin'.

     LaTeX's default is that '\oddsidemargin' is 40% of the difference
     between '\paperwidth' and '\textwidth', and '\evensidemargin' is
     the remainder.

'\paperheight'
     The height of the paper, as distinct from the height of the print
     area.  Normally set with a document class option, as in
     '\documentclass[a4paper]{article}' (*note Document class
     options::).

'\paperwidth'
     The width of the paper, as distinct from the width of the print
     area.  Normally set with a document class option, as in
     '\documentclass[a4paper]{article}' (*note Document class
     options::).

'\textheight'
     The normal vertical height of the page body.  If the document is
     set at a nominal type size of 10pt then for an 'article' or
     'report' the default is '43\baselineskip', while for a 'book' it is
     '41\baselineskip'.  At a type size of 11pt the default is
     '38\baselineskip' for all document classes.  At 12pt it is
     '36\baselineskip' for all classes.

'\textwidth'
     The full horizontal width of the entire page body.  For an
     'article' or 'report' document, the default is '345pt' when the
     chosen type size is 10pt, the default is '360pt' at 11pt, and it is
     '390pt' at 12pt.  For a 'book' document, the default is '4.5in' at
     a type size of 10pt, and '5in' at 11pt or 12pt.

     In multi-column output, '\textwidth' remains the width of the
     entire page body, while '\columnwidth' is the width of one column
     (*note \twocolumn::).

     In lists (*note list::), '\textwidth' remains the width of the
     entire page body (and '\columnwidth' the width of the entire
     column), while '\linewidth' may decrease for nested lists.

     Inside a minipage (*note minipage::) or '\parbox' (*note
     \parbox::), all the width-related parameters are set to the
     specified width, and revert to their normal values at the end of
     the 'minipage' or '\parbox'.

'\hsize'
     This entry is included for completeness: '\hsize' is the TeX
     primitive parameter used when text is broken into lines.  It should
     not be used in normal LaTeX documents.

'\topmargin'
     Space between the top of the TeX page (one inch from the top of the
     paper, by default) and the top of the header.  The value is
     computed based on many other parameters: '\paperheight - 2in -
     \headheight - \headsep - \textheight - \footskip', and then divided
     by two.

'\topskip'
     Minimum distance between the top of the page body and the baseline
     of the first line of text.  For the standard classes, the default
     is the same as the font size, e.g., '10pt' at a type size of 10pt.

5.6 '\baselineskip' & '\baselinestretch'
========================================

The '\baselineskip' is a rubber length (*note Lengths::).  It gives the
"leading", the normal distance between lines in a paragraph, from
baseline to baseline.

   Ordinarily document authors do not directly change '\baselineskip'
while writing.  Instead, it is set by the low level font selection
command '\fontsize' (*note low level font commands fontsize::).  The
'\baselineskip''s value is reset every time a font change happens and so
any direct change to '\baselineskip' would vanish the next time there
was a font switch.  For how to influence line spacing, see the
discussion of '\baselinestretch' below.

   Usually, a font's size and baseline skip is assigned by the font
designer.  These numbers are nominal in the sense that if, for instance,
a font's style file has the command '\fontsize{10pt}{12pt}' then that
does not mean that the characters in the font are 10pt tall; for
instance, parentheses and accented capitals may be taller.  Nor does it
mean that if the lines are spaced less than 12pt apart then they risk
touching.  Rather these numbers are typographic judgements.  (Often, the
'\baselineskip' is about twenty percent larger than the font size.)

   The '\baselineskip' is not a property of each line but of the entire
paragraph.  As a result, large text in the middle of a paragraph, such
as a single '{\Huge Q}', will be squashed into its line.  TeX will make
sure it doesn't scrape up against the line above but won't change the
'\baselineskip' for that one line to make extra room above.  For the
fix, use a '\strut' (*note \strut::).

   The value of '\baselineskip' that TeX uses for the paragraph is the
value in effect at the blank line or command that ends the paragraph
unit.  So if a document contains this paragraph then its lines will be
scrunched together, compared to lines in surrounding paragraphs.

     Many people see a page break between text and a displayed equation as
     bad style, so in effect the display is part of the paragraph.
     Because this display is in footnotesize, the entire paragraph has the
     baseline spacing matching that size.
     {\footnotesize $$a+b = c$$}

   The process for making paragraphs is that when a new line is added,
if the depth of the previous line plus the height of the new line is
less than '\baselineskip' then TeX inserts vertical glue to make up the
difference.  There are two fine points.  The first is that if the lines
would be too close together, closer than '\lineskiplimit', then TeX
instead uses '\lineskip' as the interline glue.  The second is that TeX
doesn't actually use the depth of the previous line.  Instead it uses
'\prevdepth', which usually contains that depth.  But at the beginning
of the paragraph (or any vertical list) or just after a rule,
'\prevdepth' has the value -1000pt and this special value tells TeX not
to insert any interline glue at the paragraph start.

   In the standard classes '\lineskiplimit' is 0pt and '\lineskip' is
1pt.  By the prior paragraph then, the distance between lines can
approach zero but if it becomes zero (or less than zero) then the lines
jump to 1pt apart.

   Sometimes authors must, for editing purposes, put the document in
double space or one-and-a-half space.  The right way to influence the
interline distance is via '\baselinestretch'.  It scales
'\baselineskip', and has a default value of 1.0.  It is a command, not a
length, so change the scale factor as in
'\renewcommand{\baselinestretch}{1.5}\selectfont'.

   The most straightforward way to change the line spacing for an entire
document is to put '\linespread{FACTOR}' in the preamble.  For double
spacing, take FACTOR to be 1.6 and for one-and-a-half spacing use 1.3.
These number are rough: for instance, since the '\baselineskip' is about
1.2 times the font size, multiplying by 1.6 gives a baseline skip to
font size ratio of about 2.  (The '\linespread' command is defined as
'\renewcommand{\baselinestretch}{FACTOR}' so it won't take effect until
a font setting happens.  But that always takes place at the start of a
document, so there you don't need to follow it with '\selectfont'.)

   A simpler approach is the 'setspace' package.  The basic example:

     \usepackage{setspace}
     \doublespacing  % or \onehalfspacing for 1.5

In the preamble these will start the document off with that sizing.  But
you can also use these declarations in the document body to change the
spacing from that point forward, and consequently there is
'\singlespacing' to return the spacing to normal.  In the document body,
a better practice than using the declarations is to use environments,
such as '\begin{doublespace} ... \end{doublespace}'.  The package also
has commands to do arbitrary spacing: '\setstretch{FACTOR}' and
'\begin{spacing}{FACTOR} ... \end{spacing}'.  This package also keeps
the line spacing single-spaced in places where that is typically
desirable, such as footnotes and figure captions.  See the package
documentation.

5.7 Floats
==========

Some typographic elements, such as figures and tables, cannot be broken
across pages.  They must be typeset outside of the normal flow of text,
for instance floating to the top of a later page.

   LaTeX can have a number of different classes of floating material.
The default is the two classes, 'figure' (*note figure::) and 'table'
(*note table::), but you can create a new class with the package
'float'.

   Within any one float class LaTeX always respects the order, so that
the first figure in a document source must be typeset before the second
figure.  However, LaTeX may mix the classes, so it can happen that while
the first table appears in the source before the first figure, it
appears in the output after it.

   The placement of floats is subject to parameters, given below, that
limit the number of floats that can appear at the top of a page, and the
bottom, etc.  If so many floats are queued that the limits prevent them
all from fitting on a page then LaTeX places what it can and defers the
rest to the next page.  In this way, floats may end up being typeset far
from their place in the source.  In particular, a float that is big may
migrate to the end of the document.  In which event, because all floats
in a class must appear in sequential order, every following float in
that class also appears at the end.

   In addition to changing the parameters, for each float you can tweak
where the float placement algorithm tries to place it by using its
PLACEMENT argument.  The possible values are a sequence of the letters
below.  The default for both 'figure' and 'table', in both 'article' and
'book' classes, is 'tbp'.

't'
     (Top)--at the top of a text page.

'b'
     (Bottom)--at the bottom of a text page.  (However, 'b' is not
     allowed for full-width floats ('figure*') with double-column
     output.  To ameliorate this, use the 'stfloats' or 'dblfloatfix'
     package, but see the discussion at caveats in the FAQ:
     <https://www.texfaq.org/FAQ-2colfloat>.

'h'
     (Here)--at the position in the text where the 'figure' environment
     appears.  However, 'h' is not allowed by itself; 't' is
     automatically added.

     To absolutely force a float to appear "here", you can
     '\usepackage{float}' and use the 'H' specifier which it defines.
     For further discussion, see the FAQ entry at
     <https://www.texfaq.org/FAQ-figurehere>.

'p'
     (Page of floats)--on a separate "float page", which is a page
     containing no text, only floats.

'!'
     Used in addition to one of the above; for this float only, LaTeX
     ignores the restrictions on both the number of floats that can
     appear and the relative amounts of float and non-float text on the
     page.  The '!' specifier does _not_ mean "put the float here"; see
     above.

   Note: the order in which letters appear in the PLACEMENT argument
does not change the order in which LaTeX tries to place the float; for
instance, 'btp' has the same effect as 'tbp'.  All that PLACEMENT does
is that if a letter is not present then the algorithm does not try that
location.  Thus, LaTeX's default of 'tbp' is to try every location
except placing the float where it occurs in the source.

   To prevent LaTeX from moving floats to the end of the document or a
chapter you can use a '\clearpage' command to start a new page and
insert all pending floats.  If a pagebreak is undesirable then you can
use the 'afterpage' package and issue '\afterpage{\clearpage}'.  This
will wait until the current page is finished and then flush all
outstanding floats.

   LaTeX can typeset a float before where it appears in the source
(although on the same output page) if there is a 't' specifier in the
PLACEMENT parameter.  If this is not desired, and deleting the 't' is
not acceptable as it keeps the float from being placed at the top of the
next page, then you can prevent it by either using the 'flafter' package
or using the command '\suppressfloats[t]', which causes floats for the
top position on this page to moved to the next page.

   Parameters relating to fractions of pages occupied by float and
non-float text (change them with '\renewcommand{PARAMETER}{DECIMAL
BETWEEN 0 AND 1}'):

'\bottomfraction'
     The maximum fraction of the page allowed to be occupied by floats
     at the bottom; default '.3'.

'\floatpagefraction'
     The minimum fraction of a float page that must be occupied by
     floats; default '.5'.

'\textfraction'
     Minimum fraction of a page that must be text; if floats take up too
     much space to preserve this much text, floats will be moved to a
     different page.  The default is '.2'.

'\topfraction'
     Maximum fraction at the top of a page that may be occupied before
     floats; default '.7'.

   Parameters relating to vertical space around floats (change them with
a command of the form '\setlength{PARAMETER}{LENGTH EXPRESSION}'):

'\floatsep'
     Space between floats at the top or bottom of a page; default '12pt
     plus2pt minus2pt'.

'\intextsep'
     Space above and below a float in the middle of the main text;
     default '12pt plus2pt minus2pt' for 10 point and 11 point
     documents, and '14pt plus4pt minus4pt' for 12 point documents.

'\textfloatsep'
     Space between the last (first) float at the top (bottom) of a page;
     default '20pt plus2pt minus4pt'.

   Counters relating to the number of floats on a page (change them with
a command of the form '\setcounter{CTRNAME}{NATURAL NUMBER}'):

'bottomnumber'
     Maximum number of floats that can appear at the bottom of a text
     page; default 1.

'dbltopnumber'
     Maximum number of full-sized floats that can appear at the top of a
     two-column page; default 2.

'topnumber'
     Maximum number of floats that can appear at the top of a text page;
     default 2.

'totalnumber'
     Maximum number of floats that can appear on a text page; default 3.

   The principal TeX FAQ entry relating to floats
<https://www.texfaq.org/FAQ-floats> contains suggestions for relaxing
LaTeX's default parameters to reduce the problem of floats being pushed
to the end.  A full explanation of the float placement algorithm is in
Frank Mittelbach's article "How to influence the position of float
environments like figure and table in LaTeX?"
(<https://www.latex-project.org/publications/2014-FMi-TUB-tb111mitt-float-placement.pdf>).

5.7.1 '\caption'
----------------

Synopsis:

     \caption{CAPTION-TEXT}

or

     \caption[SHORT-CAPTION-TEXT]{CAPTION-TEXT}

   Make a caption for a floating environment, such as a 'figure' or
'table' environment (*note figure:: or *note table::).

   In this example, LaTeX places a caption below the vertical blank
space that is left by the author for the later inclusion of a picture.

     \begin{figure}
       \vspace*{1cm}
       \caption{Alonzo Cushing, Battery A, 4th US Artillery.}
       \label{fig:CushingPic}
     \end{figure}

The '\caption' command will label the CAPTION-TEXT with something like
'Figure 1:' for an article or 'Figure 1.1:' for a book.  The text is
centered if it is shorter than the text width, or set as an unindented
paragraph if it takes more than one line.

   In addition to placing the CAPTION-TEXT in the output, the '\caption'
command also saves that information for use in a list of figures or list
of tables (*note Table of contents etc.::).

   Here the '\caption' command uses the optional SHORT-CAPTION-TEXT, so
that the shorter text appears in the list of tables, rather than the
longer CAPTION-TEXT.

     \begin{table}
       \centering
       \begin{tabular}{|*{3}{c}|}
         \hline
         4  &9  &2 \\
         3  &5  &7 \\
         8  &1  &6 \\
         \hline
       \end{tabular}
       \caption[\textit{Lo Shu} magic square]{%
         The \textit{Lo Shu} magic square, which is unique among
         squares of order three up to rotation and reflection.}
       \label{tab:LoShu}
     \end{table}

LaTeX will label the CAPTION-TEXT with something like 'Table 1:' for an
article or 'Table 1.1:' for a book.

   The caption can appear at the top of the 'figure' or 'table'.  For
instance, that would happen in the prior example by putting the
'\caption' between the '\centering' and the '\begin{tabular}'.

   Different floating environments are numbered separately, by default.
It is '\caption' that updates the counter, and so any '\label' must come
after the '\caption'.  The counter for the 'figure' environment is named
'figure', and similarly the counter for the 'table' environment is
'table'.

   The text that will be put in the list of figures or list of tables is
moving argument.  If you get the LaTeX error '! Argument of \@caption
has an extra }' then you must put '\protect' in front of any fragile
commands.  *Note \protect::.

   The 'caption' package has many options to adjust how the caption
appears, for example changing the font size, making the caption be
hanging text rather than set as a paragraph, or making the caption
always set as a paragraph rather than centered when it is short.

6 Sectioning
************

Structure your text into divisions: parts, chapters, sections, etc.  All
sectioning commands have the same form, one of:

     SECTIONING-COMMAND{TITLE}
     SECTIONING-COMMAND*{TITLE}
     SECTIONING-COMMAND[TOC-TITLE]{TITLE}

For instance, declare the start of a subsection as with
'\subsection{Motivation}'.

   The table has each SECTIONING-COMMAND in LaTeX.  All are available in
all of LaTeX's standard document classes 'book', 'report',
and 'article', except that '\chapter' is not available in 'article'.

Sectioning unit    Command            Level
--------------------------------------------------------------------
Part               '\part'            -1 ('book', 'report'), 0
                                      ('article')
Chapter            '\chapter'         0
Section            '\section'         1
Subsection         '\subsection'      2
Subsubsection      '\subsubsection'   3
Paragraph          '\paragraph'       4
Subparagraph       '\subparagraph'    5

   All these commands have a '*'-form that prints TITLE as usual but
does not number it and does not make an entry in the table of contents.
An example of using this is for an appendix in an 'article'.  The input
'\appendix\section{Appendix}' gives the output 'A Appendix' (*note
\appendix::).  You can lose the numbering 'A' by instead entering
'\section*{Appendix}' (articles often omit a table of contents and have
simple page headers so the other differences from the '\section' command
may not matter).

   The section title TITLE provides the heading in the main text, but it
may also appear in the table of contents and in the running head or foot
(*note Page styles::).  You may not want the same text in these places
as in the main text.  All of these commands have an optional argument
TOC-TITLE for these other places.

   The level number in the table above determines which sectional units
are numbered, and which appear in the table of contents.  If the
sectioning command's LEVEL is less than or equal to the value of the
counter 'secnumdepth' then the titles for this sectioning command will
be numbered (*note Sectioning/secnumdepth::).  And, if LEVEL is less
than or equal to the value of the counter 'tocdepth' then the table of
contents will have an entry for this sectioning unit (*note
Sectioning/tocdepth::).

   LaTeX expects that before you have a '\subsection' you will have a
'\section' and, in a 'book' class document, that before a '\section' you
will have a '\chapter'.  Otherwise you can get something like a
subsection numbered '3.0.1'.

   LaTeX lets you change the appearance of the sectional units.  As a
simple example, you can change the section numbering to upper-case
letters with '\renewcommand\thesection{\Alph{section}}' in the preamble
(*note \alph \Alph \arabic \roman \Roman \fnsymbol::).  CTAN has many
packages that make this adjustment easier, notably 'titlesec'.

   Two counters relate to the appearance of headings made by sectioning
commands.

'secnumdepth'
     Controls which sectioning unit are numbered.  Setting the counter
     with '\setcounter{secnumdepth}{LEVEL}' will suppress numbering of
     sectioning at any depth greater than LEVEL (*note \setcounter::).
     See the above table for the level numbers.  For instance, if the
     'secnumdepth' is 1 in an 'article' then a '\section{Introduction}'
     command will produce output like '1 Introduction' while
     '\subsection{Discussion}' will produce output like 'Discussion',
     without the number.  LaTeX's default 'secnumdepth' is 3 in
     'article' class and  2 in the 'book' and 'report' classes.

'tocdepth'
     Controls which sectioning units are listed in the table of
     contents.  The setting '\setcounter{tocdepth}{LEVEL}' makes the
     sectioning units at LEVEL be the smallest ones listed (*note
     \setcounter::).  See the above table for the level numbers.  For
     instance, if 'tocdepth' is 1 then the table of contents will list
     sections but not subsections.  LaTeX's default 'tocdepth' is 3 in
     'article' class and  2 in the 'book' and 'report' classes.

6.1 '\part'
===========

Synopsis, one of:

     \part{TITLE}
     \part*{TITLE}
     \part[TOC-TITLE]{TITLE}

   Start a document part.  The standard LaTeX classes 'book', 'report',
and 'article', all have this command.

   This produces a document part, in a book.

     \part{VOLUME I \\
            PERSONAL MEMOIRS OF  U.\ S.\ GRANT}
     \chapter{ANCESTRY--BIRTH--BOYHOOD.}
     My family is American, and has been for generations,
     in all its branches, direct and collateral.

   In each standard class the '\part' command outputs a part number such
as 'Part I', alone on its line, in boldface, and in large type.  Then
LaTeX outputs TITLE, also alone on its line, in bold and in even larger
type.  In class 'book', the LaTeX default puts each part alone on its
own page.  If the book is two-sided then LaTeX will skip a page if
needed to have the new part on an odd-numbered page.  In 'report' it is
again alone on a page, but LaTeX won't force it onto an odd-numbered
page.  In an 'article' LaTeX does not put it on a fresh page, but
instead outputs the part number and part title onto the main document
page.

   The '*' form shows TITLE but it does not show the part number, does
not increment the 'part' counter, and produces no table of contents
entry.

   The optional argument TOC-TITLE will appear as the part title in the
table of contents (*note Table of contents etc.::) and in running
headers (*note Page styles::).  If it is not present then TITLE will be
there.  This example puts a line break in TITLE but omits the break in
the table of contents.

     \part[Up from the bottom; my life]{Up from the bottom\\ my life}

   For determining which sectional units are numbered and which appear
in the table of contents, the level number of a part is -1 (*note
Sectioning/secnumdepth::, and *note Sectioning/tocdepth::).

   In the class 'article', if a paragraph immediately follows the part
title then it is not indented.  To get an indent you can use the package
'indentfirst'.

   One package to change the behavior of '\part' is 'titlesec'.  See its
documentation on CTAN.

6.2 '\chapter'
==============

Synopsis, one of:

     \chapter{TITLE}
     \chapter*{TITLE}
     \chapter[TOC-TITLE]{TITLE}

   Start a chapter.  The standard LaTeX classes 'book' and 'report' have
this command but 'article' does not.

   This produces a chapter.

     \chapter{Loomings}
     Call me Ishmael.
     Some years ago---never mind how long precisely---having little or no
     money in my purse, and nothing particular to interest me on shore, I
     thought I would sail about a little and see the watery part of
     the world.

   The LaTeX default starts each chapter on a fresh page, an
odd-numbered page if the document is two-sided.  It produces a chapter
number such as 'Chapter 1' in large boldface type (the size is '\huge').
It then puts TITLE on a fresh line, in boldface type that is still
larger (size '\Huge').  It also increments the 'chapter' counter, adds
an entry to the table of contents (*note Table of contents etc.::), and
sets the running header information (*note Page styles::).

   The '*' form shows TITLE on a fresh line, in boldface.  But it does
not show the chapter number, does not increment the 'chapter' counter,
produces no table of contents entry, and does not affect the running
header.  (If you use the page style 'headings' in a two-sided document
then the header will be from the prior chapter.)  This example
illustrates.

     \chapter*{Preamble}

   The optional argument TOC-TITLE will appear as the chapter title in
the table of contents (*note Table of contents etc.::) and in running
headers (*note Page styles::).  If it is not present then TITLE will be
there.  This shows the full name in the chapter title,

     \chapter[Weyl]{Hermann Klaus Hugo (Peter) Weyl (1885--1955)}

but only 'Weyl' on the contents page.  This puts a line break in the
title but that doesn't work well with running headers so it omits the
break in the contents

     \chapter[Given it all; my story]{Given it all\\ my story}

   For determining which sectional units are numbered and which appear
in the table of contents, the level number of a chapter is 0 (*note
Sectioning/secnumdepth:: and *note Sectioning/tocdepth::).

   The paragraph that follows the chapter title is not indented, as is a
standard typographical practice.  To get an indent use the package
'indentfirst'.

   You can change what is shown for the chapter number.  To change it to
something like 'Lecture 1', put in the preamble either
'\renewcommand{\chaptername}{Lecture}' or this (*note \makeatletter &
\makeatother::).

     \makeatletter
     \renewcommand{\@chapapp}{Lecture}
     \makeatother

To make this change because of the primary language for the document,
see the package 'babel'.

   In a two-sided document LaTeX puts a chapter on odd-numbered page, if
necessary leaving an even-numbered page that is blank except for any
running headers.  To make that page completely blank, see *note
\clearpage & \cleardoublepage::.

   To change the behavior of the '\chapter' command, you can copy its
definition from the LaTeX format file and make adjustments.  But there
are also many packages on CTAN that address this.  One is 'titlesec'.
See its documentation, but the example below gives a sense of what it
can do.

     \usepackage{titlesec}   % in preamble
     \titleformat{\chapter}
       {\Huge\bfseries}  % format of title
       {}                % label, such as 1.2 for a subsection
       {0pt}             % length of separation between label and title
       {}                % before-code hook

This omits the chapter number 'Chapter 1' from the page but unlike
'\chapter*' it keeps the chapter in the table of contents and the
running headers.

6.3 '\section'
==============

Synopsis, one of:

     \section{TITLE}
     \section*{TITLE}
     \section[TOC-TITLE]{TITLE}

   Start a section.  The standard LaTeX classes 'article', 'book', and
'report' all have this command.

   This produces a section.

     In this Part we tend to be more interested in the function,
     in the input-output behavior,
     than in the details of implementing that behavior.

     \section{Turing machines}
     Despite this desire to downplay implementation,
     we follow the approach of A~Turing that the
     first step toward defining the set of computable functions
     is to reflect on the details of what mechanisms can do.

   For the standard LaTeX classes 'book' and 'report' the default output
is like '1.2 TITLE' (for chapter 1, section 2), alone on its line and
flush left, in boldface and a larger type (the type size is '\Large').
The same holds in 'article' except that there are no chapters in that
class so it looks like '2 TITLE'.

   The '*' form shows TITLE.  But it does not show the section number,
does not increment the 'section' counter, produces no table of contents
entry, and does not affect the running header.  (If you use the page
style 'headings' in a two-sided document then the header will be from
the prior section.)

   The optional argument TOC-TITLE will appear as the section title in
the table of contents (*note Table of contents etc.::) and in running
headers (*note Page styles::).  If it is not present then TITLE will be
there.  This shows the full name in the title of the section:

     \section[Elizabeth~II]{Elizabeth the Second,
       by the Grace of God of the United Kingdom,
       Canada and Her other Realms and Territories Queen,
       Head of the Commonwealth, Defender of the Faith.}

but only 'Elizabeth II' on the contents page and in the headers.  This
has a line break in TITLE but that does not work with headers so it is
omitted from the contents and headers.

     \section[Truth is, I cheated; my life story]{Truth is,
       I cheated\\my life story}

   For determining which sectional units are numbered and which appear
in the table of contents, the level number of a section is 1 (*note
Sectioning/secnumdepth:: and *note Sectioning/tocdepth::).

   The paragraph that follows the section title is not indented, as is a
standard typographical practice.  One way to get an indent is to use the
package 'indentfirst'.

   In general, to change the behavior of the '\section' command, there
are a number of options.  One is the '\@startsection' command (*note
\@startsection::).  There are also many packages on CTAN that address
this, including 'titlesec'.  See the documentation but the example below
gives a sense of what they can do.

     \usepackage{titlesec}   % in preamble
     \titleformat{\section}
       {\normalfont\Large\bfseries}  % format of title
       {\makebox[1pc][r]{\thesection\hspace{1pc}}} % label
       {0pt}                   % length of separation between label and title
       {}                      % before-code hook
     \titlespacing*{\section}
       {-1pc}{18pt}{10pt}[10pc]

That puts the section number in the margin.

6.4 '\subsection'
=================

Synopsis, one of:

     \subsection{TITLE}
     \subsection*{TITLE}
     \subsection[TOC-TITLE]{TITLE}

   Start a subsection.  The standard LaTeX classes 'article', 'book',
and 'report' all have this command.

   This produces a subsection.

     We will show that there are more functions than Turing machines and that
     therefore some functions have no associated machine.

     \subsection{Cardinality} We will begin with two paradoxes that
     dramatize the challenge to our intuition posed by comparing the sizes of
     infinite sets.

   For the standard LaTeX classes 'book' and 'report' the default output
is like '1.2.3 TITLE' (for chapter 1, section 2, subsection 3), alone on
its line and flush left, in boldface and a larger type (the type size is
'\large').  The same holds in 'article' except that there are no
chapters in that class so it looks like '2.3 TITLE'.

   The '*' form shows TITLE.  But it does not show the subsection
number, does not increment the 'subsection' counter, and produces no
table of contents entry.

   The optional argument TOC-TITLE will appear as the subsection title
in the table of contents (*note Table of contents etc.::).  If it is not
present then TITLE will be there.  This shows the full text in the title
of the subsection:

     \subsection[$\alpha,\beta,\gamma$ paper]{\textit{The Origin of
       Chemical Elements} by R.A.~Alpher, H.~Bethe, and G.~Gamow}

but only 'α,β,γ paper' on the contents page.

   For determining which sectional units are numbered and which appear
in the table of contents, the level number of a subsection is 2 (*note
Sectioning/secnumdepth:: and *note Sectioning/tocdepth::).

   The paragraph that follows the subsection title is not indented, as
is a standard typographical practice.  One way to get an indent is to
use the package 'indentfirst'.

   There are a number of ways to change the behavior of the
'\subsection' command.  One is the '\@startsection' command (*note
\@startsection::).  There are also many packages on CTAN that address
this, including 'titlesec'.  See the documentation but the example below
gives a sense of what they can do.

     \usepackage{titlesec}   % in preamble
     \titleformat{\subsection}[runin]
       {\normalfont\normalsize\bfseries}  % format of the title
       {\thesubsection}                   % label
       {0.6em}                            % space between label and title
       {}                                 % before-code hook

That puts the subsection number and TITLE in the first line of text.

6.5 '\subsubsection', '\paragraph', '\subparagraph'
===================================================

Synopsis, one of:

     \subsubsection{TITLE}
     \subsubsection*{TITLE}
     \subsubsection[TOC-TITLE]{TITLE}

or one of:

     \paragraph{TITLE}
     \paragraph*{TITLE}
     \paragraph[TOC-TITLE]{TITLE}

or one of:

     \subparagraph{TITLE}
     \subparagraph*{TITLE}
     \subparagraph[TOC-TITLE]{TITLE}

   Start a subsubsection, paragraph, or subparagraph.  The standard
LaTeX classes 'article', 'book', and 'report' all have these commands,
although they are not commonly used.

   This produces a subsubsection.

     \subsubsection{Piston ring compressors: structural performance}
     Provide exterior/interior wall cladding assemblies
     capable of withstanding the effects of load and stresses from
     consumer-grade gasoline engine piston rings.

   The default output of each of the three does not change over the
standard LaTeX classes 'article', 'book', and 'report'.  For
'\subsubsection' the TITLE is alone on its line, in boldface and normal
size type.  For '\paragraph' the TITLE is inline with the text, not
indented, in boldface and normal size type.  For '\subparagraph' the
TITLE is inline with the text, with a paragraph indent, in boldface and
normal size type (Because an 'article' has no chapters its
subsubsections are numbered and so it looks like '1.2.3 TITLE', for
section 1, subsection 2, and subsubsection 3.  The other two divisions
are not numbered.)

   The '*' form shows TITLE.  But it does not increment the associated
counter and produces no table of contents entry (and does not show the
number for '\subsubsection').

   The optional argument TOC-TITLE will appear as the division title in
the table of contents (*note Table of contents etc.::).  If it is not
present then TITLE will be there.

   For determining which sectional units are numbered and which appear
in the table of contents, the level number of a subsubsection is 3, of a
paragraph is 4, and of a subparagraph is 5 (*note
Sectioning/secnumdepth:: and *note Sectioning/tocdepth::).

   The paragraph that follows the subsubsection title is not indented,
as is a standard typographical practice.  One way to get an indent is to
use the package 'indentfirst'.

   There are a number of ways to change the behavior of the these
commands.  One is the '\@startsection' command (*note \@startsection::).
There are also many packages on CTAN that address this, including
'titlesec'.  See the documentation on CTAN.

6.6 '\appendix'
===============

Synopsis:

     \appendix

   This does not directly produce any output.  But in a book or report
it declares that subsequent '\chapter' commands start an appendix.  In
an article it does the same, for '\section' commands.  It also resets
the 'chapter' and 'section' counters to 0 in a book or report, and in an
article resets the 'section' and 'subsection' counters.

   In this book

     \chapter{One}  ...
     \chapter{Two}  ...
      ...
     \appendix
     \chapter{Three}  ...
     \chapter{Four}  ...

the first two will generate output numbered 'Chapter 1' and 'Chapter 2'.
After the '\appendix' the numbering will be 'Appendix A' and 'Appendix
B'.  *Note Larger book template::, for another example.

   The 'appendix' package adds the command '\appendixpage' to put a
separate 'Appendices' in the document body before the first appendix,
and the command '\addappheadtotoc' to do the same in the table of
contents.  You can reset the name 'Appendices' with a command like
'\renewcommand{\appendixname}{Specification}', as well as a number of
other features.  See the documentation on CTAN.

6.7 '\frontmatter', '\mainmatter', '\backmatter'
================================================

Synopsis, one or more of:

     \frontmatter
     ...
     \mainmatter
     ...
     \backmatter
     ...

   Format a 'book' class document differently according to which part of
the document is being produced.  All three commands are optional.

   Traditionally, a book's front matter contains such things as the
title page, an abstract, a table of contents, a preface, a list of
notations, a list of figures, and a list of tables.  (Some of these
front matter pages, such as the title page, are traditionally not
numbered.)  The back matter may contain such things as a glossary,
notes, a bibliography, and an index.

   The '\frontmatter' command makes the pages numbered in lowercase
roman, and makes chapters not numbered, although each chapter's title
appears in the table of contents; if you use other sectioning commands
here, use the '*'-version (*note Sectioning::).

   The '\mainmatter' command changes the behavior back to the expected
version, and resets the page number.

   The '\backmatter' command leaves the page numbering alone but
switches the chapters back to being not numbered.

   *Note Larger book template::, for an example using these three
commands.

6.8 '\@startsection', typesetting sectional unit headings
=========================================================

Synopsis:

     \@startsection{NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}

   Used to help redefine the behavior of commands that start sectioning
divisions such as '\section' or '\subsection'.

   Note that the 'titlesec' package makes manipulation of sectioning
easier.  Further, while most requirements for sectioning commands can be
satisfied with '\@startsection', some cannot.  For instance, in the
standard LaTeX 'book' and 'report' classes the commands '\chapter' and
'\report' are not constructed in this way.  To make such a command you
may want to use the '\secdef' command.

   Technically, '\@startsection' has the form

     \@startsection{NAME}
       {LEVEL}
       {INDENT}
       {BEFORESKIP}
       {AFTERSKIP}
       {STYLE}*[TOCTITLE]{TITLE}

so that issuing

     \renewcommand{\section}{\@startsection{NAME}
       {LEVEL}
       {INDENT}
       {BEFORESKIP}
       {AFTERSKIP}
       {STYLE}}

redefines '\section' while keeping its standard calling form
'\section*[TOCTITLE]{TITLE}' (in which, for reminder, the star '*' is
optional).  *Note Sectioning::.  This implies that when you write a
command like '\renewcommand{\section}{...}', the '\@startsection{...}'
must come last in the definition.  See the examples below.

NAME
     Name of the counter used to number the sectioning header.  This
     counter must be defined separately.  Most commonly this is either
     'section', 'subsection', or 'paragraph'.  Although in those cases
     the counter name is the same as the sectioning command itself, you
     don't have to use the same name.

     Then '\the'NAME displays the title number and '\'NAME'mark' is for
     the page headers.  See the third example below.

LEVEL
     An integer giving the depth of the sectioning command.  *Note
     Sectioning::, for the list of standard level numbers.

     If LEVEL is less than or equal to the value of the counter
     'secnumdepth' then titles for this sectioning command will be
     numbered (*note Sectioning/secnumdepth::).  For instance, if
     'secnumdepth' is 1 in an 'article' then the command
     '\section{Introduction}' will produce output like "1 Introduction"
     while '\subsection{Discussion}' will produce output like
     "Discussion", without the number prefix.

     If LEVEL is less than or equal to the value of the counter TOCDEPTH
     then the table of contents will have an entry for this sectioning
     unit (*note Sectioning/tocdepth::).  For instance, in an 'article',
     if TOCDEPTH is 1 then the table of contents will list sections but
     not subsections.

INDENT
     A length giving the indentation of all of the title lines with
     respect to the left margin.  To have the title flush with the
     margin use '0pt'.  A negative indentation such as '-\parindent'
     will move the title into the left margin.

BEFORESKIP
     The absolute value of this length is the amount of vertical space
     that is inserted before this sectioning unit's title.  This space
     will be discarded if the sectioning unit happens to start at the
     beginning of a page.  If this number is negative then the first
     paragraph following the header is not indented, if it is
     non-negative then the first paragraph is indented.  (Note that the
     negative of '1pt plus 2pt minus 3pt' is '-1pt plus -2pt minus
     -3pt'.)

     For example, if BEFORESKIP is '-3.5ex plus -1ex minus -0.2ex' then
     to start the new sectioning unit, LaTeX will add about 3.5 times
     the height of a letter x in vertical space, and the first paragraph
     in the section will not be indented.  Using a rubber length, with
     'plus' and 'minus', is good practice here since it gives LaTeX more
     flexibility in making up the page (*note Lengths::).

     The full accounting of the vertical space between the baseline of
     the line prior to this sectioning unit's header and the baseline of
     the header is that it is the sum of the '\parskip' of the text
     font, the '\baselineskip' of the title font, and the absolute value
     of the BEFORESKIP.  This space is typically rubber so it may
     stretch or shrink.  (If the sectioning unit starts on a fresh page
     so that the vertical space is discarded then the baseline of the
     header text will be where LaTeX would put the baseline of the first
     text line on that page.)

AFTERSKIP
     This is a length.  If AFTERSKIP is non-negative then this is the
     vertical space inserted after the sectioning unit's title header.
     If it is negative then the title header becomes a run-in header, so
     that it becomes part of the next paragraph.  In this case the
     absolute value of the length gives the horizontal space between the
     end of the title and the beginning of the following paragraph.
     (Note that the negative of '1pt plus 2pt minus 3pt' is '-1pt plus
     -2pt minus -3pt'.)

     As with BEFORESKIP, using a rubber length, with 'plus' and 'minus'
     components, is good practice here since it gives LaTeX more
     flexibility in putting together the page.

     If 'afterskip' is non-negative then the full accounting of the
     vertical space between the baseline of the sectioning unit's header
     and the baseline of the first line of the following paragraph is
     that it is the sum of the '\parskip' of the title font, the
     '\baselineskip' of the text font, and the value of AFTER.  That
     space is typically rubber so it may stretch or shrink.  (Note that
     because the sign of 'afterskip' changes the sectioning unit
     header's from standalone to run-in, you cannot use a negative
     'afterskip' to cancel part of the '\parskip'.)

STYLE
     Controls the styling of the title.  See the examples below.
     Typical commands to use here are '\centering', '\raggedright',
     '\normalfont', '\hrule', or '\newpage'.  The last command in STYLE
     may be one that takes one argument, such as '\MakeUppercase' or
     '\fbox' that takes one argument.  The section title will be
     supplied as the argument to this command.  For instance, setting
     STYLE to '\bfseries\MakeUppercase' would produce titles that are
     bold and uppercase.

   These are LaTeX's defaults for the first three sectioning units that
are defined with '\@startsection', for the 'article', 'book', and
'report' classes.

   * For 'section': LEVEL is 1, INDENT is 0pt, BEFORESKIP is '-3.5ex
     plus -1ex minus -0.2ex', AFTERSKIP is '2.3ex plus 0.2ex', and STYLE
     is '\normalfont\Large\bfseries'.

   * For 'subsection': LEVEL is 2, INDENT is 0pt, BEFORESKIP is '-3.25ex
     plus -1ex minus -0.2ex', AFTERSKIP is '1.5ex plus 0.2ex', and STYLE
     is '\normalfont\large\bfseries'.

   * For 'subsubsection': LEVEL is 3, INDENT is 0pt, BEFORESKIP is
     '-3.25ex plus -1ex minus -0.2ex', AFTERSKIP is '1.5ex plus 0.2ex',
     and STYLE is '\normalfont\normalsize\bfseries'.

   Some examples follow.  These go either in a package or class file or
in the preamble of a LaTeX document.  If you put them in the preamble
they must go between a '\makeatletter' command and a '\makeatother'.
(Probably the error message 'You can't use `\spacefactor' in vertical
mode.' means that you forgot this.)  *Note \makeatletter &
\makeatother::.

   This will put section titles in large boldface type, centered.  It
says '\renewcommand' because LaTeX's standard classes have already
defined a '\section'.  For the same reason it does not define a
'section' counter, or the commands '\thesection' and '\l@section'.

     \renewcommand\section{%
       \@startsection{section}% *note NAME: \@startsection/name.
         {1}% *note LEVEL: \@startsection/level.
         {0pt}% *note INDENT: \@startsection/indent.
         {-3.5ex plus -1ex minus -.2ex}% *note BEFORESKIP: \@startsection/beforeskip.
         {2.3ex plus.2ex}% *note AFTERSKIP: \@startsection/afterskip.
         {\centering\normalfont\Large\bfseries}% *note STYLE: \@startsection/style.
       }

   This will put 'subsection' titles in small caps type, inline with the
paragraph.

     \renewcommand\subsection{%
       \@startsection{subsection}%  *note NAME: \@startsection/name.
         {2}% *note LEVEL: \@startsection/level.
         {0em}% *note INDENT: \@startsection/indent.
         {-1ex plus 0.1ex minus -0.05ex}% *note BEFORESKIP: \@startsection/beforeskip.
         {-1em plus 0.2em}% *note AFTERSKIP: \@startsection/afterskip.
         {\scshape}% *note STYLE: \@startsection/style.
       }

   The prior examples redefined existing sectional unit title commands.
This defines a new one, illustrating the needed counter and macros to
display that counter.

     \setcounter{secnumdepth}{6}% show counters this far down
     \newcounter{subsubparagraph}[subparagraph]% counter for numbering
     \renewcommand{\thesubsubparagraph}%               how to display
       {\thesubparagraph.\@arabic\c@subsubparagraph}%  numbering
     \newcommand{\subsubparagraph}{\@startsection
                              {subsubparagraph}%
                              {6}%
                              {0em}%
                              {\baselineskip}%
                              {0.5\baselineskip}%
                              {\normalfont\normalsize}}
     \newcommand*\l@subsubparagraph{\@dottedtocline{6}{10em}{5em}}% for toc
     \newcommand{\subsubparagraphmark}[1]{}% for page headers

7 Cross references
******************

We often want something like 'See Theorem~31'.  But by-hand typing the
31 is poor practice.  Instead you should write a "label" such as
'\label{eq:GreensThm}' and then "reference" it, as with 'See
equation~\ref{eq:GreensThm}'.  LaTeX will automatically work out the
number, put it into the output, and will change that number later if
needed.

     We will see this with Theorem~\ref{th:GreensThm}. % forward reference
     ...
     \begin{theorem} \label{th:GreensThm}
       ...
     \end{theorem}
     ...
     See Theorem~\ref{th:GreensThm} on page~\pageref{th:GreensThm}.

   LaTeX tracks cross reference information in a file having the
extension '.aux' and with the same base name as the file containing the
'\label'.  So if '\label' is in 'calculus.tex' then the information is
in 'calculus.aux'.  LaTeX puts the information in that file every time
it runs across a '\label'.

   The behavior described in the prior paragraph results in a quirk that
happens when your document has a "forward reference", a '\ref' that
appears before the associated '\label'.  If this is the first time that
you are compiling the document then you will get 'LaTeX Warning:
Label(s) may have changed. Rerun to get cross references right' and in
the output the forward reference will appear as two question marks '??',
in boldface.  A similar thing happens if you change some things so the
references changes; you get the same warning and the output contains the
old reference information.  In both cases, resolve this by compiling the
document a second time.

   The 'cleveref' package enhances LaTeX's cross referencing features.
You can arrange that if you enter
'\begin{thm}\label{th:Nerode}...\end{thm}' then '\cref{th:Nerode}' will
output 'Theorem 3.21', without you having to enter the "Theorem."

7.1 '\label'
============

Synopsis:

     \label{KEY}

   Assign a reference number to KEY.  In ordinary text '\label{KEY}'
assigns to KEY the number of the current sectional unit.  Inside an
environment with numbering, such as a 'table' or 'theorem' environment,
'\label{KEY}' assigns to KEY the number of that environment.  Retrieve
the assigned number with the '\ref{KEY}' command (*note \ref::).

   A key name can consist of any sequence of letters, digits, or common
punctuation characters.  Upper and lowercase letters are distinguished,
as usual.

   A common convention is to use labels consisting of a prefix and a
suffix separated by a colon or period.  Thus, '\label{fig:Post}' is a
label for a figure with a portrait of Emil Post.  This helps to avoid
accidentally creating two labels with the same name, and makes your
source more readable.  Some commonly-used prefixes:

'ch'
     for chapters

'sec'
'subsec'
     for lower-level sectioning commands

'fig'
     for figures

'tab'
     for tables

'eq'
     for equations

   In the auxiliary file the reference information is kept as the text
of a command of the form '\newlabel{LABEL}{{CURRENTLABEL}{PAGENUMBER}}'.
Here CURRENTLABEL is the current value of the macro '\@currentlabel'
that is usually updated whenever you call '\refstepcounter{COUNTER}'.

   Below, the key 'sec:test' will get the number of the current section
and the key 'fig:test' will get the number of the figure.
(Incidentally, put labels after captions in figures and tables.)

     \section{section name}
     \label{sec:test}
     This is Section~\ref{sec:test}.
     \begin{figure}
       ...
       \caption{caption text}
       \label{fig:test}
     \end{figure}
     See Figure~\ref{fig:test}.

7.2 '\pageref'
==============

Synopsis:

     \pageref{KEY}

   Produce the page number of the place in the text where the
corresponding '\label'{KEY} command appears.

   If there is no '\label{KEY}' then you get something like 'LaTeX
Warning: Reference `th:GrensThm' on page 1 undefined on input line 11.'

   Below, the '\label{eq:main}' is used both for the formula number and
for the page number.  (Note that the two references are forward
references so this document would need to be compiled twice to resolve
those.)

     The main result is formula~\ref{eq:main} on page~\pageref{eq:main}.
       ...
     \begin{equation} \label{eq:main}
        \mathbf{P}=\mathbf{NP}
     \end{equation}

7.3 '\ref'
==========

Synopsis:

     \ref{KEY}

   Produces the number of the sectional unit, equation, footnote,
figure, ..., of the corresponding '\label' command (*note \label::).  It
does not produce any text, such as the word 'Section' or 'Figure', just
the bare number itself.

   If there is no '\label{KEY}' then you get something like 'LaTeX
Warning: Reference `th:GrensThm' on page 1 undefined on input line 11.'

   In this example the '\ref{popular}' produces '2'.  Note that it is a
forward reference since it comes before '\label{popular}' so this
document would have to be compiled twice.

     The most widely-used format is item number~\ref{popular}.
     \begin{enumerate}
     \item Plain \TeX
     \item \label{popular} \LaTeX
     \item Con\TeX t
     \end{enumerate}

   The 'cleveref' package includes text such as 'Theorem' in the
reference.  See the documentation on CTAN.

7.4 'xr' package
================

Synopsis:

     \usepackage{xr}
       \externaldocument{DOCUMENT-BASENAME}

or

     \usepackage{xr}
       \externaldocument[REFERENCE-PREFIX]{DOCUMENT-BASENAME}

   Make cross references to the external document
'DOCUMENT-BASENAME.tex'.

   Here is an example.  If 'lectures.tex' has this in the preamble

     \usepackage{xr}
       \externaldocument{exercises}
       \externaldocument[H-]{hints}
       \externaldocument{answers}

then it can use cross reference labels from the other three documents.
Suppose that 'exercises.tex' has an enumerated list containing this,

     \item \label{exer:EulersThm} What if every vertex has odd degree?

and 'hints.tex' has an enumerated list with this,

     \item \label{exer:EulersThm} Distinguish the case of two vertices.

and 'answers.tex' has an enumerated list with this,

     \item \label{ans:EulersThm} There is no Euler path, except if there
       are exactly two vertices.

   After compiling the exercises, hints, and answers documents, entering
this in the body of 'lectures.tex' will result in the lectures getting
the reference numbers used in the other documents.

     See Exercise~\ref{exer:EulersThm}, with Hint~\ref{H-exer:EulersThm}.
     The solution is Answer~\ref{ans:EulersThm}.

   The prefix 'H-' for the reference from the hints file is needed
because the label in the hints file is the same as the label in the
exercises file.  Without that prefix, both references would get the
number from the later file.

   Note: if the document uses the 'hyperref' package then in place of
'xr', put '\usepackage{xr-hyper}' before the '\usepackage{hyperref}'.
Also, if any of the multiple documents uses 'hyperref' then they all
must use it.

8 Environments
**************

LaTeX provides many environments for delimiting certain behavior.  An
environment begins with '\begin' and ends with '\end', like this:

     \begin{ENVIRONMENT-NAME}
       ...
     \end{ENVIRONMENT-NAME}

   The ENVIRONMENT-NAME at the beginning must exactly match that at the
end.  For instance, the input '\begin{table*}...\end{table}' will cause
an error like: '! LaTeX Error: \begin{table*} on input line 5 ended by
\end{table}.'

   Environments are executed within a group.

8.1 'abstract'
==============

Synopsis:

     \begin{abstract}
     ...
     \end{abstract}

   Produce an abstract, possibly of multiple paragraphs.  This
environment is only defined in the 'article' and 'report' document
classes (*note Document classes::).

   Using the example below in the 'article' class produces a displayed
paragraph.  Document class option 'titlepage' causes the abstract to be
on a separate page (*note Document class options::); this is the default
only in the 'report' class.

     \begin{abstract}
       We compare all known accounts of the proposal made by Porter Alexander
       to Robert E Lee at the Appomattox Court House that the army continue
       in a guerrilla war, which Lee refused.
     \end{abstract}

   The next example produces a one column abstract in a two column
document (for a more flexible solution, use the package 'abstract').

     \documentclass[twocolumn]{article}
       ...
     \begin{document}
     \title{Babe Ruth as Cultural Progenitor: a Atavistic Approach}
     \author{Smith \\ Jones \\ Robinson\thanks{Railroad tracking grant.}}
     \twocolumn[
       \begin{@twocolumnfalse}
          \maketitle
          \begin{abstract}
            Ruth was not just the Sultan of Swat, he was the entire swat
            team.
          \end{abstract}
        \end{@twocolumnfalse}
        ]
     {   % by-hand insert a footnote at page bottom
      \renewcommand{\thefootnote}{\fnsymbol{footnote}}
      \footnotetext[1]{Thanks for all the fish.}
     }

8.2 'array'
===========

Synopsis:

     \begin{array}{COLS}
       COLUMN 1 ENTRY &COLUMN 2 ENTRY ... &COLUMN N ENTRY \\
       ...
     \end{array}

or:

     \begin{array}[POS]{COLS}
       COLUMN 1 ENTRY &COLUMN 2 ENTRY ... &COLUMN N ENTRY \\
       ...
     \end{array}

   Produce a mathematical array.  This environment can only be used in
math mode (*note Modes::), and normally appears within a displayed
mathematics environment such as 'equation' (*note equation::).  Inside
of each row the column entries are separated by an ampersand, ('&').
Rows are terminated with double-backslashes (*note \\::).

   This example shows a three by three array.

     \begin{equation*}
       \chi(x) =
       \left|              % vertical bar fence
         \begin{array}{ccc}
           x-a  &-b  &-c  \\
           -d   &x-e &-f  \\
           -g   &-h  &x-i
         \end{array}
      \right|
     \end{equation*}

   The required argument COLS describes the number of columns, their
alignment, and the formatting of the intercolumn regions.  For instance,
'\begin{array}{rcl}...\end{array}' gives three columns: the first flush
right, the second centered, and the third flush left.  See *note
tabular:: for the complete description of COLS and of the other common
features of the two environments, including the optional POS argument.

   There are two ways that 'array' diverges from 'tabular'.  The first
is that 'array' entries are typeset in math mode, in textstyle (*note
Math styles::) except if the COLS definition specifies the column with
'p{...}', which causes the entry to be typeset in text mode.  The second
is that, instead of 'tabular''s parameter '\tabcolsep', LaTeX's
intercolumn space in an 'array' is governed by '\arraycolsep', which
gives half the width between columns.  The default for this is '5pt' so
that between two columns comes 10pt of space.

   To obtain arrays with braces the standard is to use the 'amsmath'
package.  It comes with environments 'pmatrix' for an array surrounded
by parentheses '(...)', 'bmatrix' for an array surrounded by square
brackets '[...]', 'Bmatrix' for an array surrounded by curly
braces '{...}', 'vmatrix' for an array surrounded by vertical
bars '|...|', and 'Vmatrix' for an array surrounded by double vertical
bars '||...||', along with a number of other array constructs.

   The next example uses the 'amsmath' package.

     \usepackage{amsmath}  % in preamble

     \begin{equation}
       \begin{vmatrix}{cc}  % array with vert lines
         a  &b \\
         c  &d
       \end{vmatrix}=ad-bc
     \end{equation}

   There are many packages concerning arrays.  The 'array' package has
many useful extensions, including more column types.  The 'dcolumn'
package adds a column type to center on a decimal point.  For both see
the documentation on CTAN.

8.3 'center'
============

Synopsis:

     \begin{center}
       LINE1 \\
       LINE2 \\
       ...
     \end{center}

   Create a new paragraph consisting of a sequence of lines that are
centered within the left and right margins.  Use double-backslash, '\\',
to get a line break (*note \\::).  If some text is too long to fit on a
line then LaTeX will insert line breaks that avoid hyphenation and avoid
stretching or shrinking any interword space.

   This environment inserts space above and below the text body.  See
*note \centering:: to avoid such space, for example inside a 'figure'
environment.

   This example produces three centered lines.  There is extra vertical
space between the last two lines.

     \begin{center}
       A Thesis Submitted in Partial Fufillment \\
       of the Requirements of \\[0.5ex]
       the School of Environmental Engineering
     \end{center}

   In this example, depending on the page's line width, LaTeX may choose
a line break for the part before the double backslash.  If so, it will
center each of the two lines and if not it will center the single line.
Then LaTeX will break at the double backslash, and will center the
ending.

     \begin{center}
       My father considered that anyone who went to chapel and didn't drink
       alcohol was not to be tolerated.\\
       I grew up in that belief.  ---Richard Burton
     \end{center}

   A double backslash after the final line is optional.  If present it
doesn't add any vertical space.

   In a two-column document the text is centered in a column, not in the
entire page.

8.3.1 '\centering'
------------------

Synopsis:

     {\centering ... }

or

     \begin{group}
       \centering ...
     \end{group}

   Center the material in its scope.  It is most often used inside an
environment such as 'figure', or in a 'parbox'.

   This example's '\centering' declaration causes the graphic to be
horizontally centered.

     \begin{figure}
       \centering
       \includegraphics[width=0.6\textwidth]{ctan_lion.png}
       \caption{CTAN Lion}  \label{fig:CTANLion}
     \end{figure}

The scope of this '\centering' ends with the '\end{figure}'.

   Unlike the 'center' environment, the '\centering' command does not
add vertical space above and below the text.  That's its advantage in
the above example; there is not an excess of space.

   It also does not start a new paragraph; it simply changes how LaTeX
formats paragraph units.  If 'ww {\centering xx \\ yy} zz' is surrounded
by blank lines then LaTeX will create a paragraph whose first line 'ww
xx' is centered and whose second line, not centered, contains 'yy zz'.
Usually what is desired is for the scope of the declaration to contain a
blank line or the '\end' command of an environment such as 'figure' or
'table' that ends the paragraph unit.  Thus, if '{\centering xx \\
yy\par} zz' is surrounded by blank lines then it makes a new paragraph
with two centered lines 'xx' and 'yy', followed by a new paragraph with
'zz' that is formatted as usual.

8.4 'description'
=================

Synopsis:

     \begin{description}
       \item[LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
       \item[LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
        ...
     \end{description}

   Environment to make a list of labeled items.  Each item's LABEL is
typeset in bold and is flush left, so that long labels continue into the
first line of the item text.  There must be at least one item; having
none causes the LaTeX error 'Something's wrong--perhaps a missing
\item'.

   This example shows the environment used for a sequence of
definitions.

     \begin{description}
       \item[lama] A priest.
       \item[llama] A beast.
     \end{description}

The labels 'lama' and 'llama' are output in boldface, with the left edge
on the left margin.

   Start list items with the '\item' command (*note \item::).  Use the
optional labels, as in '\item[Main point]', because there is no sensible
default.  Following the '\item' is optional text, which may contain
multiple paragraphs.

   Since the labels are in bold style, if the label text calls for a
font change given in argument style (see *note Font styles::) then it
will come out bold.  For instance, if the label text calls for
typewriter with '\item[\texttt{label text}]' then it will appear in bold
typewriter, if that is available.  The simplest way around this, in this
example to get non-bold typewriter, is to use declarative style:
'\item[{\tt label text}]'.  Similarly, get the standard roman font with
'\item[{\rm label text}]'.

   For other major LaTeX labelled list environments, see *note itemize::
and *note enumerate::.  Unlike those environments, nesting 'description'
environments does not change the default label; it is boldface and flush
left at all levels.

   For information about list layout parameters, including the default
values, and for information about customizing list layout, see *note
list::.  The package 'enumitem' is useful for customizing lists.

   This example changes the description labels to small caps.

     \renewcommand{\descriptionlabel}[1]{%
       {\hspace{\labelsep}\textsc{#1}}}

8.5 'displaymath'
=================

Synopsis:

     \begin{displaymath}
       MATHEMATICAL TEXT
     \end{displaymath}

   Environment to typeset the MATHEMATICAL TEXT on its own line, in
display style and centered.  To make the text be flush-left use the
global option 'fleqn'; see *note Document class options::.

   In the 'displaymath' environment no equation number is added to the
math text.  One way to get an equation number is to use the 'equation'
environment (*note equation::).

   LaTeX will not break the MATH TEXT across lines.

   Note that the 'amsmath' package has significantly more extensive
displayed equation facilities.  For example, there are a number of ways
in that package for having math text broken across lines.

   The construct '\[MATH\]' is a synonym for the environment
'\begin{displaymath} MATH \end{displaymath}' but the latter is easier to
work with in the source; for instance, searching for a square bracket
may get false positives but the word 'displaymath' will likely be
unique.

   (Aside: The construct '$$MATH$$' from Plain TeX is sometimes
mistakenly used as a synonym for 'displaymath'.  It is not a synonym,
and is not officially supported in LaTeX at all; '$$' doesn't support
the 'fleqn' option (*note Document class options::), has different
vertical spacing, and doesn't perform consistency checks.)

   The output from this example is centered and alone on its line.

     \begin{displaymath}
       \int_1^2 x^2\,dx=7/3
     \end{displaymath}

Also, the integral sign is larger than the inline version '\( \int_1^2
x^2\,dx=7/3 \)' produces.

8.6 'document'
==============

The 'document' environment encloses the entire body of a document.  It
is required in every LaTeX document.  *Note Starting and ending::.

8.6.1 '\AtBeginDocument'
------------------------

Synopsis:

     \AtBeginDocument{CODE}

   Save CODE and execute it when '\begin{document}' is executed, at the
very end of the preamble.  The code is executed after the font selection
tables have been set up, so the normal font for the document is the
current font.  However, the code is executed as part of the preamble so
you cannot do any typesetting with it.

   You can issue this command more than once; the successive code lines
will be executed in the order that you gave them.

8.6.2 '\AtEndDocument'
----------------------

Synopsis:

     \AtEndDocument{CODE}

   Save CODE and execute it near the end of the document.  Specifically,
it is executed when '\end{document}' is executed, before the final page
is finished and before any leftover floating environments are processed.
If you want some of the code to be executed after these two processes
then include a '\clearpage' at the appropriate point in CODE.

   You can issue this command more than once; the successive code lines
will be executed in the order that you gave them.

8.7 'enumerate'
===============

Synopsis:

     \begin{enumerate}
       \item[OPTIONAL LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
       \item[OPTIONAL LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
       ...
     \end{enumerate}

   Environment to produce a numbered list of items.  The format of the
label numbering depends on the nesting level of this environment; see
below.  The default top-level numbering is '1.', '2.', etc.  Each
'enumerate' list environment must have at least one item; having none
causes the LaTeX error 'Something's wrong--perhaps a missing \item'.

   This example gives the first two finishers in the 1908 Olympic
marathon.  As a top-level list the labels would come out as '1.' and
'2.'.

     \begin{enumerate}
      \item Johnny Hayes (USA)
      \item Charles Hefferon (RSA)
     \end{enumerate}

   Start list items with the '\item' command (*note \item::).  If you
give '\item' an optional argument by following it with square brackets,
as in '\item[Interstitial label]', then the next item will continue the
interrupted sequence (*note \item::).  That is, you will get labels like
'1.', then 'Interstitial label', then '2.'.  Following the '\item' is
optional text, which may contain multiple paragraphs.

   Enumerations may be nested within other 'enumerate' environments, or
within any paragraph-making environment such as 'itemize' (*note
itemize::), up to four levels deep.  This gives LaTeX's default for the
format at each nesting level, where 1 is the top level, the outermost
level.

  1. arabic number followed by a period: '1.', '2.', ...
  2. lowercase letter inside parentheses: '(a)', '(b)' ...
  3. lowercase roman numeral followed by a period: 'i.', 'ii.', ...
  4. uppercase letter followed by a period: 'A.', 'B.', ...

   The 'enumerate' environment uses the counters '\enumi' through
'\enumiv' (*note Counters::).

   For other major LaTeX labeled list environments, see *note
description:: and *note itemize::.  For information about list layout
parameters, including the default values, and for information about
customizing list layout, see *note list::.  The package 'enumitem' is
useful for customizing lists.

   To change the format of the label use '\renewcommand' (*note
\newcommand & \renewcommand::) on the commands '\labelenumi' through
'\labelenumiv'.  For instance, this first level list will be labelled
with uppercase letters, in boldface, and without a trailing period.

     \renewcommand{\labelenumi}{\textbf{\Alph{enumi}}}
     \begin{enumerate}
       \item Shows as boldface A
       \item Shows as boldface B
     \end{enumerate}

   For a list of counter-labeling commands see *note \alph \Alph \arabic
\roman \Roman \fnsymbol::.

8.8 'eqnarray'
==============

The 'eqnarray' environment is obsolete.  It has infelicities, including
spacing that is inconsistent with other mathematics elements.  (See
"Avoid eqnarray!" by Lars Madsen
<https://tug.org/TUGboat/tb33-1/tb103madsen.pdf>).  New documents should
include the 'amsmath' package and use the displayed mathematics
environments provided there, such as the 'align' environment.  We
include a description only for completeness and for working with old
documents.

   Synopsis:

     \begin{eqnarray}
       FIRST FORMULA LEFT  &FIRST FORMULA MIDDLE  &FIRST FORMULA RIGHT \\
       ...
     \end{eqnarray}

or

     \begin{eqnarray*}
       FIRST FORMULA LEFT  &FIRST FORMULA MIDDLE  &FIRST FORMULA RIGHT \\
       ...
     \end{eqnarray*}

   Display a sequence of equations or inequalities.  The left and right
sides are typeset in display mode, while the middle is typeset in text
mode.

   It is similar to a three-column 'array' environment, with items
within a row separated by an ampersand ('&'), and with rows separated by
double backslash  '\\').  The starred form of line break ('\\*') can
also be used to separate equations, and will disallow a page break there
(*note \\::).

   The unstarred form 'eqnarray' places an equation number on every line
(using the 'equation' counter), unless that line contains a '\nonumber'
command.  The starred form 'eqnarray*' omits equation numbering, while
otherwise being the same.

   The command '\lefteqn' is used for splitting long formulas across
lines.  It typesets its argument in display style flush left in a box of
zero width.

   This example shows three lines.  The first two lines make an
inequality, while the third line has not entry on the left side.

     \begin{eqnarray*}
       \lefteqn{x_1+x_2+\cdots+x_n}     \\
         &\leq &y_1+y_2+\cdots+y_n      \\
         &=    &z+y_3+\cdots+y_n
     \end{eqnarray*}

8.9 'equation'
==============

Synopsis:

     \begin{equation}
       MATHEMATICAL TEXT
     \end{equation}

   The same as a 'displaymath' environment (*note displaymath::) except
that LaTeX puts an equation number flush to the right margin.  The
equation number is generated using the 'equation' counter.

   You should have no blank lines between '\begin{equation}' and
'\begin{equation}', or LaTeX will tell you that there is a missing
dollar sign.

   The package 'amsmath' package has extensive displayed equation
facilities.  New documents should include this package.

8.10 'figure'
=============

Synopsis:

     \begin{figure}[PLACEMENT]
       FIGURE BODY
       \caption[LOFTITLE]{TITLE}  % optional
       \label{LABEL}              % optional
     \end{figure}

or:

     \begin{figure*}[PLACEMENT]
       FIGURE BODY
       \caption[LOFTITLE]{TITLE}  % optional
       \label{LABEL}              % optional
     \end{figure*}

   Figures are for material that is not part of the normal text.  An
example is material that you cannot have split between two pages, such
as a graphic.  Because of this, LaTeX does not typeset figures in
sequence with normal text but instead "floats" them to a convenient
place, such as the top of a following page (*note Floats::).

   The FIGURE BODY can consist of imported graphics (*note Graphics::),
or text, LaTeX commands, etc.  It is typeset in a 'parbox' of width
'\textwidth'.

   The possible values of PLACEMENT are 'h' for 'here', 't' for 'top',
'b' for 'bottom', and 'p' for 'on a separate page of floats'.  For the
effect of these options on the float placement algorithm, see *note
Floats::.

   The starred form 'figure*' is used when a document is in
double-column mode (*note \twocolumn::).  It produces a figure that
spans both columns, at the top of the page.  To add the possibility of
placing at a page bottom see the discussion of PLACEMENT 'b' in *note
Floats::.

   The label is optional; it is used for cross references (*note Cross
references::).  The optional '\caption' command specifies caption text
for the figure (*note \caption::).  By default it is numbered.  If
LOFTITLE is present, it is used in the list of figures instead of TITLE
(*note Table of contents etc.::).

   This example makes a figure out of a graphic.  LaTeX will place that
graphic and its caption at the top of a page or, if it is pushed to the
end of the document, on a page of floats.

     \usepackage{graphicx}  % in preamble
       ...
     \begin{figure}[t]
       \centering
       \includegraphics[width=0.5\textwidth]{CTANlion.png}
       \caption{The CTAN lion, by Duane Bibby}
     \end{figure}

8.11 'filecontents'
===================

Synopsis:

     \begin{filecontents}[OPTION]{FILENAME}
       TEXT
     \end{filecontents}

or

     \begin{filecontents*}[OPTION]{FILENAME}
       TEXT
     \end{filecontents*}

   Create a file named FILENAME in the current directory (or the output
directory, if specified; *note output directory::) and write TEXT to it.
By default, an existing file is not overwritten.

   The unstarred version of the environment 'filecontents' prefixes the
content of the created file with a header of TeX comments; see the
example below.  The starred version 'filecontents*' does not include the
header.

   The possible options are:

'force'
'overwrite'
     Overwrite an existing file.

'noheader'
     Omit the header.  Equivalent to using 'filecontents*'.

'nosearch'
     Only check the current directory (and the output directory, if
     specified) for an existing file, not the entire search path.

   These options were added in a 2019 release of LaTeX.

   This environment can be used anywhere in the preamble, although it
often appears before the '\documentclass' command.  It is commonly used
to create a '.bib' or other such data file from the main document
source, to make the source file self-contained.  Similarly, it can be
used to create a custom style or class file, again making the source
self-contained.

   For example, this document:

     \documentclass{article}
     \begin{filecontents}{JH.sty}
     \newcommand{\myname}{Jim Hef{}feron}
     \end{filecontents}
     \usepackage{JH}
     \begin{document}
     Article by \myname.
     \end{document}

produces this file 'JH.sty':

     %% LaTeX2e file `JH.sty'
     %% generated by the `filecontents' environment
     %% from source `test' on 2015/10/12.
     %%
     \newcommand{\myname}{Jim Hef{}feron}

8.12 'flushleft'
================

Synopsis:

     \begin{flushleft}
       LINE1 \\
       LINE2 \\
       ...
     \end{flushleft}

   An environment that creates a paragraph whose lines are flush to the
left-hand margin, and ragged right.  If you have lines that are too long
then LaTeX will linebreak them in a way that avoids hyphenation and
stretching or shrinking interword spaces.  To force a new line use a
double backslash, '\\'.  For the declaration form see *note
\raggedright::.

   This creates a box of text that is at most 3 inches wide, with the
text flush left and ragged right.

     \noindent\begin{minipage}{3in}
     \begin{flushleft}
       A long sentence that will be broken by \LaTeX{}
         at a convenient spot. \\
       And, a fresh line forced by the double backslash.
     \end{flushleft}
     \end{minipage}

8.12.1 '\raggedright'
---------------------

Synopses:

     {\raggedright  ... }

or

     \begin{ENVIRONMENT} \raggedright
       ...
     \end{ENVIRONMENT}

   A declaration which causes lines to be flush to the left margin and
ragged right.  It can be used inside an ENVIRONMENT such as 'quote' or
in a 'parbox'.  For the environment form see *note flushleft::.

   Unlike the 'flushleft' environment, the '\raggedright' command does
not start a new paragraph; it only changes how LaTeX formats paragraph
units.  To affect a paragraph unit's format, the scope of the
declaration must contain the blank line or '\end' command that ends the
paragraph unit.

   Here '\raggedright' in each second column keeps LaTeX from doing very
awkward typesetting to fit the text into the narrow column.  Note that
'\raggedright' is inside the curly braces '{...}' to delimit its effect.

     \begin{tabular}{rp{2in}}
       Team alpha  &{\raggedright This team does all the real work.} \\
       Team beta   &{\raggedright This team ensures that the water
                     cooler is never empty.}                         \\
     \end{tabular}

8.13 'flushright'
=================

     \begin{flushright}
       LINE1 \\
       LINE2 \\
       ...
     \end{flushright}

   An environment that creates a paragraph whose lines are flush to the
right-hand margin and ragged left.  If you have lines that are too long
to fit the margins then LaTeX will linebreak them in a way that avoids
hyphenation and stretching or shrinking inter-word spaces.  To force a
new line use a double backslash, '\\'.  For the declaration form
see *note \raggedleft::.

   For an example related to this environment, see *note flushleft::,
where one just have mutatis mutandis to replace 'flushleft' by
'flushright'.

8.13.1 '\raggedleft'
--------------------

Synopses:

     {\raggedleft  ... }

or

     \begin{ENVIRONMENT} \raggedleft
       ...
     \end{ENVIRONMENT}

   A declaration which causes lines to be flush to the right margin and
ragged left.  It can be used inside an ENVIRONMENT such as 'quote' or in
a 'parbox'.  For the environment form see *note flushright::.

   Unlike the 'flushright' environment, the '\raggedleft' command does
not start a new paragraph; it only changes how LaTeX formats paragraph
units.  To affect a paragraph unit's format, the scope of the
declaration must contain the blank line or '\end' command that ends the
paragraph unit.

   For an example related to this environment, see *note \raggedright::,
where one just have mutatis mutandis to replace '\raggedright' by
'\raggedleft'.

8.14 'itemize'
==============

Synopsis:

     \begin{itemize}
       \item[OPTIONAL LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
       \item[OPTIONAL LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
       ...
     \end{itemize}

   Produce an "unordered list", sometimes called a bullet list.  There
must be at least one '\item' within the environment; having none causes
the LaTeX error 'Something's wrong--perhaps a missing \item'.

   This gives a two-item list.

     \begin{itemize}
      \item Pencil and watercolor sketch by Cassandra
      \item Rice portrait
     \end{itemize}

With the default locale--without loading e.g. 'babel' package with
another language than USenglish--as a top-level list each label would
come out as a bullet, *.  The format of the labeling depends on the
nesting level; see below.

   Start list items with the '\item' command (*note \item::).  If you
give '\item' an optional argument by following it with square brackets,
as in '\item[OPTIONAL LABEL]', then by default OPTIONAL LABEL will
appear in bold and be flush right, so it could extend into the left
margin.  For labels that are flush left see the *note description::
environment.  Following the '\item' is the text of the item, which may
be empty or contain multiple paragraphs.

   Unordered lists can be nested within one another, up to four levels
deep.  They can also be nested within other paragraph-making
environments, such as 'enumerate' (*note enumerate::).

   The 'itemize' environment uses the commands '\labelitemi' through
'\labelitemiv' to produce the default label (note the convention of
lowercase roman numerals at the end of the command names that signify
the nesting level).  These are the default marks at each level.

  1. * (bullet, from '\textbullet')
  2. -- (bold en-dash, from '\normalfont\bfseries\textendash')
  3. * (asterisk, from '\textasteriskcentered')
  4. .  (vertically centered dot, rendered here as a period, from
     '\textperiodcentered')

   Change the labels with '\renewcommand'.  For instance, this makes the
first level use diamonds.

     \renewcommand{\labelitemi}{$\diamond$}

   The distance between the left margin of the enclosing environment and
the left margin of the 'itemize' list is determined by the parameters
'\leftmargini' through '\leftmarginvi'.  (This also uses the convention
of using lowercase roman numerals a the end of the command name to
denote the nesting level.)  The defaults are: '2.5em' in level 1 ('2em'
in two-column mode), '2.2em' in level 2, '1.87em' in level 3, and
'1.7em' in level 4, with smaller values for more deeply nested levels.

   For other major LaTeX labeled list environments, see *note
description:: and *note enumerate::.  The 'itemize', 'enumerate' and
'description' environment use the same list layout parameters.  For a
description, including the default values, and for information about
customizing list layout, see *note list::.  The package 'enumitem' is
useful for customizing lists.

   This example greatly reduces the margin space for outermost itemized
lists.

     \setlength{\leftmargini}{1.25em} % default 2.5em

   Especially for lists with short items, it may be desirable to elide
space between items.  Here is an example defining an 'itemize*'
environment with no extra spacing between items, or between paragraphs
within a single item ('\parskip' is not list-specific, *note \parindent
& \parskip::):

     \newenvironment{itemize*}%
       {\begin{itemize}%
         \setlength{\itemsep}{0pt}%
         \setlength{\parsep}{0pt}}%
         \setlength{\parskip}{0pt}}%
       {\end{itemize}}

8.15 'letter' environment: writing letters
==========================================

This environment is used for creating letters.  *Note Letters::.

8.16 'list'
===========

Synopsis:

     \begin{list}{LABELING}{SPACING}
       \item[OPTIONAL LABEL OF FIRST ITEM] TEXT OF FIRST ITEM
       \item[OPTIONAL LABEL OF SECOND ITEM] TEXT OF SECOND ITEM
       ...
     \end{list}

   An environment for constructing lists.

   Note that this environment does not typically appear in the document
body.  Most lists created by LaTeX authors are the ones that come
standard: the 'description', 'enumerate', and 'itemize' environments
(*note description::, *note enumerate::, and *note itemize::).

   Instead, the 'list' environment is most often used in macros.  For
example, many standard LaTeX environments that do not immediately appear
to be lists are in fact constructed using 'list', including 'quotation',
'quote', and 'center' (*note quotation & quote::, *note center::).

   This uses the 'list' environment to define a new custom environment.

     \newcounter{namedlistcounter}  % number the items
     \newenvironment{named}
       {\begin{list}
          {Item~\Roman{namedlistcounter}.} % labeling
          {\usecounter{namedlistcounter}   % set counter
           \setlength{\leftmargin}{3.5em}} % set spacing
       }
       {\end{list}}

     \begin{named}
       \item Shows as ``Item~I.''
       \item[Special label.] Shows as ``Special label.''
       \item Shows as ``Item~II.''
     \end{named}

   The mandatory first argument LABELING specifies the default labeling
of list items.  It can contain text and LaTeX commands, as above where
it contains both 'Item' and '\Roman{...}'.  LaTeX forms the label by
putting the LABELING argument in a box of width '\labelwidth'.  If the
label is wider than that, the additional material extends to the right.
When making an instance of a 'list' you can override the default
labeling by giving '\item' an optional argument by including square
braces and the text, as in the above '\item[Special label.]'; *note
\item::.

   The mandatory second argument SPACING has a list of commands.  This
list can be empty.  A command that can go in here is
'\usecounter{COUNTERNAME}' (*note \usecounter::).  Use this to tell
LaTeX to number the items using the given counter.  The counter will be
reset to zero each time LaTeX enters the environment, and the counter is
incremented by one each time LaTeX encounters an '\item' that does not
have an optional argument.

   Another command that can go in SPACING is '\makelabel', which
constructs the label box.  By default it puts the contents flush right.
Its only argument is the label, which it typesets in LR mode (*note
Modes::).  One example of changing its definition is that to the above
'named' example, before the definition of the environment add
'\newcommand{\namedmakelabel}[1]{\textsc{#1}}', and between the
'\setlength' command and the parenthesis that closes the SPACING
argument also add '\let\makelabel\namedmakelabel'.  Then the labels will
be typeset in small caps.  Similarly, changing the second code line to
'\let\makelabel\fbox' puts the labels inside a framed box.  Another
example of the '\makelabel' command is below, in the definition of the
'redlabel' environment.

   Also often in SPACING are commands to redefine the spacing for the
list.  Below are the spacing parameters with their default values.
(Default values for derived environments such as 'itemize' can be
different than the values shown here.)  See also the figure that follows
the list.  Each is a length (*note Lengths::).  The vertical spaces are
normally rubber lengths, with 'plus' and 'minus' components, to give TeX
flexibility in setting the page.  Change each with a command such as
'\setlength{itemsep}{2pt plus1pt minus1pt}'.  For some effects these
lengths should be zero or negative.

'\itemindent'
     Extra horizontal space indentation, beyond 'leftmargin', of the
     first line each item.  Its default value is '0pt'.

'\itemsep'
     Vertical space between items, beyond the '\parsep'.  The defaults
     for the first three levels in LaTeX's 'article', 'book', and
     'report' classes at 10 point size are: '4pt plus2pt minus1pt',
     '\parsep' (that is, '2pt plus1pt minus1pt'), and '\topsep' (that
     is, '2pt plus1pt minus1pt').  The defaults at 11 point are: '4.5pt
     plus2pt minus1pt', '\parsep' (that is, '2pt plus1pt minus1pt'), and
     '\topsep' (that is, '2pt plus1pt minus1pt').  The defaults at 12
     point are: '5pt plus2.5pt minus1pt', '\parsep' (that is, '2.5pt
     plus1pt minus1pt'), and '\topsep' (that is, '2.5pt plus1pt
     minus1pt').

'\labelsep'
     Horizontal space between the label and text of an item.  The
     default for LaTeX's 'article', 'book', and 'report' classes is
     '0.5em'.

'\labelwidth'
     Horizontal width.  The box containing the label is nominally this
     wide.  If '\makelabel' returns text that is wider than this then
     the first line of the item will be indented to make room for this
     extra material.  If '\makelabel' returns text of width less than or
     equal to '\labelwidth' then LaTeX's default is that the label is
     typeset flush right in a box of this width.

