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| author | Karl Berry <karl@freefriends.org> | 2006-01-09 00:49:07 +0000 |
|---|---|---|
| committer | Karl Berry <karl@freefriends.org> | 2006-01-09 00:49:07 +0000 |
| commit | 007f67a693e4d031fd3d792df8e4d5f43e2cb2e7 (patch) | |
| tree | 90d17e00e572ecb1e24764b6f29c80e098b08d29 /Master/texmf-dist/doc/latex/amslatex | |
| parent | 950209b26f70aa87ed07c54f82a95b6f03b7c3a0 (diff) | |
doc/latex
git-svn-id: svn://tug.org/texlive/trunk@84 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/amslatex')
43 files changed, 16426 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/amslatex/00readme.txt b/Master/texmf-dist/doc/latex/amslatex/00readme.txt new file mode 100644 index 00000000000..0dec0fb6419 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/00readme.txt @@ -0,0 +1,143 @@ +00readme.txt for amsrefs 2.0 [2004-06-30] + +See also install.txt and manifest.txt. There is a history of changes at +the end of this file. + +Please send bug reports and questions to tech-support@ams.org. + +======================================================================== + +The amsrefs package deals with bibliographies and citations in LaTeX +documents. The basic citation command remains more or less the same as +in standard LaTeX (\cite), but a number of additional variations address +certain known pitfalls or gaps in the standard LaTeX set of citation +features. + +The command for bibliography items is different---\bib instead of +\bibitem---for reasons that will be evident upon further reading in the +documentation. + +A set of BibTeX style files are provided to allow people to extract +data from .bib files and produce .bbl files in amsrefs format instead +of conventional \bibitem format. + +User documentation is in amsrdoc.pdf. + +Technical documentation (including documentation for package writers) +is in amsrefs.pdf. + +======================================================================== +I. FEATURES + +---Preservation of structure. + +The internal structural information of the bibliography entries is not +lost when they are imported from the database file into the LaTeX +document. This takes on its greatest significance when archiving +documents in LaTeX form or transmitting them to another user (such as a +publisher). + +---Deferred formatting. + +This means that the style of the bibliography can be changed on demand +without reimporting everything from the original database(s). + +---More natural data format for titles. + +Proper nouns do not need to have braces added to prevent capitalization +problems. + +---Less ambiguous format for author names. + +When author names are given in inverted order (last name first) it is +possible for LaTeX to unambiguously identify the last name without any +further markup, even in cases like Saunders Mac Lane (Mac Lane, +Saunders) versus Stephen H. Lane (Lane, Stephen H.), or Cam Van Tran +(Tran, Cam Van) versus Bert Van Keulen (Van Keulen, Bert). In +BibTeX some of these would need to have extra braces added to ensure +that the surname is accurately distinguished. + +---Author-year citations. + +There is integrated support for citations in author-year form. + +---Back-reference support. + +Works in conjunction with the hyperref package. + +---Setup requires only LaTeX knowledge. + +All bibliography setup can be done in LaTeX; learning another +programming language (such as, the one used in BibTeX bst files) is +unnecessary. + +---Self-printable database files. + +A LaTeX document that contains only a bibliography in amsrefs forms can +be used as a database for exporting entries to other documents. And +because it is a LaTeX document, the database can be printed directly at +any time simply by running it through LaTeX in the usual way. + +---Self-contained. + +In many cases it seems possible to do without BibTeX entirely. For +example, if the entries are extracted from a single database file that +is maintained in sorted order, the bibliography can be printed directly +by LaTeX on the first pass and the citations resolved on the second +pass. + +======================================================================== +II. GETTING STARTED + +1. Install the package, referring to install.txt as needed. + +2. There are four example files provided: + + cite-xa : Demonstrates an author-year citation scheme. The + bibliography is embedded in the .tex file instead of + residing in a separate .bbl file. + + cite-xb : Demonstrates usage with more-or-less standard BibTeX + methods. + + cite-xs : Shows how the bbl file can be created by LaTeX itself from a + suitably presorted ltb file. + + cite-xh : A working hyperref/backrefs example. + +3. Run LaTeX on cite-xa.tex. Take a look at the messages that have to do +with citations and the bibliography section. Run LaTeX again to resolve +the citations and check the output. + +4. Run LaTeX on cite-xb.tex. Run BibTeX. Look at the bbl file. +Interesting, huh? Run LaTeX twice more to resolve the citations. + +5. Run LaTeX on cite-xs.tex and look at the output. + +6. Run pdflatex on cite-xh.tex (it is set up to use BibTeX also, like +cite-xb). + +======================================================================== +III. REMARKS ON THIS RELEASE + +This is a thorough overhaul and rewrite of the the amsrefs package. +Many (perhaps even most) of the internals have changed and a number of +new features have been added. Backwards compatibility for documents +created with previous versions of this package has been + +See changes.pdf for information on the user-visible changes. + +======================================================================== +IV. SETTING UP A CUSTOM BIBLIOGRAPHY STYLE + +More documentation is needed here, but the discussion in amsrefs.pdf +should be enough to get you started. See especially sections 4, 6.10, +6.26.15, and 6.27. + +======================================================================== +V. CHANGE LOG + +*amsrefs.dtx 2.0 2004-06-30 11:24:39 EDT + +Major rewrite of internals. See changes.pdf for information on the +user-visible changes. diff --git a/Master/texmf-dist/doc/latex/amslatex/amsart.template b/Master/texmf-dist/doc/latex/amslatex/amsart.template new file mode 100644 index 00000000000..1923a23557c --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsart.template @@ -0,0 +1,61 @@ +%----------------------------------------------------------------------- +% Beginning of amsart.template +%----------------------------------------------------------------------- +% +% AMS-LaTeX v.2 template for use with amsart +% +% Remove any commented or uncommented macros you do not use. + +\documentclass{amsart} + +\newtheorem{theorem}{Theorem}[section] +\newtheorem{lemma}[theorem]{Lemma} + +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{example}[theorem]{Example} +\newtheorem{xca}[theorem]{Exercise} + +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} + +\numberwithin{equation}{section} + +\begin{document} + +\title{} + +% Remove any unused author tags. + +% author one information +\author{} +\address{} +\curraddr{} +\email{} +\thanks{} + +% author two information +\author{} +\address{} +\curraddr{} +\email{} +\thanks{} + +\subjclass[2000]{Primary } + +\keywords{} + +\date{} + +\dedicatory{} + +\begin{abstract} +\end{abstract} + +\maketitle + +\end{document} + +%----------------------------------------------------------------------- +% End of amsart.template +%----------------------------------------------------------------------- diff --git a/Master/texmf-dist/doc/latex/amslatex/amsbook.template b/Master/texmf-dist/doc/latex/amslatex/amsbook.template new file mode 100644 index 00000000000..4ac9c928dd9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsbook.template @@ -0,0 +1,99 @@ +%----------------------------------------------------------------------- +% Beginning of amsbook.template +%----------------------------------------------------------------------- +% +% AMS-LaTeX v.2 driver file template for use with amsbook +% +% Remove any commented or uncommented macros you do not use. + +\documentclass{amsart} + +% For use when working on individual chapters +%\includeonly{} + +% Include referenced packages here. +\usepackage{} + +\newtheorem{theorem}{Theorem}[chapter] +\newtheorem{lemma}[theorem]{Lemma} + +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{example}[theorem]{Example} +\newtheorem{xca}[theorem]{Exercise} + +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} + +\numberwithin{section}{chapter} +\numberwithin{equation}{chapter} + +% For a single index; for multiple indexes, see the manual +% "Instructions for preparation of papers and monographs: +% AMS-LaTeX" (instr-l.pdf in the AMS-LaTeX distribution). +\makeindex + +\begin{document} + +\frontmatter + +\title{} + +% Remove any unused author tags. + +% author one information +\author{} +\address{} +\curraddr{} +\email{} +\thanks{} + +% author two information +\author{} +\address{} +\curraddr{} +\email{} +\thanks{} + +\subjclass[2000]{Primary } + +\keywords{} + +\date{} + +\begin{abstract} +\end{abstract} + +\maketitle + +\setcounter{page}{4} + +% See the AMS Author FAQ, http://www.ams.org/authors/author-faq.html +% regarding a dedication page. + +\tableofcontents + +% Include unnumbered chapters (preface, acknowledgments, etc.) here. +\include{} + +\mainmatter +% Include main chapters here. +\include{} + +\appendix +% Include appendix "chapters" here. +\include{} + +\backmatter +% Bibliography styles amsplain or harvard are also acceptable. +\bibliographystyle{amsalpha} +\bibliography{} +% See note above about multiple indexes. +\printindex +\end{document} + +\end{document} + +%----------------------------------------------------------------------- +% End of amsbook.template +%----------------------------------------------------------------------- diff --git a/Master/texmf-dist/doc/latex/amslatex/amsldoc.pdf 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"American Mathematical Society, +%%% Technical Support, +%%% Electronic Products and Services, +%%% P. O. Box 6248, +%%% Providence, RI 02940, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% copyright = "Copyright 1999 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% supported = "yes", +%%% keywords = "latex, amsmath", +%%% abstract = "This file is the source file for the user's +%%% guide of the \LaTeX{} package amsmath .", +%%% docstring = "The checksum field above contains a CRC-16 +%%% checksum as the first value, followed by the +%%% equivalent of the standard UNIX wc (word +%%% count) utility output of lines, words, and +%%% characters. This is produced by Robert +%%% Solovay's checksum utility.", +%%% } +%%% ==================================================================== +\documentclass[leqno,titlepage,openany]{amsldoc}[1999/12/13] + +\ifx\UndEfiNed\url + \ClassError{amsldoc}{% + This version of amsldoc.tex must be processed\MessageBreak + with a newer version of amsldoc.cls (2.02 or later)}{} +\fi + +\title{User's Guide for the \pkg{amsmath} Package (Version~2.0)} +\author{American Mathematical Society} +\date{1999-12-13 (revised 2002-02-25)} + +% Use the amsmath package and amscd package in order to print +% examples. +\usepackage{amsmath} +\usepackage{amscd} + +\makeindex % generate index data +\providecommand{\see}[2]{\textit{see} #1} + +% The amsldoc class includes a number of features useful for +% documentation about TeX, including: +% +% ---Commands \tex/, \amstex/, \latex/, ... for uniform treatment +% of the various logos and easy handling of following spaces. +% +% ---Commands for printing various common elements: \cn for command +% names, \fn for file names (including font-file names), \env for +% environments, \pkg and \cls for packages and classes, etc. + +% Many of the command names used here are rather long and will +% contribute to poor linebreaking if we follow the \latex/ practice +% of not hyphenating anything set in tt font; instead we selectively +% allow some hyphenation. +\allowtthyphens % defined in amsldoc.cls + +\hyphenation{ac-cent-ed-sym-bol add-to-counter add-to-length align-at + aligned-at allow-dis-play-breaks ams-art ams-cd ams-la-tex amsl-doc + ams-symb ams-tex ams-text ams-xtra bmatrix bold-sym-bol cen-ter-tags + eqn-ar-ray idots-int int-lim-its latex med-space neg-med-space + neg-thick-space neg-thin-space no-int-lim-its no-name-lim-its + over-left-arrow over-left-right-arrow over-right-arrow pmatrix + qed-sym-bol set-length side-set small-er tbinom the-equa-tion + thick-space thin-space un-der-left-arrow un-der-left-right-arrow + un-der-right-arrow use-pack-age var-inj-lim var-proj-lim vmatrix + xalign-at xx-align-at} + +% Prepare for illustrating the \vec example +\newcommand{\vect}[1]{\mathbf{#1}} + +\newcommand{\booktitle}[1]{\textit{#1}} +\newcommand{\journalname}[1]{\textit{#1}} +\newcommand{\seriesname}[1]{\textit{#1}} + +% Command to insert and index a particular phrase. Doesn't work for +% certain kinds of special characters in the argument. +\newcommand{\ii}[1]{#1\index{#1}} + +\newcommand{\vstrut}[1]{\vrule width0pt height#1\relax} + +% An environment for presenting comprehensive address information: +\newenvironment{infoaddress}{% + \par\topsep\medskipamount + \trivlist\centering + \item[]% + \begin{minipage}{.7\columnwidth}% + \raggedright +}{% + \end{minipage}% + \endtrivlist +} + +\newenvironment{eqxample}{% + \par\addvspace\medskipamount + \noindent\begin{minipage}{.5\columnwidth}% + \def\producing{\end{minipage}\begin{minipage}{.5\columnwidth}% + \hbox\bgroup\kern-.2pt\vrule width.2pt% + \vbox\bgroup\parindent0pt\relax +% The 3pt is to cancel the -\lineskip from \displ@y + \abovedisplayskip3pt \abovedisplayshortskip\abovedisplayskip + \belowdisplayskip0pt \belowdisplayshortskip\belowdisplayskip + \noindent} +}{% + \par +% Ensure that a lonely \[\] structure doesn't take up width less than +% \hsize. + \hrule height0pt width\hsize + \egroup\vrule width.2pt\kern-.2pt\egroup + \end{minipage}% + \par\addvspace\medskipamount +} + +% The chapters are so short, perhaps we shouldn't call them by the +% name `Chapter'. We make \chaptername read an argument in order to +% remove a following \space or "{} " (both possibilities are present +% in book.cls). + +\renewcommand{\chaptername}[1]{} +\newcommand{\chapnum}[1]{\mdash #1\mdash } +\makeatletter +\def\@makechapterhead#1{% + \vspace{1.5\baselineskip}% + {\parindent \z@ \raggedright \reset@font + \ifnum \c@secnumdepth >\m@ne + \large\bfseries \chapnum{\thechapter}% + \par\nobreak + \vskip.5\baselineskip\relax + \fi + #1\par\nobreak + \vskip\baselineskip + }} +\makeatother + +% A command for ragged-right parbox in a tabular. +\newcommand{\rp}{\let\PBS\\\raggedright\let\\\PBS} + +% Non-indexed file name +\newcommand{\nfn}[1]{\texttt{#1}} + +% For the examples in the math spacing