     The left edge of the label box is
     '\leftmargin'+'\itemindent'-'\labelsep'-'\labelwidth' from the left
     margin of the enclosing environment.

     The default for LaTeX's 'article', 'book', and 'report' classes at
     the top level is '\leftmargini'-'\labelsep', (which is '2em' in one
     column mode and '1.5em' in two column mode).  At the second level
     it is '\leftmarginii'-'\labelsep', and at the third level it is
     '\leftmarginiii'-'\labelsep'.  These definitions make the label's
     left edge coincide with the left margin of the enclosing
     environment.

'\leftmargin'
     Horizontal space between the left margin of the enclosing
     environment (or the left margin of the page if this is a top-level
     list), and the left margin of this list.  It must be non-negative.

     In the standard LaTeX document classes, a top-level list has this
     set to the value of '\leftmargini', while a list that is nested
     inside a top-level list has this margin set to '\leftmarginii'.
     More deeply nested lists get the values of '\leftmarginiii' through
     '\leftmarginvi'.  (Nesting greater than level five generates the
     error message 'Too deeply nested'.)

     The defaults for the first three levels in LaTeX's 'article',
     'book', and 'report' classes are: '\leftmargini' is '2.5em' (in two
     column mode, '2em'), '\leftmarginii' is '2.2em', and
     '\leftmarginiii' is '1.87em'.

'\listparindent'
     Horizontal space of additional line indentation, beyond
     '\leftmargin', for second and subsequent paragraphs within a list
     item.  A negative value makes this an "outdent".  Its default value
     is '0pt'.

'\parsep'
     Vertical space between paragraphs within an item.  The defaults for
     the first three levels in LaTeX's 'article', 'book', and 'report'
     classes at 10 point size are: '4pt plus2pt minus1pt', '2pt plus1pt
     minus1pt', and '0pt'.  The defaults at 11 point size are: '4.5pt
     plus2pt minus1pt', '2pt plus1pt minus1pt', and '0pt'.  The defaults
     at 12 point size are: '5pt plus2.5pt minus1pt', '2.5pt plus1pt
     minus1pt', and '0pt'.

'\partopsep'
     Vertical space added, beyond '\topsep'+'\parskip', to the top and
     bottom of the entire environment if the list instance is preceded
     by a blank line.  (A blank line in the LaTeX source before the list
     changes spacing at both the top and bottom of the list; whether the
     line following the list is blank does not matter.)

     The defaults for the first three levels in LaTeX's 'article',
     'book', and 'report' classes at 10 point size are: '2pt plus1
     minus1pt', '2pt plus1pt minus1pt', and '1pt plus0pt minus1pt'.  The
     defaults at 11 point are: '3pt plus1pt minus1pt', '3pt plus1pt
     minus1pt', and '1pt plus0pt minus1pt').  The defaults at 12 point
     are: '3pt plus2pt minus3pt', '3pt plus2pt minus2pt', and '1pt
     plus0pt minus1pt'.

'\rightmargin'
     Horizontal space between the right margin of the list and the right
     margin of the enclosing environment.  Its default value is '0pt'.
     It must be non-negative.

'\topsep'
     Vertical space added to both the top and bottom of the list, in
     addition to '\parskip' (*note \parindent & \parskip::).  The
     defaults for the first three levels in LaTeX's 'article', 'book',
     and 'report' classes at 10 point size are: '8pt plus2pt minus4pt',
     '4pt plus2pt minus1pt', and '2pt plus1pt minus1pt'.  The defaults
     at 11 point are: '9pt plus3pt minus5pt', '4.5pt plus2pt minus1pt',
     and '2pt plus1pt minus1pt'.  The defaults at 12 point are: '10pt
     plus4pt minus6pt', '5pt plus2.5pt minus1pt', and '2.5pt plus1pt
     minus1pt'.

   This shows the horizontal and vertical distances.

.......................................................................
..............Surrounding environment, preceding material.............. -
                                                                        | v0 
 |---h0--|-h1-|                                                         |
 ..Label..    .....First item.....................................      -
      ............................................................
      ............................................................      -
                                                                        | v1
           ........First item, second paragraph ..................      -
      |-h2-|                                                            | v2
                                                                        |
 ..Label..    .....Second item....................................      -
      ............................................................
      ............................................................      -
|-h3--|-h4-|                                                     |-h5-| |v3
                                                                        |
..............Surrounding environment, following material.............. -
.......................................................................

   The lengths shown are listed below.  The key relationship is that the
right edge of the bracket for H1 equals the right edge of the bracket
for H4, so that the left edge of the label box is at H3+H4-(H0+H1).

V0
     '\topsep' + '\parskip' if the list environment does not start a new
     paragraph, and '\topsep'+'\parskip'+'\partopsep' if it does

V1
     '\parsep'

V2
     '\itemsep'+'\parsep'

V3
     Same as V0.  (This space is affected by whether a blank line
     appears in the source above the environment; whether a blank line
     appears in the source below the environment does not matter.)

H0
     '\labelwidth'

H1
     '\labelsep'

H2
     '\listparindent'

H3
     '\leftmargin'

H4
     '\itemindent'

H5
     '\rightmargin'

   The list's left and right margins, shown above as H3 and H5, are with
respect to the ones provided by the surrounding environment, or with
respect to the page margins for a top-level list.  The line width used
for typesetting the list items is '\linewidth' (*note Page layout
parameters::).  For instance, set the list's left margin to be one
quarter of the distance between the left and right margins of the
enclosing environment with '\setlength{\leftmargin}{0.25\linewidth}'.

   Page breaking in a list structure is controlled by the three
parameters below.  For each, the LaTeX default is '-\@lowpenalty', that
is, '-51'.  Because it is negative, it somewhat encourages a page break
at each spot.  Change it with, e.g., '\@beginparpenalty=9999'; a value
of 10000 prohibits a page break.

'\@beginparpenalty'
     The page breaking penalty for breaking before the list (default
     '-51').

'\@itempenalty'
     The page breaking penalty for breaking before a list item (default
     '-51').

'\@endparpenalty'
     The page breaking penalty for breaking after a list (default
     '-51').

   The package 'enumitem' is useful for customizing lists.

   This example has the labels in red.  They are numbered, and the left
edge of the label lines up with the left edge of the item text.  *Note
\usecounter::.

     \usepackage{color}
     \newcounter{cnt}
     \newcommand{\makeredlabel}[1]{\textcolor{red}{#1.}}
     \newenvironment{redlabel}
       {\begin{list}
         {\arabic{cnt}}
         {\usecounter{cnt}
          \setlength{\labelwidth}{0em}
          \setlength{\labelsep}{0.5em}
          \setlength{\leftmargin}{1.5em}
          \setlength{\itemindent}{0.5em} % equals \labelwidth+\labelsep
          \let\makelabel=\makeredlabel
         }
       }
     {\end{list}}

8.16.1 '\item': An entry in a list
----------------------------------

Synopsis:

     \item text of item

or

     \item[OPTIONAL-LABEL] text of item

   An entry in a list.  The entries are prefixed by a label, whose
default depends on the list type.

   Because the optional label is surrounded by square brackets '[...]',
if you have an item whose text starts with [, you have to hide the
bracket inside curly braces, as in: '\item {[} is an open square
bracket'; otherwise, LaTeX will think it marks the start of an optional
label.

   Similarly, if the item does have the optional label and you need a
close square bracket inside that label, you must hide it in the same
way: '\item[Close square bracket, {]}]'.  *Note LaTeX command syntax::.

   In this example the enumerate list has two items that use the default
label and one that uses the optional label.

     \begin{enumerate}
       \item Moe
       \item[sometimes] Shemp
       \item Larry
     \end{enumerate}

   The first item is labelled '1.', the second item is labelled
'sometimes', and the third item is labelled '2.'.  Because of the
optional label in the second item, the third item is not labelled '3.'.

8.16.2 'trivlist': A restricted form of 'list'
----------------------------------------------

Synopsis:

     \begin{trivlist}
       ...
     \end{trivlist}

   A restricted version of the list environment, in which margins are
not indented and an '\item' without an optional argument produces no
text.  It is most often used in macros, to define an environment where
the '\item' command is part of the environment's definition.  For
instance, the 'center' environment is defined essentially like this:

     \newenvironment{center}
       {\begin{trivlist}\centering\item\relax}
       {\end{trivlist}}

   Using 'trivlist' in this way allows the macro to inherit some common
code: combining vertical space of two adjacent environments; detecting
whether the text following the environment should be considered a new
paragraph or a continuation of the previous one; adjusting the left and
right margins for possible nested list environments.

   Specifically, 'trivlist' uses the current values of the list
parameters (*note list::), except that '\parsep' is set to the value of
'\parskip', and '\leftmargin', '\labelwidth', and '\itemindent' are set
to zero.

   This example outputs the items as two paragraphs, except that (by
default) they have no paragraph indent and are vertically separated.

     \begin{trivlist}
     \item The \textit{Surprise} is not old; no one would call her old.
     \item She has a bluff bow, lovely lines.
     \end{trivlist}

8.17 'math'
===========

Synopsis:

     \begin{math}
     MATH
     \end{math}

   The 'math' environment inserts given MATH material within the running
text.  '\(...\)' and '$...$' are synonyms.  *Note Math formulas::.

8.18 'minipage'
===============

Synopses:

     \begin{minipage}{WIDTH}
       CONTENTS
     \end{minipage}

or

     \begin{minipage}[POSITION][HEIGHT][INNER-POS]{WIDTH}
       CONTENTS
     \end{minipage}

   Put CONTENTS into a box that is WIDTH wide.  This is like a small
version of a page; it can contain its own footnotes, itemized lists,
etc.  (There are some restrictions, including that it cannot have
floats.)  This box will not be broken across pages.  So 'minipage' is
similar to '\parbox' (*note \parbox::) but here you can have paragraphs.

   This example will be 3 inches wide, and has two paragraphs.

     \begin{minipage}{3in}
       Stephen Kleene was a founder of the Theory of Computation.

       He was a student of Church, wrote three influential texts,
       was President of the Association for Symbolic Logic,
       and won the National Medal of Science.
     \end{minipage}

See below for a discussion of the paragraph indent inside a 'minipage'.

   The required argument WIDTH is a rigid length (*note Lengths::).  It
gives the width of the box into which CONTENTS are typeset.

   There are three optional arguments, POSITION, HEIGHT, and INNER-POS.
You need not include all three.  For example, get the default POSITION
and set the HEIGHT with '\begin{minipage}[c][2.54cm]{\columnwidth}
CONTENTS \end{minipage}'.  (Get the natural height with an empty
argument, '[]'.)

   The optional argument POSITION governs how the 'minipage' vertically
aligns with the surrounding material.

'c'
     (synonym 'm') Default.  Positions the 'minipage' so its vertical
     center lines up with the center of the adjacent text line.

't'
     Align the baseline of the top line in the 'minipage' with the
     baseline of the surrounding text (plain TeX's '\vtop').

'b'
     Align the baseline of the bottom line in the 'minipage' with the
     baseline of the surrounding text (plain TeX's '\vbox').

   To see the effects of these, contrast running this

     ---\begin{minipage}[c]{0.25in}
       first\\ second\\ third
     \end{minipage}

with the results of changing 'c' to 'b' or 't'.

   The optional argument HEIGHT is a rigid length (*note Lengths::).  It
sets the height of the 'minipage'.  You can enter any value larger than,
or equal to, or smaller than the 'minipage''s natural height and LaTeX
will not give an error or warning.  You can also set it to a height of
zero or a negative value.

   The final optional argument INNER-POS controls the placement of
CONTENTS inside the box.  These are the possible values are (the default
is the value of POSITION).

't'
     Place CONTENTS at the top of the box.

'c'
     Place it in the vertical center.

'b'
     Place it at the box bottom.

's'
     Stretch CONTENTS out vertically; it must contain vertically
     stretchable space.

   The INNER-POS argument makes sense when the HEIGHT option is set to a
value larger than the 'minipage''s natural height.  To see the effect of
the options, run this example with the various choices in place of 'b'.

     Text before
     \begin{center}
       ---\begin{minipage}[c][3in][b]{0.25\textwidth}
            first\\ second\\ third
       \end{minipage}
     \end{center}
     Text after

   By default paragraphs are not indented in a 'minipage'.  Change that
with a command such as '\setlength{\parindent}{1pc}' at the start of
CONTENTS.

   Footnotes in a 'minipage' environment are handled in a way that is
particularly useful for putting footnotes in figures or tables.  A
'\footnote' or '\footnotetext' command puts the footnote at the bottom
of the minipage instead of at the bottom of the page, and it uses the
'\mpfootnote' counter instead of the ordinary 'footnote' counter (*note
Counters::).

   This puts the footnote at the bottom of the table, not the bottom of
the page.

     \begin{center}           % center the minipage on the line
     \begin{minipage}{2.5in}
       \begin{center}         % center the table inside the minipage
         \begin{tabular}{ll}
           \textsc{Monarch}  &\textsc{Reign}             \\ \hline
           Elizabeth II      &63 years\footnote{to date} \\
           Victoria          &63 years                   \\
           George III        &59 years
         \end{tabular}
       \end{center}
     \end{minipage}
     \end{center}

   If you nest minipages then there is an oddness when using footnotes.
Footnotes appear at the bottom of the text ended by the next
'\end{minipage}' which may not be their logical place.

   This puts a table containing data side by side with a map graphic.
They are vertically centered.

     % siunitx to have the S column specifier,
     % which aligns numbers on their decimal point.
     \usepackage{siunitx}
     \newcommand*{\vcenteredhbox}[1]{\begin{tabular}{@{}c@{}}#1\end{tabular}}
       ...
     \begin{center}
       \vcenteredhbox{\includegraphics[width=0.3\textwidth]{nyc.png}}
       \hspace{0.1\textwidth}
       \begin{minipage}{0.5\textwidth}
         \begin{tabular}{r|S}
           % \multicolumn to remove vertical bar between column headers
           \multicolumn{1}{r}{Borough} &
           % braces to prevent siunitx from misinterpreting the
           % period as a decimal separator
           {Pop. (million)}  \\ \hline
           The Bronx      &1.5  \\
           Brooklyn       &2.6  \\
           Manhattan      &1.6  \\
           Queens         &2.3  \\
           Staten Island  &0.5
         \end{tabular}
       \end{minipage}
     \end{center}

8.19 'picture'
==============

Synopses:
     \begin{picture}(WIDTH,HEIGHT)
        PICTURE COMMAND
     \end{picture}

or

     \begin{picture}(WIDTH,HEIGHT)(XOFFSET,YOFFSET)
       PICTURE COMMAND
     \end{picture}

Where there may be any number of PICTURE COMMAND's.

   An environment to create simple pictures containing lines, arrows,
boxes, circles, and text.  This environment is not obsolete, but new
documents typically use much more powerful graphics creation systems,
such as TikZ, PSTricks, MetaPost, or Asymptote.  None of these are
covered in this document; see CTAN.

   To start, here's an example showing the parallelogram law for adding
vectors.

     \setlength{\unitlength}{1cm}
     \begin{picture}(6,6)      % picture box will be 6cm wide by 6cm tall
       \put(0,0){\vector(2,1){4}}  % for every 2 over this vector goes 1 up
         \put(2,1){\makebox(0,0)[l]{\ first leg}}
       \put(4,2){\vector(1,2){2}}
         \put(5,4){\makebox(0,0)[l]{\ second leg}}
       \put(0,0){\vector(1,1){6}}
         \put(3,3){\makebox(0,0)[r]{sum\ }}
     \end{picture}

   The 'picture' environment has one required argument, a pair of
positive real numbers (WIDTH,HEIGHT).  Multiply these by the value
'\unitlength' to get the nominal size of the output, i.e. the space that
LaTeX reserves on the output page.  This nominal size need not be how
large the picture really is; LaTeX will draw things from the picture
outside the picture's box.

   This environment also has an optional argument (XOFFSET,YOFFSET).  It
is used to shift the origin.  Unlike most optional arguments, this one
is not contained in square brackets.  As with the required argument, it
consists of a pair of two real numbers, but these may also be negative
or null.  Multiply these by '\unitlength' to get the coordinates of the
point at the lower-left corner of the picture.

   For example, if '\unitlength' has been set to '1mm', the command

     \begin{picture}(100,200)(10,20)

produces a box of width 100 millimeters and height 200 millimeters.  The
picture's origin is the point (10mm,20mm) and so the lower-left corner
is there, and the upper-right corner is at (110mm,220mm).  When you
first draw a picture you typically omit the optional argument, leaving
the origin at the lower-left corner.  If you then want to modify your
picture by shifting everything, you can just add the appropriate
optional argument.

   Each PICTURE COMMAND tells LaTeX where to put something by providing
its position.  A "position" is a pair such as '(2.4,-5)' giving the x-
and y-coordinates.  A "coordinate" is a not a length, it is a real
number (it may have a decimal point or a minus sign).  It specifies a
length in multiples of the unit length '\unitlength', so if
'\unitlength' has been set to '1cm', then the coordinate '2.54'
specifies a length of 2.54 centimeters.

   LaTeX's default for '\unitlength' is '1pt'.  It is a rigid length
(*note Lengths::).  Change it with the '\setlength' command (*note
\setlength::).  Make this change only outside of a 'picture'
environment.

   The 'picture' environment supports using standard arithmetic
expressions as well as numbers.

   Coordinates are given with respect to an origin, which is by default
at the lower-left corner of the picture.  Note that when a position
appears as an argument, as with '\put(1,2){...}', it is not enclosed in
braces since the parentheses serve to delimit the argument.  Also,
unlike in some computer graphics systems, larger y-coordinates are
further up the page, for example, y = 1 is _above_ y = 0.

   There are four ways to put things in a picture: '\put', '\multiput',
'\qbezier', and '\graphpaper'.  The most often used is '\put'.  This

     \put(11.3,-0.3){...}

places the object with its reference point at coordinates (11.3,-0.3).
The reference points for various objects will be described below.  The
'\put' command creates an "LR box" (*note Modes::).  Anything that can
go in an '\mbox' (*note \mbox & \makebox::) can go in the text argument
of the '\put' command.  The reference point will be the lower left
corner of the box.  In this picture

     \setlength{\unitlength}{1cm}
     ...\begin{picture}(1,1)
       \put(0,0){\line(1,0){1}}
       \put(0,0){\line(1,1){1}}
     \end{picture}

the three dots are just slightly left of the point of the angle formed
by the two lines.  (Also, '\line(1,1){1}' does not call for a line of
length one; rather the line has a change in the x coordinate of 1.)

   The '\multiput', 'qbezier', and 'graphpaper' commands are described
below.

   You can also use this environment to place arbitrary material at an
exact location.  For example:

     \usepackage{color,graphicx}  % in preamble
       ...
     \begin{center}
     \setlength{\unitlength}{\textwidth}
     \begin{picture}(1,1)      % leave space, \textwidth wide and tall
       \put(0,0){\includegraphics[width=\textwidth]{desertedisland.jpg}}
       \put(0.25,0.35){\textcolor{red}{X Treasure here}}
     \end{picture}
     \end{center}

The red X will be precisely a quarter of the '\textwidth' from the left
margin, and '0.35\textwidth' up from the bottom of the picture.  Another
example of this usage is to put similar code in the page header to get
repeat material on each of a document's pages.

8.19.1 '\put'
-------------

Synopsis:

     \put(XCOORD,YCOORD){CONTENT}

   Place CONTENT at the coordinate (XCOORD,YCOORD).  See the discussion
of coordinates and '\unitlength' in *note picture::.  The CONTENT is
processed in LR mode (*note Modes::) so it cannot contain line breaks.

   This includes the text into the 'picture'.

     \put(4.5,2.5){Apply the \textit{unpoke} move}

   The reference point, the location (4.5,2.5), is the lower left of the
text, at the bottom left of the 'A'.

8.19.2 '\multiput'
------------------

Synopsis:

     \multiput(X,Y)(DELTA_X,DELTA_Y){NUM-COPIES}{OBJ}

   Copy OBJ a total of NUM-COPIES times, with an increment of
DELTA_X,DELTA_Y.  The OBJ first appears at position (x,y), then at
(x+\delta_x,y+\delta_y), and so on.

   This draws a simple grid with every fifth line in bold (see also
*note \graphpaper::).

     \begin{picture}(10,10)
       \linethickness{0.05mm}
       \multiput(0,0)(1,0){10}{\line(0,1){10}}
       \multiput(0,0)(0,1){10}{\line(1,0){10}}
       \linethickness{0.5mm}
       \multiput(0,0)(5,0){3}{\line(0,1){10}}
       \multiput(0,0)(0,5){3}{\line(1,0){10}}
     \end{picture}

8.19.3 '\qbezier'
-----------------

Synopsis:

     \qbezier(X1,Y1)(X2,Y2)(X3,Y3)
     \qbezier[NUM](X1,Y1)(X2,Y2)(X3,Y3)

   Draw a quadratic Bezier curve whose control points are given by the
three required arguments '(X1,Y1)', '(X2,Y2)', and '(X3,Y3)'.  That is,
the curve runs from (X1,Y1) to (X3,Y3), is quadratic, and is such that
the tangent line at (X1,Y1) passes through (X2,Y2), as does the tangent
line at (X3,Y3).

   This draws a curve from the coordinate (1,1) to (1,0).

     \qbezier(1,1)(1.25,0.75)(1,0)

The curve's tangent line at (1,1) contains (1.25,0.75), as does the
curve's tangent line at (1,0).

   The optional argument NUM gives the number of calculated intermediate
points.  The default is to draw a smooth curve whose maximum number of
points is '\qbeziermax' (change this value with '\renewcommand').

   This draws a rectangle with a wavy top, using '\qbezier' for that
curve.

     \begin{picture}(8,4)
       \put(0,0){\vector(1,0){8}}  % x axis
       \put(0,0){\vector(0,1){4}}  % y axis
       \put(2,0){\line(0,1){3}}       % left side
       \put(4,0){\line(0,1){3.5}}     % right side
       \qbezier(2,3)(2.5,2.9)(3,3.25)
         \qbezier(3,3.25)(3.5,3.6)(4,3.5)
       \thicklines                 % below here, lines are twice as thick
       \put(2,3){\line(4,1){2}}
       \put(4.5,2.5){\framebox{Trapezoidal Rule}}
     \end{picture}

8.19.4 '\graphpaper'
--------------------

Synopsis:

     \graphpaper(X_INIT,Y_INIT)(X_DIMEN,Y_DIMEN)
     \graphpaper[SPACING](X_INIT,Y_INIT)(X_DIMEN,Y_DIMEN)

   Draw a coordinate grid.  Requires the 'graphpap' package.  The grid's
origin is '(X_INIT,Y_INIT)'.  Grid lines come every SPACING units (the
default is 10).  The grid extends X_DIMEN units to the right and Y_DIMEN
units up.  All arguments must be positive integers.

   This make a grid with seven vertical lines and eleven horizontal
lines.

     \usepackage{graphpap}    % in preamble
       ...
     \begin{picture}(6,20)    % in document body
       \graphpaper[2](0,0)(12,20)
     \end{picture}

The lines are numbered every ten units.

8.19.5 '\line'
--------------

Synopsis:

     \line(X_RUN,Y_RISE){TRAVEL}

   Draw a line.  It slopes such that it vertically rises Y_RISE for
every horizontal X_RUN.  The TRAVEL is the total horizontal change--it
is not the length of the vector, it is the change in x.  In the special
case of vertical lines, where (X_RUN,Y_RISE)=(0,1), the TRAVEL gives the
change in y.

   This draws a line starting at coordinates (1,3).

     \put(1,3){\line(2,5){4}}

For every over 2, this line will go up 5.  Because TRAVEL specifies that
this goes over 4, it must go up 10.  Thus its endpoint is
(1,3)+(4,10)=(5,13).  In particular, note that TRAVEL=4 is not the
length of the line, it is the change in x.

   The arguments X_RUN and Y_RISE are integers that can be positive,
negative, or zero.  (If both are 0 then LaTeX treats the second as 1.)
With '\put(X_INIT,Y_INIT){\line(X_RUN,Y_RISE){TRAVEL}}', if X_RUN is
negative then the line's ending point has a first coordinate that is
less than X_INIT.  If Y_RISE is negative then the line's ending point
has a second coordinate that is less than Y_INIT.

   If TRAVEL is negative then you get 'LaTeX Error: Bad \line or \vector
argument.'

   Standard LaTeX can only draw lines with a limited range of slopes
because these lines are made by putting together line segments from
pre-made fonts.  The two numbers X_RUN and Y_RISE must have integer
values from -6 through 6.  Also, they must be relatively prime, so that
(X_RUN,Y_RISE) can be (2,1) but not (4,2) (if you choose the latter then
instead of lines you get sequences of arrowheads; the solution is to
switch to the former).  To get lines of arbitrary slope and plenty of
other shapes in a system like 'picture', see the package 'pict2e'
(<https://ctan.org/pkg/pict2e>).  Another solution is to use a
full-featured graphics system such as TikZ, PSTricks, MetaPost, or
Asymptote.

8.19.6 '\linethickness'
-----------------------

Synopsis:

     \linethickness{DIM}

   Declares the thickness of subsequent horizontal and vertical lines in
a picture to be DIM, which must be a positive length (*note Lengths::).
It differs from '\thinlines' and '\thicklines' in that it does not
affect the thickness of slanted lines, circles, or ovals (*note
\oval::).

8.19.7 '\thinlines'
-------------------

Declaration to set the thickness of subsequent lines, circles, and ovals
in a picture environment to be 0.4pt.  This is the default thickness, so
this command is unnecessary unless the thickness has been changed with
either *note \linethickness:: or *note \thicklines::.

8.19.8 '\thicklines'
--------------------

Declaration to set the thickness of subsequent lines, circles, and ovals
in a picture environment to be 0.8pt.  See also *note \linethickness::
and *note \thinlines::.  This command is illustrated in the Trapezoidal
Rule example of *note \qbezier::.

8.19.9 '\circle'
----------------

Synopsis:

     \circle{DIAMETER}
     \circle*{DIAMETER}

   Produces a circle with a diameter as close as possible to the
specified one.  The '*' form produces a filled-in circle.

   This draws a circle of radius 6, centered at '(5,7)'.

     \put(5,7){\circle{6}}

   The available radii for '\circle' are, in points, the even numbers
from 2 to 20, inclusive.  For '\circle*' they are all the integers from
1 to 15.

8.19.10 '\oval'
---------------

Synopsis:

     \oval(WIDTH,HEIGHT)
     \oval(WIDTH,HEIGHT)[PORTION]

   Produce a rectangle with rounded corners, hereinafter referred to as
an "oval".  The optional argument PORTION allows you to produce only
half or a quarter of the oval.  For half an oval take PORTION to be one
of these.

't'
     top half
'b'
     bottom half
'r'
     right half
'l'
     left half

   Produce only one quarter of the oval by setting PORTION to 'tr',
'br', 'bl', or 'tl'.

   This draws the top half of an oval that is 3 wide and 7 tall.

     \put(5,7){\oval(3,7)[t]}

The (5,7) is the center of the entire oval, not just the center of the
top half.

   These shapes are not ellipses.  They are rectangles whose corners are
made with quarter circles.  These circles have a maximum radius of 20pt
(*note \circle:: for the sizes).  Thus large ovals are just frames with
a small amount of corner rounding.

8.19.11 '\shortstack'
---------------------

Synopsis:

     \shortstack[POSITION]{LINE 1 \\ ... }

   Produce a vertical stack of objects.

   This labels the y axis by writing the word 'y' above the word 'axis'.

     \setlength{\unitlength}{1cm}
     \begin{picture}(5,2.5)(-0.75,0)
        \put(0,0){\vector(1,0){4}}   % x axis
        \put(0,0){\vector(0,1){2}}   % y
        \put(-0.2,2){\makebox(0,0)[r]{\shortstack[r]{$y$\\ axis}}}
     \end{picture}

For a short stack, the reference point is the lower left of the stack.
In the above example the '\makebox' (*note \mbox & \makebox::) puts the
stack flush right in a zero width box so in total the short stack sits
slightly to the left of the y axis.

   The valid positions are:

'r'
     Make objects flush right
'l'
     Make objects flush left
'c'
     Center objects (default)

   Separate objects into lines with '\\'.  These stacks are short in
that, unlike in a 'tabular' or 'array' environment, here the rows are
not spaced out to be of even baseline skips.  Thus, in
'\shortstack{X\\o\\o\\X}' the first and last rows are taller than the
middle two, and therefore the baseline skip between the two middle rows
is smaller than that between the third and last row.  You can adjust row
heights and depths either by putting in the usual interline spacing with
'\shortstack{X\\ \strut o\\o\\X}' (*note \strut::), or explicitly, via
an zero-width box '\shortstack{X \\ \rule{0pt}{12pt} o\\o\\X}' or by
using '\\''s optional argument '\shortstack{X\\[2pt] o\\o\\X}'.

   The '\shortstack' command is also available outside the 'picture'
environment.

8.19.12 '\vector'
-----------------

Synopsis:

     \vector(X_RUN,Y_RISE){TRAVEL}

   Draw a line ending in an arrow.  The slope of that line is: it
vertically rises Y_RISE for every horizontal X_RUN.  The TRAVEL is the
total horizontal change--it is not the length of the vector, it is the
change in x.  In the special case of vertical vectors, if
(X_RUN,Y_RISE)=(0,1), then TRAVEL gives the change in y.

   For an example see *note picture::.

   For elaboration on X_RUN and Y_RISE see *note \line::.  As there, the
values of X_RUN and Y_RISE are limited.  For '\vector' you must chooses
integers between -4 and 4, inclusive.  Also, the two you choose must be
relatively prime.  Thus, '\vector(2,1){4}' is acceptable but
'\vector(4,2){4}' is not (if you use the latter then you get a sequence
of arrowheads).

8.19.13 '\makebox' (picture)
----------------------------

Synopsis:

     \makebox(REC-WIDTH,REC-HEIGHT){TEXT}
     \makebox(REC-WIDTH,REC-HEIGHT)[POSITION]{TEXT}

   Make a box to hold TEXT.  This command fits with the 'picture'
environment, although you can use it outside of there, because REC-WIDTH
and REC-HEIGHT are numbers specifying distances in terms of the
'\unitlength' (*note picture::).  This command is similar to the normal
'\makebox' command (*note \mbox & \makebox::) except here that you must
specify the width and height.  This command is fragile (*note
\protect::).

   This makes a box of length 3.5 times '\unitlength' and height 4 times
'\unitlength'.

     \put(1,2){\makebox(3.5,4){...}}

   The optional argument 'POSITION' specifies where in the box the TEXT
appears.  The default is to center it, both horizontally and vertically.
To place it somewhere else, use a string with one or two of these
letters.

't'
     Puts TEXT the top of the box.

'b'
     Put TEXT at the bottom.

'l'
     Put TEXT on the left.

'r'
     Put TEXT on the right.

8.19.14 '\framebox' (picture)
-----------------------------

Synopsis:

     \framebox(REC-WIDTH,REC-HEIGHT){TEXT}
     \framebox(REC-WIDTH,REC-HEIGHT)[POSITION]{TEXT}

   This is the same as *note \makebox (picture):: except that it puts a
frame around the outside of the box that it creates.  The reference
point is the bottom left corner of the frame.  This command fits with
the 'picture' environment, although you can use it outside of there,
because lengths are numbers specifying the distance in terms of the
'\unitlength' (*note picture::).  This command is fragile (*note
\protect::).

   This example creates a frame 2.5 inches by 3 inches and puts the text
in the center.

     \setlength{\unitlength}{1in}
     \framebox(2.5,3){test text}

   The required arguments are that the rectangle has overall width
RECT-WIDTH units and height RECT-HEIGHT units.

   The optional argument POSITION specifies the position of TEXT; see
*note \makebox (picture):: for the values that it can take.

   The rule has thickness '\fboxrule' and there is a blank space
'\fboxsep' between the frame and the contents of the box.

   For this command, you must specify the WIDTH and HEIGHT.  If you want
to just put a frame around some contents whose dimension is determined
in some other way then either use '\fbox' (*note \fbox & \framebox::) or
'\frame' (*note \frame::).

8.19.15 '\frame'
----------------

Synopsis:

     \frame{CONTENTS}

   Puts a rectangular frame around CONTENTS.  The reference point is the
bottom left corner of the frame.  In contrast to '\framebox' (*note
\framebox (picture)::), this command puts no extra space is put between
the frame and the object.  It is fragile (*note \protect::).

8.19.16 '\dashbox'
------------------

Synopsis:

     \dashbox{DASH-LEN}(RECT-WIDTH,RECT-HEIGHT){TEXT}
     \dashbox{DASH-LEN}(RECT-WIDTH,RECT-HEIGHT)[POSITION]{TEXT}

   Create a dashed rectangle around TEXT.  This command fits with the
'picture' environment, although you can use it outside of there, because
lengths are numbers specifying the distance in terms of the
'\unitlength' (*note picture::).

   The required arguments are: dashes are DASH-LEN units long, with the
same length gap, and the rectangle has overall width RECT-WIDTH units
and height RECT-HEIGHT units.

   The optional argument POSITION specifies the position of TEXT; see
*note \makebox (picture):: for the values that it can take.

   This shows that you can use non-integer value for DASH-LEN.

     \put(0,0){\dashbox{0.1}(5,0.5){My hovercraft is full of eels.}}

Each dash will be '0.1\unitlength' long, the box's width is
'5\unitlength' and its height is '0.5\unitlength'.

   As in that example, a dashed box looks best when RECT-WIDTH and
RECT-HEIGHT are multiples of the DASH-LEN.

8.20 'quotation' & 'quote'
==========================

Synopsis:

     \begin{quotation}
       TEXT
     \end{quotation}

or

     \begin{quote}
       TEXT
     \end{quote}

   Include a quotation.  Both environments indent margins on both sides
by '\leftmargin' and the text is right-justified.

   They differ in how they treat paragraphs.  In the 'quotation'
environment, paragraphs are indented by 1.5em and the space between
paragraphs is small, '0pt plus 1pt'.  In the 'quote' environment,
paragraphs are not indented and there is vertical space between
paragraphs (it is the rubber length '\parsep').

     \begin{quotation} \small\it
       Four score and seven years ago
       ... shall not perish from the earth.
       \hspace{1em plus 1fill}---Abraham Lincoln
     \end{quotation}

8.21 'tabbing'
==============

Synopsis:

     \begin{tabbing}
     ROW1COL1 \= ROW1COL2 ...  \\
     ROW2COL1 \> ROW2COL2 ...  \\
     ...
     \end{tabbing}

   Align text in columns, by setting tab stops and tabbing to them much
as was done on a typewriter.  This is less often used than the
environments 'tabular' (*note tabular::) or 'array' (*note array::)
because in those the width of each column need not be constant and need
not be known in advance.

   This example has a first line where the tab stops are set to explicit
widths, ended by a '\kill' command (which is described below):

     \begin{tabbing}
     \hspace{1.2in}\=\hspace{1in}\=\kill
     Ship                \>Guns             \>Year    \\
     \textit{Sophie}     \>14               \>1800    \\
     \textit{Polychrest} \>24               \>1803    \\
     \textit{Lively}     \>38               \>1804    \\
     \textit{Surprise}   \>28               \>1805    \\
     \end{tabbing}

   Both the 'tabbing' environment and the more widely-used 'tabular'
environment put text in columns.  The most important distinction is that
in 'tabular' the width of columns is determined automatically by LaTeX,
while in 'tabbing' the user sets the tab stops.  Another distinction is
that 'tabular' generates a box, but 'tabbing' can be broken across
pages.  Finally, while 'tabular' can be used in any mode, 'tabbing' can
be used only in paragraph mode and it always starts a new paragraph,
without indentation.

   Moreover, as shown in the example above, there is no need to use the
starred form of the '\hspace' command at the beginning of a tabbed row.
The right margin of the 'tabbing' environment is the end of line, so
that the width of the environment is '\linewidth'.

   The 'tabbing' environment contains a sequence of "tabbed rows".  The
first tabbed row begins immediately after '\begin{tabbing}' and each row
ends with '\\' or '\kill'.  The last row may omit the '\\' and end with
just '\end{tabbing}'.

   At any point the 'tabbing' environment has a "current tab stop
pattern", a sequence of N > 0 tab stops, numbered 0, 1, etc.  These
create N corresponding columns.  Tab stop 0 is always the left margin,
defined by the enclosing environment.  Tab stop number I is set if it is
assigned a horizontal position on the page.  Tab stop number I can only
be set if all the stops 0, ..., i-1 have already been set; normally
later stops are to the right of earlier ones.

   By default any text typeset in a 'tabbing' environment is typeset
ragged right and left-aligned on the current tab stop.  Typesetting is
done in LR mode (*note Modes::).

   The following commands can be used inside a 'tabbing' environment.
They are all fragile (*note \protect::).

'\\ (tabbing)'
     End a tabbed line and typeset it.

'\= (tabbing)'
     Sets a tab stop at the current position.

'\> (tabbing)'
     Advances to the next tab stop.

'\<'
     Put following text to the left of the local margin (without
     changing the margin).  Can only be used at the start of the line.

'\+'
     Moves the left margin of the next and all the following commands
     one tab stop to the right, beginning tabbed line if necessary.

'\-'
     Moves the left margin of the next and all the following commands
     one tab stop to the left, beginning tabbed line if necessary.

'\' (tabbing)'
     Moves everything that you have typed so far in the current column,
     i.e., everything from the most recent '\>', '\<', '\'', '\\', or
     '\kill' command, to the previous column and aligned to the right,
     flush against the current column's tab stop.

'\` (tabbing)'
     Allows you to put text flush right against any tab stop, including
     tab stop 0.  However, it can't move text to the right of the last
     column because there's no tab stop there.  The '\`' command moves
     all the text that follows it, up to the '\\' or '\end{tabbing}'
     command that ends the line, to the right margin of the 'tabbing'
     environment.  There must be no '\>' or '\'' command between the
     '\`' and the '\\' or '\end{tabbing}' command that ends the line.

'\a (tabbing)'
     In a 'tabbing' environment, the commands '\=', '\'' and '\`' do not
     produce accents as usual (*note Accents::).  Instead, use the
     commands '\a=', '\a'' and '\a`'.

'\kill'
     Sets tab stops without producing text.  Works just like '\\' except
     that it throws away the current line instead of producing output
     for it.  Any '\=', '\+' or '\-' commands in that line remain in
     effect.

'\poptabs'
     Restores the tab stop positions saved by the last '\pushtabs'.

'\pushtabs'
     Saves all current tab stop positions.  Useful for temporarily
     changing tab stop positions in the middle of a 'tabbing'
     environment.

'\tabbingsep'
     Distance of the text moved by '\'' to left of current tab stop.

   This example typesets a Pascal function:

     \begin{tabbing}
     function \= fact(n : integer) : integer;\\
              \> begin \= \+ \\
                    \> if \= n > 1 then \+ \\
                             fact := n * fact(n-1) \- \\
                       else \+ \\
                             fact := 1; \-\- \\
                 end;\\
     \end{tabbing}

The output looks like this.

     function fact(n : integer) : integer;
              begin
                    if n > 1 then
                       fact := n * fact(n-1);
                    else
                       fact := 1;
              end;

This example is just for illustration of the environment.  To actually
typeset computer code in typewriter like this, a verbatim environment
(*note verbatim::) would normally be best.  For pretty-printed code,
there are quite a few packages, including 'algorithm2e', 'fancyvrb',
'listings', and 'minted'.

8.22 'table'
============

Synopsis:

     \begin{table}[PLACEMENT]
       TABLE BODY
       \caption[LOFTITLE]{TITLE}  % optional
       \label{LABEL}              % also optional
     \end{table}

   A class of floats (*note Floats::).  They cannot be split across
pages and so they are not typeset in sequence with the normal text but
instead are floated to a convenient place, such as the top of a
following page.

   This example 'table' environment contains a 'tabular'

     \begin{table}
       \centering\small
       \begin{tabular}{ll}
         \multicolumn{1}{c}{\textit{Author}}
           &\multicolumn{1}{c}{\textit{Piece}}  \\ \hline
         Bach            &Cello Suite Number 1  \\
         Beethoven       &Cello Sonata Number 3 \\
         Brahms          &Cello Sonata Number 1
       \end{tabular}
       \caption{Top cello pieces}
       \label{tab:cello}
     \end{table}

but you can put many different kinds of content in a 'table': the TABLE
BODY may contain text, LaTeX commands, graphics, etc.  It is typeset in
a 'parbox' of width '\textwidth'.

   For the possible values of PLACEMENT and their effect on the float
placement algorithm, see *note Floats::.

   The label is optional; it is used for cross references (*note Cross
references::).  The '\caption' command is also optional.  It specifies
caption text TITLE for the table (*note \caption::).  By default it is
numbered.  If its optional LOTTITLE is present then that text is used in
the list of tables instead of TITLE (*note Table of contents etc.::).

   In this example the table and caption will float to the bottom of a
page, unless it is pushed to a float page at the end.

     \begin{table}[b]
       \centering
       \begin{tabular}{r|p{2in}} \hline
         One &The loneliest number \\
         Two &Can be as sad as one.
              It's the loneliest number since the number one.
       \end{tabular}
       \caption{Cardinal virtues}
       \label{tab:CardinalVirtues}
     \end{table}

8.23 'tabular'
==============

Synopsis:

     \begin{tabular}[POS]{COLS}
       COLUMN 1 ENTRY  &COLUMN 2 ENTRY  ...  &COLUMN N ENTRY \\
       ...
     \end{tabular}

or

     \begin{tabular*}{WIDTH}[POS]{COLS}
       COLUMN 1 ENTRY  &COLUMN 2 ENTRY  ...  &COLUMN N ENTRY \\
       ...
     \end{tabular*}

   Produce a table, a box consisting of a sequence of horizontal rows.
Each row consists of items that are aligned vertically in columns.  This
illustrates many of the features.

     \begin{tabular}{l|l}
       \textit{Player name}  &\textit{Career home runs}  \\
       \hline
       Hank Aaron  &755 \\
       Babe Ruth   &714
     \end{tabular}

The output will have two left-aligned columns with a vertical bar
between them.  This is specified in 'tabular''s argument '{l|l}'.  Put
the entries into different columns by separating them with an ampersand,
'&'.  The end of each row is marked with a double backslash, '\\'.  Put
a horizontal rule below a row, after a double backslash, with '\hline'.
After the last row the '\\' is optional, unless an '\hline' command
follows to put a rule below the table.

   The required and optional arguments to 'tabular' consist of:

POS
     Optional.  Specifies the table's vertical position.  The default is
     to align the table so its vertical center matches the baseline of
     the surrounding text.  There are two other possible alignments: 't'
     aligns the table so its top row matches the baseline of the
     surrounding text, and 'b' aligns on the bottom row.

     This only has an effect if there is other text.  In the common case
     of a 'tabular' alone in a 'center' environment this option makes no
     difference.

COLS
     Required.  Specifies the formatting of columns.  It consists of a
     sequence of the following specifiers, corresponding to the types of
     column and intercolumn material.

     'l'
          A column of left-aligned items.

     'r'
          A column of right-aligned items.

     'c'
          A column of centered items.

     '|'
          A vertical line the full height and depth of the environment.

     '@{TEXT OR SPACE}'
          Insert TEXT OR SPACE at this location in every row.  The TEXT
          OR SPACE material is typeset in LR mode.  This text is fragile
          (*note \protect::).

          If between two columns there is no @-expression then LaTeX's
          'book', 'article', and 'report' classes will put on either
          side of each column a space of length '\tabcolsep', which by
          default is 6pt.  That is, by default adjacent columns are
          separated by 12pt (so '\tabcolsep' is misleadingly named since
          it is only half of the separation between tabular columns).
          In addition, a space of 6pt also comes before the first column
          and after the final column, unless you put a '@{...}' or '|'
          there.

          If you override the default and use an @-expression then LaTeX
          does not insert '\tabcolsep' so you must insert any desired
          space yourself, as in '@{\hspace{1em}}'.

          An empty expression '@{}' will eliminate the space.  In
          particular, sometimes you want to eliminate the space before
          the first column or after the last one, as in the example
          below where the tabular lines need to lie on the left margin.

               \begin{flushleft}
                 \begin{tabular}{@{}l}
                   ...
                 \end{tabular}
               \end{flushleft}

          The next example shows text, a decimal point between the
          columns, arranged so the numbers in the table are aligned on
          it.

               \begin{tabular}{r@{$.$}l}
                 $3$ &$14$  \\
                 $9$ &$80665$
               \end{tabular}

          An '\extracolsep{WD}' command in an @-expression causes an
          extra space of width WD to appear to the left of all
          subsequent columns, until countermanded by another
          '\extracolsep'.  Unlike ordinary intercolumn space, this extra
          space is not suppressed by an @-expression.  An '\extracolsep'
          command can be used only in an @-expression in the 'cols'
          argument.  Below, LaTeX inserts the right amount of
          intercolumn space to make the entire table 4 inches wide.

               \begin{tabular*}{4in}{l@{\extracolsep{\fill}}l}
                 Seven times down, eight times up \ldots
                 &such is life!
               \end{tabular*}

          To insert commands that are automatically executed before a
          given column, load the 'array' package and use the '>{...}'
          specifier.

     'p{WD}'
          Each item in the column is typeset in a parbox of width WD, as
          if it were the argument of a '\parbox[t]{wd}{...}' command.

          A line break double backslash '\\' may not appear in the item,
          except inside an environment like 'minipage', 'array', or
          'tabular', or inside an explicit '\parbox', or in the scope of
          a '\centering', '\raggedright', or '\raggedleft' declaration
          (when used in a 'p'-column element these declarations must
          appear inside braces, as with '{\centering .. \\ ..}').
          Otherwise LaTeX will misinterpret the double backslash as
          ending the tabular row.  Instead, to get a line break in there
          use '\newline' (*note \newline::).

     '*{NUM}{COLS}'
          Equivalent to NUM copies of COLS, where NUM is a positive
          integer and COLS is a list of specifiers.  Thus the specifier
          '\begin{tabular}{|*{3}{l|r}|}' is equivalent to the specifier
          '\begin{tabular}{|l|rl|rl|r|}'.  Note that COLS may contain
          another '*'-expression.

WIDTH
     Required for 'tabular*', not allowed for 'tabular'.  Specifies the
     width of the 'tabular*' environment.  The space between columns
     should be rubber, as with '@{\extracolsep{\fill}}', to allow the
     table to stretch or shrink to make the specified width, or else you
     are likely to get the 'Underfull \hbox (badness 10000) in alignment
     ...' warning.

   Parameters that control formatting:

'\arrayrulewidth'
     A length that is the thickness of the rule created by '|',
     '\hline', and '\vline' in the 'tabular' and 'array' environments.
     The default is '.4pt'.  Change it as in
     '\setlength{\arrayrulewidth}{0.8pt}'.

'\arraystretch'
     A factor by which the spacing between rows in the 'tabular' and
     'array' environments is multiplied.  The default is '1', for no
     scaling.  Change it as '\renewcommand{\arraystretch}{1.2}'.

'\doublerulesep'
     A length that is the distance between the vertical rules produced
     by the '||' specifier.  The default is '2pt'.

'\tabcolsep'
     A length that is half of the space between columns.  The default is
     '6pt'.  Change it with '\setlength'.

   The following commands can be used inside the body of a 'tabular'
environment, the first two inside an entry and the second two between
lines:

8.23.1 '\multicolumn'
---------------------

Synopsis:

     \multicolumn{NUMCOLS}{COLS}{TEXT}

   Make an 'array' or 'tabular' entry that spans several columns.  The
first argument NUMCOLS gives the number of columns to span.  The second
argument COLS specifies the formatting of the entry, with 'c' for
centered, 'l' for flush left, or 'r' for flush right.  The third
argument TEXT gives the contents of that entry.

   In this example, in the first row, the second and third columns are
spanned by the single heading 'Name'.

     \begin{tabular}{lccl}
       \textit{ID}       &\multicolumn{2}{c}{\textit{Name}} &\textit{Age} \\
       \hline
       978-0-393-03701-2 &O'Brian &Patrick                  &55           \\
         ...
     \end{tabular}

   What counts as a column is: the column format specifier for the
'array' or 'tabular' environment is broken into parts, where each part
(except the first) begins with 'l', 'c', 'r', or 'p'.  So from
'\begin{tabular}{|r|ccp{1.5in}|}' the parts are '|r|', 'c', 'c',
and 'p{1.5in}|'.

   The COLS argument overrides the 'array' or 'tabular' environment's
intercolumn area default adjoining this multicolumn entry.  To affect
that area, this argument can contain vertical bars '|' indicating the
placement of vertical rules, and '@{...}' expressions.  Thus if COLS is
'|c|' then this multicolumn entry will be centered and a vertical rule
will come in the intercolumn area before it and after it.  This table
details the exact behavior.

     \begin{tabular}{|cc|c|c|}
       \multicolumn{1}{r}{w}       % entry one
         &\multicolumn{1}{|r|}{x}  % entry two
         &\multicolumn{1}{|r}{y}   % entry three
         &z                        % entry four
     \end{tabular}

Before the first entry the output will not have a vertical rule because
the '\multicolumn' has the COLS specifier 'r' with no initial vertical
bar.  Between entry one and entry two there will be a vertical rule;
although the first COLS does not have an ending vertical bar, the second
COLS does have a starting one.  Between entry two and entry three there
is a single vertical rule; despite that the COLS in both of the
surrounding 'multicolumn''s call for a vertical rule, you only get one
rule.  Between entry three and entry four there is no vertical rule; the
default calls for one but the COLS in the entry three '\multicolumn'
leaves it out, and that takes precedence.  Finally, following entry four
there is a vertical rule because of the default.

   The number of spanned columns NUMCOLS can be 1.  Besides giving the
ability to change the horizontal alignment, this also is useful to
override for one row the 'tabular' definition's default intercolumn area
specification, including the placement of vertical rules.

   In the example below, in the 'tabular' definition the first column is
specified to default to left justified but in the first row the entry is
centered with '\multicolumn{1}{c}{\textsc{Period}}'.  Also in the first
row, the second and third columns are spanned by a single entry with
'\multicolumn{2}{c}{\textsc{Span}}', overriding the specification to
center those two columns on the page range en-dash.

     \begin{tabular}{l|r@{--}l}
       \multicolumn{1}{c}{\textsc{Period}}
         &\multicolumn{2}{c}{\textsc{Span}} \\ \hline
       Baroque          &1600           &1760         \\
       Classical        &1730           &1820         \\
       Romantic         &1780           &1910         \\
       Impressionistic  &1875           &1925
     \end{tabular}

Although the 'tabular' specification by default puts a vertical rule
between the first and second columns, no such vertical rule appears in
the first row here.  That's because there is no vertical bar in the COLS
part of the first row's first '\multicolumn' command.

8.23.2 '\vline'
---------------

Draw a vertical line in a 'tabular' or 'array' environment extending the
full height and depth of an entry's row.  Can also be used in an
@-expression, although its synonym vertical bar '|' is more common.
This command is rarely used in the body of a table; typically a table's
vertical lines are specified in 'tabular''s COLS argument and overridden
as needed with '\multicolumn' (*note tabular::).

   The example below illustrates some pitfalls.  In the first row's
second entry the '\hfill' moves the '\vline' to the left edge of the
cell.  But that is different than putting it halfway between the two
columns, so between the first and second columns there are two vertical
rules, with the one from the '{c|cc}' specifier coming before the one
produced by the '\vline\hfill'.  In contrast, the first row's third
entry shows the usual way to put a vertical bar between two columns.  In
the second row, the 'ghi' is the widest entry in its column so in the
'\vline\hfill' the '\hfill' has no effect and the vertical line in that
entry appears immediately next to the 'g', with no whitespace.

     \begin{tabular}{c|cc}
       x   &\vline\hfill y   &\multicolumn{1}{|r}{z} \\ % row 1
       abc &def &\vline\hfill ghi                       % row 2
     \end{tabular}

8.23.3 '\cline'
---------------

Synopsis:

     \cline{I-J}

   In an 'array' or 'tabular' environment, draw a horizontal rule
beginning in column I and ending in column J.  The dash, '-', must
appear in the mandatory argument.  To span a single column use the
number twice, as with '\cline{2-2}'.

   This example puts two horizontal lines between the first and second
rows, one line in the first column only, and the other spanning the
third and fourth columns.  The two lines are side-by-side, at the same
height.

     \begin{tabular}{llrr}
       a &b &c &d \\ \cline{1-1} \cline{3-4}
       e &f &g &h
     \end{tabular}

8.23.4 '\hline'
---------------

Draw a horizontal line the width of the enclosing 'tabular' or 'array'
environment.  It's most commonly used to draw a line at the top, bottom,
and between the rows of a table.

   In this example the top of the table has two horizontal rules, one
above the other, that span both columns.  The bottom of the table has a
single rule spanning both columns.  Because of the '\hline', the
'tabular' second row's line ending double backslash '\\' is required.

     \begin{tabular}{ll} \hline\hline
       Baseball   &Red Sox  \\
       Basketball &Celtics  \\ \hline
     \end{tabular}

8.24 'thebibliography'
======================

Synopsis:

     \begin{thebibliography}{WIDEST-LABEL}
       \bibitem[LABEL]{CITE_KEY}
       ...
     \end{thebibliography}

   Produce a bibliography or reference list.  There are two ways to
produce bibliographic lists.  This environment is suitable when you have
only a few references and can maintain the list by hand.  *Note Using
BibTeX::, for a more sophisticated approach.

   This shows the environment with two entries.

     This work is based on \cite{latexdps}.
     Together they are \cite{latexdps, texbook}.
       ...
     \begin{thebibliography}{9}
     \bibitem{latexdps}
       Leslie Lamport.
       \textit{\LaTeX{}: a document preparation system}.
       Addison-Wesley, Reading, Massachusetts, 1993.
     \bibitem{texbook}
       Donald Ervin Knuth.
       \textit{The \TeX book}.
       Addison-Wesley, Reading, Massachusetts, 1983.
     \end{thebibliography}

This styles the first reference as '[1] Leslie ...', and so that '...
based on \cite{latexdps}' produces the matching '... based on [1]'.  The
second '\cite' produces '[1, 2]'.  You must compile the document twice
to resolve these references.

   The mandatory argument WIDEST-LABEL is text that, when typeset, is as
wide as the widest item label produced by the '\bibitem' commands.  The
tradition is to use '9' for bibliographies with less than 10 references,
'99' for ones with less than 100, etc.

   The bibliographic list is headed by a title such as 'Bibliography'.
To change it there are two cases.  In the 'book' and 'report' classes,
where the top level sectioning is '\chapter' and the default title is
'Bibliography', that title is in the macro '\bibname'.  For 'article',
where the class's top level sectioning is '\section' and the default is
'References', the title is in macro '\refname'.  Change it by redefining
the command, as with '\renewcommand{\refname}{Cited references}', after
'\begin{document}'.

   Language support packages such as 'babel' will automatically redefine
'\refname' or '\bibname' to fit the selected language.

   *Note list::, for the list layout control parameters.

8.24.1 '\bibitem'
-----------------

Synopsis:

     \bibitem{CITE_KEY}

or

     \bibitem[LABEL]{CITE_KEY}

   Generate an entry labeled by default by a number generated using the
'enumi' counter.  The "citation key" CITE_KEY can be any string of
letters, numbers, and punctuation symbols (but not comma).

   *Note thebibliography::, for an example.

   When provided, the optional LABEL becomes the entry label and the
'enumi' counter is not incremented.  With this

     \begin{thebibliography}
     \bibitem[Lamport 1993]{latexdps}
       Leslie Lamport.
       \textit{\LaTeX{}: a document preparation system}.
       Addison-Wesley, Reading, Massachusetts, 1993.
     \bibitem{texbook}
       Donald Ervin Knuth.
       \textit{The \TeX book}.
       Addison-Wesley, Reading, Massachusetts, 1983.
     \end{thebibliography}

the first entry will be styled as '[Lamport 1993] Leslie ...' (The
amount of horizontal space that LaTeX leaves for the label depends on
the WIDEST-LABEL argument of the 'thebibliography' environment; see
*note thebibliography::.)  Similarly, '... based on \cite{latexdps}'
will produce '... based on [Lamport 1994]'.

   If you mix '\bibitem' entries having a LABEL with those that do not
then LaTeX will number the unlabelled ones sequentially.  In the example
above the 'texbook' entry will appear as '[1] Donald ...', despite that
it is the second entry.

   If you use the same CITE_KEY twice then you get 'LaTeX Warning: There
were multiply-defined labels'.

   Under the hood, LaTeX remembers the CITE_KEY and LABEL information
because '\bibitem' writes it to the auxiliary file 'JOBNAME.aux' (*note
Jobname::).  For instance, the above example causes the two
'\bibcite{latexdps}{Lamport, 1993}' and '\bibcite{texbook}{1}' to appear
in that file.  The '.aux' file is read by the '\begin{document}' command
and then the information is available for '\cite' commands.  This
explains why you need to run LaTeX twice to resolve references: once to
write it out and once to read it in.

   Because of this two-pass algorithm, when you add a '\bibitem' or
change its CITE_KEY you may get 'LaTeX Warning: Label(s) may have
changed. Rerun to get cross-references right'.  Fix it by recompiling.

8.24.2 '\cite'
--------------

Synopsis:

     \cite{KEYS}

or

     \cite[SUBCITE]{KEYS}

   Generate as output a citation to the references associated with KEYS.
The mandatory KEYS is a citation key, or a comma-separated list of
citation keys (*note \bibitem::).

   This

     The ultimate source is \cite{texbook}.
       ...
     \begin{thebibliography}
     \bibitem{texbook}
       Donald Ervin Knuth.
       \textit{The \TeX book}.
       Addison-Wesley, Reading, Massachusetts, 1983.
     \end{thebibliography}

produces output like '... source is [1]'.  You can change the appearance
of the citation and of the reference by using bibliography styles if you
generate automatically the 'thebibliography' environment.  More
information in *note Using BibTeX::.

   The optional argument SUBCITE is appended to the citation.  For
example, 'See 14.3 in \cite[p.~314]{texbook}' might produce 'See 14.3 in
[1, p. 314]'.

   In addition to what appears in the output, '\cite' writes information
to the auxiliary file 'JOBNAME.aux' (*note Jobname::).  For instance,
'\cite{latexdps}' writes '\citation{latexdps}' to that file.  This
information is used by BibTeX to include in your reference list only
those works that you have actually cited; see *note \nocite:: also.

   If KEYS is not in your bibliography information then you get 'LaTeX
Warning: There were undefined references', and in the output the
citation shows as a boldface question mark between square brackets.
There are two possible causes.  If you have mistyped something, as in
'\cite{texbok}' then you need to correct the spelling.  On the other
hand, if you have just added or modified the bibliographic information
and so changed the '.aux' file (*note \bibitem::) then the fix may be to
run LaTeX again.

8.24.3 '\nocite'
----------------

Synopsis:

     \nocite{KEYS}

   Produces no output but writes KEYS to the auxiliary file
'JOBNAME.aux' (*note Jobname::).

   The mandatory argument KEYS is a comma-separated list of one or more
citation keys (*note \bibitem::).  This information is used by BibTeX to
include these works in your reference list even though you have not
explicitly cited them (*note \cite::).

8.24.4 Using BibTeX
-------------------

As described in 'thebibliography' (*note thebibliography::), a
sophisticated approach to managing bibliographies is provided by the
BibTeX program.  This is only an introduction; see the full
documentation on CTAN (*note CTAN::).

   With BibTeX, you don't use the 'thebibliography' environment directly
(*note thebibliography::).  Instead, include these lines:

     \bibliographystyle{BIBSTYLE}
     \bibliography{BIBFILE1, BIBFILE2, ...}

The BIBSTYLE refers to a file 'BIBSTYLE.bst', which defines how your
citations will look.  The standard BIBSTYLE's distributed with BibTeX
are:

'alpha'
     Labels are formed from name of author and year of publication.  The
     bibliographic items are sorted alphabetically.
'plain'
     Labels are integers.  Sort the bibliographic items alphabetically.
'unsrt'
     Like 'plain', but entries are in order of citation.
'abbrv'
     Like 'plain', but more compact labels.

Many, many other BibTeX style files exist, tailored to the demands of
various publications.  See the CTAN topic
<https://ctan.org/topic/bibtex-sty>.

   The '\bibliography' command is what actually produces the
bibliography.  Its argument is a comma-separated list, referring to
files named 'BIBFILE1.bib', 'BIBFILE2.bib', ... These contain your
database in BibTeX format.  This shows a typical couple of entries in
that format.

     @book{texbook,
       title     = {The {{\TeX}}book},
       author    = {D.E. Knuth},
       isbn      = {0201134489},
       series    = {Computers \& typesetting},
       year      = {1983},
       publisher = {Addison-Wesley}
     }
     @book{sexbook,
         author    = {W.H. Masters and V.E. Johnson},
         title     = {Human Sexual Response},
         year      = {1966},
         publisher = {Bantam Books}
     }

   Only the bibliographic entries referred to via '\cite' and '\nocite'
will be listed in the document's bibliography.  Thus you can keep all
your sources together in one file, or a small number of files, and rely
on BibTeX to include in this document only those that you used.

   With BibTeX, the KEYS argument to '\nocite' can also be the single
character '*'.  This means to implicitly cite all entries from all given
bibliographies.

8.24.4.1 BibTeX error messages
..............................

If you forget to use '\bibliography' or '\bibliographystyle' in your
document (or, less likely, any '\cite' or '\nocite' command), BibTeX
will issue an error message.  Because BibTeX can be used with any
program, not just LaTeX, the error messages refer to the internal
commands read by BibTeX (from the '.aux' file), rather than the
user-level commands described above.

   Here is a table showing internal commands mentioned in the BibTeX
errors, and the corresponding user-level commands.

'\bibdata'
     '\bibliography'

'\bibstyle'
     '\bibliographystyle'

'\citation'
     '\cite', '\nocite'

   For example, if your document has no '\bibliographystyle' command,
BibTeX complains as follows:

     I found no \bibstyle command---while reading file DOCUMENT.aux

8.25 'theorem'
==============

Synopsis:

     \begin{theorem}
       THEOREM BODY
     \end{theorem}

   Produces 'Theorem N' in boldface followed by THEOREM BODY in italics.
The numbering possibilities for N are described under '\newtheorem'
(*note \newtheorem::).

     \newtheorem{lem}{Lemma}      % in preamble
     \newtheorem{thm}{Theorem}
       ...
     \begin{lem}                  % in  document body
       text of lemma
     \end{lem}

     The next result follows immediately.
     \begin{thm}[Gauss]   %  put `Gauss' in parens after theorem head
       text of theorem
     \end{thm}

   Most new documents use the packages 'amsthm' and 'amsmath' from the
American Mathematical Society.  Among other things these packages
include a large number of options for theorem environments, such as
styling options.

8.26 'titlepage'
================

Synopsis:

     \begin{titlepage}
       ... text and spacing ...
     \end{titlepage}

   Create a title page, a page with no printed page number or heading
and with succeeding pages numbered starting with page one.

   In this example all formatting, including vertical spacing, is left
to the author.

     \begin{titlepage}
     \vspace*{\stretch{1}}
     \begin{center}
       {\huge\bfseries Thesis \\[1ex]
                       title}                  \\[6.5ex]
       {\large\bfseries Author name}           \\
       \vspace{4ex}
       Thesis  submitted to                    \\[5pt]
       \textit{University name}                \\[2cm]
       in partial fulfilment for the award of the degree of \\[2cm]
       \textsc{\Large Doctor of Philosophy}    \\[2ex]
       \textsc{\large Mathematics}             \\[12ex]
       \vfill
       Department of Mathematics               \\
       Address                                 \\
       \vfill
       \today
     \end{center}
     \vspace{\stretch{2}}
     \end{titlepage}

   To instead produce a standard title page without a 'titlepage'
environment, use '\maketitle' (*note \maketitle::).

8.27 'verbatim'
===============

Synopsis:

     \begin{verbatim}
     LITERAL-TEXT
     \end{verbatim}

   A paragraph-making environment in which LaTeX produces as output
exactly what you type as input.  For instance inside LITERAL-TEXT the
backslash '\' character does not start commands, it produces a printed
'\', and carriage returns and blanks are taken literally.  The output
appears in a monospaced typewriter-like font ('\tt').

     \begin{verbatim}
     Symbol swearing: %&$#?!.
     \end{verbatim}

   The only restriction on 'literal-text' is that it cannot include the
string '\end{verbatim}'.

   You cannot use the verbatim environment in the argument to macros,
for instance in the argument to a '\section'.  This is not the same as
commands being fragile (*note \protect::), instead it just cannot work,
as the 'verbatim' environment changes the catcode regime before
processing its contents, and restore it immediately afterward,
nevertheless with a macro argument the content of the argument has
already be converted to a token list along the catcode regime in effect
when the macro was called.  However, the 'cprotect' package can help
with this.

   One common use of verbatim input is to typeset computer code.  There
are packages that are an improvement the 'verbatim' environment.  For
instance, one improvement is to allow the verbatim inclusion of external
files, or parts of those files.  Such packages include 'listings', and
'minted'.

   A package that provides many more options for verbatim environments
is 'fancyvrb'.  Another is 'verbatimbox'.

   For a list of all the relevant packages, see CTAN (*note CTAN::).

8.27.1 '\verb'
--------------

Synopsis:

     \verb CHAR LITERAL-TEXT CHAR
     \verb* CHAR LITERAL-TEXT CHAR

   Typeset LITERAL-TEXT as it is input, including special characters and
spaces, using the typewriter ('\tt') font.

   This example shows two different invocations of '\verb'.

     This is \verb!literally! the biggest pumpkin ever.
     And this is the best squash, \verb+literally!+

The first '\verb' has its LITERAL-TEXT surrounded with exclamation
point, '!'.  The second instead uses plus, '+', because the exclamation
point is part of 'literal-text'.

   The single-character delimiter CHAR surrounds LITERAL-TEXT--it must
be the same character before and after.  No spaces come between '\verb'
or '\verb*' and CHAR, or between CHAR and LITERAL-TEXT, or between
LITERAL-TEXT and the second occurrence of CHAR (the synopsis shows a
space only to distinguish one component from the other).  The delimiter
must not appear in LITERAL-TEXT.  The LITERAL-TEXT cannot include a line
break.

   The '*'-form differs only in that spaces are printed with a visible
space character.

   The output from this will include a visible space on both side of
word 'with':

     The command's first argument is \verb*!filename with extension! and ...

   For typesetting Internet addresses, urls, the package 'url' is a
better option than the '\verb' command, since it allows line breaks.

   For computer code there are many packages with advantages over
'\verb'.  One is 'listings', another is 'minted'.

   You cannot use '\verb' in the argument to a macro, for instance in
the argument to a '\section'.  It is not a question of '\verb' being
fragile (*note \protect::), instead it just cannot work, as the '\verb'
command changes the catcode regime before reading its argument, and
restore it immediately afterward, nevertheless with a macro argument the
content of the argument has already be converted to a token list along
the catcode regime in effect when the macro was called.  However, the
'cprotect' package can help with this.

8.28 'verse'
============

Synopsis:

     \begin{verse}
       LINE1 \\
       LINE2 \\
       ...
     \end{verse}

   An environment for poetry.

   Here are two lines from Shakespeare's Romeo and Juliet.

     Then plainly know my heart's dear love is set \\
     On the fair daughter of rich Capulet.

   Separate the lines of each stanza with '\\', and use one or more
blank lines to separate the stanzas.

     \begin{verse}
     \makebox[\linewidth][c]{\textit{Shut Not Your Doors} ---Walt Whitman}
       \\[1\baselineskip]
     Shut not your doors to me proud libraries,                  \\
     For that which was lacking on all your well-fill'd shelves, \\
     \qquad yet needed most, I bring,                             \\
     Forth from the war emerging, a book I have made,            \\
     The words of my book nothing, the drift of it every thing,  \\
     A book separate, not link'd with the rest nor felt by the intellect, \\
     But you ye untold latencies will thrill to every page.
     \end{verse}

The output has margins indented on the left and the right, paragraphs
are not indented, and the text is not right-justified.

9 Line breaking
***************

The first thing LaTeX does when processing ordinary text is to translate
your input file into a sequence of glyphs and spaces.  To produce a
printed document, this sequence must be broken into lines (and these
lines must be broken into pages).

   LaTeX usually does the line (and page) breaking in the text body for
you but in some environments you manually force line breaks.

   A common workflow is to get a final version of the document content
before taking a final pass through and considering line breaks (and page
breaks).  This differs from word processing, where you are formatting
text as you input it.  Putting these off until the end prevents a lot of
fiddling with breaks that will change anyway.

9.1 '\\'
========

Synopsis, one of:

     \\
     \\[MORESPACE]

or one of:

     \\*
     \\*[MORESPACE]

   End the current line.  The optional argument MORESPACE specifies
extra vertical space to be inserted before the next line.  This is a
rubber length (*note Lengths::) and can be negative.  The text before
the line break is set at its normal length, that is, it is not stretched
to fill out the line width.  This command is fragile (*note \protect::).

     \title{My story: \\[0.25in]
            a tale of woe}

The starred form, '\\*', tells LaTeX not to start a new page between the
two lines, by issuing a '\nobreak'.

   Explicit line breaks in the main text body are unusual in LaTeX.  In
particular, don't start new paragraphs with '\\'.  Instead leave a blank
line between the two paragraphs.  And don't put in a sequence of '\\''s
to make vertical space.  Instead use '\vspace{LENGTH}', or
'\leavevmode\vspace{LENGTH}', or '\vspace*{LENGTH}' if you want the
space to not be thrown out at the top of a new page (*note \vspace::).

   The '\\' command is mostly used outside of the main flow of text such
as in a 'tabular' or 'array' environment or in an equation environment.

   The '\\' command is a synonym for '\newline' (*note \newline::) under
ordinary circumstances (an example of an exception is the 'p{...}'
column in a 'tabular' environment; *note tabular::).

   The '\\' command is a macro, and its definition changes by context so
that its definition in normal text, a 'center' environment, a
'flushleft' environment, and a 'tabular' are all different.  In normal
text when it forces a linebreak it is essentially a shorthand for
'\newline'.  It does not end horizontal mode or end the paragraph, it
just inserts some glue and penalties so that when the paragraph does end
a linebreak will occur at that point, with the short line padded with
white space.

   You get 'LaTeX Error: There's no line here to end' if you use '\\' to
ask for a new line, rather than to end the current line.  An example is
if you have '\begin{document}\\' or, more likely, something like this.

     \begin{center}
       \begin{minipage}{0.5\textwidth}
       \\
       In that vertical space put your mark.
       \end{minipage}
     \end{center}

Fix it by replacing the double backslash with something like
'\vspace{\baselineskip}'.

9.2 '\obeycr' & '\restorecr'
============================

The '\obeycr' command makes a return in the input file ('^^M',
internally) the same as '\\', followed by '\relax'.  So each new line in
the input will also be a new line in the output.  The '\restorecr'
command restores normal line-breaking behavior.

   This is not the way to show verbatim text or computer code.  Use
'verbatim' (*note verbatim::) instead.

   With LaTeX's usual defaults, this

     aaa
     bbb

     \obeycr
     ccc
     ddd
        eee

     \restorecr
     fff
     ggg

     hhh
     iii

produces output like this.

       aaa bbb
       ccc
     ddd
     eee

     fff ggg
       hhh iii

The indents are paragraph indents.

9.3 '\newline'
==============

In ordinary text, this ends a line in a way that does not right-justify
it, so the text before the end of line is not stretched.  That is, in
paragraph mode (*note Modes::), the '\newline' command is equivalent to
double-backslash (*note \\::).  This command is fragile (*note
\protect::).

   However, the two commands are different inside a 'tabular' or 'array'
environment.  In a column with a specifier producing a paragraph box
such as typically 'p{...}', '\newline' will insert a line end inside of
the column; that is, it does not break the entire tabular row.  To break
the entire row use '\\' or its equivalent '\tabularnewline'.

   This will print 'Name:' and 'Address:' as two lines in a single cell
of the table.

     \begin{tabular}{p{1in}@{\hspace{2in}}p{1in}}
       Name: \newline Address: &Date: \\ \hline
     \end{tabular}

The 'Date:' will be baseline-aligned with 'Name:'.

9.4 '\-' (discretionary hyphen)
===============================

Tell LaTeX that it may hyphenate the word at that point.  When you
insert '\-' commands in a word, the word will only be hyphenated at
those points and not at any of the other hyphenation points that LaTeX
might otherwise have chosen.  This command is robust (*note \protect::).

   LaTeX is good at hyphenating and usually finds most of the correct
hyphenation points, while almost never using an incorrect one.  The '\-'
command is for exceptional cases.

   For example, LaTeX does not ordinarily hyphenate words containing a
hyphen.  Below, the long and hyphenated word means LaTeX has to put in
unacceptably large spaces to set the narrow column.

     \begin{tabular}{rp{1.75in}}
       Isaac Asimov &The strain of
                    anti-intellectualism
                    % an\-ti-in\-tel\-lec\-tu\-al\-ism
                    has been a constant thread winding its way through our
                    political and cultural life, nurtured by
                    the false notion that democracy means that
                    `my ignorance is just as good as your knowledge'.
     \end{tabular}

Commenting out the third line and uncommenting the fourth makes a much
better fit.

   The '\-' command only allows LaTeX to break there, it does not
require that it break there.  You can force a split with something like
'Hef-\linebreak feron'.  Of course, if you later change the text then
this forced break may look very odd, so this approach requires care.

9.5 '\discretionary' (generalized hyphenation point)
====================================================

Synopsis:

     \discretionary{PRE-BREAK}{POST-BREAK}{NO-BREAK}

   Handle word changes around hyphens.  This command is not often used
in LaTeX documents.

   If a line break occurs at the point where '\discretionary' appears
then TeX puts PRE-BREAK at the end of the current line and puts
POST-BREAK at the start of the next line.  If there is no line break
here then TeX puts NO-BREAK.

   In 'difficult' the three letters 'ffi' form a ligature.  But TeX can
nonetheless break between the two 'f''s with this.

     di\discretionary{f-}{fi}{ffi}cult

   Note that users do not have to do this.  It is typically handled
automatically by TeX's hyphenation algorithm.

9.6 '\fussy' & '\sloppy'
========================

Declarations to make TeX more picky or less picky about line breaking.
Declaring '\fussy' usually avoids too much space between words, at the
cost of an occasional overfull box.  Conversely, '\sloppy' avoids
overfull boxes while suffering loose interword spacing.

   The default is '\fussy'.  Line breaking in a paragraph is controlled
by whichever declaration is current at the end of the paragraph, i.e.,
at the blank line or '\par' or displayed equation ending that paragraph.
So to affect the line breaks, include that paragraph-ending material in
the scope of the command.

9.6.1 'sloppypar'
-----------------

Synopsis:

     \begin{sloppypar}
       ... paragraphs ...
     \end{sloppypar}

   Typeset the paragraphs with '\sloppy' in effect (*note \fussy &
\sloppy::).  Use this to locally adjust line breaking, to avoid
'Overfull box' or 'Underfull box' errors.

   The example is simple.

     \begin{sloppypar}
       Her plan for the morning thus settled, she sat quietly down to her
       book after breakfast, resolving to remain in the same place and the
       same employment till the clock struck one; and from habitude very
       little incommoded by the remarks and ejaculations of Mrs.\ Allen,
       whose vacancy of mind and incapacity for thinking were such, that
       as she never talked a great deal, so she could never be entirely
       silent; and, therefore, while she sat at her work, if she lost her
       needle or broke her thread, if she heard a carriage in the street,
       or saw a speck upon her gown, she must observe it aloud, whether
       there were anyone at leisure to answer her or not.
     \end{sloppypar}

9.7 '\hyphenation'
==================

Synopsis:

     \hyphenation{WORD1 ...}

   Declares allowed hyphenation points within the words in the list.
The words in that list are separated by spaces.  Show permitted points
for hyphenation with a dash character, '-'.

   Here is an example:

     \hyphenation{hat-er il-lit-e-ra-ti tru-th-i-ness}

   Use lowercase letters.  TeX will only hyphenate if the word matches
exactly, no inflections are tried.  Multiple '\hyphenation' commands
accumulate.

9.8 '\linebreak' & '\nolinebreak'
=================================

Synopses, one of:

     \linebreak
     \linebreak[ZERO-TO-FOUR]

or one of these.

     \nolinebreak
     \nolinebreak[ZERO-TO-FOUR]

   Encourage or discourage a line break.  The optional ZERO-TO-FOUR is
an integer lying between 0 and 4 that allows you to soften the
instruction.  The default is 4, so that without the optional argument
these commands entirely force or prevent the break.  But for instance,
'\nolinebreak[1]' is a suggestion that another place may be better.  The
higher the number, the more insistent the request.  Both commands are
fragile (*note \protect::).

   Here we tell LaTeX that a good place to put a linebreak is after the
standard legal text.

     \boilerplatelegal{} \linebreak[2]
     We especially encourage applications from members of traditionally
     underrepresented groups.

   When you issue '\linebreak', the spaces in the line are stretched out
so that the break point reaches the right margin.  *Note \\:: and *note
\newline::, to have the spaces not stretched out.

10 Page breaking
****************

Ordinarily LaTeX automatically takes care of breaking output into pages
with its usual aplomb.  But if you are writing commands, or tweaking the
final version of a document, then you may need to understand how to
influence its actions.

   LaTeX's algorithm for splitting a document into pages is more complex
than just waiting until there is enough material to fill a page and
outputting the result.  Instead, LaTeX typesets more material than would
fit on the page and then chooses a break that is optimal in some way (it
has the smallest badness).  An example of the advantage of this approach
is that if the page has some vertical space that can be stretched or
shrunk, such as with rubber lengths between paragraphs, then LaTeX can
use that to avoid widow lines (where a new page starts with the last
line of a paragraph; LaTeX can squeeze the extra line onto the first
page) and orphans (where the first line of paragraph is at the end of a
page; LaTeX can stretch the material of the first page so the extra line
falls on the second page).  Another example is where LaTeX uses
available vertical shrinkage to fit on a page not just the header for a
new section but also the first two lines of that section.

   But LaTeX does not optimize over the entire document's set of page
breaks.  So it can happen that the first page break is great but the
second one is lousy; to break the current page LaTeX doesn't look as far
ahead as the next page break.  So occasionally you may want to influence
page breaks while preparing a final version of a document.

   *Note Layout::, for more material that is relevant to page breaking.

10.1 '\clearpage' & '\cleardoublepage'
======================================

Synopsis:

     \clearpage

or

     \cleardoublepage

   End the current page and output all of the pending floating figures
and tables (*note Floats::).  If there are too many floats to fit on the
page then LaTeX will put in extra pages containing only floats.  In
two-sided printing, '\cleardoublepage' also makes the next page of
content a right-hand page, an odd-numbered page, if necessary inserting
a blank page.  The '\clearpage' command is robust while
'\cleardoublepage' is fragile (*note \protect::).

   LaTeX's page breaks are optimized so ordinarily you only use this
command in a document body to polish the final version, or inside
commands.

   The '\cleardoublepage' command will put in a blank page, but it will
have the running headers and footers.  To get a really blank page, use
this command.

     \let\origdoublepage\cleardoublepage
     \newcommand{\clearemptydoublepage}{%
       \clearpage
       {\pagestyle{empty}\origdoublepage}%
     }

If you want LaTeX's standard '\chapter' command to do this then add the
line '\let\cleardoublepage\clearemptydoublepage'.

   The command '\newpage' (*note \newpage::) also ends the current page,
but without clearing pending floats.  And, if LaTeX is in two-column
mode then '\newpage' ends the current column while '\clearpage' and
'\cleardoublepage' end the current page.

10.2 '\newpage'
===============

Synopsis:

     \newpage

   End the current page.  This command is robust (*note \protect::).

   LaTeX's page breaks are optimized so ordinarily you only use this
command in a document body to polish the final version, or inside
commands.

   While the commands '\clearpage' and '\cleardoublepage' also end the
current page, in addition they clear pending floats (*note \clearpage &
\cleardoublepage::).  And, if LaTeX is in two-column mode then
'\clearpage' and '\cleardoublepage' end the current page, possibly
leaving an empty column, while '\newpage' only ends the current column.

   In contrast with '\pagebreak' (*note \pagebreak & \nopagebreak::),
the '\newpage' command will cause the new page to start right where
requested.  This

     Four score and seven years ago our fathers brought forth on this
     continent,
     \newpage
     \noindent a new nation, conceived in Liberty, and dedicated to the
     proposition that all men are created equal.

makes a new page start after 'continent', and the cut-off line is not
right justified.  In addition, '\newpage' does not vertically stretch
out the page, as '\pagebreak' does.

10.3 '\enlargethispage'
=======================

Synopsis, one of:

     \enlargethispage{size}
     \enlargethispage*{size}

   Enlarge the '\textheight' for the current page.  The required
argument SIZE must be a rigid length (*note Lengths::).  It may be
positive or negative.  This command is fragile (*note \protect::).

   A common strategy is to wait until you have the final text of a
document, and then pass through it tweaking line and page breaks.  This
command allows you some page size leeway.

   This will allow one extra line on the current page.

     \enlargethispage{\baselineskip}

   The starred form '\enlargesthispage*' tries to squeeze the material
together on the page as much as possible, for the common use case of
getting one more line on the page.  This is often used together with an
explicit '\pagebreak'.

10.4 '\pagebreak' & '\nopagebreak'
==================================

Synopses:

     \pagebreak
     \pagebreak[ZERO-TO-FOUR]

or

     \nopagebreak
     \nopagebreak[ZERO-TO-FOUR]

   Encourage or discourage a page break.  The optional ZERO-TO-FOUR is
an integer that allows you to soften the request.  The default is 4, so
that without the optional argument these commands entirely force or
prevent the break.  But for instance '\nopagebreak[1]' suggests to LaTeX
that another spot might be preferable.  The higher the number, the more
insistent the request.  Both commands are fragile (*note \protect::).

   LaTeX's page endings are optimized so ordinarily you only use this
command in a document body to polish the final version, or inside
commands.

   If you use these inside a paragraph, they apply to the point
following the line in which they appear.  So this

     Four score and seven years ago our fathers brought forth on this
     continent,
     \pagebreak
     a new nation, conceived in Liberty, and dedicated to the proposition
     that all men are created equal.

does not give a page break at 'continent', but instead at 'nation',
since that is where LaTeX breaks that line.  In addition, with
'\pagebreak' the vertical space on the page is stretched out where
possible so that it extends to the normal bottom margin.  This can look
strange, and if '\flushbottom' is in effect this can cause you to get
'Underfull \vbox (badness 10000) has occurred while \output is active'.
*Note \newpage::, for a command that does not have these effects.

   (There is an obsolete declaration '\samepage', which tries to only
allow a break between two paragraphs.  There is a related environment
'samepage', also obsolete.  Neither of these work reliably.  For more on
keeping material on the same page, see the FAQ entry
<https://texfaq.org/FAQ-nopagebrk>.)

11 Footnotes
************

Place a footnote at the bottom of the current page, as here.

     Noël Coward quipped that having to read a footnote is like having
     to go downstairs to answer the door, while in the midst of making
     love.\footnote{%
       I wouldn't know, I don't read footnotes.}

   You can put multiple footnotes on a page.  If the footnote text
becomes too long then it will flow to the next page.

   You can also produce footnotes by combining the '\footnotemark' and
the '\footnotetext' commands, which is useful in special circumstances.

   To make bibliographic references come out as footnotes you need to
include a bibliographic style with that behavior (*note Using BibTeX::).

11.1 '\footnote'
================

Synopsis, one of:

     \footnote{TEXT}
     \footnote[NUMBER]{TEXT}

   Place a footnote TEXT at the bottom of the current page.

     There are over a thousand footnotes in Gibbon's
     \textit{Decline and Fall of the Roman Empire}.\footnote{%
       After reading an early version with endnotes David Hume complained,
       ``One is also plagued with his Notes, according to the present Method
       of printing the Book'' and suggested that they ``only to be printed
       at the Margin or the Bottom of the Page.''}

   The optional argument NUMBER allows you to specify the number of the
footnote.  If you use this then LaTeX does not increment the 'footnote'
counter.

   By default, LaTeX uses arabic numbers as footnote markers.  Change
this with something like
'\renewcommand{\thefootnote}{\fnsymbol{footnote}}', which uses a
sequence of symbols (*note \alph \Alph \arabic \roman \Roman
\fnsymbol::).  To make this change global put that in the preamble.  If
you make the change local then you may want to reset the counter with
'\setcounter{footnote}{0}'.

   LaTeX determines the spacing of footnotes with two parameters.

'\footnoterule'
     Produces the rule separating the main text on a page from the
     page's footnotes.  Default dimensions in the standard document
     classes (except 'slides', where it does not appear) is: vertical
     thickness of '0.4pt', and horizontal size of '0.4\columnwidth'
     long.  Change the rule with something like this.

          \renewcommand{\footnoterule}{% Kerns avoid vertical space
            \kern -3pt                         % This -3 is negative
            \hrule width \textwidth height 1pt % of the sum of this 1
            \kern 2pt}                         % and this 2

'\footnotesep'
     The height of the strut placed at the beginning of the footnote
     (*note \strut::).  By default, this is set to the normal strut for
     '\footnotesize' fonts (*note Font sizes::), therefore there is no
     extra space between footnotes.  This is '6.65pt' for '10pt',
     '7.7pt' for '11pt', and '8.4pt' for '12pt'.  Change it as with
     '\setlength{\footnotesep}{11pt}'.

   The '\footnote' command is fragile (*note \protect::).

   LaTeX's default puts many restrictions on where you can use a
'\footnote'; for instance, you cannot use it in an argument to a
sectioning command such as '\chapter' (it can only be used in outer
paragraph mode; *note Modes::).  There are some workarounds; see
following sections.

   In a 'minipage' environment the '\footnote' command uses the
'mpfootnote' counter instead of the 'footnote' counter, so they are
numbered independently.  They are shown at the bottom of the
environment, not at the bottom of the page.  And by default they are
shown alphabetically.  *Note minipage:: and *note Footnotes in a
table::.

11.2 '\footnotemark'
====================

Synopsis, one of:

     \footnotemark
     \footnotemark[NUMBER]

   Put the current footnote mark in the text.  To specify associated
text for the footnote see *note \footnotetext::.  The optional argument
NUMBER causes the command to use that number to determine the footnote
mark.  This command can be used in inner paragraph mode (*note Modes::).

   If you use '\footnotemark' without the optional argument then it
increments the 'footnote' counter, but if you use the optional NUMBER
then it does not.  The next example produces several consecutive
footnote markers referring to the same footnote.

     The first theorem\footnote{Due to Gauss.}
     and the second theorem\footnotemark[\value{footnote}]
     and the third theorem.\footnotemark[\value{footnote}]

   If there are intervening footnotes then you must remember the value
of the number of the common mark.  This example gives the same
institutional affiliation to both the first and third authors ('\thanks'
is a version of '\footnote'), by-hand giving the number of the footnote.

     \title{A Treatise on the Binomial Theorem}
     \author{J Moriarty\thanks{University of Leeds}
       \and A C Doyle\thanks{Durham University}
       \and S Holmes\footnotemark[1]}
     \begin{document}
     \maketitle

   This uses a counter to remember the footnote number.  The third
sentence is followed by the same footnote marker as the first.

     \newcounter{footnoteValueSaver}
     All babies are illogical.\footnote{%
       Lewis Carroll.}\setcounter{footnoteValueSaver}{\value{footnote}}
     Nobody is despised who can manage a crocodile.\footnote{%
       Captain Hook.}
     Illogical persons are despised.\footnotemark[\value{footnoteValueSaver}]
     Therefore, anyone who can manage a crocodile is not a baby.

   This example accomplishes the same by using the package 'cleveref'.

     \usepackage{cleveref}[2012/02/15]   % in preamble
     \crefformat{footnote}{#2\footnotemark[#1]#3}
     ...
     The theorem is from Evers.\footnote{\label{fn:TE}Tinker, Evers, 1994.}
     The corollary is from Chance.\footnote{Evers, Chance, 1990.}
     But the key lemma is from Tinker.\cref{fn:TE}

   It will work with the package 'hyperref'.

11.3 '\footnotetext'
====================

Synopsis, one of:

     \footnotetext{TEXT}
     \footnotetext[NUMBER]{TEXT}

   Place TEXT at the bottom of the page as a footnote.  It pairs with
'\footnotemark' (*note \footnotemark::) and can come anywhere after that
command, but must appear in outer paragraph mode (*note Modes::).  The
optional argument NUMBER changes the number of the footnote mark.

   *Note \footnotemark:: and *note Footnotes in a table::, for usage
examples.

11.4 Footnotes in section headings
==================================

Putting a footnote in a section heading, as in:

     \section{Full sets\protect\footnote{This material due to ...}}

causes the footnote to appear at the bottom of the page where the
section starts, as usual, but also at the bottom of the table of
contents, where it is not likely to be desired.  The simplest way to
have it not appear on the table of contents is to use the optional
argument to '\section'

     \section[Please]{Please\footnote{%
       Don't footnote in chapter and section headers!}}

No '\protect' is needed in front of '\footnote' here because what gets
moved to the table of contents is the optional argument.

11.5 Footnotes in a table
=========================

Inside a 'tabular' or 'array' environment the '\footnote' command does
not work; there is a footnote mark in the table cell but the footnote
text does not appear.  The solution is to use a 'minipage' environment
as here (*note minipage::).

     \begin{center}
       \begin{minipage}{\textwidth} \centering
          \begin{tabular}{l|l}
            \textsc{Ship}           &\textsc{Book} \\ \hline
            \textit{HMS Sophie}     &Master and Commander  \\
            \textit{HMS Polychrest} &Post Captain  \\
            \textit{HMS Lively}     &Post Captain \\
            \textit{HMS Surprise}   &A number of books\footnote{%
                                       Starting with \textit{HMS Surprise}.}
          \end{tabular}
       \end{minipage}
     \end{center}

   Inside a 'minipage', footnote marks are lowercase letters.  Change
that with something like
'\renewcommand{\thempfootnote}{\arabic{mpfootnote}}' (*note \alph \Alph
\arabic \roman \Roman \fnsymbol::).

   The footnotes in the prior example appear at the bottom of the
'minipage'.  To have them appear at the bottom of the main page, as part
of the regular footnote sequence, use the '\footnotemark' and
'\footnotetext' pair and make a new counter.

     \newcounter{mpFootnoteValueSaver}
     \begin{center}
       \begin{minipage}{\textwidth}
         \setcounter{mpFootnoteValueSaver}{\value{footnote}} \centering
          \begin{tabular}{l|l}
            \textsc{Woman}             &\textsc{Relationship} \\ \hline
            Mona                       &Attached\footnotemark  \\
            Diana Villiers             &Eventual wife  \\
            Christine Hatherleigh Wood &Fiance\footnotemark
          \end{tabular}
       \end{minipage}%  percent sign keeps footnote text close to minipage
       \stepcounter{mpFootnoteValueSaver}%
         \footnotetext[\value{mpFootnoteValueSaver}]{%
           Little is known other than her death.}%
       \stepcounter{mpFootnoteValueSaver}%
         \footnotetext[\value{mpFootnoteValueSaver}]{%
           Relationship is unresolved in XXI.}
     \end{center}

   For a floating 'table' environment (*note table::), use the
'tablefootnote' package.

     \usepackage{tablefootnote}  % in preamble
        ...
     \begin{table}
       \centering
          \begin{tabular}{l|l}
          \textsc{Date}  &\textsc{Campaign} \\ \hline
          1862           &Fort Donelson \\
          1863           &Vicksburg     \\
          1865           &Army of Northern Virginia\tablefootnote{%
                           Ending the war.}
          \end{tabular}
         \caption{Forces captured by US Grant}
     \end{table}

The footnote appears at the page bottom and is numbered in sequence with
other footnotes.

11.6 Footnotes of footnotes
===========================

Particularly in the humanities, authors can have multiple classes of
footnotes, including having footnotes of footnotes.  The package
'bigfoot' extends LaTeX's default footnote mechanism in many ways,
including allow these two, as in this example.

     \usepackage{bigfoot}    % in preamble
     \DeclareNewFootnote{Default}
     \DeclareNewFootnote{from}[alph]   % create class \footnotefrom{}
      ...
     The third theorem is a partial converse of the
     second.\footnotefrom{%
       Noted in Wilson.\footnote{Second edition only.}}

12 Definitions
**************

LaTeX has support for making new commands of many different kinds.

12.1 '\newcommand' & '\renewcommand'
====================================

Synopses, one of:

     \newcommand{\CMD}{DEFN}
     \newcommand{\CMD}[NARGS]{DEFN}
     \newcommand{\CMD}[NARGS][OPTARGDEFAULT]{DEFN}
     \newcommand*{\CMD}{DEFN}
     \newcommand*{\CMD}[NARGS]{DEFN}
     \newcommand*{\CMD}[NARGS][OPTARGDEFAULT]{DEFN}

or one of these.

     \renewcommand{\CMD}[NARGS]{DEFN}
     \renewcommand{\CMD}[NARGS]{DEFN}
     \renewcommand{\CMD}[NARGS][OPTARGDEFAULT]{DEFN}
     \renewcommand*{\CMD}{DEFN}
     \renewcommand*{\CMD}[NARGS]{DEFN}
     \renewcommand*{\CMD}[NARGS][OPTARGDEFAULT]{DEFN}

   Define or redefine a command (see also the discussion of
'\DeclareRobustCommand' in *note Class and package commands::).

   The starred form of these two forbids the arguments from containing
multiple paragraphs of text (in plain TeX terms, the commands are not
'\long').  With the default form, arguments can be multiple paragraphs.

   These are the parameters:

CMD

     Required; '\CMD' is the command name.  It must begin with a
     backslash, '\', and must not begin with the four character string
     '\end'.  For '\newcommand', it must not be already defined.  For
     '\renewcommand', this name must already be defined.

NARGS
     Optional; an integer from 0 to 9, specifying the number of
     arguments that the command takes, including any optional argument.
     Omitting this argument is the same as specifying 0, meaning that
     the command has no arguments.  If you redefine a command, the new
     version can have a different number of arguments than the old
     version.

OPTARGDEFAULT
     Optional; if this argument is present then the first argument of
     '\CMD' is optional, with default value OPTARGDEFAULT (which may be
     the empty string).  If OPTARGSDEFAULT is not present then '\CMD'
     does not take an optional argument.

     That is, if '\CMD' is used with square brackets, as in
     '\CMD[OPTVAL]{...}...', then within DEFN the parameter '#1' is set
     to the value of OPTVAL.  On the other hand, if '\CMD' is called
     without the square brackets then within DEFN the parameter '#1' is
     set to the value of OPTARGDEFAULT.  In either case, the required
     arguments start with '#2'.

     Omitting '[OPTARGDEFAULT]' is different from having the square
     brackets with no contents, as in '[]'.  The former sets '#1' to the
     value of OPTARGDEFAULT; the latter sets '#1' to the empty string.

DEFN
     Required; the text to be substituted for every occurrence of
     '\CMD'.  The parameters '#1', '#2', ...  '#NARGS' are replaced by
     the values that you supply when you call the command (or by the
     default value if there is an optional argument and you don't
     exercise the option).

   TeX ignores blanks in the source following a control word (*note
Control sequences::), as in '\cmd '.  If you actually want a space
there, one solution is to type '{}' after the command ('\cmd{} ', and
another solution is to use an explicit control space ('\cmd\ ').

   A simple example of defining a new command: '\newcommand{\RS}{Robin
Smith}' results in '\RS' being replaced by the longer text.  Redefining
an existing command is similar: '\renewcommand{\qedsymbol}{{\small
QED}}'.

   If you try to define a command and the name has already been used
then you get something like 'LaTeX Error: Command \fred already defined.
Or name \end... illegal, see p.192 of the manual'.  If you try to
redefine a command and the name has not yet been used then you get
something like 'LaTeX Error: \hank undefined'.

   Here the first definition creates a command with no arguments, and
the second, one with one required argument.

     \newcommand{\student}{Ms~O'Leary}
     \newcommand{\defref}[1]{Definition~\ref{#1}}

Use the first as in 'I highly recommend \student{} to you'.  The second
has a variable argument, so that '\defref{def:basis}' expands to
'Definition~\ref{def:basis}', which ultimately expands to something like
'Definition~3.14'.

   Similarly, but with two required arguments:
'\newcommand{\nbym}[2]{$#1 \times #2$}' is invoked as '\nbym{2}{k}'.

   This example has an optional argument.

     \newcommand{\salutation}[1][Sir or Madam]{Dear #1:}

Then '\salutation' gives 'Dear Sir or Madam:' while '\salutation[John]'
gives 'Dear John:'.  And '\salutation[]' gives 'Dear :'.

   This example has an optional argument and two required arguments.

     \newcommand{\lawyers}[3][company]{#2, #3, and~#1}
     I employ \lawyers[Howe]{Dewey}{Cheatem}.

The output is 'I employ Dewey, Cheatem, and Howe'.  The optional
argument, the 'Howe', is associated with '#1', while 'Dewey' and
'Cheatem' are associated with '#2' and '#3'.  Because of the optional
argument, '\lawyers{Dewey}{Cheatem}' will give the output 'I employ
Dewey, Cheatem, and company'.

   The braces around DEFN do not define a group, that is, they do not
delimit the scope of the result of expanding DEFN.  For example, with
'\newcommand{\shipname}[1]{\it #1}', in this sentence,

     The \shipname{Monitor} met the \shipname{Merrimac}.

the words 'met the' would incorrectly be in italics.  The solution is to
put another pair of braces inside the definition:
'\newcommand{\shipname}[1]{{\it #1}}'.

12.1.1 Control sequence, control word and control symbol
--------------------------------------------------------

When reading input TeX converts the sequences of read characters into a
sequence of "tokens".  When TeX sees a backslash '\', it will handle the
following characters in a special way in order to make a "control
sequence" token.

   The control sequences fall into two categories:

   * "control word", when the control sequence is gathered from a '\'
     followed by at least one ASCII letter, followed by at least one
     blank.  The sequence of at least one ASCII letter is called the
     "control sequence name".
   * "control symbol", when the control sequence is gathered from a '\'
     followed by one non-letter character.

   Blanks after a control word are ignored and do not produce any
whitespace in the output (*note \newcommand & \renewcommand:: and *note
\(SPACE)::).

   Just as the '\relax' command does nothing, the following will print
'Hello!'--if you use the Emacs info viewer, turn on the whitespace-mode
minor mode to see the trailing spaces:

     Hel\relax   
        lo!

This is because blanks after '\relax', including the newline are
ignored, and blanks at the beginning of a line are also ignored (*note
Leading blanks::).

12.2 '\providecommand'
======================

Synopses, one of:

     \providecommand{\CMD}{DEFN}
     \providecommand{\CMD}[NARGS]{DEFN}
     \providecommand{\CMD}[NARGS][OPTARGDEFAULT]{DEFN}
     \providecommand*{\CMD}{DEFN}
     \providecommand*{\CMD}[NARGS]{DEFN}
     \providecommand*{\CMD}[NARGS][OPTARGDEFAULT]{DEFN}

   Defines a command, as long as no command of this name already exists.
If no command of this name already exists then this has the same effect
as '\newcommand'.  If a command of this name already exists then this
definition does nothing.  This is particularly useful in a file that may
be loaded more than once, such as a style file.  *Note \newcommand &
\renewcommand::, for the description of the arguments.

   This example

     \providecommand{\myaffiliation}{Saint Michael's College}
     \providecommand{\myaffiliation}{Lyc\'ee Henri IV}
     From \myaffiliation.

outputs 'From Saint Michael's College'.  Unlike '\newcommand', the
repeated use of '\providecommand' does not give an error.

12.3 '\makeatletter' & '\makeatother'
=====================================

Synopsis:

     \makeatletter
       ... definition of commands with @ in their name ..
     \makeatother

   Use this pair when you redefine LaTeX commands that are named with an
at-sign character ''@''.  The '\makeatletter' declaration makes the
at-sign character have the category code of a letter, code 11.  The
'\makeatother' declaration sets the category code of the at-sign to
code 12, its default value.

   As TeX reads characters, it assigns each one a category code, or
"catcode".  For instance, it assigns the backslash character ''\'' the
catcode 0.  Command names consist of a category 0 character, ordinarily
backslash, followed by letters, category 11 characters (except that a
command name can also consist of a category 0 character followed by a
single non-letter symbol).

   LaTeX's source code has the convention that some commands use '@' in
their name.  These commands are mainly intended for package or class
writers.  The convention prevents authors who are just using a package
or class from accidentally replacing such a command with one of their
own, because by default the at-sign has catcode 12.

   Use the pair '\makeatletter' and '\makeatother' inside a '.tex' file,
typically in the preamble, when you are defining or redefining commands
named with '@', by having them surround your definition.  Don't use
these inside '.sty' or '.cls' files since the '\usepackage' and
'\documentclass' commands already arrange that the at-sign has the
character code of a letter, catcode 11.

   For a comprehensive list of macros with an at-sign in their names see
<https://ctan.org/pkg/macros2e>.

   In this example the class file has a command '\thesis@universityname'
that the user wants to change.  These three lines should go in the
preamble, before the '\begin{document}'.

     \makeatletter
     \renewcommand{\thesis@universityname}{Saint Michael's College}
     \makeatother

12.4 '\@ifstar'
===============

Synopsis:

     \newcommand{\mycmd}{\@ifstar{\mycmd@star}{\mycmd@nostar}}
     \newcommand{\mycmd@nostar}[NOSTAR-NUM-ARGS]{NOSTAR-BODY}
     \newcommand{\mycmd@star}[STAR-NUM-ARGS]{STAR-BODY}

   Many standard LaTeX environments or commands have a variant with the
same name but ending with a star character '*', an asterisk.  Examples
are the 'table' and 'table*' environments and the '\section' and
'\section*' commands.

   When defining environments, following this pattern is straightforward
because '\newenvironment' and '\renewenvironment' allow the environment
name to contain a star.  So you just have to write
'\newenvironment{MYENV}' or '\newenvironment{MYENV*}' and continue the
definition as usual.  For commands the situation is more complex as the
star not being a letter cannot be part of the command name.  As in the
synopsis above, there will be a user-called command, given above as
'\mycmd', which peeks ahead to see if it is followed by a star.  For
instance, LaTeX does not really have a '\section*' command; instead, the
'\section' command peeks ahead.  This command does not accept arguments
but instead expands to one of two commands that do accept arguments.  In
the synopsis these two are '\mycmd@nostar' and '\mycmd@star'.  They
could take the same number of arguments or a different number, or no
arguments at all.  As always, in a LaTeX document a command using an
at-sign '@' in its name must be enclosed inside a '\makeatletter ...
\makeatother' block (*note \makeatletter & \makeatother::).

   This example of '\@ifstar' defines the command '\ciel' and a variant
'\ciel*'.  Both have one required argument.  A call to '\ciel{blue}'
will return "not starry blue sky" while '\ciel*{night}' will return
"starry night sky".

     \makeatletter
     \newcommand*{\ciel@unstarred}[1]{not starry #1 sky}
     \newcommand*{\ciel@starred}[1]{starry #1 sky}
     \newcommand*{\ciel}{\@ifstar{\ciel@starred}{\ciel@unstarred}}
     \makeatother

   In the next example, the starred variant takes a different number of
arguments than the unstarred one.  With this definition, Agent 007's
'``My name is \agentsecret*{Bond}, \agentsecret{James}{Bond}.''' is
equivalent to entering the commands '``My name is \textsc{Bond},
\textit{James} textsc{Bond}.'''

     \newcommand*{\agentsecret@unstarred}[2]{\textit{#1} \textsc{#2}}
     \newcommand*{\agentsecret@starred}[1]{\textsc{#1}}
     \newcommand*{\agentsecret}{%
       \@ifstar{\agentsecret@starred}{\agentsecret@unstarred}}

   After a command name, a star is handled similarly to an optional
argument.  (This differs from environment names in which the star is
part of the name itself and as such could be in any position.)  Thus, it
is technically possible to put any number of spaces between the command
and the star.  Thus '\agentsecret*{Bond}' and '\agentsecret *{Bond}' are
equivalent.  However, the standard practice is not to insert any such
spaces.

   There are two alternative ways to accomplish the work of '\@ifstar'.
(1) The 'suffix' package allows the construct
'\newcommand\mycommand{UNSTARRED-VARIANT}' followed by
'\WithSuffix\newcommand\mycommand*{STARRED-VARIANT}'.  (2) LaTeX
provides the 'xparse' package, which allows this code:

     \NewDocumentCommand\foo{s}{\IfBooleanTF#1
       {STARRED-VARIANT}%
       {UNSTARRED-VARIANT}%
       }

12.5 '\newcounter': Allocating a counter
========================================

Synopsis, one of:

     \newcounter{COUNTERNAME}
     \newcounter{COUNTERNAME}[SUPERCOUNTER]

   Globally defines a new counter named COUNTERNAME and initialize it to
zero (*note Counters::).

   The name COUNTERNAME must consist of letters only.  It does not begin
with a backslash.  This name must not already be in use by another
counter.

   When you use the optional argument '[SUPERCOUNTER]' then the counter
COUNTERNAME will be reset to zero whenever SUPERCOUNTER is incremented.
For example, ordinarily 'subsection' is numbered within 'section' so
that any time you increment SECTION, either with '\stepcounter' (*note
\stepcounter::) or '\refstepcounter' (*note \refstepcounter::), then
LaTeX will reset SUBSECTION to zero.

   This example

     \newcounter{asuper}  \setcounter{asuper}{1}
     \newcounter{asub}[asuper] \setcounter{asub}{3}   % Note `asuper'
     The value of asuper is \arabic{asuper} and of asub is \arabic{asub}.
     \stepcounter{asuper}
     Now asuper is \arabic{asuper} while asub is \arabic{asub}.

   produces 'The value of asuper is 1 and that of asub is 3' and 'Now
asuper is 2 while asub is 0'.

   If the counter already exists, for instance by entering 'asuper'
twice, then you get something like 'LaTeX Error: Command \c@asuper
already defined. Or name \end... illegal, see p.192 of the manual.'.

   If you use the optional argument then the super counter must already
exist.  Entering '\newcounter{jh}[lh]' when 'lh' is not a defined
counter will get you 'LaTeX Error: No counter 'lh' defined.'

12.6 '\newlength'
=================

Synopsis:

     \newlength{\LEN}

   Allocate a new length register (*note Lengths::).  The required
argument '\LEN' has to be a control sequence (*note Control
sequences::), and as such must begin with a backslash, '\' under normal
circumstances.  The new register holds rubber lengths such as '72.27pt'
or '1in plus.2in minus.1in' (a LaTeX length register is what plain TeX
calls a 'skip' register).  The initial value is zero.  The control
sequence '\LEN' must not be already defined.

   An example:

     \newlength{\graphichgt}

   If you forget the backslash then you get 'Missing control sequence
inserted'.  If the control sequence already exists then you get
something like 'LaTeX Error: Command \graphichgt already defined. Or
name \end... illegal, see p.192 of the manual'.

12.7 '\newsavebox'
==================

Synopsis:

     \newsavebox{\CMD}

   Define \CMD, the string consisting of a backslash followed by CMD, to
refer to a new bin for storing material.  These bins hold material that
has been typeset, to use multiple times or to measure or manipulate
(*note Boxes::).  The bin name \CMD is required, must start with a
backslash, \, and must not already be a defined command.  This command
is fragile (*note \protect::).

   This allocates a bin and then puts typeset material into it.

     \newsavebox{\logobox}
     \savebox{\logobox}{LoGo}
     Our logo is \usebox{\logobox}.

The output is 'Our logo is LoGo'.

   If there is an already defined bin then you get something like 'LaTeX
Error: Command \logobox already defined. Or name \end... illegal, see
p.192 of the manual'.

   The allocation of a box is global.

12.8 '\newenvironment' & '\renewenvironment'
============================================

Synopses, one of:

     \newenvironment{ENV}{BEGDEF}{ENDDEF}
     \newenvironment{ENV}[NARGS]{BEGDEF}{ENDDEF}
     \newenvironment{ENV}[NARGS][OPTARGDEFAULT]{BEGDEF}{ENDDEF}
     \newenvironment*{ENV}{BEGDEF}{ENDDEF}
     \newenvironment*{ENV}[NARGS]{BEGDEF}{ENDDEF}
     \newenvironment*{ENV}[NARGS][OPTARGDEFAULT]{BEGDEF}{ENDDEF}

or one of these.

     \renewenvironment{ENV}{BEGDEF}{ENDDEF}
     \renewenvironment{ENV}[NARGS]{BEGDEF}{ENDDEF}
     \renewenvironment{ENV}[NARGS][OPTARGDEFAULT]{BEGDEF}{ENDDEF}
     \renewenvironment*{ENV}{BEGDEF}{ENDDEF}
     \renewenvironment*{ENV}[NARGS]{BEGDEF}{ENDDEF}
     \renewenvironment*{ENV}[NARGS][OPTARGDEFAULT]{BEGDEF}{ENDDEF}

   Define or redefine the environment ENV, that is, create the construct
'\begin{ENV} ... BODY ... \end{ENV}'.

   The starred form of these commands requires that the arguments not
contain multiple paragraphs of text.  However, the body of these
environments can contain multiple paragraphs.

ENV
     Required; the environment name.  It consists only of letters or the
     '*' character, and thus does not begin with backslash, '\'.  It
     must not begin with the string 'end'.  For '\newenvironment', the
     name ENV must not be the name of an already existing environment,
     and also the command '\ENV' must be undefined.  For
     '\renewenvironment', ENV must be the name of an existing
     environment.

NARGS
     Optional; an integer from 0 to 9 denoting the number of arguments
     of that the environment takes.  When you use the environment these
     arguments appear after the '\begin', as in '\begin{ENV}{ARG1} ...
     {ARGN}'.  Omitting this is equivalent to setting it to 0; the
     environment will have no arguments.  When redefining an
     environment, the new version can have a different number of
     arguments than the old version.

OPTARGDEFAULT
     Optional; if this is present then the first argument of the defined
     environment is optional, with default value OPTARGDEFAULT (which
     may be the empty string).  If this is not in the definition then
     the environment does not take an optional argument.

     That is, when OPTARGDEFAULT is present in the definition of the
     environment then you can start the environment with square
     brackets, as in '\begin{ENV}[OPTVAL]{...} ... \end{ENV}'.  In this
     case, within BEGDEFN the parameter '#1' is set to the value of
     OPTVAL.  If you call '\begin{ENV}' without square brackets, then
     within BEGDEFN the parameter '#1' is set to the value of the
     default OPTARGDEFAULT.  In either case, any required arguments
     start with '#2'.

     Omitting '[MYVAL]' in the call is different than having the square
     brackets with no contents, as in '[]'.  The former results in '#1'
     expanding to OPTARGDEFAULT; the latter results in '#1' expanding to
     the empty string.

BEGDEF
     Required; the text expanded at every occurrence of '\begin{ENV}'.
     Within BEGDEF, the parameters '#1', '#2', ...  '#NARGS', are
     replaced by the values that you supply when you call the
     environment; see the examples below.

ENDDEF
     Required; the text expanded at every occurrence of '\end{ENV}'.
     This may not contain any parameters, that is, you cannot use '#1',
     '#2', etc., here (but see the final example below).

   All environments, that is to say the BEGDEF code, the environment
body, and the ENDDEF code, are processed within a group.  Thus, in the
first example below, the effect of the '\small' is limited to the quote
and does not extend to material following the environment.

   If you try to define an environment and the name has already been
used then you get something like 'LaTeX Error: Command \fred already
defined. Or name \end... illegal, see p.192 of the manual'.  If you try
to redefine an environment and the name has not yet been used then you
get something like 'LaTeX Error: Environment hank undefined.'.

   This example gives an environment like LaTeX's 'quotation' except
that it will be set in smaller type.

     \newenvironment{smallquote}{%
       \small\begin{quotation}
     }{%
       \end{quotation}
     }

   This has an argument, which is set in boldface at the start of a
paragraph.

     \newenvironment{point}[1]{%
       \noindent\textbf{#1}
     }{%
     }

   This one shows the use of a optional argument; it gives a quotation
environment that cites the author.

     \newenvironment{citequote}[1][Shakespeare]{%
       \begin{quotation}
       \noindent\textit{#1}:
     }{%
       \end{quotation}
     }

The author's name is optional, and defaults to 'Shakespeare'.  In the
document, use the environment like this.

     \begin{citequote}[Lincoln]
       ...
     \end{citequote}

   The final example shows how to save the value of an argument to use
in ENDDEF, in this case in a box (*note \sbox & \savebox::).

     \newsavebox{\quoteauthor}
     \newenvironment{citequote}[1][Shakespeare]{%
       \sbox\quoteauthor{#1}%
       \begin{quotation}
     }{%
       \hspace{1em plus 1fill}---\usebox{\quoteauthor}
       \end{quotation}
     }

12.9 '\newtheorem'
==================

Synopses:

     \newtheorem{NAME}{TITLE}
     \newtheorem{NAME}{TITLE}[NUMBERED_WITHIN]
     \newtheorem{NAME}[NUMBERED_LIKE]{TITLE}

   Define a new theorem-like environment.  You can specify one of
NUMBERED_WITHIN and NUMBERED_LIKE, or neither, but not both.

   The first form, '\newtheorem{NAME}{TITLE}', creates an environment
that will be labelled with TITLE; see the first example below.

   The second form, '\newtheorem{NAME}{TITLE}[NUMBERED_WITHIN]', creates
an environment whose counter is subordinate to the existing counter
NUMBERED_WITHIN, so this counter will be reset when NUMBERED_WITHIN is
reset.  See the second example below.

   The third form '\newtheorem{NAME}[NUMBERED_LIKE]{TITLE}', with
optional argument between the two required arguments, creates an
environment whose counter will share the previously defined counter
NUMBERED_LIKE.  See the third example.

   This command creates a counter named NAME.  In addition, unless the
optional argument NUMBERED_LIKE is used, inside of the theorem-like
environment the current '\ref' value will be that of
'\theNUMBERED_WITHIN' (*note \ref::).

   This declaration is global.  It is fragile (*note \protect::).

   Arguments:

NAME
     The name of the environment.  It is a string of letters.  It must
     not begin with a backslash, '\'.  It must not be the name of an
     existing environment, and the command name '\NAME' must not already
     be defined.

TITLE
     The text to be printed at the beginning of the environment, before
     the number.  For example, 'Theorem'.

NUMBERED_WITHIN
     Optional; the name of an already defined counter, usually a
     sectional unit such as 'chapter' or 'section'.  When the
     NUMBERED_WITHIN counter is reset then the NAME environment's
     counter will also be reset.

     If this optional argument is not used then the command '\theNAME'
     is set to '\arabic{NAME}'.

NUMBERED_LIKE
     Optional; the name of an already defined theorem-like environment.
     The new environment will be numbered in sequence with
     NUMBERED_LIKE.

   Without any optional arguments the environments are numbered
sequentially.  The example below has a declaration in the preamble that
results in 'Definition 1' and 'Definition 2' in the output.

     \newtheorem{defn}{Definition}
     \begin{document}
     \section{...}
     \begin{defn}
       First def
     \end{defn}

     \section{...}
     \begin{defn}
       Second def
     \end{defn}

   This example has the same document body as the prior one.  But here
'\newtheorem''s optional argument NUMBERED_WITHIN is given as 'section',
so the output is like 'Definition 1.1' and 'Definition 2.1'.

     \newtheorem{defn}{Definition}[section]
     \begin{document}
     \section{...}
     \begin{defn}
       First def
     \end{defn}

     \section{...}
     \begin{defn}
       Second def
     \end{defn}

   In the next example there are two declarations in the preamble, the
second of which calls for the new 'thm' environment to use the same
counter as 'defn'.  It gives 'Definition 1.1', followed by 'Theorem 2.1'
and 'Definition 2.2'.

     \newtheorem{defn}{Definition}[section]
     \newtheorem{thm}[defn]{Theorem}
     \begin{document}
     \section{...}
     \begin{defn}
       First def
     \end{defn}

     \section{...}
     \begin{thm}
       First thm
     \end{thm}

     \begin{defn}
       Second def
     \end{defn}

12.10 '\newfont'
================

This command is obsolete.  This description is here only to help with
old documents.  New documents should define fonts in families through
the New Font Selection Scheme which allows you to, for example,
associate a boldface with a roman (*note Fonts::).

   Synopsis:

     \newfont{\CMD}{FONT DESCRIPTION}

   Define a command '\CMD' that will change the current font.  The
control sequence must not already be defined.  It must begin with a
backslash, '\'.

   The FONT DESCRIPTION consists of a FONTNAME and an optional "at
clause".  LaTeX will look on your system for a file named
'FONTNAME.tfm'.  The at clause can have the form either 'at DIMEN' or
'scaled FACTOR', where a FACTOR of '1000' means no scaling.  For LaTeX's
purposes, all this does is scale all the character and other font
dimensions relative to the font's design size, which is a value defined
in the '.tfm' file.

   This defines two equivalent fonts and typesets a few characters in
each.

     \newfont{\testfontat}{cmb10 at 11pt}
     \newfont{\testfontscaled}{cmb10 scaled 1100}
     \testfontat abc
     \testfontscaled abc

12.11 '\protect'
================

All LaTeX commands are either "fragile" or "robust".  A fragile command
can break when it is used in the argument to certain other commands.
Commands that contain data that LaTeX writes to an auxiliary file and
re-reads later are fragile.  This includes material that goes into a
table of contents, list of figures, list of tables, etc.  Fragile
commands also include line breaks, any command that has an optional
argument, and many more.  To prevent such commands from breaking, one
solution is to preceded them with the command '\protect'.

   For example, when LaTeX runs the '\section{SECTION NAME}' command it
writes the SECTION NAME text to the '.aux' auxiliary file, moving it
there for use elsewhere in the document such as in the table of
contents.  Any argument that is internally expanded by LaTeX without
typesetting it directly is referred to as a "moving argument".  A
command is fragile if it can expand during this process into invalid TeX
code.  Some examples of moving arguments are those that appear in the
'\caption{...}' command (*note figure::), in the '\thanks{...}' command
(*note \maketitle::), and in @-expressions in the 'tabular' and 'array'
environments (*note tabular::).

   If you get strange errors from commands used in moving arguments, try
preceding it with '\protect'.  Every fragile commands must be protected
with their own '\protect'.

   Although usually a '\protect' command doesn't hurt, length commands
are robust and should not be preceded by a '\protect' command.  Nor can
a '\protect' command be used in the argument to '\addtocounter' or
'\setcounter' command.

   In this example the '\caption' command gives a mysterious error about
an extra curly brace.  Fix the problem by preceding each '\raisebox'
command with '\protect'.

     \begin{figure}
       ...
       \caption{Company headquarters of A\raisebox{1pt}{B}\raisebox{-1pt}{C}}
     \end{figure}

   In the next example the '\tableofcontents' command gives an error
because the '\(..\)' in the section title expands to illegal TeX in the
'.toc' file.  You can solve this by changing '\(..\)' to
'\protect\(..\protect\)'.

     \begin{document}
     \tableofcontents
     ...
     \section{Einstein's \( e=mc^2 \)}
     ...

12.12 '\ignorespaces & \ignorespacesafterend'
=============================================

Synopsis:

     \ignorespaces

or

     \ignorespacesafterend

   Both commands cause LaTeX to ignore blanks (that is, characters of
catcode 10 such as space or tabulation) after the end of the command up
to the first box or non-blank character.  The first is a command from
plain TeX, and the second is LaTeX-specific.

   The '\ignorespaces' is often used when defining commands via
'\newcommand', or '\newenvironment', or '\def'.  The example below
illustrates.  It allows a user to show the points values for quiz
questions in the margin but it is inconvenient because, as shown in the
'enumerate' list, users must not put any space between the command and
the question text.

     \newcommand{\points}[1]{\makebox[0pt]{\makebox[10em][l]{#1~pts}}
     \begin{enumerate}
       \item\points{10}no extra space output here
       \item\points{15} extra space between the number and the `extra'
     \end{enumerate}

The solution is to change to this.

     \newcommand{\points}[1]{%
       \makebox[0pt]{\makebox[10em][l]{#1~pts}}\ignorespaces}

   A second example shows blanks being removed from the front of text.
The commands below allow a user to uniformly attach a title to names.
But, as given, if a title accidentally starts with a space then
'\fullname' will reproduce that.

     \newcommand{\honorific}[1]{\def\honorific{#1}} % remember title
     \newcommand{\fullname}[1]{\honorific~#1}       % put title before name

     \begin{tabular}{|l|}
     \honorific{Mr/Ms}  \fullname{Jones} \\  % no extra space here
     \honorific{ Mr/Ms} \fullname{Jones}     % extra space before title
     \end{tabular}

To fix this, change to
'\newcommand{\fullname}[1]{\ignorespaces\honorific~#1}'.

   The '\ignorespaces' is also often used in a '\newenvironment' at the
end of the BEGIN clause, as in '\begin{newenvironment}{ENV NAME}{...
\ignorespaces}{...}'.

   To strip blanks off the end of an environment use
'\ignorespacesafterend'.  An example is that this will show a much
larger vertical space between the first and second environments than
between the second and third.

     \newenvironment{eq}{\begin{equation}}{\end{equation}}
     \begin{eq}
     e=mc^2
     \end{eq}
     \begin{equation}
     F=ma
     \end{equation}
     \begin{equation}
     E=IR
     \end{equation}

   Putting a comment character '%' immediately after the '\end{eq}' will
make the vertical space disappear, but that is inconvenient.  The
solution is to change to
'\newenvironment{eq}{\begin{equation}}{\end{equation}\ignorespacesafterend}'.

12.13 xspace package
====================

Synopsis:

     \usepackage{xspace}
       ...
     \newcommand{...}{...\xspace}

   The '\xspace' macro, when used at the end of a command definition,
adds a space unless the command is followed by certain punctuation
characters.

   After a command control sequence that is a control word (*note
Control sequences::, as opposed to control symbols such as '\$'), TeX
gobbles blank characters.  Thus, in the first sentence below, the output
has 'Vermont' placed snugly against the period, without any intervening
space.

     \newcommand{\VT}{Vermont}
     Our college is in \VT .
     The \VT{} summers are nice.

   But because of the gobbling, the second sentence needs the empty
curly braces or else there would be no space separating 'Vermont' from
'summers'.  (Many authors instead use a backslash-space '\ ' for this.
*Note \(SPACE)::.)

   The 'xspace' package provides '\xspace'.  It is for writing commands
which are designed to be used mainly in text.  It must be place at the
very end of the definition of these commands.  It inserts a space after
that command unless what immediately follows is in a list of exceptions.
In this example, the empty braces are not needed.

     \newcommand{\VT}{Vermont\xspace}
     Our college is in \VT .
     \VT summers are nice.

   The default exception list contains the characters ',.'/?;:!~-)', the
open curly brace and the backslash-space command discussed above, and
the commands '\footnote' or '\footnotemark'.  Add to that list as with
'\xspaceaddexceptions{\myfni \myfnii}' which adds '\myfni' and '\myfnii'
to the list, and remove from that list as with
'\xspaceremoveexception{!}'.

   A comment: many experts prefer not to use '\xspace'.  Putting it in a
definition means that the command will usually get the spacing right.
But it isn't easy to predict when to enter empty braces because
'\xspace' will get it wrong, such as when it is followed by another
command, and so '\xspace' can make editing material harder and more
error-prone than instead always inserting the empty braces.

13 Counters
***********

Everything LaTeX numbers for you has a counter associated with it.  The
name of the counter is often the same as the name of the environment or
command associated with the number, except that the counter's name has
no backslash '\'.  Thus, associated with the '\chapter' command is the
'chapter' counter that keeps track of the chapter number.

   Below is a list of the counters used in LaTeX's standard document
classes to control numbering.

     part            paragraph       figure          enumi
     chapter         subparagraph    table           enumii
     section         page            footnote        enumiii
     subsection      equation        mpfootnote      enumiv
     subsubsection

   The 'mpfootnote' counter is used by the '\footnote' command inside of
a minipage (*note minipage::).  The counters 'enumi' through 'enumiv'
are used in the 'enumerate' environment, for up to four levels of
nesting (*note enumerate::).

   Counters can have any integer value but they are typically positive.

   New counters are created with '\newcounter'.  *Note \newcounter::.

13.1 '\alph \Alph \arabic \roman \Roman \fnsymbol': Printing counters
=====================================================================

Print the value of a counter, in a specified style.  For instance, if
the counter COUNTER has the value 1 then a '\alph{COUNTER}' in your
source will result in a lowercase letter a appearing in the output.

   All of these commands take a single counter as an argument, for
instance, '\alph{enumi}'.  Note that the counter name does not start
with a backslash.

'\alph{COUNTER}'
     Print the value of COUNTER in lowercase letters: 'a', 'b', ...  If
     the counter's value is less than 1 or more than 26 then you get
     'LaTeX Error: Counter too large.'

'\Alph{COUNTER}'
     Print in uppercase letters: 'A', 'B', ...  If the counter's value
     is less than 1 or more than 26 then you get 'LaTeX Error: Counter
     too large.'

'\arabic{COUNTER}'
     Print in Arabic numbers such as '5' or '-2'.

'\roman{COUNTER}'
     Print in lowercase roman numerals: 'i', 'ii', ...  If the counter's
     value is less than 1 then you get no warning or error but LaTeX
     does not print anything in the output.

'\Roman{COUNTER}'
     Print in uppercase roman numerals: 'I', 'II', ...  If the counter's
     value is less than 1 then you get no warning or error but LaTeX
     does not print anything in the output.

'\fnsymbol{COUNTER}'
     Prints the value of COUNTER using a sequence of nine symbols that
     are traditionally used for labeling footnotes.  The value of
     COUNTER should be between 1 and 9, inclusive.  If the counter's
     value is less than 0 or more than 9 then you get 'LaTeX Error:
     Counter too large', while if it is 0 then you get no error or
     warning but LaTeX does not output anything.

     Here are the symbols:

     Number   Name                   Command                Symbol
     -----------------------------------------------------------------------------
     1        asterisk               '\ast'                 *
     2        dagger                 '\dagger'              †
     3        ddagger                '\ddagger'             ‡
     4        section-sign           '\S'                   §
     5        paragraph-sign         '\P'                   ¶
     6        double-vert            '\parallel'            ‖
     7        double-asterisk        '\ast\ast'             **
     8        double-dagger          '\dagger\dagger'       ††
     9        double-ddagger         '\ddagger\ddagger'     ‡‡

13.2 '\usecounter'
==================

Synopsis:

     \usecounter{COUNTER}

   Used in the second argument of the 'list' environment (*note list::),
this declares that list items will be numbered by COUNTER.  It
initializes COUNTER to zero, and arranges that when '\item' is called
without its optional argument then COUNTER is incremented by
'\refstepcounter', making its value be the current 'ref' value (*note
\ref::).  This command is fragile (*note \protect::).

   Put in the document preamble, this example makes a new list
environment enumerated with TESTCOUNTER:

     \newcounter{testcounter}
     \newenvironment{test}{%
       \begin{list}{}{%
         \usecounter{testcounter}
       }
     }{%
       \end{list}
     }

13.3 '\value'
=============

Synopsis:

     \value{COUNTER}

   Expands to the value of the counter COUNTER.  (Note that the name of
a counter does not begin with a backslash.)

   This example outputs 'Test counter is 6. Other counter is 5.'.

     \newcounter{test} \setcounter{test}{5}
     \newcounter{other} \setcounter{other}{\value{test}}
     \addtocounter{test}{1}

     Test counter is \arabic{test}.
     Other counter is \arabic{other}.

   The '\value' command is not used for typesetting the value of the
counter.  For that, see *note \alph \Alph \arabic \roman \Roman
\fnsymbol::.

   It is often used in '\setcounter' or '\addtocounter' but '\value' can
be used anywhere that LaTeX expects a number, such as in
'\hspace{\value{foo}\parindent}'.  It must not be preceded by '\protect'
(*note \protect::).

   This example inserts '\hspace{4\parindent}'.

     \setcounter{myctr}{3} \addtocounter{myctr}{1}
     \hspace{\value{myctr}\parindent}

13.4 '\setcounter'
==================

Synopsis:

     \setcounter{COUNTER}{VALUE}

   Globally set the counter COUNTER to have the value of the VALUE
argument, which must be an integer.  Thus, you can set a counter's value
as '\setcounter{section}{5}'.  Note that the counter name does not start
with a backslash.

   In this example if the counter 'theorem' has value 12 then the second
line will print 'XII'.

     \setcounter{exercise}{\value{theorem}}
     Here it is in Roman: \Roman{exercise}.

13.5 '\addtocounter'
====================

Synopsis:

     \addtocounter{COUNTER}{VALUE}

   Globally increment COUNTER by the amount specified by the VALUE
argument, which may be negative.

   In this example the section value appears as 'VII'.

     \setcounter{section}{5}
     \addtocounter{section}{2}
     Here it is in Roman: \Roman{section}.

13.6 '\refstepcounter'
======================

Synopsis:

     \refstepcounter{COUNTER}

   Globally increments the value of COUNTER by one, as does
'\stepcounter' (*note \stepcounter::).  The difference is that this
command resets the value of any counter numbered within it.  (For the
definition of "counters numbered within", *note \newcounter::.)

   In addition, this command also defines the current '\ref' value to be
the result of '\thecounter'.

   While the counter value is set globally, the '\ref' value is set
locally, i.e., inside the current group.

13.7 '\stepcounter'
===================

Synopsis:

     \stepcounter{COUNTER}

   Globally adds one to COUNTER and resets all counters numbered within
it.  (For the definition of "counters numbered within", *note
\newcounter::.)

   This command differs from '\refstepcounter' in that this one does not
influence references; that is, it does not define the current '\ref'
value to be the result of '\thecounter' (*note \refstepcounter::).

13.8 '\day' & '\month' & '\year'
================================

LaTeX defines the counter '\day' for the day of the month (nominally
with value between 1 and 31), '\month' for the month of the year
(nominally with value between 1 and 12), and '\year' for the year.  When
TeX starts up, they are set from the current values on the system.  The
related command '\today' produces a string representing the current day
(*note \today::).

   They counters are not updated as the job progresses so in principle
they could be incorrect by the end.  In addition, TeX does no sanity
check:

     \day=-2 \month=13 \year=-4 \today

gives no error or warning and results in the output '-2, -4' (the bogus
month value produces no output).

   *Note Command line input::, to force the date to a given value from
the command line.

14 Lengths
**********

A "length" is a measure of distance.  Many LaTeX commands take a length
as an argument.

   Lengths come in two types.  A "rigid length" such as '10pt' does not
contain a 'plus' or 'minus' component.  (Plain TeX calls this a
"dimen".)  A "rubber length" (what plain TeX calls a "skip" or "glue")
such as with '1cm plus0.05cm minus0.01cm' can contain either or both of
those components.  In that rubber length, the '1cm' is the "natural
length" while the other two, the 'plus' and 'minus' components, allow
TeX to stretch or shrink the length to optimize placement.

   The illustrations below use these two commands.

     % make a black bar 10pt tall and #1 wide
     \newcommand{\blackbar}[1]{\rule{#1}{10pt}}

     % Make a box around #2 that is #1 wide (excluding the border)
     \newcommand{\showhbox}[2]{%
       \fboxsep=0pt\fbox{\hbox to #1{#2}}}

This example uses those commands to show a black bar 100 points long
between 'XXX' and 'YYY'.  This length is rigid.

     XXX\showhbox{100pt}{\blackbar{100pt}}YYY

   As for rubber lengths, shrinking is simpler one: with '1cm minus
0.05cm', the natural length is 1cm but TeX can shrink it down as far as
0.95cm.  Beyond that, TeX refuses to shrink any more.  Thus, below the
first one works fine, producing a space of 98 points between the two
bars.

     XXX\showhbox{300pt}{%
       \blackbar{101pt}\hspace{100pt minus 2pt}\blackbar{101pt}}YYY

     XXX\showhbox{300pt}{%
       \blackbar{105pt}\hspace{100pt minus 1pt}\blackbar{105pt}}YYY

But the second one gets a warning like 'Overfull \hbox (1.0pt too wide)
detected at line 17'.  In the output the first 'Y' is overwritten by the
end of the black bar, because the box's material is wider than the 300pt
allocated, as TeX has refused to shrink the total to less than
309 points.

   Stretching is like shrinking except that if TeX is asked to stretch
beyond the given amount, it will do it.  Here the first line is fine,
producing a space of 110 points between the bars.

     XXX\showhbox{300pt}{%
       \blackbar{95pt}\hspace{100pt plus 10pt}\blackbar{95pt}}YYY

     XXX\showhbox{300pt}{%
       \blackbar{95pt}\hspace{100pt plus 1pt}\blackbar{95pt}}YYY

In the second line TeX needs a stretch of 10 points and only 1 point was
specified.  TeX stretches the space to the required length but it gives
you a warning like 'Underfull \hbox (badness 10000) detected at line
22'.  (We won't discuss badness.)

   You can put both stretch and shrink in the same length, as in '1ex
plus 0.05ex minus 0.02ex'.

   If TeX is setting two or more rubber lengths then it allocates the
stretch or shrink in proportion.

     XXX\showhbox{300pt}{%
       \blackbar{100pt}%  left
       \hspace{0pt plus 50pt}\blackbar{80pt}\hspace{0pt plus 10pt}%  middle
       \blackbar{100pt}}YYY  % right

The left and right bars take up 100 points, so the middle needs another
100.  The middle bar is 80 points so the two '\hspace''s must stretch
20 points.  Because the two are 'plus 50pt' and 'plus 10pt', TeX gets
5/6 of the stretch from the first space and 1/6 from the second.

   The 'plus' or 'minus' component of a rubber length can contain a
"fill" component, as in '1in plus2fill'.  This gives the length infinite
stretchability or shrinkability so that TeX could set it to any
distance.  Here the two figures will be equal-spaced across the page.

     \begin{minipage}{\linewidth}
       \hspace{0pt plus 1fill}\includegraphics{godel.png}%
       \hspace{0pt plus 1fill}\includegraphics{einstein.png}%
       \hspace{0pt plus 1fill}
     \end{minipage}

   TeX has three levels of infinity for glue components: 'fil', 'fill',
and 'filll'.  The later ones are more infinite than the earlier ones.
Ordinarily document authors only use the middle one (*note \hfill:: and
*note \vfill::).

   Multiplying a rubber length by a number turns it into a rigid length,
so that after '\setlength{\ylength}{1in plus 0.2in}' and
'\setlength{\zlength}{3\ylength}' then the value of '\zlength' is '3in'.

14.1 Units of length
====================

TeX and LaTeX know about these units both inside and outside of math
mode.

'pt'
     Point, 1/72.27 inch.  The (approximate) conversion to metric units
     is 1point = .35146mm = .035146cm.

'pc'
     Pica, 12 pt

'in'
     Inch, 72.27 pt

'bp'
     Big point, 1/72 inch.  This length is the definition of a point in
     PostScript and many desktop publishing systems.

'mm'
     Millimeter, 2.845 pt

'cm'
     Centimeter, 10 mm

'dd'
     Didot point, 1.07 pt

'cc'
     Cicero, 12 dd

'sp'
     Scaled point, 1/65536 pt

   Three other units are defined according to the current font, rather
than being an absolute dimension.

'ex'
     The x-height of the current font "ex", traditionally the height of
     the lowercase letter x, is often used for vertical lengths.

'em'
     Similarly "em", traditionally the width of the capital letter M, is
     often used for horizontal lengths.  This is also often the size of
     the current font, e.g., a nominal 10pt font will have 1em = 10pt.
     LaTeX has several commands to produce horizontal spaces based on
     the em (*note \enspace & \quad & \qquad::).

'mu'
     Finally, in math mode, many definitions are expressed in terms of
     the math unit "mu", defined by 1em = 18mu, where the em is taken
     from the current math symbols family.  *Note Spacing in math
     mode::.

   Using these units can help make a definition work better across font
changes.  For example, a definition of the vertical space between list
items given as '\setlength{\itemsep}{1ex plus 0.05ex minus 0.01ex}' is
more likely to still be reasonable if the font is changed than a
definition given in points.

14.2 '\setlength'
=================

Synopsis:

     \setlength{\LEN}{AMOUNT}

   Set the length \LEN to AMOUNT.  The length name '\LEN' has to be a
control sequence (*note Control sequences::), and as such must begin
with a backslash, '\' under normal circumstances.  The AMOUNT can be a
rubber length (*note Lengths::).  It can be positive, negative or zero,
and can be in any units that LaTeX understands (*note Units of
length::).

   Below, with LaTeX's defaults the first paragraph will be indented
while the second will not.

     I told the doctor I broke my leg in two places.

     \setlength{\parindent}{0em}
     He said stop going to those places.

   If you did not declare \LEN with '\newlength', for example if you
mistype it as in
'\newlength{\specparindent}\setlength{\sepcparindent}{...}', then you
get an error like 'Undefined control sequence. <argument> \sepcindent'.
If you omit the backslash at the start of the length name then you get
an error like 'Missing number, treated as zero.'.

14.3 '\addtolength'
===================

Synopsis:

     \addtolength{\LEN}{AMOUNT}

   Increment the length \LEN by AMOUNT.  The length name '\LEN' has to
be a control sequence (*note Control sequences::), and as such must
begin with a backslash, '\' under normal circumstances.  The AMOUNT is a
rubber length (*note Lengths::).  It can be positive, negative or zero,
and can be in any units that LaTeX understands (*note Units of
length::).

   Below, if '\parskip' starts with the value '0pt plus 1pt'

     Doctor: how is the boy who swallowed the silver dollar?
     \addtolength{\parskip}{1pt}

     Nurse: no change.

then it has the value '1pt plus 1pt' for the second paragraph.

   If you did not declare \LEN with '\newlength', for example if you
mistype it as in
'\newlength{\specparindent}\addtolength{\sepcparindent}{...}', then you
get an error like 'Undefined control sequence. <argument> \sepcindent'.
If the AMOUNT uses some length that has not been declared, for instance
if for example you mistype the above as
'\addtolength{\specparindent}{0.6\praindent}', then you get something
like 'Undefined control sequence. <argument> \praindent'.  If you leave
off the backslash at the start of \LEN, as in
'\addtolength{parindent}{1pt}', then you get something like 'You can't
use `the letter p' after \advance'.

14.4 '\settodepth'
==================

Synopsis:

     \settodepth{\LEN}{TEXT}

   Set the length \LEN to the depth of box that LaTeX gets on
typesetting the TEXT argument.  The length name '\LEN' has to be a
control sequence (*note Control sequences::), and as such must begin
with a backslash, '\' under normal circumstances.

   This will print how low the character descenders go.

     \newlength{\alphabetdepth}
     \settodepth{\alphabetdepth}{abcdefghijklmnopqrstuvwxyz}
     \the\alphabetdepth

   If you did not declare \LEN with '\newlength', if for example you
mistype the above as '\settodepth{\aplhabetdepth}{abc...}', then you get
something like 'Undefined control sequence. <argument> \aplhabetdepth'.
If you leave the backslash out of \LEN, as in
'\settodepth{alphabetdepth}{...}' then you get something like 'Missing
number, treated as zero. <to be read again> \setbox'.

14.5 '\settoheight'
===================

Synopsis:

     \settoheight{\LEN}{text}

   Sets the length \LEN to the height of box that LaTeX gets on
typesetting the 'text' argument.  The length name '\LEN' has to be a
control sequence (*note Control sequences::), and as such must begin
with a backslash, '\' under normal circumstances.

   This will print how high the characters go.

     \newlength{\alphabetheight}
     \settoheight{\alphabetheight}{abcdefghijklmnopqrstuvwxyz}
     \the\alphabetheight

   If no such length \LEN has been declared with '\newlength', if for
example you mistype as '\settoheight{\aplhabetheight}{abc...}', then you
get something like 'Undefined control sequence. <argument>
\alphabetheight'.  If you leave the backslash out of \LEN, as in
'\settoheight{alphabetheight}{...}' then you get something like 'Missing
number, treated as zero. <to be read again> \setbox'.

14.6 '\settowidth'
==================

Synopsis:

     \settowidth{\LEN}{TEXT}

   Set the length \LEN to the width of the box that LaTeX gets on
typesetting the TEXT argument.  The length name '\LEN' has to be a
control sequence (*note Control sequences::), and as such must begin
with a backslash, '\' under normal circumstances.

   This prints the width of the lowercase ASCII alphabet.

     \newlength{\alphabetwidth}
     \settowidth{\alphabetwidth}{abcdefghijklmnopqrstuvwxyz}
     \the\alphabetwidth

   If no such length \LEN has been declared with '\newlength', if for
example you mistype the above as '\settowidth{\aplhabetwidth}{abc...}',
then you get something like 'Undefined control sequence. <argument>
\aplhabetwidth'.  If you leave the backslash out of \LEN, as in
'\settoheight{alphabetwidth}{...}' then you get something like 'Missing
number, treated as zero. <to be read again> \setbox'.

14.7 '\stretch'
===============

Synopsis:

     \stretch{NUMBER}

   Produces a rubber length with zero natural length and NUMBER times
'\fill' units of stretchability (*note Lengths::).  The NUMBER can be
positive or negative.  This command is robust (*note \protect::).

   It works for both vertical and horizontal spacing.  In this
horizontal example, LaTeX produces three tick marks, and the distance
between the first and second is half again as long as the distance
between the second and third.

     \rule{0.4pt}{1ex}\hspace{\stretch{1.5}}%
       \rule{0.4pt}{1ex}\hspace{\stretch{1}}%
       \rule{0.4pt}{1ex}

   In this vertical example, the 'We dedicate ...' will have three times
as much space under it as above it.

     \newenvironment{dedication}{% in document preamble
       \clearpage\thispagestyle{empty}%
       \vspace*{\stretch{1}} % stretchable space at top
       \it
     }{%
       \vspace{\stretch{3}}  % space at bot is 3x as at top
       \clearpage
     }
       ...
     \begin{dedication}  % in document body
     We dedicate this book to our wives.
     \end{dedication}

14.8 Expressions
================

Synopsis, one of:

     \numexpr EXPRESSION
     \dimexpr EXPRESSION
     \glueexpr EXPRESSION
     \muglue EXPRESSION

   Any place where you may write an integer, or a TeX dimen, or TeX
glue, or muglue, you can instead write an expression to compute that
type of quantity.

   An example is that '\the\dimexpr\linewidth-4pt\relax' will produce as
output the length that is four points less than width of a line (the
only purpose of '\the' is to show the result in the document).
Analogously, '\romannumeral\numexpr6+3\relax' will produce 'ix', and
'\the\glueexpr 5pt plus 1pt * 2 \relax' will produce '10.0pt plus
2.0pt'.

   A convenience here over doing calculations by allocating registers
and then using '\advance', etc., is that the evaluation of expressions
does not involve assignments and can therefore be performed in places
where assignments are not allowed.  The next example computes the width
of the '\parbox'.

     \newlength{\offset}\setlength{\offset}{2em}
     \begin{center}
     \parbox{\dimexpr\linewidth-\offset*3}{With malice toward none
     with charity for all with firmness in the right as God gives us to see
     the right let us strive on to finish the work we are in to bind up the
     nation's wounds, to care for him who shall have borne the battle and
     for his widow and his orphan \textasciitilde\ to do all which may
     achieve and cherish a just and lasting peace among ourselves and with
     all nations.  ---Abraham Lincoln, Second Inaugural Address, from the
     memorial}
     \end{center}

   The EXPRESSION consists of one or more terms of the same type
(integer, dimension, etc.)  that are added or subtracted.  A term that
is a type of number, dimension, etc., consists of a factor of that type,
optionally multiplied or divided by factors.  A factor of a type is
either a quantity of that type or a parenthesized subexpression.  The
expression produces a result of the given type, so that '\numexpr'
produces an integer, '\dimexpr' produces a dimension, etc.

   In the quotation example above, changing to
'\dimexpr\linewidth-3*\offset' gives the error 'Illegal unit of measure
(pt inserted)'.  This is because for '\dimexpr' and '\glueexpr', the
input consists of a dimension or glue value followed by an optional
multiplication factor, and not the other way around.  Thus '\the\dimexpr
1pt*10\relax' is valid and produces '10.0pt', but '\the\dimexpr
10*1pt\relax' gives the 'Illegal unit' error.

   The expressions absorb tokens and carry out appropriate mathematics
up to a '\relax' (which will be absorbed), or up to the first non-valid
token.  Thus, '\the\numexpr2+3px' will print '5px', because LaTeX reads
the '\numexpr2+3', which is made up of numbers, and then finds the
letter 'p', which cannot be part of a number.  It therefore terminates
the expression and produces the '5', followed by the regular text 'px'.

   This termination behavior is useful in comparisons.  In
'\ifnum\numexpr\parindent*2 < 10pt Yes\else No\fi', the less than sign
terminates the expression and the result is 'No' (in a standard LaTeX
article).

   Expressions may use the operators '+', '-', '*' and '/' along with
parentheses for subexpressions, '(...)'.  In glue expressions the 'plus'
and 'minus' parts do not need parentheses to be affected by a factor.
So '\the\glueexpr 5pt plus 1pt * 2 \relax' results in '10pt plus 2pt'.

   TeX will coerce other numerical types in the same way as it does when
doing register assignment.  Thus '\the\numexpr\dimexpr 1pt\relax\relax'
will result in '65536', which is '1pt' converted to scaled points (*note
'sp': units of length sp, TeX's internal unit) and then coerced into an
integer.  With a '\glueexpr' here, the stretch and shrink would be
dropped.  Going the other way, a '\numexpr' inside a '\dimexpr' or
'\glueexpr' will need appropriate units, as in '\the\dimexpr\numexpr 1 +
2\relax pt\relax', which produces '3.0pt'.

   The details of the arithmetic: each factor is checked to be in the
allowed range, numbers must be less than 2^{31} in absolute value, and
dimensions or glue components must be less than 2^{14} points, or 'mu',
or 'fil', etc.  The arithmetic operations are performed individually,
except for a scaling operation (a multiplication immediately followed by
a division) which is done as one combined operation with a 64-bit
product as intermediate value.  The result of each operation is again
checked to be in the allowed range.

   Finally, division and scaling take place with rounding (unlike TeX's
'\divide', which truncates).  Thus '\the\dimexpr 5pt*(3/2)\relax' puts
'10.0pt' in the document, because it rounds '3/2' to '2', while
'\the\dimexpr 5pt*(4/3)\relax' produces '5.0pt'.

15 Making paragraphs
********************

To start a paragraph, just type some text.  To end the current
paragraph, put an empty line.  This is three paragraphs, the separation
of which is made by two empty lines.

     It is a truth universally acknowledged, that a single man in possession
     of a good fortune, must be in want of a wife.

     However little known the feelings or views of such a man may be on his
     first entering a neighbourhood, this truth is so well fixed in the minds
     of the surrounding families, that he is considered the rightful property
     of some one or other of their daughters.

     ``My dear Mr. Bennet,'' said his lady to him one day,
     ``have you heard that Netherfield Park is let at last?''

   A paragraph separator is made of a sequence of at least one blank
line, at least one of which is not terminated by a comment.  A blank
line is a line that is empty or made only of blank characters such as
space or tab.  Comments in source code are started with a '%' and span
up to the end of line.  In the following example the two columns are
identical:

     \documentclass[twocolumn]{article}
     \begin{document}
     First paragraph.

     Second paragraph.
     \newpage
     First paragraph.

       % separator lines may contain blank characters.

     Second paragraph.
     \end{document}

   Once LaTeX has gathered all of a paragraph's contents it divides that
content into lines in a way that is optimized over the entire paragraph
(*note Line breaking::).

   There are places where a new paragraph is not permitted.  Don't put a
blank line in math mode (*note Modes::); here the blank line before the
'\end{equation}'

     \begin{equation}
       2^{|S|} > |S|

     \end{equation}

will get you the error 'Missing $ inserted'.  Similarly, the blank line
in this '\section' argument

     \section{aaa

     bbb}

gets 'Runaway argument? {aaa ! Paragraph ended before \@sect was
complete'.

15.1 '\par'
===========

Synopsis (note that while reading the input TeX converts any sequence of
one or more blank lines to a '\par', *note Making paragraphs::):

     \par

   End the current paragraph.  The usual way to separate paragraphs is
with a blank line but the '\par' command is entirely equivalent.  This
command is robust (*note \protect::).

   This example uses '\par' rather than a blank line simply for
readability.

     \newcommand{\syllabusLegalese}{%
       \whatCheatingIs\par\whatHappensWhenICatchYou}

   In LR mode the '\par' command does nothing and is ignored.  In
paragraph mode, the '\par' command terminates paragraph mode, switching
LaTeX to vertical mode (*note Modes::).

   You cannot use the '\par' command in a math mode.  You also cannot
use it in the argument of many commands, such as the sectioning
commands, e.g. '\section' (*note Making paragraphs:: and *note
\newcommand & \renewcommand::).

   The '\par' command is not the same as the '\paragraph' command.  The
latter is, like '\section' or '\subsection', a sectioning command used
by the LaTeX document standard classes (*note \subsubsection &
\paragraph & \subparagraph::).

   The '\par' command is not the same as '\newline' or the line break
double backslash, '\\'.  The difference is that '\par' ends the
paragraph, not just the line, and also triggers the addition of the
between-paragraph vertical space '\parskip' (*note \parindent &
\parskip::).

   The output from this example

     xyz

     \setlength{\parindent}{3in}
     \setlength{\parskip}{5in}
     \noindent test\indent test1\par test2

is: after 'xyz' there is a vertical skip of 5 inches and then 'test'
appears, aligned with the left margin.  On the same line, there is an
empty horizontal space of 3 inches and then 'test1' appears.  Finally.
there is a vertical space of 5 inches, followed by a fresh paragraph
with a paragraph indent of 3 inches, and then LaTeX puts the text
'test2'.

15.2 '\indent' & '\noindent'
============================

Synopsis:

     \indent

or

     \noindent

   Go into horizontal mode (*note Modes::).  The '\indent' command first
outputs an empty box whose width is '\parindent'.  These commands are
robust (*note \protect::).

   Ordinarily you create a new paragraph by putting in a blank line.
*Note \par::, for the difference between this command and '\par'.  To
start a paragraph without an indent, or to continue an interrupted
paragraph, use '\noindent'.

   In the middle of a paragraph the '\noindent' command has no effect,
because LaTeX is already in horizontal mode there.  The '\indent'
command's only effect is to output a space.

   This example starts a fresh paragraph.

     ... end of the prior paragraph.

     \noindent This paragraph is not indented.

and this continues an interrupted paragraph.

     The data

     \begin{center}
       \begin{tabular}{rl} ... \end{tabular}
     \end{center}

     \noindent shows this clearly.

   To omit indentation in the entire document put
'\setlength{\parindent}{0pt}' in the preamble.  If you do that, you may
want to also set the length of spaces between paragraphs, '\parskip'
(*note \parindent & \parskip::).

   Default LaTeX styles have the first paragraph after a section that is
not indented, as is traditional typesetting in English.  To change that,
look on CTAN for the package 'indentfirst'.

15.3 '\parindent' & '\parskip'
==============================

Synopsis:

     \setlength{\parindent}{HORIZONTAL LEN}
     \setlength{\parskip}{VERTICAL LEN}

   Both are rubber lengths (*note Lengths::).  They affect the
indentation of ordinary paragraphs, not paragraphs inside minipages
(*note minipage::), and the vertical space between paragraphs,
respectively.

   For example, if this is put in the preamble:

     \setlength{\parindent}{0em}
     \setlength{\parskip}{1ex}

The document will have paragraphs that are not indented, but instead are
vertically separated by about the height of a lowercase 'x'.

   In LaTeX standard class documents, the default value for '\parindent'
in one-column documents is '15pt' when the default text size is '10pt',
'17pt' for '11pt', and '1.5em' for '12pt'.  In two-column documents it
is '1em'.  (These values are set before LaTeX calls '\normalfont' so
'em' is derived from the default font, Computer Modern.  If you use a
different font then to set '\parindent' to 1em matching that font, put
'\AtBeginDocument{\setlength{\parindent}{1em}}' in the preamble.)

   The default value for '\parskip' in LaTeX's standard document classes
is '0pt plus1pt'.

15.4 Marginal notes
===================

Synopsis, one of:

     \marginpar{RIGHT}
     \marginpar[LEFT]{RIGHT}

   Create a note in the margin.  The first line of the note will have
the same baseline as the line in the text where the '\marginpar' occurs.

   The margin that LaTeX uses for the note depends on the current layout
(*note Document class options::) and also on '\reversemarginpar' (see
below).  If you are using one-sided layout (document option 'oneside')
then it goes in the right margin.  If you are using two-sided layout
(document option 'twoside') then it goes in the outside margin.  If you
are in two-column layout (document option 'twocolumn') then it goes in
the nearest margin.

   If you declare '\reversemarginpar' then LaTeX will place subsequent
marginal notes in the opposite margin to that given in the prior
paragraph.  Revert that to the default position with '\normalmarginpar'.

   When you specify the optional argument LEFT then it is used for a
note in the left margin, while the mandatory argument RIGHT is used for
a note in the right margin.

   Normally, a note's first word will not be hyphenated.  You can enable
hyphenation there by beginning LEFT or RIGHT with '\hspace{0pt}'.

   These parameters affect the formatting of the note:

'\marginparpush'
     Minimum vertical space between notes; default '7pt' for '12pt'
     documents, '5pt' else.  See also *note page layout parameters
     marginparpush::.

'\marginparsep'
     Horizontal space between the main text and the note; default '11pt'
     for '10pt' documents, '10pt' else.

'\marginparwidth'
     Width of the note itself; default for a one-sided '10pt' document
     is '90pt', '83pt' for '11pt', and '68pt' for '12pt'; '17pt' more in
     each case for a two-sided document.  In two column mode, the
     default is '48pt'.

   The standard LaTeX routine for marginal notes does not prevent notes
from falling off the bottom of the page.

16 Math formulas
****************

Produce mathematical text by putting LaTeX into math mode or display
math mode (*note Modes::).  This example shows both.

     The wave equation for \( u \) is
     \begin{displaymath}
       \frac{\partial^2u}{\partial t^2} = c^2\nabla^2u
     \end{displaymath}
     where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.

Math mode is for inline mathematics.  In the above example it is invoked
by the starting '\(' and finished by the matching ending '\)'.  Display
math mode is for displayed equations and here is invoked by the
'displaymath' environment.  Note that any mathematical text whatever,
including mathematical text consisting of just one character, is handled
in math mode.

   When in math mode or display math mode, LaTeX handles many aspects of
your input text differently than in other text modes.  For example,

     contrast x+y with \( x+y \)

in math mode the letters are in italics and the spacing around the plus
sign is different.

   There are three ways to make inline formulas, to put LaTeX in math
mode.