table. +%%\newcommand{\lspx}{\mbox{\rule{5pt}{.6pt}\rule{.6pt}{6pt}}} +%%\newcommand{\rspx}{\mbox{\rule[-1pt]{.6pt}{7pt}% +%% \rule[-1pt]{5pt}{.6pt}}} +\newcommand{\lspx}{\mathord{\Rightarrow\mkern-1mu}} +\newcommand{\rspx}{\mathord{\mkern-1mu\Leftarrow}} +\newcommand{\spx}[1]{$\lspx #1\rspx$} + +% For a list of characters representing document input. +\newcommand{\clist}[1]{% + \mbox{\ntt\spaceskip.2em plus.1em \xspaceskip\spaceskip#1}} + +% Fix weird \latex/ definition of rightmark. +\makeatletter +\def\rightmark{\expandafter\@rightmark\botmark{}{}} +% Also turn off section marks. +\let\sectionmark\@gobble +\renewcommand{\chaptermark}[1]{% + \uppercase{\markboth{\rhcn#1}{\rhcn#1}}} +\newcommand{\rhcn}{\thechapter. } +\makeatother + +% Include down to \section but not \subsection, in toc: +\setcounter{tocdepth}{1} + +\DeclareMathOperator{\ix}{ix} +\DeclareMathOperator{\nul}{nul} +\DeclareMathOperator{\End}{End} +\DeclareMathOperator{\xxx}{xxx} + +\begin{document} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\frontmatter + +\maketitle +\pagestyle{headings} +\tableofcontents +\cleardoublepage % for better page number placement + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mainmatter +\chapter{Introduction} + +The \pkg{amsmath} package is a \LaTeX{} package that provides +miscellaneous enhancements for improving the information structure and +printed output of documents that contain mathematical formulas. Readers +unfamiliar with \LaTeX{} should refer to \cite{lamport}. If you have an +up-to-date version of \LaTeX{}, the \pkg{amsmath} package is normally +provided along with it. Upgrading when a newer version of the +\pkg{amsmath} package is released can be done via +\url{http://www.ams.org/tex/amsmath.html} or +\url{ftp://ftp.ams.org/pub/tex/}. + +This documentation describes the features of the \pkg{amsmath} package +and discusses how they are intended to be used. It also covers some +ancillary packages: +\begin{ctab}{ll} +\pkg{amsbsy}& \pkg{amstext}\\ +\pkg{amscd}& \pkg{amsxtra}\\ +\pkg{amsopn} +\end{ctab} +These all have something to do with the contents of math formulas. For +information on extra math symbols and math fonts, see \cite{amsfonts} +and \url{http://www.ams.org/tex/amsfonts.html}. For documentation of the +\pkg{amsthm} package or AMS document classes (\cls{amsart}, +\cls{amsbook}, etc.\@) see \cite{amsthdoc} or \cite{instr-l} and +\url{http://www.ams.org/tex/author-info.html}. + +If you are a long-time \latex/ user and have lots of mathematics in what +you write, then you may recognize solutions for some familiar problems +in this list of \pkg{amsmath} features: +\begin{itemize} + +\item A convenient way to define new `operator name' commands analogous +to \cn{sin} and \cn{lim}, including proper side spacing and automatic +selection of the correct font style and size (even when used in +sub- or superscripts). + +\item Multiple substitutes for the \env{eqnarray} environment to make +various kinds of equation arrangements easier to write. + +\item Equation numbers automatically adjust up or down to avoid +overprinting on the equation contents (unlike \env{eqnarray}). + +\item Spacing around equals signs matches the normal spacing in the +\env{equation} environment (unlike \env{eqnarray}). + +\item A way to produce multiline subscripts as are often used with +summation or product symbols. + +\item An easy way to substitute a variant equation number for a given +equation instead of the automatically supplied number. + +\item An easy way to produce subordinate equation numbers of the form +(1.3a) (1.3b) (1.3c) for selected groups of equations. + +\end{itemize} + +The \pkg{amsmath} package is distributed together with some small +auxiliary packages: +\begin{description} +\item[\pkg{amsmath}] Primary package, provides various features for + displayed equations and other mathematical constructs. + +\item[\pkg{amstext}] Provides a \cn{text} command for + typesetting a fragment of text inside a display. + +\item[\pkg{amsopn}] Provides \cn{DeclareMathOperator} for defining new + `operator names' like \cn{sin} and \cn{lim}. + +\item[\pkg{amsbsy}] For backward compatibility this package continues +to exist but use of the newer \pkg{bm} package that comes with \LaTeX{} +is recommended instead. + +\item[\pkg{amscd}] Provides a \env{CD} environment for simple + commutative diagrams (no support for diagonal arrows). + +\item[\pkg{amsxtra}] Provides certain odds and ends such as + \cn{fracwithdelims} and \cn{accentedsymbol}, for compatibility with + documents created using version 1.1. + +\end{description} + +The \pkg{amsmath} package incorporates \pkg{amstext}, \pkg{amsopn}, and +\pkg{amsbsy}. The features of \pkg{amscd} and \pkg{amsxtra}, however, +are available only by invoking those packages separately. + +\chapter{Options for the \pkg{amsmath} package}\label{options} + +The \pkg{amsmath} package has the following options: +\begin{description} + +\item[\opt{centertags}] (default) For a split equation, place equation +numbers\index{equation numbers!vertical placement} vertically centered +on the total height of the equation. + +\item[\opt{tbtags}] `Top-or-bottom tags': For a split equation, place +equation numbers\index{equation numbers!vertical placement} level with +the last (resp.\@ first) line, if numbers are on the right (resp.\@ +left). + +\item[\opt{sumlimits}] (default) Place the subscripts and +superscripts\index{subscripts and superscripts!placement}\relax +\index{limits|see{subscripts and superscripts}} of summation symbols +above and below, in displayed equations. This option also affects other +symbols of the same type\mdash $\prod$, $\coprod$, $\bigotimes$, +$\bigoplus$, and so forth\mdash but excluding integrals (see below). + +\item[\opt{nosumlimits}] Always place the subscripts and superscripts of +summation-type symbols to the side, even in displayed equations. + +\item[\opt{intlimits}] Like \opt{sumlimits}, but for +integral\index{integrals!placement of limits} symbols. + +\item[\opt{nointlimits}] (default) Opposite of \opt{intlimits}. + +\item[\opt{namelimits}] (default) Like \opt{sumlimits}, but for certain +`operator names' such as $\det$, $\inf$, $\lim$, $\max$, $\min$, that +traditionally have subscripts \index{subscripts and +superscripts!placement} placed underneath when they occur in a displayed +equation. + +\item[\opt{nonamelimits}] Opposite of \opt{namelimits}. + +\end{description} + +To use one of these package options, put the option name in the optional +argument of the \cn{usepackage} command\mdash e.g., +\verb"\usepackage[intlimits]{amsmath}". + +The \pkg{amsmath} package also recognizes the following options which +are normally selected (implicitly or explicitly) through the +\cn{documentclass} command, and thus need not be repeated in the option +list of the \cn{usepackage}|{amsmath}| statement. +\begin{description} + +\item[\opt{leqno}] Place equation numbers on the left.\index{equation +numbers!left or right placement} + +\item[\opt{reqno}] Place equation numbers on the right. + +\item[\opt{fleqn}] Position equations at a fixed indent from the left +margin rather than centered in the text column.\index{displayed +equations!centering} + +\end{description} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{Displayed equations} + +\section{Introduction} +The \pkg{amsmath} package provides a number of additional displayed +equation structures\index{displayed + equations}\index{equations|see{displayed equations}} beyond the ones +provided in basic \latex/. The augmented set includes: +\begin{verbatim} + equation equation* align align* + gather gather* flalign flalign* + multline multline* alignat alignat* + split +\end{verbatim} +(Although the standard \env{eqnarray} environment remains available, +it is better to use \env{align} or \env{equation}+\env{split} instead.) + +Except for \env{split}, each environment has both starred and unstarred +forms, where the unstarred forms have automatic numbering using +\latex/'s \env{equation} counter. You can suppress the number on any +particular line by putting \cn{notag} before the \cn{\\}; you can also +override\index{equation numbers!overriding} it with a tag of your own +using \cn{tag}|{|\<label>|}|, where \<label> means arbitrary text such +as |$*$| or |ii| used to \qq{number} the equation. There is also a +\cn{tag*} command that causes the text you supply to be typeset +literally, without adding parentheses around it. \cn{tag} and \cn{tag*} +can also be used within the unnumbered versions of all the \pkg{amsmath} +alignment structures. Some examples of the use of \cn{tag} may be found +in the sample files \fn{testmath.tex} and \fn{subeqn.tex} provided with +the \pkg{amsmath} package. + +The \env{split} environment is a special subordinate form that is used +only \emph{inside} one of the others. It cannot be used inside +\env{multline}, however. + +In the structures that do alignment (\env{split}, \env{align} and +variants), relation symbols have an \verb'&' before them but not +after\mdash unlike \env{eqnarray}. Putting the \verb'&' after the +relation symbol will interfere with the normal spacing; it has to go +before. + +\begin{table}[p] +\caption[]{Comparison of displayed equation environments (vertical lines +indicating nominal margins)}\label{displays} +\renewcommand{\theequation}{\arabic{equation}} +\begin{eqxample} +\begin{verbatim} +\begin{equation*} +a=b +\end{equation*} +\end{verbatim} +\producing +\begin{equation*} +a=b +\end{equation*} +\end{eqxample} + +\begin{eqxample} +\begin{verbatim} +\begin{equation} +a=b +\end{equation} +\end{verbatim} +\producing +\begin{equation} +a=b +\end{equation} +\end{eqxample} + +\begin{eqxample} +\begin{verbatim} +\begin{equation}\label{xx} +\begin{split} +a& =b+c-d\\ + & \quad +e-f\\ + & =g+h\\ + & =i +\end{split} +\end{equation} +\end{verbatim} +\producing +\begin{equation}\label{xx} +\begin{split} +a& =b+c-d\\ + & \quad +e-f\\ + & =g+h\\ + & =i +\end{split} +\end{equation} +\end{eqxample} + +\begin{eqxample} +\begin{verbatim} +\begin{multline} +a+b+c+d+e+f\\ ++i+j+k+l+m+n +\end{multline} +\end{verbatim} +\producing +\begin{multline} +a+b+c+d+e+f\\ ++i+j+k+l+m+n +\end{multline} +\end{eqxample} + +\begin{eqxample} +\begin{verbatim} +\begin{gather} +a_1=b_1+c_1\\ +a_2=b_2+c_2-d_2+e_2 +\end{gather} +\end{verbatim} +\producing +\begin{gather} +a_1=b_1+c_1\\ +a_2=b_2+c_2-d_2+e_2 +\end{gather} +\end{eqxample} + +\begin{eqxample} +\begin{verbatim} +\begin{align} +a_1& =b_1+c_1\\ +a_2& =b_2+c_2-d_2+e_2 +\end{align} +\end{verbatim} +\producing +\begin{align} +a_1& =b_1+c_1\\ +a_2& =b_2+c_2-d_2+e_2 +\end{align} +\end{eqxample} + +\begin{eqxample} +\begin{verbatim} +\begin{align} +a_{11}& =b_{11}& + a_{12}& =b_{12}\\ +a_{21}& =b_{21}& + a_{22}& =b_{22}+c_{22} +\end{align} +\end{verbatim} +\producing +\begin{align} +a_{11}& =b_{11}& + a_{12}& =b_{12}\\ +a_{21}& =b_{21}& + a_{22}& =b_{22}+c_{22} +\end{align} +\end{eqxample} + +\begin{eqxample} +\begin{verbatim} +\begin{flalign*} +a_{11}& =b_{11}& + a_{12}& =b_{12}\\ +a_{21}& =b_{21}& + a_{22}& =b_{22}+c_{22} +\end{flalign*} +\end{verbatim} +\producing +\begin{flalign*} +a_{11}& =b_{11}& + a_{12}& =b_{12}\\ +a_{21}& =b_{21}& + a_{22}& =b_{22}+c_{22} +\end{flalign*} +\end{eqxample} +\end{table} + +\section{Single equations} + +The \env{equation} environment is for a single equation with an +automatically generated number. The \env{equation*} environment is the +same except for omitting the number.% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\footnote{Basic \latex/ doesn't provide an \env{equation*} environment, +but rather a functionally equivalent environment named +\env{displaymath}.} + +\section{Split equations without alignment} + +The \env{multline} environment is a variation of the \env{equation} +environment used for equations that don't fit on a single line. The +first line of a \env{multline} will be at the left margin and the last +line at the right margin, except for an indention on both sides in the +amount of \cn{multlinegap}. Any additional lines in between will be +centered independently within the display width (unless the \opt{fleqn} +option is in effect). + +Like \env{equation}, \env{multline} has only a single equation number +(thus, none of the individual lines should be marked with \cn{notag}). +The equation number is placed on the last line (\opt{reqno} option) or +first line (\opt{leqno} option); vertical centering as for \env{split} +is not supported by \env{multline}. + +It's possible to force one of the middle lines to the left or right with +commands \cn{shoveleft}, \cn{shoveright}. These commands take the entire +line as an argument, up to but not including the final \cn{\\}; for +example +\begin{multline} +\framebox[.65\columnwidth]{A}\\ +\framebox[.5\columnwidth]{B}\\ +\shoveright{\framebox[.55\columnwidth]{C}}\\ +\framebox[.65\columnwidth]{D} +\end{multline} +\begin{verbatim} +\begin{multline} +\framebox[.65\columnwidth]{A}\\ +\framebox[.5\columnwidth]{B}\\ +\shoveright{\framebox[.55\columnwidth]{C}}\\ +\framebox[.65\columnwidth]{D} +\end{multline} +\end{verbatim} + +The value of \cn{multlinegap} can be changed with the usual \latex/ +commands \cn{setlength} or \cn{addtolength}. + +\section{Split equations with alignment} + +Like \env{multline}, the \env{split} environment is for \emph{single} +equations that are too long to fit on one line and hence must be split +into multiple lines. Unlike \env{multline}, however, the \env{split} +environment provides for alignment among the split lines, using |&| to +mark alignment points. Unlike the other \pkg{amsmath} equation +structures, the \env{split} environment provides no numbering, because +it is intended to be used \emph{only inside some other displayed + equation structure}, usually an \env{equation}, \env{align}, or +\env{gather} environment, which provides the numbering. For example: +\begin{equation}\label{e:barwq}\begin{split} +H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2} +\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\ +&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot +\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr]. +\kern-2em % adjust equation body to the right [mjd,13-Nov-1994] +\end{split}\end{equation} + +\begin{verbatim} +\begin{equation}\label{e:barwq}\begin{split} +H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2} +\sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\ +&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot +\Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr]. +\end{split}\end{equation} +\end{verbatim} + +The \env{split} structure should constitute the entire body of the +enclosing structure, apart from commands like \cn{label} that produce no +visible material. + +\section{Equation groups without alignment} + +The \env{gather} environment is used for a group of consecutive +equations when there is no alignment desired among them; each one is +centered separately within the text width (see Table~\ref{displays}). +Equations inside \env{gather} are separated by a \cn{\\} command. +Any equation in a \env{gather} may consist of a \verb'\begin{split}' + \dots\ \verb'\end{split}' structure\mdash for example: +\begin{verbatim} +\begin{gather} + first equation\\ + \begin{split} + second & equation\\ + & on two lines + \end{split} + \\ + third equation +\end{gather} +\end{verbatim} + +\section{Equation groups with mutual alignment} + +The \env{align} environment is used for two or more equations when +vertical alignment is desired; usually binary relations such as equal +signs are aligned (see Table~\ref{displays}). + +To have several equation columns side-by-side, use extra ampersands +to separate the columns: +\begin{align} +x&=y & X&=Y & a&=b+c\\ +x'&=y' & X'&=Y' & a'&=b\\ +x+x'&=y+y' & X+X'&=Y+Y' & a'b&=c'b +\end{align} +% +\begin{verbatim} +\begin{align} +x&=y & X&=Y & a&=b+c\\ +x'&=y' & X'&=Y' & a'&=b\\ +x+x'&=y+y' & X+X'&=Y+Y' & a'b&=c'b +\end{align} +\end{verbatim} +Line-by-line annotations on an equation can be done by judicious +application of \cn{text} inside an \env{align} environment: +\begin{align} +x& = y_1-y_2+y_3-y_5+y_8-\dots + && \text{by \eqref{eq:C}}\\ + & = y'\circ y^* && \text{by \eqref{eq:D}}\\ + & = y(0) y' && \text {by Axiom 1.