     \( MATHEMATICAL MATERIAL \)
     $ MATHEMATICAL MATERIAL $
     \begin{math} MATHEMATICAL MATERIAL \end{math}

The first form is preferred and the second is quite common, but the
third form is rarely used.  You can sometimes use one and sometimes
another, as in '\(x\) and $y$'.  You can use these in paragraph mode or
in LR mode (*note Modes::).

   To make displayed formulas, put LaTeX into display math mode with
either:

     \begin{displaymath}
       MATHEMATICAL MATERIAL
     \end{displaymath}

or

     \begin{equation}
       MATHEMATICAL MATERIAL
     \end{equation}

(*note displaymath::, *note equation::).  The only difference is that
with the 'equation' environment, LaTeX puts a formula number alongside
the formula.  The construct '\[ MATH \]' is equivalent to
'\begin{displaymath} MATH \end{displaymath}'.  These environments can
only be used in paragraph mode (*note Modes::).

   The American Mathematical Society has made freely available a set of
packages that greatly expand your options for writing mathematics,
'amsmath' and 'amssymb' (also be aware of the 'mathtools' package that
is an extension to, and loads, 'amsmath').  New documents that will have
mathematical text should use these packages.  Descriptions of these
packages is outside the scope of this document; see their documentation
on CTAN.

16.1 Subscripts & superscripts
==============================

Synopsis (in math mode or display math mode), one of:

     BASE^EXP
     BASE^{EXP}

or, one of:

     BASE_EXP
     BASE_{EXP}

   Make EXP appear as a superscript of BASE (with the caret
character, '^') or a subscript (with underscore, '_').

   In this example the '0''s and '1''s are subscripts while the '2''s
are superscripts.

     \( (x_0+x_1)^2 \leq (x_0)^2+(x_1)^2 \)

   To have the subscript or superscript contain more than one character,
surround the expression with curly braces, as in 'e^{-2x}'.  This
example's fourth line shows curly braces used to group an expression for
the exponent.

     \begin{displaymath}
       (3^3)^3=27^3=19\,683
       \qquad
       3^{(3^3)}=3^{27}=7\,625\,597\,484\,987
     \end{displaymath}

   LaTeX knows how to handle a superscript on a superscript, or a
subscript on a subscript, or supers on subs, or subs on supers.  So,
expressions such as 'e^{x^2}' and 'x_{i_0}' give correct output.  Note
the use in those expressions of curly braces to give the BASE a
determined EXP.  If you enter '\(3^3^3\)' then you get 'Double
superscript'.

   LaTeX does the right thing when something has both a subscript and a
superscript.  In this example the integral has both.  They come out in
the correct place without any author intervention.

     \begin{displaymath}
       \int_{x=a}^b f'(x)\,dx = f(b)-f(a)
     \end{displaymath}

Note the parentheses around 'x=a' to make the entire expression a
subscript.

   To put a superscript or subscript before a symbol, use a construct
like '{}_t K^2'.  The empty curly braces '{}' give the subscript
something to attach to and keeps it from accidentally attaching to a
prior symbols.

   Using the subscript or superscript character outside of math mode or
display math mode, as in 'the expression x^2', will get you the error
'Missing $ inserted'.

   A common reason to want subscripts outside of a mathematics mode is
to typeset chemical formulas.  There are packages for that, such as
'mhchem'; see CTAN.

16.2 Math symbols
=================

LaTeX provides almost any mathematical or technical symbol that anyone
uses.  For example, if you include '$\pi$' in your source, you will get
the pi symbol π.  See the "Comprehensive LaTeX Symbol List" package at
<https://ctan.org/pkg/comprehensive>.

   Here is a list of commonly-used symbols.  It is by no means
exhaustive.  Each symbol is described with a short phrase, and its
symbol class, which determines the spacing around it, is given in
parenthesis.  Unless said otherwise, the commands for these symbols can
be used only in math mode.  To redefine a command so that it can be used
whatever the current mode, see *note \ensuremath::.

'\|'
     ∥ Parallel (relation).  Synonym: '\parallel'.

'\aleph'
     ℵ Aleph, transfinite cardinal (ordinary).

'\alpha'
     α Lowercase Greek letter alpha (ordinary).

'\amalg'
     ⨿ Disjoint union (binary)

'\angle'
     ∠ Geometric angle (ordinary).  Similar: less-than sign '<' and
     angle bracket '\langle'.

'\approx'
     ≈ Almost equal to (relation).

'\ast'
     ∗ Asterisk operator, convolution, six-pointed (binary).
     Synonym: '*', which is often a superscript or subscript, as in the
     Kleene star.  Similar: '\star', which is five-pointed, and is
     sometimes used as a general binary operation, and sometimes
     reserved for cross-correlation.

'\asymp'
     ≍ Asymptotically equivalent (relation).

'\backslash'
     \ Backslash (ordinary).  Similar: set minus '\setminus', and
     '\textbackslash' for backslash outside of math mode.

'\beta'
     β Lowercase Greek letter beta (ordinary).

'\bigcap'
     ⋂ Variable-sized, or n-ary, intersection (operator).  Similar:
     binary intersection '\cap'.

'\bigcirc'
     ⚪ Circle, larger (binary).  Similar: function composition '\circ'.

'\bigcup'
     ⋃ Variable-sized, or n-ary, union (operator).  Similar: binary
     union '\cup'.

'\bigodot'
     ⨀ Variable-sized, or n-ary, circled dot operator (operator).

'\bigoplus'
     ⨁ Variable-sized, or n-ary, circled plus operator (operator).

'\bigotimes'
     ⨂ Variable-sized, or n-ary, circled times operator (operator).

'\bigtriangledown'
     ▽ Variable-sized, or n-ary, open triangle pointing down (operator).

'\bigtriangleup'
     △ Variable-sized, or n-ary, open triangle pointing up (operator).

'\bigsqcup'
     ⨆ Variable-sized, or n-ary, square union (operator).

'\biguplus'
     ⨄ Variable-sized, or n-ary, union operator with a plus (operator).
     (Note that the name has only one p.)

'\bigvee'
     ⋁ Variable-sized, or n-ary, logical-or (operator).

'\bigwedge'
     ⋀ Variable-sized, or n-ary, logical-and (operator).

'\bot'
     ⊥, Up tack, bottom, least element of a partially ordered set, or a
     contradiction (ordinary).  See also '\top'.

'\bowtie'
     ⋈ Natural join of two relations (relation).

'\Box'
     □ Modal operator for necessity; square open box (ordinary).  Not
     available in plain TeX.  In LaTeX you need to load the 'amssymb'
     package.

'\bullet'
     • Bullet (binary).  Similar: multiplication dot '\cdot'.

'\cap'
     ∩ Intersection of two sets (binary).  Similar: variable-sized
     operator '\bigcap'.

'\cdot'
     ⋅ Multiplication (binary).  Similar: Bullet dot '\bullet'.

'\chi'
     χ Lowercase Greek chi (ordinary).

'\circ'
     ∘ Function composition, ring operator (binary).  Similar:
     variable-sized operator '\bigcirc'.

'\clubsuit'
     ♣ Club card suit (ordinary).

'\complement'
     ∁, Set complement, used as a superscript as in '$S^\complement$'
     (ordinary).  Not available in plain TeX.  In LaTeX you need to load
     the 'amssymb' package.  Also used: '$S^{\mathsf{c}}$'
     or '$\bar{S}$'.

'\cong'
     ≅ Congruent (relation).

'\coprod'
     ∐ Coproduct (operator).

'\cup'
     ∪ Union of two sets (binary).  Similar: variable-sized
     operator '\bigcup'.

'\dagger'
     † Dagger relation (binary).

'\dashv'
     ⊣ Dash with vertical, reversed turnstile (relation).  Similar:
     turnstile '\vdash'.

'\ddagger'
     ‡ Double dagger relation (binary).

'\Delta'
     Δ Greek uppercase delta, used for increment (ordinary).

'\delta'
     δ Greek lowercase delta (ordinary).

'\Diamond'
     ◇ Large diamond operator (ordinary).  Not available in plain TeX.
     In LaTeX you need to load the 'amssymb' package.

'\diamond'
     ⋄ Diamond operator (binary).  Similar: large diamond '\Diamond',
     circle bullet '\bullet'.

'\diamondsuit'
     ♢ Diamond card suit (ordinary).

'\div'
     ÷ Division sign (binary).

'\doteq'
     ≐ Approaches the limit (relation).  Similar: geometrically equal
     to '\Doteq'.

'\downarrow'
     ↓ Down arrow, converges (relation).  Similar: '\Downarrow' double
     line down arrow.

'\Downarrow'
     ⇓ Double line down arrow (relation).  Similar: '\downarrow' single
     line down arrow.

'\ell'
     ℓ Lowercase cursive letter l (ordinary).

'\emptyset'
     ∅ Empty set symbol (ordinary).  The variant form is '\varnothing'.

'\epsilon'
     ϵ Lowercase lunate epsilon (ordinary).  Similar to Greek text
     letter.  More widely used in mathematics is the script small letter
     epsilon '\varepsilon' ε.  Related: the set membership relation
     '\in' ∈.

'\equiv'
     ≡ Equivalence (relation).

'\eta'
     η Lowercase Greek letter (ordinary).

'\exists'
     ∃ Existential quantifier (ordinary).

'\flat'
     ♭ Musical flat (ordinary).

'\forall'
     ∀ Universal quantifier (ordinary).

'\frown'
     ⌢ Downward curving arc (ordinary).

'\Gamma'
     Γ uppercase Greek letter (ordinary).

'\gamma'
     γ Lowercase Greek letter (ordinary).

'\ge'
     ≥ Greater than or equal to (relation).  This is a synonym
     for '\geq'.

'\geq'
     ≥ Greater than or equal to (relation).  This is a synonym
     for '\ge'.

'\gets'
     ← Is assigned the value (relation).  Synonym: '\leftarrow'.

'\gg'
     ≫ Much greater than (relation).  Similar: much less than '\ll'.

'\hbar'
     ℏ Planck constant over two pi (ordinary).

'\heartsuit'
     ♡ Heart card suit (ordinary).

'\hookleftarrow'
     ↩ Hooked left arrow (relation).

'\hookrightarrow'
     ↪ Hooked right arrow (relation).

'\iff'
     ⟷ If and only if (relation).  It is '\Longleftrightarrow' with a
     '\thickmuskip' on either side.

'\Im'
     ℑ Imaginary part (ordinary).  See: real part '\Re'.

'\imath'
     Dotless i; used when you are putting an accent on an i (*note Math
     accents::).

'\in'
     ∈ Set element (relation).  See also: lowercase lunate
     epsilon '\epsilon'ϵ and small letter script epsilon '\varepsilon'.

'\infty'
     ∞ Infinity (ordinary).

'\int'
     ∫ Integral (operator).

'\iota'
     ι Lowercase Greek letter (ordinary).

'\Join'
     ⨝ Condensed bowtie symbol (relation).  Not available in Plain TeX.

'\jmath'
     Dotless j; used when you are putting an accent on a j (*note Math
     accents::).

'\kappa'
     κ Lowercase Greek letter (ordinary).

'\Lambda'
     Λ uppercase Greek letter (ordinary).

'\lambda'
     λ Lowercase Greek letter (ordinary).

'\land'
     ∧ Logical and (binary).  Synonym: '\wedge'.  See also
     logical or '\lor'.

'\langle'
     ⟨ Left angle, or sequence, bracket (opening).  Similar:
     less-than '<'.  Matches '\rangle'.

'\lbrace'
     { Left curly brace (opening).  Synonym: '\{'.  Matches '\rbrace'.

'\lbrack'
     [ Left square bracket (opening).  Synonym: '['.  Matches '\rbrack'.

'\lceil'
     ⌈ Left ceiling bracket, like a square bracket but with the bottom
     shaved off (opening).  Matches '\rceil'.

'\le'
     ≤ Less than or equal to (relation).  This is a synonym for '\leq'.

'\leadsto'
     ⇝ Squiggly right arrow (relation).  To get this symbol outside of
     math mode you can put
     '\newcommand*{\Leadsto}{\ensuremath{\leadsto}}' in the preamble and
     then use '\Leadsto' instead.

'\Leftarrow'
     ⇐ Is implied by, double-line left arrow (relation).  Similar:
     single-line left arrow '\leftarrow'.

'\leftarrow'
     ← Single-line left arrow (relation).  Synonym: '\gets'.  Similar:
     double-line left arrow '\Leftarrow'.

'\leftharpoondown'
     ↽ Single-line left harpoon, barb under bar (relation).

'\leftharpoonup'
     ↼ Single-line left harpoon, barb over bar (relation).

'\Leftrightarrow'
     ⇔ Bi-implication; double-line double-headed arrow (relation).
     Similar: single-line double headed arrow '\leftrightarrow'.

'\leftrightarrow'
     ↔ Single-line double-headed arrow (relation).  Similar: double-line
     double headed arrow '\Leftrightarrow'.

'\leq'
     ≤ Less than or equal to (relation).  This is a synonym for '\le'.

'\lfloor'
     ⌊ Left floor bracket (opening).  Matches: '\floor'.

'\lhd'
     ◁ Arrowhead, that is, triangle, pointing left (binary).  For the
     normal subgroup symbol you should load 'amssymb' and
     use '\vartriangleleft' (which is a relation and so gives better
     spacing).

'\ll'
     ≪ Much less than (relation).  Similar: much greater than '\gg'.

'\lnot'
     ¬ Logical negation (ordinary).  Synonym: '\neg'.

'\longleftarrow'
     ⟵ Long single-line left arrow (relation).  Similar: long
     double-line left arrow '\Longleftarrow'.

'\longleftrightarrow'
     ⟷ Long single-line double-headed arrow (relation).  Similar: long
     double-line double-headed arrow '\Longleftrightarrow'.

'\longmapsto'
     ⟼ Long single-line left arrow starting with vertical bar
     (relation).  Similar: shorter version '\mapsto'.

'\longrightarrow'
     ⟶ Long single-line right arrow (relation).  Similar: long
     double-line right arrow '\Longrightarrow'.

'\lor'
     ∨ Logical or (binary).  Synonym: '\vee'.  See also
     logical and '\land'.

'\mapsto'
     ↦ Single-line left arrow starting with vertical bar (relation).
     Similar: longer version '\longmapsto'.

'\mho'
     ℧ Conductance, half-circle rotated capital omega (ordinary).

'\mid'
     ∣ Single-line vertical bar (relation).  A typical use of '\mid' is
     for a set '\{\, x \mid x\geq 5 \,\}'.

     Similar: '\vert' and '|' produce the same single-line vertical bar
     symbol but without any spacing (they fall in class ordinary) and
     you should not use them as relations but instead only as ordinals,
     i.e., footnote symbols.  For absolute value, see the entry
     for '\vert' and for norm see the entry for '\Vert'.

'\models'
     ⊨ Entails, or satisfies; double turnstile, short double dash
     (relation).  Similar: long double dash '\vDash'.

'\mp'
     ∓ Minus or plus (relation).

'\mu'
     μ Lowercase Greek letter (ordinary).

'\nabla'
     ∇ Hamilton's del, or differential, operator (ordinary).

'\natural'
     ♮ Musical natural notation (ordinary).

'\ne'
     ≠ Not equal (relation).  Synonym: '\neq'.

'\nearrow'
     ↗ North-east arrow (relation).

'\neg'
     ¬ Logical negation (ordinary).  Synonym: '\lnot'.  Sometimes
     instead used for negation: '\sim'.

'\neq'
     ≠ Not equal (relation).  Synonym: '\ne'.

'\ni'
     ∋ Reflected membership epsilon; has the member (relation).
     Synonym: '\owns'.  Similar: is a member of '\in'.

'\not'
         Long solidus, or slash, used to overstrike a following operator
     (relation).

     Many negated operators are available that don't require '\not',
     particularly with the 'amssymb' package.  For example, '\notin' is
     typographically preferable to '\not\in'.

'\notin'
     ∉ Not an element of (relation).  Similar: not subset
     of '\nsubseteq'.

'\nu'
     ν Lowercase Greek letter (ordinary).

'\nwarrow'
     ↖ North-west arrow (relation).

'\odot'
     ⊙ Dot inside a circle (binary).  Similar: variable-sized
     operator '\bigodot'.

'\oint'
     ∮ Contour integral, integral with circle in the middle (operator).

'\Omega'
     Ω uppercase Greek letter (ordinary).

'\omega'
     ω Lowercase Greek letter (ordinary).

'\ominus'
     ⊖ Minus sign, or dash, inside a circle (binary).

'\oplus'
     ⊕ Plus sign inside a circle (binary).  Similar: variable-sized
     operator '\bigoplus'.

'\oslash'
     ⊘ Solidus, or slash, inside a circle (binary).

'\otimes'
     ⊗ Times sign, or cross, inside a circle (binary).  Similar:
     variable-sized operator '\bigotimes'.

'\owns'
     ∋ Reflected membership epsilon; has the member (relation).
     Synonym: '\ni'.  Similar: is a member of '\in'.

'\parallel'
     ∥ Parallel (relation).  Synonym: '\|'.

'\partial'
     ∂ Partial differential (ordinary).

'\perp'
     ⟂ Perpendicular (relation).  Similar: '\bot' uses the same glyph
     but the spacing is different because it is in the class ordinary.

'\Phi'
     Φ Uppercase Greek letter (ordinary).

'\phi'
     ϕ Lowercase Greek letter (ordinary).  The variant form is
     '\varphi' φ.

'\Pi'
     Π uppercase Greek letter (ordinary).

'\pi'
     π Lowercase Greek letter (ordinary).  The variant form is
     '\varpi' ϖ.

'\pm'
     ± Plus or minus (binary).

'\prec'
     ≺ Precedes (relation).  Similar: less than '<'.

'\preceq'
     ⪯ Precedes or equals (relation).  Similar: less than or
     equals '\leq'.

'\prime'
     ′ Prime, or minute in a time expression (ordinary).  Typically used
     as a superscript: '$f^\prime$'; '$f^\prime$' and '$f'$' produce the
     same result.  An advantage of the second is that '$f'''$' produces
     the desired symbol, that is, the same result as
     '$f^{\prime\prime\prime}$', but uses rather less typing.  You can
     only use '\prime' in math mode.  Using the right single quote '''
     in text mode produces a different character (apostrophe).

'\prod'
     ∏ Product (operator).

'\propto'
     ∝ Is proportional to (relation)

'\Psi'
     Ψ uppercase Greek letter (ordinary).

'\psi'
     ψ Lowercase Greek letter (ordinary).

'\rangle'
     ⟩ Right angle, or sequence, bracket (closing).  Similar: greater
     than '>'.  Matches:'\langle'.

'\rbrace'
     } Right curly brace (closing).  Synonym: '\}'.  Matches '\lbrace'.

'\rbrack'
     ] Right square bracket (closing).  Synonym: ']'.
     Matches '\lbrack'.

'\rceil'
     ⌉ Right ceiling bracket (closing).  Matches '\lceil'.

'\Re'
     ℜ Real part, real numbers, cursive capital R (ordinary).  Related:
     double-line, or blackboard bold, R '\mathbb{R}'; to access this,
     load the 'amsfonts' package.

'\restriction'
     ↾, Restriction of a function (relation).  Synonym:
     '\upharpoonright'.  Not available in plain TeX.  In LaTeX you need
     to load the 'amssymb' package.

'\revemptyset'
     ⦰, Reversed empty set symbol (ordinary).  Related: '\varnothing'.
     Not available in plain TeX.  In LaTeX you need to load the 'stix'
     package.

'\rfloor'
     ⌋ Right floor bracket, a right square bracket with the top cut off
     (closing).  Matches '\lfloor'.

'\rhd'
     ◁ Arrowhead, that is, triangle, pointing right (binary).  For the
     normal subgroup symbol you should instead load 'amssymb' and
     use '\vartriangleright' (which is a relation and so gives better
     spacing).

'\rho'
     ρ Lowercase Greek letter (ordinary).  The variant form is
     '\varrho' ϱ.

'\Rightarrow'
     ⇒ Implies, right-pointing double line arrow (relation).  Similar:
     right single-line arrow '\rightarrow'.

'\rightarrow'
     → Right-pointing single line arrow (relation).  Synonym: '\to'.
     Similar: right double line arrow '\Rightarrow'.

'\rightharpoondown'
     ⇁ Right-pointing harpoon with barb below the line (relation).

'\rightharpoonup'
     ⇀ Right-pointing harpoon with barb above the line (relation).

'\rightleftharpoons'
     ⇌ Right harpoon up above left harpoon down (relation).

'\searrow'
     ↘ Arrow pointing southeast (relation).

'\setminus'
     ⧵ Set difference, reverse solidus or reverse slash, like \
     (binary).  Similar: backslash '\backslash' and also
     '\textbackslash' outside of math mode.

'\sharp'
     ♯ Musical sharp (ordinary).

'\Sigma'
     Σ uppercase Greek letter (ordinary).

'\sigma'
     σ Lowercase Greek letter (ordinary).  The variant form is
     '\varsigma' ς.

'\sim'
     ∼ Similar, in a relation (relation).

'\simeq'
     ≃ Similar or equal to, in a relation (relation).

'\smallint'
     ∫ Integral sign that does not change to a larger size in a display
     (operator).

'\smile'
     ⌣ Upward curving arc, smile (ordinary).

'\spadesuit'
     ♠ Spade card suit (ordinary).

'\sqcap'
     ⊓ Square intersection symbol (binary).  Similar:
     intersection 'cap'.

'\sqcup'
     ⊔ Square union symbol (binary).  Similar: union 'cup'.  Related:
     variable-sized operator '\bigsqcup'.

'\sqsubset'
     ⊏, Square subset symbol (relation).  Similar: subset '\subset'.
     Not available in plain TeX.  In LaTeX you need to load the
     'amssymb' package.

'\sqsubseteq'
     ⊑ Square subset or equal symbol (binary).  Similar: subset or equal
     to '\subseteq'.

'\sqsupset'
     ⊐, Square superset symbol (relation).  Similar: superset '\supset'.
     Not available in plain TeX.  In LaTeX you need to load the
     'amssymb' package.

'\sqsupseteq'
     ⊒ Square superset or equal symbol (binary).  Similar: superset or
     equal '\supseteq'.

'\star'
     ⋆ Five-pointed star, sometimes used as a general binary operation
     but sometimes reserved for cross-correlation (binary).  Similar:
     the synonyms asterisk '*' and '\ast', which are six-pointed, and
     more often appear as a superscript or subscript, as with the Kleene
     star.

'\subset'
     ⊂ Subset (occasionally, is implied by) (relation).

'\subseteq'
     ⊆ Subset or equal to (relation).

'\succ'
     ≻ Comes after, succeeds (relation).  Similar: is less than '>'.

'\succeq'
     ⪰ Succeeds or is equal to (relation).  Similar: less than or equal
     to '\leq'.

'\sum'
     ∑ Summation (operator).  Similar: Greek capital sigma '\Sigma'.

'\supset'
     ⊃ Superset (relation).

'\supseteq'
     ⊇ Superset or equal to (relation).

'\surd'
     √ Radical symbol (ordinary).  The LaTeX command '\sqrt{...}'
     typesets the square root of the argument, with a bar that extends
     to cover the argument.

'\swarrow'
     ↙ Southwest-pointing arrow (relation).

'\tau'
     τ Lowercase Greek letter (ordinary).

'\theta'
     θ Lowercase Greek letter (ordinary).  The variant form is
     '\vartheta' ϑ.

'\times'
     × Primary school multiplication sign (binary).  See also '\cdot'.

'\to'
     → Right-pointing single line arrow (relation).
     Synonym: '\rightarrow'.

'\top'
     ⊤ Top, greatest element of a partially ordered set (ordinary).  See
     also '\bot'.

'\triangle'
     △ Triangle (ordinary).

'\triangleleft'
     ◁ Not-filled triangle pointing left (binary).  Similar: '\lhd'.
     For the normal subgroup symbol you should load 'amssymb' and
     use '\vartriangleleft' (which is a relation and so gives better
     spacing).

'\triangleright'
     ▷ Not-filled triangle pointing right (binary).  For the normal
     subgroup symbol you should instead load 'amssymb' and
     use '\vartriangleright' (which is a relation and so gives better
     spacing).

'\unlhd'
     ⊴ Left-pointing not-filled underlined arrowhead, that is, triangle,
     with a line under (binary).  For the normal subgroup symbol load
     'amssymb' and use '\vartrianglelefteq' (which is a relation and so
     gives better spacing).

'\unrhd'
     ⊵ Right-pointing not-filled underlined arrowhead, that is,
     triangle, with a line under (binary).  For the normal subgroup
     symbol load 'amssymb' and use '\vartrianglerighteq' (which is a
     relation and so gives better spacing).

'\Uparrow'
     ⇑ Double-line upward-pointing arrow (relation).  Similar:
     single-line up-pointing arrow '\uparrow'.

'\uparrow'
     ↑ Single-line upward-pointing arrow, diverges (relation).  Similar:
     double-line up-pointing arrow '\Uparrow'.

'\Updownarrow'
     ⇕ Double-line upward-and-downward-pointing arrow (relation).
     Similar: single-line upward-and-downward-pointing
     arrow '\updownarrow'.

'\updownarrow'
     ↕ Single-line upward-and-downward-pointing arrow (relation).
     Similar: double-line upward-and-downward-pointing
     arrow '\Updownarrow'.

'\upharpoonright'
     ↾, Up harpoon, with barb on right side (relation).
     Synonym: '\restriction'.  Not available in plain TeX.  In LaTeX you
     need to load the 'amssymb' package.

'\uplus'
     ⊎ Multiset union, a union symbol with a plus symbol in the middle
     (binary).  Similar: union '\cup'.  Related: variable-sized
     operator '\biguplus'.

'\Upsilon'
     Υ uppercase Greek letter (ordinary).

'\upsilon'
     υ Lowercase Greek letter (ordinary).

'\varepsilon'
     ε Small letter script epsilon (ordinary).  This is more widely used
     in mathematics than the non-variant lunate epsilon form
     '\epsilon' ϵ.  Related: set membership '\in'.

'\vanothing'
     ∅, Empty set symbol.  Similar: '\emptyset'.  Related:
     '\revemptyset'.  Not available in plain TeX.  In LaTeX you need to
     load the 'amssymb' package.

'\varphi'
     φ Variant on the lowercase Greek letter (ordinary).  The
     non-variant form is '\phi' ϕ.

'\varpi'
     ϖ Variant on the lowercase Greek letter (ordinary).  The
     non-variant form is '\pi' π.

'\varrho'
     ϱ Variant on the lowercase Greek letter (ordinary).  The
     non-variant form is '\rho' ρ.

'\varsigma'
     ς Variant on the lowercase Greek letter (ordinary).  The
     non-variant form is '\sigma' σ.

'\vartheta'
     ϑ Variant on the lowercase Greek letter (ordinary).  The
     non-variant form is '\theta' θ.

'\vdash'
     ⊢ Provable; turnstile, vertical and a dash (relation).  Similar:
     turnstile rotated a half-circle '\dashv'.

'\vee'
     ∨ Logical or; a downwards v shape (binary).  Related: logical
     and '\wedge'.  Similar: variable-sized operator '\bigvee'.

'\Vert'
     ‖ Vertical double bar (ordinary).  *Note Delimiters::, for how to
     use the 'mathtools' package to create flexibly-sized norm symbols.

'\vert'
     | Single line vertical bar (ordinary).  For "such that", as in the
     definition of a set, use '\mid' because it is a relation.  *Note
     Delimiters::, for how to use the 'mathtools' package to create
     flexibly-sized absolute-value symbols.

'\wedge'
     ∧ Logical and (binary).  Synonym: '\land'.  See also logical or
     '\vee'.  Similar: variable-sized operator '\bigwedge'.

'\wp'
     ℘ Weierstrass p (ordinary).

'\wr'
     ≀ Wreath product (binary).

'\Xi'
     Ξ uppercase Greek letter (ordinary).

'\xi'
     ξ Lowercase Greek letter (ordinary).

'\zeta'
     ζ Lowercase Greek letter (ordinary).

   The following symbols are most often used in plain text but LaTeX
provides versions to use in mathematical text.

'\mathdollar'
     Dollar sign in math mode: $.

'\mathparagraph'
     Paragraph sign (pilcrow) in math mode, ¶.

'\mathsection'
     Section sign in math mode §.

'\mathsterling'
     Sterling sign in math mode: £.

'\mathunderscore'
     Underscore in math mode: _.

16.2.1 Arrows
-------------

These are the arrows that come with standard LaTeX.  The 'latexsym' and
'amsfonts' packages contain many more.

Symbol  Command
---------------------------------------------------------------------------
⇓       '\Downarrow'
↓       '\downarrow'
↩       '\hookleftarrow'
↪       '\hookrightarrow'
←       '\leftarrow'
⇐       '\Leftarrow'
⇔       '\Leftrightarrow'
↔       '\leftrightarrow'
⟵       '\longleftarrow'
⟸       '\Longleftarrow'
⟷       '\longleftrightarrow'
⟺       '\Longleftrightarrow'
⟼       '\longmapsto'
⟹       '\Longrightarrow'
⟶       '\longrightarrow'
↦       '\mapsto'
↗       '\nearrow'
↖       '\nwarrow'
⇒       '\Rightarrow'
→       '\rightarrow', or '\to'
↘       '\searrow'
↙       '\swarrow'
↑       '\uparrow'
⇑       '\Uparrow'
↕       '\updownarrow'
⇕       '\Updownarrow'

   An example of the difference between '\to' and '\mapsto' is: '\(
f\colon D\to C \) given by \( n\mapsto n^2 \)'.

   For commutative diagrams there are a number of packages, including
'tikz-cd' and 'amscd'.

16.2.2 '\boldmath' & '\unboldmath'
----------------------------------

Synopsis (used in paragraph mode or LR mode):

     \boldmath \( MATH \)

or

     \unboldmath \( MATH \)

   Declarations to change the letters and symbols in MATH to be in a
bold font, or to countermand that and bring back the regular (non-bold)
default.  They must be used when not in math mode or display math mode
(*note Modes::).  Both commands are fragile (*note \protect::).

   In this example each '\boldmath' command takes place inside an
'\mbox',

     we have $\mbox{\boldmath \( v \)} = 5\cdot\mbox{\boldmath \( u \)$}$

which means '\boldmath' is only called in a text mode, here LR mode, and
explains why LaTeX must switch to math mode to set 'v' and 'u'.

   If you use either command inside math mode, as with 'Trouble: \(
\boldmath x \)', then you get something like 'LaTeX Font Warning:
Command \boldmath invalid in math mode on input line 11' and 'LaTeX Font
Warning: Command \mathversion invalid in math mode on input line 11'.

   There are many issues with '\boldmath'.  New documents should use the
'bm' package provided by the LaTeX Project team.  A complete description
is outside the scope of this document (see the full documentation on
CTAN) but even this small example

     \usepackage{bm}   % in preamble
     ...
     we have $\bm{v} = 5\cdot\bm{u}$

shows that it is an improvement over '\boldmath'.

16.2.3 Blackboard bold
----------------------

Synopsis:

     \usepackage{amssymb}   % in preamble
       ...
     \mathbb{UPPERCASE-LETTER}

   Provide blackboard bold symbols, sometimes also known as doublestruck
letters, used to denote number sets such as the natural numbers, the
integers, etc.

   Here

     \( \forall n \in \mathbb{N}, n^2 \geq 0 \)

the '\mathbb{N}' gives blackboard bold symbol ℕ, representing the
natural numbers.

   If you use other than an uppercase letter then you do not get an
error but you get strange results, including unexpected characters.

   There are packages that give access to symbols other than just the
capital letters; look on CTAN.

16.2.4 Calligraphic
-------------------

Synopsis:

     \mathcal{UPPERCASE-LETTERS}

   Use a script-like font.

   In this example the graph identifier is output in a cursive font.

     Let the graph be \( \mathcal{G} \).

   If you use something other than an uppercase letter then you do not
get an error but you also do not get math calligraphic output.  For
instance, '\mathcal{g}' outputs a close curly brace symbol.

16.2.5 Delimiters
-----------------

Delimiters are parentheses, braces, or other characters used to mark the
start and end of subformulas.  This formula has three sets of
parentheses delimiting the three subformulas.

     (z-z_0)^2 = (x-x_0)^2 + (y-y_0)^2

The delimiters do not need to match, so you can enter '\( [0,1) \)'.

   Here are the common delimiters:

DelimiterCommand        Name
------------------------------------------------------
(        '('            Left parenthesis
)        ')'            Right parenthesis
\}       '{' or         Left brace
         '\lbrace'
\{       '}' or         Right brace
         '\rbrace'
[        '[' or         Left bracket
         '\lbrack'
]        ']' or         Right bracket
         '\rbrack'
⌊        '\lfloor'      Left floor bracket
⌋        '\rfloor'      Right floor bracket
⌈        '\lceil'       Left ceiling bracket
⌉        '\rceil'       Right ceiling bracket
⟨        '\langle'      Left angle bracket
⟩        '\rangle'      Right angle bracket
/        '/'            Slash, or forward slash
\        '\backslash'   Reverse slash, or backslash
|        '|' or         Vertical bar
         '\vert'
‖        '\|' or        Double vertical bar
         '\Vert'

   The 'mathtools' package allows you to create commands for paired
delimiters.  For instance, if you put
'\DeclarePairedDelimiter\abs{\lvert}{\rvert}' in your preamble then you
get two commands for single-line vertical bars (they only work in math
mode).  The starred form, such as '\abs*{\frac{22}{7}}', has the height
of the vertical bars match the height of the argument.  The unstarred
form, such as '\abs{\frac{22}{7}}', has the bars fixed at a default
height.  This form accepts an optional argument, as in '\abs[SIZE
COMMAND]{\frac{22}{7}}', where the height of the bars is given in SIZE
COMMAND, such as '\Bigg'.  Using instead '\lVert' and '\rVert' as the
symbols will give you a norm symbol with the same behavior.

16.2.5.1 '\left' & '\right'
...........................

Synopsis:

     \left DELIMITER1 ... \right DELIMITER2

   Make matching parentheses, braces, or other delimiters.  LaTeX makes
the delimiters tall enough to just cover the size of the formula that
they enclose.

   This makes a unit vector surrounded by parentheses tall enough to
cover the entries.

     \begin{equation}
       \left(\begin{array}{c}
         1   \\
         0   \\
       \end{array}\right)
     \end{equation}

   *Note Delimiters::, for a list of the common delimiters.

   Every '\left' must have a matching '\right'.  In the above example,
leaving out the '\left(' gets the error message 'Extra \right'.  Leaving
out the '\right)' gets 'You can't use `\eqno' in math mode'.

   However, DELIMITER1 and DELIMITER2 need not match.  A common case is
that you want an unmatched brace, as below.  Use a period, '.', as a
null delimiter.

     \begin{equation}
       f(n)=\left\{\begin{array}{ll}
                     1             &\mbox{--if \(n=0\)} \\
                     f(n-1)+3n^2   &\mbox{--else}
            \end{array}\right.
     \end{equation}

Note that to get a curly brace as a delimiter you must prefix it with a
backslash, '\{' (*note Reserved characters::).  (The packages 'amsmath'
and 'mathtools' allow you to get the above construct through in a
'cases' environment.)

   The '\left ... \right' pair make a group.  One consequence is that
the formula enclosed in the '\left ... \right' pair cannot have line
breaks in the output.  This includes both manual line breaks and
LaTeX-generated automatic ones.  In this example, LaTeX breaks the
equation to make the formula fit the margins.

     Lorem ipsum dolor sit amet
     \( (a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z) \)

But with '\left' and '\right'

     Lorem ipsum dolor sit amet
     \( \left(a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z\right) \)

LaTeX won't break the line, causing the formula to extend into the
margin.

   Because '\left ... \right' make a group, all the usual grouping rules
hold.  Here, the value of '\testlength' set inside the equation will be
forgotten, and the output is '1.2pt'.

     \newlength{\testlength} \setlength{\testlength}{1.2pt}
     \begin{equation}
       \left( a+b=c \setlength{\testlength}{3.4pt} \right)
       \the\testlength
     \end{equation}

   The '\left ... \right' pair affect the horizontal spacing of the
enclosed formula, in two ways.  The first is that in '\( \sin(x) =
\sin\left(x\right) \)' the one after the equals sign has more space
around the 'x'.  That's because '\left( ... \right)' inserts an inner
node while '( ... )' inserts an opening node.  The second way that the
pair affect the horizontal spacing is that because they form a group,
the enclosed subformula will be typeset at its natural width, with no
stretching or shrinking to make the line fit better.

   TeX scales the delimiters according to the height and depth of the
enclosed formula.  Here LaTeX grows the brackets to extend the full
height of the integral.

     \begin{equation}
       \left[ \int_{x=r_0}^{\infty} -G\frac{Mm}{r^2}\, dr \right]
     \end{equation}

   Manual sizing is often better.  For instance, although below the rule
has no depth, TeX will create delimiters that extend far below the rule.

     \begin{equation}
       \left( \rule{1pt}{1cm} \right)
     \end{equation}

TeX can choose delimiters that are too small, as in '\( \left| |x|+|y|
\right| \)'.  It can also choose delimiters that are too large, as here.

     \begin{equation}
       \left( \sum_{0\leq i<n} i^k \right)
     \end{equation}

A third awkward case is when a long displayed formula is on more than
one line and you must match the sizes of the opening and closing
delimiter; you can't use '\left' on the first line and '\right' on the
last because they must be paired.

   To size the delimiters manually, see *note \bigl & \bigr etc.::.

16.2.5.2 '\bigl', '\bigr', etc.
...............................

Synopsis, one of:

     \bigl DELIMITER1 ... \bigr DELIMITER2
     \Bigl DELIMITER1 ... \bigr DELIMITER2
     \biggl DELIMITER1 ... \biggr DELIMITER2
     \Biggl DELIMITER1 ... \Biggr DELIMITER2

(as with '\bigl[...\bigr]'; strictly speaking they need not be paired,
see below), or one of:

     \bigm DELIMITER
     \Bigm DELIMITER
     \biggm DELIMITER
     \Biggm DELIMITER

(as with '\bigm|'), or one of:

     \big DELIMITER
     \Big DELIMITER
     \bigg DELIMITER
     \Bigg DELIMITER

(as with '\big[').

   Produce manually-sized delimiters.  For delimiters that are
automatically sized see *note \left & \right::).

   This produces slightly larger outer vertical bars.

       \bigl| |x|+|y| \bigr|

   The commands above are listed in order of increasing size.  You can
use the smallest size such as '\bigl...\bigr' in a paragraph without
causing LaTeX to spread the lines apart.  The larger sizes are meant for
displayed equations.

   *Note Delimiters::, for a list of the common delimiters.  In the
family of commands with 'l' or 'r', DELIMITER1 and DELIMITER2 need not
match together.

   The 'l' and 'r' commands produce open and close delimiters that
insert no horizontal space between a preceding atom and the delimiter,
while the commands without 'l' and 'r' insert some space (because each
delimiter is set as an ordinary variable).  Compare these two.

     \begin{tabular}{l}
       \(\displaystyle \sin\biggl(\frac{1}{2}\biggr) \)  \\  % good
       \(\displaystyle \sin\bigg(\frac{1}{2}\bigg)  \)   \\  % bad
     \end{tabular}

The traditional typographic treatment is on the first line.  On the
second line the output will have some extra space between the '\sin' and
the open parenthesis.

   Commands without 'l' or 'r' do give correct spacing in some
circumstances, as with this large vertical line

     \begin{equation}
       \int_{x=a}^b x^2\,dx = \frac{1}{3} x^3 \Big|_{x=a}^b
     \end{equation}

(many authors would replace '\frac' with the '\tfrac' command from the
'amsmath' package), and as with this larger slash.

     \begin{equation}
       \lim_{n\to\infty}\pi(n) \big/ (n/\log n) = 1
     \end{equation}

   Unlike the '\left...\right' pair (*note \left & \right::), the
commands here with 'l' or 'r' do not make a group.  Strictly speaking
they need not be matched so you can write something like this.

     \begin{equation}
       \Biggl[ \pi/6 ]
     \end{equation}

   The commands with 'm' are for relations, which are in the middle of
formulas, as here.

     \begin{equation}
       \biggl\{ a\in B \biggm| a=\sum_{0\leq i<n}3i^2+4 \biggr\}
     \end{equation}

16.2.6 Dots, horizontal or vertical
-----------------------------------

Ellipses are the three dots (usually three) indicating that a pattern
continues.

     \begin{array}{cccc}
       a_{0,0}    &a_{0,1}   &a_{0,2} &\ldots \\
       a_{1,0}    &\ddots                     \\
       \vdots
     \end{array}

   LaTeX provides these.

'\cdots'
     Horizontal ellipsis with the dots raised to the center of the line,
     as in ⋯.  Used as: '\( a_0\cdot a_1\cdots a_{n-1} \)'.

'\ddots'
     Diagonal ellipsis, ⋱.  See the above array example for a usage.

'\ldots'
     Ellipsis on the baseline, ….  Used as: '\( x_0,\ldots x_{n-1} \)'.
     Another example is the above array example.  A synonym is
     '\mathellipsis'.  A synonym from the 'amsmath' package is '\hdots'.

     You can also use this command outside of mathematical text, as in
     'The gears, brakes, \ldots{} are all broken'.  (In a paragraph mode
     or LR mode a synonym for '\ldots' is '\dots'.)

'\vdots'
     Vertical ellipsis, ⋮.  See the above array example for a usage.

   The 'amsmath' package has the command '\dots' to semantically mark up
ellipses.  This example produces two different-looking outputs for the
first two uses of the '\dots' command.

     \usepackage{amsmath}  % in preamble
       ...
     Suppose that \( p_0, p_1, \dots, p_{n-1} \) lists all of the primes.
     Observe that \( p_0\cdot p_1 \dots \cdot p_{n-1} +1 \) is not a
       multiple of any \( p_i \).
     Conclusion: there are infinitely many primes \( p_0, p_1, \dotsc \).

In the first line LaTeX looks to the comma following '\dots' to
determine that it should output an ellipsis on the baseline.  The second
line has a '\cdot' following '\dots' so LaTeX outputs an ellipsis that
is on the math axis, vertically centered.  However, the third usage has
no follow-on character so you have to tell LaTeX what to do.  You can
use one of the commands: '\dotsc' if you need the ellipsis appropriate
for a comma following, '\dotsb' if you need the ellipses that fits when
the dots are followed by a binary operator or relation symbol, '\dotsi'
for dots with integrals, or '\dotso' for others.

16.2.7 Greek letters
--------------------

The upper case versions of these Greek letters are only shown when they
differ from Roman upper case letters.

Symbol  Command                Name
----------------------------------------------------------------------------
α       '\alpha'               Alpha
β       '\beta'                Beta
γ, Γ    '\gamma', '\Gamma'     Gamma
δ, Δ    '\delta', '\Delta'     Delta
ε, ϵ    '\varepsilon',         Epsilon
        '\epsilon'
ζ       '\zeta'                Zeta
η       '\eta'                 Eta
θ, ϑ    '\theta',              Theta
        '\vartheta'
ι       '\iota'                Iota
κ       '\kappa'               Kappa
λ, Λ    '\lambda', '\Lambda'   Lambda
μ       '\mu'                  Mu
ν       '\nu'                  Nu
ξ, Ξ    '\xi', '\Xi'           Xi
π, Π    '\pi', '\Pi'           Pi
ρ, ϱ    '\rho', '\varrho'      Rho
σ, Σ    '\sigma', '\Sigma'     Sigma
τ       '\tau'                 Tau
ϕ, φ,   '\phi', '\varphi',     Phi
Φ       '\Phi'
χ       '\chi'                 chi
ψ, Ψ    '\psi', '\Psi'         Psi
ω, Ω    '\omega', '\Omega'     Omega

   For omicron, if you are using LaTeX's default Computer Modern font
then enter omicron just as 'o' or 'O'.  If you like having the name or
if your font shows a difference then you can use something like
'\newcommand\omicron{o}'.  The package 'unicode-math' has '\upomicron'
for upright omicron and '\mitomicron' for math italic.

   While the set membership relation symbol ∈ generated by '\in' is
related to epsilon, it is never used for a variable.

16.3 Math functions
===================

These commands produce roman function names in math mode with proper
spacing.

'\arccos'
     Inverse cosine

'\arcsin'
     Inverse sine

'\arctan'
     Inverse tangent

'\arg'
     Angle between the real axis and a point in the complex plane

'\bmod'
     Binary modulo operator, used as in '\( 5\bmod 3=2 \)'

'\cos'
     Cosine

'\cosh'
     Hyperbolic cosine

'\cot'
     Cotangent

'\coth'
     Hyperbolic cotangent

'\csc'
     Cosecant

'\deg'
     Degrees

'\det'
     Determinant

'\dim'
     Dimension

'\exp'
     Exponential

'\gcd'
     Greatest common divisor

'\hom'
     Homomorphism

'\inf'
     Infinum

'\ker'
     Kernel

'\lg'
     Base 2 logarithm

'\lim'
     Limit

'\liminf'
     Limit inferior

'\limsup'
     Limit superior

'\ln'
     Natural logarithm

'\log'
     Logarithm

'\max'
     Maximum

'\min'
     Minimum

'\pmod'
     Parenthesized modulus, as used in '\( 5\equiv 2\pmod 3 \)'

'\Pr'
     Probability

'\sec'
     Secant

'\sin'
     Sine

'\sinh'
     Hyperbolic sine

'\sup'
     sup

'\tan'
     Tangent

'\tanh'
     Hyperbolic tangent

   The 'amsmath' package adds improvements on some of these, and also
allows you to define your own.  The full documentation is on CTAN, but
briefly, you can define an identity operator with
'\DeclareMathOperator{\identity}{id}' that is like the ones above but
prints as 'id'.  The starred form '\DeclareMathOperator*{\op}{op}' sets
any limits above and below, as is traditional with '\lim', '\sup', or
'\max'.

16.4 Math accents
=================

LaTeX provides a variety of commands for producing accented letters in
math.  These are different from accents in normal text (*note
Accents::).

'\acute'
     Math acute accent

'\bar'
     Math bar-over accent

'\breve'
     Math breve accent

'\check'
     Math háček (check) accent

'\ddot'
     Math dieresis accent

'\dot'
     Math dot accent

'\grave'
     Math grave accent

'\hat'
     Math hat (circumflex) accent

'\mathring'
     Math ring accent

'\tilde'
     Math tilde accent

'\vec'
     Math vector symbol

'\widehat'
     Math wide hat accent

'\widetilde'
     Math wide tilde accent

   When you are putting an accent on an i or a j, the tradition is to
use one without a dot, '\imath' or 'jmath' (*note Math symbols::).

16.5 Over- and Underlining
==========================

LaTeX provides commands for making overlines or underlines, or putting
braces over or under some material.

'\underline{TEXT}'
     Underline TEXT.  Works inside math mode, and outside.  The line is
     always completely below the text, taking account of descenders, so
     in '\(\underline{y}\)' the line is lower than in
     '\(\underline{x}\)'.  This command is fragile (*note \protect::).

     Note that the package 'ulem' does text mode underlining and allows
     line breaking as well as a number of other features.  See the
     documentation on CTAN. See also *note \hrulefill & \dotfill:: for
     producing a line, for such things as a signature.

'\overline{TEXT}'
     Put a horizontal line over TEXT.  Works inside math mode, and
     outside.  For example, '\overline{x+y}'.  Note that this differs
     from the command '\bar' (*note Math accents::).

'\underbrace{MATH}'
     Put a brace under MATH.  For example, this
     '(1-\underbrace{1/2)+(1/2}-1/3)' emphasizes the telescoping part.
     Attach text to the brace by using subscript, '_', or superscript,
     '^', as here.

          \begin{displaymath}
            1+1/2+\underbrace{1/3+1/4}_{>1/2}+
                 \underbrace{1/5+1/6+1/7+1/8}_{>1/2}+\cdots
          \end{displaymath}

     The superscript appears on top of the expression, and so can look
     unconnected to the underbrace.

'\overbrace{MATH}'
     Put a brace over MATH, as with
     '\overbrace{x+x+\cdots+x}^{\mbox{\(k\) times}}'.  See also
     '\underbrace'.

   The package 'mathtools' adds an over- and underbrace, as well as some
improvements on the braces.  See the documentation on CTAN.

16.6 Spacing in math mode
=========================

When typesetting mathematics, LaTeX puts in spacing according to the
normal rules for mathematics texts.  If you enter 'y=m x' then LaTeX
ignores the space and in the output the m is next to the x, as y=mx.

   But LaTeX's rules occasionally need tweaking.  For example, in an
integral the tradition is to put a small extra space between the 'f(x)'
and the 'dx', here done with the '\,' command:

     \int_0^1 f(x)\,dx

   LaTeX provides the commands that follow for use in math mode.  Many
of these spacing definitions are expressed in terms of the math unit
"mu".  It is defined as 1/18em, where the em is taken from the current
math symbols family (*note Units of length::).  Thus, a '\thickspace' is
something like 5/18 times the width of a 'M'.

'\;'

     Synonym: '\thickspace'.  Normally '5.0mu plus 5.0mu'.  With the
     'amsmath' package, or as of the 2020-10-01 LaTeX release, can be
     used in text mode as well as math mode; otherwise, in math mode
     only.

'\negthickspace'
     Normally '-5.0mu plus 2.0mu minus 4.0mu'.  With the 'amsmath'
     package, or as of the 2020-10-01 LaTeX release, can be used in text
     mode as well as math mode; otherwise, in math mode only.

'\:'
'\>'
     Synonym: '\medspace'.  Normally '4.0mu plus 2.0mu minus 4.0mu'.
     With the 'amsmath' package, or as of the 2020-10-01 LaTeX release,
     can be used in text mode as well as math mode; before that, in math
     mode only.

'\negmedspace'
     Normally '-4.0mu plus 2.0mu minus 4.0mu'.  With the 'amsmath'
     package, or as of the 2020-10-01 LaTeX release, can be used in text
     mode as well as math mode; before that, in math mode only.

'\,'
     Synonym: '\thinspace'.  Normally '3mu', which is 1/6em.  Can be
     used in both math mode and text mode (*note \thinspace &
     \negthinspace::).

     This space is widely used, for instance between the function and
     the infinitesimal in an integral '\int f(x)\,dx' and, if an author
     does this, before punctuation in a displayed equation.

          The antiderivative is
          \begin{equation}
            3x^{-1/2}+3^{1/2}\,.
          \end{equation}

'\!'
     Synonym: '\negthinspace'.  A negative thin space.  Normally '-3mu'.
     With the 'amsmath' package, or as of the 2020-10-01 LaTeX release,
     can be used in text mode as well as math mode; otherwise, the '\!'
     command is math mode only but the '\negthinspace' command has
     always also worked in text mode (*note \thinspace &
     \negthinspace::).

'\quad'
     This is 18mu, that is, 1em.  This is often used for space
     surrounding equations or expressions, for instance for the space
     between two equations inside a 'displaymath' environment.  It is
     available in both text and math mode.

'\qquad'
     A length of 2 quads, that is, 36mu = 2em.  It is available in both
     text and math mode.

16.6.1 '\smash'
---------------

Synopsis:

     \smash{SUBFORMULA}

   Typeset SUBFORMULA as if its height and depth were zero.

   In this example the exponential is so tall that without the '\smash'
command LaTeX would separate its line from the line above it, and the
uneven line spacing might be unsightly.

     To compute the tetration $\smash{2^{2^{2^2}}}$,
     evaluate from the top down, as $2^{2^4}=2^{16}=65536$.

   (Because of the '\smash' the printed expression could run into the
line above so you may want to wait until the final version of the
document to make such adjustments.)

   This pictures the effect of '\smash' by using '\fbox' to surround the
box that LaTeX will put on the line.  The '\blackbar' command makes a
bar extending from 10 points below the baseline to 20 points above.

     \newcommand{\blackbar}{\rule[-10pt]{5pt}{30pt}}
     \fbox{\blackbar}
     \fbox{\smash{\blackbar}}

   The first box that LaTeX places is 20 points high and 10 points deep.
But the second box is treated by LaTeX as having zero height and zero
depth, despite that the ink printed on the page still extends well above
and below the line.

   The '\smash' command appears often in mathematics to adjust the size
of an element that surrounds a subformula.  Here the first radical
extends below the baseline while the second lies just on the baseline.

     \begin{equation}
     \sqrt{\sum_{0\leq k< n} f(k)}
     \sqrt{\vphantom{\sum}\smash{\sum_{0\leq k< n}} f(k)}
     \end{equation}

   Note the use of '\vphantom' to give the '\sqrt' command an argument
with the height of the '\sum' (*note \phantom & \vphantom &
\hphantom::).

   While most often used in mathematics, the '\smash' command can appear
in other contexts.  However, it doesn't change into horizontal mode.  So
if it starts a paragraph then you should first put a '\leavevmode', as
in the bottom line below.

     xxx xxx xxx

     \smash{yyy}  % no paragraph indent

     \leavevmode\smash{zzz}  % usual paragraph indent

   The package 'mathtools' has operators that provide even finer control
over smashing a subformula box.

16.6.2 '\phantom' & '\vphantom' & '\hphantom'
---------------------------------------------

Synopsis:

     \phantom{SUBFORMULA}

   or

     \vphantom{SUBFORMULA}

   or

     \hphantom{SUBFORMULA}

   The '\phantom' command creates a box with the same height, depth, and
width as SUBFORMULA, but empty.  That is, this command causes LaTeX to
typeset the space but not fill it with the material.  Here LaTeX will
put a blank line that is the correct width for the answer, but will not
show that answer.

     \begin{displaymath}
       \int x^2\,dx=\mbox{\underline{$\phantom{(1/3)x^3+C}$}}
     \end{displaymath}

   The '\vphantom' variant produces an invisible box with the same
vertical size as SUBFORMULA, the same height and depth, but having zero
width.  And '\hphantom' makes a box with the same width as SUBFORMULA
but with zero height and depth.

   In this example, the tower of exponents in the second summand
expression is so tall that TeX places this expression further down than
its default.  Without adjustment, the two summand expressions would be
at different levels.  The '\vphantom' in the first expression tells TeX
to leave as much vertical room as it does for the tower, so the two
expressions come out at the same level.

     \begin{displaymath}
         \sum_{j\in\{0,\ldots\, 10\}\vphantom{3^{3^{3^j}}}}
           \sum_{i\in\{0,\ldots\, 3^{3^{3^j}}\}} i\cdot j
     \end{displaymath}

   These commands are often used in conjunction with '\smash'.  *Note
\smash::, which includes another example of '\vphantom'.

   The three phantom commands appear often but note that LaTeX provides
a suite of other commands to work with box sizes that may be more
convenient, including '\makebox' (*note \mbox & \makebox::) as well as
'\settodepth' (*note \settodepth::), '\settoheight' (*note
\settoheight::), and '\settowidth' (*note \settowidth::).  In addition,
the 'mathtools' package has many commands that offer fine-grained
control over spacing.

   All three commands produce an ordinary box, without any special
mathematics status.  So to do something like attaching a superscript you
should give it such a status, for example with the '\operatorname'
command from the package 'amsmath'.

   While most often used in mathematics, these three can appear in other
contexts.  However, they don't cause LaTeX to change into horizontal
mode.  So if one of these starts a paragraph then you should prefix it
with '\leavevmode'.

16.6.3 '\mathstrut'
-------------------

Synopsis:

     \mathstrut

   The analogue of '\strut' for mathematics.  *Note \strut::.

   The input '$\sqrt{x} + \sqrt{x^i}$' gives output where the second
radical is taller than the first.  To add extra vertical space without
any horizontal space, so that the two have the same height, use
'$\sqrt{x\mathstrut} + \sqrt{x^i\mathstrut}$'.

   The '\mathstrut' command adds the vertical height of an open
parenthesis, '(', but no horizontal space.  It is defined as
'\vphantom{(}', so see *note \phantom & \vphantom & \hphantom:: for
more.  An advantage over '\strut' is that '\mathstrut' adds no depth,
which is often the right thing for formulas.  Using the height of an
open parenthesis is just a convention; for complete control over the
amount of space, use '\rule' with a width of zero.  *Note \rule::.

16.7 Math styles
================

TeX's rules for typesetting a formula depend on the context.  For
example, inside a displayed equation, the input '\sum_{0\leq
i<n}k^m=\frac{n^{m+1}}{m+1}+\mbox{lower order terms}' will give output
with the summation index centered below the summation symbol.  But if
that input is inline then the summation index is off to the right rather
than below, so it won't push the lines apart.  Similarly, in a displayed
context, the symbols in the numerator and denominator will be larger
than for an inline context, and in display math subscripts and
superscripts are further apart then they are in inline math.

   TeX uses four math styles.

   * Display style is for a formula displayed on a line by itself, such
     as with '\begin{equation} ... \end{equation}'.

   * Text style is for an inline formula, as with 'so we have $ ... $'.

   * Script style is for parts of a formula in a subscript or
     superscript.

   * Scriptscript style is for parts of a formula at a second level (or
     more) of subscript or superscript.

   TeX determines a default math style but you can override it with a
declaration of '\displaystyle', or '\textstyle', or '\scriptstyle', or
'\scriptscriptstyle'.

   In this example, the 'Arithmetic' line's fraction will look
scrunched.

     \begin{tabular}{r|cc}
       \textsc{Name}  &\textsc{Series}  &\textsc{Sum}  \\  \hline
       Arithmetic     &$a+(a+b)+(a+2b)+\cdots+(a+(n-1)b)$
                        &$na+(n-1)n\cdot\frac{b}{2}$  \\
       Geometric      &$a+ab+ab^2+\cdots+ab^{n-1}$
                        &$\displaystyle a\cdot\frac{1-b^n}{1-b}$  \\
     \end{tabular}

But because of the '\displaystyle' declaration, the 'Geometric' line's
fraction will be easy to read, with characters the same size as in the
rest of the line.

   Another example is that, compared to the same input without the
declaration, the result of

     we get
     $\pi=2\cdot{\displaystyle\int_{x=0}^1 \sqrt{1-x^2}\,dx}$

will have an integral sign that is much taller.  Note that here the
'\displaystyle' applies to only part of the formula, and it is delimited
by being inside curly braces, as '{\displaystyle ...}'.

   The last example is a continued fraction.

     \begin{equation}
     a_0+\frac{1}{
            \displaystyle a_1+\frac{\mathstrut 1}{
            \displaystyle a_2+\frac{\mathstrut 1}{
            \displaystyle a_3}}}
     \end{equation}

Without the '\displaystyle' declarations, the denominators would be set
in script style and scriptscript style.  (The '\mathstrut' improves the
height of the denominators; *note \mathstrut::.)

16.8 Math miscellany
====================

LaTeX contains a wide variety of mathematics facilities.  Here are some
that don't fit into other categories.

16.8.1 Colon character ':' & '\colon'
-------------------------------------

Synopsis, one of:

     :
     \colon

   In mathematics, the colon character, ':', is a relation.

     With side ratios \( 3:4 \) and \( 4:5 \), the triangle is right.

Ordinary LaTeX defines '\colon' to produce the colon character with the
spacing appropriate for punctuation, as in set-builder notation
'\{x\colon 0\leq x<1\}'.

   But the widely-used 'amsmath' package defines '\colon' for use in the
definition of functions 'f\colon D\to C'.  So if you want the colon
character as a punctuation then use '\mathpunct{:}'.

16.8.2 '\*'
-----------

Synopsis:

     \*

   A multiplication symbol that allows a line break.  If there is a
break then LaTeX puts a '\times' symbol, ×, before that break.

   In '\( A_1\* A_2\* A_3\* A_4 \)', if there is no line break then
LaTeX outputs it as though it were '\( A_1 A_2 A_3 A_4 \)'.  If a line
break does happen, for example between the two middle ones, then LaTeX
sets it like '\( A_1 A_2 \times \)', followed by the break, followed by
'\( A_3 A_4 \)'.

16.8.3 '\frac'
--------------

Synopsis:

     \frac{NUMERATOR}{DENOMINATOR}

   Produces the fraction.  Used as: '\begin{displaymath}
\frac{1}{\sqrt{2\pi\sigma}} \end{displaymath}'.  In inline math mode it
comes out small; see the discussion of '\displaystyle' (*note Math
formulas::).

16.8.4 '\sqrt'
--------------

Synopsis, one of:

     \sqrt{ARG}
     \sqrt[ROOT-NUMBER]{ARG}

   The square root, or optionally other roots, of ARG.  The optional
argument ROOT-NUMBER gives the root, i.e., enter the cube root of 'x+y'
as '\sqrt[3]{x+y}'.  The radical grows with the size of ARG (as the
height of the radical grows, the angle on the leftmost part gets
steeper, until for a large enough 'arg', it is vertical).

   LaTeX has a separate '\surd' character (*note Math symbols::).

16.8.5 '\stackrel'
------------------

Synopsis, one of:

     \stackrel{TEXT}{RELATION}

   Put TEXT above RELATION.  To put a function name above an arrow enter
'\stackrel{f}{\longrightarrow}'.

17 Modes
********

As LaTeX processes your document, at any point it is in one of six
modes.  They fall into three categories of two each, the horizontal
modes, the math modes, and the vertical modes.  Some commands only work
in one mode or another (in particular, many commands only work in one of
the math modes), and error messages will refer to these.

   * "Paragraph mode" (in plain TeX this is called "horizontal mode") is
     what LaTeX is in when processing ordinary text.  It breaks the
     input text into lines and finds the positions of line breaks, so
     that in vertical mode page breaks can be done.  This is the mode
     LaTeX is in most of the time.

     "LR mode" (for left-to-right mode; in plain TeX this is called
     "restricted horizontal mode") is in effect when LaTeX starts making
     a box with an '\mbox' command.  As in paragraph mode, LaTeX's
     output is a string of words with spaces between them.  Unlike in
     paragraph mode, in LR mode LaTeX never starts a new line, it just
     keeps going from left to right.  (Although LaTeX will not complain
     that the LR box is too long, when it is finished and next tries to
     put that box into a line, it could very well complain that the
     finished LR box won't fit there.)

   * "Math mode" is when LaTeX is generating an inline mathematical
     formula.

     "Display math mode" is when LaTeX is generating a displayed
     mathematical formula.  (Displayed formulas differ somewhat from
     inline ones.  One example is that the placement of the subscript on
     '\int' differs in the two situations.)

   * "Vertical mode" is when LaTeX is building the list of lines and
     other material making the output page, which comprises insertion of
     page breaks.  This is the mode LaTeX is in when it starts a
     document.

     "Internal vertical mode" is in effect when LaTeX starts making a
     '\vbox'.  It has not such thing as page breaks, and as such is the
     vertical analogue of LR mode.

For instance, if you begin a LaTeX article with 'Let \( x \) be ...'
then these are the modes: first LaTeX starts every document in vertical
mode, then it reads the 'L' and switches to paragraph mode, then the
next switch happens at the '\(' where LaTeX changes to math mode, and
then when it leaves the formula it pops back to paragraph mode.

   Paragraph mode has two subcases.  If you use a '\parbox' command or a
'minipage' then LaTeX is put into paragraph mode.  But it will not put a
page break here.  Inside one of these boxes, called a "parbox", LaTeX is
in "inner paragraph mode".  Its more usual situation, where it can put
page breaks, is "outer paragraph mode" (*note Page breaking::).

17.1 '\ensuremath'
==================

Synopsis:

     \ensuremath{FORMULA}

   Ensure that FORMULA is typeset in math mode.

   For instance, you can redefine commands that ordinarily can be used
only in math mode, so that they can be used both in math and in plain
text.

     \newcommand{\dx}{\ensuremath{dx}}
     In $\int f(x)\, \dx$, the \dx{} is an infinitesimal.

   Caution: the '\ensuremath' command is useful but not a panacea.

     \newcommand{\alf}{\ensuremath{\alpha}}
     You get an alpha in text mode: \alf.
     But compare the correct spacing in $\alf+\alf$ with that in \alf+\alf.

Best is to typeset math things in a math mode.

18 Page styles
**************

The style of a page determines where LaTeX places the components of that
page, such as headers and footers, and the text body.  This includes
pages in the main part of the document but also includes special pages
such as the title page of a book, a page from an index, or the first
page of an article.

   The package 'fancyhdr' is very helpful for constructing page styles.
See its documentation on CTAN.

18.1 '\maketitle'
=================

Synopsis:

     \maketitle

   Generate a title.  In the standard classes the title appears on a
separate page, except in the 'article' class where it is at the top of
the first page.  (*Note Document class options::, for information about
the 'titlepage' document class option.)

   This example shows '\maketitle' appearing in its usual place,
immediately after '\begin{document}'.

     \documentclass{article}
     \title{Constructing a Nuclear Reactor Using Only Coconuts}
     \author{Jonas Grumby\thanks{%
         With the support of a Ginger Grant from the Roy Hinkley Society.} \\
       Skipper, \textit{Minnow}
       \and
       Willy Gilligan\thanks{%
         Thanks to the Mary Ann Summers foundation
         and to Thurston and Lovey Howell.}           \\
       Mate, \textit{Minnow}
       }
     \date{1964-Sep-26}
     \begin{document}
     \maketitle
     Just sit right back and you'll hear a tale, a tale of a fateful trip.
     That started from this tropic port, aboard this tiny ship. The mate was
     a mighty sailin' man, the Skipper brave and sure. Five passengers set
     sail that day for a three hour tour. A three hour tour.
       ...

   You tell LaTeX the information used to produce the title by making
the following declarations.  These must come before the '\maketitle',
either in the preamble or in the document body.

'\author{NAME1 \and NAME2 \and ...}'
     Required.  Declare the document author or authors.  The argument is
     a list of authors separated by '\and' commands.  To separate lines
     within a single author's entry, for instance to give the author's
     institution or address, use a double backslash, '\\'.  If you omit
     the '\author' declaration then you get 'LaTeX Warning: No \author
     given'.

'\date{TEXT}'
     Optional.  Declare TEXT to be the document's date.  The TEXT
     doesn't need to be in a date format; it can be any text at all.  If
     you omit '\date' then LaTeX uses the current date (*note \today::).
     To have no date, instead use '\date{}'.

'\thanks{TEXT}'
     Optional.  Produce a footnote.  You can use it in the author
     information for acknowledgements as illustrated above, but you can
     also use it in the title, or any place a footnote makes sense.  It
     can be any text at all so you can use it for any purpose, such as
     to print an email address.

'\title{TEXT}'
     Required.  Declare TEXT to be the title of the document.  Get line
     breaks inside TEXT with a double backslash, '\\'.  If you omit the
     '\title' declaration then you get 'LaTeX Error: No \title given'.

   To make your own title page, see *note titlepage::.  You can either
create this as a one-off or you can include it as part of a renewed
'\maketitle' command.  (Many publishers will provide a class to use in
place of 'article' that formats the title according to their house
requirements.)

18.2 '\pagenumbering'
=====================

Synopsis:

     \pagenumbering{NUMBER-STYLE}

   Specifies the style of page numbers, and resets the page number.  The
numbering style is reflected on the page, and also in the table of
contents and other page references.  This declaration has global scope
so its effect is not delimited by braces or environments.

   In this example, before the Main section the pages are numbered 'a',
etc.  Starting on the page containing that section, the pages are
numbered '1', etc.

     \begin{document}\pagenumbering{alph}
       ...
     \section{Main}\pagenumbering{arabic}
       ...

   The argument NUMBER-STYLE is one of the following (see also *note
\alph \Alph \arabic \roman \Roman \fnsymbol::).

'arabic'
     Arabic numerals: 1, 2, ...

'roman'
     lowercase Roman numerals: i, ii, ...

'Roman'
     uppercase Roman numerals: I, II, ...

'alph'
     lowercase letters: a, b, ... If you have more than 26 pages then
     you get 'LaTeX Error: Counter too large'.

'Alph'
     uppercase letters: A, B, ... If you have more than 26 pages then
     you get 'LaTeX Error: Counter too large'.

'gobble'
     LaTeX does not output a page number, although it does get reset.
     References to that page also are blank.  (This does not work with
     the popular package 'hyperref' so to have the page number not
     appear you may want to instead use '\pagestyle{empty}' or
     '\thispagestyle{empty}'.)

   Traditionally, if a document has front matter--preface, table of
contents, etc.--then it is numbered with lowercase Roman numerals.  The
main matter of a document uses arabic.  *Note \frontmatter & \mainmatter
& \backmatter::.

   If you want to change where the page number appears on the page,
see *note \pagestyle::.  If you want to change the value of the page
number, then you manipulate the 'page' counter (*note Counters::).

18.3 '\pagestyle'
=================

Synopsis:

     \pagestyle{STYLE}

   Declaration that specifies how the page headers and footers are
typeset, from the current page onwards.

   A discussion with an example is below.  Note first that the package
'fancyhdr' is now the standard way to manipulate headers and footers.
New documents that need to do anything other than one of the standard
options below should use this package.  See its documentation on CTAN.

   Values for STYLE:

'plain'
     The header is empty.  The footer contains only a page number,
     centered.

'empty'
     The header and footer are both empty.

'headings'
     Put running headers and footers on each page.  The document style
     specifies what goes in there; see the discussion below.

'myheadings'
     Custom headers, specified via the '\markboth' or the '\markright'
     commands.

   Some discussion of the motivation for LaTeX's mechanism will help you
work with the options 'headings' or 'myheadings'.  The document source
below produces an article, two-sided, with the pagestyle 'headings'.  On
this document's left hand pages, LaTeX wants (in addition to the page
number) the title of the current section.  On its right hand pages LaTeX
wants the title of the current subsection.  When it makes up a page,
LaTeX gets this information from the commands '\leftmark' and
'\rightmark'.  So it is up to '\section' and '\subsection' to store that
information there.

     \documentclass[twoside]{article}
     \pagestyle{headings}
     \begin{document}
       ... \section{Section 1} ... \subsection{Subsection 1.1} ...
     \section{Section 2}
       ...
     \subsection{Subsection 2.1}
       ...
     \subsection{Subsection 2.2}
       ...

Suppose that the second section falls on a left page.  Although when the
page starts it is in the first section, LaTeX will put 'Section 2' in
the left page header.  As to the right header, if no subsection starts
before the end of the right page then LaTeX blanks the right hand
header.  If a subsection does appear before the right page finishes then
there are two cases.  If at least one subsection starts on the right
hand page then LaTeX will put in the right header the title of the first
subsection starting on that right page.  If at least one of 2.1, 2.2,
..., starts on the left page but none starts on the right then LaTeX
puts in the right hand header the title of the last subsection to start,
that is, the one in effect during the right hand page.

   To accomplish this, in a two-sided article, LaTeX has '\section'
issue a command '\markboth', setting '\leftmark' to 'Section 2' and
setting '\rightmark' to blank.  And, LaTeX has '\subsection' issue a
command '\markright', setting '\rightmark' to 'Subsection 2.1', etc.

   Here are the descriptions of '\markboth' and '\markright':

'\markboth{LEFT-HEAD}{RIGHT-HEAD}'
     Sets both the right hand and left hand heading information for
     either a page style of 'headings' or 'myheadings'.  A left hand
     page heading LEFT-HEAD is generated by the last '\markboth' command
     before the end of the page.  A right hand page heading RIGHT-HEAD
     is generated by the first '\markboth' or '\markright' that comes on
     the page if there is one, otherwise by the last one that came
     before that page.

'\markright{RIGHT}'
     Sets the right hand page heading, leaving the left unchanged.

18.4 '\thispagestyle'
=====================

Synopsis:

     \thispagestyle{STYLE}

   Works in the same way as the '\pagestyle' (*note \pagestyle::),
except that it changes to STYLE for the current page only.  This
declaration has global scope, so its effect is not delimited by braces
or environments.

   Often the first page of a chapter or section has a different style.
For example, this LaTeX book document has the first page of the first
chapter in 'plain' style, as is the default (*note Page styles::).

     \documentclass{book}
     \pagestyle{headings}
     \begin{document}
     \chapter{First chapter}
       ...
     \chapter{Second chapter}\thispagestyle{empty}
       ...

The 'plain' style has a page number on it, centered in the footer.  To
make the page entirely empty, the command '\thispagestyle{empty}'
immediately follows the second '\chapter'.

19 Spaces
*********

LaTeX has many ways to produce white space, or filled space.  Some of
these are best suited to mathematical text; for these see *note Spacing
in math mode::.

19.1 '\enspace' & '\quad' & '\qquad'
====================================

Synopsis, one of:

     \enspace
     \quad
     \qquad

   Insert a horizontal space of 1/2em, 1em, or 2em.  The em is a length
defined by a font designer, often thought of as being the width of a
capital M. One advantage of describing space in ems is that it can be
more portable across documents than an absolute measurement such as
points (*note Lengths/em::).

   This puts a suitable gap between two graphics.

     \begin{center}
       \includegraphics{womensmile.png}%
       \qquad\includegraphics{mensmile.png}
     \end{center}

*Note Spacing in math mode::, for '\quad' and '\qquad'.  These are
lengths from centuries of typesetting and so may be a better choice in
many circumstances than arbitrary lengths, such as you get with
'\hspace'.

19.2 '\hspace'
==============

Synopsis, one of:

     \hspace{LENGTH}
     \hspace*{LENGTH}

   Insert the amount LENGTH of horizontal space.  The LENGTH can be
positive, negative, or zero; adding a negative amount of space is like
backspacing.  It is a rubber length, that is, it may contain a 'plus' or
'minus' component, or both (*note Lengths::).  Because the space is
stretchable and shrinkable, it is sometimes called "glue".

   This makes a line with 'Name:' an inch from the right margin.

     \noindent\makebox[\linewidth][r]{Name:\hspace{1in}}

   The '*'-form inserts horizontal space that is non-discardable.  More
precisely, when TeX breaks a paragraph into lines any white space--glues
and kerns--that come at a line break are discarded.  The '*'-form avoids
that (technically, it adds a non-discardable invisible item in front of
the space).

   In this example

     \parbox{0.8\linewidth}{%
       Fill in each blank: Four \hspace*{1in} and seven years ago our
       fathers brought forth on this continent, a new \hspace*{1in},
       conceived in \hspace*{1in}, and dedicated to the proposition
       that all men are created \hspace*{1in}.}

the 1 inch blank following 'conceived in' falls at the start of a line.
If you erase the '*' then LaTeX discards the blank.

   Here, the '\hspace' separates the three graphics.

     \begin{center}
       \includegraphics{lion.png}%   comment keeps out extra space
       \hspace{1cm minus 0.25cm}\includegraphics{tiger.png}%
       \hspace{1cm minus 0.25cm}\includegraphics{bear.png}
     \end{center}

Because the argument to each '\hspace' has 'minus 0.25cm', each can
shrink a little if the three figures are too wide.  But each space won't
shrink more than 0.25cm (*note Lengths::).

19.3 '\hfill'
=============

Synopsis:

     \hfill

   Produce a rubber length which has no natural space but that can
stretch horizontally as far as needed (*note Lengths::).

   This creates a one-line paragraph with 'Name:' on the left side of
the page and 'Quiz One' on the right.

     \noindent Name:\hfill Quiz One

   The '\hfill' command is equivalent to '\hspace{\fill}' and so the
space can be discarded at line breaks.  To avoid that instead use
'\hspace*{\fill}' (*note \hspace::).

   Here the graphs are evenly spaced in the middle of the figure.

     \newcommand*{\vcenteredhbox}[1]{\begin{tabular}{@{}c@{}}#1\end{tabular}}
       ...
     \begin{figure}
       \hspace*{\fill}%
       \vcenteredhbox{\includegraphics{graph0.png}}%
         \hfill\vcenteredhbox{\includegraphics{graph1.png}}%
       \hspace*{\fill}%
       \caption{Comparison of two graphs} \label{fig:twographs}
     \end{figure}

Note the '\hspace*''s where the space could otherwise be dropped.

19.4 '\hss'
===========

Synopsis:

     \hss

   Produce a horizontal space that is infinitely shrinkable as well as
infinitely stretchable (this command is a TeX primitive).  LaTeX authors
should reach first for the '\makebox' command to get the effects of
'\hss' (*note \mbox & \makebox::).

   Here, the first line's '\hss' makes the Z stick out to the right,
overwriting the Y. In the second line the Z sticks out to the left,
overwriting the X.

     X\hbox to 0pt{Z\hss}Y
     X\hbox to 0pt{\hss Z}Y

Without the '\hss' you get something like 'Overfull \hbox (6.11111pt too
wide) detected at line 20'.

19.5 '\spacefactor'
===================

Synopsis:

     \spacefactor=INTEGER

   Influence LaTeX's glue stretch and shrink behavior.  Most user-level
documents do not use this command.

   While LaTeX is laying out the material, it may stretch or shrink the
gaps between words.  (This space is not a character; it is called the
"interword glue"; *note \hspace::).  The '\spacefactor' command (from
Plain TeX) allows you to, for instance, have the space after a period
stretch more than the space after a word-ending letter.

   After LaTeX places each character, or rule or other box, it sets a
parameter called the "space factor".  If the next thing in the input is
a space then this parameter affects how much stretching or shrinking can
happen.  A space factor that is larger than the normal value means that
the glue can stretch more and shrink less.  Normally, the space factor
is 1000.  This value is in effect following most characters, and any
non-character box or math formula.  But it is 3000 after a period,
exclamation mark, or question mark, it is 2000 after a colon, 1500 after
a semicolon, 1250 after a comma, and 0 after a right parenthesis or
bracket, or closing double quote or single quote.  Finally, it is 999
after a capital letter.

   If the space factor F is 1000 then the glue gap will be the font's
normal space value (for Computer Modern Roman 10 point this is
3.3333 points).  Otherwise, if the space factor F is greater than 2000
then TeX adds the font's extra space value (for Computer Modern Roman 10
point this is 1.11111 points), and then the font's normal stretch value
is multiplied by f /1000 and the normal shrink value is multiplied by
1000/f (for Computer Modern Roman 10 point these are 1.66666 and
1.11111 points).

   For example, consider the period ending 'A man's best friend is his
dog.' After it, TeX puts in a fixed extra space, and also allows the
glue to stretch 3 times as much and shrink 1/3 as much, as the glue
after 'friend', which does not end in a period.

   The rules for space factors are even more complex because they play
additional roles.  In practice, there are two consequences.  First, if a
period or other punctuation is followed by a right parenthesis or
bracket, or right single or double quote then the spacing effect of that
period carries through those characters (that is, the following glue
will have increased stretch and shrink).  Second, if punctuation comes
after a capital letter then its effect is not in place so you get an
ordinary space.  This second case also affects abbreviations that do not
end in a capital letter (*note \@::).

   You can only use '\spacefactor' in paragraph mode or LR mode (*note
Modes::).  You can see the current value with '\the\spacefactor' or
'\showthe\spacefactor'.

   (Comment, not really related to '\spacefactor': if you get errors
like 'You can't use `\spacefactor' in vertical mode', or 'You can't use
`\spacefactor' in math mode.', or 'Improper \spacefactor' then you have
probably tried to redefine an internal command.  *Note \makeatletter &
\makeatother::.)

19.5.1 '\@'
-----------

Synopsis:

     CAPITAL-LETTER\@.

   Treat a period as sentence-ending, where LaTeX would otherwise think
it is part of an abbreviation.  LaTeX thinks that a period ends an
abbreviation if the period comes after a capital letter, and otherwise
thinks the period ends the sentence.  By default, in justifying a line
LaTeX adjusts the space after a sentence-ending period (or a question
mark, exclamation point, comma, or colon) more than it adjusts the space
between words (*note \spacefactor::).

   This example shows the two cases to remember.

     The songs \textit{Red Guitar}, etc.\ are by Loudon Wainwright~III\@.

The second period ends the sentence, despite that it is preceded by a
capital.  We tell LaTeX that it ends the sentence by putting '\@' before
it.  The first period ends the abbreviation 'etc.' but not the sentence.
The backslash-space, '\ ', produces a mid-sentence space.

   So: if you have a capital letter followed by a period that ends the
sentence, then put '\@' before the period.  This holds even if there is
an intervening right parenthesis or bracket, or right single or double
quote, because the spacing effect of that period carries through those
characters.  For example, this

     Use the \textit{Instructional Practices Guide},
     (a book by the MAA)\@.

will have correct inter-sentence spacing after the period.

   The '\@' command is only for a text mode.  If you use it outside of a
text mode then you get 'You can't use `\spacefactor' in vertical mode'
(*note Modes::).

   Comment: the converse case is a period ending an abbreviation whose
last letter is not a capital letter, and that abbreviation is not the
last word in the sentence.  For that case follow the period with a
backslash-space, ('\ '), or a tie, ('~'), or '\@'.  Examples are 'Nat.\
Acad.\ Science', and 'Mr.~Bean', and '(manure, etc.\@) for sale' (note
in the last one that the '\@' comes before the closing parenthesis).

19.5.2 '\frenchspacing' & '\nonfrenchspacing'
---------------------------------------------

Synopsis, one of:

     \frenchspacing
     \nonfrenchspacing

   The first declaration causes LaTeX to handle spacing between
sentences in the same way as spacing between words in the middle of a
sentence.  The second switches back to the default handling in which
spacing between sentences stretches or shrinks more (*note
\spacefactor::).

   Some typographic traditions, including English, prefer to adjust the
space between sentences (or spaces following a question mark,
exclamation point, comma, or colon) more than the space between words
that are in the middle of a sentence.  Declaring '\frenchspacing' (the
command is from plain TeX) switches to the tradition that all spaces are
treated equally.

19.5.3 '\normalsfcodes'
-----------------------

Synopsis:

     \normalsfcodes

   Reset the LaTeX space factors to the default values (*note
\spacefactor::).

19.6 Backslash-space, '\ '
==========================

This section refers to the command consisting of two characters, a
backslash followed by a space.
Synopsis:

     \ 

   Produce a space.  By default it produces white space of length
3.33333pt plus 1.66666pt minus 1.11111pt.

   When you type one or more blanks between words, LaTeX produces white
space.  But that is different than an explicit space.  This illustrates.

     \begin{tabular}{rl}
     One blank:& makes some space \\
     Three blanks:&   in a row \\
     Three spaces:&\ \ \ in a row \\
     \end{tabular}

On the first line LaTeX puts some space after the colon.  On the second
line LaTeX collapses the three blanks to output one whitespace, so you
end with the same space after the colon as in the first line.  LaTeX
would similarly collapse them to a single whitespace if one, two or all
of the three blanks were replaced by a tab, or by a newline.  However,
the bottom line asks for three spaces so the white area is wider.  That
is, the backslash-space command creates a fixed amount of horizontal
space.  (Note that you can define a horizontal space of any width at all
with '\hspace'; see *note \hspace::.)

   The backslash-space command has two main uses.  It is often used
after control sequences to keep them from gobbling the blank that
follows, as after '\TeX' in '\TeX\ (or \LaTeX)'.  (But using curly
braces has the advantage of still working whether the next character is
a blank or any other non-letter, as in '\TeX{} (or \LaTeX{})' in which
'{}' can be added after '\LaTeX' as well as after '\TeX'.)  The other
common use is that it marks a period as ending an abbreviation instead
of ending a sentence, as in 'Prof.\ Smith' or 'Jones et al.\ (1993)'
(*note \@::).

   Under normal circumstances, '\'<TAB> and '\'<NEWLINE> are equivalent
to backslash-space, '\ '.

   Please also note that in order to allow source code indentation,
under normal circumstances, TeX ignores leading blanks in a line.  So
the following prints 'one word':

     one
      word

where the white space between 'one' and 'word' is produced by the
newline after 'one', not by the space before 'word'.

19.7 '~'
========

Synopsis:

     BEFORE~AFTER

   The "tie" character, '~', produces a space between BEFORE and AFTER
at which the line will not be broken.  By default the white space has
length 3.33333pt plus 1.66666pt minus 1.11111pt (*note Lengths::).

   Note that the word 'tie' has this meaning in the TeX/Texinfo
community; this differs from the typographic term "tie", which is a
diacritic in the shape of an arc, called a "tie-after" accent in 'The
TeXbook'.

   Here LaTeX will not break the line between the final two words:

     Thanks to Prof.~Lerman.

In addition, despite the period, LaTeX does not use the end-of-sentence
spacing (*note \@::).

   Ties prevent the end of line separation of things where that could
cause confusion.  They also still allow hyphenation (of either of the
tied words), so they are generally preferable to putting consecutive
words in an '\mbox' (*note \mbox & \makebox::).

   They are also matters of taste, sometimes alarmingly dogmatic taste,
among readers.  Nevertheless, here are some usage models, many of them
from 'The TeXbook'.

   * Between an enumerator label and number, such as in references:
     'Chapter~12', or 'Theorem~\ref{th:Wilsons}', or
     'Figure~\ref{fig:KGraph}'.

   * When cases are enumerated inline: '(b)~Show that $f(x)$ is
     (1)~continuous, and (2)~bounded'.

   * Between a number and its unit: '$745.7.8$~watts' (the 'siunitx'
     package has a special facility for this) or '144~eggs'.  This
     includes between a month and day number in a date: 'October~12' or
     '12~Oct'.  In general, in any expressions where numbers and
     abbreviations or symbols are separated by a space: 'AD~565', or
     '2:50~pm', or 'Boeing~747', or '268~Plains Road', or
     '\$$1.4$~billion'.  Other common choices here are a thin space
     (*note \thinspace & \negthinspace::) and no space at all.

   * When mathematical phrases are rendered in words: 'equals~$n$', or
     'less than~$\epsilon$', or 'given~$X$', or 'modulo~$p^e$ for all
     large~$n$' (but compare 'is~$15$' with 'is $15$~times the height').
     Between mathematical symbols in apposition with nouns:
     'dimension~$d$' or 'function~$f(x)$' (but compare 'with length
     $l$~or more').  When a symbol is a tightly bound object of a
     preposition: 'of~$x$', or 'from $0$ to~$1$', or 'in common
     with~$m$'.

   * Between symbols in series: '$1$,~$2$, or~$3$' or '$1$,~$2$,
     \ldots,~$n$'.

   * Between a person's given names and between multiple surnames:
     'Donald~E. Knuth', or 'Luis~I. Trabb~Pardo', or 'Charles~XII'--but
     you must give TeX places to break the line so you might do 'Charles
     Louis Xavier~Joseph de~la Vall\'ee~Poussin'.

19.8 '\thinspace' & '\negthinspace'
===================================

Synopsis, one of:

     \thinspace
     \negthinspace

   These produce unbreakable and unstretchable spaces of 1/6em and
-1/6em, respectively.  These are the text mode equivalents of '\,' and
'\!' (*note Spacing in math mode/\thinspace::).

   You can use '\,' as a synonym for '\thinspace' in text mode.

   One common use of '\thinspace' is as the space between nested quotes:

     Killick replied, ``I heard the Captain say, `Ahoy there.'\thinspace''

Another use is that some style guides call for a '\thinspace' between an
ellipsis and a sentence ending period (other style guides, think the
three dots and/or four dots are plenty).  Another style-specific use is
between initials, as in 'D.\thinspace E.\ Knuth'.

   LaTeX provides a variety of similar spacing commands for math mode
(*note Spacing in math mode::).  With the 'amsmath' package, or as of
the 2020-10-01 LaTeX release, they can be used in text mode as well as
math mode, including '\!' for '\negthinspace'; but otherwise, they are
available only in math mode.

19.9 '\/'
=========

Synopsis:

     BEFORE-CHARACTER\/AFTER-CHARACTER

   Insert an "italic correction", a small space defined by the font
designer for each character (possibly zero), to avoid the character
colliding with whatever follows.  When you use '\/', LaTeX takes the
correction from the font metric file, scales it by any scaling that has
been applied to the font, and then inserts that much horizontal space.

   Here, were it not for the '\/', the BEFORE-CHARACTER italic f would
hit the AFTER-CHARACTER roman H

     \newcommand{\companylogo}{{\it f}\/H}

because the italic letter f leans far to the right.

   If AFTER-CHARACTER is a period or comma then don't insert an italic
correction since those punctuation symbols are so low to the baseline
already.  However, with semicolons or colons, as well as with normal
letters, the italic correction can help.  It is typically used between a
switch from italic or slanted fonts to an upright font.

   When you use commands such as '\emph' and '\textit' and '\textsl' to
change fonts, LaTeX automatically inserts the italic correction when
needed (*note Font styles::).  However, declarations such as '\em' and
'\itshape' and '\slshape' do not automatically insert italic
corrections.

   Upright characters can also have an italic correction.  An example
where this is needed is the name 'pdf\/\TeX'.  However, most upright
characters have a zero italic correction.  Some font creators do not
include italic correction values even for italic fonts.

   Technically, LaTeX uses another font-specific value, the so-called
"slant parameter" (namely '\fontdimen1'), to determine whether to
possibly insert an italic correction, rather than tying the action to
particular font commands.

   There is no concept of italic correction in math mode; math spacing
is done in a different way.

19.10 '\hrulefill' & '\dotfill'
===============================

Synopsis, one of:

     \hrulefill
     \dotfill

   Produce an infinite horizontal rubber length (*note Lengths::) that
LaTeX fills with a rule (that is, a line) or with dots, instead of white
space.

   This outputs a line 2 inches long.

     Name:~\makebox[2in]{\hrulefill}

This example, when placed between blank lines, creates a paragraph that
is left and right justified and where the middle is filled with evenly
spaced dots.

     \noindent John Aubrey, RN \dotfill{} Melbury Lodge

   To make the rule or dots go to the line's end use '\null' at the
start or end.

   To change the rule's thickness, copy the definition and adjust it, as
here

     \renewcommand{\hrulefill}{%
       \leavevmode\leaders\hrule height 1pt\hfill\kern0pt }

which changes the default thickness of 0.4pt to 1pt.  Similarly, adjust
the dot spacing as with

     \renewcommand{\dotfill}{%
       \leavevmode\cleaders\hbox to 1.00em{\hss .\hss }\hfill\kern0pt }

which changes the default length of 0.33em to 1.00em.

   This example produces a line for a signature.

     \begin{minipage}{4cm}
       \centering
       \hrulefill\\
       Signed
     \end{minipage}

The line is 4cm long.

19.11 '\bigskip' & '\medskip' & '\smallskip'
============================================

Synopsis, one of:

     \bigskip
     \medskip
     \smallskip

   Produce an amount of vertical space, large or medium-sized or small.
These commands are fragile (*note \protect::).

   Here the skip suggests the passage of time (from The Golden Ocean by
O'Brian).

     Mr Saumarez would have something rude to say to him, no doubt: he
     was at home again, and it was delightful.

     \bigskip
     ``A hundred and fifty-seven miles and one third, in twenty-four hours,''
     said Peter.

   Each command is associated with a length defined in the document
class file.

'\bigskip'
     The same as '\vspace{\bigskipamount}', ordinarily about one line
     space, with stretch and shrink.  The default for the 'book' and
     'article' classes is '12pt plus 4pt minus 4pt'.

'\medskip'
     The same as '\vspace{\medskipamount}', ordinarily about half of a
     line space, with stretch and shrink.  The default for the 'book'
     and 'article' classes is '6pt plus 2pt minus 2pt'.

'\smallskip'
     The same as '\vspace{\smallskipamount}', ordinarily about a quarter
     of a line space, with stretch and shrink.  The default for the
     'book' and 'article' classes is '3pt plus 1pt minus 1pt'.

   Because each command is a '\vspace', if you use it in mid-paragraph
then it will insert its vertical space between the line in which you use
it and the next line, not necessarily at the place that you use it.  So
these are best between paragraphs.

   The commands '\bigbreak', '\medbreak', and '\smallbreak' are similar
but also suggest to LaTeX that this is a good place to put a page break
(*note \bigbreak & \medbreak & \smallbreak::.

19.12 '\bigbreak' & '\medbreak' & '\smallbreak'
===============================================

Synopsis, one of:

     \bigbreak
     \medbreak
     \smallbreak

   Produce a vertical space that is big or medium-sized or small, and
suggest to LaTeX that this is a good place to break the page.  (The
associated penalties are -200, -100, and -50.)

   *Note \bigskip & \medskip & \smallskip::, for more.  These commands
produce the same vertical space but differ in that they also remove a
preceding vertical space if it is less than what they would insert (as
with '\addvspace').  In addition, they terminate a paragraph where they
are used: this example

     abc\bigbreak def ghi

     jkl mno pqr

will output three paragraphs, the first ending in 'abc' and the second
starting, after an extra vertical space and a paragraph indent, with
'def'.

19.13 '\strut'
==============

Synopsis:

     \strut

   Ensure that the current line has height at least '0.7\baselineskip'
and depth at least '0.3\baselineskip'.  Essentially, LaTeX inserts into
the line a rectangle having zero width,
'\rule[-0.3\baselineskip]{0pt}{\baselineskip}' (*note \rule::).  The
'\baselineskip' changes with the current font or fontsize.

   In this example the '\strut' keeps the box inside the frame from
having zero height.

     \setlength{\fboxsep}{0pt}\framebox[2in]{\strut}

   This example has four lists.  In the first there is a much bigger gap
between items 2 and 3 than there is between items 1 and 2.  The second
list fixes that with a '\strut' at the end of its first item's second
line.

     \setlength{\fboxsep}{0pt}
     \noindent\begin{minipage}[t]{0.2\linewidth}
     \begin{enumerate}
       \item \parbox[t]{15pt}{test \\ test}
       \item test
       \item test
     \end{enumerate}
     \end{minipage}%
     \begin{minipage}[t]{0.2\linewidth}
     \begin{enumerate}
       \item \parbox[t]{15pt}{test \\ test\strut}
       \item test
       \item test
     \end{enumerate}
     \end{minipage}%
     \begin{minipage}[t]{0.2\linewidth}
     \begin{enumerate}
       \item \fbox{\parbox[t]{15pt}{test \\ test}}
       \item \fbox{test}
       \item \fbox{test}
     \end{enumerate}
     \end{minipage}%
     \begin{minipage}[t]{0.2\linewidth}
     \begin{enumerate}
       \item \fbox{\parbox[t]{15pt}{test \\ test\strut}}
       \item \fbox{test}
       \item \fbox{test}
     \end{enumerate}
     \end{minipage}%

The final two lists use '\fbox' to show what's happening.  The first
item '\parbox' of the third list goes only to the bottom of its second
'test', which happens not have any characters that descend below the
baseline.  The fourth list adds the strut that gives the needed extra
below-baseline space.

   The '\strut' command is often useful in graphics, such as in 'TikZ'
or 'Asymptote'.  For instance, you may have a command such as
'\graphnode{NODE-NAME}' that fits a circle around NODE-NAME.  However,
unless you are careful the NODE-NAME's 'x' and 'y' will produce
different-diameter circles because the characters are different sizes.
A careful '\graphnode' might insert a '\strut', then NODE-NAME, and then
draw the circle.

   The general approach of using a zero width '\rule' is useful in many
circumstances.  In this table, the zero-width rule keeps the top of the
first integral from hitting the '\hline'.  Similarly, the second rule
keeps the second integral from hitting the first.

     \begin{tabular}{rl}
       \textsc{Integral}   &\textsc{Value}           \\
       \hline
       $\int_0^x t\, dt$   &$x^2/2$  \rule{0em}{2.5ex} \\
       $\int_0^x t^2\, dt$ &$x^3/3$  \rule{0em}{2.5ex}
     \end{tabular}

(Although the line-ending double backslash command has an available
optional argument to change the corresponding baseline skip, that won't
solve this issue.  Changing the first double backslash to something like
'\\[2.5ex]' will put more room between the header line and the '\hline'
rule, and the integral would still hit the rule.)

19.14 '\vspace'
===============

Synopsis, one of:

     \vspace{LENGTH}
     \vspace*{LENGTH}

   Add the vertical space LENGTH.  The LENGTH can be positive, negative,
or zero.  It is a rubber length--it may contain a 'plus' or 'minus'
component (*note Lengths::).

   This puts space between the two paragraphs.

     And I slept.

     \vspace{1ex plus 0.5ex}
     The new day dawned cold.

(*Note \bigskip & \medskip & \smallskip::, for common inter-paragraph
spaces.)

   The '*'-form inserts vertical space that is non-discardable.  More
precisely, LaTeX discards vertical space at a page break and the
'*'-form causes the space to stay.  This example leaves space between
the two questions.

     Question: Find the integral of \( 5x^4+5 \).

     \vspace*{2cm plus 0.5cm}
     Question: Find the derivative of \( x^5+5x+9 \).

That space will be present even if the page break happens to fall
between the questions.

   If you use '\vspace' in the middle of a paragraph (i.e., in
horizontal mode) then the space is inserted after the line containing
the '\vspace' command; it does not start a new paragraph at the
'\vspace' command.

   In this example the two questions will be evenly spaced vertically on
the page, with at least one inch of space below each.

     \begin{document}
     1) Who put the bomp in the bomp bah bomp bah bomp?
     \vspace{1in plus 1fill}

     2) Who put the ram in the rama lama ding dong?
     \vspace{1in plus 1fill}
     \end{document}

19.15 '\vfill'
==============

Synopsis:

     \vfill

   End the current paragraph and insert a vertical rubber length that is
infinite, so it can stretch or shrink as far as needed (*note
Lengths::).

   It is often used in the same way as '\vspace{\fill}', except that
'\vfill' ends the current paragraph whereas '\vspace{\fill}' adds the
infinite vertical space below its line, irrespective of the paragraph
structure.  In both cases that space will disappear at a page boundary;
to circumvent this see the starred option in *note \vspace::.

   In this example the page is filled, so the top and bottom lines
contain the text 'Lost Dog!' and the second 'Lost Dog!' is exactly
halfway between them.

     \begin{document}
     Lost Dog!
     \vfill
     Lost Dog!  % perfectly in the middle
     \vfill
     Lost Dog!
     \end{document}

19.16 '\addvspace'
==================

Synopsis:

     \addvspace{VERT-LENGTH}

   Add a vertical space of VERT-LENGTH.  However, if there are two or
more '\addvspace''s in a sequence then together they only add the space
needed to make the natural length equal to the maximum of the
VERT-LENGTH's in that sequence.  This command is fragile (*note
\protect::).  The VERT-LENGTH is a rubber length (*note Lengths::).

   This example illustrates.  The 'picture' draws a scale over which to
rules are placed.  In a standard LaTeX article the length
'\baselineskip' is 12pt.  As shown by the scale, the two rules are 22pt
apart: the sum of the '\baselineskip' and the 10pt from the first
'\addvspace'.

     \documentclass{article}
     \usepackage{color}
     \begin{document}
     \setlength{\unitlength}{2pt}%
     \noindent\begin{picture}(0,0)%
       \multiput(0,0)(0,-1){25}{{\color{blue}\line(1,0){1}}}
       \multiput(0,0)(0,-5){6}{{\color{red}\line(1,0){2}}}
     \end{picture}%
     \rule{0.25\linewidth}{0.1pt}%
     \par\addvspace{10pt}% \addvspace{20pt}%
     \par\noindent\rule{0.25\linewidth}{0.1pt}%
     \end{document}

Now uncomment the second '\addvspace'.  It does not make the gap 20pt
longer; instead the gap is the sum of '\baselineskip' and 20pt.  So
'\addvspace' in a sense does the opposite of its name--it makes sure
that multiple vertical spaces do not accumulate, but instead that only
the largest one is used.

   LaTeX uses this command to adjust the vertical space above or below
an environment that starts a new paragraph.  For instance, a 'theorem'
environment begins and ends with '\addvspace' so that two consecutive
'theorem''s are separated by one vertical space, not two.

   A error 'Something's wrong--perhaps a missing \item' pointing to an
'\addvspace' means that you were not in vertical mode when you hit this
command.  One way to change that is to precede '\addvspace' with a
'\par' command (*note \par::), as in the above example.

20 Boxes
********

At its core, LaTeX puts things in boxes and then puts the boxes on a
page.  So these commands are central.

   There are many packages on CTAN that are useful for manipulating
boxes.  One useful adjunct to the commands here is 'adjustbox'.

20.1 '\mbox' & '\makebox'
=========================

Synopsis, one of:

     \mbox{TEXT}
     \makebox{TEXT}
     \makebox[WIDTH]{TEXT}
     \makebox[WIDTH][POSITION]{TEXT}

   Create a box, a container for material.  The TEXT is typeset in LR
mode (*note Modes::) so it is not broken into lines.  The '\mbox'
command is robust, while '\makebox' is fragile (*note \protect::).

   Because 'text' is not broken into lines, you can use '\mbox' to
prevent hyphenation.  In this example, LaTeX will not hyphenate the tank
name, 'T-34'.

     The soviet tank \mbox{T-34} is a symbol of victory against nazism.

   The first two command synopsis versions, '\mbox' and '\makebox', are
roughly equivalent.  They create a box just wide enough to contain the
TEXT.  (They are like plain TeX's '\hbox'.)

   In the third version the optional argument WIDTH specifies the width
of the box.  Note that the space occupied by the text need not equal the
width of the box.  For one thing, TEXT can be too small; this creates a
full-line box

     \makebox[\linewidth]{Chapter Exam}

with 'Chapter Exam' centered.  But TEXT can also be too wide for WIDTH.
See the example below of zero-width boxes.

   In the WIDTH argument you can use the following lengths that refer to
the dimension of the box that LaTeX gets on typesetting TEXT: '\depth',
'\height', '\width', '\totalheight' (this is the box's height plus its
depth).  For example, to make a box with the text stretched to double
the natural size you can say this.

     \makebox[2\width]{Get a stretcher}

   For the fourth command synopsis version the optional argument
POSITION gives position of the text within the box.  It may take the
following values:

'c'
     The TEXT is centered (default).

'l'
     The TEXT is flush left.

'r'
     Flush right.

's'
     Stretch the interword space in TEXT across the entire WIDTH.  The
     TEXT must contain stretchable space for this to work.  For
     instance, this could head a press release:
     '\noindent\makebox[\textwidth][s]{\large\hfil IMMEDIATE\hfil
     RELEASE\hfil}'

   A common use of '\makebox' is to make zero-width text boxes.  This
puts the value of the quiz questions to the left of those questions.

     \newcommand{\pts}[1]{\makebox[0em][r]{#1 points\hspace*{1em}}}
     \pts{10}What is the air-speed velocity of an unladen swallow?

     \pts{90}An African or European swallow?


   The right edge of the output '10 points ' (note the ending space
after 'points') will be just before the 'What'.  You can use '\makebox'
similarly when making graphics, such as in 'TikZ' or 'Asymptote', where
you put the edge of the text at a known location, regardless of the
length of that text.

   For boxes with frames see *note \fbox & \framebox::.  For colors
see *note Colored boxes::.

   There is a related version of '\makebox' that is used within the
'picture' environment, where the length is given in terms of
'\unitlength' (*note \makebox (picture)::).

   As TEXT is typeset in LR mode, neither a double backslash '\\' nor
'\par' will give you a new line; for instance '\makebox{abc def \\ ghi}'
outputs 'abc defghi' while '\makebox{abc def \par ghi}' outputs 'abc def
ghi', both on a single line.  To get multiple lines see *note \parbox::
and *note minipage::.

20.2 '\fbox' & '\framebox'
==========================

Synopses, one of:

     \fbox{TEXT}
     \framebox{TEXT}
     \framebox[WIDTH]{TEXT}
     \framebox[WIDTH][POSITION]{TEXT}

   Create a box with an enclosing frame, four rules surrounding the
TEXT.  These commands are the same as '\mbox' and '\makebox' except for
the frame (*note \mbox & \makebox::).  The '\fbox' command is robust,
the '\framebox' command is fragile (*note \protect::).

     \fbox{Warning! No work shown, no credit given.}

LaTeX puts the text into a box, the text cannot be hyphenated.  Around
that box, separated from it by a small gap, are four rules making a
frame.

   The first two command invocations, '\fbox{...}' and '\framebox{...}',
are roughly the same.  As to the third and fourth invocations, the
optional arguments allow you to specify the box width as WIDTH and the
position of the text inside that box as POSITION.  *Note \mbox &
\makebox::, for the full description but here is an example creating an
empty box that is 1/4in wide.

     \setlength{\fboxsep}{0pt}\framebox[0.25in]{\strut}}

The '\strut' ensures a total height of '\baselineskip' (*note \strut::).

   These parameters determine the frame layout.

'\fboxrule'
     The thickness of the rules around the enclosed box.  The default is
     0.2pt.  Change it with a command such as
     '\setlength{\fboxrule}{0.8pt}' (*note \setlength::).

'\fboxsep'
     The distance from the frame to the enclosed box.  The default is
     3pt.  Change it with a command such as '\setlength{\fboxsep}{0pt}'
     (*note \setlength::).  Setting it to 0pt is useful sometimes: this
     will put a frame around the picture with no white border.

          {\setlength{\fboxsep}{0pt}%
           \framebox{%
             \includegraphics[width=0.5\textwidth]{prudence.jpg}}}

     The extra curly braces keep the effect of the '\setlength' local.

   As with '\mbox' and '\makebox', LaTeX will not break lines in TEXT.
But this example has LaTeX break lines to make a paragraph, and then
frame the result.

     \framebox{%
       \begin{minipage}{0.6\linewidth}
         My dear, here we must run as fast as we can, just to stay in place.
         And if you wish to go anywhere you must run twice as fast as that.
       \end{minipage}}

   *Note Colored boxes::, for colors other than black and white.

   The 'picture' environment has a version of the '\framebox' command
where the units depend on 'picture''s '\unitlength' (*note \framebox
(picture)::).

20.3 '\parbox'
==============

Synopses, one of:

     \parbox{WIDTH}{CONTENTS}
     \parbox[POSITION]{WIDTH}{CONTENTS}
     \parbox[POSITION][HEIGHT]{WIDTH}{CONTENTS}
     \parbox[POSITION][HEIGHT][INNER-POS]{WIDTH}{CONTENTS}

   Produce a box of text that is WIDTH wide.  Use this command to make a
box of small pieces of text, of a single paragraph.  This command is
fragile (*note \protect::).

     \begin{picture}(0,0)
       ...
       \put(1,2){\parbox{1.75in}{\raggedright Because the graph is a line on
                              this semilog paper, the relationship is
                              exponential.}}
     \end{picture}

   The CONTENTS are processed in a text mode (*note Modes::) so LaTeX
will break lines to make a paragraph.  But it won't make multiple
paragraphs; for that, use a 'minipage' environment (*note minipage::).

   The options for '\parbox' (except for CONTENTS) are the same as those
for 'minipage'.  For convenience a summary of the options is here but
see *note minipage:: for a complete description.

   There are two required arguments.  The WIDTH is a rigid length (*note
Lengths::).  It sets the width of the box into which LaTeX typesets
CONTENTS.  The CONTENTS is the text that is placed in that box.  It
should not have any paragraph-making components.

   There are three optional arguments, POSITION, HEIGHT, and INNER-POS.
The POSITION gives the vertical alignment of the "parbox" with respect
to the surrounding material.  The supported values are 'c' or 'm' to
make the vertical center of the parbox lines up with the center of the
adjacent text line (this is the default), or 't' to match the top line
of the parbox with the baseline of the surrounding material, or 'b' to
match the bottom line.

   The optional argument HEIGHT overrides the natural height of the box.

   The optional argument INNER-POS controls the placement of CONTENT
inside the 'parbox'.  Its default is the value of POSITION.  Its
possible values are: 't' to put the CONTENT at the top of the box, 'c'
to put it in the vertical center, 'b' to put it at the bottom of the
box, and 's' to stretch it out vertically (for this, the text must
contain vertically stretchable space).

20.4 '\raisebox'
================

Synopsis, one of:

     \raisebox{DISTANCE}{TEXT}
     \raisebox{DISTANCE}[HEIGHT]{TEXT}
     \raisebox{DISTANCE}[HEIGHT][DEPTH]{TEXT}

   Raise or lower TEXT.  This command is fragile (*note \protect::).

   This example makes a command for denoting the restriction of a
function by lowering the vertical bar symbol.

     \newcommand*\restricted[1]{\raisebox{-.5ex}{$|$}_{#1}}
     $f\restricted{A}$

   The first mandatory argument DISTANCE specifies how far to raise the
second mandatory argument TEXT.  This is a rigid length (*note
Lengths::).  If it is negative then it lowers TEXT.  The TEXT is
processed in LR mode so it cannot contain line breaks (*note Modes::).

   The optional arguments HEIGHT and DEPTH are dimensions.  If they are
specified, they override the natural height and depth of the box LaTeX
gets by typesetting TEXT.

   In the arguments DISTANCE, HEIGHT, and DEPTH you can use the
following lengths that refer to the dimension of the box that LaTeX gets
on typesetting TEXT: '\depth', '\height', '\width', '\totalheight' (this
is the box's height plus its depth).

   This will align two graphics on their top (*note Graphics::).

     \usepackage{graphicx,calc}  % in preamble
        ...
     \begin{center}
       \raisebox{1ex-\height}{%
         \includegraphics[width=0.4\linewidth]{lion.png}}
       \qquad
       \raisebox{1ex-\height}{%
         \includegraphics[width=0.4\linewidth]{meta.png}}
     \end{center}

The first '\height' is the height of 'lion.png' while the second is the
height of 'meta.png'.

20.5 '\sbox' & '\savebox'
=========================

Synopsis, one of:

     \sbox{BOX-CMD}{TEXT}
     \savebox{BOX-CMD}{TEXT}
     \savebox{BOX-CMD}[WIDTH]{TEXT}
     \savebox{BOX-CMD}[WIDTH][POS]{TEXT}

   Typeset TEXT just as with '\makebox' (*note \mbox & \makebox::)
except that LaTeX does not output it but instead saves it in a box
register referred to by a variable named BOX-CMD.  The variable name
BOX-CMD begins with a backslash, '\'.  You must have previously
allocated the box register BOX-CMD with '\newsavebox' (*note
\newsavebox::).  The '\sbox' command is robust while '\savebox' is
fragile (*note \protect::).

   This creates and uses a box register.

     \newsavebox{\fullname}
     \sbox{\fullname}{John Jacob Jingleheimer Schmidt}
       ...
     \usebox{\fullname}! His name is my name, too!
     Whenever we go out, the people always shout!
     There goes \usebox{\fullname}!  Ya da da da da da da.

One advantage of using and reusing a box register over a '\newcommand'
macro variable is efficiency, that LaTeX need not repeatedly retypeset
the contents.  See the example below.

   The first two command invocations, '\sbox{BOX-CMD}{TEXT}' and
'\savebox{BOX-CMD}{TEXT}', are roughly equivalent.  As to the third and
fourth, the optional arguments allow you to specify the box width as
WIDTH, and the position of the text inside that box as POSITION.  *Note
\mbox & \makebox::, for the full description.

   In the '\sbox' and '\savebox' commands the TEXT is typeset in LR mode
so it does not have line breaks (*note Modes::).  If you use these then
LaTeX doesn't give you an error but it ignores what you want: if you
enter '\sbox{\newreg}{test \\ test}' and '\usebox{\newreg}' then you get
'testtest', while if you enter '\sbox{\newreg}{test \par test}' and
'\usebox{\newreg}' then you get 'test test', but no error or warning.
To fix this use a '\parbox' or 'minipage' as here.

     \newsavebox{\areg}
     \savebox{\areg}{%
       \begin{minipage}{\linewidth}
         \begin{enumerate}
           \item First item
           \item Second item
         \end{enumerate}
       \end{minipage}}
       ...
     \usebox{\areg}

   As an example of the efficiency of reusing a register's contents,
this puts the same picture on each page of the document by putting it in
the header.  LaTeX only typesets it once.

     \usepackage{graphicx}  % all this in the preamble
     \newsavebox{\sealreg}
     \savebox{\sealreg}{%
       \setlength{\unitlength}{1in}%
       \begin{picture}(0,0)%
          \put(1.5,-2.5){%
            \begin{tabular}{c}
               \includegraphics[height=2in]{companylogo.png} \\
               Office of the President
            \end{tabular}}
       \end{picture}%
     }
     \markright{\usebox{\sealreg}}
     \pagestyle{headings}

The 'picture' environment is good for fine-tuning the placement.

   If the register '\noreg' has not already been defined then you get
something like 'Undefined control sequence. <argument> \noreg'.

20.6 'lrbox'
============

Synopsis:

     \begin{lrbox}{BOX-CMD}
       TEXT
     \end{lrbox}

   This is the environment form of the '\sbox' and '\savebox' commands,
and is equivalent to them.  *Note \sbox & \savebox::, for the full
description.

   The TEXT inside the environment is saved in the box register referred
to by variable 'BOX-CMD'.  The variable name BOX-CMD must begin with a
backslash, '\'.  You must allocate this box register in advance with
'\newsavebox' (*note \newsavebox::).  In this example the environment is
convenient for entering the 'tabular'.

     \newsavebox{\jhreg}
     \begin{lrbox}{\jhreg}
       \begin{tabular}{c}
         \includegraphics[height=1in]{jh.png} \\
         Jim Hef{}feron
       \end{tabular}
     \end{lrbox}
       ...
     \usebox{\jhreg}

20.7 '\usebox'
==============

Synopsis:

     \usebox{BOX-CMD}

   Produce the box most recently saved in the box register BOX-CMD by
the commands '\sbox' or '\savebox', or the 'lrbox' environment.  For
more information and examples, *note \sbox & \savebox::.  (Note that the
variable name BOX-CMD starts with a backslash, '\'.)  This command is
robust (*note \protect::).

21 Color
********

You can add color to text, rules, etc.  You can also have color in a box
or on an entire page and write text on top of it.

   Color support comes as an additional package.  So put
'\usepackage{color}' in your document preamble to use the commands
described here.

   Many other packages also supplement LaTeX's color abilities.
Particularly worth mentioning is 'xcolor', which is widely used and
significantly extends the capabilities described here, including adding
'HTML' and 'Hsb' color models.

21.1 'color' package options
============================

Synopsis (must be in the document preamble):

     \usepackage[COMMA-SEPARATED OPTION LIST]{color}

   When you load the 'color' package there are two kinds of available
options.

   The first specifies the "printer driver".  LaTeX doesn't contain
information about different output systems but instead depends on
information stored in a file.  Normally you should not specify the
driver option in the document, and instead rely on your system's
default.  One advantage of this is that it makes the document portable
across systems.  For completeness we include a list of the drivers.  The
currently relevant ones are: 'dvipdfmx', 'dvips', 'dvisvgm', 'luatex',
'pdftex', 'xetex'.  The two 'xdvi' and 'oztex' are essentially aliases
for 'dvips' (and 'xdvi' is monochrome).  Ones that should not be used
for new systems are: 'dvipdf', 'dvipdfm', 'dviwin', 'dvipsone', 'emtex',
'pctexps', 'pctexwin', 'pctexhp', 'pctex32', 'truetex', 'tcidvi', 'vtex'
(and 'dviwindo' is an alias for 'dvipsone').

   The second kind of options, beyond the drivers, are below.

'monochrome'
     Disable the color commands, so that they do not generate errors but
     do not generate color either.

'dvipsnames'
     Make available a list of 68 color names that are often used,
     particularly in legacy documents.  These color names were
     originally provided by the 'dvips' driver, giving the option name.

'nodvipsnames'
     Do not load that list of color names, saving LaTeX a tiny amount of
     memory space.

21.2 Color models
=================

A "color model" is a way of representing colors.  LaTeX's capabilities
depend on the printer driver.  However, the 'pdftex', 'xetex', and
'luatex' printer drivers are today by far the most commonly used.  The
models below work for those drivers.  All but one of these is also
supported by essentially all other printer drivers used today.

   Note that color combination can be additive or subtractive.  Additive
mixes colors of light, so that for instance combining full intensities
of red, green, and blue produces white.  Subtractive mixes pigments,
such as with inks, so that combining full intensity of cyan, magenta,
and yellow makes black.

'cmyk'
     A comma-separated list with four real numbers between 0 and 1,
     inclusive.  The first number is the intensity of cyan, the second
     is magenta, and the others are yellow and black.  A number value of
     0 means minimal intensity, while a 1 is for full intensity.  This
     model is often used in color printing.  It is a subtractive model.

'gray'
     A single real number between 0 and 1, inclusive.  The colors are
     shades of grey.  The number 0 produces black while 1 gives white.

'rgb'
     A comma-separated list with three real numbers between 0 and 1,
     inclusive.  The first number is the intensity of the red component,
     the second is green, and the third the blue.  A number value of 0
     means that none of that component is added in, while a 1 means full
     intensity.  This is an additive model.

'RGB'
     ('pdftex', 'xetex', 'luatex' drivers) A comma-separated list with
     three integers between 0 and 255, inclusive.  This model is a
     convenience for using 'rgb' since outside of LaTeX colors are often
     described in a red-green-blue model using numbers in this range.
     The values entered here are converted to the 'rgb' model by
     dividing by 255.

'named'
     Colors are accessed by name, such as 'PrussianBlue'.  The list of
     names depends on the driver, but all support the names 'black',
     'blue', 'cyan', 'green', 'magenta', 'red', 'white', and 'yellow'
     (See the 'dvipsnames' option in *note Color package options::).

21.3 Commands for color
=======================

These are the commands available with the 'color' package.

21.3.1 Define colors
--------------------

Synopsis:

     \definecolor{NAME}{MODEL}{SPECIFICATION}

   Give the name NAME to the color.  For example, after this

     \definecolor{silver}{rgb}{0.75,0.75,0.74}

you can use that color name with 'Hi ho, \textcolor{silver}{Silver}!'.

   This example gives the color a more abstract name, so it could change
and not be misleading.

     \definecolor{logocolor}{RGB}{145,92,131}    % RGB needs pdflatex
     \newcommand{\logo}{\textcolor{logocolor}{Bob's Big Bagels}}

   Often a document's colors are defined in the preamble, or in the
class or style, rather than in the document body.

21.3.2 Colored text
-------------------

Synopses:

     \textcolor{NAME}{...}
     \textcolor[COLOR MODEL]{COLOR SPECIFICATION}{...}

or

     \color{NAME}
     \color[COLOR MODEL]{SPECIFICATION}

   The affected text gets the color.  This line

     \textcolor{magenta}{My name is Ozymandias, king of kings:}
     Look on my works, ye Mighty, and despair!

causes the first half to be in magenta while the rest is in black.  You
can use a color declared with '\definecolor' in exactly the same way
that we just used the builtin color 'magenta'.

     \definecolor{MidlifeCrisisRed}{rgb}{1.0,0.11,0.0}
     I'm thinking about getting a \textcolor{MidlifeCrisisRed}{sports car}.

   The two '\textcolor' and '\color' differ in that the first is a
command form, enclosing the text to be colored as an argument.  Often
this form is more convenient, or at least more explicit.  The second
form is a declaration, as in 'The moon is made of {\color{green} green}
cheese', so it is in effect until the end of the current group or
environment.  This is sometimes useful when writing macros or as below
where it colors everything inside the 'center' environment, including
the vertical and horizontal lines.

     \begin{center} \color{blue}
       \begin{tabular}{l|r}
         UL &UR \\ \hline
         LL &LR
       \end{tabular}
     \end{center}

   You can use color in equations.  A document might have this
definition in the preamble

     \definecolor{highlightcolor}{RGB}{225,15,0}

and then contain this equation.

     \begin{equation}
       \int_a^b \textcolor{highlightcolor}{f'(x)}\,dx=f(b)-f(a)
     \end{equation}

   Typically the colors used in a document are declared in a class or
style but sometimes you want a one-off.  Those are the second forms in
the synopses.

     Colors of \textcolor[rgb]{0.33,0.14,0.47}{Purple} and
     {\color[rgb]{0.72,0.60,0.37}Gold} for the team.

   The format of COLOR SPECIFICATION depends on the color model (*note
Color models::).  For instance, while 'rgb' takes three numbers, 'gray'
takes only one.

     The selection was \textcolor[gray]{0.5}{grayed out}.

   Colors inside colors do not combine.  Thus

     \textcolor{green}{kind of \textcolor{blue}{blue}}

has a final word that is blue, not a combination of blue and green.

21.3.3 Colored boxes
--------------------

Synopses:

     \colorbox{NAME}{...}
     \colorbox[MODEL NAME]{BOX BACKGROUND COLOR}{...}

or

     \fcolorbox{FRAME COLOR}{BOX BACKGROUND COLOR}{...}
     \fcolorbox[MODEL NAME]{FRAME COLOR}{BOX BACKGROUND COLOR}{...}

   Make a box with the stated background color.  The '\fcolorbox'
command puts a frame around the box.  For instance this

     Name:~\colorbox{cyan}{\makebox[5cm][l]{\strut}}

makes a cyan-colored box that is five centimeters long and gets its
depth and height from the '\strut' (so the depth is '-.3\baselineskip'
and the height is '\baselineskip').  This puts white text on a blue
background.

     \colorbox{blue}{\textcolor{white}{Welcome to the machine.}}

   The '\fcolorbox' commands use the same parameters as '\fbox' (*note
\fbox & \framebox::), '\fboxrule' and '\fboxsep', to set the thickness
of the rule and the boundary between the box interior and the
surrounding rule.  LaTeX's defaults are '0.4pt' and '3pt', respectively.

   This example changes the thickness of the border to 0.8 points.  Note
that it is surrounded by curly braces so that the change ends at the end
of the second line.

     {\setlength{\fboxrule}{0.8pt}
     \fcolorbox{black}{red}{Under no circumstances turn this knob.}}

21.3.4 Colored pages
--------------------

Synopses:

     \pagecolor{NAME}
     \pagecolor[COLOR MODEL]{COLOR SPECIFICATION}
     \nopagecolor

   The first two set the background of the page, and all subsequent
pages, to the color.  For an explanation of the specification in the
second form *note Colored text::.  The third returns the background to
normal, which is a transparent background.  (If that is not supported
use '\pagecolor{white}', although that will make a white background
rather than the default transparent background.)

      ...
     \pagecolor{cyan}
      ...
     \nopagecolor

22 Graphics
***********

You can use graphics such as PNG or PDF files in your LaTeX document.
You need an additional package, which comes standard with LaTeX.  This
example is the short how-to.

     \include{graphicx}  % goes in the preamble
       ...
     \includegraphics[width=0.5\linewidth]{plot.pdf}

   To use the commands described here your document preamble must
contain either '\usepackage{graphicx}' or '\usepackage{graphics}'.  Most
of the time, 'graphicx' is the better choice.

   Graphics come in two main types, raster and vector.  LaTeX can use
both.  In raster graphics the file contains an entry for each location
in an array, describing what color it is.  An example is a photograph in
JPG format.  In vector graphics, the file contains a list of
instructions such as 'draw a circle with this radius and that center'.
An example is a line drawing produced by the Asymptote program, in PDF
format.  Generally vector graphics are more useful because you can
rescale their size without pixelation or other problems, and because
they often have a smaller size.

   There are systems particularly well-suited to make graphics for a
LaTeX document.  For example, these allow you to use the same fonts as
in your document.  LaTeX comes with a 'picture' environment (*note
picture::) that has simple capabilities.  Besides that, there are other
ways to include the graphic-making commands in the document.  Two such
systems are the PSTricks and TikZ packages.  There are also systems
external to LaTeX, that generate a graphic that you include using the
commands of this chapter.  Two that use a programming language are
Asymptote and MetaPost.  One that uses a graphical interface is Xfig.
Full description of these systems is outside the scope of this document;
see their documentation on CTAN.

22.1 'graphics' package options
===============================

Synopsis (must be in the document preamble):

     \usepackage[COMMA-SEPARATED OPTION LIST]{graphics}

or

     \usepackage[COMMA-SEPARATED OPTION LIST]{graphicx}

   The 'graphicx' package has a format for optional arguments to the
'\includegraphics' command that is convenient (it is the key-value
format), so it is the better choice for new documents.  When you load
the 'graphics' or 'graphicx' package with '\usepackage' there are two
kinds of available options.

   The first is that LaTeX does not contain information about different
output systems but instead depends on information stored in a "printer
driver" file.  Normally you should not specify the driver option in the
document, and instead rely on your system's default.  One advantage of
this is that it makes the document portable across systems.

   For completeness here is a list of the drivers.  The currently
relevant ones are: 'dvipdfmx', 'dvips', 'dvisvgm', 'luatex', 'pdftex',
'xetex'.  The two 'xdvi' and 'oztex' are essentially aliases for 'dvips'
(and 'xdvi' is monochrome).  Ones that should not be used for new
systems are: 'dvipdf', 'dvipdfm', 'dviwin', 'dvipsone', 'emtex',
'pctexps', 'pctexwin', 'pctexhp', 'pctex32', 'truetex', 'tcidvi', 'vtex'
(and 'dviwindo' is an alias for 'dvipsone').  These are stored in files
with a '.def' extension, such as 'pdftex.def'.

   The second kind of options are below.

'demo'
     Instead of an image file, LaTeX puts in a 150 pt by 100 pt
     rectangle (unless another size is specified in the
     '\includegraphics' command).

'draft'
     For each graphic file, it is not shown but instead its file name is
     printed in a box of the correct size.  In order to determine the
     size, the file must be present.

'final'
     (Default) Override any previous 'draft' option, so that the
     document shows the contents of the graphic files.

'hiderotate'
     Do not show rotated text.  (This allows for the possibility that a
     previewer does not have the capability to rotate text.)

'hidescale'
     Do not show scaled text.  (This allows for the possibility that a
     previewer does not have the capability to scale.)

'hiresbb'
     In a PS or EPS file the graphic size may be specified in two ways.
     The '%%BoundingBox' lines describe the graphic size using integer
     multiples of a PostScript point, that is, integer multiples of 1/72
     inch.  A later addition to the PostScript language allows decimal
     multiples, such as 1.23, in '%%HiResBoundingBox' lines.  This
     option has LaTeX to read the size from the latter.

22.2 'graphics' package configuration
=====================================

These commands configure the way LaTeX searches the file system for the
graphic.

   The behavior of file system search code is necessarily platform
dependent.  In this document we cover GNU/Linux, Macintosh, and Windows,
as those systems are typically configured.  For other situations consult
the documentation in 'grfguide.pdf', or the LaTeX source, or your TeX
distribution's documentation.

22.2.1 '\graphicspath'
----------------------

Synopsis:

     \graphicspath{LIST OF DIRECTORIES INSIDE CURLY BRACES}

   Declare a list of directories to search for graphics files.  This
allows you to later say something like '\includegraphics{lion.png}'
instead of having to give its path.

   LaTeX always looks for graphic files first in the current directory
(and the output directory, if specified; *note output directory::).  The
declaration below tells the system to then look in the subdirectory
'pix', and then '../pix'.

     \usepackage{graphicx}   % or graphics; put in preamble
       ...
     \graphicspath{ {pix/} {../pix/} }

   The '\graphicspath' declaration is optional.  If you don't include it
then LaTeX's default is to search all of the places that it usually
looks for a file (it uses LaTeX's '\input@path').  In particular, in
this case one of the places it looks is the current directory.

   Enclose each directory name in curly braces; for example, above it
says ''{pix}''.  Do this even if there is only one directory.  Each
directory name must end in a forward slash, '/'.  This is true even on
Windows, where good practice is to use forward slashes for all the
directory separators since it makes the document portable to other
platforms.  If you have spaces in your directory name then use double
quotes, as with '{"my docs/"}'.  Getting one of these rules wrong will
cause LaTeX to report 'Error: File `FILENAME' not found'.

   Basically, the algorithm is that with this example, after looking in
the current directory,

     \graphicspath{ {pix/} {../pix/} }
     ...
     \usepackage{lion.png}

for each of the listed directories, LaTeX concatenates it with the
filename and searches for the result, checking for 'pix/lion.png' and
then '../pix/lion.png'.  This algorithm means that the '\graphicspath'
command does not recursively search subdirectories: if you issue
'\graphicspath{{a/}}' and the graphic is in 'a/b/lion.png' then LaTeX
will not find it.  It also means that you can use absolute paths such as
'\graphicspath{{/home/jim/logos/}}' or
'\graphicspath{{C:/Users/Albert/Pictures/}}'.  However, using these
means that the document is not portable.  (You could preserve
portability by adjusting your TeX system settings configuration file
parameter 'TEXINPUTS'; see the documentation of your system.)

   You can use '\graphicspath' anywhere in the document.  You can use it
more than once.  Show its value with
'\makeatletter\typeout{\Ginput@path}\makeatother'.

   The directories are taken with respect to the base file.  That is,
suppose that you are working on a document based on 'book/book.tex' and
it contains '\include{chapters/chap1}'.  If in 'chap1.tex' you put
'\graphicspath{{plots/}}' then LaTeX will not search for graphics in
'book/chapters/plots', but instead in 'book/plots'.

22.2.2 '\DeclareGraphicsExtensions'
-----------------------------------

Synopses:

     \DeclareGraphicsExtensions{COMMA-SEPARATED LIST OF FILE EXTENSIONS}

   Declare the filename extensions to try.  This allows you to specify
the order in which to choose graphic formats when you include graphic
files by giving the filename without the extension, as in
'\includegraphics{functionplot}'.

   In this example, LaTeX will find files in the PNG format before PDF
files.

     \DeclareGraphicsExtensions{.png,PNG,.pdf,.PDF}
       ...
     \includegraphics{lion}   % will find lion.png before lion.pdf

Because the filename 'lion' does not have a period, LaTeX uses the
extension list.  For each directory in the graphics path (*note
\graphicspath::), LaTeX will try the extensions in the order given.  If
it does not find such a file after trying all the directories and
extensions then it reports '! LaTeX Error: File `'lion'' not found'.
Note that you must include the periods at the start of the extensions.

   Because GNU/Linux and Macintosh filenames are case sensitive, the
list of file extensions is case sensitive on those platforms.  The
Windows platform is not case sensitive.

   You are not required to include '\DeclareGraphicsExtensions' in your
document; the printer driver has a sensible default.  For example, the
most recent 'pdftex.def' has this extension list.

     .pdf,.png,.jpg,.mps,.jpeg,.jbig2,.jb2,.PDF,.PNG,.JPG,.JPEG,.JBIG2,.JB2

   To change the order, use the 'grfext' package.

   You can use this command anywhere in the document.  You can use it
more than once.  Show its value with
'\makeatletter\typeout{\Gin@extensions}\makeatother'.

22.2.3 '\DeclareGraphicsRule'
-----------------------------

Synopsis:

     \DeclareGraphicsRule{EXTENSION}{TYPE}{SIZE-FILE EXTENSION}{COMMAND}

   Declare how to handle graphic files whose names end in EXTENSION.

   This example declares that all files with names of the form
'filename-without-dot.mps' will be treated as output from MetaPost,
meaning that the printer driver will use its MetaPost-handling code to
input the file.

     \DeclareGraphicsRule{.mps}{mps}{.mps}{}

   This

     \DeclareGraphicsRule{*}{mps}{*}{}

tells LaTeX that it should handle as MetaPost output any file with an
extension not covered by another rule, so it covers 'filename.1',
'filename.2', etc.

   This describes the four arguments.

EXTENSION
     The file extension to which this rule applies.  The extension is
     anything after and including the first dot in the filename.  Use
     the Kleene star, '*', to denote the default behavior for all
     undeclared extensions.

TYPE
     The type of file involved.  This type is a string that must be
     defined in the printer driver.  For instance, files with extensions
     '.ps', '.eps', or '.ps.gz' may all be classed as type 'eps'.  All
     files of the same type will be input with the same internal command
     by the printer driver.  For example, the file types that 'pdftex'
     recognizes are: 'jpg', 'jbig2', 'mps', 'pdf', 'png', 'tif'.

SIZE-FILE EXTENSION
     The extension of the file to be read to determine the size of the
     graphic, if there is such a file.  It may be the same as EXTENSION
     but it may be different.

     As an example, consider a PostScript graphic.  To make it smaller,
     it might be compressed into a '.ps.gz' file.  Compressed files are
     not easily read by LaTeX so you can put the bounding box
     information in a separate file.  If SIZE-FILE EXTENSION is empty
     then you must specify size information in the arguments of
     '\includegraphics'.

     If the driver file has a procedure for reading size files for
     'type' then that will be used, otherwise it will use the procedure
     for reading '.eps' files.  (Thus you may specify the size of bitmap
     files in a file with a PostScript style '%%BoundingBox' line if no
     other format is available.)

COMMAND
     A command that will be applied to the file.  This is very often
     left empty.  This command must start with a single backward quote.
     Thus, '\DeclareGraphicsRule{.eps.gz}{eps}{.eps.bb}{`gunzip -c #1}'
     specifies that any file with the extension '.eps.gz' should be
     treated as an 'eps' file, with the BoundingBox information stored
     in the file with extension '.eps.bb', and that the command 'gunzip
     -c' will run on your platform to decompresses the file.

     Such a command is specific to your platform.  In addition, your TeX
     system must allow you to run external commands; as a security
     measure modern systems restrict running commands unless you
     explicitly allow it.  See the documentation for your TeX
     distribution.

22.3 Commands for graphics
==========================

These are the commands available with the 'graphics' and 'graphicx'
packages.

22.3.1 '\includegraphics'
-------------------------

Synopses for 'graphics' package:

     \includegraphics{FILENAME}
     \includegraphics[URX,URY]{FILENAME}
     \includegraphics[LLX,LLY][URX,URY]{FILENAME}
     \includegraphics*{FILENAME}
     \includegraphics*[URX,URY]{FILENAME}
     \includegraphics*[LLX,LLY][URX,URY]{FILENAME}

   Synopses for 'graphicx' package:

     \includegraphics{FILENAME}
     \includegraphics[KEY-VALUE LIST]{FILENAME}
     \includegraphics*{FILENAME}
     \includegraphics*[KEY-VALUE LIST]{FILENAME}

   Include a graphics file.  The starred form '\includegraphics*' will
clip the graphic to the size specified, while for the unstarred form any
part of the graphic that is outside the box of the specified size will
over-print the surrounding area.

   This

     \usepackage{graphicx}  % in preamble
       ...
     \begin{center}
       \includegraphics{plot.pdf}
     \end{center}

will incorporate into the document the graphic in 'plot.pdf', centered
and at its nominal size.  You can also give a path to the file, as with
'\includegraphics{graphics/plot.pdf}'.  To specify a list of locations
to search for the file, *note \graphicspath::.

   If your filename includes spaces then put it in double quotes.  An
example is '\includegraphics{"sister picture.jpg"}'.

   The '\includegraphics{FILENAME}' command decides on the type of
graphic by splitting FILENAME on the first dot.  You can instead use
FILENAME with no dot, as in '\includegraphics{turing}', and then LaTeX
tries a sequence of extensions such as '.png' and '.pdf' until it finds
a file with that extension (*note \DeclareGraphicsExtensions::).

   If your file name contains dots before the extension then you can
hide them with curly braces, as in
'\includegraphics{{plot.2018.03.12.a}.pdf}'.  Or, if you use the
'graphicx' package then you can use the options 'type' and 'ext'; see
below.  This and other filename issues are also handled with the package
'grffile'.

   This example puts a graphic in a 'figure' environment so LaTeX can
move it to the next page if fitting it on the current page is awkward
(*note figure::).

     \begin{figure}
       \centering
       \includegraphics[width=3cm]{lungxray.jpg}
       \caption{The evidence is overwhelming: don't smoke.}  \label{fig:xray}
     \end{figure}

   This places a graphic that will not float, so it is sure to appear at
this point in the document even if makes LaTeX stretch the text or
resort to blank areas on the page.  It will be centered and will have a
caption.

     \usepackage{caption}  % in preamble
       ...
     \begin{center}
       \includegraphics{pix/nix.png}
       \captionof{figure}{The spirit of the night} \label{pix:nix} % optional
     \end{center}

   This example puts a box with a graphic side by side with one having
text, with the two vertically centered.

     \newcommand*{\vcenteredhbox}[1]{\begin{tabular}{@{}c@{}}#1\end{tabular}}
       ...
     \begin{center}
       \vcenteredhbox{\includegraphics[width=0.4\textwidth]{plot}}
       \hspace{1em}
       \vcenteredhbox{\begin{minipage}{0.4\textwidth}
                        \begin{displaymath}
                          f(x)=x\cdot \sin (1/x)
                        \end{displaymath}
                      \end{minipage}}
     \end{center}

   If you use the 'graphics' package then the only options involve the
size of the graphic (but see *note \rotatebox:: and *note \scalebox::).
When one optional argument is present then it is '[URX,URY]' and it
gives the coordinates of the top right corner of the image, as a pair of
TeX dimensions (*note Units of length::).  If the units are omitted they
default to 'bp'.  In this case, the lower left corner of the image is
assumed to be at (0,0).  If two optional arguments are present then the
leading one is '[LLX,LLY]', specifying the coordinates of the image's
lower left.  Thus, '\includegraphics[1in,0.618in]{...}' calls for the
graphic to be placed so it is 1 inch wide and 0.618 inches tall and so
its origin is at (0,0).

   The 'graphicx' package gives you many more options.  Specify them in
a key-value form, as here.

     \begin{center}
       \includegraphics[width=1in,angle=90]{lion}
       \hspace{2em}
       \includegraphics[angle=90,width=1in]{lion}
     \end{center}

The options are read left-to-right.  So the first graphic above is made
one inch wide and then rotated, while the second is rotated and then
made one inch wide.  Thus, unless the graphic is perfectly square, the
two will end with different widths and heights.

   There are many options.  The primary ones are listed first.

   Note that a graphic is placed by LaTeX into a box, which is
traditionally referred to as its "bounding box" (distinct from the
PostScript BoundingBox described below).  The graphic's printed area may
go beyond this box, or sit inside this box, but when LaTeX makes up a
page it puts together boxes and this is the box allocated for the
graphic.

'width'
     The graphic will be shown so its bounding box is this width.  An
     example is '\includegraphics[width=1in]{plot}'.  You can use the
     standard TeX dimensions (*note Units of length::) and also
     convenient is '\linewidth', or in a two-column document,
     '\columnwidth' (*note Page layout parameters::).  An example is
     that by using the 'calc' package you can make the graphic be 1 cm
     narrower than the width of the text with
     '\includegraphics[width=\linewidth-1.0cm]{hefferon.jpg}'.

'height'
     The graphic will be shown so its bounding box is this height.  You
     can use the standard TeX dimensions (*note Units of length::), and
     also convenient are '\pageheight' and '\textheight' (*note Page
     layout parameters::).  For instance, the command
     '\includegraphics[height=0.25\textheight]{godel}' will make the
     graphic a quarter of the height of the text area.

'totalheight'
     The graphic will be shown so its bounding box has this height plus
     depth.  This differs from the height if the graphic was rotated.
     For instance, if it has been rotated by -90 then it will have zero
     height but a large depth.

'keepaspectratio'
     If set to 'true', or just specified as here

          \includegraphics[...,keepaspectratio,...]{...}

     and you give as options both 'width' and 'height' (or
     'totalheight'), then LaTeX will make the graphic is as large as
     possible without distortion.  That is, LaTeX will ensure that
     neither is the graphic wider than 'width' nor taller than 'height'
     (or 'totalheight').

'scale'
     Factor by which to scale the graphic.  To make a graphic twice its
     nominal size, enter '\includegraphics[scale=2.0]{...}'.  This
     number may be any value; a number between 0 and 1 will shrink the
     graphic and a negative number will reflect it.

'angle'
     Rotate the graphic.  The angle is taken in degrees and
     counterclockwise.  The graphic is rotated about its 'origin'; see
     that option.  For a complete description of how rotated material is
     typeset, *note \rotatebox::.

'origin'
     The point of the graphic about which the rotation happens.
     Possible values are any string containing one or two of: 'l' for
     left, 'r' for right, 'b' for bottom, 'c' for center, 't' for top,
     and 'B' for baseline.  Thus, entering the command
     '\includegraphics[angle=180,origin=c]{moon}' will turn the picture
     upside down about that picture's center, while the command
     '\includegraphics[angle=180,origin=lB]{LeBateau}' will turn its
     picture upside down about its left baseline.  (The character 'c'
     gives the horizontal center in 'bc' or 'tc', but gives the vertical
     center in 'lc' or 'rc'.)  The default is 'lB'.

     To rotate about an arbitrary point, *note \rotatebox::.

   These are lesser-used options.

'viewport'
     Pick out a subregion of the graphic to show.  Takes four arguments,
     separated by spaces and given in TeX dimensions, as with
     '\includegraphics[.., viewport=0in 0in 1in 0.618in]{...}'.  When
     the unit is omitted, the dimensions default to big points, 'bp'.
     They are taken relative to the origin specified by the bounding
     box.  See also the 'trim' option.

'trim'
     Gives parts of the graphic to not show.  Takes four arguments,
     separated by spaces, that are given in TeX dimensions, as with
     '\includegraphics[.., trim= 0in 0.1in 0.2in 0.3in, ...]{...}'.
     These give the amounts of the graphic not to show, that is, LaTeX
     will crop the picture by 0 inches on the left, 0.1 inches on the
     bottom, 0.2 inches on the right, and 0.3 inches on the top.  See
     also the 'viewport' option.

'clip'
     If set to 'true', or just specified as here

          \includegraphics[...,clip,...]{...}

     then the graphic is cropped to the bounding box.  This is the same
     as using the starred form of the command,
     '\includegraphics*[...]{...}'.

'page'
     Give the page number of a multi-page PDF file.  The default is
     'page=1'.

'pagebox'
     Specifies which bounding box to use for PDF files from among
     'mediabox', 'cropbox', 'bleedbox', 'trimbox', or 'artbox'.  PDF
     files do not have the BoundingBox that PostScript files have, but
     may specify up to four predefined rectangles.  The MediaBox gives
     the boundaries of the physical medium.  The CropBox is the region
     to which the contents of the page are to be clipped when displayed.
     The BleedBox is the region to which the contents of the page should
     be clipped in production.  The TrimBox is the intended dimensions
     of the finished page.  The ArtBox is the extent of the page's
     meaningful content.  The driver will set the image size based on
     CropBox if present, otherwise it will not use one of the others,
     with a driver-defined order of preference.  MediaBox is always
     present.

'interpolate'
     Enable or disable interpolation of raster images by the viewer.
     Can be set with 'interpolate=true' or just specified as here.

          \includegraphics[...,interpolate,...]{...}

'quiet'
     Do not write information to the log.  You can set it with
     'quiet=true' or just specified it with
     '\includegraphics[...,quiet,...]{...}',

'draft'
     If you set it with 'draft=true' or just specify it with

          \includegraphics[...,draft,...]{...}

     then the graphic will not appear in the document, possibly saving
     color printer ink.  Instead, LaTeX will put an empty box of the
     correct size with the filename printed in it.

   These options address the bounding box for Encapsulated PostScript
graphic files, which have a size specified with a line '%%BoundingBox'
that appears in the file.  It has four values, giving the lower x
coordinate, lower y coordinate, upper x coordinate, and upper y
coordinate.  The units are PostScript points, equivalent to TeX's big
points, 1/72 inch.  For example, if an '.eps' file has the line
'%%BoundingBox 10 20 40 80' then its natural size is 30/72 inch wide by
60/72 inch tall.

'bb'
     Specify the bounding box of the displayed region.  The argument is
     four dimensions separated by spaces, as with '\includegraphics[..,
     bb= 0in 0in 1in 0.618in]{...}'.  Usually '\includegraphics' reads
     the BoundingBox numbers from the EPS file automatically, so this
     option is only useful if the bounding box is missing from that file
     or if you want to change it.

'bbllx, bblly, bburx, bbury'
     Set the bounding box.  These four are obsolete, but are retained
     for compatibility with old packages.

'natwidth, natheight'
     An alternative for 'bb'.  Setting

          \includegraphics[...,natwidth=1in,natheight=0.618in,...]{...}

     is the same as setting 'bb=0 0 1in 0.618in'.

'hiresbb'
     If set to 'true', or just specified as with

          \includegraphics[...,hiresbb,...]{...}

     then LaTeX will look for '%%HiResBoundingBox' lines instead of
     '%%BoundingBox' lines.  (The 'BoundingBox' lines use only natural
     numbers while the 'HiResBoundingBox' lines use decimals; both use
     units equivalent to TeX's big points, 1/72 inch.)  To override a
     prior setting of 'true', you can set it to 'false'.

   These following options allow a user to override LaTeX's method of
choosing the graphic type based on the filename extension.  An example
is that '\includegraphics[type=png,ext=.xxx,read=.xxx]{lion}' will read
the file 'lion.xxx' as though it were 'lion.png'.  For more on these,
*note \DeclareGraphicsRule::.

'type'
     Specify the graphics type.

'ext'
     Specify the graphics extension.  Only use this in conjunction with
     the option 'type'.

'read'
     Specify the file extension of the read file.  Only use this in
     conjunction with the option 'type'.

'command'
     Specify a command to be applied to this file.  Only use this in
     conjunction with the option 'type'.  *Note Command line options::,
     for a discussion of enabling the '\write18' functionality to run
     external commands.

22.3.2 '\rotatebox'
-------------------

Synopsis if you use the 'graphics' package:

     \rotatebox{ANGLE}{MATERIAL}

   Synopses if you use the 'graphicx' package:

     \rotatebox{ANGLE}{MATERIAL}
     \rotatebox[KEY-VALUE LIST]{ANGLE}{MATERIAL}

   Put MATERIAL in a box and rotate it ANGLE degrees counterclockwise.

   This example rotates the table column heads forty-five degrees.

     \begin{tabular}{ll}
       \rotatebox{45}{Character} &\rotatebox{45}{NATO phonetic}   \\
       A                         &AL-FAH  \\
       B                         &BRAH-VOH
     \end{tabular}

   The MATERIAL can be anything that goes in a box, including a graphic.

       \rotatebox[origin=c]{45}{\includegraphics[width=1in]{lion}}

   To place the rotated material, the first step is that LaTeX sets
MATERIAL in a box, with a reference point on the left baseline.  The
second step is the rotation, by default about the reference point.  The
third step is that LaTeX computes a box to bound the rotated material.
Fourth, LaTeX moves this box horizontally so that the left edge of this
new bounding box coincides with the left edge of the box from the first
step (they need not coincide vertically).  This new bounding box, in its
new position, is what LaTeX uses as the box when typesetting this
material.

   If you use the 'graphics' package then the rotation is about the
reference point of the box.  If you use the 'graphicx' package then
these are the options that can go in the KEY-VALUE LIST, but note that
you can get the same effect without needing this package, except for the
'x' and 'y' options (*note \includegraphics::).

'origin'
     The point of the MATERIAL's box about which the rotation happens.
     Possible value is any string containing one or two of: 'l' for
     left, 'r' for right, 'b' for bottom, 'c' for center, 't' for top,
     and 'B' for baseline.  Thus, the first line here

          \rotatebox[origin=c]{180}{moon}
          \rotatebox[origin=lB]{180}{LeBateau}

     will turn the picture upside down from the center while the second
     will turn its picture upside down about its left baseline.  (The
     character 'c' gives the horizontal center in 'bc' or 'tc' but gives
     the vertical center in 'lc' or 'rc', and gives both in 'c'.)  The
     default is 'lB'.

'x, y'
     Specify an arbitrary point of rotation with '\rotatebox[x=TeX
     DIMENSION,y=TeX DIMENSION]{...}' (*note Units of length::).  These
     give the offset from the box's reference point.

'units'
     This key allows you to change the default of degrees
     counterclockwise.  Setting 'units=-360' changes the direction to
     degrees clockwise and setting 'units=6.283185' changes to radians
     counterclockwise.

22.3.3 '\scalebox'
------------------

Synopses:

     \scalebox{HORIZONTAL FACTOR}{MATERIAL}
     \scalebox{HORIZONTAL FACTOR}[VERTICAL FACTOR]{MATERIAL}
     \reflectbox{MATERIAL}

   Scale the MATERIAL.

   This example halves the size, both horizontally and vertically, of
the first text and doubles the size of the second.

     \scalebox{0.5}{DRINK ME} and \scalebox{2.0}{Eat Me}

   If you do not specify the optional VERTICAL FACTOR then it defaults
to the same value as the HORIZONTAL FACTOR.

   You can use this command to resize a graphic, as here.

     \scalebox{0.5}{\includegraphics{lion}}

If you use the 'graphicx' package then you can accomplish the same thing
with optional arguments to '\includegraphics' (*note
\includegraphics::).

   The '\reflectbox' command abbreviates '\scalebox{-1}[1]{MATERIAL}'.
Thus, 'Able was I\reflectbox{Able was I}' will show the phrase 'Able was
I' immediately followed by its mirror reflection against a vertical
axis.

22.3.4 '\resizebox'
-------------------

Synopses:

     \resizebox{HORIZONTAL LENGTH}{VERTICAL LENGTH}{MATERIAL}
     \resizebox*{HORIZONTAL LENGTH}{VERTICAL LENGTH}{MATERIAL}

   Given a size, such as '3cm', transform MATERIAL to make it that size.
If either HORIZONTAL LENGTH or VERTICAL LENGTH is an exclamation
point '!' then the other argument is used to determine a scale factor
for both directions.

   This example makes the graphic be a half inch wide and scales it
vertically by the same factor to keep it from being distorted.

     \resizebox{0.5in}{!}{\includegraphics{lion}}

   The unstarred form '\resizebox' takes VERTICAL LENGTH to be the box's
height while the starred form '\resizebox*' takes it to be height+depth.
For instance, make the text have a height+depth of a quarter-inch with
'\resizebox*{!}{0.25in}{\parbox{3.5in}{This box has both height and
depth.}}'.

   You can use '\depth', '\height', '\totalheight', and '\width' to
refer to the original size of the box.  Thus, make the text two inches
wide but keep the original height with '\resizebox{2in}{\height}{Two
inches}'.

23 Special insertions
*********************

LaTeX provides commands for inserting characters that have a special
meaning do not correspond to simple characters you can type.

23.1 Reserved characters
========================

LaTeX sets aside the following characters for special purposes.  For
example, the percent sign '%' is for comments.  They are called
"reserved characters" or "special characters".  They are all discussed
elsewhere in this manual.

     # $ % & { } _ ~ ^ \

   If you want a reserved character to be printed as itself, in the text
body font, for all but the final three characters in that list simply
put a backslash '\' in front of the character.  Thus, typing '\$1.23'
will produce '$1.23' in your output.

   As to the last three characters, to get a tilde in the text body font
use '\~{}' (omitting the curly braces would result in the next character
receiving a tilde accent).  Similarly, to get a text body font
circumflex use '\^{}'.  To get a backslash in the font of the text body,
enter '\textbackslash{}'.

   To produce the reserved characters in a typewriter font use '\verb!!'
as below (the double backslash '\\' is only there to split the lines in
the output).

     \begin{center}
       \# \$ \% \& \{ \} \_ \~{} \^{} \textbackslash \\
       \verb!# $ % & { } _ ~ ^ \!
     \end{center}

23.2 Upper and lower case
=========================

Synopsis:

     \uppercase{TEXT}
     \lowercase{TEXT}
     \MakeUppercase{TEXT}
     \MakeLowercase{TEXT}

   Change the case of characters.  The TeX primitive commands
'\uppercase' and '\lowercase' are set up by default to work only with
the 26 letters a-z and A-Z. The LaTeX commands '\MakeUppercase' and
'\MakeLowercase' commands also change characters accessed by commands
such as '\ae' or '\aa'.  The commands '\MakeUppercase' and
'\MakeLowercase' are robust but they have moving arguments (*note
\protect::).

   These commands do not change the case of letters used in the name of
a command within TEXT.  But they do change the case of every other Latin
letter inside the argument TEXT.  Thus, '\MakeUppercase{Let $y=f(x)$'}
produces 'LET Y=F(X)'.  Another example is that the name of an
environment will be changed, so that '\MakeUppercase{\begin{tabular} ...
\end{tabular}}' will produce an error because the first half is changed
to '\begin{TABULAR}'.

   LaTeX uses the same fixed table for changing case throughout a
document, The table used is designed for the font encoding T1; this
works well with the standard TeX fonts for all Latin alphabets but will
cause problems when using other alphabets.

   To change the case of text that results from a macro inside TEXT you
need to do expansion.  Here the '\Schoolname' produces 'COLLEGE OF
MATHEMATICS'.

     \newcommand{\schoolname}{College of Mathematics}
     \newcommand{\Schoolname}{\expandafter\MakeUppercase
                                \expandafter{\schoolname}}

   The 'textcase' package brings some of the missing feature of the
standard LaTeX commands '\MakeUppercase' and '\MakeLowerCase'.

   To uppercase only the first letter of words, you can use the package
'mfirstuc'.

   Handling all the casing rules specified by Unicode, e.g., for
non-Latin scripts, is a much bigger job than anything envisioned in the
original TeX and LaTeX.  It has been implemented in the 'expl3' package
as of 2020.  The article "Case changing: From TeX primitives to the
Unicode algorithm", (Joseph Wright, 'TUGboat' 41:1,
<https://tug.org/TUGboat/tb41-1/tb127wright-case.pdf>), gives a good
overview of the topic, past and present.

23.3 Symbols by font position
=============================

You can access any character of the current font using its number with
the '\symbol' command.  For example, the visible space character used in
the '\verb*' command has the code decimal 32 in the standard Computer
Modern typewriter font, so it can be typed as '\symbol{32}'.

   You can also specify numbers in octal (base 8) by using a ''' prefix,
or hexadecimal (base 16) with a '"' prefix, so the visible space at 32
decimal could also be written as '\symbol{'40}' or '\symbol{"20}'.

23.4 Text symbols
=================

LaTeX provides commands to generate a number of non-letter symbols in
running text.  Some of these, especially the more obscure ones, are not
available in OT1.  As of the LaTeX February 2020 release, all symbols
are available by default; before that, it was necessary to use the
'textcomp' package for some (technically, those in the 'TS1' font
encoding).

'\copyright'
'\textcopyright'
     (C) The copyright symbol.

'\dag'
     † The dagger symbol (in text).

'\ddag'
     ‡ The double dagger symbol (in text).

'\LaTeX'
     The LaTeX logo.

'\LaTeXe'
     The LaTeX2e logo.

'\guillemotleft («)'
'\guillemotright (»)'
'\guilsinglleft (‹)'
'\guilsinglright (›)'
     «, », ‹, › Double and single angle quotation marks, commonly used
     in French.

'\ldots'
'\dots'
'\textellipsis'
     ... An ellipsis (three dots at the baseline): '\ldots' and '\dots'
     also work in math mode.

'\lq'
     ' Left (opening) quote.

'\P'
'\textparagraph'
     ¶ Paragraph sign (pilcrow).

'\pounds'
'\textsterling'
     £ English pounds sterling.

'\quotedblbase („)'
'\quotesinglbase (‚)'
     „ and ‚ Double and single quotation marks on the baseline.

'\rq'
     ' Right (closing) quote.

'\S'
'\textsection'
     § Section sign.

'\TeX'
     The TeX logo.

'\textasciicircum'
     ^ ASCII circumflex.

'\textasciitilde'
     ~ ASCII tilde.

'\textasteriskcentered'
     * Centered asterisk.

'\textbackslash'
     \ Backslash.

'\textbar'
     | Vertical bar.

'\textbardbl'
     ⏸ Double vertical bar.