} +\end{align} +% +\begin{verbatim} +\begin{align} +x& = y_1-y_2+y_3-y_5+y_8-\dots + && \text{by \eqref{eq:C}}\\ + & = y'\circ y^* && \text{by \eqref{eq:D}}\\ + & = y(0) y' && \text {by Axiom 1.} +\end{align} +\end{verbatim} +A variant environment \env{alignat} allows the horizontal space between +equations to be explicitly specified. This environment takes one argument, +the number of \qq{equation columns}: count the maximum number of \verb'&'s +in any row, add 1 and divide by 2. +\begin{alignat}{2} +x& = y_1-y_2+y_3-y_5+y_8-\dots + &\quad& \text{by \eqref{eq:C}}\\ + & = y'\circ y^* && \text{by \eqref{eq:D}}\\ + & = y(0) y' && \text {by Axiom 1.} +\end{alignat} +% +\begin{verbatim} +\begin{alignat}{2} +x& = y_1-y_2+y_3-y_5+y_8-\dots + &\quad& \text{by \eqref{eq:C}}\\ + & = y'\circ y^* && \text{by \eqref{eq:D}}\\ + & = y(0) y' && \text {by Axiom 1.} +\end{alignat} +\end{verbatim} + +\section{Alignment building blocks} + +Like \env{equation}, the multi-equation environments \env{gather}, +\env{align}, and \env{alignat} are designed to produce a structure +whose width is the full line width. This means, for example, that one +cannot readily add parentheses around the entire structure. But variants +\env{gathered}, \env{aligned}, and \env{alignedat} are provided whose +total width is the actual width of the contents; thus they can be used +as a component in a containing expression. E.g., +\begin{equation*} +\left.\begin{aligned} + B'&=-\partial\times E,\\ + E'&=\partial\times B - 4\pi j, +\end{aligned} +\right\} +\qquad \text{Maxwell's equations} +\end{equation*} +\begin{verbatim} +\begin{equation*} +\left.\begin{aligned} + B'&=-\partial\times E,\\ + E'&=\partial\times B - 4\pi j, +\end{aligned} +\right\} +\qquad \text{Maxwell's equations} +\end{equation*} +\end{verbatim} +Like the \env{array} environment, these \texttt{-ed} variants also take +an optional \verb'[t]' or \verb'[b]' argument to specify vertical +positioning. + +\qq{Cases} constructions like the following are common in +mathematics: +\begin{equation}\label{eq:C} +P_{r-j}= + \begin{cases} + 0& \text{if $r-j$ is odd},\\ + r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. + \end{cases} +\end{equation} +and in the \pkg{amsmath} package there is a \env{cases} environment to +make them easy to write: +\begin{verbatim} +P_{r-j}=\begin{cases} + 0& \text{if $r-j$ is odd},\\ + r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. + \end{cases} +\end{verbatim} +Notice the use of \cn{text} (cf.~\secref{text}) and the nested +math formulas. + +\section{Adjusting tag placement} + +Placing equation numbers can be a rather complex problem in multiline +displays. The environments of the \pkg{amsmath} package try hard to +avoid overprinting an equation number on the equation contents, if +necessary moving the number down or up to a separate line. Difficulties +in accurately calculating the profile of an equation can occasionally +result in number movement that doesn't look right. There is a +\cn{raisetag} command provided to adjust the vertical position of the +current equation number, if it has been shifted away from its normal +position. To move a particular number up by six points, write +|\raisetag{6pt}|. This kind of adjustment is fine tuning like line +breaks and page breaks, and should therefore be left undone until your +document is nearly finalized, or you may end up redoing the fine tuning +several times to keep up with changing document contents. + +\section{Vertical spacing and page breaks in multiline displays} + +You can use the \cn{\\}|[|\<dimension>|]| command to get extra vertical +space between lines in all the \pkg{amsmath} displayed equation +environments, as is usual in \latex/. When the \pkg{amsmath} package is +in use \ii{page breaks} between equation lines are normally disallowed; +the philosophy is that page breaks in such material should receive +individual attention from the author. To get an individual page break +inside a particular displayed equation, a \cn{displaybreak} command is +provided. \cn{displaybreak} is best placed immediately before the +\cn{\\} where it is to take effect. Like \latex/'s \cn{pagebreak}, +\cn{displaybreak} takes an optional argument between 0 and 4 denoting +the desirability of the pagebreak. |\displaybreak[0]| means \qq{it is + permissible to break here} without encouraging a break; +\cn{displaybreak} with no optional argument is the same as +|\displaybreak[4]| and forces a break. + +If you prefer a strategy of letting page breaks fall where they may, +even in the middle of a multi-line equation, then you might put +\cn{allowdisplaybreaks}\texttt{[1]} in the preamble of your document. An +optional argument 1\ndash 4 can be used for finer control: |[1]| means +allow page breaks, but avoid them as much as possible; values of 2,3,4 +mean increasing permissiveness. When display breaks are enabled with +\cn{allowdisplaybreaks}, the \cn{\\*} command can be used to prohibit a +pagebreak after a given line, as usual. + +\begin{bfseries} +Note: Certain equation environments wrap their contents in an +unbreakable box, with the consequence that neither \cn{displaybreak} nor +\cn{allowdisplaybreaks} will have any effect on them. These include +\env{split}, \env{aligned}, \env{gathered}, and \env{alignedat}. +\end{bfseries} + +\section{Interrupting a display} + +The command \cn{intertext} is used for a short interjection of one or +two lines of text\index{text fragments inside math} in the middle of a +multiple-line display structure (see also the \cn{text} command in +\secref{text}). Its salient feature is preservation of the alignment, +which would not happen if you simply ended the display and then started +it up again afterwards. \cn{intertext} may only appear right after a +\cn{\\} or \cn{\\*} command. Notice the position of the word \qq{and} in +this example. +\begin{align} +A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'),\\ +A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega),\\ +\intertext{and} +A_3&=\mathcal{N}(\lambda;\omega). +\end{align} +\begin{verbatim} +\begin{align} +A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'),\\ +A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega),\\ +\intertext{and} +A_3&=\mathcal{N}(\lambda;\omega). +\end{align} +\end{verbatim} + +\section{Equation numbering} + +\subsection{Numbering hierarchy} +In \latex/ if you wanted to have equations numbered within +sections\mdash that is, have +equation numbers (1.1), (1.2), \dots, (2.1), (2.2), +\dots, in sections 1, 2, and so forth\mdash you could redefine +\cn{theequation} as suggested in the \latex/ manual \cite[\S6.3, \S +C.8.4]{lamport}: +\begin{verbatim} +\renewcommand{\theequation}{\thesection.\arabic{equation}} +\end{verbatim} + +This works pretty well, except that the equation counter won't be reset +to zero at the beginning of a new section or chapter, unless you do it +yourself using \cn{setcounter}. To make this a little more convenient, +the \pkg{amsmath} package provides a command\index{equation +numbers!hierarchy} \cn{numberwithin}. To have equation numbering tied to +section numbering, with automatic reset of the equation counter, write +\begin{verbatim} +\numberwithin{equation}{section} +\end{verbatim} +As its name implies, the \cn{numberwithin} command can be applied to +any counter, not just the \texttt{equation} counter. + +\subsection{Cross references to equation numbers} + +To make cross-references to equations easier, an \cn{eqref} +command\index{equation numbers!cross-references} is provided. This +automatically supplies the parentheses around the equation number. I.e., +if \verb'\ref{abc}' produces 3.2 then \verb'\eqref{abc}' produces +(3.2). + +\subsection{Subordinate numbering sequences} + +The \pkg{amsmath} package provides also a \env{subequations} +environment\index{equation numbers!subordinate numbering} to make it +easy to number equations in a particular group with a subordinate +numbering scheme. For example +\begin{verbatim} +\begin{subequations} +... +\end{subequations} +\end{verbatim} +causes all numbered equations within that part of the document to be +numbered (4.9a) (4.9b) (4.9c) \dots, if the preceding numbered +equation was (4.8). A \cn{label} command immediately after +\verb/\begin{subequations}/ will produce a \cn{ref} of the parent +number 4.9, not 4.9a. The counters used by the subequations +environment are \verb/parentequation/ and \verb/equation/ and +\cn{addtocounter}, \cn{setcounter}, \cn{value}, etc., can be applied +as usual to those counter names. To get anything other than lowercase +letters for the subordinate numbers, use standard \latex/ methods for +changing numbering style \cite[\S6.3, \S C.8.4]{lamport}. For example, +redefining \cn{theequation} as follows will produce roman numerals. +\begin{verbatim} +\begin{subequations} +\renewcommand{\theequation}{\theparentequation \roman{equation}} +... +\end{verbatim} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\chapter{Miscellaneous mathematical features} + +\section{Matrices}\label{ss:matrix} + +The \pkg{amsmath} package provides some environments for +matrices\index{matrices} beyond the basic \env{array} environment of +\latex/. The \env{pmatrix}, \env{bmatrix}, \env{Bmatrix}, \env{vmatrix} +and \env{Vmatrix} have (respectively) $(\,)$, $[\,]$, $\lbrace\,\rbrace$, +$\lvert\,\rvert$, and +$\lVert\,\rVert$ delimiters built in. For naming consistency there is a +\env{matrix} environment sans delimiters. This is not entirely redundant +with the \env{array} environment; the matrix environments all use more +economical horizontal spacing than the rather prodigal spacing of the +\env{array} environment. Also, unlike the \env{array} environment, you +don't have to give column specifications for any of the matrix +environments; by default you can have up to 10 centered columns.% +\footnote{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +More precisely: The maximum number of columns in a matrix is determined +by the counter |MaxMatrixCols| (normal value = 10), which you can change +if necessary using \latex/'s \cn{setcounter} or \cn{addtocounter} +commands.% +}\space%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +(If you need left or right alignment in a column or other special +formats you must resort to \env{array}.) + +To produce a small matrix suitable for use in text, there is a +\env{smallmatrix} environment (e.g., +\begin{math} +\bigl( \begin{smallmatrix} + a&b\\ c&d +\end{smallmatrix} \bigr) +\end{math}) +that comes closer to fitting within a single text line than a normal +matrix. Delimiters must be provided; there are no |p|,|b|,|B|,|v|,|V| +versions of \env{smallmatrix}. The above example was produced by +\begin{verbatim} +\bigl( \begin{smallmatrix} + a&b\\ c&d +\end{smallmatrix} \bigr) +\end{verbatim} + +\cn{hdotsfor}|{|\<number>|}| produces a row of dots in a +matrix\index{matrices!ellipsis dots}\index{ellipsis dots!in +matrices}\index{dots|see{ellipsis dots}} spanning the given number of +columns. For example, +\begin{center} +\begin{minipage}{.3\columnwidth} +\noindent$\begin{matrix} a&b&c&d\\ +e&\hdotsfor{3} \end{matrix}$ +\end{minipage}% +\qquad +\begin{minipage}{.45\columnwidth} +\begin{verbatim} +\begin{matrix} a&b&c&d\\ +e&\hdotsfor{3} \end{matrix} +\end{verbatim} +\end{minipage}% +\end{center} + +The spacing of the dots can be varied through use of a square-bracket +option, for example, |\hdotsfor[1.5]{3}|. The number in square brackets +will be used as a multiplier (i.e., the normal value is 1.0). +\begin{equation}\label{eq:D} +\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\ +-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\ +\hdotsfor[2]{4}\\ +-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}, +\end{equation} +\begin{verbatim} +\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\ +-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\ +\hdotsfor[2]{4}\\ +-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix} +\end{verbatim} + +\section{Math spacing commands} + +The \pkg{amsmath} package slightly extends the set of math +spacing\index{horizontal space!in math mode} commands, as shown below. +Both the spelled-out and abbreviated forms of these commands are robust, +and they can also be used outside of math. +\begin{ctab}{lll|lll} +Abbrev.& Spelled out& Example & Abbrev.& Spelled out& Example\\ +\hline +\vstrut{2.5ex} +& no space& \spx{}& & no space & \spx{}\\ +\cn{\,}& \cn{thinspace}& \spx{\,}& + \cnbang& \cn{negthinspace}& \spx{\!}\\ +\cn{\:}& \cn{medspace}& \spx{\:}& + & \cn{negmedspace}& \spx{\negmedspace}\\ +\cn{\;}& \cn{thickspace}& \spx{\;}& + & \cn{negthickspace}& \spx{\negthickspace}\\ +& \cn{quad}& \spx{\quad}\\ +& \cn{qquad}& \spx{\qquad} +\end{ctab} +For the greatest possible control over math spacing, use \cn{mspace} +and `math units'. One math unit, or |mu|, is equal to 1/18 em. Thus to +get a negative \cn{quad} you could write |\mspace{-18.0mu}|. + +\section{Dots} + +For preferred placement of ellipsis dots (raised or on-line) in various +contexts there is no general consensus. It may therefore be considered a +matter of taste. By using the semantically oriented commands +\begin{itemize} +\item \cn{dotsc} for \qq{dots with commas} +\item \cn{dotsb} for \qq{dots with binary operators/relations} +\item \cn{dotsm} for \qq{multiplication dots} +\item \cn{dotsi} for \qq{dots with integrals} +\item \cn{dotso} for \qq{other dots} (none of the above) +\end{itemize} +instead of \cn{ldots} and \cn{cdots}, you make it possible for your +document to be adapted to different conventions on the fly, in case (for +example) you have to submit it to a publisher who insists on following +house tradition in this respect. The default treatment for the various +kinds follows American Mathematical Society conventions: +\begin{center} +\begin{tabular}{@{}l@{}l@{}} +\begin{minipage}[t]{.54\textwidth} +\begin{verbatim} +Then we have the series $A_1, A_2, +\dotsc$, the regional sum $A_1 ++A_2 +\dotsb $, the orthogonal +product $A_1 A_2 \dotsm $, and +the infinite integral +\[\int_{A_1}\int_{A_2}\dotsi\]. +\end{verbatim} +\end{minipage} +& +\begin{minipage}[t]{.45\textwidth} +\noindent +Then we have the series $A_1,A_2,\dotsc$, +the regional sum $A_1+A_2+\dotsb$, +the orthogonal product $A_1A_2\dotsm$, +and the infinite integral +\[\int_{A_1}\int_{A_2}\dotsi.\] +\end{minipage} +\end{tabular} +\end{center} + +\section{Nonbreaking dashes} + +A command \cn{nobreakdash} is provided to suppress the possibility +of a linebreak after the following hyphen or dash. For example, if you +write `pages 1\ndash 9' as |pages 1\nobreakdash--9| then a linebreak will +never occur between the dash and the 9. You can also use +\cn{nobreakdash} to prevent undesirable hyphenations in combinations +like |$p$-adic|. For frequent use, it's advisable to make abbreviations, +e.g., +\begin{verbatim} +\newcommand{\p}{$p$\nobreakdash}% for "\p-adic" +\newcommand{\Ndash}{\nobreakdash--}% for "pages 1\Ndash 9" +% For "\n dimensional" ("n-dimensional"): +\newcommand{\n}[1]{$n$\nobreakdash-\hspace{0pt}} +\end{verbatim} +The last example shows how to prohibit a linebreak after the hyphen but +allow normal hyphenation in the following word. (It suffices to add a +zero-width space after the hyphen.) + +\section{Accents in math} + +In ordinary \LaTeX{} the placement of the second accent in doubled math +accents is often poor. With the \pkg{amsmath} package you +will get improved placement of the second accent: +$\hat{\hat{A}}$ (\cn{hat}|{\hat{A}}|). + +The commands \cn{dddot} and \cn{ddddot} are available to produce triple +and quadruple dot accents in addition to the \cn{dot} and \cn{ddot} +accents already available in \latex/. + +To get a superscripted hat or tilde character, load the \pkg{amsxtra} +package and use \cn{sphat} or \cn{sptilde}. Usage is \verb'A\sphat' +(note the absence of the \verb'^' character). + +To place an arbitrary symbol in math accent position, or to get under +accents, see the \pkg{accents} package by Javier Bezos. + +\section{Roots} + +In ordinary \latex/ the placement of root indices is sometimes not so +good: $\sqrt[\beta]{k}$ (|\sqrt||[\beta]{k}|). In the +\pkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust +the position of the root: +\begin{verbatim} + \sqrt[\leftroot{-2}\uproot{2}\beta]{k} +\end{verbatim} +will move the beta up and to the right: +$\sqrt[\leftroot{-2}\uproot{2}\beta]{k}$. The negative argument used +with \cn{leftroot} moves the $\beta$ to the right. The units are a small +amount that is a useful size for such adjustments. + +\section{Boxed formulas} + +The command \cn{boxed} puts a box around its +argument, like \cn{fbox} except that the contents are in math mode: +\begin{equation} +\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))} +\end{equation} +\begin{verbatim} + \boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))} +\end{verbatim} + +\section{Over and under arrows} + +Basic \latex/ provides \cn{overrightarrow} and \cn{overleftarrow} +commands. Some additional over and under arrow commands are provided +by the \pkg{amsmath} package to extend the set: + +\begin{tabbing} +\qquad\=\ncn{overleftrightarrow}\qquad\=\kill +\> \cn{overleftarrow} \> \cn{underleftarrow} \+\\ + \cn{overrightarrow} \> \cn{underrightarrow} \\ + \cn{overleftrightarrow}\> \cn{underleftrightarrow} +\end{tabbing} + +\section{Extensible arrows} + +\cn{xleftarrow} and \cn{xrightarrow} produce +arrows\index{arrows!extensible} that extend automatically to accommodate +unusually wide subscripts or superscripts. These commands take one +optional argument (the subscript) and one mandatory argument (the +superscript, possibly empty): +\begin{equation} +A\xleftarrow{n+\mu-1}B \xrightarrow[T]{n\pm i-1}C +\end{equation} +\begin{verbatim} + \xleftarrow{n+\mu-1}\quad \xrightarrow[T]{n\pm i-1} +\end{verbatim} + +\section{Affixing symbols to other symbols} + +\latex/ provides \cn{stackrel} for placing a +superscript\index{subscripts and superscripts} above a binary relation. +In the \pkg{amsmath} package there are somewhat more general commands, +\cn{overset} and \cn{underset}, that can be used to place one symbol +above or below another symbol, whether it's a relation or something +else. The input |\overset{*}{X}| will place a superscript-size $*$ above +the $X$: $\overset{*}{X}$; \cn{underset} is the analog for adding a +symbol underneath. + +See also the description of \cn{sideset} in \secref{sideset}. + +\section{Fractions and related constructions} + +\subsection{The \cn{frac}, \cn{dfrac}, and \cn{tfrac} commands} + +The \cn{frac} command, which is in the basic command set of +\latex/,\index{fractions} takes two arguments\mdash numerator and +denominator\mdash and typesets them in normal fraction form. The +\pkg{amsmath} package provides also \cn{dfrac} and \cn{tfrac} as +convenient abbreviations for |{\displaystyle\frac| |...| |}| +and\indexcs{textstyle}\relax +\indexcs{displaystyle} |{\textstyle\frac| |...| |}|. +\begin{equation} +\frac{1}{k}\log_2 c(f)\quad\tfrac{1}{k}\log_2 c(f)\quad +\sqrt{\frac{1}{k}\log_2 c(f)}\quad\sqrt{\dfrac{1}{k}\log_2 c(f)} +\end{equation} +\begin{verbatim} +\begin{equation} +\frac{1}{k}\log_2 c(f)\;\tfrac{1}{k}\log_2 c(f)\; +\sqrt{\frac{1}{k}\log_2 c(f)}\;\sqrt{\dfrac{1}{k}\log_2 c(f)} +\end{equation} +\end{verbatim} + +\subsection{The \cn{binom}, \cn{dbinom}, and \cn{tbinom} commands} + +For binomial expressions\index{binomials} such as $\binom{n}{k}$ +\pkg{amsmath} has \cn{binom}, \cn{dbinom} and \cn{tbinom}: +\begin{equation} +2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2} +\end{equation} +\begin{verbatim} +2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2} +\end{verbatim} + +\subsection{The \cn{genfrac} command} + +The capabilities of \cn{frac}, \cn{binom}, and their variants are +subsumed by a generalized fraction command \cn{genfrac} with six +arguments. The last two correspond to \cn{frac}'s numerator and +denominator; the first two are optional delimiters (as seen in +\cn{binom}); the third is a line thickness override (\cn{binom} uses +this to set the fraction line thickness to 0\mdash i.e., invisible); and +the fourth argument is a mathstyle override: integer values 0\ndash 3 select +respectively \cn{displaystyle}, \cn{textstyle}, \cn{scriptstyle}, and +\cn{scriptscriptstyle}. If the third argument is left empty, the line +thickness defaults to `normal'. + +\begin{center}\begin{minipage}{.85\columnwidth} +\raggedright \normalfont\ttfamily \exhyphenpenalty10000 +\newcommand{\ma}[1]{% + \string{{\normalfont\itshape#1}\string}\penalty9999 \ignorespaces} +\string\genfrac \ma{left-delim} \ma{right-delim} \ma{thickness} +\ma{mathstyle} \ma{numerator} \ma{denominator} +\end{minipage}\end{center} +To illustrate, here is how \cn{frac}, \cn{tfrac}, and +\cn{binom} might be defined. +\begin{verbatim} +\newcommand{\frac}[2]{\genfrac{}{}{}{}{#1}{#2}} +\newcommand{\tfrac}[2]{\genfrac{}{}{}{1}{#1}{#2}} +\newcommand{\binom}[2]{\genfrac{(}{)}{0pt}{}{#1}{#2}} +\end{verbatim} +If you find yourself repeatedly using \cn{genfrac} throughout a document +for a particular notation, you will do yourself a favor (and your +publisher) if you define a meaningfully-named abbreviation for that +notation, along the lines of \cn{frac} and \cn{binom}. + +The primitive generalized fraction commands \cs{over}, \cs{overwithdelims}, +\cs{atop}, \cs{atopwithdelims}, \cs{above}, \cs{abovewithdelims} produce +warning messages if used with the \pkg{amsmath} package, for reasons +discussed in \fn{technote.tex}. + +\section{Continued fractions} + +The continued fraction\index{continued fractions} +\begin{equation} +\cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+\cdots +}}} +\end{equation} +can be obtained by typing +{\samepage +\begin{verbatim} +\cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+\dotsb +}}} +\end{verbatim} +}% End of \samepage +This produces better-looking results than straightforward use of +\cn{frac}. Left or right placement of any of the numerators is +accomplished by using \cn{cfrac}|[l]| or \cn{cfrac}|[r]| instead of +\cn{cfrac}. + +\section{Smash options} + +The command \cn{smash} is used to typeset a subformula with an effective height and depth of zero, which is sometimes +useful in adjusting the subformula's position with respect to adjacent +symbols. With the \pkg{amsmath} package \cn{smash} has optional +arguments |t| and |b|, because occasionally it is advantageous to be +able to \qq{smash} only the top or only the bottom of something while +retaining the natural depth or height. For example, when adjacent +radical symbols are unevenly sized or positioned because of differences +in the height and depth of their contents, \cn{smash} can be employed to +make them more consistent. Compare +$\sqrt{x}+\sqrt{y}+\sqrt{z}$ and $\sqrt{x}+\sqrt{\smash[b]{y}}+\sqrt{z}$, +where the latter was produced by +\verb"$\sqrt{x}" \verb"+" +\verb"\sqrt{"\5\verb"\smash[b]{y}}" \verb"+" \verb"\sqrt{z}$". + +\section{Delimiters} + +\subsection{Delimiter sizes}\label{bigdel} + +The automatic delimiter sizing done by \cn{left} and \cn{right} has two +limitations: First, it is applied mechanically to produce delimiters +large enough to encompass the largest contained item, and second, the +range of sizes is not even approximately continuous but has fairly large +quantum jumps. This means that a math fragment that is infinitesimally +too large for a given delimiter size will get the next larger size, a +jump of 3pt or so in normal-sized text. There are two or three +situations where the delimiter size is commonly adjusted, using a set of +commands that have `big' in their names. +\begin{ctab}{l|llllll} +Delimiter& + text& \ncn{left}& \ncn{bigl}& \ncn{Bigl}& \ncn{biggl}& \ncn{Biggl}\\ +size& + size& \ncn{right}& \ncn{bigr}& \ncn{Bigr}& \ncn{biggr}& \ncn{Biggr}\\ +\hline +Result\vstrut{5ex}& + $\displaystyle(b)(\frac{c}{d})$& + $\displaystyle\left(b\right)\left(\frac{c}{d}\right)$& + $\displaystyle\bigl(b\bigr)\bigl(\frac{c}{d}\bigr)$& + $\displaystyle\Bigl(b\Bigr)\Bigl(\frac{c}{d}\Bigr)$& + $\displaystyle\biggl(b\biggr)\biggl(\frac{c}{d}\biggr)$& + $\displaystyle\Biggl(b\Biggr)\Biggl(\frac{c}{d}\Biggr)$ +\end{ctab} +The first kind of situation is a cumulative operator with limits above +and below. With \cn{left} and \cn{right} the delimiters usually turn out +larger than necessary, and using the |Big| or |bigg| +sizes\index{big@\cn{big}, \cn{Big}, \cn{bigg}, \dots\ delimiters} +instead gives better results: +\begin{equation*} +\left[\sum_i a_i\left\lvert\sum_j x_{ij}\right\rvert^p\right]^{1/p} +\quad\text{versus}\quad +\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p} +\end{equation*} +\begin{verbatim} +\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p} +\end{verbatim} +The second kind of situation is clustered pairs of delimiters where +\cn{left} and \cn{right} make them all the same size (because that is +adequate to cover the encompassed material) but what you really want +is to make some of the delimiters slightly larger to make the nesting +easier to see. +\begin{equation*} +\left((a_1 b_1) - (a_2 b_2)\right) +\left((a_2 b_1) + (a_1 b_2)\right) +\quad\text{versus}\quad +\bigl((a_1 b_1) - (a_2 b_2)\bigr) +\bigl((a_2 b_1) + (a_1 b_2)\bigr) +\end{equation*} +\begin{verbatim} +\left((a_1 b_1) - (a_2 b_2)\right) +\left((a_2 b_1) + (a_1 b_2)\right) +\quad\text{versus}\quad +\bigl((a_1 b_1) - (a_2 b_2)\bigr) +\bigl((a_2 b_1) + (a_1 b_2)\bigr) +\end{verbatim} +The third kind of situation is a slightly oversize object in running +text, such as $\left\lvert\frac{b'}{d'}\right\rvert$ where the +delimiters produced by \cn{left} and \cn{right} cause too much line +spreading. In that case \ncn{bigl} and \ncn{bigr}\index{big@\cn{big}, +\cn{Big}, \cn{bigg}, \dots\ delimiters} can be used to produce +delimiters that are slightly larger than the base size but still able to +fit within the normal line spacing: +$\bigl\lvert\frac{b'}{d'}\bigr\rvert$. + +In ordinary \latex/ \ncn{big}, \ncn{bigg}, \ncn{Big}, and \ncn{Bigg} +delimiters aren't scaled properly over the full range of \latex/ font +sizes. With the \pkg{amsmath} package they are. + +\subsection{Vertical bar notations} + +The \pkg{amsmath} package provides commands \cn{lvert}, \cn{rvert}, +\cn{lVert}, \cn{rVert} (compare \cn{langle}, \cn{rangle}) to address the +problem of overloading for the vert bar character \qc{\|}. This +character is currently used in \latex/ documents to represent a wide +variety of mathematical objects: the `divides' relation in a +number-theory expression like $p\vert q$, or the absolute-value +operation $\lvert z\rvert$, or the `such that' condition in set +notation, or the `evaluated at' notation $f_\zeta(t)\bigr\rvert_{t=0}$. +The multiplicity of uses in itself is not so bad; what is bad, however, +is that fact that not all of the uses take the same typographical +treatment, and that the complex discriminatory powers of a knowledgeable +reader cannot be replicated in computer processing of mathematical +documents. It is recommended therefore that there should be a one-to-one +correspondence in any given document between the vert bar character +\qc{\|} and a selected mathematical notation, and similarly for the +double-bar command \ncn{\|}\index{"|@\verb"*+"\"|+}. This immediately +rules out the use of \qc{|} +and \ncn{\|}\index{"|@\verb"*+"\"|+} for delimiters, because left and right +delimiters are distinct usages that do not relate in the same way to +adjacent symbols; recommended practice is therefore to define suitable +commands in the document preamble for any paired-delimiter use of vert +bar symbols: +\begin{verbatim} +\providecommand{\abs}[1]{\lvert#1\rvert} +\providecommand{\norm}[1]{\lVert#1\rVert} +\end{verbatim} +whereupon the document would contain |\abs{z}| to produce $\lvert +z\rvert$ and |\norm{v}| to produce $\lVert v\rVert$. + +\chapter{Operator names} + +\section{Defining new operator names}\label{s:opname} + +Math functions\index{operator names}\relax \index{function +names|see{operator names}} such as $\log$, $\sin$, and $\lim$ are +traditionally typeset in roman type to make them visually more distinct +from one-letter math variables, which are set in math italic. The more +common ones have predefined names, \cn{log}, \cn{sin}, \cn{lim}, and so +forth, but new ones come up all the time in mathematical papers, so the +\pkg{amsmath} package provides a general mechanism for defining new +`operator names'. To define a math function \ncn{xxx} to