'\textbigcircle'
     ◯, Big circle symbol.

'\textbraceleft'
     { Left brace.

'\textbraceright'
     } Right brace.

'\textbullet'
     * Bullet.

'\textcircled{LETTER}'
     Ⓐ, Circle around LETTER.

'\textcompwordmark'
'\textcapitalcompwordmark'
'\textascendercompwordmark'
     Used to separate letters that would normally ligature.  For
     example, 'f\textcompwordmark i' produces 'fi' without a ligature.
     This is most useful in non-English languages.  The
     '\textcapitalcompwordmark' form has the cap height of the font
     while the '\textascendercompwordmark' form has the ascender height.

'\textdagger'
     † Dagger.

'\textdaggerdbl'
     ‡ Double dagger.

'\textdollar (or '\$')'
     $ Dollar sign.

'\textemdash (or '---')'
     -- Em-dash.  Used for punctuation, usually similar to commas or
     parentheses, as in ''The playoffs---if you're lucky enough to make
     the playoffs---are more like a sprint.'' Conventions for spacing
     around em-dashes vary widely.

'\textendash (or '--')'
     - En-dash.  Used for ranges, as in ''see pages 12--14''.

'\texteuro'

     The Euro currency symbol: €.

     For an alternative glyph design, try the 'eurosym' package; also,
     most fonts nowadays come with their own Euro symbol (Unicode
     U+20AC).

'\textexclamdown (or '!`')'
     ¡  Upside down exclamation point.

'\textfiguredash'
     Dash used between numerals, Unicode U+2012.  Defined in the June
     2021 release of LaTeX.  When used in pdfTeX, approximated by an
     en-dash; with a Unicode engine, either typesets the glyph if
     available in the current font, or writes the usual "Missing
     character" warning to the log file.

'\textgreater'
     > Greater than symbol.

'\texthorizontalbar'
     Horizontal bar character, Unicode U+2015.  Defined in the June 2021
     release of LaTeX.  Behavior as with '\textfiguredash' above; the
     pdfTeX approximation is an em-dash.

'\textless'
     < Less than symbol.

'\textleftarrow'
     ←, Left arrow.

'\textnonbreakinghyphen'
     Non-breaking hyphen character, Unicode U+2011.  Defined in the June
     2021 release of LaTeX.  Behavior as with '\textfiguredash' above;
     the pdfTeX approximation is a regular ASCII hyphen (with breaks
     disallowed after).

'\textordfeminine'
'\textordmasculine'
     ª, º Feminine and masculine ordinal symbols.

'\textperiodcentered'
     · Centered period.

'\textquestiondown (or '?`')'
     ¿  Upside down question mark.

'\textquotedblleft (or '``')'
     " Double left quote.

'\textquotedblright (or '''')'
     " Double right quote.

'\textquoteleft (or '`')'
     ' Single left quote.

'\textquoteright (or ''')'
     ' Single right quote.

'\textquotesingle'
     ', Straight single quote.  (From TS1 encoding.)

'\textquotestraightbase'
'\textquotestraightdblbase'
     Single and double straight quotes on the baseline.

'\textregistered'
     (R) Registered symbol.

'\textrightarrow'
     →, Right arrow.

'\textthreequartersemdash'
     ﹘, "Three-quarters" em-dash, between en-dash and em-dash.

'\texttrademark'
     ™ Trademark symbol.

'\texttwelveudash'
     ﹘, "Two-thirds" em-dash, between en-dash and em-dash.

'\textunderscore'
     _ Underscore.

'\textvisiblespace'
     ␣, Visible space symbol.

23.5 Accents
============

LaTeX has wide support for many of the world's scripts and languages,
provided through the core 'babel' package, which supports pdfLaTeX,
XeLaTeX and LuaLaTeX.  The 'polyglossia' package provides similar
support with the latter two engines.

   This section does not cover that support.  It only lists the core
LaTeX commands for creating accented characters.  The '\capital...'
commands shown here produce alternative forms for use with capital
letters.  These are not available with OT1.

   Below, to make them easier to find, the accents are all illustrated
with lowercase 'o'.

   Note that '\i' produces a dotless i, and '\j' produces a dotless j.
These are often used in place of their dotted counterparts when they are
accented.

'\"'
'\capitaldieresis'
     ö Umlaut (dieresis).

'\''
'\capitalacute'
     ó Acute accent.

'\.'
     ȯ Dot accent.

'\='
'\capitalmacron'
     ō Macron (overbar) accent.

'\^'
'\capitalcircumflex'
     ô Circumflex (hat) accent.

'\`'
'\capitalgrave'
     ò Grave accent.

'\~'
'\capitaltilde'
     ñ Tilde accent.

'\b'
     o̲ Bar accent underneath.

     Related to this, '\underbar{TEXT}' produces a bar under TEXT.  The
     argument is always processed in LR mode (*note Modes::).  The bar
     is always a fixed position under the baseline, thus crossing
     through descenders.  See also '\underline' in *note Math
     miscellany::.

'\c'
'\capitalcedilla'
     ç Cedilla accent underneath.

'\d'
'\capitaldotaccent'
     ọ Dot accent underneath.

'\H'
'\capitalhungarumlaut'
     ő Long Hungarian umlaut accent.

'\k'
'\capitalogonek'
     ǫ Ogonek.  Not available in the OT1 encoding.

'\r'
'\capitalring'
     o̊ Ring accent.

'\t'
'\capitaltie'
'\newtie'
'\capitalnewtie'
     Tie-after accent (used for transliterating from Cyrillic, such as
     in the ALA-LC romanization).  It expects that the argument has two
     characters.  The '\newtie' form is centered in its box.

'\u'
'\capitalbreve'
     ŏ Breve accent.

'\v'
'\capitalcaron'
     ǒ Háček (check, caron) accent.

23.5.1 '\accent'
----------------

Synopsis:

     \accent NUMBER CHARACTER

   A TeX primitive command used to generate accented characters from
accent marks and letters.  The accent mark is selected by NUMBER, a
numeric argument, followed by a space and then a CHARACTER argument to
construct the accented character in the current font.

   These are accented 'e' characters.

     \accent18 e
     \accent20 e
     \accent21 e
     \accent22 e
     \accent23 e

The first is a grave, the second a caron, the third a breve, the fourth
a macron, and the fifth a ring above.

   The position of the accent is determined by the font designer and so
the outcome of '\accent' use may differ between fonts.  In LaTeX it is
desirable to have glyphs for accented characters rather than building
them using '\accent'.  Using glyphs that already contain the accented
characters (as in T1 encoding) allows correct hyphenation whereas
'\accent' disables hyphenation (specifically with OT1 font encoding
where accented glyphs are absent).

   There can be an optional font change between NUMBER and CHARACTER.
Note also that this command sets the '\spacefactor' to 1000 (*note
\spacefactor::).

   An unavoidable characteristic of some Cyrillic letters and the
majority of accented Cyrillic letters is that they must be assembled
from multiple elements (accents, modifiers, etc.)  while '\accent'
provides for a single accent mark and a single letter combination.
There are also cases where accents must appear between letters that
\accent does not support.  Still other cases exist where the letters I
and J have dots above their lowercase counterparts that conflict with
dotted accent marks.  The use of '\accent' in these cases will not work
as it cannot analyze upper/lower case.

23.6 Additional Latin letters
=============================

Here are the basic LaTeX commands for inserting letters beyond A-Z that
extend the Latin alphabet, used primarily in languages other than
English.

'\aa'
'\AA'
     å and Å.

'\ae'
'\AE'
     æ and Æ.

'\dh'
'\DH'
     Icelandic letter eth: ð and Ð. Not available with OT1 encoding, you
     need the 'fontenc' package to select an alternate font encoding,
     such as T1.

'\dj'
'\DJ'
     Crossed d and D, a.k.a. capital and small letter d with stroke.
     Not available with OT1 encoding, you need the 'fontenc' package to
     select an alternate font encoding, such as T1.

'\ij'
'\IJ'
     ij and IJ (except somewhat closer together than appears here).

'\l'
'\L'
     ł and Ł.

'\ng'
'\NG'
     Lappish letter eng, also used in phonetics.

'\o'
'\O'
     ø and Ø.

'\oe'
'\OE'
     œ and Œ.

'\ss'
'\SS'
     ß and SS.

'\th'
'\TH'
     Icelandic letter thorn: þ and Þ. Not available with OT1 encoding,
     you need the 'fontenc' package to select an alternate font
     encoding, such as T1.

23.7 'inputenc' package
=======================

Synopsis:

     \usepackage[ENCODING-NAME]{inputenc}

   Declare the input file's text encoding to be ENCODING-NAME.  The
default, if this package is not loaded, is UTF-8.  Technically,
specifying the encoding name is optional, but in practice it is not
useful to omit it.

   In a computer file, the characters are stored according to a scheme
called the "encoding".  There are many different encodings.  The
simplest is ASCII, which supports 95 printable characters, not enough
for most of the world's languages.  For instance, to typeset the
a-umlaut character 'ä' in an ASCII-encoded LaTeX source file, the
sequence '\"a' is used.  This would make source files for anything but
English hard to read; even for English, often a more extensive encoding
is more convenient.

   The modern encoding standard, in some ways a union of the others, is
UTF-8, one of the representations of Unicode.  This is the default for
LaTeX since 2018.

   The 'inputenc' package is how LaTeX knows what encoding is used.  For
instance, the following command explicitly says that the input file is
UTF-8 (note the lack of a dash).

     \usepackage[utf8]{inputenc}

   Caution: use 'inputenc' only with the pdfTeX engine (*note TeX
engines::).  (The XeTeX and LuaTeX engines assume that the input file is
UTF-8 encoded.)  If you invoke LaTeX with either the 'xelatex' command
or the 'lualatex' command, and try to declare a non-UTF-8 encoding with
'inputenc', such as 'latin1', then you will get the error 'inputenc is
not designed for xetex or luatex'.

   An 'inputenc' package error such as 'Invalid UTF-8 byte "96' means
that some of the material in the input file does not follow the encoding
scheme.  Often these errors come from copying material from a document
that uses a different encoding than the input file; this one is a left
single quote from a web page using 'latin1' inside a LaTeX input file
that uses UTF-8.  The simplest solution is to replace the non-UTF-8
character with its UTF-8 equivalent, or use a LaTeX equivalent command
or character.

   In some documents, such as a collection of journal articles from a
variety of authors, changing the encoding in mid-document may be
necessary.  Use the command '\inputencoding{ENCODING-NAME}'.  The most
common values for ENCODING-NAME are: 'ascii', 'latin1', 'latin2',
'latin3', 'latin4', 'latin5', 'latin9', 'latin10', and 'utf8'.

23.8 '\rule'
============

Synopsis, one of:

     \rule{WIDTH}{THICKNESS}
     \rule[RAISE]{WIDTH}{THICKNESS}

   Produce a "rule", a filled-in rectangle.

   This example produces a rectangular blob, sometimes called a Halmos
symbol, or just "qed", often used to mark the end of a proof:

     \newcommand{\qedsymbol}{\rule{0.4em}{2ex}}

The 'amsthm' package includes this command, with a somewhat
different-looking symbol.

   The mandatory arguments give the horizontal WIDTH and vertical
THICKNESS of the rectangle.  They are rigid lengths (*note Lengths::).
The optional argument RAISE is also a rigid length, and tells LaTeX how
much to raise the rule above the baseline, or lower it if the length is
negative.

   This produces a line, a rectangle that is wide but not tall.

     \noindent\rule{\textwidth}{0.4pt}

The line is the width of the page and 0.4 points tall.  This line
thickness is common in LaTeX.

   A rule that has zero width, or zero thickness, will not show up in
the output, but can cause LaTeX to change the output around it.  *Note
\strut::, for examples.

23.9 '\today'
=============

Synopsis:

     \today

   Produce today's date in the format 'MONTH DD, YYYY'.  An example of a
date in that format is 'July 4, 1976'.

   Multilingual packages such as 'babel' or 'polyglossia', or classes
such as 'lettre', will localize '\today'.  For example, the following
will output '4 juillet 1976':

     \year=1976 \month=7 \day=4
     \documentclass{minimal}
     \usepackage[french]{babel}
     \begin{document}
     \today
     \end{document}

'\today' uses the counters '\day', '\month', and '\year' (*note \day &
\month & \year::).

   A number of package on CTAN work with dates.  One is 'datetime'
package which can produce a wide variety of date formats, including ISO
standards.

   The date is not updated as the LaTeX process runs, so in principle
the date could be incorrect by the time the program finishes.

24 Splitting the input
**********************

LaTeX lets you split a large document into several smaller ones.  This
can simplify editing or allow multiple authors to work on the document.
It can also speed processing.

   Regardless of how many separate files you use, there is always one
"root file", on which LaTeX compilation starts.  This shows such a file
with five included files.

     \documentclass{book}
     \includeonly{  % comment out lines below to omit compiling
       pref,
       chap1,
       chap2,
       append,
       bib
       }
     \begin{document}
     \frontmatter
     \include{pref}
     \mainmatter
     \include{chap1}
     \include{chap2}
     \appendix
     \include{append}
     \backmatter
     \include{bib}
     \end{document}

This will bring in material from 'pref.tex', 'chap1.tex', 'chap2.tex',
'append.tex', and 'bib.tex'.  If you compile this file, and then comment
out all of the lines inside '\includeonly{...}' except for 'chap1', and
compile again, then LaTeX will only process the material in the first
chapter.  Thus, your output will appear more quickly and be shorter to
print.  However, the advantage of the '\includeonly' command is that
LaTeX will retain the page numbers and all of the cross reference
information from the other parts of the document so these will appear in
your output correctly.

   *Note Larger book template::, for another example of '\includeonly'.

24.1 '\endinput'
================

Synopsis:

     \endinput

   When you '\include{filename}', inside 'filename.tex' the material
after '\endinput' will not be included.  This command is optional; if
'filename.tex' has no '\endinput' then LaTeX will read all of the file.

   For example, suppose that a document's root file has '\input{chap1}'
and this is 'chap1.tex'.

     \chapter{One}
     This material will appear in the document.
     \endinput
     This will not appear.

   This can be useful for putting documentation or comments at the end
of a file, or for avoiding junk characters that can be added if the file
is transmitted in the body of an email.  It is also useful for
debugging: one strategy to localize errors is to put '\endinput' halfway
through the included file and see if the error disappears.  Now, knowing
which half contains the error, moving '\endinput' to halfway through
that area further narrows down the location.  This process rapidly finds
the offending line.

   After reading '\endinput', LaTeX continues to read to the end of the
line, so something can follow this command and be read nonetheless.
This allows you, for instance, to close an '\if...' with a '\fi'.

24.2 '\include' & '\includeonly'
================================

Synopsis:

     \includeonly{  % in document preamble
       ...
       FILENAME,
       ...
       }
       ...
     \include{FILENAME}  % in document body

   Bring material from the external file 'FILENAME.tex' into a LaTeX
document.

   The '\include' command does three things: it executes '\clearpage'
(*note \clearpage & \cleardoublepage::), then it inputs the material
from 'FILENAME.tex' into the document, and then it does another
'\clearpage'.  This command can only appear in the document body.

   The '\includeonly' command controls which files will be read by LaTeX
under subsequent '\include' commands.  Its list of filenames is
comma-separated.  It must appear in the preamble or even earlier, e.g.,
the command line; it can't appear in the document body.

   This example root document, 'constitution.tex', brings in three
files, 'preamble.tex', 'articles.tex', and 'amendments.tex'.

     \documentclass{book}
     \includeonly{
       preamble,
       articles,
       amendments
       }
     \begin{document}
     \include{preamble}
     \include{articles}
     \include{amendments}
     \end{document}

The file 'preamble.tex' contains no special code; you have just
excerpted the chapter from 'consitution.tex' and put it in a separate
file just for editing convenience.

     \chapter{Preamble}
     We the People of the United States,
     in Order to form a more perfect Union, ...

Running LaTeX on 'constitution.tex' makes the material from the three
files appear in the document but also generates the auxiliary files
'preamble.aux', 'articles.aux', and 'amendments.aux'.  These contain
information such as page numbers and cross-references (*note Cross
references::).  If you now comment out '\includeonly''s lines with
'preamble' and 'amendments' and run LaTeX again then the resulting
document shows only the material from 'articles.tex', not the material
from 'preamble.tex' or 'amendments.tex'.  Nonetheless, all of the
auxiliary information from the omitted files is still there, including
the starting page number of the chapter.

   If the document preamble does not have '\includeonly' then LaTeX will
include all the files you call for with '\include' commands.

   The '\include' command makes a new page.  To avoid that, see *note
\input:: (which, however, does not retain the auxiliary information).

   *Note Larger book template::, for another example using '\include'
and '\includeonly'.  That example also uses '\input' for some material
that will not necessarily start on a new page.

   File names can involve paths.

     \documentclass{book}
     \includeonly{
       chapters/chap1,
       }
     \begin{document}
     \include{chapters/chap1}
     \end{document}

   To make your document portable across distributions and platforms you
should avoid spaces in the file names.  The tradition is to instead use
dashes or underscores.  Nevertheless, for the name 'amo amas amat', this
works under TeX Live on GNU/Linux:

     \documentclass{book}
     \includeonly{
       "amo\space amas\space amat"
       }
     \begin{document}
     \include{"amo\space amas\space amat"}
     \end{document}

   and this works under MiKTeX on Windows:

     \documentclass{book}
     \includeonly{
       {"amo amas amat"}
       }
     \begin{document}
     \include{{"amo amas amat"}}
     \end{document}

   You cannot use '\include' inside a file that is being included or you
get 'LaTeX Error: \include cannot be nested.' The '\include' command
cannot appear in the document preamble; you will get 'LaTeX Error:
Missing \begin{document}'.

   If a file that you '\include' does not exist, for instance if you
'\include{athiesm}' but you meant '\include{atheism}', then LaTeX does
not give you an error but will warn you 'No file athiesm.tex.' (It will
also create 'athiesm.aux'.)

   If you '\include' the root file in itself then you first get 'LaTeX
Error: Can be used only in preamble.' Later runs get 'TeX capacity
exceeded, sorry [text input levels=15]'.  To fix this, you must remove
the inclusion '\include{ROOT}' but also delete the file 'ROOT.aux' and
rerun LaTeX.

24.3 '\input'
=============

Synopsis:

     \input{FILENAME}

   LaTeX processes the file as if its contents were inserted in the
current file.  For a more sophisticated inclusion mechanism see *note
\include & \includeonly::.

   If FILENAME does not end in '.tex' then LaTeX first tries the
filename with that extension; this is the usual case.  If FILENAME ends
with '.tex' then LaTeX looks for the filename as it is.

   For example, this

     \input{macros}

will cause LaTeX to first look for 'macros.tex'.  If it finds that file
then it processes its contents as thought they had been copy-pasted in.
If there is no file of the name 'macros.tex' then LaTeX tries the name
'macros', without an extension.  (This may vary by distribution.)

   To make your document portable across distributions and platforms you
should avoid spaces in the file names.  The tradition is to instead use
dashes or underscores.  Nevertheless, for the name 'amo amas amat', this
works under TeX Live on GNU/Linux:

     \input{"amo\space amas\space amat"}

   and this works under MiKTeX on Windows:

     \input{{"amo amas amat"}}

25 Front/back matter
********************

25.1 Table of contents, list of figures, list of tables
=======================================================

Synopsis, one of:

     \tableofcontents
     \listoffigures
     \listoftables

   Produce a table of contents, or list of figures, or list of tables.
Put the command in the input file where you want the table or list to
go.  You do not type the entries; for example, typically the table of
contents entries are automatically generated from the sectioning
commands '\chapter', etc.

   This example illustrates the first command, '\tableofcontents'.
LaTeX will produce a table of contents on the book's first page.

     \documentclass{book}
     % \setcounter{tocdepth}{1}
     \begin{document}
     \tableofcontents\newpage
       ...
     \chapter{...}
       ...
     \section{...}
       ...
     \subsection{...}
       ...
     \end{document}

Uncommenting the second line would cause that table to contain chapter
and section listings but not subsection listings, because the '\section'
command has level 1.  *Note Sectioning::, for level numbers of the
sectioning units.  For more on the 'tocdepth' *note
Sectioning/tocdepth::.

   Another example of the use of '\tableofcontents' is in *note Larger
book template::.

   If you want a page break after the table of contents, write a
'\newpage' command after the '\tableofcontents' command, as above.

   To make the table of contents, LaTeX stores the information in an
auxiliary file named 'ROOT-FILE.toc' (*note Splitting the input::).  For
example, this LaTeX file 'test.tex'

     \documentclass{article}
     \begin{document}
     \tableofcontents\newpage
     \section{First section}
     \subsection{First subsection}
       ...

writes these lines to 'test.toc'.

     \contentsline {section}{\numberline {1}First section}{2}
     \contentsline {subsection}{\numberline {1.1}First subsection}{2}

Each line contains a single command, '\contentsline' (*note
\contentsline::).  The first argument, the 'section' or 'subsection', is
the sectioning unit.  The second argument has two components.  The hook
'\numberline' determines how the sectioning number, '1' or '1.1',
appears in the table of contents (*note \numberline::).  The remainder
of the second argument of '\contentsline', 'First section' or 'First
subsection', is the sectioning title text.  Finally, the third argument,
'2', is the page number on which this sectioning unit starts.

   To typeset these lines, the document class provides '\l@SECTION-UNIT'
commands such as '\l@section{TEXT}{PAGENUMBER}' and
'\l@subsection{TEXT}{PAGENUMBER}'.  These commands often use the
'\@dottedtocline' command (*note \@dottedtocline::).

   A consequence of LaTeX's strategy of using auxiliary files is that to
get the correct information in the document you must run LaTeX twice,
once to store the information and the second time to retrieve it.  In
the ordinary course of writing a document authors run LaTeX a number of
times, but you may notice that the first time that you compile a new
document, the table of contents page will be empty except for its
'Contents' header.  Just run LaTeX again.

   The commands '\listoffigures' and '\listoftables' produce a list of
figures and a list of tables.  Their information is stored in files with
extension '.lof' and '.lot'.  They work the same way as
'\tableofcontents' but the latter is more common, so we use it for most
examples.

   You can manually add material to the table of contents, the list of
figures, and the list of tables.  For instance, add a line about a
section to the table of contents with
'\addcontentsline{toc}{section}{TEXT}'.  (*note \addcontentsline::).
Add arbitrary material, that is, non-line material, with
'\addtocontents', as with the command
'\addtocontents{lof}{\protect\vspace{2ex}}', which adds vertical space
to the list of figures (*note \addtocontents::).

   Lines in the table of contents, the list of figures, and the list of
tables, have four parts.  First is an indent.  Next is a box into which
sectioning numbers are placed, and then the third box holds the title
text, such as 'First section'.  Finally there is a box up against the
right margin, inside of which LaTeX puts the page number box.  For the
indent and the width of the number box, *note \@dottedtocline::.  The
right margin box has width '\@tocrmarg' and the page number is flush
right in that space, inside a box of width '\@pnumwidth'.  By default
'\@tocrmarg' is '2.55em' and '\@pnumwidth' is '1.55em'.  Change these as
with '\renewcommand{\@tocrmarg}{3.5em}'.

   CTAN has many packages for the table of contents and lists of figures
and tables (*note CTAN::).  The package 'tocloft' is convenient for
adjusting some aspects of the default such as spacing.  And,
'tocbibbind' will automatically add the bibliography, index, etc.  to
the table of contents.

   To change the header for the table of contents page, do something
like these commands before you call '\tableofcontents', etc.

     \renewcommand{\contentsname}{Table of Contents}
     \renewcommand{\listfigurename}{Plots}
     \renewcommand{\listtablename}{Specifications}


   Internationalization packages such as 'babel' or 'polyglossia' will
change these headers depending on the chosen base language.

25.1.1 '\@dottedtocline'
------------------------

Synopsis:

     \@dottedtocline{SECTION-LEVEL-NUM}{INDENT}{NUMWIDTH}{TEXT}{PAGENUMBER}

   Used internally by LaTeX to format an entry line in the table of
contents, list of figures, or list of tables.  Authors do not directly
enter '\@dottedtocline' commands.

   This command is typically used by '\l@section', '\l@subsection',
etc., to format the content lines.  For example, the 'article.cls' file
contains these definitions:

     \newcommand*\l@section{\@dottedtocline{1}{1.5em}{2.3em}}
     \newcommand*\l@subsection{\@dottedtocline{2}{3.8em}{3.2em}}
     \newcommand*\l@subsubsection{\@dottedtocline{3}{7.0em}{4.1em}}

In this example, '\@dottedcline' appears to have been given only three
arguments.  But tracing the internal code shows that it picks up the
final TEXT and PAGENUMBER arguments in the synopsis from a call to
'\contentsline' (*note \contentsline::).

   Between the box for the title text of a section and the right margin
box, these '\@dottedtocline' commands insert "leaders", that is,
evenly-spaced dots.  The dot-to-dot space is given by the command
'\@dotsep'.  By default it is 4.5 (it is in math units, aka. 'mu', which
are '1/18' em.  Change it using '\renewcommand', as in
'\renewcommand{\@dotsep}{3.5}'.

   In the standard 'book' class, LaTeX does not use dotted leaders for
the Part and Chapter table entries, and in the standard 'article' class
it does not use dotted leaders for Section entries.

25.1.2 '\addcontentsline'
-------------------------

Synopsis:

     \addcontentsline{EXT}{UNIT}{TEXT}

   Add an entry to the auxiliary file with extension EXT.

   The following will result in an 'Appendices' line in the table of
contents.

     \addcontentsline{toc}{section}{\protect\textbf{Appendices}}

It will appear at the same indentation level as the sections, will be in
boldface, and will be assigned the page number associated with the point
where the command appears in the input file.

   The '\addcontentsline' command writes information to the file
'ROOT-NAME.EXT', where ROOT-NAME is the file name of the root file
(*note Splitting the input::).  It writes that information as the text
of the command '\contentsline{UNIT}{TEXT}{NUM}', where 'NUM' is the
current value of counter 'UNIT' (*note \contentsline::).  The most
common case is the table of contents and there NUM is the page number of
the first page of UNIT.

   This command is invoked by the sectioning commands '\chapter', etc.
(*note Sectioning::), and also by '\caption' inside a float environment
(*note Floats::).  But it is also directly used by authors.  For
example, an author writing a book whose style is to have an unnumbered
preface may use the starred '\chapter*'.  But that command leaves out
table of contents information, which can be entered manually, as here.

     \chapter*{Preface}
     \addcontentsline{toc}{chapter}{\protect\numberline{}Preface}

In the 'ROOT-NAME.toc' file LaTeX will put the line '\contentsline
{chapter}{\numberline {}Preface}{3}'; note that the page number '3' is
automatically generated by the system, not entered manually.

   All of the arguments for '\addcontentsline' are required.

EXT
     Typically one of the strings 'toc' for the table of contents, 'lof'
     for the list of figures, or 'lot' for the list of tables.  The
     filename extension of the information file.

UNIT
     A string that depends on the value of the EXT argument, typically
     one of:

     'toc'
          For the table of contents, this is the name of a sectional
          unit: 'part', 'chapter', 'section', 'subsection', etc.

     'lof'
          For the list of figures: 'figure'.

     'lot'
          For the list of tables: 'table'.

TEXT
     The text of the entry.  You must '\protect' any fragile commands
     (*note \protect::) used in it.

   The '\addcontentsline' command has an interaction with '\include'
(*note \include & \includeonly::).  If you use them at the same level,
as with '\addcontentsline{...}{...}{...}\include{...}' then lines in the
table of contents can come out in the wrong order.  The solution is to
move '\addcontentsline' into the file being included.

   If you use a UNIT that LaTeX does not recognize, as with the typo
here

     \addcontentsline{toc}{setcion}{\protect\textbf{Appendices}}

then you don't get an error but the formatting in the table of contents
will not make sense.

25.1.3 '\addtocontents'
-----------------------

Synopsis:

     \addtocontents{EXT}{TEXT}

   Add TEXT, which may be text or formatting commands, directly to the
auxiliary file with extension EXT.  This is most commonly used for the
table of contents so that is the discussion here, but it also applies to
the list of figures and list of tables.

   This will put some vertical space in the table of contents after the
'Contents' header.

     \tableofcontents\newpage
     \addtocontents{toc}{\protect\vspace*{3ex}}

This puts the word 'Page', in boldface, above the column of page numbers
and after the header.

     \tableofcontents
     \addtocontents{toc}{~\hfill\textbf{Page}\par}
     \chapter{...}

This adds a line announcing work by a new author.

     \addtocontents{toc}{%
       \protect\vspace{2ex}
       \textbf{Chapters by N. Other Author}\par}

   The difference between '\addtocontents' and '\addcontentsline' is
that the latter is strictly for lines, such as with a line giving the
page number for the start of a new subset of the chapters.  As the above
examples show, '\addtocontents' is for material such as spacing.

   The '\addtocontents' command has two arguments.  Both are required.

EXT
     Typically one of: 'toc' for the table of contents, 'lof' for the
     list of figures, or 'lot' for the list of tables.  The extension of
     the file holding the information.

TEXT
     The text, and possibly commands, to be written.

   The sectioning commands such as '\chapter' use the '\addcontentsline'
command to store information.  This command creates lines in the '.toc'
auxiliary file containing the '\contentsline' command (*note
\addcontentsline::).  In contrast, the command '\addtocontents' puts
material directly in that file.

   The '\addtocontents' command has an interaction with '\include'
(*note \include & \includeonly::).  If you use them at the same level,
as with '\addtocontents{...}{...}\include{...}' then lines in the table
of contents can come out in the wrong order.  The solution is to move
'\addtocontents' into the file being included.

25.1.4 '\contentsline'
----------------------

Synopsis:

     \contentsline{UNIT}{TEXT}{PAGENUMBER}

   Used internally by LaTeX to typeset an entry of the table of
contents, list of figures, or list of tables (*note Table of contents
etc.::).  Authors do not directly enter '\contentsline' commands.

   Usually adding material to these lists is done automatically by the
commands '\chapter', '\section', etc.  for the table of contents, or by
the '\caption' command inside of a '\figure' or '\table' environment
(*note figure:: and *note table::).  Thus, where the root file is
'thesis.tex', and contains the declaration '\tableofcontents', the
command '\chapter{Chapter One}' produces something like this in the file
'thesis.toc'.

     \contentsline {chapter}{\numberline {1}Chapter One}{3}

   If the file contains the declaration '\listoffigures' then a figure
environment involving '\caption{Test}' will produce something like this
in 'thesis.lof'.

     \contentsline {figure}{\numberline {1.1}{\ignorespaces Test}}{6}

   To manually add material, use
'\addcontentsline{FILETYPE}{UNIT}{TEXT}', where FILETYPE is 'toc',
'lof', or 'lot' (*note \addcontentsline::).

   For manipulating how the '\contentline' material is typeset, see the
'tocloft' package.

   Note that the 'hyperref' package changes the definition of
'\contentsline' (and '\addcontentsline') to add more arguments, to make
hyperlinks.  This is the source of the error 'Argument of \contentsline
has an extra }' when one adds/remove the use of package 'hyperref' and a
compilation was already run.  Fix this error by deleting the '.toc' or
'.lof' or '.lot' file, and running LaTeX again.

25.1.5 '\nofiles'
-----------------

Synopsis:

     \nofiles

   Prevent LaTeX from writing any auxiliary files.  The only output will
be the '.log' and '.pdf' (or '.dvi') files.  This command must go in the
preamble.

   Because of the '\nofiles' command this example will not produce a
'.toc' file.

     \documentclass{book}
     \nofiles
     \begin{document}
     \tableofcontents\newpage
     \chapter{...}
       ...

LaTeX will not erase any existing auxiliary files, so if you insert the
'\nofiles' command after you have run the file and gotten a '.toc' then
the table of contents page will continue to show the old information.

25.1.6 '\numberline'
--------------------

Synopsis:

     \numberline{NUMBER}

   Typeset its argument flush left in a box.  This is used in a
'\contentsline' command to typeset the section number (*note
\contentsline::).

   For example, this line in a '.toc' file causes the '1.1' to be
typeset flush left.

     \contentsline {subsection}{\numberline {1.1}Motivation}{2}

   By default, LaTeX typesets the section numbers in a box of length
'\@tempdima'.  That length is set by the commands '\l@section',
'\l@subsection', etc.  Put section numbers inside a natural-width box
with '\renewcommand{\numberline}[1]{#1~}' before '\tableofcontents'.

   This command is fragile so you may need to precede it with '\protect'
(*note \protect::).  An example is the use of '\protect' in this
command,

     \addcontentsline{toc}{section}{\protect\numberline{}Summary}

to get the '\numberline' into the '\contentsline' command in the '.toc'
file: '\contentsline {section}{\numberline {}Summary}{6}' (the page
number '6' is automatically added by LaTeX; *note \addcontentsline::).

25.2 Indexes
============

If you tell LaTeX what terms you want to appear in an index then it can
produce that index, alphabetized and with the page numbers automatically
maintained.  This illustrates the basics.

     \documentclass{article}
     \usepackage{makeidx}  % Provide indexing commands
       \makeindex
     % \usepackage{showidx}  % Show marginal notes of index entries
       ...
     \begin{document}
       ...
     Wilson's Theorem\index{Wilson's Theorem}
     says that a number $n>1$ is prime if and only if the factorial
     of $n-1$ is congruent to $-1$
     modulo~$n$.\index{congruence!and Wilson's Theorem}
       ...
     \printindex
     \end{document}

As that shows, declare index entries with the '\index' command (*note
\index::).  When you run LaTeX, the '\index' writes its information,
such as 'Wilson's Theorem' and the page number, to an auxiliary file
whose name ends in '.idx'.  Next, to alphabetize and do other
manipulations, run an external command, typically 'makeindex' (*note
makeindex::), which writes a file whose name ends in '.ind'.  Finally,
'\printindex' brings this manipulated information into the output (*note
\printindex::).

   Thus, if the above example is in the file 'numth.tex' then running
'pdflatex numth' will save index entry and page number information to
'numth.idx'.  Then running 'makeindex numth' will alphabetize and save
the results to 'numth.ind'.  Finally, again running 'pdflatex numth'
will show the desired index, at the place where the '\printindex'
command is in the source file.

   There are many options for the output.  An example is that the
exclamation point in '\index{congruence!and Wilson's Theorem}' produces
a main entry of 'congruence' with a subentry of 'and Wilson's Theorem'.
For more, *note makeindex::.

   The '\makeindex' and '\printindex' commands are independent.  Leaving
out the '\makeindex' will stop LaTeX from saving the index entries to
the auxiliary file.  Leaving out the '\printindex' will cause LaTeX to
not show the index in the document output.

   There are many packages in the area of indexing.  The 'showidx'
package causes each index entries to be shown in the margin on the page
where the '\index' appears.  This can help in preparing the index.  The
'multind' package, among others, supports multiple indexes.  See also
the TeX FAQ entry on this topic, <https://www.texfaq.org/FAQ-multind>,
and the CTAN topic, <https://ctan.org/topic/index-multi>.

25.2.1 Produce the index manually
---------------------------------

Documents that are small and static can have a manually produced index.
This will make a separate page labeled 'Index', in twocolumn format.

     \begin{theindex}
     \item acorn squash, 1
     \subitem maple baked, 2
     \indexspace
     \item bacon, 3
     \subitem maple baked, 4
     \end{theindex}

   Note that the author must enter the page numbers, which is tedious
and which will result in wrong numbers if the document changes.  This is
why in most cases automated methods such as 'makeindex' are best.  *Note
Indexes::.

   However we cover the commands for completeness, and because the
automated methods are based on these commands.  There are three levels
of entries.  As the example shows, a main entry uses '\item', subentries
use '\subitem', and the lowest level uses '\subsubitem'.  Blank lines
between entries have no effect.  The example above includes
'\indexspace' to produce vertical space in the output that some index
styles use before the first entry starting with a new letter.

25.2.2 '\index'
---------------

Synopsis:

     \index{INDEX-ENTRY-STRING}

   Declare an entry in the index.  This command is fragile (*note
\protect::).

   For example, as described in *note Indexes::, one way to get an index
from what's below is to compile the document with 'pdflatex test', then
process the index entries with 'makeindex test', and then compile again
with 'pdflatex test'.

     % file test.tex
       ...
     W~Ackermann (1896--1962).\index{Ackermann}
       ...
     Ackermann function\index{Ackermann!function}
       ...
     rate of growth\index{Ackermann!function!growth rate}

All three index entries will get a page number, such as 'Ackermann, 22'.
LaTeX will format the second as a subitem of the first, on the line
below it and indented, and the third as a subitem of the second.  Three
levels deep is as far as you can nest subentries.  (If you add
'\index{Ackermann!function!growth rate!comparison}' then 'makeindex'
says 'Scanning input file test.idx....done (4 entries accepted, 1
rejected)' and the fourth level is silently missing from the index.)

   If you enter a second '\index' with the same INDEX-ENTRY-STRING then
you will get a single index entry with two page numbers (unless they
happen to fall on the same page).  Thus, adding 'as for
Ackermann.\index{Ackermann}' later in the same document as above will
give an index entry like 'Ackermann, 22, 151'.  Also, you can enter the
index entries in any order, so for instance '\index{Ackermann!function}'
could come before '\index{Ackermann}'.

   Get a page range in the output, like 'Hilbert, 23--27', as here.

     W~Ackermann (1896--1962).\index{Ackermann}
       ...
     D~Hilbert (1862--1943)\index{Ackermann!Hilbert|(}
       ...
     disapproved of his marriage.\index{Ackermann!Hilbert|)}

If the beginning and ending of the page range are equal then the system
just gives a single page number, not a range.

   If you index subentries but not a main entry, as with
'\index{Jones!program}' and '\index{Jones!results}', then the output is
the item 'Jones' with no comma or page number, followed by two subitems,
like 'program, 50' and 'results, 51'.

   Generate a index entry that says 'see' by using a vertical bar
character: '\index{Ackermann!function|see{P\'eter's function}}'.  You
can instead get 'see also' with 'seealso'.  (The text 'see' is defined
by '\seename', and 'see also' by '\alsoname'.  You can redefine these
either by using an internationalization package such as 'babel' or
'polyglossia', or directly as with '\renewcommand{\alsoname}{Also
see}'.)

   The 'see' feature is part of a more general functionality.  After the
vertical bar you can put the name of a one-input command, as in
'\index{group|textit}' (note the missing backslash on the '\textit'
command) and the system will apply that command to the page number, here
giving something like '\textit{7}'.  You can define your own one-input
commands, such as '\newcommand{\definedpage}[1]{{\color{blue}#1}}' and
then '\index{Ackermann!function|definedpage}' will give a blue page
number (*note Color::).  Another, less practical, example is this,

     \newcommand\indexownpage[1]{#1, \thepage}
       ... Epimenides.\index{self-reference|indexownpage}

which creates an entry citing the page number of its own index listing.

   The two functions just described combine, as here

     \index{Ackermann!function|(definedpage}
       ...
     \index{Ackermann!function|)}

which outputs an index entry like 'function, 23--27' where the page
number range is in blue.

   Consider an index entry such as 'α-ring'.  Entering it as
'$\alpha$-ring' will cause it to be alphabetized according to the dollar
sign.  You can instead enter it using an at-sign, as
'\index{alpha-ring@$\alpha$-ring}'.  If you specify an entry with an
at-sign separating two strings, 'POS@TEXT', then POS gives the
alphabetical position of the entry while TEXT produces the text of the
entry.  Another example is that '\index{Saint Michael's College@SMC}'
produces an index entry 'SMC' alphabetized into a different location
than its spelling would naturally give it.

   To put a '!', or '@', or '|', or '"' character in an index entry,
escape it by preceding it with a double quote, '"'.  (The double quote
gets deleted before alphabetization.)

   A number of packages on CTAN have additional functionality beyond
that provided by 'makeidx'.  One is 'index', which allows for multiple
indices and contains a command '\index*{INDEX-ENTRY-STRING}' that prints
the INDEX-ENTRY-STRING as well as indexing it.

   The '\index' command writes the indexing information to the file
'ROOT-NAME.idx' file.  Specifically, it writes text of the command
'\indexentry{INDEX-ENTRY-STRING}{PAGE-NUM}', where PAGE-NUM is the value
of the '\thepage' counter.  On occasion, when the '\printindex' command
is confused, you have to delete this file to start with a fresh slate.

   If you omit the closing brace of an '\index' command then you get a
message like this.

     Runaway argument?  {Ackermann!function
     !  Paragraph ended before \@wrindex was complete.

25.2.3 'makeindex'
------------------

Synopsis, one of:

     makeindex FILENAME
     makeindex -s STYLE-FILE FILENAME
     makeindex OPTIONS FILENAME0 ...

   Sort, and otherwise process, the index information in the auxiliary
file FILENAME.  This is a command line program.  It takes one or more
raw index files, 'FILENAME.idx' files, and produces the actual index
file, the 'FILENAME.ind' file that is input by '\printindex' (*note
\printindex::).

   The first form of the command suffices for many uses.  The second
allows you to format the index by using an "index style file", a '.isty'
file.  The third form is the most general; see the full documentation on
CTAN.

   This is a simple '.isty' file.

     % book.isty
     %   $ makeindex -s book.isty -p odd book.idx
     % creates the index as book.ind, starting on an odd page.
     preamble
     "\\pagestyle{empty}
     \\small
     \\begin{theindex}
     \\thispagestyle{empty}"

     postamble
     "\n
     \\end{theindex}"

   The description here covers only some of the index formatting
possibilities in STYLE-FILE.  For a full list see the documentation on
CTAN.

   A style file consists of a list of pairs: SPECIFIER and ATTRIBUTE.
These can appear in the file in any order.  All of the ATTRIBUTEs are
strings, except where noted.  Strings are surrounded with double quotes,
'"', and the maximum length of a string is 144 characters.  The '\n' is
for a newline and '\t' is for a tab.  Backslashes are escaped with
another backslash, '\\'.  If a line begins with a percent sign, '%',
then it is a comment.

'preamble'
     Preamble of the output index file.  Defines the context in which
     the index is formatted.  Default: '"\\begin{theindex}\n"'.

'postamble'
     Postamble of the output index file.  Default:
     '"\n\n\\end{theindex}\n"'.

'group_skip'
     Traditionally index items are broken into groups, typically a group
     for entries starting with letter 'a', etc.  This specifier gives
     what is inserted when a new group begins.  Default: '"\n\n
     \\indexspace\n"' ('\indexspace' is a command inserting a rubber
     length, by default '10pt plus5pt minus3pt').

'lethead_flag'
     An integer.  It governs what is inserted for a new group or letter.
     If it is 0 (which is the default) then other than 'group_skip'
     nothing will be inserted before the group.  If it is positive then
     at a new letter the 'lethead_prefix' and 'lethead_suffix' will be
     inserted, with that letter in uppercase between them.  If it is
     negative then what will be inserted is the letter in lowercase.
     The default is 0.

'lethead_prefix'
     If a new group begins with a different letter then this is the
     prefix inserted before the new letter header.  Default: '""'

'lethead_suffix'
     If a group begins with a different letter then this is the suffix
     inserted after the new letter header.  Default: '""'.

'item_0'
     What is put between two level 0 items.  Default: '"\n \\item "'.

'item_1'
     Put between two level 1 items.  Default: '"\n \\subitem "'.

'item_2'
     put between two level 2 items.  Default: '"\n \\subsubitem "'.

'item_01'
     What is put between a level 0 item and a level 1 item.  Default:
     '"\n \\subitem "'.

'item_x1'
     What is put between a level 0 item and a level 1 item in the case
     that the level 0 item doesn't have any page numbers (as in
     '\index{aaa|see{bbb}}').  Default: '"\n \\subitem "'.

'item_12'
     What is put between a level 1 item and a level 2 item.  Default:
     '"\n \\subsubitem "'.

'item_x2'
     What is put between a level 1 item and a level 2 item, if the
     level 1 item doesn't have page numbers.  Default: '"\n \\subsubitem
     "'.

'delim_0'
     Delimiter put between a level 0 key and its first page number.
     Default: a comma followed by a blank, '", "'.

'delim_1'
     Delimiter put between a level 1 key and its first page number.
     Default: a comma followed by a blank, '", "'.

'delim_2'
     Delimiter between a level 2 key and its first page number.
     Default: a comma followed by a blank, '", "'.

'delim_n'
     Delimiter between two page numbers for the same key (at any level).
     Default: a comma followed by a blank, '", "'.

'delim_r'
     What is put between the starting and ending page numbers of a
     range.  Default: '"--"'.

'line_max'
     An integer.  Maximum length of an index entry's line in the output,
     beyond which the line wraps.  Default: '72'.

'indent_space'
     What is inserted at the start of a wrapped line.  Default:
     '"\t\t"'.

'indent_length'
     A number.  The length of the wrapped line indentation.  The default
     'indent_space' is two tabs and each tab is eight spaces so the
     default here is '16'.

'page_precedence'
     A document may have pages numbered in different ways.  For example,
     a book may have front matter pages numbered in lowercase roman
     while main matter pages are in arabic.  This string specifies the
     order in which they will appear in the index.  The 'makeindex'
     command supports five different types of numerals: lowercase roman
     'r', and numeric or arabic 'n', and lowercase alphabetic 'a', and
     uppercase roman 'R', and uppercase alphabetic 'A'.  Default:
     '"rnaRA"'.

   There are a number of other programs that do the job 'makeindex'
does.  One is 'xindy' (<https://ctan.org/pkg/xindy>), which does
internationalization and can process indexes for documents marked up
using LaTeX and a number of other languages.  It is written in Lisp,
highly configurable, both in markup terms and in terms of the collating
order of the text, as described in its documentation.

   A more recent indexing program supporting Unicode is 'xindex',
written in Lua (<https://ctan.org/pkg/xindex>).

25.2.4 '\printindex'
--------------------

Synopsis:

     \printindex

   Place the index into the output.

   To get an index you must first include
'\usepackage{makeidx}\makeindex' in the document preamble and compile
the document, then run the system command 'makeindex', and then compile
the document again.  *Note Indexes::, for further discussion and an
example of the use of '\printindex'.

25.3 Glossaries
===============

Synopsis:

     \usepackage{glossaries} \makeglossaries
       ...
     \newglossaryentry{LABEL}{SETTINGS}
       ...
     \gls{LABEL}.
       ...
     \printglossaries

   The 'glossaries' package allows you to make glossaries, including
multiple glossaries, as well as lists of acronyms.

   To get the output from this example, compile the document (for
instance with 'pdflatex filename'), then run the command line command
'makeglossaries filename', and then compile the document again.

     \documentclass{...}
     \usepackage{glossaries} \makeglossaries
     \newglossaryentry{tm}{%
       name={Turing machine},
       description={A model of a machine that computes.  The model is simple
                    but can compute anything any existing device can compute.
                    It is the standard model used in Computer Science.},
       }
     \begin{document}
     Everything begins with the definition of a \gls{tm}.
       ...
     \printglossaries
     \end{document}

That gives two things.  In the main text it outputs '... definition of a
Turing machine'.  In addition, in a separate sectional unit headed
'Glossary' there appears a description list.  In boldface it says
'Turing machine' and the rest of the item says in normal type 'A model
of a machine ... Computer Science'.

   The command '\makeglossary' opens the file that will contain the
entry information, 'ROOT-FILE.glo'.  Put the '\printglossaries' command
where you want the glossaries to appear in your document.

   The 'glossaries' package is very powerful.  For instance, besides the
commands '\newglossaryentry' and '\gls', there are similar commands for
a list of acronyms.  See the package documentations on CTAN.

25.3.1 '\newglossaryentry'
--------------------------

Synopsis, one of:

     \newglossaryentry{LABEL}
     {
       name={NAME},
       description={DESCRIPTION},
       OTHER OPTIONS, ...
     }

   or

     \longnewglossaryentry{LABEL}
     {
       name={NAME},
       OTHER OPTIONS ...,
     }
     {DESCRIPTION}

   Declare a new entry for a glossary.  The LABEL must be unique for the
document.  The settings associated with the label are pairs:
'KEY=VALUE'.

   This puts the blackboard bold symbol for the real numbers ℝ, in the
glossary.

     \newglossaryentry{R}
     {
       name={\ensuremath{\mathbb{R}}},
       description={the real numbers},
     }

   Use the second command form if the DESCRIPTION spans more than one
paragraph.

   For a full list of KEYs see the package documentation on CTAN but
here are a few.

'name'
     (Required.)  The word, phrase, or symbol that you are defining.

'description'
     (Required.)  The description that will appear in the glossary.  If
     this has more than one paragraph then you must use the second
     command form given in the synopsis.

'plural'
     The plural form of NAME.  Refer to the plural form using '\glspl'
     or '\Glspl' (*note \gls::).

'sort'
     How to place this entry in the list of entries that the glossary
     holds.

'symbol'
     A symbol, such as a mathematical symbol, besides the name.

25.3.2 '\gls'
-------------

Synopsis, one of:

     \gls{LABEL}
     \glspl{LABEL}
     \Gls{LABEL}
     \Glspl{LABEL}

   Refer to a glossary entry.  The entries are declared with
'\newglossaryentry' (*note \newglossaryentry::).

   This

     \newglossaryentry{N}{%
       name={the natural numbers},
       description={The numbers $0$, $1$, $2$, $\ldots$\@},
       symbol={\ensuremath{\mathbb{N}}},
       }
       ...
     Consider \gls{N}.

gives the output 'Consider the natural numbers'.

   The second command form '\glspl{LABEL}' produces the plural of NAME
(by default it tries adding an 's').  The third form capitalizes the
first letter of NAME, as does the fourth form, which also takes the
plural.

26 Letters
**********

Synopsis:

     \documentclass{letter}
     \address{SENDERS ADDRESS}   % return address
     \signature{SENDER NAME}
     \begin{document}
     \begin{letter}{RECIPIENT ADDRESS}
     \opening{SALUTATION}
       LETTER BODY
     \closing{CLOSING TEXT}
     \end{letter}
        ...
     \end{document}

   Produce one or more letters.

   Each letter is in a separate 'letter' environment, whose argument
RECIPIENT ADDRESS often contains multiple lines separated with a double
backslash, ('\\').  For example, you might have:

      \begin{letter}{Ninon de l'Enclos \\
                     l'h\^otel Sagonne}
        ...
      \end{letter}

   The start of the 'letter' environment resets the page number to 1,
and the footnote number to 1 also.

   The SENDER ADDRESS and SENDER NAME are common to all of the letters,
whether there is one or more, so these are best put in the preamble.  As
with the recipient address, often SENDER ADDRESS contains multiple lines
separated by a double backslash ('\\').  LaTeX will put the SENDER NAME
under the closing, after a vertical space for the traditional
hand-written signature.

   Each 'letter' environment body begins with a required '\opening'
command such as '\opening{Dear Madam or Sir:}'.  The LETTER BODY text is
ordinary LaTeX so it can contain everything from enumerated lists to
displayed math, except that commands such as '\chapter' that make no
sense in a letter are turned off.  Each 'letter' environment body
typically ends with a '\closing' command such as '\closing{Yours,}'.

   Additional material may come after the '\closing'.  You can say who
is receiving a copy of the letter with a command like '\cc{the Boss \\
the Boss's Boss}'.  There's a similar '\encl' command for a list of
enclosures.  And, you can add a postscript with '\ps'.

   LaTeX's default is to indent the sender name and the closing above it
by a length of '\longindentation'.  By default this is '0.5\textwidth'.
To make them flush left, put '\setlength{\longindentation}{0em}' in your
preamble.

   To set a fixed date use something like
'\renewcommand{\today}{1958-Oct-12}'.  If put in your preamble then it
will apply to all the letters.

   This example shows only one 'letter' environment.  The three lines
marked as optional are typically omitted.

     \documentclass{letter}
     \address{Sender's street \\ Sender's town}
     \signature{Sender's name \\ Sender's title}
     % optional: \location{Mailbox 13}
     % optional: \telephone{(102) 555-0101}
     \begin{document}
     \begin{letter}{Recipient's name \\ Recipient's address}
     \opening{Sir:}
     % optional: \thispagestyle{firstpage}
     I am not interested in entering a business arrangement with you.
     \closing{Your most humble, etc.,}
     \end{letter}
     \end{document}

   These commands are used with the 'letter' class.

26.1 '\address'
===============

Synopsis:

     \address{SENDERS ADDRESS}

   Specify the return address, as it appears on the letter and on the
envelope.  Separate multiple lines in SENDERS ADDRESS with a double
backslash, '\\'.

   Because it can apply to multiple letters this declaration is often
put in the preamble.  However, it can go anywhere, including inside an
individual 'letter' environment.

   This command is optional: if you do not use it then the letter is
formatted with some blank space on top, for copying onto pre-printed
letterhead paper.  If you do use the '\address' declaration then it is
formatted as a personal letter.

   Here is an example.

     \address{Stephen Maturin \\
              The Grapes of the Savoy}

26.2 '\cc'
==========

Synopsis:

     \cc{NAME0 \\
          ... }

   Produce a list of names to which copies of the letter were sent.
This command is optional.  If it appears then typically it comes after
'\closing'.  Put the names on different lines by separating them with a
double backslash, '\\', as in:

     \cc{President \\
         Vice President}

26.3 '\closing'
===============

Synopsis:

     \closing{TEXT}

   Produce the letter's closing.  This is optional, but usual.  It
appears at the end of a letter, above a handwritten signature.  For
example:

     \closing{Regards,}

26.4 '\encl'
============

Synopsis:

     \encl{FIRST ENCLOSED OBJECT \\
            ... }

   Produce a list of things included with the letter.  This command is
optional; when it is used, it typically is put after '\closing'.
Separate multiple lines with a double backslash, '\\'.

     \encl{License \\
           Passport}

26.5 '\location'
================

Synopsis:

     \location{TEXT}

   The TEXT appears centered at the bottom of the page.  It only appears
if the page style is 'firstpage'.

26.6 '\makelabels'
==================

Synopsis:

     \makelabels   % in preamble

   Optional, for a document that contains 'letter' environments.  If you
just put '\makelabels' in the preamble then at the end of the document
you will get a sheet with labels for all the recipients, one for each
letter environment, that you can copy to a sheet of peel-off address
labels.

   Customize the labels by redefining the commands '\startlabels',
'\mlabel', and '\returnaddress' (and perhaps '\name') in the preamble.
The command '\startlabels' sets the width, height, number of columns,
etc., of the page onto which the labels are printed.  The command
'\mlabel{RETURN ADDRESS}{RECIPIENT ADDRESS}' produces the two labels (or
one, if you choose to ignore the RETURN ADDRESS) for each letter
environment.  The first argument, RETURN ADDRESS, is the value returned
by the macro '\returnaddress'.  The second argument, RECIPIENT ADDRESS,
is the value passed in the argument to the 'letter' environment.  By
default '\mlabel' ignores the first argument, the RETURN ADDRESS,
causing the default behavior described in the prior paragraph.

   This illustrates customization.  Its output includes a page with two
columns having two labels each.

     \documentclass{letter}
     \renewcommand*{\returnaddress}{Fred McGuilicuddy \\
                                    Oshkosh, Mineola 12305}
     \newcommand*\originalMlabel{}
     \let\originalMlabel\mlabel
     \def\mlabel#1#2{\originalMlabel{}{#1}\originalMlabel{}{#2}}
     \makelabels
       ...
     \begin{document}
     \begin{letter}{A Einstein \\
                    112 Mercer Street \\
                    Princeton, New Jersey, USA 08540}
       ...
     \end{letter}
     \begin{letter}{K G\"odel \\
                    145 Linden Lane \\
                    Princeton, New Jersey, USA 08540}
       ...
     \end{letter}
     \end{document}

The first column contains the return address twice.  The second column
contains the address for each recipient.

   The package 'envlab' makes formatting the labels easier, with
standard sizes already provided.  The preamble lines
'\usepackage[personalenvelope]{envlab}' and '\makelabels' are all that
you need to print envelopes.

26.7 '\name'
============

Synopsis:

     \name{NAME}

   Optional.  Sender's name, used for printing on the envelope together
with the return address.

26.8 '\opening'
===============

Synopsis:

     \opening{SALUTATION}

   Required.  Follows the '\begin{letter}{...}'.  The argument
SALUTATION is mandatory.  For instance:

     \opening{Dear John:}

26.9 '\ps'
==========

Synopsis:

     \ps{TEXT}

   Add a postscript.  This command is optional and usually is used after
'\closing'.

     \ps{P.S. After you have read this letter, burn it. Or eat it.}

26.10 '\signature'
==================

Synopsis:

     \signature{FIRST LINE \\
                 ... }

   The sender's name.  This command is optional, although its inclusion
is usual.

   The argument text appears at the end of the letter, after the
closing.  LaTeX leaves some vertical space for a handwritten signature.
Separate multiple lines with a double backslash, '\\'.  For example:

     \signature{J Fred Muggs \\
                White House}

   LaTeX's default for the vertical space from the '\closing' text down
to the '\signature' text is '6\medskipamount', which is six times
'\medskipamount' (where '\medskipamount' is equal to a '\parskip', which
in turn is defined by default here to 0.7em).

   This command is usually in the preamble, to apply to all the letters
in the document.  To have it apply to one letter only, put it inside a
'letter' environment and before the '\closing'.

   You can include a graphic in the signature as here.

     \signature{\vspace{-6\medskipamount}\includegraphics{sig.png}\\
                  My name}

For this you must put '\usepackage{graphicx}' in the preamble (*note
Graphics::).

26.11 '\telephone'
==================

Synopsis:

     \telephone{NUMBER}

   The sender's telephone number.  This is typically in the preamble,
where it applies to all letters.  This only appears if the 'firstpage'
pagestyle is selected.  If so, it appears on the lower right of the
page.

27 Input/output
***************

LaTeX uses the ability to write to a file and later read it back in to
build document components such as a table of contents or index.  You can
also read a file that other programs written, or write a file for others
to read.  You can communicate with users through the terminal.  And, you
can issue instructions for the operating system.

27.1 '\openin' & '\openout'
===========================

Synopsis:

     \openin NUMBER=FILENAME

   or:

     \openout NUMBER=FILENAME

   Open a file for reading material, or for writing it.  In most
engines, the NUMBER must be between 0 and 15, as in '\openin3'; in
LuaLaTeX, NUMBER can be between 0 and 127.

   Here TeX opens the file 'presidents.tex' for reading.

     \newread\presidentsfile
     \openin\presidentsfile=presidents
     \typeout{presidentsfile is \the\presidentsfile}
     \read\presidentsfile to\presidentline
     \typeout{\presidentline}

The '\newread' command allocates input stream numbers from 0 to 15
(there is also a '\newwrite').  The '\presidentsfile' is more memorable
but under the hood it is still a number; the first '\typeout' gives
something like 'presidentsfile is 1'.  In addition, '\newread' keeps
track of the allocation so that if you use too many then you get an
error like '! No room for a new \read'.  The second '\typeout' gives the
first line of the file, something like '1 Washington, George'.

   Ordinarily TeX will not try to open the file until the next page
shipout.  To change this, use '\immediate\openin NUMBER=FILENAME' or
'\immediate\openout NUMBER=FILENAME'.

   Close files with '\closein NUMBER' and '\closeout NUMBER'.

   How LaTeX handles filenames varies among distributions, and even can
vary among versions of a distribution.  If the file does not have an
extension then TeX will add a '.tex'.  This creates 'presidents.tex',
writes one line to it, and closes it.

     \newwrite\presidentsfile
     \openout\presidentsfile=presidents
     \write\presidentsfile{1 Washington, George}
     \closeout\presidentsfile

But filenames with a period can cause trouble: if TeX finds a FILENAME
of 'presidents.dat' it could look first for 'presidents.dat.tex' and
later for 'presidents.dat', or it could do the opposite.  Your
distribution's documentation should say more, and if you find something
that works for you then you are good, but to ensure complete portability
the best thing is to use file names containing only the twenty six ASCII
letters (not case-sensitive) and the ten digits, along with underscore
and dash, and in particular with no dot or space.

   For '\openin', if TeX cannot find the file then it does not give an
error.  It just considers that the stream is not open (test for this
with '\ifeof'; one recourse is the command '\InputIfFileExists', *note
Class and package commands::).  If you try to use the same number twice,
LaTeX won't give you an error.  If you try to use a bad number then you
get an error message like '! Bad number (16). <to be read again> = l.30
\openin16=test.jh'.

27.2 '\read'
============

Synopsis:

     \read NUMBER toMACRO

   Make the command MACRO contain the next line of input from text
stream NUMBER, as in '\read5 to\data'.

   This opens the file 'email.tex' for reading, puts the contents of the
first line into the command '\email', and then closes the file.

     \newread\recipientfile
     \openin\recipientfile=email
     \read\recipientfile to\email
     \typeout{Email address: \email}
     \closein\recipientfile

   If NUMBER is outside the range from 0 to 15 or if no file of that
number is open, or if the file has ended, then '\read' will take input
from the terminal (or exit if interaction is not allowed, e.g.,
'\nonstopmode'; *note interaction modes::).  (However, the natural way
in LaTeX to take input from the terminal is '\typein' (*note \typein::.)

   To read an entire file as additional LaTeX source, use '\input'
(*note \input::) or '\include' (*note \include & \includeonly::).

   A common reason to want to read from a data file is to do mail
merges.  CTAN has a number of packages for that; one is 'datatool'.

27.3 '\typein'
==============

Synopsis, one of:

     \typein{PROMPT-MSG}
     \typein[CMD]{PROMPT-MSG}

   Print PROMPT-MSG on the terminal and cause LaTeX to stop and wait for
you to type a line of input.  This line of input ends when you hit the
return key.

   For example, this

     As long as I live I shall never forget \typein{Enter student name:}

coupled with this command line interaction

     Enter student name:

     \@typein=Aphra Behn

gives the output '... never forget Aphra Behn'.

   The first command version, '\typein{PROMPT-MSG}', causes the input
you typed to be processed as if it had been included in the input file
in place of the '\typein' command.

   In the second command version the optional argument 'CMD' argument
must be a command name, that is, it must begin with a backslash, \.
This command name is then defined or redefined to be the input that you
typed.  For example, this

     \typein[\student]{Enter student name:}
     \typeout{Recommendation for \student .}

gives this output on the command line,

     Enter student name:

     \student=John Dee
     Recommendation for John Dee.

where the user has entered 'John Dee.'

27.4 '\typeout'
===============

Synopsis:

     \typeout{MSG}

   Print 'msg' on the terminal and in the 'log' file.

   This

     \newcommand{\student}{John Dee}
     \typeout{Recommendation for \student .}

outputs 'Recommendation for John Dee'.  Like what happens here with
'\student', commands that are defined with '\newcommand' or
'\renewcommand' (among others) are replaced by their definitions before
being printed.

   LaTeX's usual rules for treating multiple spaces as a single space
and ignoring spaces after a command name apply to 'msg'.  Use the
command '\space' to get a single space, independent of surrounding
spaces.  Use '^^J' to get a newline.  Get a percent character with
'\csname @percentchar\endcsname'.

   This command can be useful for simple debugging, as here:

     \newlength{\jhlength}
     \setlength{\jhlength}{5pt}
     \typeout{The length is \the\jhlength.}

produces on the command line 'The length is 5.0pt'.

27.5 '\write'
=============

Synopsis:

     \write NUMBER{STRING}

   Write STRING to the log file, to the terminal, or to a file opened by
'\openout'.  For instance, '\write6' writes to text stream number 6.

   If the following appears in 'BASEFILE.tex' then it opens
'BASEFILE.jh', writes 'Hello World!' and a newline to it, and closes
that file.

     \newwrite\myfile
     \immediate\openout\myfile=\jobname.jh  % \jobname is root file basename
     ...
     \immediate\write\myfile{Hello world!}
     ...
     \immediate\closeout\myfile

The '\newwrite' allocates a stream number, giving it a symbolic name to
make life easier, so that 'stream \newwrite\myfile\the\myfile' produces
something like 'stream 3'.  Then '\openout' associates the stream number
with the given file name.  TeX ultimately executed '\write3' which puts
the string in the file.

   Typically NUMBER is between 0 and 15, because typically LaTeX authors
follow the prior example and the number is allocated by the system.  If
NUMBER is outside the range from 0 to 15 or if it is not associated with
an open file then LaTeX writes STRING to the log file.  If NUMBER is
positive then in addition LaTeX writes STRING to the terminal.

   Thus, 'test \write-1{Hello World!}' puts 'Hello World!' followed by a
newline in the log file.  (This is what the '\wlog' command does; *note
\wlog::).  And '\write100{Hello World!}' puts the same in the log file
but also puts 'Hello World!' followed by a newline in the terminal
output.  (But 16, 17, and 18 are special as NUMBER; see below.)

   In LuaTeX, instead of 16 output streams there are 256 (*note TeX
engines::).

   Use '\write\@auxout{STRING}' to write to the current '.aux' file,
which is associated with either the root file or with the current
include file; and use '\write\@mainaux{STRING}' to write to the main
'.aux'.  These symbolic names are defined by LaTeX.

   By default LaTeX does not write STRING to the file right away.  This
is because, for example, you may need '\write' to save the current page
number, but when TeX comes across a '\write' it typically does not know
what the page number is, since it has not yet done the page breaking.
So, you use '\write' in one of three contexts:

     \immediate\write\@auxout{STRING}      %1
     \write\@auxout{STRING}                %2
     \protected@write\@auxout{}{STRING}    %3

  1. With the first, LaTeX writes STRING to the file immediately.  Any
     macros in STRING are fully expanded (just as in '\edef') so to
     prevent expansion you must use '\noexpand', 'toks', etc., except
     that you should use '#' instead of '##').

  2. With the second, STRING is stored on the current list of things (as
     a TeX "whatsit" item) and kept until the page is shipped out and
     likewise the macros are unexpanded until '\shipout'.  At
     '\shipout', STRING is fully expanded.

  3. The third, '\protected@write', is like the second except that you
     can use '\protect' to avoid expansion.  The extra first argument
     allows you to locally insert extra definitions to make more macros
     protected or to have some other special definition for the write.

   As a simple example of expansion with '\write', STRING here contains
a control sequence '\triplex' which we've defined to be the text 'XYZ':

     \newwrite\jhfile
     \openout\jhfile=test.jh
     \newcommand{\triplex}{XYZ}
     \write\jhfile{test \triplex test}

This results in the file 'test.jh' containing the text 'test XYZtest'
followed by a newline.

   The cases where NUMBER is 16, 17, or 18 are special.  Because of
'\write''s behavior when NUMBER is outside the range from 0 to 15
described above, in Plain TeX '\write16' and '\write17' were sometimes
used to write to the log file and the terminal; however, in LaTeX, the
natural way to do that is with '\typeout' (*note \typeout::).  The
'\write18' command is even more special; modern TeX systems use it for
giving commands to the operating system (*note \write18::).

   Ordinarily '\write' outputs a single line.  You can include a newline
with '^^J'.  Thus, this produces two lines in the log file:

     \wlog{Parallel lines have a lot in common.^^JBut they never meet.}

   A common case where authors need to write their own file is for
answers to exercises, or another situation where you want to write out
verbatim, without expanding the macros.  CTAN has a number of packages
for this; one is 'answers'.

27.5.1 '\write' and security
----------------------------

The ability to write files raises security issues.  If you compiled a
downloaded LaTeX file and it overwrote your password file then you would
be justifiably troubled.

   Thus, by default TeX systems only allow you to open files for writing
that are in the current directory or output directory, if specified
(*note output directory::), or in a subdirectory of those.  So, this
code

     \newwrite\jhfile
     \openout\jhfile=../test.jh

gives an error like:
     Not writing to ../test.jh (openout_any = p).
     ! I can't write on file `../test.jh'

   You can get just such an error when using commands such as
'\include{../filename}' because LaTeX will try to open
'../filename.aux'.  The simplest solution is to put the included files
in the same directory as the root file, or in subdirectories.

27.5.2 '\message'
-----------------

Synopsis:

     \message{STRING}

   Write STRING to the log file and the terminal.

   Typically, LaTeX authors use '\typeout' (*note \typeout::).  It
allows you to use '\protect' on any fragile commands in STRING (*note
\protect::).  But '\typeout' always inserts a newline at the end of
STRING while '\message' does not, so the latter can be useful.

   With this example document body.

     before\message{One Two}\message{Three}\message{Four^^JI}
     \message{declare a thumb war.}After

under some circumstances (see below) LaTeX writes the following to both
the terminal and the log file.

     One Two Three Four
     I declare a thumb war.

The '^^J' produces a newline.  Also, in the output document, between
'before' and 'After' will be a single space (from the end of line
following 'I}').

   While '\message' allows you more control over formatting, a gotcha is
that LaTeX may mess up that formatting because it inserts line breaks
depending on what it has already written.  Contrast this document body,
where the 'Two' has moved, to the one given above.

     before\message{One}\message{Two Three}\message{Four^^JI}
     \message{declare a thumb war.}After

   This can happen: when LaTeX is outputting the messages to the
terminal, now the message with 'One' is shorter and it fits at the end
of the output terminal line, and so LaTeX breaks the line between it and
the 'Two Three'.  That line break appears also in the log file.  This
line break insertion can depend on, for instance, the length of the full
path names of included files.  So producing finely-formatted lines in a
way that is portable is hard, likely requiring starting your message at
the beginning of a line.

27.5.3 '\wlog'
--------------

Synopsis:

     \wlog{STRING}

   Write STRING to the log file.

     \wlog{Did you hear about the mathematician who hates negatives?}
     \wlog{He'll stop at nothing to avoid them.}

   Ordinarily STRING appears in a single separate line.  Use '^^J' to
insert a newline.

     \wlog{Helvetica and Times Roman walk into a bar.}
     \wlog{The barman says,^^JWe don't serve your type.}

27.5.4 '\write18'
-----------------

Synopsis:

     \write18{SHELL_COMMAND}

   Issue a command to the operating system shell.  The operating system
runs the command and LaTeX's execution is blocked until that finishes.

   This sequence (on Unix)

     \usepackage{graphicx}  % in preamble
       ...
     \newcommand{\fignum}{1}
     \immediate\write18{cd pix && asy figure\fignum}
     \includegraphics{pix\figure\fignum.pdf}

will run Asymptote (the 'asy' program) on 'pix/figure1.asy', so that the
document can later read in the resulting graphic (*note
\includegraphics::).  Like any '\write', here LaTeX expands macros in
SHELL_COMMAND so that '\fignum' is replaced by '1'.

   Another example is that you can automatically run BibTeX at the start
of each LaTeX run (*note Using BibTeX::) by including
'\immediate\write18{bibtex8 \jobname}' as the first line of the file.
Note that '\jobname' expands to the basename of the root file unless the
'--jobname' option is passed on the command line, in which case this is
the option argument.

   You sometimes need to do a multi-step process to get the information
that you want.  This will insert into the input a list of all PDF files
in the current directory (but see 'texosquery' below):

     \immediate\write18{ls *.pdf > tmp.dat}
     \input{tmp.dat}

   The standard behavior of any '\write' is to wait until a page is
being shipped out before expanding the macros or writing to the stream
(*note \write::).  But sometimes you want it done now.  For this, use
'\immediate\write18{SHELL_COMMAND}'.

   There are obvious security issues with allowing system commands
inside a LaTeX file.  If you download a file off the net and it contains
commands to delete all your files then you would be unhappy.  The
standard settings in modern distributions turn off full shell access.
You can turn it on, if you are sure the shell commands are safe, by
compiling with 'latex --enable-write18 FILENAME' (*note Command line
options::).  (The '--shell-escape' option is a synonym, in TeX Live.)

   In the place of full shell access, modern distributions by default
use a restricted version that allows some commands to work, such as
those that run Metafont to generate missing fonts, even if you do not
use the 'enable-write18' option.  By default this list of allowed
commands is short and features only commands that are under the control
of the distribution maintainers (*note Command line options::).

   The SHELL_COMMAND text is always passed to '/bin/sh' on Unix-like
operating systems, and the DOS command interpreter 'cmd.exe' on Windows.
Any different shell set by the user, and the 'SHELL' environment
variable, is ignored.

   If what you need is system information, such as the operating system
name, locale information, or directory contents, take a look at the
'texosquery' package, which provides a convenient and secure interface
for this, unlike the above examples using the raw '\write18':
<https://ctan.org/pkg/texosquery>.

   LaTeX provides a package 'shellesc' on top of the primitive
'\write18' command.  Its primary purpose is to provide a command
'\ShellEscape' which works identically on all TeX engines; LuaTeX
intentionally did not retain '\write18' as a way to invoke a shell
command, so some engine-specific code is needed.  The 'shellesc' package
also provides a command '\DelayedShellEscape', executed at '\output'
time, for the same reason.

28 Command line interface
*************************

Synopsis (from a terminal command line):

     pdflatex OPTIONS ARGUMENT

   Run LaTeX on ARGUMENT.  In place of 'pdflatex' you can also use (for
PDF output) 'xelatex' or 'lualatex', or (for DVI output) 'latex' or
'dvilualatex', among others (*note TeX engines::).

   For example, this will run LaTeX on the file 'thesis.tex', creating
the output 'thesis.pdf'.

     pdflatex thesis

Note that '.tex' is the default file name extension.

   pdfTeX is an extension of the original TeX program, as are XeTeX and
LuaTeX (*note TeX engines::).  The first two are completely backward
compatible and the latter, almost so.  Perhaps the most fundamental new
feature for all three is that the original TeX output its own DVI
format, while the newer ones can output directly to PDF. This allows
them to take advantage of the extra features in PDF such as hyperlinks,
support for modern image formats such as JPG and PNG, and ubiquitous
viewing programs.  In short, if you run 'pdflatex' or 'xelatex' or
'lualatex' then you will by default get PDF and have access to all its
modern features.  If you run 'latex', or 'dvilualatex', then you will
get DVI. The description here assumes pdfLaTeX.

   *Note Command line options::, for a selection of the most useful
command line options.  As to ARGUMENT, the usual case is that it does
not begin with a backslash, so the system takes it to be the name of a
file and it compiles that file.  If ARGUMENT begins with a backslash
then the system will interpret it as a line of LaTeX input, which can be
used for special effects (*note Command line input::).

   If you gave no arguments or options then 'pdflatex' prompts for input
from the terminal.  You can escape from this by entering 'CTRL-D'.

   If LaTeX finds an error in your document then by default it stops and
asks you about it.  *Note Recovering from errors::, for an outline of
what to do.

28.1 Command line options
=========================

These are the command-line options relevant to ordinary document
authoring.  For a full list, try running 'latex --help' from the command
line.

   With many implementations you can specify command line options by
prefixing them with '-' or '--'.  This is the case for both TeX Live
(including MacTeX) and MiKTeX.  We will use both conventions
interchangeably.  If an option takes a value, it can be specified either
as a separate argument ('--foo val'), or as one argument with an '='
sign ('--foo=val'), but there can be no spaces around the '='.  We will
generally use the '=' syntax.

'-version'
     Show the current version, like 'pdfTeX 3.14159265-2.6-1.40.16 (TeX
     Live 2015/Debian)' along with a small amount of additional
     information, and exit.

'-help'
     Give a brief usage message that is useful as a prompt and exit.

'-interaction=MODE'
     TeX compiles a document in one of four interaction modes:
     'batchmode', 'nonstopmode', 'scrollmode', 'errorstopmode'.  In
     "errorstopmode" (the default), TeX stops at each error and asks for
     user intervention.  In "batchmode" it prints nothing on the
     terminal, errors are scrolled as if the user hit 'RETURN' at every
     error, and missing files cause the job to abort.  In "nonstopmode",
     diagnostic message appear on the terminal but as in batch mode
     there is no user interaction.  In "scrollmode", TeX stops for
     missing files or keyboard input, but nothing else.

     For instance, starting LaTeX with this command line

          pdflatex -interaction=batchmode FILENAME

     eliminates most terminal output.

'-jobname=STRING'
     Set the value of TeX's "jobname" to the string.  The log file and
     output file will then be named 'STRING.log' and 'STRING.pdf'.
     *note Jobname::.

'-output-directory=DIRECTORY'
     Write files in the directory DIRECTORY.  It must already exist.
     This applies to all external files created by TeX or LaTeX, such as
     the '.log' file for the run, the '.aux', '.toc', etc., files
     created by LaTeX, as well as the main '.pdf' or '.dvi' output file
     itself.

     When specified, the output directory DIRECTORY is also
     automatically checked first for any file that it is input, so that
     the external files can be read back in, if desired.  The true
     current directory (in which LaTeX was run) remains unchanged, and
     is also checked for input files.

'--enable-write18'
'--disable-write18'
'--shell-escape'
'--no-shell-escape'
     Enable or disable '\write18{SHELL_COMMAND}' (*note \write18::).
     The first two options are supported by both TeX Live and MiKTeX,
     while the second two are synonyms supported by TeX Live.

     Enabling this functionality has major security implications, since
     it allows a LaTeX file to run any command whatsoever.  Thus, by
     default, unrestricted '\write18' is not allowed.  (The default for
     TeX Live, MacTeX, and MiKTeX is to allow the execution of a limited
     number of TeX-related programs, which they distribute.)

     For example, if you invoke LaTeX with the option 'no-shell-escape',
     and in your document you call '\write18{ls -l}', then you do not
     get an error but the log file says 'runsystem(ls -l)...disabled'.

'-halt-on-error'
     Stop processing at the first error.

'-file-line-error'
'-no-file-line-error'
     Enable or disable 'FILENAME:LINENO:ERROR'-style error messages.
     These are only available with TeX Live or MacTeX.