work like +\cn{sin}, you write +\begin{verbatim} +\DeclareMathOperator{\xxx}{xxx} +\end{verbatim} +whereupon ensuing uses of \ncn{xxx} will produce {\upshape xxx} in the +proper font and automatically add proper spacing\index{horizontal +space!around operator names} on either side when necessary, so that you +get $A\xxx B$ instead of $A\mathrm{xxx}B$. In the second argument of +\cn{DeclareMathOperator} (the name text), a pseudo-text mode prevails: +the hyphen character \qc{\-} will print as a text hyphen rather than a +minus sign and an asterisk \qc{\*} will print as a raised text asterisk +instead of a centered math star. (Compare +\textit{a}-\textit{b}*\textit{c} and $a-b*c$.) But otherwise the name +text is printed in math mode, so that you can use, e.g., subscripts and +superscripts there. + +If the new operator should have subscripts and superscripts placed in +`limits' position above and below as with $\lim$, $\sup$, or $\max$, use +the \qc{\*} form of the \cn{DeclareMathOperator} command: +\begin{verbatim} +\DeclareMathOperator*{\Lim}{Lim} +\end{verbatim} +See also the discussion of subscript placement in +Section~\ref{subplace}. + +The following operator names are predefined: +\begin{ctab}{rlrlrlrl} +\cn{arccos}& $\arccos$ &\cn{deg}& $\deg$ & \cn{lg}& $\lg$ & \cn{projlim}& $\projlim$\\ +\cn{arcsin}& $\arcsin$ &\cn{det}& $\det$ & \cn{lim}& $\lim$ & \cn{sec}& $\sec$\\ +\cn{arctan}& $\arctan$ &\cn{dim}& $\dim$ & \cn{liminf}& $\liminf$ &\cn{sin}& $\sin$\\ +\cn{arg}& $\arg$ & \cn{exp}& $\exp$ & \cn{limsup}& $\limsup$ &\cn{sinh}& $\sinh$\\ +\cn{cos}& $\cos$ & \cn{gcd}& $\gcd$ & \cn{ln}& $\ln$ & \cn{sup}& $\sup$\\ +\cn{cosh}& $\cosh$ & \cn{hom}& $\hom$ & \cn{log}& $\log$ & \cn{tan}& $\tan$\\ +\cn{cot}& $\cot$ & \cn{inf}& $\inf$ & \cn{max}& $\max$ & \cn{tanh}& $\tanh$\\ +\cn{coth}& $\coth$ & \cn{injlim}& $\injlim$ &\cn{min}& $\min$\\ +\cn{csc}& $\csc$ & \cn{ker}& $\ker$ & \cn{Pr}& $\Pr$ +\end{ctab} +\begin{ctab}{rlrl} +\cn{varlimsup}& $\displaystyle\varlimsup$& + \cn{varinjlim}& $\displaystyle\varinjlim$\\ +\cn{varliminf}& $\displaystyle\varliminf$& + \cn{varprojlim}& $\displaystyle\varprojlim$ +\end{ctab} + +There is also a command \cn{operatorname} such that using +\begin{verbatim} +\operatorname{abc} +\end{verbatim} +in a math formula is equivalent to a use of \ncn{abc} defined by +\cn{DeclareMathOperator}. This may be occasionally useful for +constructing more complex notation or other purposes. (Use the variant +\cn{operatorname*} to get limits.) + +\section{\cn{mod} and its relatives} + +Commands \cn{mod}, \cn{bmod}, \cn{pmod}, \cn{pod} are provided to deal +with the special spacing conventions of \qq{mod} notation. \cn{bmod} and +\cn{pmod} are available in \latex/, but with the \pkg{amsmath} package +the spacing of \cn{pmod} will adjust to a smaller value if it's used in +a non-display-mode formula. \cn{mod} and \cn{pod} are variants of +\cn{pmod} preferred by some authors; \cn{mod} omits the parentheses, +whereas \cn{pod} omits the \qq{mod} and retains the parentheses. +\begin{equation} +\gcd(n,m\bmod n);\quad x\equiv y\pmod b; +\quad x\equiv y\mod c;\quad x\equiv y\pod d +\end{equation} +\begin{verbatim} +\gcd(n,m\bmod n);\quad x\equiv y\pmod b; +\quad x\equiv y\mod c;\quad x\equiv y\pod d +\end{verbatim} + +\chapter{The \cn{text} command}\label{text} + +The main use of the command \cn{text} is for words or +phrases\index{text fragments inside math} in a display. It is very +similar to the \latex/ command \cn{mbox} in its effects, but has a +couple of advantages. If you want a word or phrase of text in a +subscript, you can type |..._{\text{word or phrase}}|, which is slightly +easier than the \cn{mbox} equivalent: |..._{\mbox{\scriptsize| |word| +|or| |phrase}}|. The other advantage is the more descriptive name. +\begin{equation} +f_{[x_{i-1},x_i]} \text{ is monotonic,} +\quad i = 1,\dots,c+1 +\end{equation} +\begin{verbatim} +f_{[x_{i-1},x_i]} \text{ is monotonic,} +\quad i = 1,\dots,c+1 +\end{verbatim} + +\chapter{Integrals and sums} + +\section{Multiline subscripts and superscripts} + +The \cn{substack} command can be used to produce a multiline subscript +or superscript:\index{subscripts and superscripts!multi-line}\relax +\index{superscripts|see{subscripts and superscripts}} for example +\begin{ctab}{ll} +\begin{minipage}[t]{.6\columnwidth} +\begin{verbatim} +\sum_{\substack{ + 0\le i\le m\\ + 0<j<n}} + P(i,j) +\end{verbatim} +\end{minipage} +& +$\displaystyle +\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)$ +\end{ctab} +A slightly more generalized form is the \env{subarray} environment which +allows you to specify that each line should be left-aligned instead of +centered, as here: +\begin{ctab}{ll} +\begin{minipage}[t]{.6\columnwidth} +\begin{verbatim} +\sum_{\begin{subarray}{l} + i\in\Lambda\\ 0<j<n + \end{subarray}} + P(i,j) +\end{verbatim} +\end{minipage} +& +$\displaystyle + \sum_{\begin{subarray}{l} + i\in \Lambda\\ 0<j<n + \end{subarray}} + P(i,j)$ +\end{ctab} + +\section{The \cn{sideset} command}\label{sideset} + +There's also a command called \cn{sideset}, for a rather special +purpose: putting symbols at the subscript and +superscript\index{subscripts and superscripts!on sums} corners of a +large operator symbol such as $\sum$ or $\prod$. \emph{Note: this +command is not designed to be applied to anything other than sum-class symbols.} The prime +example is the case when you want to put a prime on a sum symbol. If +there are no limits above or below the sum, you could just use +\cn{nolimits}: here's +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +|\sum\nolimits' E_n| in display mode: +\begin{equation} +\sum\nolimits' E_n +\end{equation} +If, however, you want not only the prime but also something below or +above the sum symbol, it's not so easy\mdash indeed, without +\cn{sideset}, it would be downright difficult. With \cn{sideset}, you +can write +\begin{ctab}{ll} +\begin{minipage}[t]{.6\columnwidth} +\begin{verbatim} +\sideset{}{'} + \sum_{n<k,\;\text{$n$ odd}} nE_n +\end{verbatim} +\end{minipage} +&$\displaystyle +\sideset{}{'}\sum_{n<k,\;\text{$n$ odd}} nE_n +$ +\end{ctab} +The extra pair of empty braces is explained by the fact that +\cn{sideset} has the capability of putting an extra symbol or symbols at +each corner of a large operator; to put an asterisk at each corner of a +product symbol, you would type +\begin{ctab}{ll} +\begin{minipage}[t]{.6\columnwidth} +\begin{verbatim} +\sideset{_*^*}{_*^*}\prod +\end{verbatim} +\end{minipage} +&$\displaystyle +\sideset{_*^*}{_*^*}\prod +$ +\end{ctab} + +\section{Placement of subscripts and limits}\label{subplace} + +The default positioning for subscripts depends on the +base symbol involved. The default for sum-class symbols is +`displaylimits' positioning: When a sum-class symbol appears +in a displayed formula, subscript and superscript are placed in `limits' +position above and below, but in an inline formula, they are placed to +the side, to avoid unsightly and wasteful spreading of the +surrounding text lines. +The default for integral-class symbols is to have sub- and +superscripts always to the side, even in displayed formulas. +(See the discussion of the \opt{intlimits} and related options in +Section~\ref{options}.) + +Operator names such as $\sin$ or $\lim$ may have either `displaylimits' +or `limits' positioning depending on how they were defined. The standard +operator names are defined according to normal mathematical usage. + +The commands \cn{limits} and \cn{nolimits} can be used to override the +normal behavior of a base symbol: +\begin{equation*} +\sum\nolimits_X,\qquad \iint\limits_{A}, +\qquad\varliminf\nolimits_{n\to \infty} +\end{equation*} +To define a command whose subscripts follow the +same `displaylimits' behavior as \cn{sum}, put +\cn{displaylimits} at the tail end of the definition. When multiple +instances of \cn{limits}, \cn{nolimits}, or \cn{displaylimits} occur +consecutively, the last one takes precedence. + +\section{Multiple integral signs} + +\cn{iint}, \cn{iiint}, and \cn{iiiint} give multiple integral +signs\index{integrals!multiple} with the spacing between them nicely +adjusted, in both text and display style. \cn{idotsint} is an extension +of the same idea that gives two integral signs with dots between them. +\begin{gather} +\iint\limits_A f(x,y)\,dx\,dy\qquad\iiint\limits_A +f(x,y,z)\,dx\,dy\,dz\\ +\iiiint\limits_A +f(w,x,y,z)\,dw\,dx\,dy\,dz\qquad\idotsint\limits_A f(x_1,\dots,x_k) +\end{gather} + +\chapter{Commutative diagrams}\label{s:commdiag} + +Some commutative diagram commands like the ones in \amstex/ are +available as a separate package, \pkg{amscd}. For complex commutative +diagrams authors will need to turn to more comprehensive packages like +\pkg{kuvio} or \xypic/, but for simple diagrams without diagonal +arrows\index{arrows!in commutative diagrams} the \pkg{amscd} commands +may be more convenient. Here is one example. +\begin{equation*} +\begin{CD} +S^{{\mathcal{W}}_\Lambda}\otimes T @>j>> T\\ +@VVV @VV{\End P}V\\ +(S\otimes T)/I @= (Z\otimes T)/J +\end{CD} +\end{equation*} +\begin{verbatim} +\begin{CD} +S^{{\mathcal{W}}_\Lambda}\otimes T @>j>> T\\ +@VVV @VV{\End P}V\\ +(S\otimes T)/I @= (Z\otimes T)/J +\end{CD} +\end{verbatim} +In the \env{CD} environment the commands |@>>>|, +|@<<<|, |@VVV|, and |@AAA| give respectively right, left, down, and up +arrows. For the horizontal arrows, material between the first and second +|>| or |<| symbols will be typeset as a superscript, and material +between the second and third will be typeset as a subscript. Similarly, +material between the first and second or second and third |A|s or |V|s +of vertical arrows will be typeset as left or right \qq{sidescripts}. +The commands |@=| and \verb'@|' give horizontal and vertical double lines. +A \qq{null arrow} command |@.| can be used instead of a visible arrow +to fill out an array where needed. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{Using math fonts} + +\section{Introduction} + +For more comprehensive information on font use in \latex/, see the +\latex/ font guide (\fn{fntguide.tex}) or \booktitle{The \latex/ +Companion} \cite{tlc}. The basic set of math font commands\index{math +fonts}\relax \index{math symbols|see{math fonts}} in \latex/ includes +\cn{mathbf}, \cn{mathrm}, \cn{mathcal}, \cn{mathsf}, \cn{mathtt}, +\cn{mathit}. Additional math alphabet commands such as +\cn{mathbb} for blackboard bold, \cn{mathfrak} for Fraktur, and +\cn{mathscr} for Euler script are available through the packages +\pkg{amsfonts} and \pkg{euscript} (distributed separately). + +\section{Recommended use of math font commands} + +If you find yourself employing math font commands frequently in your +document, you might wish that they had shorter names, such as \ncn{mb} +instead of \cn{mathbf}. Of course, there is nothing to keep you from +providing such abbreviations for yourself by suitable \cn{newcommand} +statements. But for \latex/ to provide shorter names would actually be a +disservice to authors, as that would obscure a much better alternative: +defining custom command names derived from the names of the underlying +mathematical objects, rather than from the names of the fonts used to +distinguish the objects. For example, if you are using bold to indicate +vectors, then you will be better served in the long run if you define a +`vector' command instead of a `math-bold' command: +\begin{verbatim} + \newcommand{\vect}[1]{\mathbf{#1}} +\end{verbatim} +you can write |\vect{a} + \vect{b}| to produce $\vect{a} + +\vect{b}$. +If you decide several months down the road that you want to use the bold +font for some other purpose, and mark vectors by a small over-arrow +instead, then you can put the change into effect merely by changing the +definition of \ncn{vect}; otherwise you would have to replace all +occurrences of \cn{mathbf} throughout your document, perhaps even +needing to inspect each one to see whether it is indeed +an instance of a vector. + +It can also be useful to assign distinct +command names for different letters of a particular font: +\begin{verbatim} +\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}% or use amsfonts package +\DeclareMathSymbol{\C}{\mathalpha}{AMSb}{"43} +\DeclareMathSymbol{\R}{\mathalpha}{AMSb}{"52} +\end{verbatim} +These statements would define the commands \cn{C} and \cn{R} to produce +blackboard-bold letters from the `AMSb' math symbols font. If you refer +often to the\break complex numbers or real numbers in your document, you +might find this method more convenient than (let's say) defining a +\ncn{field} command and writing\break |\field{C}|, |\field{R}|. But for +maximum flexibility and control, define such a \ncn{field} command and +then define \ncn{C} and \ncn{R} in terms of that +command:\indexcs{mathbb} +\begin{verbatim} +\usepackage{amsfonts}% to get the \mathbb alphabet +\newcommand{\field}[1]{\mathbb{#1}} +\newcommand{\C}{\field{C}} +\newcommand{\R}{\field{R}} +\end{verbatim} + +\section{Bold math symbols} + +The \cn{mathbf} command is commonly used to obtain bold Latin letters in +math, but for most other kinds of math symbols it has no effect, or its +effects depend unreliably on the set of math fonts that are in use. For +example, writing +\begin{verbatim} +\Delta \mathbf{\Delta}\mathbf{+}\delta \mathbf{\delta} +\end{verbatim} +produces $\Delta \mathbf{\Delta}\mathbf{+}\delta +\mathbf{\delta}$; the \cn{mathbf} has no effect on the plus +sign or the small delta. + +The \pkg{amsmath} package therefore provides two additional commands, +\cn{boldsymbol} and \cn{pmb}, that can be applied to other kinds of math +symbols. \cn{boldsymbol} can be used for a math symbol that remains +unaffected by \cn{mathbf} if (and only if) your current math font set +includes a bold version of that symbol. \cn{pmb} can be used as a last +resort for any math symbols that do not have a true bold version +provided by your set of math fonts; \qq{pmb} stands for \qq{poor man's +bold} and the command works by typesetting multiple copies of the symbol +with slight offsets. The quality of the output is inferior, especially +for symbols that contain any hairline strokes. When the standard default set of +\latex/ math fonts are in use (Computer Modern), the only symbols that +are likely to require \cn{pmb} are large operator symbols like \cn{sum}, +extended delimiter symbols, or the extra math symbols provided by +the \pkg{amssymb} package \cite{amsfonts}. + +The following formula shows some of the results that are possible: +\begin{verbatim} +A_\infty + \pi A_0 +\sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+} + \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}} +\sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}} +\end{verbatim} +\begin{equation*} +A_\infty + \pi A_0 +\sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+} + \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}} +\sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}} +\end{equation*} +If you want to use only the \cn{boldsymbol} command without loading the +whole \pkg{amsmath} package, the \pkg{bm} package is recommended (this +is a standard \latex/ package, not an AMS package; you probably have it +already if you have a 1997 or newer version of \latex/). + +\section{Italic Greek letters} + +For italic versions of the capital Greek letters, the following commands +are provided: +\begin{ctab}{rlrl} +\cn{varGamma}& $\varGamma$& \cn{varSigma}& $\varSigma$\\ +\cn{varDelta}& $\varDelta$& \cn{varUpsilon}& $\varUpsilon$\\ +\cn{varTheta}& $\varTheta$& \cn{varPhi}& $\varPhi$\\ +\cn{varLambda}& $\varLambda$& \cn{varPsi}& $\varPsi$\\ +\cn{varXi}& $\varXi$& \cn{varOmega}& $\varOmega$\\ +\cn{varPi}& $\varPi$ +\end{ctab} + +\chapter{Error messages and output problems} + +\section{General remarks} + +This is a supplement to Chapter~8 of the \latex/ manual \cite{lamport} (first +edition: Chapter~6). For the reader's convenience, the set of error +messages discussed here overlaps somewhat with the set in that chapter, +but please be aware that we don't provide exhaustive coverage here. +The error messages are arranged in alphabetical order, disregarding +unimportant text such as |! LaTeX Error:| at the beginning, and +nonalphabetical characters such as \qc{\\}. Where examples are given, we +show also the help messages that appear on screen when you respond to an +error message prompt by entering |h|. + +There is also a section discussing some output errors, i.e., instances +where the printed document has something wrong but there was no \latex/ +error during typesetting. + +\section{Error messages} + +\begin{error}{\begin{split} won't work here.} +\errexa +\begin{verbatim} +! Package amsmath Error: \begin{split} won't work here. + ... + +l.8 \begin{split} + +? h +\Did you forget a preceding \begin{equation}? +If not, perhaps the `aligned' environment is what you want. +? +\end{verbatim} +\errexpl +The \env{split} environment does not construct a stand-alone displayed +equation; it needs to be used within some other environment such as +\env{equation} or \env{gather}. + +\end{error} + +\begin{error}{Extra & on this line} +\errexa +\begin{verbatim} +! Package amsmath Error: Extra & on this line. + +See the amsmath package documentation for explanation. +Type H <return> for immediate help. + ... + +l.9 \end{alignat} + +? h +\An extra & here is so disastrous that you should probably exit + and fix things up. +? +\end{verbatim} +\errexpl +In an \env{alignat} structure the number of alignment points per line +is dictated by the numeric argument given after |\begin{alignat}|. +If you use more alignment points in a line it is assumed that you +accidentally left out a newline command \cn{\\} and the above error is +issued. +\end{error} + +\begin{error}{Improper argument for math accent} +\errexa +\begin{verbatim} +! Package amsmath Error: Improper argument for math accent: +(amsmath) Extra braces must be added to +(amsmath) prevent wrong output. + +See the amsmath package documentation for explanation. +Type H <return> for immediate help. + ... + +l.415 \tilde k_{\lambda_j} = P_{\tilde \mathcal + {M}} +? +\end{verbatim} +\errexpl +Non-simple arguments for any \LaTeX{} command should be enclosed in +braces. In this example extra braces are needed as follows: +\begin{verbatim} +... P_{\tilde{\mathcal{M}}} +\end{verbatim} +\end{error} + +\begin{error}{Font OMX/cmex/m/n/7=cmex7 not loadable ...} +\errexa +\begin{verbatim} +! Font OMX/cmex/m/n/7=cmex7 not loadable: Metric (TFM) file not found. +<to be read again> + relax +l.8 $a + b+b^2$ +? h +I wasn't able to read the size data for this font, +so I will ignore the font specification. +[Wizards can fix TFM files using TFtoPL/PLtoTF.] +You might try inserting a different font spec; +e.g., type `I\font<same font id>=<substitute font name>'. +? +\end{verbatim} +\errexpl +Certain extra sizes of some Computer Modern fonts that were formerly +available mainly through the AMSFonts\index{AMSFonts collection} +distribution are considered part of standard \latex/ (as of June 1994): +\fn{cmex7}\ndash \texttt{9}, \fn{cmmib5}\ndash \texttt{9}, and +\fn{cmbsy5}\ndash \texttt{9}. If these extra sizes are missing on your +system, you should try first to get them from the source where you +obtained \latex/. If that fails, you could try getting the fonts from +CTAN (e.g., in the form of Metafont\index{Metafont source files} source +files, directory \nfn{/tex-archive/fonts/latex/mf}, or in PostScript +Type 1 format, directory +\nfn{/tex-archive/fonts/cm/ps-type1/bakoma}\index{BaKoMa fonts}\relax +\index{PostScript fonts}). + +If the font name begins with \fn{cmex}, there is a special option +\fn{cmex10} for the \pkg{amsmath} package that provides a temporary +workaround. I.e., change the \cn{usepackage} to +\begin{verbatim} +\usepackage[cmex10]{amsmath} +\end{verbatim} +This will force the use of the 10-point size of the \fn{cmex} font in +all cases. Depending on the contents of your document this may be +adequate. +\end{error} + +\begin{error}{Math formula deleted: Insufficient extension fonts} +\errexa +\begin{verbatim} +! Math formula deleted: Insufficient extension fonts. +l.8 $ab+b^2$ + +? +\end{verbatim} +\errexpl +This usually follows a previous error |Font ... not loadable|; see the +discussion of that error (above) for solutions. +\end{error} + +\begin{error}{Missing number, treated as zero} +\errexa +\begin{verbatim} +! Missing number, treated as zero. +<to be read again> + a +l.100 \end{alignat} + +? h +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +? +\end{verbatim} +\errexpl +There are many possibilities that can lead to this error. However, one +possibility that is relevant for the \pkg{amsmath} package is that you +forgot to give the number argument of an \env{alignat} environment, as +in: +\begin{verbatim} +\begin{alignat} + a& =b& c& =d\\ +a'& =b'& c'& =d' +\end{alignat} +\end{verbatim} +where the first line should read instead +\begin{verbatim} +\begin{alignat}{2} +\end{verbatim} + +Another possibility is that you have a left bracket character |[| +following a linebreak command \cn{\\} in a multiline construction such +as \env{array}, \env{tabular}, or \env{eqnarray}. This will be +interpreted by \latex/ as the beginning of an `additional vertical +space' request \cite[\S C.1.6]{lamport}, even if it occurs on the following +line and is intended to be part of the contents. For example +\begin{verbatim} +\begin{array} +a+b\\ +[f,g]\\ +m+n +\end{array} +\end{verbatim} +To prevent the error message in such a case, you can +add braces as discussed in the \latex/ manual \cite[\S C.1.1]{lamport}: +\begin{verbatim} +\begin{array} +a+b\\ +{[f,g]}\\ +m+n +\end{array} +\end{verbatim} + +\end{error} + +\begin{error}{Missing \right. inserted} +\errexa +\begin{verbatim} +! Missing \right. inserted. +<inserted text> + \right . +l.10 \end{multline} + +? h +I've inserted something that you may have forgotten. +(See the <inserted text> above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. +\end{verbatim} +\errexpl +This error typically arises when you try to insert a linebreak inside a +\cn{left}-\cn{right} pair of delimiters in a \env{multline} or +\env{split} environment: +\begin{verbatim} +\begin{multline} +AAA\left(BBB\\ + CCC\right) +\end{multline} +\end{verbatim} +There are two possible solutions: (1)~instead of using \cn{left} and +\cn{right}, use `big' delimiters of fixed size (\cn{bigl} \cn{bigr} +\cn{biggl} \cn{biggr} \dots; see \secref{bigdel}); or (2)~use null +delimiters to break up the \cn{left}-\cn{right} pair into parts for each +line: +\begin{verbatim} +AAA\left(BBB\right.\\ + \left.CCC\right) +\end{verbatim} +The latter solution may result in mismatched delimiter sizes; +ensuring that they match requires using \cn{vphantom} in the line +that has the smaller delimiter (or possibly \cn{smash} in the line that +has the larger delimiter). In the argument of \cn{vphantom} put a copy +of the tallest element that occurs in the other line, e.g., +\begin{verbatim} +xxx \left(\int_t yyy\right.\\ + \left.\vphantom{\int_t} zzz ... \right) +\end{verbatim} +\end{error} + +\begin{error}{Paragraph ended before \xxx was complete} +\errexa +\begin{verbatim} +Runaway argument? + +! Paragraph ended before \multline was complete. +<to be read again> + \par +l.100 + +? h +I suspect you've forgotten a `}', causing me to apply this +control sequence to too much text. How can we recover? +My plan is to forget the whole thing and hope for the best. +? +\end{verbatim} +\errexpl +This might be produced by a misspelling in the |\end{multline}| command, +e.g., +\begin{verbatim} +\begin{multline} +... +\end{multiline} +\end{verbatim} +or by using abbreviations for certain environments, such as |\bal| and +|\eal| for |\begin{align}| and |\end{align}|: +\begin{verbatim} +\bal +... +\eal +\end{verbatim} +For technical reasons that kind of abbreviation does not work with +the more complex displayed equation environments of the \pkg{amsmath} package +(\env{gather}, \env{align}, \env{split}, etc.; cf.\@ \fn{technote.tex}). +\end{error} + +\begin{error}{Runaway argument?} +See the discussion for the error message +\texttt{Paragraph ended before \ncn{xxx} was complete}. +\end{error} + +\begin{error}{Unknown option `xxx' for package `yyy'} +\errexa +\begin{verbatim} +! LaTeX Error: Unknown option `intlim' for package `amsmath'. +... +? h +The option `intlim' was not declared in package `amsmath', perhaps you +misspelled its name. Try typing <return> to proceed. +? +\end{verbatim} +\errexpl +This means that you misspelled the option name, or the package simply +does not have an option that you expected it to have. Consult the +documentation for the given package. +\end{error} + +\begin{error}{Old form `\pmatrix' should be \begin{pmatrix}.} +\errexa +\begin{verbatim} +! Package amsmath Error: Old form `\pmatrix' should be + \begin{pmatrix}. + +See the amsmath package documentation for explanation. +Type H <return> for immediate help. + ... + +\pmatrix ->\left (\matrix@check \pmatrix + \env@matrix +l.16 \pmatrix + {a&b\cr c&d\cr} +? h +`\pmatrix{...}' is old Plain-TeX syntax whose use is +ill-advised in LaTeX. +? +\end{verbatim} +\errexpl +When the \pkg{amsmath} package is used, the old forms of \cn{pmatrix}, +\cn{matrix}, and \cn{cases} cannot be used any longer because of naming +conflicts. Their syntax did not conform with standard \LaTeX{} syntax +in any case. +\end{error} + +\begin{error}{Erroneous nesting of equation structures} +\errexa +\begin{verbatim} +! Package amsmath Error: Erroneous nesting of equation structures; +(amsmath) trying to recover with `aligned'. + +See the amsmath package documentation for explanation. +Type H <return> for immediate help. + ... + +l.260 \end{alignat*} + \end{equation*} +\end{verbatim} +\errexpl +The structures \env{align}, \env{alignat}, etc., are designed +for top-level use and for the most part cannot be nested inside some +other displayed equation structure. The chief exception is that +\env{align} and most of its variants can be used inside the +\env{gather} environment. +\end{error} + +\section{Warning messages} + +\begin{error}{Foreign command \over [or \atop or \above]} +\errexa +\begin{verbatim} +Package amsmath Warning: Foreign command \over; \frac or \genfrac +(amsmath) should be used instead. +\end{verbatim} +\errexpl The primitive generalized fraction commands of \tex/\mdash +\cs{over}, \cs{atop}, \cs{above}\mdash are deprecated when the +\pkg{amsmath} package is used because their syntax is foreign to \latex/ +and \pkg{amsmath} provides native \latex/ equivalents. See +\fn{technote.tex} for further information. +\end{error} + +\begin{error}{Cannot use `split' here} +\errexa +\begin{verbatim} +Package amsmath Warning: Cannot use `split' here; +(amsmath) trying to recover with `aligned' +\end{verbatim} +\errexpl The \env{split} environment is designed to serve as the entire +body of an equation, or an entire line of an \env{align} or \env{gather} +environment. There cannot be any printed material before or +after it within the same enclosing structure: +\begin{verbatim} +\begin{equation} +\left\{ % <-- Not allowed +\begin{split} +... +\end{split} +\right. % <-- Not allowed +\end{equation} +\end{verbatim} +\end{error} + +\section{Wrong output} + +\subsection{Section numbers 0.1, 5.1, 8.1 instead of 1, 2, 3} +\label{numinverse} + +This most likely means that you have the arguments for \cn{numberwithin} +in reverse order: +\begin{verbatim} +\numberwithin{section}{equation} +\end{verbatim} +That means `print the section number as \textit{equation +number}.