28.2 Command line input
=======================

As part of the command line invocation

     LATEX-ENGINE OPTIONS ARGUMENT

you can specify arbitrary LaTeX input by starting ARGUMENT with a
backslash.  (All the engines support this.)  This allows you to do some
special effects.

   For example, this file (which uses the 'hyperref' package for
hyperlinks) can produce two kinds of output, one to be read on physical
paper and one to be read online.

     \ifdefined\paperversion        % in preamble
     \newcommand{\urlcolor}{black}
     \else
     \newcommand{\urlcolor}{blue}
     \fi
     \usepackage[colorlinks=true,urlcolor=\urlcolor]{hyperref}
       ...
     \href{https://www.ctan.org}{CTAN}  % in body
       ...

Compiling this document 'book.tex' with the command line 'pdflatex book'
will give the 'CTAN' link in blue.  But compiling it with

     pdflatex "\def\paperversion{}\input book.tex"

has the link in black.  We use double quotes to prevent interpretation
of the symbols by the command line shell.  (This usually works on both
Unix and Windows systems, but there are many peculiarities to shell
quoting, so read your system documentation if need be.)

   In a similar way, from the single file 'main.tex' you can compile two
different versions.

     pdflatex -jobname=students "\def\student{}\input{main}"
     pdflatex -jobname=teachers "\def\teachers{}\input{main}"

The 'jobname' option is there because otherwise both files would be
called 'main.pdf' and the second would overwrite the first.  (*note
Jobname::.)

   In this example we use the command line to select which parts of a
document to include.  For a book named 'mybook.tex' and structured like
this.

     \documentclass{book}
     \begin{document}
        ...
     \include{chap1}
     \include{chap2}
       ...
     \end{document}

the command line

     pdflatex "\includeonly{chap1}\input{mybook}"

will give output that has the first chapter but no other chapter.  *Note
Splitting the input::.

28.3 Jobname
============

Running LaTeX creates a number of files, including the main PDF (or DVI)
output but also including others.  These files are named with the
so-called "jobname".  The most common case is also the simplest, where
for instance the command 'pdflatex thesis' creates 'thesis.pdf' and also
'thesis.log' and 'thesis.aux'.  Here the job name is 'thesis'.

   In general, LaTeX is invoked as 'LATEX-ENGINE OPTIONS ARGUMENT',
where LATEX-ENGINE is 'pdflatex', 'lualatex', etc. (*note TeX
engines::).  If ARGUMENT does not start with a backslash, as is the case
above with 'thesis', then TeX considers it to be the name of the file to
input as the main document.  This file is referred to as the "root file"
(*note Splitting the input::, and *note \input::).  The name of that
root file, without the '.tex' extension if any, is the jobname.  If
ARGUMENT does start with a backslash, or if TeX is in interactive mode,
then it waits for the first '\input' command, and the jobname is the
argument to '\input'.

   There are two more possibilities for the jobname.  It can be directly
specified with the '-jobname' option, as in 'pdflatex -jobname=myname'
(*note Command line input:: for a real example).

   The final possibility is 'texput', which is the final fallback
default if no other name is available to TeX.  That is, if no '-jobname'
option was specified, and the compilation stops before any input file is
met, then the log file will be named 'texput.log'.

   A special case of this is that in LaTeX versions of (approximately)
2020 or later, the jobname is also 'texput' if the first '\input' occurs
as a result of being called by either '\documentclass' or
'\RequirePackage'.  So this will produce a file named 'texput.pdf':

     pdflatex "\documentclass{minimal}\begin{document}Hello!\end{document}"

   However, this special case only applies to those two commands.  Thus,
with

     pdflatex "\documentclass{article}\usepackage{lipsum}\input{thesis}"

the output file is 'lipsum.pdf', as '\usepackage' calls '\input'.

   Within the document, the macro '\jobname' expands to the jobname.
(When you run LaTeX on a file whose name contains spaces, the string
returned by '\jobname' contains matching start and end quotes.)  In the
expansion of that macro, all characters are of catcode 12 (other) except
that spaces are category 10, including letters that are normally
catcode 11.

   Because of this catcode situation, using the jobname in a conditional
can become complicated.  One solution is to use the macro '\IfBeginWith'
from the 'xstring' package in its star variant, which is insensitive to
catcode.  For example, in the following text the footnote "Including
Respublica Bananensis Francorum." is only present if the task name
starts with 'my-doc'.

     If a democracy is just a regime where citizens vote then
     all banana republics \IfBeginWith*{\jobname}{my-doc}%
     {\footnote{Including Respublica Bananensis Francorum.}}{} are
     democracies.

   Manipulating the value of '\jobname' inside of a document does not
change the name of the output file or the log file.

28.4 Recovering from errors
===========================

If LaTeX finds an error in your document then it gives you an error
message and prompts you with a question mark, '?'.  For instance,
running LaTeX on this file

     \newcommand{\NP}{\ensuremath{\textbf{NP}}}
     The \PN{} problem is a million dollar one.

causes it show this, and wait for input.

     ! Undefined control sequence.
     l.5 The \PN
                {} problem is a million dollar one.
     ?

The simplest thing is to enter 'x' and 'RETURN' and fix the typo.  You
could instead enter '?' and 'RETURN' to see other options.

   There are two other error scenarios.  The first is that you forgot to
include the '\end{document}' or misspelled it.  In this case LaTeX gives
you a '*' prompt.  You can get back to the command line by typing
'\stop' and 'RETURN'; this command does its best to exit LaTeX
immediately, whatever state it may be in.

   The last scenario is that you mistyped the filename.  For instance,
instead of 'pdflatex test' you might type 'pdflatex tste'.

     ! I can't find file `tste'.
     <*> tste

     (Press Enter to retry, or Control-D to exit)
     Please type another input file name:

The simplest thing is to enter 'CTRL d' (holding the Control and d keys
down at the same time), and then retype the correct command line.

Appendix A Document templates
*****************************

Although illustrative material, perhaps these document templates will be
useful.  Additional template resources are listed at
<https://tug.org/interest.html#latextemplates>.

A.1 'beamer' template
=====================

The 'beamer' class creates presentation slides.  It has a vast array of
features, but here is a basic template:

\documentclass{beamer}

\title{Beamer Class template}
\author{Alex Author}
\date{July 31, 2020}

\begin{document}

\maketitle

% without [fragile], any {verbatim} code gets mysterious errors.
\begin{frame}[fragile]
 \frametitle{First Slide}

\begin{verbatim}
  This is \verbatim!
\end{verbatim}

\end{frame}

\end{document}

   The Beamer package on CTAN: <https://ctan.org/pkg/beamer>.

A.2 'article' template
======================

A simple template for an article.

\documentclass{article}
\title{Article Class Template}
\author{Alex Author}

\begin{document}
\maketitle

\section{First section}
Some text.

\subsection{First section, first subsection}
Additional text.

\section{Second section}
Some more text.

\end{document}

A.3 'book' template
===================

This is a straightforward template for a book.  *Note Larger book
template::, for a more elaborate one.

\documentclass{book}
\title{Book Class Template}
\author{Alex Author}

\begin{document}
\maketitle

\chapter{First}
Some text.

\chapter{Second}
Some other text.

\section{A subtopic}
The end.

\end{document}

A.4 Larger 'book' template
==========================

This is a somewhat elaborate template for a book.  *Note book
template::, for a simpler one.

   This template uses '\frontmatter', '\mainmatter', and '\backmatter'
to control the typography of the three main areas of a book (*note
\frontmatter & \mainmatter & \backmatter::).  The book has a
bibliography and an index.

   Also notable is that it uses '\include' and '\includeonly' (*note
Splitting the input::).  While you are working on a chapter you can
comment out all the other chapter entries from the argument to
'\includeonly'.  That will speed up compilation without losing any
information such as cross-references.  (Material that does not need to
come on a new page is brought in with '\input' instead of '\include'.
You don't get the cross-reference benefit with '\input'.)

\documentclass[titlepage]{book}
\usepackage{makeidx}\makeindex

\title{Book Class Template}
\author{Alex Author}

\includeonly{%
% frontcover,
  preface,
  chap1,
% appenA,
  }

\begin{document}
\frontmatter
\include{frontcover}
  % maybe comment out while drafting:
\maketitle \input{dedication} \input{copyright}
\tableofcontents
\include{preface}

\mainmatter
\include{chap1}
...
\appendix
\include{appenA}
...

\backmatter
\bibliographystyle{apalike}
\addcontentsline{toc}{chapter}{Bibliography}
\bibliography
\addcontentsline{toc}{chapter}{Index}
\printindex

\include{backcover}
\end{document}

Index
*****

* Menu:

* $ inline math:                         math.              (line  4754)
* $$...$$ plain TeX display math:        displaymath.       (line  3860)
* & for table cells:                     tabular.           (line  5726)
* * prompt:                              Recovering from errors.
                                                            (line 16296)
* *, to \nocite all keys:                Using BibTeX.      (line  6257)
* *-form of environment commands:        \newenvironment & \renewenvironment.
                                                            (line  7646)
* *-form of sectioning commands:         Sectioning.        (line  2657)
* *-form, defining new commands:         \newcommand & \renewcommand.
                                                            (line  7248)
* --disable-write18 command-line option: Command line options.
                                                            (line 16121)
* --enable-write18 command-line option:  Command line options.
                                                            (line 16121)
* --file-line-error command-line option: Command line options.
                                                            (line 16142)
* --halt-on-error command-line option:   Command line options.
                                                            (line 16139)
* --help command-line option:            Command line options.
                                                            (line 16083)
* --interaction command-line option:     Command line options.
                                                            (line 16086)
* --jobname command-line option:         Command line options.
                                                            (line 16103)
* --no-file-line-error command-line option: Command line options.
                                                            (line 16142)
* --no-shell-escape command-line option: Command line options.
                                                            (line 16121)
* --output-directory command-line option: Command line options.
                                                            (line 16108)
* --shell-escape command-line option:    Command line options.
                                                            (line 16121)
* --version command-line option:         Command line options.
                                                            (line 16078)
* -1, write stream number:               \write.            (line 15781)
* .aux file:                             Output files.      (line   490)
* .aux file and BibTeX commands:         BibTeX error messages.
                                                            (line  6264)
* .dvi file:                             Output files.      (line   467)
* .fmt file:                             TeX engines.       (line   509)
* .glo file:                             Glossaries.        (line 15180)
* .idx file:                             Indexes.           (line 14770)
* .idx file <1>:                         makeindex.         (line 14969)
* .ind file:                             makeindex.         (line 14969)
* .isty file:                            makeindex.         (line 14981)
* .lof file:                             Output files.      (line   500)
* .lof file <1>:                         Table of contents etc..
                                                            (line 14377)
* .lof file <2>:                         \contentsline.     (line 14673)
* .log file:                             Output files.      (line   485)
* .lot file:                             Output files.      (line   500)
* .lot file <1>:                         Table of contents etc..
                                                            (line 14377)
* .lot file <2>:                         \contentsline.     (line 14673)
* .pdf file:                             Output files.      (line   477)
* .tex, default extension:               Command line interface.
                                                            (line 16035)
* .toc file:                             Output files.      (line   500)
* .toc file <1>:                         Table of contents etc..
                                                            (line 14377)
* .toc file <2>:                         \contentsline.     (line 14673)
* .xdv file:                             TeX engines.       (line   545)
* /bin/sh, used by \write18:             \write18.          (line 16000)
* 10pt option:                           Document class options.
                                                            (line   739)
* 11pt option:                           Document class options.
                                                            (line   739)
* 12pt option:                           Document class options.
                                                            (line   739)
* : for math:                            Colon character & \colon.
                                                            (line 10927)
* [...] for optional arguments:          LaTeX command syntax.
                                                            (line   595)
* \  (backslash-space):                  \(SPACE).          (line 11606)
* \ character starting commands:         LaTeX command syntax.
                                                            (line   595)
* \!:                                    Spacing in math mode.
                                                            (line 10688)
* \" (umlaut accent):                    Accents.           (line 13851)
* \#:                                    Reserved characters.
                                                            (line 13532)
* \$:                                    Reserved characters.
                                                            (line 13532)
* \%:                                    Reserved characters.
                                                            (line 13532)
* \&:                                    Reserved characters.
                                                            (line 13532)
* \' (acute accent):                     Accents.           (line 13855)
* \' (tabbing):                          tabbing.           (line  5574)
* \(...\) inline math:                   math.              (line  4754)
* \*:                                    \*.                (line 10947)
* \+:                                    tabbing.           (line  5566)
* \,:                                    Spacing in math mode.
                                                            (line 10674)
* \-:                                    tabbing.           (line  5570)
* \- (hyphenation):                      \- (hyphenation).  (line  6633)
* \. (dot-over accent):                  Accents.           (line 13858)
* \/:                                    \/.                (line 11754)
* \::                                    Spacing in math mode.
                                                            (line 10663)
* \;:                                    Spacing in math mode.
                                                            (line 10650)
* \<:                                    tabbing.           (line  5562)
* \= (macron accent):                    Accents.           (line 13862)
* \= (tabbing):                          tabbing.           (line  5556)
* \>:                                    tabbing.           (line  5560)
* \> <1>:                                Spacing in math mode.
                                                            (line 10663)
* \> (tabbing):                          tabbing.           (line  5559)
* \@:                                    \@.                (line 11529)
* \@auxout:                              \write.            (line 15796)
* \@beginparpenalty:                     list.              (line  4636)
* \@dottedtocline:                       \@dottedtocline.   (line 14501)
* \@endparpenalty:                       list.              (line  4644)
* \@fnsymbol:                            \footnote.         (line  6997)
* \@ifstar:                              \@ifstar.          (line  7460)
* \@itempenalty:                         list.              (line  4640)
* \@mainaux:                             \write.            (line 15796)
* \@startsection:                        \@startsection.    (line  3141)
* \a (tabbing):                          tabbing.           (line  5589)
* \a' (acute accent in tabbing):         tabbing.           (line  5590)
* \a= (macron accent in tabbing):        tabbing.           (line  5590)
* \aa (å):                               Additional Latin letters.
                                                            (line 13975)
* \AA (Å):                               Additional Latin letters.
                                                            (line 13975)
* \accent:                               \accent.           (line 13924)
* \acute:                                Math accents.      (line 10544)
* \addcontentsline:                      \addcontentsline.  (line 14536)
* \address:                              \address.          (line 15358)
* \addtocontents{EXT}{TEXT}:             \addtocontents.    (line 14615)
* \addtocounter:                         \addtocounter.     (line  8242)
* \addtolength:                          \addtolength.      (line  8500)
* \addvspace:                            \addvspace.        (line 12089)
* \ae (æ):                               Additional Latin letters.
                                                            (line 13979)
* \AE (Æ):                               Additional Latin letters.
                                                            (line 13979)
* \aleph:                                Math symbols.      (line  9130)
* \Alph example:                         enumerate.         (line  3971)
* \alpha:                                Math symbols.      (line  9133)
* \alph{COUNTER}:                        \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                            (line  8117)
* \Alph{COUNTER}:                        \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                            (line  8122)
* \alsoname:                             \index.            (line 14904)
* \amalg:                                Math symbols.      (line  9136)
* \and for \author:                      \maketitle.        (line 11128)
* \angle:                                Math symbols.      (line  9139)
* \appendix:                             \appendix.         (line  3072)
* \approx:                               Math symbols.      (line  9143)
* \arabic{COUNTER}:                      \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                            (line  8127)
* \arccos:                               Math functions.    (line 10427)
* \arcsin:                               Math functions.    (line 10430)
* \arctan:                               Math functions.    (line 10433)
* \arg:                                  Math functions.    (line 10436)
* \arraycolsep:                          array.             (line  3657)
* \arrayrulewidth:                       tabular.           (line  5851)
* \arraystretch:                         tabular.           (line  5857)
* \ast:                                  Math symbols.      (line  9146)
* \asymp:                                Math symbols.      (line  9153)
* \AtBeginDocument:                      \AtBeginDocument.  (line  3884)
* \AtBeginDvi:                           Class and package commands.
                                                            (line   919)
* \AtEndDocument:                        \AtEndDocument.    (line  3900)
* \AtEndOfClass:                         Class and package commands.
                                                            (line   924)
* \AtEndOfPackage:                       Class and package commands.
                                                            (line   924)
* \author{NAME1 \and NAME2 \and ...}:    \maketitle.        (line 11127)
* \a` (grave accent in tabbing):         tabbing.           (line  5590)
* \b (bar-under accent):                 Accents.           (line 13877)
* \backmatter:                           \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* \backslash:                            Math symbols.      (line  9156)
* \bar:                                  Math accents.      (line 10547)
* \baselineskip:                         Low-level font commands.
                                                            (line  1992)
* \baselineskip <1>:                     \baselineskip & \baselinestretch.
                                                            (line  2315)
* \baselinestretch:                      \baselineskip & \baselinestretch.
                                                            (line  2315)
* \begin:                                Environments.      (line  3549)
* \beta:                                 Math symbols.      (line  9160)
* \bf:                                   Font styles.       (line  1770)
* \bfseries:                             Font styles.       (line  1735)
* \bibdata:                              BibTeX error messages.
                                                            (line  6274)
* \bibitem:                              \bibitem.          (line  6079)
* \bibliography:                         Using BibTeX.      (line  6202)
* \bibliography and internal \bibdata:   BibTeX error messages.
                                                            (line  6275)
* \bibliographystyle:                    Using BibTeX.      (line  6202)
* \bibliographystyle and internal \bibstyle: BibTeX error messages.
                                                            (line  6278)
* \bibname:                              thebibliography.   (line  6062)
* \bibstyle:                             BibTeX error messages.
                                                            (line  6277)
* \bigcap:                               Math symbols.      (line  9163)
* \bigcirc:                              Math symbols.      (line  9167)
* \bigcup:                               Math symbols.      (line  9170)
* \bigodot:                              Math symbols.      (line  9174)
* \bigoplus:                             Math symbols.      (line  9177)
* \bigotimes:                            Math symbols.      (line  9180)
* \bigskip:                              \bigskip & \medskip & \smallskip.
                                                            (line 11870)
* \bigskipamount:                        \bigskip & \medskip & \smallskip.
                                                            (line 11871)
* \bigsqcup:                             Math symbols.      (line  9189)
* \bigtriangledown:                      Math symbols.      (line  9183)
* \bigtriangleup:                        Math symbols.      (line  9186)
* \biguplus:                             Math symbols.      (line  9192)
* \bigvee:                               Math symbols.      (line  9196)
* \bigwedge:                             Math symbols.      (line  9199)
* \bmod:                                 Math functions.    (line 10439)
* \boldmath:                             \boldmath & \unboldmath.
                                                            (line 10000)
* \boldmath <1>:                         \boldmath & \unboldmath.
                                                            (line 10008)
* \bot:                                  Math symbols.      (line  9202)
* \bottomfraction:                       Floats.            (line  2496)
* \bottomfraction <1>:                   Floats.            (line  2497)
* \bowtie:                               Math symbols.      (line  9206)
* \Box:                                  Math symbols.      (line  9209)
* \breve:                                Math accents.      (line 10550)
* \bullet:                               Math symbols.      (line  9214)
* \c (cedilla accent):                   Accents.           (line 13887)
* \cal:                                  Font styles.       (line  1773)
* \cap:                                  Math symbols.      (line  9217)
* \capitalacute:                         Accents.           (line 13855)
* \capitalbreve:                         Accents.           (line 13915)
* \capitalcaron:                         Accents.           (line 13919)
* \capitalcedilla:                       Accents.           (line 13887)
* \capitalcircumflex:                    Accents.           (line 13866)
* \capitaldieresis:                      Accents.           (line 13851)
* \capitaldotaccent:                     Accents.           (line 13891)
* \capitalgrave:                         Accents.           (line 13870)
* \capitalhungarumlaut:                  Accents.           (line 13895)
* \capitalmacron:                        Accents.           (line 13862)
* \capitalnewtie:                        Accents.           (line 13909)
* \capitalogonek:                        Accents.           (line 13899)
* \capitalring:                          Accents.           (line 13903)
* \capitaltie:                           Accents.           (line 13909)
* \capitaltilde:                         Accents.           (line 13874)
* \caption:                              \caption.          (line  2558)
* \caption <1>:                          figure.            (line  4094)
* \caption <2>:                          table.             (line  5678)
* \cc:                                   \cc.               (line 15383)
* \cdot:                                 Math symbols.      (line  9221)
* \cdots:                                Dots.              (line 10338)
* \centering:                            \centering.        (line  3736)
* \chapter:                              Sectioning.        (line  2632)
* \chapter <1>:                          \chapter.          (line  2772)
* \check:                                Math accents.      (line 10553)
* \CheckCommand:                         Class and package commands.
                                                            (line   931)
* \CheckCommand*:                        Class and package commands.
                                                            (line   931)
* \chi:                                  Math symbols.      (line  9224)
* \circ:                                 Math symbols.      (line  9227)
* \circle:                               \circle.           (line  5223)
* \citation:                             BibTeX error messages.
                                                            (line  6280)
* \cite:                                 \cite.             (line  6137)
* \cite and internal \citation:          BibTeX error messages.
                                                            (line  6281)
* \ClassError:                           Class and package commands.
                                                            (line   951)
* \ClassInfo:                            Class and package commands.
                                                            (line   951)
* \ClassInfoNoLine:                      Class and package commands.
                                                            (line   951)
* \ClassWarning:                         Class and package commands.
                                                            (line   951)
* \ClassWarningNoLine:                   Class and package commands.
                                                            (line   951)
* \cleardoublepage:                      \clearpage & \cleardoublepage.
                                                            (line  6814)
* \clearpage:                            \clearpage & \cleardoublepage.
                                                            (line  6814)
* \cline:                                \cline.            (line  5985)
* \closein:                              \openin & \openout.
                                                            (line 15584)
* \closeout:                             \openin & \openout.
                                                            (line 15584)
* \closing:                              \closing.          (line 15399)
* \clubsuit:                             Math symbols.      (line  9231)
* \colon:                                Colon character & \colon.
                                                            (line 10927)
* \columnsep:                            \twocolumn.        (line  2057)
* \columnsep <1>:                        Page layout parameters.
                                                            (line  2182)
* \columnsep <2>:                        Page layout parameters.
                                                            (line  2185)
* \columnseprule:                        \twocolumn.        (line  2063)
* \columnseprule <1>:                    Page layout parameters.
                                                            (line  2183)
* \columnseprule <2>:                    Page layout parameters.
                                                            (line  2185)
* \columnwidth:                          \twocolumn.        (line  2070)
* \columnwidth <1>:                      Page layout parameters.
                                                            (line  2184)
* \columnwidth <2>:                      Page layout parameters.
                                                            (line  2185)
* \complement:                           Math symbols.      (line  9234)
* \cong:                                 Math symbols.      (line  9240)
* \contentsline:                         Table of contents etc..
                                                            (line 14433)
* \contentsline <1>:                     \addcontentsline.  (line 14540)
* \contentsline <2>:                     \contentsline.     (line 14673)
* \coprod:                               Math symbols.      (line  9243)
* \copyright:                            Text symbols.      (line 13627)
* \cos:                                  Math functions.    (line 10442)
* \cosh:                                 Math functions.    (line 10445)
* \cot:                                  Math functions.    (line 10448)
* \coth:                                 Math functions.    (line 10451)
* \csc:                                  Math functions.    (line 10454)
* \cup:                                  Math symbols.      (line  9246)
* \CurrentOption:                        Class and package commands.
                                                            (line   970)
* \d (dot-under accent):                 Accents.           (line 13891)
* \dag:                                  Text symbols.      (line 13631)
* \dagger:                               Math symbols.      (line  9250)
* \dashbox:                              \dashbox.          (line  5433)
* \dashv:                                Math symbols.      (line  9253)
* \date{TEXT}:                           \maketitle.        (line 11135)
* \day:                                  \day & \month & \year.
                                                            (line  8291)
* \dblfloatpagefraction:                 \twocolumn.        (line  2103)
* \dblfloatsep:                          \twocolumn.        (line  2109)
* \dbltextfloatsep:                      \twocolumn.        (line  2116)
* \dbltopfraction:                       \twocolumn.        (line  2082)
* \dbltopnumber:                         \twocolumn.        (line  2121)
* \ddag:                                 Text symbols.      (line 13634)
* \ddagger:                              Math symbols.      (line  9257)
* \ddot:                                 Math accents.      (line 10556)
* \ddots:                                Dots.              (line 10342)
* \DeclareFontEncoding:                  \DeclareFontEncoding.
                                                            (line  1384)
* \DeclareGraphicsExtensions:            \DeclareGraphicsExtensions.
                                                            (line 12954)
* \DeclareGraphicsRule:                  \DeclareGraphicsRule.
                                                            (line 12996)
* \DeclareOption:                        Class and package commands.
                                                            (line   976)
* \DeclareOption*:                       Class and package commands.
                                                            (line   976)
* \DeclareRobustCommand:                 Class and package commands.
                                                            (line  1006)
* \DeclareRobustCommand*:                Class and package commands.
                                                            (line  1006)
* \DeclareTextAccent:                    \DeclareTextAccent.
                                                            (line  1418)
* \DeclareTextAccent <1>:                \DeclareTextAccentDefault.
                                                            (line  1442)
* \DeclareTextAccentDefault:             \DeclareTextAccentDefault.
                                                            (line  1442)
* \DeclareTextCommand:                   \DeclareTextCommand & \ProvideTextCommand.
                                                            (line  1470)
* \DeclareTextCommand <1>:               \DeclareTextCommandDefault & \ProvideTextCommandDefault.
                                                            (line  1519)
* \DeclareTextCommandDefault:            \DeclareTextCommandDefault & \ProvideTextCommandDefault.
                                                            (line  1519)
* \DeclareTextComposite:                 \DeclareTextComposite.
                                                            (line  1551)
* \DeclareTextCompositeCommand:          \DeclareTextCompositeCommand.
                                                            (line  1575)
* \DeclareTextSymbol:                    \DeclareTextCommand & \ProvideTextCommand.
                                                            (line  1501)
* \DeclareTextSymbol <1>:                \DeclareTextSymbol.
                                                            (line  1593)
* \DeclareTextSymbol <2>:                \DeclareTextSymbolDefault.
                                                            (line  1620)
* \DeclareTextSymbolDefault:             \DeclareTextSymbolDefault.
                                                            (line  1620)
* \deg:                                  Math functions.    (line 10457)
* \DelayedShellEscape:                   \write18.          (line 16011)
* \Delta:                                Math symbols.      (line  9260)
* \delta:                                Math symbols.      (line  9263)
* \det:                                  Math functions.    (line 10460)
* \dh (ð):                               Additional Latin letters.
                                                            (line 13983)
* \DH (Ð):                               Additional Latin letters.
                                                            (line 13983)
* \Diamond:                              Math symbols.      (line  9266)
* \diamond:                              Math symbols.      (line  9270)
* \diamondsuit:                          Math symbols.      (line  9274)
* \dim:                                  Math functions.    (line 10463)
* \displaystyle:                         Math styles.       (line 10876)
* \div:                                  Math symbols.      (line  9277)
* \dj:                                   Additional Latin letters.
                                                            (line 13989)
* \DJ:                                   Additional Latin letters.
                                                            (line 13989)
* \documentclass:                        Document classes.  (line   696)
* \documentclass, and texput jobname:    Jobname.           (line 16240)
* \dot:                                  Math accents.      (line 10559)
* \doteq:                                Math symbols.      (line  9280)
* \dotfill:                              \hrulefill & \dotfill.
                                                            (line 11799)
* \dots:                                 Text symbols.      (line 13651)
* \doublerulesep:                        tabular.           (line  5862)
* \downarrow:                            Math symbols.      (line  9284)
* \Downarrow:                            Math symbols.      (line  9288)
* \ell:                                  Math symbols.      (line  9292)
* \emph:                                 Font styles.       (line  1755)
* \emptyset:                             Math symbols.      (line  9295)
* \encl:                                 \encl.             (line 15412)
* \end:                                  Environments.      (line  3549)
* \endinput:                             \endinput.         (line 14188)
* \enlargethispage:                      \enlargethispage.  (line  6888)
* \enspace:                              \enspace & \quad & \qquad.
                                                            (line 11338)
* \enumi:                                enumerate.         (line  3957)
* \enumii:                               enumerate.         (line  3957)
* \enumiii:                              enumerate.         (line  3957)
* \enumiv:                               enumerate.         (line  3957)
* \epsilon:                              Math symbols.      (line  9298)
* \equiv:                                Math symbols.      (line  9304)
* \eta:                                  Math symbols.      (line  9307)
* \evensidemargin:                       Document class options.
                                                            (line   809)
* \evensidemargin <1>:                   Page layout parameters.
                                                            (line  2243)
* \evensidemargin <2>:                   Page layout parameters.
                                                            (line  2244)
* \ExecuteOptions:                       Class and package commands.
                                                            (line  1082)
* \exists:                               Math symbols.      (line  9310)
* \exp:                                  Math functions.    (line 10466)
* \externaldocument:                     xr package.        (line  3495)
* \extracolsep:                          tabular.           (line  5802)
* \fbox:                                 \fbox & \framebox. (line 12236)
* \fboxrule:                             \framebox (picture).
                                                            (line  5410)
* \fboxrule <1>:                         \fbox & \framebox. (line 12268)
* \fboxrule <2>:                         \fbox & \framebox. (line 12267)
* \fboxsep:                              \framebox (picture).
                                                            (line  5410)
* \fboxsep <1>:                          \fbox & \framebox. (line 12273)
* \fboxsep <2>:                          \fbox & \framebox. (line 12272)
* \fill:                                 \hfill.            (line 11424)
* \flat:                                 Math symbols.      (line  9313)
* \floatpagefraction:                    Floats.            (line  2500)
* \floatpagefraction <1>:                Floats.            (line  2501)
* \floatsep:                             Floats.            (line  2516)
* \floatsep <1>:                         Floats.            (line  2517)
* \flushbottom:                          \flushbottom.      (line  2150)
* \fnsymbol, and footnotes:              \footnote.         (line  6997)
* \fnsymbol{COUNTER}:                    \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                            (line  8140)
* \fontdimen1:                           \/.                (line 11788)
* \fontencoding:                         Low-level font commands.
                                                            (line  1902)
* \fontfamily:                           Low-level font commands.
                                                            (line  1912)
* \fontseries:                           Low-level font commands.
                                                            (line  1939)
* \fontshape:                            Low-level font commands.
                                                            (line  1979)
* \fontsize:                             Low-level font commands.
                                                            (line  1992)
* \footnote:                             \footnote.         (line  6979)
* \footnotemark:                         \footnotemark.     (line  7045)
* \footnoterule:                         \footnote.         (line  7007)
* \footnotesep:                          \footnote.         (line  7019)
* \footnotesize:                         Font sizes.        (line  1845)
* \footnotetext:                         \footnotetext.     (line  7101)
* \footskip:                             Page layout parameters.
                                                            (line  2202)
* \footskip <1>:                         Page layout parameters.
                                                            (line  2203)
* \forall:                               Math symbols.      (line  9316)
* \frac:                                 \frac.             (line 10963)
* \frame:                                \frame.            (line  5421)
* \framebox:                             \framebox (picture).
                                                            (line  5385)
* \framebox <1>:                         \fbox & \framebox. (line 12236)
* \frenchspacing:                        \frenchspacing & \nonfrenchspacing.
                                                            (line 11575)
* \frontmatter:                          \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* \frown:                                Math symbols.      (line  9319)
* \fussy:                                \fussy & \sloppy.  (line  6690)
* \Gamma:                                Math symbols.      (line  9322)
* \gamma:                                Math symbols.      (line  9325)
* \gcd:                                  Math functions.    (line 10469)
* \ge:                                   Math symbols.      (line  9328)
* \geq:                                  Math symbols.      (line  9332)
* \gets:                                 Math symbols.      (line  9336)
* \gg:                                   Math symbols.      (line  9339)
* \gls:                                  \gls.              (line 15250)
* \graphicspath:                         \graphicspath.     (line 12891)
* \graphpaper:                           \graphpaper.       (line  5126)
* \grave:                                Math accents.      (line 10562)
* \guillemotleft («):                    Text symbols.      (line 13643)
* \guillemotright (»):                   Text symbols.      (line 13644)
* \guilsinglleft (‹):                    Text symbols.      (line 13645)
* \guilsinglright (›):                   Text symbols.      (line 13646)
* \H (Hungarian umlaut accent):          Accents.           (line 13895)
* \hat:                                  Math accents.      (line 10565)
* \hbar:                                 Math symbols.      (line  9342)
* \headheight:                           Page layout parameters.
                                                            (line  2190)
* \headheight <1>:                       Page layout parameters.
                                                            (line  2191)
* \headsep:                              Page layout parameters.
                                                            (line  2195)
* \headsep <1>:                          Page layout parameters.
                                                            (line  2196)
* \heartsuit:                            Math symbols.      (line  9345)
* \hfill:                                \hfill.            (line 11412)
* \hline:                                \hline.            (line  6007)
* \hom:                                  Math functions.    (line 10472)
* \hookleftarrow:                        Math symbols.      (line  9348)
* \hookrightarrow:                       Math symbols.      (line  9351)
* \hrulefill:                            \hrulefill & \dotfill.
                                                            (line 11799)
* \hsize:                                Page layout parameters.
                                                            (line  2295)
* \hsize <1>:                            Page layout parameters.
                                                            (line  2296)
* \hspace:                               \hspace.           (line 11365)
* \hss:                                  \hss.              (line 11445)
* \huge:                                 Font sizes.        (line  1845)
* \Huge:                                 Font sizes.        (line  1845)
* \hyphenation:                          \hyphenation.      (line  6732)
* \i (dotless i):                        Accents.           (line 13845)
* \IfBeginWith* macro from xstring:      Jobname.           (line 16261)
* \iff:                                  Math symbols.      (line  9354)
* \IfFileExists:                         Class and package commands.
                                                            (line  1038)
* \ignorespaces:                         \ignorespaces & \ignorespacesafterend.
                                                            (line  7955)
* \ignorespacesafterend:                 \ignorespaces & \ignorespacesafterend.
                                                            (line  7955)
* \ij (ij):                              Additional Latin letters.
                                                            (line 13995)
* \IJ (IJ):                              Additional Latin letters.
                                                            (line 13995)
* \Im:                                   Math symbols.      (line  9358)
* \imath:                                Math symbols.      (line  9361)
* \immediate\write:                      \write.            (line 15811)
* \in:                                   Math symbols.      (line  9365)
* \include:                              \include & \includeonly.
                                                            (line 14220)
* \includegraphics:                      \includegraphics.  (line 13075)
* \includeonly:                          \include & \includeonly.
                                                            (line 14220)
* \indent:                               \indent & \noindent.
                                                            (line  8855)
* \index:                                Indexes.           (line 14770)
* \index <1>:                            \index.            (line 14852)
* \indexentry:                           \index.            (line 14954)
* \indexspace:                           Produce the index manually.
                                                            (line 14841)
* \indexspace <1>:                       makeindex.         (line 15022)
* \inf:                                  Math functions.    (line 10475)
* \infty:                                Math symbols.      (line  9369)
* \input:                                \input.            (line 14339)
* \inputencoding:                        inputenc package.  (line 14070)
* \InputIfFileExists:                    Class and package commands.
                                                            (line  1038)
* \int:                                  Math symbols.      (line  9372)
* \intextsep:                            Floats.            (line  2520)
* \intextsep <1>:                        Floats.            (line  2521)
* \iota:                                 Math symbols.      (line  9375)
* \it:                                   Font styles.       (line  1776)
* \item:                                 description.       (line  3803)
* \item <1>:                             enumerate.         (line  3939)
* \item <2>:                             itemize.           (line  4289)
* \item <3>:                             itemize.           (line  4313)
* \item <4>:                             Produce the index manually.
                                                            (line 14841)
* \itemindent:                           list.              (line  4460)
* \itemsep:                              list.              (line  4464)
* \itshape:                              Font styles.       (line  1729)
* \j (dotless j):                        Accents.           (line 13845)
* \jmath:                                Math symbols.      (line  9381)
* \jobname:                              Jobname.           (line 16214)
* \jobname <1>:                          Jobname.           (line 16254)
* \Join:                                 Math symbols.      (line  9378)
* \k (ogonek):                           Accents.           (line 13899)
* \kappa:                                Math symbols.      (line  9385)
* \ker:                                  Math functions.    (line 10478)
* \kill:                                 tabbing.           (line  5594)
* \l (ł):                                Additional Latin letters.
                                                            (line 13999)
* \L (Ł):                                Additional Latin letters.
                                                            (line 13999)
* \l@chapter:                            \contentsline.     (line 14673)
* \l@section:                            \contentsline.     (line 14673)
* \l@subsection:                         \contentsline.     (line 14673)
* \label:                                \label.            (line  3384)
* \labelenumi:                           enumerate.         (line  3966)
* \labelenumii:                          enumerate.         (line  3966)
* \labelenumiii:                         enumerate.         (line  3966)
* \labelenumiv:                          enumerate.         (line  3966)
* \labelitemi:                           itemize.           (line  4325)
* \labelitemii:                          itemize.           (line  4325)
* \labelitemiii:                         itemize.           (line  4325)
* \labelitemiv:                          itemize.           (line  4325)
* \labelsep:                             list.              (line  4476)
* \labelwidth:                           list.              (line  4481)
* \Lambda:                               Math symbols.      (line  9388)
* \lambda:                               Math symbols.      (line  9391)
* \land:                                 Math symbols.      (line  9394)
* \langle:                               Math symbols.      (line  9398)
* \large:                                Font sizes.        (line  1845)
* \Large:                                Font sizes.        (line  1845)
* \LARGE:                                Font sizes.        (line  1845)
* \LastDeclaredEncoding:                 \LastDeclaredEncoding.
                                                            (line  1646)
* \LaTeX:                                Text symbols.      (line 13637)
* \LaTeXe:                               Text symbols.      (line 13640)
* \lbrace:                               Math symbols.      (line  9402)
* \lbrack:                               Math symbols.      (line  9405)
* \lceil:                                Math symbols.      (line  9408)
* \ldots:                                Dots.              (line 10345)
* \ldots <1>:                            Text symbols.      (line 13650)
* \le:                                   Math symbols.      (line  9412)
* \leadsto:                              Math symbols.      (line  9415)
* \left:                                 \left & \right.    (line 10133)
* \Leftarrow:                            Math symbols.      (line  9421)
* \leftarrow:                            Math symbols.      (line  9425)
* \lefteqn:                              eqnarray.          (line  4021)
* \leftharpoondown:                      Math symbols.      (line  9429)
* \leftharpoonup:                        Math symbols.      (line  9432)
* \leftmargin:                           itemize.           (line  4341)
* \leftmargin <1>:                       list.              (line  4501)
* \leftmargini:                          itemize.           (line  4341)
* \leftmarginii:                         itemize.           (line  4341)
* \leftmarginiii:                        itemize.           (line  4341)
* \leftmarginiv:                         itemize.           (line  4341)
* \leftmarginv:                          itemize.           (line  4341)
* \leftmarginvi:                         itemize.           (line  4341)
* \Leftrightarrow:                       Math symbols.      (line  9435)
* \leftrightarrow:                       Math symbols.      (line  9439)
* \leq:                                  Math symbols.      (line  9443)
* \lfloor:                               Math symbols.      (line  9446)
* \lg:                                   Math functions.    (line 10481)
* \lhd:                                  Math symbols.      (line  9449)
* \lim:                                  Math functions.    (line 10484)
* \liminf:                               Math functions.    (line 10487)
* \limsup:                               Math functions.    (line 10490)
* \line:                                 \line.             (line  5150)
* \linebreak:                            \linebreak & \nolinebreak.
                                                            (line  6751)
* \lineskip:                             \baselineskip & \baselinestretch.
                                                            (line  2354)
* \lineskiplimit:                        \baselineskip & \baselinestretch.
                                                            (line  2354)
* \linespread:                           Low-level font commands.
                                                            (line  2003)
* \linespread <1>:                       \baselineskip & \baselinestretch.
                                                            (line  2315)
* \linethickness:                        \linethickness.    (line  5194)
* \linewidth:                            Page layout parameters.
                                                            (line  2209)
* \linewidth <1>:                        Page layout parameters.
                                                            (line  2210)
* \listoffigures:                        Table of contents etc..
                                                            (line 14377)
* \listoffigures <1>:                    \contentsline.     (line 14673)
* \listoftables:                         Table of contents etc..
                                                            (line 14377)
* \listoftables <1>:                     \contentsline.     (line 14673)
* \listparindent:                        list.              (line  4518)
* \ll:                                   Math symbols.      (line  9455)
* \ln:                                   Math functions.    (line 10493)
* \lnot:                                 Math symbols.      (line  9458)
* \LoadClass:                            Class and package commands.
                                                            (line  1058)
* \LoadClassWithOptions:                 Class and package commands.
                                                            (line  1058)
* \location:                             \location.         (line 15427)
* \log:                                  Math functions.    (line 10496)
* \long:                                 \newcommand & \renewcommand.
                                                            (line  7248)
* \longleftarrow:                        Math symbols.      (line  9461)
* \longleftrightarrow:                   Math symbols.      (line  9465)
* \longmapsto:                           Math symbols.      (line  9469)
* \longrightarrow:                       Math symbols.      (line  9473)
* \lor:                                  Math symbols.      (line  9477)
* \lq:                                   Text symbols.      (line 13656)
* \mainmatter:                           \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* \makebox:                              \mbox & \makebox.  (line 12146)
* \makebox (for picture):                \makebox (picture).
                                                            (line  5347)
* \makeglossary:                         Glossaries.        (line 15143)
* \makeglossary <1>:                     Glossaries.        (line 15180)
* \makeindex:                            Indexes.           (line 14770)
* \makelabel:                            list.              (line  4437)
* \makelabels:                           \makelabels.       (line 15437)
* \maketitle:                            \maketitle.        (line 11091)
* \mapsto:                               Math symbols.      (line  9481)
* \marginpar:                            Marginal notes.    (line  8936)
* \marginparpush:                        Page layout parameters.
                                                            (line  2216)
* \marginparpush <1>:                    Page layout parameters.
                                                            (line  2219)
* \marginparpush <2>:                    Marginal notes.    (line  8965)
* \marginparsep:                         Marginal notes.    (line  8970)
* \marginparwidth:                       Page layout parameters.
                                                            (line  2218)
* \marginparwidth <1>:                   Page layout parameters.
                                                            (line  2219)
* \marginparwidth <2>:                   Marginal notes.    (line  8974)
* \marginsep:                            Page layout parameters.
                                                            (line  2217)
* \marginsep <1>:                        Page layout parameters.
                                                            (line  2219)
* \markboth{LEFT-HEAD}{RIGHT-HEAD}:      \pagestyle.        (line 11288)
* \markright{RIGHT}:                     \pagestyle.        (line 11297)
* \mathbf:                               Font styles.       (line  1806)
* \mathcal:                              Font styles.       (line  1822)
* \mathdollar:                           Math symbols.      (line  9941)
* \mathnormal:                           Font styles.       (line  1819)
* \mathparagraph:                        Math symbols.      (line  9944)
* \mathring:                             Math accents.      (line 10568)
* \mathrm:                               Font styles.       (line  1803)
* \mathsection:                          Math symbols.      (line  9947)
* \mathsf:                               Font styles.       (line  1809)
* \mathsterling:                         Math symbols.      (line  9950)
* \mathstrut:                            \mathstrut.        (line 10831)
* \mathtt:                               Font styles.       (line  1812)
* \mathunderscore:                       Math symbols.      (line  9953)
* \mathversion:                          Font styles.       (line  1824)
* \max:                                  Math functions.    (line 10499)
* \mbox:                                 \mbox & \makebox.  (line 12146)
* \mdseries:                             Font styles.       (line  1732)
* \medskip:                              \bigskip & \medskip & \smallskip.
                                                            (line 11875)
* \medskipamount:                        \bigskip & \medskip & \smallskip.
                                                            (line 11876)
* \medspace:                             Spacing in math mode.
                                                            (line 10663)
* \message:                              \message.          (line 15882)
* \mho:                                  Math symbols.      (line  9485)
* \mid:                                  Math symbols.      (line  9488)
* \min:                                  Math functions.    (line 10502)
* \models:                               Math symbols.      (line  9498)
* \month:                                \day & \month & \year.
                                                            (line  8291)
* \mp:                                   Math symbols.      (line  9502)
* \mu:                                   Math symbols.      (line  9505)
* \multicolumn:                          \multicolumn.      (line  5877)
* \multiput:                             \multiput.         (line  5063)
* \nabla:                                Math symbols.      (line  9508)
* \name:                                 \name.             (line 15494)
* \natural:                              Math symbols.      (line  9511)
* \ne:                                   Math symbols.      (line  9514)
* \nearrow:                              Math symbols.      (line  9517)
* \NeedsTeXFormat:                       Class and package commands.
                                                            (line  1092)
* \neg:                                  Math symbols.      (line  9520)
* \negmedspace:                          Spacing in math mode.
                                                            (line 10669)
* \negthickspace:                        Spacing in math mode.
                                                            (line 10657)
* \negthinspace:                         Spacing in math mode.
                                                            (line 10688)
* \negthinspace <1>:                     \thinspace & \negthinspace.
                                                            (line 11725)
* \neq:                                  Math symbols.      (line  9524)
* \newcommand:                           \newcommand & \renewcommand.
                                                            (line  7227)
* \newcounter:                           \newcounter.       (line  7532)
* \newenvironment:                       \newenvironment & \renewenvironment.
                                                            (line  7625)
* \newfont:                              \newfont.          (line  7871)
* \newglossaryentry:                     \newglossaryentry. (line 15191)
* \newlength:                            \newlength.        (line  7573)
* \newline:                              \newline.          (line  6609)
* \<NEWLINE>:                            \(SPACE).          (line 11606)
* \newpage:                              \newpage.          (line  6855)
* \newsavebox:                           \newsavebox.       (line  7597)
* \newtheorem:                           \newtheorem.       (line  7759)
* \newtie:                               Accents.           (line 13909)
* \newwrite:                             \write.            (line 15775)
* \ng:                                   Additional Latin letters.
                                                            (line 14003)
* \NG:                                   Additional Latin letters.
                                                            (line 14003)
* \ni:                                   Math symbols.      (line  9527)
* \nocite:                               \nocite.           (line  6187)
* \nocite and internal \citation:        BibTeX error messages.
                                                            (line  6281)
* \nocite {*}, for all keys:             Using BibTeX.      (line  6257)
* \nocorr:                               Font styles.       (line  1717)
* \nocorrlist:                           Font styles.       (line  1717)
* \nofiles:                              \nofiles.          (line 14714)
* \noindent:                             \indent & \noindent.
                                                            (line  8855)
* \nolinebreak:                          \linebreak & \nolinebreak.
                                                            (line  6751)
* \nonfrenchspacing:                     \frenchspacing & \nonfrenchspacing.
                                                            (line 11575)
* \nonumber:                             eqnarray.          (line  4016)
* \nopagebreak:                          \pagebreak & \nopagebreak.
                                                            (line  6913)
* \normalfont:                           Font styles.       (line  1753)
* \normalmarginpar:                      Marginal notes.    (line  8952)
* \normalsfcodes:                        \normalsfcodes.    (line 11596)
* \normalsize:                           Font sizes.        (line  1845)
* \not:                                  Math symbols.      (line  9531)
* \notin:                                Math symbols.      (line  9539)
* \nu:                                   Math symbols.      (line  9543)
* \numberline:                           \numberline.       (line 14739)
* \nwarrow:                              Math symbols.      (line  9546)
* \o (ø):                                Additional Latin letters.
                                                            (line 14007)
* \O (Ø):                                Additional Latin letters.
                                                            (line 14007)
* \obeycr:                               \obeycr & \restorecr.
                                                            (line  6569)
* \oddsidemargin:                        Document class options.
                                                            (line   809)
* \oddsidemargin <1>:                    Page layout parameters.
                                                            (line  2242)
* \oddsidemargin <2>:                    Page layout parameters.
                                                            (line  2244)
* \odot:                                 Math symbols.      (line  9549)
* \oe (œ):                               Additional Latin letters.
                                                            (line 14011)
* \OE (Œ):                               Additional Latin letters.
                                                            (line 14011)
* \oint:                                 Math symbols.      (line  9553)
* \oldstylenums:                         Font styles.       (line  1828)
* \Omega:                                Math symbols.      (line  9556)
* \omega:                                Math symbols.      (line  9559)
* \ominus:                               Math symbols.      (line  9562)
* \onecolumn:                            \onecolumn.        (line  2031)
* \openin:                               \openin & \openout.
                                                            (line 15584)
* \opening:                              \opening.          (line 15504)
* \openout:                              \openin & \openout.
                                                            (line 15584)
* \oplus:                                Math symbols.      (line  9565)
* \OptionNotUsed:                        Class and package commands.
                                                            (line  1110)
* \oslash:                               Math symbols.      (line  9569)
* \otimes:                               Math symbols.      (line  9572)
* \oval:                                 \oval.             (line  5242)
* \overbrace{MATH}:                      Over- and Underlining.
                                                            (line 10622)
* \overline{TEXT}:                       Over- and Underlining.
                                                            (line 10603)
* \owns:                                 Math symbols.      (line  9576)
* \P:                                    Text symbols.      (line 13659)
* \PackageError:                         Class and package commands.
                                                            (line   951)
* \PackageInfo:                          Class and package commands.
                                                            (line   951)
* \PackageInfoNoLine:                    Class and package commands.
                                                            (line   951)
* \PackageWarning:                       Class and package commands.
                                                            (line   951)
* \PackageWarningNoLine:                 Class and package commands.
                                                            (line   951)
* \pagebreak:                            \pagebreak & \nopagebreak.
                                                            (line  6913)
* \pagenumbering:                        \pagenumbering.    (line 11162)
* \pageref:                              \pageref.          (line  3442)
* \pagestyle:                            \pagestyle.        (line 11219)
* \paperheight:                          Page layout parameters.
                                                            (line  2255)
* \paperheight <1>:                      Page layout parameters.
                                                            (line  2256)
* \paperwidth:                           Page layout parameters.
                                                            (line  2261)
* \paperwidth <1>:                       Page layout parameters.
                                                            (line  2262)
* \par:                                  \par.              (line  8802)
* \paragraph:                            Sectioning.        (line  2632)
* \paragraph <1>:                        \subsubsection & \paragraph & \subparagraph.
                                                            (line  3007)
* \parallel:                             Math symbols.      (line  9580)
* \parbox:                               \parbox.           (line 12303)
* \parindent:                            minipage.          (line  4857)
* \parindent <1>:                        \indent & \noindent.
                                                            (line  8855)
* \parindent <2>:                        \parindent & \parskip.
                                                            (line  8904)
* \parsep:                               list.              (line  4524)
* \parskip:                              \parindent & \parskip.
                                                            (line  8904)
* \parskip example:                      itemize.           (line  4361)
* \part:                                 Sectioning.        (line  2632)
* \part <1>:                             \part.             (line  2718)
* \partial:                              Math symbols.      (line  9583)
* \partopsep:                            list.              (line  4533)
* \PassOptionsToClass:                   Class and package commands.
                                                            (line  1116)
* \PassOptionsToPackage:                 Class and package commands.
                                                            (line  1116)
* \pdfpageheight:                        Document class options.
                                                            (line   765)
* \pdfpagewidth:                         Document class options.
                                                            (line   765)
* \perp:                                 Math symbols.      (line  9586)
* \Phi:                                  Math symbols.      (line  9590)
* \phi:                                  Math symbols.      (line  9593)
* \Pi:                                   Math symbols.      (line  9597)
* \pi:                                   Math symbols.      (line  9600)
* \pm:                                   Math symbols.      (line  9604)
* \pmod:                                 Math functions.    (line 10505)
* \poptabs:                              tabbing.           (line  5600)
* \poptabs <1>:                          tabbing.           (line  5601)
* \pounds:                               Text symbols.      (line 13663)
* \Pr:                                   Math functions.    (line 10508)
* \prec:                                 Math symbols.      (line  9607)
* \preceq:                               Math symbols.      (line  9610)
* \prevdepth:                            \baselineskip & \baselinestretch.
                                                            (line  2354)
* \prime:                                Math symbols.      (line  9614)
* \printglossaries:                      Glossaries.        (line 15143)
* \printglossaries <1>:                  Glossaries.        (line 15180)
* \printindex:                           \printindex.       (line 15128)
* \ProcessOptions:                       Class and package commands.
                                                            (line  1153)
* \ProcessOptions*:                      Class and package commands.
                                                            (line  1153)
* \prod:                                 Math symbols.      (line  9623)
* \propto:                               Math symbols.      (line  9626)
* \protect:                              \protect.          (line  7903)
* \protected@write:                      \write.            (line 15821)
* \providecommand:                       \providecommand.   (line  7386)
* \ProvidesClass:                        Class and package commands.
                                                            (line  1191)
* \ProvidesFile:                         Class and package commands.
                                                            (line  1224)
* \ProvidesPackage:                      Class and package commands.
                                                            (line  1191)
* \ProvideTextCommand:                   \DeclareTextCommand & \ProvideTextCommand.
                                                            (line  1470)
* \ProvideTextCommand <1>:               \DeclareTextCommandDefault & \ProvideTextCommandDefault.
                                                            (line  1519)
* \ProvideTextCommandDefault:            \DeclareTextCommandDefault & \ProvideTextCommandDefault.
                                                            (line  1519)
* \ps:                                   \ps.               (line 15516)
* \Psi:                                  Math symbols.      (line  9629)
* \psi:                                  Math symbols.      (line  9632)
* \pushtabs:                             tabbing.           (line  5603)
* \put:                                  \put.              (line  5045)
* \qbezier:                              \qbezier.          (line  5086)
* \qquad:                                Spacing in math mode.
                                                            (line 10702)
* \qquad <1>:                            \enspace & \quad & \qquad.
                                                            (line 11338)
* \quad:                                 Spacing in math mode.
                                                            (line 10696)
* \quad <1>:                             \enspace & \quad & \qquad.
                                                            (line 11338)
* \quotedblbase („):                     Text symbols.      (line 13667)
* \quotesinglbase (‚):                   Text symbols.      (line 13668)
* \r (ring accent):                      Accents.           (line 13903)
* \raggedbottom:                         \raggedbottom.     (line  2171)
* \raggedleft:                           \raggedleft.       (line  4262)
* \raggedright:                          \raggedright.      (line  4209)
* \raisebox:                             \raisebox.         (line 12354)
* \rangle:                               Math symbols.      (line  9635)
* \rbrace:                               Math symbols.      (line  9639)
* \rbrack:                               Math symbols.      (line  9642)
* \rceil:                                Math symbols.      (line  9646)
* \Re:                                   Math symbols.      (line  9649)
* \read:                                 \read.             (line 15648)
* \ref:                                  \ref.              (line  3466)
* \reflectbox:                           \scalebox.         (line 13458)
* \refname:                              thebibliography.   (line  6062)
* \refstepcounter:                       \refstepcounter.   (line  8258)
* \renewenvironment:                     \newenvironment & \renewenvironment.
                                                            (line  7625)
* \RequirePackage:                       Class and package commands.
                                                            (line  1233)
* \RequirePackage, and texput jobname:   Jobname.           (line 16240)
* \RequirePackageWithOptions:            Class and package commands.
                                                            (line  1233)
* \resizebox:                            \resizebox.        (line 13490)
* \restorecr:                            \obeycr & \restorecr.
                                                            (line  6569)
* \restriction:                          Math symbols.      (line  9654)
* \revemptyset:                          Math symbols.      (line  9659)
* \reversemarginpar:                     Marginal notes.    (line  8952)
* \rfloor:                               Math symbols.      (line  9664)
* \rhd:                                  Math symbols.      (line  9668)
* \rho:                                  Math symbols.      (line  9674)
* \right:                                \left & \right.    (line 10133)
* \Rightarrow:                           Math symbols.      (line  9678)
* \rightarrow:                           Math symbols.      (line  9682)
* \rightharpoondown:                     Math symbols.      (line  9686)
* \rightharpoonup:                       Math symbols.      (line  9689)
* \rightleftharpoons:                    Math symbols.      (line  9692)
* \rightmargin:                          list.              (line  4548)
* \rm:                                   Font styles.       (line  1779)
* \rmfamily:                             Font styles.       (line  1726)
* \roman{COUNTER}:                       \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                            (line  8130)
* \Roman{COUNTER}:                       \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                            (line  8135)
* \rotatebox:                            \rotatebox.        (line 13390)
* \rq:                                   Text symbols.      (line 13671)
* \rule:                                 \rule.             (line 14079)
* \S:                                    Text symbols.      (line 13674)
* \samepage:                             \pagebreak & \nopagebreak.
                                                            (line  6951)
* \savebox:                              \sbox & \savebox.  (line 12400)
* \sbox:                                 \sbox & \savebox.  (line 12400)
* \sc:                                   Font styles.       (line  1782)
* \scalebox:                             \scalebox.         (line 13458)
* \scriptscriptstyle:                    Math styles.       (line 10876)
* \scriptsize:                           Font sizes.        (line  1845)
* \scriptstyle:                          Math styles.       (line 10876)
* \scshape:                              Font styles.       (line  1747)
* \searrow:                              Math symbols.      (line  9695)
* \sec:                                  Math functions.    (line 10511)
* \section:                              Sectioning.        (line  2632)
* \section <1>:                          \section.          (line  2865)
* \seename:                              \index.            (line 14904)
* \selectfont:                           Low-level font commands.
                                                            (line  2009)
* \setcounter:                           \setcounter.       (line  8224)
* \setlength:                            \setlength.        (line  8471)
* \setminus:                             Math symbols.      (line  9698)
* \settodepth:                           \settodepth.       (line  8535)
* \settoheight:                          \settoheight.      (line  8560)
* \settowidth:                           \settowidth.       (line  8585)
* \sf:                                   Font styles.       (line  1785)
* \sffamily:                             Font styles.       (line  1744)
* \sharp:                                Math symbols.      (line  9703)
* \ShellEscape:                          \write18.          (line 16011)
* \shipout and expansion:                \write.            (line 15816)
* \shortstack:                           \shortstack.       (line  5279)
* \Sigma:                                Math symbols.      (line  9706)
* \sigma:                                Math symbols.      (line  9709)
* \signature:                            \signature.        (line 15533)
* \sim:                                  Math symbols.      (line  9713)
* \simeq:                                Math symbols.      (line  9716)
* \sin:                                  Math functions.    (line 10514)
* \sinh:                                 Math functions.    (line 10517)
* \sl:                                   Font styles.       (line  1788)
* \sloppy:                               \fussy & \sloppy.  (line  6690)
* \slshape:                              Font styles.       (line  1741)
* \small:                                Font sizes.        (line  1845)
* \smallint:                             Math symbols.      (line  9719)
* \smallskip:                            \bigskip & \medskip & \smallskip.
                                                            (line 11880)
* \smallskipamount:                      \bigskip & \medskip & \smallskip.
                                                            (line 11881)
* \smile:                                Math symbols.      (line  9723)
* \<SPACE>:                              \(SPACE).          (line 11606)
* \<SPACE> <1>:                          \(SPACE).          (line 11606)
* \space:                                \include & \includeonly.
                                                            (line 14302)
* \space <1>:                            \input.            (line 14365)
* \space <2>:                            \typeout.          (line 15740)
* \spacefactor:                          \spacefactor.      (line 11471)
* \spadesuit:                            Math symbols.      (line  9726)
* \sqcap:                                Math symbols.      (line  9729)
* \sqcup:                                Math symbols.      (line  9733)
* \sqrt:                                 \sqrt.             (line 10975)
* \sqsubset:                             Math symbols.      (line  9737)
* \sqsubseteq:                           Math symbols.      (line  9742)
* \sqsupset:                             Math symbols.      (line  9746)
* \sqsupseteq:                           Math symbols.      (line  9751)
* \ss (ß):                               Additional Latin letters.
                                                            (line 14015)
* \SS (SS):                              Additional Latin letters.
                                                            (line 14015)
* \stackrel:                             \stackrel.         (line 10991)
* \star:                                 Math symbols.      (line  9755)
* \stepcounter:                          \stepcounter.      (line  8276)
* \stop:                                 Recovering from errors.
                                                            (line 16296)
* \stretch:                              \stretch.          (line  8610)
* \strut:                                \strut.            (line 11924)
* \subitem:                              Produce the index manually.
                                                            (line 14841)
* \subparagraph:                         Sectioning.        (line  2632)
* \subparagraph <1>:                     \subsubsection & \paragraph & \subparagraph.
                                                            (line  3007)
* \subsection:                           Sectioning.        (line  2632)
* \subsection <1>:                       \subsection.       (line  2943)
* \subset:                               Math symbols.      (line  9762)
* \subseteq:                             Math symbols.      (line  9765)
* \subsubitem:                           Produce the index manually.
                                                            (line 14841)
* \subsubsection:                        Sectioning.        (line  2632)
* \subsubsection <1>:                    \subsubsection & \paragraph & \subparagraph.
                                                            (line  3007)
* \succ:                                 Math symbols.      (line  9768)
* \succeq:                               Math symbols.      (line  9771)
* \sum:                                  Math symbols.      (line  9775)
* \sup:                                  Math functions.    (line 10520)
* \suppressfloats:                       Floats.            (line  2489)
* \supset:                               Math symbols.      (line  9778)
* \supseteq:                             Math symbols.      (line  9781)
* \surd:                                 Math symbols.      (line  9784)
* \swarrow:                              Math symbols.      (line  9789)
* \symbol:                               Symbols by font position.
                                                            (line 13608)
* \t (tie-after accent):                 Accents.           (line 13909)
* \<TAB>:                                \(SPACE).          (line 11606)
* \tabbingsep:                           tabbing.           (line  5608)
* \tabcolsep:                            tabular.           (line  5866)
* \tableofcontents:                      Table of contents etc..
                                                            (line 14377)
* \tableofcontents <1>:                  \contentsline.     (line 14673)
* \tan:                                  Math functions.    (line 10523)
* \tanh:                                 Math functions.    (line 10526)
* \tau:                                  Math symbols.      (line  9792)
* \telephone:                            \telephone.        (line 15563)
* \TeX:                                  Text symbols.      (line 13678)
* \textascendercompwordmark:             Text symbols.      (line 13716)
* \textasciicircum:                      Text symbols.      (line 13681)
* \textasciitilde:                       Text symbols.      (line 13684)
* \textasteriskcentered:                 Text symbols.      (line 13687)
* \textbackslash:                        Reserved characters.
                                                            (line 13537)
* \textbackslash <1>:                    Text symbols.      (line 13690)
* \textbar:                              Text symbols.      (line 13693)
* \textbardbl:                           Text symbols.      (line 13696)
* \textbf:                               Font styles.       (line  1735)
* \textbigcircle:                        Text symbols.      (line 13699)
* \textbraceleft:                        Text symbols.      (line 13702)
* \textbraceright:                       Text symbols.      (line 13705)
* \textbullet:                           Text symbols.      (line 13708)
* \textcapitalcompwordmark:              Text symbols.      (line 13715)
* \textcircled{LETTER}:                  Text symbols.      (line 13711)
* \textcompwordmark:                     Text symbols.      (line 13714)
* \textcopyright:                        Text symbols.      (line 13628)
* \textdagger:                           Text symbols.      (line 13723)
* \textdaggerdbl:                        Text symbols.      (line 13726)
* \textdollar (or \$):                   Text symbols.      (line 13729)
* \textellipsis:                         Text symbols.      (line 13652)
* \textemdash (or ---):                  Text symbols.      (line 13732)
* \textendash (or --):                   Text symbols.      (line 13738)
* \texteuro:                             Text symbols.      (line 13741)
* \textexclamdown (or !`):               Text symbols.      (line 13749)
* \textfiguredash:                       Text symbols.      (line 13752)
* \textfloatsep:                         Floats.            (line  2525)
* \textfloatsep <1>:                     Floats.            (line  2526)
* \textfraction:                         Floats.            (line  2504)
* \textfraction <1>:                     Floats.            (line  2505)
* \textgreater:                          Text symbols.      (line 13759)
* \textheight:                           Page layout parameters.
                                                            (line  2267)
* \textheight <1>:                       Page layout parameters.
                                                            (line  2268)
* \texthorizontalbar:                    Text symbols.      (line 13762)
* \textit:                               Font styles.       (line  1729)
* \textleftarrow:                        Text symbols.      (line 13770)
* \textless:                             Text symbols.      (line 13767)
* \textmd:                               Font styles.       (line  1732)
* \textnonbreakinghyphen:                Text symbols.      (line 13773)
* \textnormal:                           Font styles.       (line  1753)
* \textordfeminine:                      Text symbols.      (line 13779)
* \textordmasculine:                     Text symbols.      (line 13780)
* \textparagraph:                        Text symbols.      (line 13660)
* \textperiodcentered:                   Text symbols.      (line 13783)
* \textquestiondown (or ?`):             Text symbols.      (line 13786)
* \textquotedblleft (or ``):             Text symbols.      (line 13789)
* \textquotedblright (or ''):            Text symbols.      (line 13792)
* \textquoteleft (or `):                 Text symbols.      (line 13795)
* \textquoteright (or '):                Text symbols.      (line 13798)
* \textquotesingle:                      Text symbols.      (line 13801)
* \textquotestraightbase:                Text symbols.      (line 13804)
* \textquotestraightdblbase:             Text symbols.      (line 13805)
* \textregistered:                       Text symbols.      (line 13808)
* \textrightarrow:                       Text symbols.      (line 13811)
* \textrm:                               Font styles.       (line  1726)
* \textsc:                               Font styles.       (line  1747)
* \textsection:                          Text symbols.      (line 13675)
* \textsf:                               Font styles.       (line  1744)
* \textsl:                               Font styles.       (line  1741)
* \textsterling:                         Text symbols.      (line 13664)
* \textstyle:                            Math styles.       (line 10876)
* \textthreequartersemdash:              Text symbols.      (line 13814)
* \texttrademark:                        Text symbols.      (line 13817)
* \texttt:                               Font styles.       (line  1750)
* \texttwelveudash:                      Text symbols.      (line 13820)
* \textunderscore:                       Text symbols.      (line 13823)
* \textup:                               Font styles.       (line  1738)
* \textvisiblespace:                     Text symbols.      (line 13826)
* \textwidth:                            Page layout parameters.
                                                            (line  2275)
* \textwidth <1>:                        Page layout parameters.
                                                            (line  2276)
* \th (þ):                               Additional Latin letters.
                                                            (line 14019)
* \TH (Þ):                               Additional Latin letters.
                                                            (line 14019)
* \thanks{TEXT}:                         \maketitle.        (line 11141)
* \theta:                                Math symbols.      (line  9795)
* \thicklines:                           \thicklines.       (line  5215)
* \thickspace:                           Spacing in math mode.
                                                            (line 10650)
* \thinlines:                            \thinlines.        (line  5207)
* \thinspace:                            Spacing in math mode.
                                                            (line 10674)
* \thinspace <1>:                        \thinspace & \negthinspace.
                                                            (line 11725)
* \thispagestyle:                        \thispagestyle.    (line 11303)
* \tilde:                                Math accents.      (line 10571)
* \times:                                Math symbols.      (line  9799)
* \tiny:                                 Font sizes.        (line  1845)
* \title{TEXT}:                          \maketitle.        (line 11148)
* \to:                                   Math symbols.      (line  9802)
* \today:                                \today.            (line 14114)
* \top:                                  Math symbols.      (line  9806)
* \topfraction:                          Floats.            (line  2509)
* \topfraction <1>:                      Floats.            (line  2510)
* \topmargin:                            Page layout parameters.
                                                            (line  2300)
* \topsep:                               list.              (line  4553)
* \topskip:                              Page layout parameters.
                                                            (line  2307)
* \topskip <1>:                          Page layout parameters.
                                                            (line  2308)
* \triangle:                             Math symbols.      (line  9810)
* \triangleleft:                         Math symbols.      (line  9813)
* \triangleright:                        Math symbols.      (line  9819)
* \tt:                                   Font styles.       (line  1791)
* \ttfamily:                             Font styles.       (line  1750)
* \twocolumn:                            \twocolumn.        (line  2043)
* \typein:                               \typein.           (line 15679)
* \typeout:                              \typeout.          (line 15724)
* \u (breve accent):                     Accents.           (line 13915)
* \unboldmath:                           \boldmath & \unboldmath.
                                                            (line 10000)
* \unboldmath <1>:                       \boldmath & \unboldmath.
                                                            (line 10008)
* \underbar:                             Accents.           (line 13879)
* \underbrace{MATH}:                     Over- and Underlining.
                                                            (line 10608)
* \underline{TEXT}:                      Over- and Underlining.
                                                            (line 10592)
* \unitlength:                           picture.           (line  4940)
* \unlhd:                                Math symbols.      (line  9825)
* \unrhd:                                Math symbols.      (line  9831)
* \Uparrow:                              Math symbols.      (line  9837)
* \uparrow:                              Math symbols.      (line  9841)
* \Updownarrow:                          Math symbols.      (line  9845)
* \updownarrow:                          Math symbols.      (line  9850)
* \upharpoonright:                       Math symbols.      (line  9855)
* \uplus:                                Math symbols.      (line  9860)
* \upshape:                              Font styles.       (line  1738)
* \Upsilon:                              Math symbols.      (line  9865)
* \upsilon:                              Math symbols.      (line  9868)
* \usebox:                               \usebox.           (line 12509)
* \usecounter:                           \usecounter.       (line  8165)
* \usefont:                              Low-level font commands.
                                                            (line  2017)
* \usepackage:                           Additional packages.
                                                            (line   830)
* \UseTextAccent:                        \UseTextSymbol & \UseTextAccent.
                                                            (line  1663)
* \UseTextSymbol:                        \UseTextSymbol & \UseTextAccent.
                                                            (line  1663)
* \v (breve accent):                     Accents.           (line 13919)
* \value:                                \value.            (line  8191)
* \vanothing:                            Math symbols.      (line  9876)
* \varepsilon:                           Math symbols.      (line  9871)
* \varphi:                               Math symbols.      (line  9881)
* \varpi:                                Math symbols.      (line  9885)
* \varrho:                               Math symbols.      (line  9889)
* \varsigma:                             Math symbols.      (line  9893)
* \vartheta:                             Math symbols.      (line  9897)
* \vbox (plain TeX):                     minipage.          (line  4811)
* \vdash:                                Math symbols.      (line  9901)
* \vdots:                                Dots.              (line 10354)
* \vec:                                  Math accents.      (line 10574)
* \vector:                               \vector.           (line  5325)
* \vee:                                  Math symbols.      (line  9905)
* \verb:                                 \verb.             (line  6403)
* \Vert:                                 Math symbols.      (line  9909)
* \vert:                                 Math symbols.      (line  9913)
* \vfill:                                \vfill.            (line 12060)
* \vline:                                \vline.            (line  5959)
* \vspace:                               \vspace.           (line 12009)
* \vtop plain TeX:                       minipage.          (line  4807)
* \wedge:                                Math symbols.      (line  9919)
* \widehat:                              Math accents.      (line 10577)
* \widetilde:                            Math accents.      (line 10580)
* \wlog:                                 \wlog.             (line 15928)
* \wp:                                   Math symbols.      (line  9923)
* \wr:                                   Math symbols.      (line  9926)
* \write:                                \write.            (line 15757)
* \write and security:                   \write and security.
                                                            (line 15858)
* \write streams 16, 17, 18:             \write.            (line 15837)
* \write18:                              \write18.          (line 15946)
* \write18, enabling:                    Command line options.
                                                            (line 16121)
* \Xi:                                   Math symbols.      (line  9929)
* \xi:                                   Math symbols.      (line  9932)
* \xspace:                               xspace package.    (line  8030)
* \year:                                 \day & \month & \year.
                                                            (line  8291)
* \zeta:                                 Math symbols.      (line  9935)
* \[...\] display math:                  displaymath.       (line  3854)
* \\ (for center):                       center.            (line  3698)
* \\ (for eqnarray):                     eqnarray.          (line  4006)
* \\ (for flushright):                   flushright.        (line  4248)
* \\ (for \shortstack objects):          \shortstack.       (line  5308)
* \\ (tabbing):                          tabbing.           (line  5553)
* \\ for flushleft:                      flushleft.         (line  4188)
* \\ for letters:                        Letters.           (line 15322)
* \\ for tabular:                        tabular.           (line  5730)
* \\ for verse:                          verse.             (line  6469)
* \\ for \author:                        \maketitle.        (line 11128)
* \\ for \title:                         \maketitle.        (line 11149)
* \\ force line break:                   \\.                (line  6507)
* \\* (for eqnarray):                    eqnarray.          (line  4012)
* \^:                                    Reserved characters.
                                                            (line 13537)
* \^ (circumflex accent):                Accents.           (line 13866)
* \_:                                    Reserved characters.
                                                            (line 13532)
* \` (grave accent):                     Accents.           (line 13870)
* \` (tabbing):                          tabbing.           (line  5580)
* \{:                                    Reserved characters.
                                                            (line 13532)
* \|:                                    Math symbols.      (line  9127)
* \}:                                    Reserved characters.
                                                            (line 13532)
* \~:                                    Reserved characters.
                                                            (line 13537)
* \~ (tilde accent):                     Accents.           (line 13874)
* ^ superscript:                         Subscripts & superscripts.
                                                            (line  9052)
* ^^J, in \write:                        \write.            (line 15845)
* _ subscript:                           Subscripts & superscripts.
                                                            (line  9052)
* {...} for required arguments:          LaTeX command syntax.
                                                            (line   595)
* ~:                                     ~.                 (line 11660)
* a4paper option:                        Document class options.
                                                            (line   744)
* a5paper option:                        Document class options.
                                                            (line   744)
* abstract environment:                  abstract.          (line  3566)
* abstract package:                      abstract.          (line  3587)
* abstracts:                             abstract.          (line  3566)
* accents:                               Accents.           (line 13832)
* accents, defining:                     \DeclareFontEncoding.
                                                            (line  1384)
* accents, defining <1>:                 \DeclareTextAccent.
                                                            (line  1418)
* accents, defining <2>:                 \DeclareTextAccentDefault.
                                                            (line  1442)
* accents, defining <3>:                 \DeclareTextComposite.
                                                            (line  1551)
* accents, defining <4>:                 \DeclareTextCompositeCommand.
                                                            (line  1575)
* accents, defining <5>:                 \DeclareTextSymbolDefault.
                                                            (line  1620)
* accents, mathematical:                 Math accents.      (line 10540)
* accessing any character of a font:     Symbols by font position.
                                                            (line 13608)
* acronyms, list of:                     Glossaries.        (line 15143)
* acute accent:                          Accents.           (line 13855)
* acute accent, math:                    Math accents.      (line 10545)
* additional packages, loading:          Additional packages.
                                                            (line   830)
* adjustbox package:                     Boxes.             (line 12140)
* ae ligature:                           Additional Latin letters.
                                                            (line 13979)
* algorithm2e package:                   tabbing.           (line  5633)
* align environment, from amsmath:       eqnarray.          (line  3983)
* aligning equations:                    eqnarray.          (line  3983)
* alignment via tabbing:                 tabbing.           (line  5493)
* amscd package:                         Arrows.            (line  9994)
* amsfonts package:                      Math formulas.     (line  9041)
* amsfonts package <1>:                  Arrows.            (line  9959)
* amsmath package:                       array.             (line  3661)
* amsmath package <1>:                   array.             (line  3669)
* amsmath package <2>:                   displaymath.       (line  3850)
* amsmath package <3>:                   equation.          (line  4051)
* amsmath package <4>:                   theorem.           (line  6313)
* amsmath package <5>:                   Math formulas.     (line  9041)
* amsmath package <6>:                   \left & \right.    (line 10157)
* amsmath package <7>:                   \bigl & \bigr etc..
                                                            (line 10302)
* amsmath package <8>:                   Dots.              (line 10357)
* amsmath package <9>:                   Math functions.    (line 10529)
* amsmath package <10>:                  Spacing in math mode.
                                                            (line 10650)
* amsmath package <11>:                  \phantom & \vphantom & \hphantom.
                                                            (line 10818)
* amsmath package <12>:                  Colon character & \colon.
                                                            (line 10936)
* amsmath package <13>:                  Colon character & \colon.
                                                            (line 10940)
* amsmath package <14>:                  \thinspace & \negthinspace.
                                                            (line 11745)
* amsmath package, replacing eqnarray:   eqnarray.          (line  3983)
* amsthm package:                        theorem.           (line  6313)
* amsthm package <1>:                    \rule.             (line 14091)
* answers package:                       \write.            (line 15850)
* appendices:                            \appendix.         (line  3072)
* appendix:                              \appendix.         (line  3072)
* appendix package:                      \appendix.         (line  3095)
* aring:                                 Additional Latin letters.
                                                            (line 13975)
* array environment:                     array.             (line  3612)
* array package:                         array.             (line  3680)
* arrays, math:                          array.             (line  3612)
* arrow, left, in text:                  Text symbols.      (line 13771)
* arrow, right, in text:                 Text symbols.      (line 13812)
* arrows:                                Arrows.            (line  9959)
* article class:                         Document classes.  (line   701)
* ascender height:                       Text symbols.      (line 13717)
* ASCII circumflex, in text:             Text symbols.      (line 13682)
* ASCII tilde, in text:                  Text symbols.      (line 13685)
* asterisk, centered, in text:           Text symbols.      (line 13688)
* Asymptote package:                     \line.             (line  5179)
* Asymptote package <1>:                 \strut.            (line 11980)
* Asymptote package <2>:                 \mbox & \makebox.  (line 12214)
* Asymptote package <3>:                 \write18.          (line 15953)
* at clause, in font definitions:        \newfont.          (line  7884)
* at-sign:                               \@.                (line 11529)
* author, for titlepage:                 \maketitle.        (line 11128)
* auxiliary file:                        Output files.      (line   490)
* b5paper option:                        Document class options.
                                                            (line   744)
* babel package:                         \chapter.          (line  2837)
* babel package <1>:                     thebibliography.   (line  6071)
* babel package <2>:                     Accents.           (line 13832)
* babel package <3>:                     \today.            (line 14121)
* babel package <4>:                     Table of contents etc..
                                                            (line 14494)
* babel package <5>:                     \index.            (line 14904)
* back matter of a book:                 \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* background, colored:                   Colored pages.     (line 12757)
* backslash, in text:                    Text symbols.      (line 13691)
* bar, double vertical, in text:         Text symbols.      (line 13697)
* bar, vertical, in text:                Text symbols.      (line 13694)
* bar-over accent:                       Accents.           (line 13862)
* bar-over accent, math:                 Math accents.      (line 10548)
* bar-under accent:                      Accents.           (line 13877)
* basics of LaTeX:                       Overview.          (line   402)
* batchmode:                             Command line options.
                                                            (line 16087)
* beamer package:                        beamer template.   (line 16324)
* beamer template and class:             beamer template.   (line 16324)
* beginning of document hook:            \AtBeginDocument.  (line  3884)
* bibliography format, open:             Document class options.
                                                            (line   792)
* bibliography, creating (automatically): Using BibTeX.     (line  6202)
* bibliography, creating (manually):     thebibliography.   (line  6024)
* BibTeX error messages:                 BibTeX error messages.
                                                            (line  6264)
* bibTeX, using:                         Using BibTeX.      (line  6202)
* big circle symbols, in text:           Text symbols.      (line 13700)
* big point:                             Units of length.   (line  8424)
* bigfoot package:                       Footnotes of footnotes.
                                                            (line  7206)
* black boxes, omitting:                 Document class options.
                                                            (line   778)
* blackboard bold:                       Blackboard bold.   (line 10040)
* bm package:                            \boldmath & \unboldmath.
                                                            (line 10026)
* bold font:                             Font styles.       (line  1771)
* bold math:                             Font styles.       (line  1824)
* bold typewriter, avoiding:             description.       (line  3808)
* boldface mathematics:                  \boldmath & \unboldmath.
                                                            (line 10000)
* book class:                            Document classes.  (line   701)
* book, back matter:                     \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* book, end matter:                      \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* book, front matter:                    \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* book, main matter:                     \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* bottomnumber:                          Floats.            (line  2532)
* bottomnumber <1>:                      Floats.            (line  2533)
* bounding box:                          \includegraphics.  (line 13190)
* box:                                   \mbox & \makebox.  (line 12146)
* box, allocating new:                   \newsavebox.       (line  7597)
* box, bounding:                         \includegraphics.  (line 13190)
* box, colored:                          Colored boxes.     (line 12720)
* box, save:                             \sbox & \savebox.  (line 12400)
* box, use saved box:                    \usebox.           (line 12509)
* boxes:                                 Boxes.             (line 12137)
* bp:                                    Units of length.   (line  8423)
* brace, left, in text:                  Text symbols.      (line 13703)
* brace, right, in text:                 Text symbols.      (line 13706)
* braces:                                Delimiters.        (line 10083)
* brackets:                              Delimiters.        (line 10083)
* breaking lines:                        Line breaking.     (line  6490)
* breaking pages:                        Page breaking.     (line  6783)
* breaks, multiplication discretionary:  \*.                (line 10947)
* breve accent:                          Accents.           (line 13915)
* breve accent, math:                    Math accents.      (line 10551)
* bug reporting:                         About this document.
                                                            (line   378)
* bullet lists:                          itemize.           (line  4289)
* bullet symbol:                         Math symbols.      (line  9215)
* bullet, in text:                       Text symbols.      (line 13709)
* bulleted lists:                        itemize.           (line  4289)
* calligraphic fonts:                    Calligraphic.      (line 10066)
* calligraphic letters for math:         Font styles.       (line  1774)
* cap height:                            Text symbols.      (line 13717)
* caption package:                       \caption.          (line  2624)
* captions:                              \caption.          (line  2558)
* caron accent:                          Accents.           (line 13919)
* catcode:                               \makeatletter & \makeatother.
                                                            (line  7426)
* category code, character:              \makeatletter & \makeatother.
                                                            (line  7426)
* cc:                                    Units of length.   (line  8436)
* cc list, in letters:                   \cc.               (line 15383)
* cedilla accent:                        Accents.           (line 13887)
* center environment:                    center.            (line  3688)
* centered asterisk, in text:            Text symbols.      (line 13688)
* centered equations:                    Document class options.
                                                            (line   782)
* centered period, in text:              Text symbols.      (line 13784)
* centering text, declaration for:       \centering.        (line  3736)
* centering text, environment for:       center.            (line  3688)
* centimeter:                            Units of length.   (line  8431)
* changing case of characters:           Upper and lower case.
                                                            (line 13555)
* chapter:                               Sectioning.        (line  2632)
* chapter <1>:                           \chapter.          (line  2772)
* chapter counter:                       Counters.          (line  8091)
* character category code:               \makeatletter & \makeatother.
                                                            (line  7426)
* character encoding:                    inputenc package.  (line 14035)
* character, invisible:                  \phantom & \vphantom & \hphantom.
                                                            (line 10768)
* character, invisible <1>:              \mathstrut.        (line 10831)
* characters, accented:                  Accents.           (line 13832)
* characters, case of:                   Upper and lower case.
                                                            (line 13555)
* characters, non-English:               Additional Latin letters.
                                                            (line 13969)
* characters, reserved:                  Reserved characters.
                                                            (line 13525)
* characters, special:                   Reserved characters.
                                                            (line 13525)
* check accent:                          Accents.           (line 13919)
* check accent, math:                    Math accents.      (line 10554)
* cicero:                                Units of length.   (line  8437)
* circle symbol, big, in text:           Text symbols.      (line 13700)
* circled letter, in text:               Text symbols.      (line 13712)
* circumflex accent:                     Accents.           (line 13866)
* circumflex accent, math:               Math accents.      (line 10566)
* circumflex, ASCII, in text:            Text symbols.      (line 13682)
* citation key:                          \bibitem.          (line  6088)
* class and package commands:            Class and package commands.
                                                            (line   916)
* class and package difference:          Class and package construction.
                                                            (line   855)
* class and package structure:           Class and package structure.
                                                            (line   869)
* class file example:                    Class and package structure.
                                                            (line   902)
* class file layout:                     Class and package structure.
                                                            (line   869)
* class options:                         Document class options.
                                                            (line   731)
* class options <1>:                     Class and package structure.
                                                            (line   869)
* class options <2>:                     Class and package commands.
                                                            (line   976)
* classes of documents:                  Document classes.  (line   696)
* cleveref package:                      Cross references.  (line  3376)
* cleveref package <1>:                  \ref.              (line  3489)
* cleveref package <2>:                  \footnotemark.     (line  7087)
* CLI:                                   Command line interface.
                                                            (line 16022)
* clock option to slides class:          Document class options.
                                                            (line   824)
* closing letters:                       \closing.          (line 15399)
* closing quote:                         Text symbols.      (line 13672)
* cm:                                    Units of length.   (line  8430)
* cm-super package:                      fontenc package.   (line  1328)
* cmd.exe, used by \write18:             \write18.          (line 16000)
* code, typesetting:                     verbatim.          (line  6360)
* colon character:                       Colon character & \colon.
                                                            (line 10927)
* color:                                 Color.             (line 12522)
* color <1>:                             Define colors.     (line 12627)
* color <2>:                             Colored text.      (line 12649)
* color <3>:                             Colored boxes.     (line 12720)
* color <4>:                             Colored pages.     (line 12757)
* color models:                          Color models.      (line 12575)
* color package commands:                Commands for color.
                                                            (line 12622)
* color package options:                 Color package options.
                                                            (line 12537)
* color, define:                         Define colors.     (line 12627)
* colored boxes:                         Colored boxes.     (line 12720)
* colored page:                          Colored pages.     (line 12757)
* colored text:                          Colored text.      (line 12649)
* command line interface:                Command line interface.
                                                            (line 16022)
* command syntax:                        LaTeX command syntax.
                                                            (line   595)
* commands, class and package:           Class and package commands.
                                                            (line   916)
* commands, defining new ones:           \newcommand & \renewcommand.
                                                            (line  7227)
* commands, defining new ones <1>:       \providecommand.   (line  7386)
* commands, document class:              Class and package construction.
                                                            (line   846)
* commands, graphics package:            Commands for graphics.
                                                            (line 13069)
* commands, ignore spaces:               \ignorespaces & \ignorespacesafterend.
                                                            (line  7955)
* commands, ignore spaces <1>:           xspace package.    (line  8030)
* commands, redefining:                  \newcommand & \renewcommand.
                                                            (line  7227)
* commands, run from LaTeX:              \write18.          (line 15946)
* commands, star-variants:               \@ifstar.          (line  7460)
* composite word mark, in text:          Text symbols.      (line 13717)
* comprehensive package:                 Math symbols.      (line  9115)
* computer programs, typesetting:        verbatim.          (line  6360)
* configuration, graphics package:       Graphics package configuration.
                                                            (line 12879)
* contents file:                         Output files.      (line   500)
* copyright symbol:                      Text symbols.      (line 13629)
* counters, a list of:                   Counters.          (line  8082)
* counters, defining new:                \newcounter.       (line  7532)
* counters, getting value of:            \value.            (line  8191)
* counters, printing:                    \alph \Alph \arabic \roman \Roman \fnsymbol.
                                                            (line  8109)
* counters, setting:                     \setcounter.       (line  8224)
* cprotect package:                      verbatim.          (line  6379)
* cprotect package <1>:                  \verb.             (line  6442)
* creating pictures:                     picture.           (line  4918)
* creating tables:                       table.             (line  5642)
* credit footnote:                       \maketitle.        (line 11142)
* cross references:                      Cross references.  (line  3344)
* cross references, resolving:           Output files.      (line   490)
* cross referencing with page number:    \pageref.          (line  3442)
* cross referencing, across documents:   xr package.        (line  3495)
* cross referencing, symbolic:           \ref.              (line  3466)
* CTAN:                                  CTAN.              (line   668)
* curly braces:                          Delimiters.        (line 10083)
* currency, dollar:                      Text symbols.      (line 13730)
* currency, euro:                        Text symbols.      (line 13742)
* dagger, double, in text:               Text symbols.      (line 13727)
* dagger, in text:                       Text symbols.      (line 13632)
* dagger, in text <1>:                   Text symbols.      (line 13724)
* DANTE e.V.:                            CTAN.              (line   682)
* datatool package:                      \read.             (line 15673)
* date, for titlepage:                   \maketitle.        (line 11136)
* date, today's:                         \today.            (line 14114)
* datetime package:                      \today.            (line 14135)
* dbltopnumber:                          Floats.            (line  2536)
* dbltopnumber <1>:                      Floats.            (line  2537)
* dcolumn package:                       array.             (line  3680)
* dd:                                    Units of length.   (line  8433)
* declaration form of font size commands: Font sizes.       (line  1858)
* declaration form of font style commands: Font styles.     (line  1703)
* define color:                          Define colors.     (line 12627)
* defining a new command:                \newcommand & \renewcommand.
                                                            (line  7227)
* defining a new command <1>:            \providecommand.   (line  7386)
* defining new environments:             \newenvironment & \renewenvironment.
                                                            (line  7625)
* defining new fonts:                    \newfont.          (line  7871)
* defining new theorems:                 \newtheorem.       (line  7759)
* definitions:                           Definitions.       (line  7222)
* delayed \write:                        \write.            (line 15816)
* delimiters:                            Delimiters.        (line 10083)
* delimiters, paired:                    \left & \right.    (line 10133)
* delim_0:                               makeindex.         (line 15072)
* delim_1:                               makeindex.         (line 15076)
* delim_2:                               makeindex.         (line 15080)
* delim_n:                               makeindex.         (line 15084)
* delim_r:                               makeindex.         (line 15088)
* description:                           \newglossaryentry. (line 15231)
* description environment:               description.       (line  3778)
* description lists, creating:           description.       (line  3778)
* design size, in font definitions:      \newfont.          (line  7884)
* didot point:                           Units of length.   (line  8434)
* dieresis accent:                       Accents.           (line 13851)
* difference between class and package:  Class and package construction.
                                                            (line   855)
* dimen plain TeX:                       Lengths.           (line  8316)
* directory listings, from system:       \write18.          (line 16005)
* discretionary breaks, multiplication:  \*.                (line 10947)
* discretionary hyphenation:             \discretionary.    (line  6667)
* display math mode:                     Modes.             (line 11026)
* display style:                         Math styles.       (line 10865)
* displaying quoted text with paragraph indentation: quotation & quote.
                                                            (line  5463)
* displaying quoted text without paragraph indentation: quotation & quote.
                                                            (line  5463)
* displaymath environment:               displaymath.       (line  3834)
* displaymath environment <1>:           Math formulas.     (line  8986)
* document class commands:               Class and package construction.
                                                            (line   846)
* document class options:                Document class options.
                                                            (line   731)
* document class, defined:               Starting and ending.
                                                            (line   442)
* document classes:                      Document classes.  (line   696)
* document environment:                  document.          (line  3878)
* document root name:                    Jobname.           (line 16214)
* document templates:                    Document templates.
                                                            (line 16317)
* dollar sign:                           Text symbols.      (line 13730)
* dot accent:                            Accents.           (line 13858)
* dot over accent, math:                 Math accents.      (line 10560)
* dot-over accent:                       Accents.           (line 13858)
* dot-under accent:                      Accents.           (line 13891)
* dotless i:                             Accents.           (line 13845)
* dotless i, math:                       Math symbols.      (line  9362)
* dotless j:                             Accents.           (line 13845)
* dotless j, math:                       Math symbols.      (line  9382)
* dots:                                  Dots.              (line 10327)
* double angle quotation marks:          Text symbols.      (line 13647)
* double dagger, in text:                Text symbols.      (line 13635)
* double dagger, in text <1>:            Text symbols.      (line 13727)
* double dot accent, math:               Math accents.      (line 10557)
* double guillemets:                     Text symbols.      (line 13647)
* double left quote:                     Text symbols.      (line 13790)
* double low-9 quotation mark:           Text symbols.      (line 13669)
* double quote, straight base:           Text symbols.      (line 13806)
* double right quote:                    Text symbols.      (line 13793)
* double spacing:                        \baselineskip & \baselinestretch.
                                                            (line  2315)
* double vertical bar, in text:          Text symbols.      (line 13697)
* doublestruck:                          Blackboard bold.   (line 10040)
* draft option:                          Document class options.
                                                            (line   774)
* dvilualatex-dev:                       TeX engines.       (line   566)
* dvipdfmx command:                      Output files.      (line   467)
* dvips command:                         Output files.      (line   467)
* dvitype command:                       Output files.      (line   467)
* e-dash:                                Text symbols.      (line 13739)
* e-TeX:                                 TeX engines.       (line   519)
* ellipses:                              Dots.              (line 10327)
* ellipsis:                              Text symbols.      (line 13653)
* em:                                    Units of length.   (line  8450)
* em <1>:                                Units of length.   (line  8449)
* em-dash:                               Text symbols.      (line 13733)
* em-dash, three-quarters:               Text symbols.      (line 13815)
* em-dash, two-thirds:                   Text symbols.      (line 13821)
* emphasis:                              Font styles.       (line  1755)
* enclosure list:                        \encl.             (line 15412)
* encoding, font:                        \DeclareFontEncoding.
                                                            (line  1384)
* encoding, of input files:              inputenc package.  (line 14035)
* end matter of a book:                  \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* end of document hook:                  \AtEndDocument.    (line  3900)
* ending and starting:                   Starting and ending.
                                                            (line   431)
* engines, TeX:                          TeX engines.       (line   509)
* enlarge current page:                  \enlargethispage.  (line  6888)
* enumerate environment:                 enumerate.         (line  3916)
* enumi counter:                         Counters.          (line  8091)
* enumii counter:                        Counters.          (line  8091)
* enumiii counter:                       Counters.          (line  8091)
* enumitem package:                      itemize.           (line  4349)
* enumitem package <1>:                  list.              (line  4648)
* enumiv counter:                        Counters.          (line  8091)
* environment:                           Starting and ending.
                                                            (line   450)
* environment form of font size commands: Font sizes.       (line  1881)
* environment, abstract:                 abstract.          (line  3566)
* environment, array:                    array.             (line  3612)
* environment, center:                   center.            (line  3688)
* environment, description:              description.       (line  3778)
* environment, displaymath:              displaymath.       (line  3834)
* environment, displaymath <1>:          Math formulas.     (line  8986)
* environment, document:                 document.          (line  3878)
* environment, enumerate:                enumerate.         (line  3916)
* environment, eqnarray:                 eqnarray.          (line  3983)
* environment, equation:                 equation.          (line  4037)
* environment, equation <1>:             Math formulas.     (line  8986)
* environment, figure:                   figure.            (line  4057)
* environment, filecontents:             filecontents.      (line  4115)
* environment, filecontents*:            filecontents.      (line  4115)
* environment, flushleft:                flushleft.         (line  4180)
* environment, flushright:               flushright.        (line  4242)
* environment, itemize:                  itemize.           (line  4289)
* environment, letter:                   letter.            (line  4377)
* environment, list:                     list.              (line  4382)
* environment, math:                     math.              (line  4748)
* environment, math <1>:                 Math formulas.     (line  8986)
* environment, minipage:                 minipage.          (line  4760)
* environment, picture:                  picture.           (line  4918)
* environment, quotation:                quotation & quote. (line  5463)
* environment, quote:                    quotation & quote. (line  5463)
* environment, sloppypar:                sloppypar.         (line  6704)
* environment, tabbing:                  tabbing.           (line  5493)
* environment, table:                    table.             (line  5642)
* environment, tabular:                  tabular.           (line  5700)
* environment, thebibliography:          thebibliography.   (line  6024)
* environment, theindex:                 Produce the index manually.
                                                            (line 14828)
* environment, theorem:                  theorem.           (line  6291)
* environment, theorem-like:             \newtheorem.       (line  7759)
* environment, titlepage:                titlepage.         (line  6321)
* environment, verbatim:                 verbatim.          (line  6360)
* environment, verse:                    verse.             (line  6454)
* environments:                          Environments.      (line  3549)
* environments, defining:                \newenvironment & \renewenvironment.
                                                            (line  7625)
* envlab package:                        \makelabels.       (line 15486)
* EPS files:                             \includegraphics.  (line 13075)
* eqnarray environment:                  eqnarray.          (line  3983)
* equation counter:                      Counters.          (line  8091)
* equation environment:                  equation.          (line  4037)
* equation environment <1>:              Math formulas.     (line  8986)
* equation number, cross referencing:    \ref.              (line  3466)
* equation numbers, left vs. right:      Document class options.
                                                            (line   788)
* equation numbers, omitting:            eqnarray.          (line  4016)
* equations, aligning:                   eqnarray.          (line  3983)
* equations, environment for:            equation.          (line  4037)
* equations, flush left vs. centered:    Document class options.
                                                            (line   782)
* error messages, from BibTeX:           BibTeX error messages.
                                                            (line  6264)
* errorstopmode:                         Command line options.
                                                            (line 16087)
* es-zet German letter:                  Additional Latin letters.
                                                            (line 14015)
* etex command:                          TeX engines.       (line   519)
* eth, Icelandic letter:                 Additional Latin letters.
                                                            (line 13983)
* etoolbox package:                      Class and package commands.
                                                            (line  1020)
* euro symbol:                           Text symbols.      (line 13742)
* eurosym package:                       Text symbols.      (line 13742)
* eurosym package <1>:                   Text symbols.      (line 13743)
* ex:                                    Units of length.   (line  8446)
* ex <1>:                                Units of length.   (line  8445)
* exclamation point, upside-down:        Text symbols.      (line 13750)
* executivepaper option:                 Document class options.
                                                            (line   744)
* expl3 package:                         LaTeX command syntax.
                                                            (line   624)
* expl3 package <1>:                     Upper and lower case.
                                                            (line 13597)
* exponent:                              Subscripts & superscripts.
                                                            (line  9052)
* expressions:                           Expressions.       (line  8646)
* extended Latin:                        Additional Latin letters.
                                                            (line 13969)
* external commands:                     \write18.          (line 15946)
* external files, writing:               filecontents.      (line  4115)
* fallback jobname:                      Jobname.           (line 16235)
* families, of fonts:                    Low-level font commands.
                                                            (line  1912)
* fancyhdr package:                      Page styles.       (line 11085)
* fancyhdr package <1>:                  \pagestyle.        (line 11226)
* fancyvrb package:                      tabbing.           (line  5633)
* fancyvrb package <1>:                  verbatim.          (line  6395)
* feminine ordinal symbol:               Text symbols.      (line 13781)
* figure counter:                        Counters.          (line  8091)
* figure dash character:                 Text symbols.      (line 13753)
* figure environment:                    figure.            (line  4057)
* figure number, cross referencing:      \ref.              (line  3466)
* figures, footnotes in:                 minipage.          (line  4861)
* figures, inserting:                    figure.            (line  4057)
* file, closing:                         \openin & \openout.
                                                            (line 15584)
* file, opening:                         \openin & \openout.
                                                            (line 15584)
* file, reading:                         \read.             (line 15648)
* file, root:                            Splitting the input.
                                                            (line 14149)
* file, root <1>:                        Jobname.           (line 16214)
* filecontents environment:              filecontents.      (line  4115)
* filecontents* environment:             filecontents.      (line  4115)
* filename for current job:              Command line options.
                                                            (line 16103)
* final option:                          Document class options.
                                                            (line   774)
* first-latex-doc document:              About this document.
                                                            (line   390)
* fixed-width font:                      Font styles.       (line  1792)
* flafter package:                       Floats.            (line  2484)
* fleqn option:                          Document class options.
                                                            (line   774)
* float package:                         Floats.            (line  2454)
* float page:                            Floats.            (line  2460)
* flush left equations:                  Document class options.
                                                            (line   782)
* flushing floats and starting a page:   \clearpage & \cleardoublepage.
                                                            (line  6814)
* flushleft environment:                 flushleft.         (line  4180)
* flushright environment:                flushright.        (line  4242)
* font catalogue:                        Low-level font commands.
                                                            (line  1912)
* font commands, low-level:              Low-level font commands.
                                                            (line  1897)
* font dimension, slant:                 \/.                (line 11788)
* font encoding:                         fontenc package.   (line  1298)
* font encoding <1>:                     \DeclareTextAccent.
                                                            (line  1418)
* font encoding, declaring:              \DeclareFontEncoding.
                                                            (line  1384)
* font size:                             Low-level font commands.
                                                            (line  1992)
* font sizes:                            Font sizes.        (line  1840)
* font styles:                           Font styles.       (line  1701)
* font symbols, by number:               Symbols by font position.
                                                            (line 13608)
* fontenc:                               fontenc package.   (line  1298)
* fonts:                                 Fonts.             (line  1261)
* fonts, new commands for:               \newfont.          (line  7871)
* fonts, script:                         Calligraphic.      (line 10066)
* fontspec package:                      fontenc package.   (line  1309)
* footer style:                          \pagestyle.        (line 11219)
* footer, parameters for:                Page layout parameters.
                                                            (line  2182)
* footnote counter:                      Counters.          (line  8091)
* footnote number, cross referencing:    \ref.              (line  3466)
* footnote parameters:                   \footnote.         (line  7007)
* footnote, in a table:                  Footnotes in a table.
                                                            (line  7136)
* footnote, in section headings:         Footnotes in section headings.
                                                            (line  7117)
* footnote, of a footnote:               Footnotes of footnotes.
                                                            (line  7206)
* footnotes in figures:                  minipage.          (line  4861)
* footnotes, creating:                   Footnotes.         (line  6960)
* footnotes, in a minipage:              \footnote.         (line  7035)
* footnotes, symbols instead of numbers: \footnote.         (line  6997)
* force option for filecontents:         filecontents.      (line  4140)
* format files, TeX:                     TeX engines.       (line   509)
* formulas, environment for:             equation.          (line  4037)
* formulas, math:                        Math formulas.     (line  8986)
* forward reference:                     Cross references.  (line  3365)
* forward references, resolving:         Output files.      (line   490)
* fraction:                              \frac.             (line 10963)
* fragile commands:                      \protect.          (line  7903)
* frame rule width:                      \fbox & \framebox. (line 12268)
* frame, line width:                     \fbox & \framebox. (line 12268)
* frame, separation from contents:       \fbox & \framebox. (line 12273)
* French quotation marks:                Text symbols.      (line 13647)
* front matter of a book:                \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* functions, math:                       Math functions.    (line 10424)
* geometry package:                      Document class options.
                                                            (line   765)
* geometry package <1>:                  Document class options.
                                                            (line   769)
* global options:                        Document class options.
                                                            (line   731)
* global options <1>:                    Additional packages.
                                                            (line   839)
* glossaries:                            Glossaries.        (line 15143)
* glossary:                              Glossaries.        (line 15143)
* glossary, entries:                     \newglossaryentry. (line 15191)
* glossary, entry reference:             \gls.              (line 15250)
* glue plain TeX:                        Lengths.           (line  8316)
* glue register, plain TeX:              \newlength.        (line  7573)
* graphics:                              Graphics.          (line 12778)
* graphics <1>:                          Graphics package configuration.
                                                            (line 12879)
* graphics <2>:                          \includegraphics.  (line 13075)
* graphics package:                      Graphics.          (line 12778)
* graphics package <1>:                  Graphics package configuration.
                                                            (line 12879)
* graphics package <2>:                  \includegraphics.  (line 13075)
* graphics package commands:             Commands for graphics.
                                                            (line 13069)
* graphics package options:              Graphics package options.
                                                            (line 12815)
* graphics packages:                     \line.             (line  5179)
* graphics, resizing:                    \scalebox.         (line 13458)
* graphics, resizing <1>:                \resizebox.        (line 13490)
* graphics, scaling:                     \scalebox.         (line 13458)
* graphics, scaling <1>:                 \resizebox.        (line 13490)
* graphpap package:                      \graphpaper.       (line  5131)
* grave accent:                          Accents.           (line 13870)
* grave accent, math:                    Math accents.      (line 10563)
* greater than symbol, in text:          Text symbols.      (line 13760)
* greek letters:                         Math symbols.      (line  9115)
* Greek letters:                         Greek letters.     (line 10381)
* grfext package:                        \DeclareGraphicsExtensions.
                                                            (line 12987)
* group, and environments:               Environments.      (line  3561)
* group_skip:                            makeindex.         (line 15021)
* hacek accent:                          Accents.           (line 13919)
* Halmos symbol:                         \rule.             (line 14086)
* hard space:                            ~.                 (line 11660)
* hat accent:                            Accents.           (line 13866)
* hat accent, math:                      Math accents.      (line 10566)
* header style:                          \pagestyle.        (line 11219)
* header, parameters for:                Page layout parameters.
                                                            (line  2182)
* hello, world:                          Starting and ending.
                                                            (line   431)
* here, putting floats:                  Floats.            (line  2454)
* home page for manual:                  About this document.
                                                            (line   360)
* horizontal bar character:              Text symbols.      (line 13763)
* horizontal paragraph indentation:      \parindent & \parskip.
                                                            (line  8904)
* horizontal space:                      \hss.              (line 11445)
* horizontal space, stretchable:         \hss.              (line 11445)
* horizontal spacing:                    \phantom & \vphantom & \hphantom.
                                                            (line 10768)
* hungarian umlaut accent:               Accents.           (line 13895)
* hyperref package:                      \footnotemark.     (line  7087)
* hyperref package <1>:                  \footnotemark.     (line  7096)
* hyperref package <2>:                  \pagenumbering.    (line 11201)
* hyperref package <3>:                  \contentsline.     (line 14704)
* hyperref package <4>:                  Command line input.
                                                            (line 16158)
* hyphen character, non-breaking:        Text symbols.      (line 13774)
* hyphenation, defining:                 \hyphenation.      (line  6732)
* hyphenation, discretionary:            \discretionary.    (line  6667)
* hyphenation, forcing:                  \- (hyphenation).  (line  6633)
* hyphenation, preventing:               \mbox & \makebox.  (line 12146)
* háček accent, math:                    Math accents.      (line 10554)
* Icelandic eth:                         Additional Latin letters.
                                                            (line 13983)
* Icelandic thorn:                       Additional Latin letters.
                                                            (line 14019)
* idx file:                              \index.            (line 14954)
* ij letter, Dutch:                      Additional Latin letters.
                                                            (line 13995)
* immediate \write:                      \write.            (line 15811)
* implementations of TeX:                TeX engines.       (line   509)
* importing graphics:                    \includegraphics.  (line 13075)
* in:                                    Units of length.   (line  8420)
* inch:                                  Units of length.   (line  8421)
* including graphics:                    \includegraphics.  (line 13075)
* indent, forcing:                       \indent & \noindent.
                                                            (line  8855)
* indentation of paragraphs, in minipage: minipage.         (line  4857)
* indentfirst package:                   \part.             (line  2762)
* indentfirst package <1>:               \chapter.          (line  2824)
* indentfirst package <2>:               \section.          (line  2919)
* indentfirst package <3>:               \subsection.       (line  2985)
* indentfirst package <4>:               \subsubsection & \paragraph & \subparagraph.
                                                            (line  3060)
* indentfirst package <5>:               \indent & \noindent.
                                                            (line  8897)
* indent_length:                         makeindex.         (line 15100)
* indent_space:                          makeindex.         (line 15096)
* index entries, subentries:             \index.            (line 14872)
* index entries, 'see' and 'see also':   \index.            (line 14904)
* index entry:                           \index.            (line 14852)
* index package:                         \index.            (line 14949)
* index, multiple:                       Indexes.           (line 14815)
* index, page range:                     \index.            (line 14888)
* index, printing:                       \printindex.       (line 15128)
* index, processing:                     makeindex.         (line 14969)
* index, producing manually:             Produce the index manually.
                                                            (line 14825)
* index, style file:                     makeindex.         (line 14981)
* indexes:                               Indexes.           (line 14770)
* infinite horizontal stretch:           \hfill.            (line 11412)
* infinite vertical stretch:             \vfill.            (line 12060)
* inline formulas:                       math.              (line  4748)
* inner paragraph mode:                  Modes.             (line 11046)
* input file:                            Splitting the input.
                                                            (line 14145)
* input, on command line:                Command line input.
                                                            (line 16150)
* input/output:                          Input/output.      (line 15575)
* input/output, to terminal:             Input/output.      (line 15575)
* inputenc:                              inputenc package.  (line 14026)
* inserting figures:                     figure.            (line  4057)
* insertions of special characters:      Special insertions.
                                                            (line 13519)
* interface, command line:               Command line interface.
                                                            (line 16022)
* interline space:                       \baselineskip & \baselinestretch.
                                                            (line  2315)
* internal vertical mode:                Modes.             (line 11036)
* invisible character:                   \phantom & \vphantom & \hphantom.
                                                            (line 10768)
* invisible character <1>:               \mathstrut.        (line 10831)
* italic correction:                     \/.                (line 11754)
* italic font:                           Font styles.       (line  1777)
* itemize environment:                   itemize.           (line  4289)
* item_0:                                makeindex.         (line 15045)
* item_01:                               makeindex.         (line 15054)
* item_1:                                makeindex.         (line 15048)
* item_12:                               makeindex.         (line 15063)
* item_2:                                makeindex.         (line 15051)
* item_x1:                               makeindex.         (line 15058)
* item_x2:                               makeindex.         (line 15067)
* jobname:                               Command line options.
                                                            (line 16103)
* jobname <1>:                           Jobname.           (line 16214)
* JPEG files:                            \includegraphics.  (line 13075)
* JPG files:                             \includegraphics.  (line 13075)
* justification, ragged left:            \raggedleft.       (line  4262)
* justification, ragged right:           \raggedright.      (line  4209)
* Knuth, Donald E.:                      Overview.          (line   402)
* label:                                 Cross references.  (line  3344)
* labelled lists, creating:              description.       (line  3778)
* Lamport TeX:                           Overview.          (line   423)
* Lamport, Leslie:                       Overview.          (line   402)
* landscape option:                      Document class options.
                                                            (line   774)
* landscape orientation:                 Document class options.
                                                            (line   785)
* latex:                                 TeX engines.       (line   517)
* latex command:                         Output files.      (line   467)
* LaTeX format (.fmt) files:             TeX engines.       (line   509)
* LaTeX logo:                            Text symbols.      (line 13638)
* LaTeX overview:                        Overview.          (line   402)
* LaTeX Project team:                    About this document.
                                                            (line   374)
* LaTeX vs. LaTeX2e:                     About this document.
                                                            (line   370)
* latex-dev:                             TeX engines.       (line   567)
* latex-doc-ptr document:                About this document.
                                                            (line   387)
* LaTeX2e logo:                          Text symbols.      (line 13641)
* LaTeX3 syntax:                         LaTeX command syntax.
                                                            (line   624)
* <latexrefman@tug.org> email address:   About this document.
                                                            (line   374)
* latexsym package:                      Arrows.            (line  9959)
* Latin letters, additional:             Additional Latin letters.
                                                            (line 13969)
* layout commands:                       Layout.            (line  2026)
* layout, page parameters for:           Page layout parameters.
                                                            (line  2182)
* leaders, dots in table of contents:    \@dottedtocline.   (line 14522)
* leading:                               \baselineskip & \baselinestretch.
                                                            (line  2315)
* left angle quotation marks:            Text symbols.      (line 13647)
* left arrow, in text:                   Text symbols.      (line 13771)
* left brace, in text:                   Text symbols.      (line 13703)
* left quote:                            Text symbols.      (line 13657)
* left quote, double:                    Text symbols.      (line 13790)
* left quote, single:                    Text symbols.      (line 13796)
* left-hand equation numbers:            Document class options.
                                                            (line   788)
* left-justifying text:                  \raggedright.      (line  4209)
* left-justifying text, environment for: flushleft.         (line  4180)
* left-to-right mode:                    Modes.             (line 11013)
* legalpaper option:                     Document class options.
                                                            (line   744)
* lengths, adding to:                    \addtolength.      (line  8500)
* lengths, allocating new:               \newlength.        (line  7573)
* lengths, defining and using:           Lengths.           (line  8313)
* lengths, setting:                      \setlength.        (line  8471)
* leqno option:                          Document class options.
                                                            (line   774)
* less than symbol, in text:             Text symbols.      (line 13768)
* lethead_flag:                          makeindex.         (line 15028)
* lethead_prefix:                        makeindex.         (line 15037)
* lethead_suffix:                        makeindex.         (line 15041)
* letter class:                          Document classes.  (line   701)
* letter environment:                    letter.            (line  4377)
* letterpaper option:                    Document class options.
                                                            (line   744)
* letters, accented:                     Accents.           (line 13832)
* letters, additional Latin:             Additional Latin letters.
                                                            (line 13969)
* letters, ending:                       \closing.          (line 15399)
* letters, starting:                     \opening.          (line 15504)
* letters, writing:                      Letters.           (line 15280)
* line break, forcing:                   \\.                (line  6507)
* line breaking:                         Line breaking.     (line  6490)
* line breaks, changing:                 \fussy & \sloppy.  (line  6690)
* line breaks, forcing:                  \linebreak & \nolinebreak.
                                                            (line  6751)
* line breaks, multiplication discretionary: \*.            (line 10947)
* line breaks, preventing:               \linebreak & \nolinebreak.
                                                            (line  6751)
* lines in tables:                       tabular.           (line  5700)
* line_max:                              makeindex.         (line 15092)
* lining numerals:                       Font styles.       (line  1828)
* lining text up in tables:              tabular.           (line  5700)
* lining text up using tab stops:        tabbing.           (line  5493)
* list environment:                      list.              (line  4382)
* list items, specifying counter:        \usecounter.       (line  8165)
* list of figures file:                  Output files.      (line   500)
* list of tables file:                   Output files.      (line   500)
* listings package:                      tabbing.           (line  5633)
* listings package <1>:                  verbatim.          (line  6389)
* listings package <2>:                  \verb.             (line  6439)
* lists of items:                        itemize.           (line  4289)
* lists of items, generic:               list.              (line  4382)
* lists of items, numbered:              enumerate.         (line  3916)
* lmodern package:                       fontenc package.   (line  1328)
* loading additional packages:           Additional packages.
                                                            (line   830)
* locale information, from system:       \write18.          (line 16005)
* log file:                              Output files.      (line   485)
* log file, writing to:                  \write.            (line 15781)
* logo, LaTeX:                           Text symbols.      (line 13638)
* logo, LaTeX2e:                         Text symbols.      (line 13641)
* logo, TeX:                             Text symbols.      (line 13679)
* long command:                          Class and package commands.
                                                            (line   933)
* low-9 quotation marks, single and double: Text symbols.   (line 13669)
* low-level font commands:               Low-level font commands.
                                                            (line  1897)
* lowercase:                             Upper and lower case.
                                                            (line 13555)
* LR box:                                picture.           (line  5005)
* LR mode:                               Modes.             (line 11013)
* lrbox:                                 lrbox.             (line 12480)
* lshort document:                       About this document.
                                                            (line   393)
* lualatex:                              TeX engines.       (line   535)
* lualatex-dev:                          TeX engines.       (line   568)
* LuaTeX:                                TeX engines.       (line   536)
* LuaTeX, 256 output streams in:         \write.            (line 15793)
* m-width:                               Units of length.   (line  8450)
* macron accent:                         Accents.           (line 13862)
* macron accent, math:                   Math accents.      (line 10548)
* macros2e package:                      \makeatletter & \makeatother.
                                                            (line  7446)
* Madsen, Lars:                          eqnarray.          (line  3983)
* mail merges:                           \read.             (line 15673)
* main matter of a book:                 \frontmatter & \mainmatter & \backmatter.
                                                            (line  3105)
* make a box:                            \mbox & \makebox.  (line 12146)
* makeidx package:                       \printindex.       (line 15134)
* makeindex program:                     makeindex.         (line 14969)
* makeindex, program:                    makeindex.         (line 14969)
* makeindex, style file:                 makeindex.         (line 14981)
* making a title page:                   titlepage.         (line  6321)
* making paragraphs:                     Making paragraphs. (line  8741)
* marginal notes:                        Marginal notes.    (line  8936)
* masculine ordinal symbol:              Text symbols.      (line 13781)
* matching brackets:                     \left & \right.    (line 10133)
* matching parentheses:                  \left & \right.    (line 10133)
* math accents:                          Math accents.      (line 10540)
* math environment:                      math.              (line  4748)
* math environment <1>:                  Math formulas.     (line  8986)
* math formulas:                         Math formulas.     (line  8986)
* math functions:                        Math functions.    (line 10424)
* math miscellany:                       Math miscellany.   (line 10921)
* math mode:                             Modes.             (line 11023)
* math mode, entering:                   Math formulas.     (line  8986)
* math mode, spacing:                    Spacing in math mode.
                                                            (line 10633)
* math mode, spacing <1>:                \phantom & \vphantom & \hphantom.
                                                            (line 10768)
* math mode, spacing <2>:                \mathstrut.        (line 10831)
* math mode, vertical space:             \smash.            (line 10708)
* math styles:                           Math styles.       (line 10853)
* math symbols:                          Math symbols.      (line  9115)
* math, arrows:                          Arrows.            (line  9959)
* math, bold:                            Font styles.       (line  1824)
* mathtools package:                     Math formulas.     (line  9041)
* mathtools package <1>:                 Delimiters.        (line 10118)
* mathtools package <2>:                 \left & \right.    (line 10157)
* mathtools package <3>:                 Over- and Underlining.
                                                            (line 10627)
* mathtools package <4>:                 \smash.            (line 10762)
* mathtools package <5>:                 \phantom & \vphantom & \hphantom.
                                                            (line 10810)
* MetaPost package:                      \line.             (line  5179)
* mfirstuc package:                      Upper and lower case.
                                                            (line 13594)
* mhchem package:                        Subscripts & superscripts.
                                                            (line  9108)
* millimeter:                            Units of length.   (line  8428)
* minipage environment:                  minipage.          (line  4760)
* minipage, creating a:                  minipage.          (line  4760)
* minted package:                        tabbing.           (line  5633)
* minted package <1>:                    verbatim.          (line  6389)
* minted package <2>:                    \verb.             (line  6439)
* mirrors of CTAN:                       CTAN.              (line   687)
* mm:                                    Units of length.   (line  8427)
* modes:                                 Modes.             (line 11001)
* monospace font:                        Font styles.       (line  1792)
* moving arguments:                      \protect.          (line  7916)
* mpfootnote counter:                    \footnote.         (line  7035)
* mpfootnote counter <1>:                Counters.          (line  8091)
* mu:                                    Units of length.   (line  8456)
* mu, math unit:                         Units of length.   (line  8457)
* multicolumn text:                      \twocolumn.        (line  2043)
* multilingual support:                  Accents.           (line 13832)
* multind package:                       Indexes.           (line 14815)
* multiple indexes:                      Indexes.           (line 14815)
* multiplication, discretionary:         \*.                (line 10947)
* name:                                  \newglossaryentry. (line 15228)
* name of document root:                 Jobname.           (line 16214)
* NBSP:                                  ~.                 (line 11660)
* nested \include, not allowed:          \include & \includeonly.
                                                            (line 14320)
* new class commands:                    Class and package construction.
                                                            (line   846)
* new command, check:                    Class and package commands.
                                                            (line   931)
* new command, definition:               Class and package commands.
                                                            (line  1006)
* new commands, defining:                \newcommand & \renewcommand.
                                                            (line  7227)
* new commands, defining <1>:            \providecommand.   (line  7386)
* new line, output as input:             \obeycr & \restorecr.
                                                            (line  6569)
* new line, starting:                    \\.                (line  6507)
* new line, starting (paragraph mode):   \newline.          (line  6609)
* new page, starting:                    \newpage.          (line  6855)
* newline, in \write:                    \write.            (line 15845)
* noheader option for filecontents:      filecontents.      (line  4143)
* non-breaking hyphen character:         Text symbols.      (line 13774)
* non-English characters:                Additional Latin letters.
                                                            (line 13969)
* nonstopmode:                           Command line options.
                                                            (line 16087)
* nosearch option for filecontents:      filecontents.      (line  4146)
* notes in the margin:                   Marginal notes.    (line  8936)
* notitlepage option:                    Document class options.
                                                            (line   774)
* null delimiter:                        \left & \right.    (line 10133)
* numbered items, specifying counter:    \usecounter.       (line  8165)
* numerals, old-style:                   Font styles.       (line  1828)
* oblique font:                          Font styles.       (line  1789)
* oe ligature:                           Additional Latin letters.
                                                            (line 14011)
* ogonek:                                Accents.           (line 13899)
* old-style numerals:                    Font styles.       (line  1828)
* one-column output:                     \onecolumn.        (line  2031)
* onecolumn option:                      Document class options.
                                                            (line   803)
* oneside option:                        Document class options.
                                                            (line   803)
* open a file:                           \openin & \openout.
                                                            (line 15584)
* openany option:                        Document class options.
                                                            (line   803)
* openbib option:                        Document class options.
                                                            (line   774)
* opening quote:                         Text symbols.      (line 13657)
* openright option:                      Document class options.
                                                            (line   803)
* OpenType fonts:                        TeX engines.       (line   509)
* operating system information:          \write18.          (line 16005)
* options, class:                        Class and package commands.
                                                            (line   976)
* options, color package:                Color package options.
                                                            (line 12537)
* options, command line:                 Command line options.
                                                            (line 16066)
* options, document class:               Document class options.
                                                            (line   731)
* options, document class <1>:           Class and package structure.
                                                            (line   869)
* options, global:                       Additional packages.
                                                            (line   839)
* options, graphics package:             Graphics package options.
                                                            (line 12815)
* options, package:                      Class and package structure.
                                                            (line   869)
* options, package <1>:                  Class and package commands.
                                                            (line   976)
* ordinals, feminine and masculine:      Text symbols.      (line 13781)
* oslash:                                Additional Latin letters.
                                                            (line 14007)
* OT1:                                   fontenc package.   (line  1298)
* outer paragraph mode:                  Modes.             (line 11046)
* output directory for all external files: Command line options.
                                                            (line 16108)
* overbar accent:                        Accents.           (line 13862)
* overdot accent, math:                  Math accents.      (line 10560)
* overlining:                            Over- and Underlining.
                                                            (line 10589)
* overview of LaTeX:                     Overview.          (line   402)
* overwrite option for filecontents:     filecontents.      (line  4140)
* package file layout:                   Class and package structure.
                                                            (line   869)
* package options:                       Class and package structure.
                                                            (line   869)
* package options <1>:                   Class and package commands.
                                                            (line   976)
* package, abstract:                     abstract.          (line  3587)
* package, adjustbox:                    Boxes.             (line 12140)
* package, algorithm2e:                  tabbing.           (line  5633)
* package, amscd:                        Arrows.            (line  9994)
* package, amsfonts:                     Math formulas.     (line  9041)
* package, amsfonts <1>:                 Arrows.            (line  9959)
* package, amsmath:                      array.             (line  3661)
* package, amsmath <1>:                  array.             (line  3669)
* package, amsmath <2>:                  displaymath.       (line  3850)
* package, amsmath <3>:                  equation.          (line  4051)
* package, amsmath <4>:                  theorem.           (line  6313)
* package, amsmath <5>:                  Math formulas.     (line  9041)
* package, amsmath <6>:                  \left & \right.    (line 10157)
* package, amsmath <7>:                  \bigl & \bigr etc..
                                                            (line 10302)
* package, amsmath <8>:                  Dots.              (line 10357)
* package, amsmath <9>:                  Math functions.    (line 10529)
* package, amsmath <10>:                 Spacing in math mode.
                                                            (line 10650)
* package, amsmath <11>:                 \phantom & \vphantom & \hphantom.
                                                            (line 10818)
* package, amsmath <12>:                 Colon character & \colon.
                                                            (line 10936)
* package, amsmath <13>:                 Colon character & \colon.
                                                            (line 10940)
* package, amsmath <14>:                 \thinspace & \negthinspace.
                                                            (line 11745)
* package, amsthm:                       theorem.           (line  6313)
* package, amsthm <1>:                   \rule.             (line 14091)
* package, answers:                      \write.            (line 15850)
* package, appendix:                     \appendix.         (line  3095)
* package, array:                        array.             (line  3680)
* package, Asymptote:                    \line.             (line  5179)
* package, Asymptote <1>:                \strut.            (line 11980)
* package, Asymptote <2>:                \mbox & \makebox.  (line 12214)
* package, Asymptote <3>:                \write18.          (line 15953)
* package, babel:                        \chapter.          (line  2837)
* package, babel <1>:                    thebibliography.   (line  6071)
* package, babel <2>:                    Accents.           (line 13832)
* package, babel <3>:                    \today.            (line 14121)
* package, babel <4>:                    Table of contents etc..
                                                            (line 14494)
* package, babel <5>:                    \index.            (line 14904)
* package, beamer:                       beamer template.   (line 16324)
* package, bigfoot:                      Footnotes of footnotes.
                                                            (line  7206)
* package, bm:                           \boldmath & \unboldmath.
                                                            (line 10026)
* package, caption:                      \caption.          (line  2624)
* package, cleveref:                     Cross references.  (line  3376)
* package, cleveref <1>:                 \ref.              (line  3489)
* package, cleveref <2>:                 \footnotemark.     (line  7087)
* package, cm-super:                     fontenc package.   (line  1328)
* package, comprehensive:                Math symbols.      (line  9115)
* package, cprotect:                     verbatim.          (line  6379)
* package, cprotect <1>:                 \verb.             (line  6442)
* package, datatool:                     \read.             (line 15673)
* package, datetime:                     \today.            (line 14135)
* package, dcolumn:                      array.             (line  3680)
* package, enumitem:                     itemize.           (line  4349)
* package, enumitem <1>:                 list.              (line  4648)
* package, envlab:                       \makelabels.       (line 15486)
* package, etoolbox:                     Class and package commands.
                                                            (line  1020)
* package, eurosym:                      Text symbols.      (line 13742)
* package, eurosym <1>:                  Text symbols.      (line 13743)
* package, expl3:                        LaTeX command syntax.
                                                            (line   624)
* package, expl3 <1>:                    Upper and lower case.
                                                            (line 13597)
* package, fancyhdr:                     Page styles.       (line 11085)
* package, fancyhdr <1>:                 \pagestyle.        (line 11226)
* package, fancyvrb:                     tabbing.           (line  5633)
* package, fancyvrb <1>:                 verbatim.          (line  6395)
* package, flafter:                      Floats.            (line  2484)
* package, float:                        Floats.            (line  2454)
* package, fontspec:                     fontenc package.   (line  1309)
* package, geometry:                     Document class options.
                                                            (line   765)
* package, geometry <1>:                 Document class options.
                                                            (line   769)
* package, graphpap:                     \graphpaper.       (line  5131)
* package, grfext:                       \DeclareGraphicsExtensions.
                                                            (line 12987)
* package, hyperref:                     \footnotemark.     (line  7087)
* package, hyperref <1>:                 \footnotemark.     (line  7096)
* package, hyperref <2>:                 \pagenumbering.    (line 11201)
* package, hyperref <3>:                 \contentsline.     (line 14704)
* package, hyperref <4>:                 Command line input.
                                                            (line 16158)
* package, indentfirst:                  \part.             (line  2762)
* package, indentfirst <1>:              \chapter.          (line  2824)
* package, indentfirst <2>:              \section.          (line  2919)
* package, indentfirst <3>:              \subsection.       (line  2985)
* package, indentfirst <4>:              \subsubsection & \paragraph & \subparagraph.
                                                            (line  3060)
* package, indentfirst <5>:              \indent & \noindent.
                                                            (line  8897)
* package, index:                        \index.            (line 14949)
* package, latexsym:                     Arrows.            (line  9959)
* package, listings:                     tabbing.           (line  5633)
* package, listings <1>:                 verbatim.          (line  6389)
* package, listings <2>:                 \verb.             (line  6439)
* package, lmodern:                      fontenc package.   (line  1328)
* package, macros2e:                     \makeatletter & \makeatother.
                                                            (line  7446)
* package, makeidx:                      \printindex.       (line 15134)
* package, mathtools:                    Math formulas.     (line  9041)
* package, mathtools <1>:                Delimiters.        (line 10118)
* package, mathtools <2>:                \left & \right.    (line 10157)
* package, mathtools <3>:                Over- and Underlining.
                                                            (line 10627)
* package, mathtools <4>:                \smash.            (line 10762)
* package, mathtools <5>:                \phantom & \vphantom & \hphantom.
                                                            (line 10810)
* package, MetaPost:                     \line.             (line  5179)
* package, mfirstuc:                     Upper and lower case.
                                                            (line 13594)
* package, mhchem:                       Subscripts & superscripts.
                                                            (line  9108)
* package, minted:                       tabbing.           (line  5633)
* package, minted <1>:                   verbatim.          (line  6389)
* package, minted <2>:                   \verb.             (line  6439)
* package, multind:                      Indexes.           (line 14815)
* package, pict2e:                       \line.             (line  5179)
* package, polyglossia:                  Accents.           (line 13832)
* package, polyglossia <1>:              \today.            (line 14121)
* package, polyglossia <2>:              Table of contents etc..
                                                            (line 14495)
* package, polyglossia <3>:              \index.            (line 14904)
* package, PSTricks:                     \line.             (line  5179)
* package, setspace:                     \baselineskip & \baselinestretch.
                                                            (line  2388)
* package, shellesc:                     \write18.          (line 16011)
* package, showidx:                      Indexes.           (line 14815)
* package, siunitx:                      minipage.          (line  4891)
* package, siunitx <1>:                  ~.                 (line 11696)
* package, suffix:                       \@ifstar.          (line  7518)
* package, tablefootnote:                Footnotes in a table.
                                                            (line  7183)
* package, texosquery:                   \write18.          (line 16005)
* package, textcase:                     Upper and lower case.
                                                            (line 13591)
* package, TikZ:                         \line.             (line  5179)
* package, TikZ <1>:                     \strut.            (line 11980)
* package, TikZ <2>:                     \mbox & \makebox.  (line 12213)
* package, tikz-cd:                      Arrows.            (line  9994)
* package, titlesec:                     Sectioning.        (line  2686)
* package, titlesec <1>:                 \part.             (line  2766)
* package, titlesec <2>:                 \chapter.          (line  2845)
* package, titlesec <3>:                 \section.          (line  2923)
* package, titlesec <4>:                 \subsection.       (line  2989)
* package, titlesec <5>:                 \subsubsection & \paragraph & \subparagraph.
                                                            (line  3064)
* package, tocbibbind:                   Table of contents etc..
                                                            (line 14481)
* package, tocloft:                      Table of contents etc..
                                                            (line 14481)
* package, tocloft <1>:                  \contentsline.     (line 14701)
* package, ulem:                         Over- and Underlining.
                                                            (line 10598)
* package, unicode-math:                 Greek letters.     (line 10412)
* package, url:                          \verb.             (line  6436)
* package, verbatimbox:                  verbatim.          (line  6395)
* package, xparse:                       LaTeX command syntax.
                                                            (line   624)
* package, xparse <1>:                   \@ifstar.          (line  7518)
* package, xr:                           xr package.        (line  3495)
* package, xr-hyper:                     xr package.        (line  3495)
* package, xspace:                       xspace package.    (line  8030)
* package, xstring:                      Jobname.           (line 16261)
* packages, loading additional:          Additional packages.
                                                            (line   830)
* page break, forcing:                   \pagebreak & \nopagebreak.
                                                            (line  6913)
* page break, preventing:                \pagebreak & \nopagebreak.
                                                            (line  6913)
* page breaking:                         Page breaking.     (line  6783)
* page counter:                          Counters.          (line  8091)
* page layout parameters:                Page layout parameters.
                                                            (line  2182)
* page number, cross referencing:        \pageref.          (line  3442)
* page numbering style:                  \pagenumbering.    (line 11162)
* page style, this page:                 \thispagestyle.    (line 11303)
* page styles:                           Page styles.       (line 11079)
* page, colored:                         Colored pages.     (line 12757)
* page_precedence:                       makeindex.         (line 15105)
* paired delimiters:                     \left & \right.    (line 10133)
* paragraph:                             Sectioning.        (line  2632)
* paragraph <1>:                         \subsubsection & \paragraph & \subparagraph.
                                                            (line  3007)
* paragraph counter:                     Counters.          (line  8091)
* paragraph indentation:                 \parindent & \parskip.
                                                            (line  8904)
* paragraph indentation, in minipage:    minipage.          (line  4857)
* paragraph indentations in quoted text: quotation & quote. (line  5463)
* paragraph indentations in quoted text, omitting: quotation & quote.
                                                            (line  5463)
* paragraph mode:                        Modes.             (line 11007)
* paragraph mode <1>:                    \parbox.           (line 12303)
* paragraph symbol:                      Text symbols.      (line 13661)
* paragraph, ending:                     \par.              (line  8802)
* paragraph, in a box:                   \parbox.           (line 12303)
* paragraphs:                            Making paragraphs. (line  8741)
* parameters, for footnotes:             \footnote.         (line  7007)
* parameters, page layout:               Page layout parameters.
                                                            (line  2182)
* parent directories, cannot write to:   \write and security.
                                                            (line 15874)
* parentheses:                           Delimiters.        (line 10083)
* part:                                  Sectioning.        (line  2632)
* part <1>:                              \part.             (line  2718)
* part counter:                          Counters.          (line  8091)
* pattern, current tab stops, tabbing:   tabbing.           (line  5538)
* pc:                                    Units of length.   (line  8417)
* PDF graphic files:                     \includegraphics.  (line 13075)
* pdflatex:                              TeX engines.       (line   518)
* pdflatex command:                      Output files.      (line   477)
* pdflatex-dev:                          TeX engines.       (line   569)
* pdfTeX:                                Output files.      (line   477)
* pdfTeX engine:                         TeX engines.       (line   519)
* period, abbreviation-ending:           \@.                (line 11529)
* period, centered, in text:             Text symbols.      (line 13784)
* period, sentence-ending:               \@.                (line 11529)
* period, spacing after:                 \@.                (line 11529)
* pica:                                  Units of length.   (line  8418)
* pict2e package:                        \line.             (line  5179)
* picture environment:                   picture.           (line  4918)
* pictures, creating:                    picture.           (line  4918)
* pilcrow:                               Text symbols.      (line 13661)
* placement of floats:                   Floats.            (line  2433)
* platex:                                TeX engines.       (line   557)
* platex-dev:                            TeX engines.       (line   570)
* plural:                                \newglossaryentry. (line 15236)
* PNG files:                             \includegraphics.  (line 13075)
* poetry, an environment for:            verse.             (line  6454)
* point:                                 Units of length.   (line  8414)
* polish l:                              Additional Latin letters.
                                                            (line 13999)
* polyglossia package:                   Accents.           (line 13832)
* polyglossia package <1>:               \today.            (line 14121)
* polyglossia package <2>:               Table of contents etc..
                                                            (line 14495)
* polyglossia package <3>:               \index.            (line 14904)
* portrait orientation:                  Document class options.
                                                            (line   785)
* position, in picture:                  picture.           (line  4976)
* positional parameter:                  \newcommand & \renewcommand.
                                                            (line  7275)
* postamble:                             makeindex.         (line 15017)
* PostScript point:                      Units of length.   (line  8424)
* postscript, in letters:                \ps.               (line 15516)
* pounds symbol:                         Text symbols.      (line 13665)
* preamble:                              makeindex.         (line 15013)
* preamble, defined:                     Starting and ending.
                                                            (line   447)
* prerelease testing:                    TeX engines.       (line   573)
* prompt, *:                             Recovering from errors.
                                                            (line 16296)
* pronunciation:                         Overview.          (line   423)
* PSTricks package:                      \line.             (line  5179)
* pt:                                    Units of length.   (line  8413)
* quad:                                  Spacing in math mode.
                                                            (line 10696)
* question mark, upside-down:            Text symbols.      (line 13787)
* quotation environment:                 quotation & quote. (line  5463)
* quotation marks, French:               Text symbols.      (line 13647)
* quote environment:                     quotation & quote. (line  5463)
* quote, single straight:                Text symbols.      (line 13802)
* quote, straight base:                  Text symbols.      (line 13806)
* quoted text with paragraph indentation, displaying: quotation & quote.
                                                            (line  5463)
* quoted text without paragraph indentation, displaying: quotation & quote.
                                                            (line  5463)
* radical:                               \sqrt.             (line 10975)
* ragged left text:                      \raggedleft.       (line  4262)
* ragged left text, environment for:     flushright.        (line  4242)
* ragged right text:                     \raggedright.      (line  4209)
* ragged right text, environment for:    flushleft.         (line  4180)
* read a file:                           \read.             (line 15648)
* redefining environments:               \newenvironment & \renewenvironment.
                                                            (line  7625)
* reference, forward:                    Cross references.  (line  3365)
* references, resolving forward:         Output files.      (line   490)
* registered symbol:                     Text symbols.      (line 13809)
* relation, text above:                  \stackrel.         (line 10991)
* release candidates:                    TeX engines.       (line   573)
* remarks in the margin:                 Marginal notes.    (line  8936)
* report class:                          Document classes.  (line   701)
* reporting bugs:                        About this document.
                                                            (line   378)
* reserved characters:                   Reserved characters.
                                                            (line 13525)
* resizing:                              \scalebox.         (line 13458)
* resizing <1>:                          \resizebox.        (line 13490)
* restricted shell access:               \write18.          (line 15993)
* right angle quotation marks:           Text symbols.      (line 13647)
* right arrow, in text:                  Text symbols.      (line 13812)
* right brace, in text:                  Text symbols.      (line 13706)
* right quote:                           Text symbols.      (line 13672)
* right quote, double:                   Text symbols.      (line 13793)
* right quote, single:                   Text symbols.      (line 13799)
* right-hand equation numbers:           Document class options.
                                                            (line   788)
* right-justifying text:                 \raggedleft.       (line  4262)
* right-justifying text, environment for: flushright.       (line  4242)
* rigid lengths:                         Lengths.           (line  8316)
* ring accent:                           Accents.           (line 13903)
* ring accent, math:                     Math accents.      (line 10569)
* robust commands:                       \protect.          (line  7903)
* roman font:                            Font styles.       (line  1780)
* root file:                             Splitting the input.
                                                            (line 14149)
* root file <1>:                         Jobname.           (line 16214)
* roots:                                 \sqrt.             (line 10975)
* rotating graphics:                     \rotatebox.        (line 13390)
* rotating text:                         \rotatebox.        (line 13390)
* rotation:                              \rotatebox.        (line 13390)
* row, tabbing:                          tabbing.           (line  5533)
* rubber lengths:                        Lengths.           (line  8316)
* rubber lengths, defining new:          \newlength.        (line  7573)
* running header and footer:             Page layout parameters.
                                                            (line  2182)
* running header and footer style:       \pagestyle.        (line 11219)
* samepage environment:                  \pagebreak & \nopagebreak.
                                                            (line  6951)
* sans serif font:                       Font styles.       (line  1786)
* scaled point:                          Units of length.   (line  8440)
* scaling:                               \scalebox.         (line 13458)
* scaling <1>:                           \resizebox.        (line 13490)
* script fonts:                          Calligraphic.      (line 10066)
* script letters for math:               Font styles.       (line  1774)
* script style:                          Math styles.       (line 10870)
* scriptscript style:                    Math styles.       (line 10873)
* scrollmode:                            Command line options.
                                                            (line 16087)
* secnumdepth:                           Sectioning.        (line  2695)
* secnumdepth counter:                   Sectioning.        (line  2696)
* section:                               Sectioning.        (line  2632)
* section <1>:                           \section.          (line  2865)
* section counter:                       Counters.          (line  8091)
* section number, cross referencing:     \ref.              (line  3466)
* section numbers, printing:             Sectioning.        (line  2696)
* section symbol:                        Text symbols.      (line 13676)
* section, redefining:                   \@startsection.    (line  3141)
* sectioning commands:                   Sectioning.        (line  2632)
* sectioning, part:                      \part.             (line  2718)
* security and \write:                   \write and security.
                                                            (line 15858)
* see and see also index entries:        \index.            (line 14904)
* self-contained sources:                filecontents.      (line  4151)
* series, of fonts:                      Low-level font commands.
                                                            (line  1939)
* setspace package:                      \baselineskip & \baselinestretch.
                                                            (line  2388)
* setting counters:                      \setcounter.       (line  8224)
* sh, used by \write18:                  \write18.          (line 16000)
* shapes, of fonts:                      Low-level font commands.
                                                            (line  1979)
* sharp S letters:                       Additional Latin letters.
                                                            (line 14015)
* shell access:                          \write18.          (line 15946)
* shell escape:                          Command line options.
                                                            (line 16121)
* SHELL, environment variables:          \write18.          (line 16000)
* shellesc package:                      \write18.          (line 16011)
* showidx package:                       Indexes.           (line 14815)
* simulating typed text:                 verbatim.          (line  6360)
* single angle quotation marks:          Text symbols.      (line 13647)
* single guillemets:                     Text symbols.      (line 13647)
* single left quote:                     Text symbols.      (line 13796)
* single low-9 quotation mark:           Text symbols.      (line 13669)
* single quote, straight:                Text symbols.      (line 13802)
* single right quote:                    Text symbols.      (line 13799)
* siunitx package:                       minipage.          (line  4891)
* siunitx package <1>:                   ~.                 (line 11696)
* sizes of text:                         Font sizes.        (line  1840)
* skip plain TeX:                        Lengths.           (line  8316)
* skip register, plain TeX:              \newlength.        (line  7573)
* slanted font:                          Font styles.       (line  1789)
* slides class:                          Document classes.  (line   701)
* sloppypar environment:                 sloppypar.         (line  6704)
* sloppypar environment <1>:             sloppypar.         (line  6704)
* slot, font:                            \DeclareTextAccent.
                                                            (line  1425)
* small caps font:                       Font styles.       (line  1783)
* sort:                                  \newglossaryentry. (line 15240)
* source files, making self-contained:   filecontents.      (line  4151)
* sp:                                    Units of length.   (line  8439)
* space between lines:                   \baselineskip & \baselinestretch.
                                                            (line  2315)
* space, inserting horizontal:           \hss.              (line 11445)
* space, inserting vertical:             \addvspace.        (line 12089)
* space, negative thin:                  \thinspace & \negthinspace.
                                                            (line 11725)
* space, thin:                           \thinspace & \negthinspace.
                                                            (line 11725)
* space, unbreakable:                    ~.                 (line 11660)
* space, vertical:                       \vspace.           (line 12009)
* spaces:                                Spaces.            (line 11331)
* spaces, ignore around commands:        \ignorespaces & \ignorespacesafterend.
                                                            (line  7955)
* spaces, ignore around commands <1>:    xspace package.    (line  8030)
* spacing within math mode:              Spacing in math mode.
                                                            (line 10633)
* spacing, inter-sentence:               \frenchspacing & \nonfrenchspacing.
                                                            (line 11575)
* spacing, inter-sentence <1>:           \normalsfcodes.    (line 11596)
* spacing, math mode:                    \phantom & \vphantom & \hphantom.
                                                            (line 10768)
* spacing, math mode <1>:                \mathstrut.        (line 10831)
* Spanish ordinals, feminine and masculine: Text symbols.   (line 13781)
* special characters:                    Reserved characters.
                                                            (line 13525)
* special characters <1>:                Additional Latin letters.
                                                            (line 13969)
* special insertions:                    Special insertions.
                                                            (line 13519)
* specifier, float placement:            Floats.            (line  2433)
* splitting the input file:              Splitting the input.
                                                            (line 14145)
* square root:                           \sqrt.             (line 10975)
* stack math:                            \stackrel.         (line 10991)
* star-variants, commands:               \@ifstar.          (line  7460)
* starred form, defining new commands:   \newcommand & \renewcommand.
                                                            (line  7248)
* starting a new page:                   \newpage.          (line  6855)
* starting a new page and clearing floats: \clearpage & \cleardoublepage.
                                                            (line  6814)
* starting and ending:                   Starting and ending.
                                                            (line   431)
* starting on a right-hand page:         \clearpage & \cleardoublepage.
                                                            (line  6814)
* sterling symbol:                       Text symbols.      (line 13665)
* straight double quote, base:           Text symbols.      (line 13806)
* straight quote, base:                  Text symbols.      (line 13806)
* straight single quote:                 Text symbols.      (line 13802)
* stretch, infinite horizontal:          \hfill.            (line 11412)
* stretch, infinite vertical:            \vfill.            (line 12060)
* stretch, omitting vertical:            \raggedbottom.     (line  2171)
* strut:                                 \footnote.         (line  7020)
* strut <1>:                             \strut.            (line 11924)
* strut, math:                           \mathstrut.        (line 10831)
* styles of text:                        Font styles.       (line  1701)
* styles, page:                          Page styles.       (line 11079)
* subparagraph:                          Sectioning.        (line  2632)
* subparagraph <1>:                      \subsubsection & \paragraph & \subparagraph.
                                                            (line  3007)
* subparagraph counter:                  Counters.          (line  8091)
* subscript:                             Subscripts & superscripts.
                                                            (line  9052)
* subsection:                            Sectioning.        (line  2632)
* subsection <1>:                        \subsection.       (line  2943)
* subsection counter:                    Counters.          (line  8091)
* subsubsection:                         Sectioning.        (line  2632)
* subsubsection <1>:                     \subsubsection & \paragraph & \subparagraph.
                                                            (line  3007)
* subsubsection counter:                 Counters.          (line  8091)
* suffix package:                        \@ifstar.          (line  7518)
* superscript:                           Subscripts & superscripts.
                                                            (line  9052)
* symbol:                                \newglossaryentry. (line 15244)
* symbol, defining:                      \DeclareTextSymbol.
                                                            (line  1593)
* symbols, arrows:                       Arrows.            (line  9959)
* symbols, boldface:                     \boldmath & \unboldmath.
                                                            (line 10000)
* symbols, math:                         Math symbols.      (line  9115)
* symbols, text:                         Text symbols.      (line 13620)
* system commands, run from LaTeX:       \write18.          (line 15946)
* system information:                    \write18.          (line 16005)
* T1:                                    fontenc package.   (line  1298)
* tab stops, using:                      tabbing.           (line  5493)
* tabbing environment:                   tabbing.           (line  5493)
* table counter:                         Counters.          (line  8091)
* table environment:                     table.             (line  5642)
* table of contents:                     \contentsline.     (line 14673)
* table of contents entry, create dotted line: \@dottedtocline.
                                                            (line 14501)
* table of contents entry, manually adding: \addcontentsline.
                                                            (line 14536)
* table of contents file:                Output files.      (line   500)
* table of contents, avoiding footnotes: Footnotes in section headings.
                                                            (line  7117)
* table of contents, creating:           Table of contents etc..
                                                            (line 14377)
* table of contents, sectioning numbers printed: Sectioning.
                                                            (line  2707)
* tablefootnote package:                 Footnotes in a table.
                                                            (line  7183)
* tables, creating:                      table.             (line  5642)
* tabular environment:                   tabular.           (line  5700)
* template (simple), article:            article template.  (line 16354)
* template, beamer:                      beamer template.   (line 16324)
* template, book:                        book template.     (line 16377)
* template, book <1>:                    Larger book template.
                                                            (line 16401)
* templates, document:                   Document templates.
                                                            (line 16317)
* terminal input/output:                 Input/output.      (line 15575)
* terminal, writing to:                  \write.            (line 15781)
* TeX format (.fmt) files:               TeX engines.       (line   509)
* TeX logo:                              Text symbols.      (line 13679)
* texosquery package:                    \write18.          (line 16005)
* texput, jobname default:               Jobname.           (line 16235)
* text style:                            Math styles.       (line 10868)
* text symbols:                          Text symbols.      (line 13620)
* text, resizing:                        \scalebox.         (line 13458)
* text, resizing <1>:                    \resizebox.        (line 13490)
* text, scaling:                         \scalebox.         (line 13458)
* text, scaling <1>:                     \resizebox.        (line 13490)
* textcase package:                      Upper and lower case.
                                                            (line 13591)
* textcomp package:                      Text symbols.      (line 13620)
* thanks, for titlepage:                 \maketitle.        (line 11142)
* thebibliography environment:           thebibliography.   (line  6024)
* theindex:                              Produce the index manually.
                                                            (line 14825)
* theindex environment:                  Produce the index manually.
                                                            (line 14828)
* theorem environment:                   theorem.           (line  6291)
* theorem-like environment:              \newtheorem.       (line  7759)
* theorems, defining:                    \newtheorem.       (line  7759)
* theorems, typesetting:                 theorem.           (line  6291)
* thin space:                            Spacing in math mode.
                                                            (line 10674)
* thin space <1>:                        \thinspace & \negthinspace.
                                                            (line 11725)
* thin space, negative:                  Spacing in math mode.
                                                            (line 10688)
* thin space, negative <1>:              \thinspace & \negthinspace.
                                                            (line 11725)
* thorn, Icelandic letter:               Additional Latin letters.
                                                            (line 14019)
* three-quarters em-dash:                Text symbols.      (line 13815)
* tie:                                   ~.                 (line 11660)
* tie-after accent:                      Accents.           (line 13909)
* TikZ package:                          \line.             (line  5179)
* TikZ package <1>:                      \strut.            (line 11980)
* TikZ package <2>:                      \mbox & \makebox.  (line 12213)
* tikz-cd package:                       Arrows.            (line  9994)
* tilde accent:                          Accents.           (line 13874)
* tilde accent, math:                    Math accents.      (line 10572)
* tilde, ASCII, in text:                 Text symbols.      (line 13685)
* title page, separate or run-in:        Document class options.
                                                            (line   796)
* title pages, creating:                 titlepage.         (line  6321)
* title, for titlepage:                  \maketitle.        (line 11149)
* titlepage environment:                 titlepage.         (line  6321)
* titlepage option:                      Document class options.
                                                            (line   774)
* titles, making:                        \maketitle.        (line 11091)
* titlesec package:                      Sectioning.        (line  2686)
* titlesec package <1>:                  \part.             (line  2766)
* titlesec package <2>:                  \chapter.          (line  2845)
* titlesec package <3>:                  \section.          (line  2923)
* titlesec package <4>:                  \subsection.       (line  2989)
* titlesec package <5>:                  \subsubsection & \paragraph & \subparagraph.
                                                            (line  3064)
* tocbibbind package:                    Table of contents etc..
                                                            (line 14481)
* tocdepth:                              Sectioning.        (line  2706)
* tocdepth counter:                      Sectioning.        (line  2707)
* tocloft package:                       Table of contents etc..
                                                            (line 14481)
* tocloft package <1>:                   \contentsline.     (line 14701)
* today's date:                          \today.            (line 14114)
* tombstone:                             \rule.             (line 14086)
* topmargin:                             Page layout parameters.
                                                            (line  2301)
* topnumber:                             Floats.            (line  2540)
* topnumber <1>:                         Floats.            (line  2541)
* totalnumber:                           Floats.            (line  2544)
* totalnumber <1>:                       Floats.            (line  2545)
* trademark symbol:                      Text symbols.      (line 13818)
* transcript file:                       Output files.      (line   485)
* TrueType fonts:                        TeX engines.       (line   509)
* TS1 encoding:                          Text symbols.      (line 13620)
* two-column output:                     \twocolumn.        (line  2043)
* two-thirds em-dash:                    Text symbols.      (line 13821)
* twocolumn option:                      Document class options.
                                                            (line   803)
* twoside option:                        Document class options.
                                                            (line   803)
* type styles:                           Font styles.       (line  1701)
* typed text, simulating:                verbatim.          (line  6360)
* typeface sizes:                        Font sizes.        (line  1840)
* typefaces:                             Fonts.             (line  1261)
* typewriter font:                       Font styles.       (line  1792)
* typewriter labels in lists:            description.       (line  3808)
* ulem package:                          Over- and Underlining.
                                                            (line 10598)
* umlaut accent:                         Accents.           (line 13851)
* unbreakable space:                     ~.                 (line 11660)
* underbar:                              Accents.           (line 13879)
* underlining:                           Over- and Underlining.
                                                            (line 10589)
* underscore, in text:                   Text symbols.      (line 13824)
* Unicode:                               inputenc package.  (line 14035)
* Unicode input, native:                 TeX engines.       (line   509)
* unicode-math package:                  Greek letters.     (line 10412)
* units, of length:                      Units of length.   (line  8410)
* unofficial nature of this manual:      About this document.
                                                            (line   374)
* unordered lists:                       itemize.           (line  4289)
* uplatex:                               TeX engines.       (line   558)
* uplatex-dev:                           TeX engines.       (line   571)
* uppercase:                             Upper and lower case.
                                                            (line 13555)
* url package:                           \verb.             (line  6436)
* using BibTeX:                          Using BibTeX.      (line  6202)
* UTF-8, default LaTeX input encoding:   Overview.          (line   408)
* UTF-8, engine support for:             TeX engines.       (line   509)
* UTF-8, font support for:               fontenc package.   (line  1298)
* variables, a list of:                  Counters.          (line  8082)
* vector symbol, math:                   Math accents.      (line 10575)
* verbatim environment:                  verbatim.          (line  6360)
* verbatim text:                         verbatim.          (line  6360)
* verbatim text, inline:                 \verb.             (line  6403)
* verbatimbox package:                   verbatim.          (line  6395)
* verse environment:                     verse.             (line  6454)
* vertical bar, double, in text:         Text symbols.      (line 13697)
* vertical bar, in text:                 Text symbols.      (line 13694)
* vertical mode:                         Modes.             (line 11031)
* vertical space:                        \vspace.           (line 12009)
* vertical space <1>:                    \addvspace.        (line 12089)
* vertical space before paragraphs:      \parindent & \parskip.
                                                            (line  8904)
* vertical spacing:                      \phantom & \vphantom & \hphantom.
                                                            (line 10768)
* vertical spacing <1>:                  \mathstrut.        (line 10831)
* vertical spacing, math mode:           \smash.            (line 10708)
* visible space:                         \verb.             (line  6428)
* visible space symbol, in text:         Text symbols.      (line 13827)
* weights, of fonts:                     Low-level font commands.
                                                            (line  1949)
* whatsit item:                          \write.            (line 15816)
* white space:                           Spaces.            (line 11331)
* wide hat accent, math:                 Math accents.      (line 10578)
* wide tilde accent, math:               Math accents.      (line 10581)
* widths, of fonts:                      Low-level font commands.
                                                            (line  1961)
* Wright, Joseph:                        Upper and lower case.
                                                            (line 13597)
* writing external files:                filecontents.      (line  4115)
* writing letters:                       Letters.           (line 15280)
* x-height:                              Units of length.   (line  8446)
* xdvi command:                          Output files.      (line   467)
* xdvipdfmx:                             TeX engines.       (line   545)
* xelatex:                               TeX engines.       (line   544)
* xelatex-dev:                           TeX engines.       (line   572)
* XeTeX:                                 TeX engines.       (line   545)
* xindex program:                        makeindex.         (line 15122)
* xindy program:                         makeindex.         (line 15115)
* xparse package:                        LaTeX command syntax.
                                                            (line   624)
* xparse package <1>:                    \@ifstar.          (line  7518)
* xr package:                            xr package.        (line  3495)
* xr-hyper package:                      xr package.        (line  3495)
* xspace package:                        xspace package.    (line  8030)
* xstring package:                       Jobname.           (line 16261)