\textit{section number} and reset to 1 every time an equation +occurs' when what you probably wanted was the inverse +\begin{verbatim} +\numberwithin{equation}{section} +\end{verbatim} + +\subsection{The \cn{numberwithin} command had no effect on equation +numbers} + +Are you looking at the first section in your document? Check the section +numbers elsewhere to see if the problem is the one described in +\secref{numinverse}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\chapter{Additional information} + +\section{Converting existing documents} + +\subsection{Converting from plain \LaTeX{}} + +A \LaTeX{} document will typically continue to work the same in most +respects if \verb'\usepackage{amsmath}' is added in the document +preamble. By default, however, the \pkg{amsmath} package suppresses page +breaks inside multiple-line displayed equation structures such as +\env{eqnarray}, \env{align}, and \env{gather}. To continue allowing page +breaks inside \env{eqnarray} after switching to \pkg{amsmath}, you will +need to add the following line in your document preamble: +\begin{verbatim} +\allowdisplaybreaks[1] +\end{verbatim} +To ensure normal spacing around relation symbols, you might also want to +change \env{eqnarray} to \env{align}, \env{multline}, or +\env{equation}\slash\env{split} as appropriate. + +Most of the other differences in \pkg{amsmath} usage can be considered +optional refinements, e.g., using +\begin{verbatim} +\DeclareMathOperator{\Hom}{Hom} +\end{verbatim} +instead of \verb'\newcommand{\Hom}{\mbox{Hom}}'. + +\subsection{Converting from \amslatex/ 1.1} +See \fn{diffs-m.txt}. + +\section{Technical notes} +The file \fn{technote.tex} contains some remarks on miscellaneous +technical questions that are less likely to be of general interest. + +\section{Getting help} + +Questions or comments regarding \pkg{amsmath} and related packages +should be sent to: +\begin{infoaddress} +American Mathematical Society\\ +Technical Support\\ +Electronic Products and Services\\ +P. O. Box 6248\\ +Providence, RI 02940\\[3pt] +Phone: 800-321-4AMS (321-4267) \quad or \quad 401-455-4080\\ +Internet: \mail{tech-support@ams.org} +\end{infoaddress} +If you are reporting a problem you should include +the following information to make proper investigation possible: +\begin{enumerate} +\item The source file where the problem occurred, preferably reduced + to minimum size by removing any material that can be removed without + affecting the observed problem. +\item A \latex/ log file showing the error message (if applicable) and + the version numbers of the document class and option files being used. +\end{enumerate} + +\section{Of possible interest}\label{a:possible-interest} +Information about obtaining AMSFonts or other \tex/-related +software from the AMS Internet archive \fn{e-math.ams.org} +can be obtained by sending a request through electronic mail to: +\mail{webmaster@ams.org}. + +Information about obtaining the \pkg{amsmath} distribution on diskette +from the AMS is available from: +\begin{infoaddress} +American Mathematical Society\\ +Customer Services\\ +P. O. Box 6248\\ +Providence, RI 02940\\[3pt] +Phone: 800-321-4AMS (321-4267) \quad or \quad 401-455-4000\\ +Internet: \mail{cust-serv@ams.org} +\end{infoaddress} + +The \tex/ Users Group\index{TeX Users@\tex/ Users Group} is a nonprofit +organization that publishes a journal +(\journalname{TUGboat}\index{TUGboat@\journalname{TUGboat}}), holds +meetings, and serves as a clearing-house of general information about +\tex/ and \tex/-related software. +\begin{infoaddress} +\tex/ Users Group\\ +PO Box 2311\\ +Portland, OR 97208-2311\\ +USA\\[3pt] +Phone: +1-503-223-9994\\ +Email: \mail{office@tug.org} +\end{infoaddress} +Membership in the \tex/ Users Group is a good way to support continued +development of free \tex/-related software. There are also many local +\tex/ user groups in other countries; information about contacting a +local user group can be gotten from the \tex/ Users Group. + +There is a Usenet newsgroup called \fn{comp.text.tex} that is a fairly +good source of information about \latex/ and \tex/ in general. If you +don't know about reading newsgroups, check with your local system +administrator to see if newsgroup service is available at your site. + +\begin{thebibliography}{9} +\addcontentsline{toc}{chapter}{Bibliography} + +\bibitem{amsfonts}\booktitle{AMSFonts version \textup{2.2}\mdash user's guide}, +Amer. Math. Soc., Providence, RI, 1994; distributed +with the AMSFonts package. + +\bibitem{instr-l}\booktitle{Instructions for preparation of +papers and monographs\mdash \amslatex/}, +Amer. Math. Soc., Providence, RI, 1996, 1999. + +\bibitem{amsthdoc}\booktitle{Using the \pkg{amsthm} Package}, +Amer. Math. Soc., Providence, RI, 1999. + +\bibitem{tlc} Michel Goossens, Frank Mittelbach, and Alexander Samarin, +\booktitle{The \latex/ companion}, Addison-Wesley, Reading, MA, 1994. + [\emph{Note: The 1994 edition is not a reliable guide for the + \pkg{amsmath} package unless you refer to the errata for Chapter + 8\mdash file \fn{compan.err}, distributed with \LaTeX{}.}] + +% Deal with a line breaking problem +\begin{raggedright} +\bibitem{mil} G. Gr\"{a}tzer, +\emph{Math into \LaTeX{}: An Introduction to \LaTeX{} and AMS-\LaTeX{}} + \url{http://www.ams.org/cgi-bin/bookstore/bookpromo?fn=91&arg1=bookvideo&itmc=MLTEX}, +Birkh\"{a}user, Boston, 1995.\par +\end{raggedright} + +\bibitem{kn} Donald E. Knuth, \booktitle{The \tex/book}, +Addison-Wesley, Reading, MA, 1984. + +\bibitem{lamport} Leslie Lamport, \booktitle{\latex/: A document preparation +system}, 2nd revised ed., Addison-Wesley, Reading, MA, 1994. + +\bibitem{msf} Frank Mittelbach and Rainer Sch\"opf, +\textit{The new font family selection\mdash user +interface to standard \latex/}, \journalname{TUGboat} \textbf{11}, +no.~2 (June 1990), pp.~297\ndash 305. + +\bibitem{jt} Michael Spivak, \booktitle{The joy of \tex/}, 2nd revised ed., +Amer. Math. Soc., Providence, RI, 1990. + +\end{thebibliography} + +\begin{theindex} + + \item {\normalfont \ttfamily \bslchar \qcbang }, 11 + \item \verb*+\,+, 11 + \item \verb*+\:+, 11 + \item \verb*+\;+, 11 + \item \verb*+\\+, 3, 5, 6, 8, 9, 24, 26 + \item \verb*+\\*+, 9 + \item \verb*+\|+, 16 + + \indexspace + + \item \verb*+\above+, 14, 29 + \item \verb*+\abovewithdelims+, 14 + \item \verb*+\accentedsymbol+, 2 + \item \texttt{accents} package, 12 + \item \verb*+\addtocounter+, 10 + \item \verb*+\addtolength+, 5 + \item \texttt{align} environment, 3, 5--7, 28--30 + \item \texttt{alignat} environment, 7, 24, 26, 29 + \item \texttt{aligned} environment, 7, 9 + \item \texttt{alignedat} environment, 7, 9 + \item \verb*+\allowdisplaybreaks+, 8, 9 + \item \texttt{amsart} class, 1 + \item \texttt{amsbook} class, 1 + \item \texttt{amsbsy} package, 1, 2 + \item \texttt{amscd} package, 1, 2, 20 + \item \texttt{amsfonts} package, 21 + \item AMSFonts collection, 25 + \item \texttt{amsmath} package, i, 1--3, 5, 8--18, 22, 23, 25, 26, + 28--32 + \item \texttt{amsopn} package, 1, 2 + \item \texttt{amssymb} package, 22 + \item \texttt{amstext} package, 1, 2 + \item \texttt{amsthm} package, 1, 32 + \item \texttt{amsxtra} package, 1, 2, 12 + \item \verb*+\arccos+, 18 + \item \verb*+\arcsin+, 18 + \item \verb*+\arctan+, 18 + \item \verb*+\arg+, 18 + \item \texttt{array} environment, 8, 10, 26 + \item arrows + \subitem extensible, 13 + \subitem in commutative diagrams, 20 + \item \verb*+\atop+, 14, 29 + \item \verb*+\atopwithdelims+, 14 + + \indexspace + + \item BaKoMa fonts, 25 + \item \cn{big}, \cn{Big}, \cn{bigg}, \dots\ delimiters, 16 + \item \verb*+\biggl+, 27 + \item \verb*+\biggr+, 27 + \item \verb*+\bigl+, 27 + \item \verb*+\bigr+, 27 + \item \verb*+\binom+, 14 + \item binomials, 14 + \item \texttt{bm} package, 2, 23 + \item \texttt{Bmatrix} environment, 10 + \item \texttt{bmatrix} environment, 10 + \item \verb*+\bmod+, 18 + \item \verb*+\boldsymbol+, 22, 23 + \item \verb*+\boxed+, 13 + + \indexspace + + \item \verb*+\C+, 22 + \item \texttt{cases} environment, 8 + \item \verb*+\cases+, 28 + \item \texttt{CD} environment, 2, 21 + \item \verb*+\cdots+, 12 + \item \texttt{centertags} option, 2 + \item \verb*+\cfrac+, 15 + \item \texttt{cmbsy5}, 25 + \item \texttt{cmex}, 25 + \item \texttt{cmex10}, 25 + \item \texttt{cmex7}, 25 + \item \texttt{cmmib5}, 25 + \item \texttt{comp.text.tex}, 31 + \item \texttt{compan.err}, 32 + \item continued fractions, 15 + \item \verb*+\cos+, 18 + \item \verb*+\cosh+, 18 + \item \verb*+\cot+, 18 + \item \verb*+\coth+, 18 + \item \verb*+\csc+, 18 + + \indexspace + + \item \verb*+\dbinom+, 14 + \item \verb*+\ddddot+, 12 + \item \verb*+\dddot+, 12 + \item \verb*+\ddot+, 12 + \item \verb*+\DeclareMathOperator+, 2, 17, 18 + \item \verb*+\deg+, 18 + \item \verb*+\det+, 18 + \item \verb*+\dfrac+, 14 + \item \texttt{diffs-m.txt}, 30 + \item \verb*+\dim+, 18 + \item \verb*+\displaybreak+, 8, 9 + \item displayed equations, 3 + \item displayed equations + \subitem centering, 3 + \item \verb*+\displaylimits+, 20 + \item \texttt{displaymath} environment, 3 + \item \verb*+\displaystyle+, 14 + \item \verb*+\documentclass+, 2 + \item \verb*+\dot+, 12 + \item dots, \see{ellipsis dots}{11} + \item \verb*+\dotsb+, 12 + \item \verb*+\dotsc+, 12 + \item \verb*+\dotsi+, 12 + \item \verb*+\dotsm+, 12 + \item \verb*+\dotso+, 12 + + \indexspace + + \item \texttt{e-math.ams.org}, 31 + \item ellipsis dots + \subitem in matrices, 11 + \item \texttt{eqnarray} environment, 1, 3, 26, 30 + \item \verb*+\eqref+, 10 + \item \texttt{equation} environment, 1, 3, 5, 7, 24, 30 + \item equation numbers + \subitem cross-references, 10 + \subitem hierarchy, 9 + \subitem left or right placement, 3 + \subitem overriding, 3 + \subitem subordinate numbering, 10 + \subitem vertical placement, 2 + \item \texttt{equation*} environment, 3 + \item equations, \see{displayed equations}{3} + \item \texttt{euscript} package, 21 + \item \verb*+\exp+, 18 + + \indexspace + + \item \verb*+\fbox+, 13 + \item \texttt{fleqn} option, 3, 5 + \item \texttt{fntguide.tex}, 21 + \item \verb*+\frac+, 14, 15 + \item fractions, 14 + \item \verb*+\fracwithdelims+, 2 + \item function names, \see{operator names}{17} + + \indexspace + + \item \texttt{gather} environment, 5--7, 24, 28--30 + \item \texttt{gathered} environment, 7, 9 + \item \verb*+\gcd+, 18 + \item \verb*+\genfrac+, 14 + + \indexspace + + \item \verb*+\hat+, 12 + \item \verb*+\hdotsfor+, 11 + \item \verb*+\hom+, 18 + \item horizontal space + \subitem around operator names, 17 + \subitem in math mode, 11 + + \indexspace + + \item \verb*+\idotsint+, 20 + \item \verb*+\iiiint+, 20 + \item \verb*+\iiint+, 20 + \item \verb*+\iint+, 20 + \item \verb*+\inf+, 18 + \item \verb*+\injlim+, 18 + \item integrals + \subitem multiple, 20 + \subitem placement of limits, 2 + \item \verb*+\intertext+, 9 + \item \texttt{intlimits} option, 2, 20 + + \indexspace + + \item \verb*+\ker+, 18 + \item \texttt{kuvio} package, 20 + + \indexspace + + \item \verb*+\label+, 6, 10 + \item \verb*+\langle+, 16 + \item \verb*+\ldots+, 12 + \item \verb*+\left+, 15, 16, 27 + \item \verb*+\leftroot+, 13 + \item \texttt{leqno} option, 3, 5 + \item \verb*+\lg+, 18 + \item \verb*+\lim+, 1, 2, 17, 18 + \item \verb*+\liminf+, 18 + \item limits, \see{subscripts and superscripts}{2} + \item \verb*+\limits+, 20 + \item \verb*+\limsup+, 18 + \item \verb*+\ln+, 18 + \item \verb*+\log+, 17, 18 + \item \verb*+\lVert+, 16 + \item \verb*+\lvert+, 16 + + \indexspace + + \item math fonts, 21 + \item math symbols, \see{math fonts}{21} + \item \verb*+\mathbb+, 21, 22 + \item \verb*+\mathbf+, 21, 22 + \item \verb*+\mathcal+, 21 + \item \verb*+\mathfrak+, 21 + \item \verb*+\mathit+, 21 + \item \verb*+\mathrm+, 21 + \item \verb*+\mathscr+, 21 + \item \verb*+\mathsf+, 21 + \item \verb*+\mathtt+, 21 + \item matrices, 10 + \subitem ellipsis dots, 11 + \item \texttt{matrix} environment, 10 + \item \verb*+\matrix+, 28 + \item \verb*+\max+, 18 + \item \verb*+\mbox+, 18 + \item \verb*+\medspace+, 11 + \item Metafont source files, 25 + \item \verb*+\min+, 18 + \item \verb*+\mod+, 18 + \item \verb*+\mspace+, 11 + \item \texttt{multline} environment, 3, 5, 27, 30 + \item \verb*+\multlinegap+, 5 + + \indexspace + + \item \texttt{namelimits} option, 2 + \item \verb*+\negmedspace+, 11 + \item \verb*+\negthickspace+, 11 + \item \verb*+\negthinspace+, 11 + \item \verb*+\newcommand+, 21 + \item \verb*+\nobreakdash+, 12 + \item \texttt{nointlimits} option, 2 + \item \verb*+\nolimits+, 19, 20 + \item \texttt{nonamelimits} option, 2 + \item \texttt{nosumlimits} option, 2 + \item \verb*+\notag+, 3, 5 + \item \verb*+\numberwithin+, 9, 29, 30 + + \indexspace + + \item operator names, 17 + \item \verb*+\operatorname+, 18 + \item \verb*+\operatorname*+, 18 + \item \verb*+\over+, 14, 29 + \item \verb*+\overleftarrow+, 13 + \item \verb*+\overleftrightarrow+, 13 + \item \verb*+\overrightarrow+, 13 + \item \verb*+\overset+, 13 + \item \verb*+\overwithdelims+, 14 + + \indexspace + + \item page breaks, 8 + \item \verb*+\pagebreak+, 8 + \item \texttt{pmatrix} environment, 10 + \item \verb*+\pmatrix+, 28 + \item \verb*+\pmb+, 22 + \item \verb*+\pmod+, 18 + \item \verb*+\pod+, 18 + \item PostScript fonts, 25 + \item \verb*+\Pr+, 18 + \item \verb*+\projlim+, 18 + + \indexspace + + \item \verb*+\qquad+, 11 + \item \verb*+\quad+, 11 + + \indexspace + + \item \verb*+\R+, 22 + \item \verb*+\raisetag+, 8 + \item \verb*+\rangle+, 16 + \item \verb*+\ref+, 10 + \item \texttt{reqno} option, 3, 5 + \item \verb*+\right+, 15, 16, 27 + \item \verb*+\rVert+, 16 + \item \verb*+\rvert+, 16 + + \indexspace + + \item \verb*+\scriptscriptstyle+, 14 + \item \verb*+\scriptstyle+, 14 + \item \verb*+\sec+, 18 + \item \verb*+\setcounter+, 9, 10 + \item \verb*+\setlength+, 5 + \item \verb*+\shoveleft+, 5 + \item \verb*+\shoveright+, 5 + \item \verb*+\sideset+, 13, 19 + \item \verb*+\sin+, 1, 2, 17, 18 + \item \verb*+\sinh+, 18 + \item \texttt{smallmatrix} environment, 11 + \item \verb*+\smash+, 15, 27 + \item \verb*+\sphat+, 12 + \item \texttt{split} environment, 3, 5, 6, 9, 24, 27--30 + \item \verb*+\sptilde+, 12 + \item \verb*+\stackrel+, 13 + \item \texttt{subarray} environment, 19 + \item \texttt{subeqn.tex}, 3 + \item \texttt{subequations} environment, 10 + \item subscripts and superscripts, 13 + \subitem multi-line, 19 + \subitem on sums, 19 + \subitem placement, 2 + \item \verb*+\substack+, 19 + \item \verb*+\sum+, 20, 22 + \item \texttt{sumlimits} option, 2 + \item \verb*+\sup+, 18 + \item superscripts, \see{subscripts and superscripts}{19} + + \indexspace + + \item \texttt{tabular} environment, 26 + \item \verb*+\tag+, 3 + \item \verb*+\tag*+, 3 + \item \verb*+\tan+, 18 + \item \verb*+\tanh+, 18 + \item \verb*+\tbinom+, 14 + \item \texttt{tbtags} option, 2 + \item \texttt{technote.tex}, 14, 28--30 + \item \texttt{testmath.tex}, 3 + \item \tex/ Users Group, 31 + \item \verb*+\text+, 2, 7--9, 18 + \item text fragments inside math, 9, 18 + \item \verb*+\textstyle+, 14 + \item \verb*+\tfrac+, 14 + \item \verb*+\theequation+, 9, 10 + \item \verb*+\thickspace+, 11 + \item \verb*+\thinspace+, 11 + \item \journalname{TUGboat}, 31 + + \indexspace + + \item \verb*+\underleftarrow+, 13 + \item \verb*+\underleftrightarrow+, 13 + \item \verb*+\underrightarrow+, 13 + \item \verb*+\underset+, 13 + \item \verb*+\uproot+, 13 + \item \verb*+\usepackage+, 2, 25 + + \indexspace + + \item \verb*+\value+, 10 + \item \verb*+\varDelta+, 23 + \item \verb*+\varGamma+, 23 + \item \verb*+\varinjlim+, 18 + \item \verb*+\varLambda+, 23 + \item \verb*+\varliminf+, 18 + \item \verb*+\varlimsup+, 18 + \item \verb*+\varOmega+, 23 + \item \verb*+\varPhi+, 23 + \item \verb*+\varPi+, 23 + \item \verb*+\varprojlim+, 18 + \item \verb*+\varPsi+, 23 + \item \verb*+\varSigma+, 23 + \item \verb*+\varTheta+, 23 + \item \verb*+\varUpsilon+, 23 + \item \verb*+\varXi+, 23 + \item \texttt{Vmatrix} environment, 10 + \item \texttt{vmatrix} environment, 10 + \item \verb*+\vphantom+, 27 + + \indexspace + + \item \verb*+\xleftarrow+, 13 + \item \verb*+\xrightarrow+, 13 + +\end{theindex} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/amsproc.template b/Master/texmf-dist/doc/latex/amslatex/amsproc.template new file mode 100644 index 00000000000..2409fc62991 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsproc.template @@ -0,0 +1,61 @@ +%----------------------------------------------------------------------- +% Beginning of amsproc.template +%----------------------------------------------------------------------- +% +% AMS-LaTeX v.2 template for use with amsproc +% +% Remove any commented or uncommented macros you do not use. + +\documentclass{amsproc} + +\newtheorem{theorem}{Theorem}[section] +\newtheorem{lemma}[theorem]{Lemma} + +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\newtheorem{example}[theorem]{Example} +\newtheorem{xca}[theorem]{Exercise} + +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} + +\numberwithin{equation}{section} + +\begin{document} + +\title{} + +% Remove any unused author tags. + +% author one information +\author{} +\address{} +\curraddr{} +\email{} +\thanks{} + +% author two information +\author{} +\address{} +\curraddr{} +\email{} +\thanks{} + +\subjclass[2000]{Primary } + +\keywords{} + +\date{} + +\dedicatory{} + +\begin{abstract} +\end{abstract} + +\maketitle + +\end{document} + +%----------------------------------------------------------------------- +% End of amsproc.template +%----------------------------------------------------------------------- diff --git a/Master/texmf-dist/doc/latex/amslatex/amsrdoc.pdf b/Master/texmf-dist/doc/latex/amslatex/amsrdoc.pdf Binary files differnew file mode 100644 index 00000000000..ab9fe5ab91d --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsrdoc.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/amsrefs.faq b/Master/texmf-dist/doc/latex/amslatex/amsrefs.faq new file mode 100644 index 00000000000..3484e5d13d8 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsrefs.faq @@ -0,0 +1,15 @@ +amsrefs.faq [2004/06/30] American Mathematical Society + +Frequently asked questions about the amsrefs package and its companion +packages. + +Suggestions? Please send mail to tech-support@ams.org. + +------------------------------------------------------------------------ +(1) Question: Where should I look for documentation? + +Answer: User documentation is found in the file amsrdoc.pdf (or +amsrdoc.dvi). + +Some example files (cite-xa.tex cite-xb.tex cite-xh.tex cite-xs.tex +gktest.ltb) are also provided. diff --git a/Master/texmf-dist/doc/latex/amslatex/amsrefs.pdf b/Master/texmf-dist/doc/latex/amslatex/amsrefs.pdf Binary files differnew file mode 100644 index 00000000000..79061f69b83 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsrefs.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/amsthdoc.pdf b/Master/texmf-dist/doc/latex/amslatex/amsthdoc.pdf Binary files differnew file mode 100644 index 00000000000..5a0a59efa2f --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsthdoc.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/amsthdoc.tex b/Master/texmf-dist/doc/latex/amslatex/amsthdoc.tex new file mode 100644 index 00000000000..21e824f5ba0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/amsthdoc.tex @@ -0,0 +1,374 @@ +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "amsthdoc.tex", +%%% version = "2.20", +%%% date = "2004/08/03", +%%% time = "15:02:46 EDT", +%%% checksum = "15807 374 1763 14655", +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1999, 2004 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Publications Technical Group, +%%% 201 Charles Street, +%%% Providence, RI 02904, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% codetable = "ISO/ASCII", +%%% supported = "yes", +%%% keywords = "latex, theorem, proof, amsthm", +%%% abstract = "This file is the User's Guide for the amsthm +%%% package.", +%%% docstring = "The checksum field above contains a CRC-16 +%%% checksum as the first value, followed by the +%%% equivalent of the standard UNIX wc (word +%%% count) utility output of lines, words, and +%%% characters. This is produced by Robert +%%% Solovay's checksum utility.", +%%% } +%%% ==================================================================== +\documentclass[twoside]{article} +\pagestyle{myheadings} + +% Use the same version numbers as for the amslatex instructions. +\def\instrversion{2.20} +\def\instrdate{August 2004} + +\title{Using the \pkg{amsthm} Package} +\author{Version \instrversion, \instrdate\\American Mathematical Society} +\date{} + +\providecommand{\qq}[1]{\textquotedblleft#1\textquotedblright} +\providecommand{\mdash}{\textemdash\penalty\hyphenpenalty} + +% Embedded \index commands are a legacy from the time when this +% documentation was part of amsldoc. Since they don't hurt anything, +% let's leave them in. Maybe they will become useful again in the +% future. [mjd,2000/06/06] + +\chardef\bslchar=`\\ % p. 424, TeXbook +\newcommand{\ntt}{% + \fontfamily\ttdefault \fontseries\mddefault \fontshape\updefault + \selectfont +} +\DeclareRobustCommand{\cn}[1]{{\ntt\bslchar#1}} +\DeclareRobustCommand{\cls}[1]{{\ntt#1}} +\DeclareRobustCommand{\pkg}[1]{{\ntt#1}} +\DeclareRobustCommand{\opt}[1]{{\ntt#1}} +\DeclareRobustCommand{\env}[1]{{\ntt#1}} +\DeclareRobustCommand{\fn}[1]{{\ntt#1}} + +\providecommand{\qedsymbol}{\leavevmode + \hbox to.77778em{% + \hfil\vrule + \vbox to.675em{\hrule width.6em\vfil\hrule}% + \vrule\hfil}} + +%% Provide a meta-command facility; provide an alternate escape +%% character so it can be used within the verbatim environment. + +\catcode`\|=0 +\begingroup \catcode`\>=13 % in LaTeX2e verbatim env makes > active +\gdef\?#1>{{\normalfont$\langle$\textup{#1}$\rangle$}} +\gdef\0{\relax} +\endgroup +\def\<#1>{{\normalfont$\langle$\textup{#1}$\rangle$}} +\def\ntnote#1{{\normalfont$^{#1}$}} + +\hfuzz4pt \vbadness9999 \hbadness5000 +\def\latex/{{\protect\LaTeX}} + +\setlength{\textwidth}{210mm}\addtolength{\textwidth}{-2in} +\setlength{\oddsidemargin}{39pt} +\setlength{\evensidemargin}{39pt} +\addtolength{\textwidth}{-2\oddsidemargin} + +\begin{document} +\maketitle +\markboth{USING THE \pkg{amsthm} PACKAGE}{USING THE \pkg{amsthm} PACKAGE} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Introduction} + +\begin{sloppypar} +The \pkg{amsthm} package provides an enhanced version of \latex/'s +\cn{newtheorem} command for defining theorem-like environments. The +enhanced \cn{newtheorem} recognizes a +\cn{theoremstyle} specification (as in Mittelbach's \pkg{theorem} +package) and has a \verb'*' form for defining unnumbered environments. The +\pkg{amsthm} package also defines a \env{proof} environment that +automatically adds a QED symbol at the end. AMS document classes +incorporate the \pkg{amsthm} package, so everything described here +applies to them as well. +\end{sloppypar} + +If the \pkg{amsthm} package is used with a non-AMS document class and +with the \pkg{amsmath} package, \pkg{amsthm} must be loaded +\emph{after} \pkg{amsmath}, not before. + +Examples are given in the file \fn{thmtest.tex}. For best understanding, +examine the output side-by-side with the input. + + +\section{The \cn{newtheorem} command} + +In mathematical research articles and books, theorems\index{theorems} +and proofs\index{proofs} are among the most common elements, but authors +also use many others that fall in the same general class: lemmas, +propositions, axioms, corollaries, conjectures, definitions, remarks, +cases, steps, and so forth. It is natural to handle these elements as +\latex/ environments, but document classes do not +provide predefined environments for theorem-like elements because +(a)~that would make it difficult for authors to exercise the necessary +control over the automatic numbering, and (b)~the variety of such +elements is so wide that it's not possible for a document class to +provide every one that will ever be needed. Instead there is a command +\cn{newtheorem}, similar in effect to \cn{newenvironment}, that makes it +easy for authors to set up the elements required for a particular +document. + +The \cn{newtheorem} command has two mandatory arguments; the first one +is the environment name that the author would like to use for this +element; the second one is the heading text. For example, +\begin{verbatim} +\newtheorem{lem}{Lemma} +\end{verbatim} +means that instances in the document of +\begin{verbatim} +\begin{lem} Text text ... \end{lem} +\end{verbatim} +will produce +\[\makebox[.8\columnwidth]{% + \textbf{Lemma 1.} \textit{Text text \dots}\hfill}\] +where the heading consists of the specified text \qq{Lemma} and an +automatically generated number and punctuation. + +If \cn{newtheorem*} is used instead of \cn{newtheorem} in this +example, numbers will not be generated automatically for +any of the lemmas in the document. This form of the command can be +useful if you have only one lemma and don't want it to be +numbered; more often, though, it is used to produce a special named +variant of one of the common theorem types. For example, if you have a +lemma that should be labeled \qq{Klein's Lemma}, then the statement +\begin{verbatim} +\newtheorem*{KL}{Klein's Lemma} +\end{verbatim} +would allow you to write +\begin{verbatim} +\begin{KL} Text text ... \end{KL} +\end{verbatim} +and get the desired output. + +Sometimes additional information is desired in the heading of a +theorem or lemma, often because it is cited from another source. +An optional argument is used to provide this information: +\begin{verbatim} +\begin{lem}[Alinhac-Lerner \cite{a-l}] +\end{verbatim} +yielding the output +\[\makebox[.8\columnwidth]{% + \textbf{Lemma 2.} (Alinhac-Lerner [1]). \textit{Text text \dots}\hfill}\] + + +\section{Numbering modifications} + +In addition to the two mandatory arguments, \cn{newtheorem} has two +mutually exclusive optional arguments. These affect the +sequencing\index{theorems!numbering} and hierarchy of the numbering. + +By default each kind of theorem-like environment is numbered +independently. Thus if you have three lemmas and two theorems +interspersed, they will be numbered something like this: Lemma 1, Lemma +2, Theorem 1, Lemma 3, Theorem 2. If you want lemmas and theorems to +share the same numbering sequence\mdash Lemma 1, Lemma 2, Theorem 3, Lemma +4, Theorem 5\mdash then you should indicate the desired relationship as +follows: +\begin{verbatim} +\newtheorem{thm}{Theorem} +\newtheorem{lem}[thm]{Lemma} +\end{verbatim} +The optional argument \verb'[thm]' in the second statement means that +the \texttt{lem} environment should share the \texttt{thm} numbering +sequence instead of having its own independent sequence. + +To have a theorem environment numbered subordinately within a +sectional unit\mdash e.g., to get propositions numbered Proposition 2.1, +Proposition 2.2, and so on in Section~2\mdash put the name of the parent +unit in square brackets in final position: +\begin{verbatim} +\newtheorem{prop}{Proposition}[section] +\end{verbatim} +With the optional argument \verb'[section]', the \verb'prop' counter +will be reset to 0 whenever the parent counter \verb'section' is +incremented, and the proposition label will have the section number +prepended. + +Note that theorem numbering is not accomplished by the same method +as the \cn{numberwithin} facility of \pkg{amsmath}, so an attempt to +use that to relate theorem numbers to equation numbers will not work +in the expected way. A method for accomplishing that, as well as +some other variations, is given in the AMS Author FAQ \cite{AF}, +in the section on \qq{Theorems in AMS-\LaTeX}. + + +\section{Changing styles for theorem-like environments} + +\subsection{The \cn{theoremstyle} command} + +The \pkg{amsthm} package supports the notion of a current theorem style, +which determines what will be produced by a given \cn{newtheorem} +command. The three theorem styles provided\mdash +\verb'plain',\index{plain theo@\texttt{plain} theorem style}\relax +\index{definition theo@\texttt{definition} theorem style}\relax +\index{remark theo@\texttt{remark} theorem style} \verb'definition', +and \verb'remark'\mdash specify different degrees of +visual emphasis corresponding to their relative importance. The +details of this typographical treatment may vary depending on the +document class, but typically the \verb'plain' style produces italic +body text, while the other two styles produce roman body text. + +If no \cn{theoremstyle} command is given, the style used will be +\texttt{plain}. To specify different styles, +divide your \cn{new\-theorem} commands into groups and preface each +group with the appropriate \cn{theo\-rem\-style}. Some examples: +\begin{verbatim} +\theoremstyle{plain}% default +\newtheorem{thm}{Theorem}[section] +\newtheorem{lem}[thm]{Lemma} +\newtheorem{prop}[thm]{Proposition} +\newtheorem*{cor}{Corollary} +\newtheorem*{KL}{Klein's Lemma} + +\theoremstyle{definition} +\newtheorem{defn}{Definition}[section] +\newtheorem{conj}{Conjecture}[section] +\newtheorem{exmp}{Example}[section] + +\theoremstyle{remark} +\newtheorem*{rem}{Remark} +\newtheorem*{note}{Note} +\newtheorem{case}{Case} +\end{verbatim} + +The following list summarizes the types of structures which are +normally associated with each theorem style. + +\smallskip +\begin{tabular}{ll} + \relax\env{plain} & Theorem, Lemma, Corollary, Proposition, Conjecture, \\ + & Criterion, Algorithm \\ + \relax\env{definition} \quad & Definition, Condition, Problem, Example \\ + \relax\env{remark} & Remark, Note, Notation, Claim, Summary, \\ + & Acknowledgment, Case, Conclusion +\end{tabular} + +\subsection{Number swapping} + +A common style variation is to have the theorem number at the beginning +of the heading instead of at the end, for example \qq{1.4 Theorem} +instead of \qq{Theorem 1.4}. As this variation is usually applied +to all \cn{theoremstyle}s, it is done by +placing a \cn{swapnumbers} command at the beginning of the list of +\cn{newtheorem} statements that should be affected. For example: +\begin{verbatim} +\swapnumbers +\theoremstyle{plain} +\newtheorem{thm}{Theorem} +\theoremstyle{remark} +\newtheorem{rem}{Remark} +\end{verbatim} + +In AMS document classes, when numbers are swapped, the style of the +numbers matches that of section headings; this may not be the same +style as the rest of the theorem heading. + +\subsection{New theorem styles} + +The \pkg{amsthm} package provides a \cn{newtheoremstyle} command +to aid in the creation of custom styles, should the three predefined +styles prove insufficient. The following example illustrates the use +of the \cn{newtheoremstyle} command. +\begin{verbatim} +\newtheoremstyle{note}% |?name> + {3pt}% |?Space above> + {3pt}% |?Space below> + {}% |?Body font> + {}% |?Indent amount>|ntnote1 + {\itshape}% |?Theorem head font> + {:}% |?Punctuation after theorem head> + {.5em}% |?Space after theorem head>|ntnote2 + {}% |?Theorem head spec (can be left empty, meaning `normal')> +\end{verbatim} +\noindent +\ntnote1 Indent amount: empty = no indent, \cn{parindent} = normal + paragraph indent + +\noindent +\ntnote2 Space after theorem head: \verb+{ }+ = normal interword space; + \cn{newline} = linebreak + +\smallskip +Apply the new theorem style in the same manner as the predefined ones. +For examples, see the file \fn{thmtest.tex}. + + +\section{Proofs} + +A predefined \env{proof} environment provided by the \pkg{amsthm} +package produces the heading \qq{Proof} with appropriate spacing and +punctuation. The proof environment is primarily intended for short +proofs, no more than a page or two in length; longer proofs are +usually better done as a separate \cn{section} or \cn{subsection} in +your document. + +An optional argument of the proof environment allows you to substitute +a different name for the standard \qq{Proof\/}. If you want +the proof heading to be, say, \qq{Proof of the Main Theorem}, then write +\begin{verbatim} +\begin{proof}[Proof of the Main Theorem] +\end{verbatim} + +A QED symbol, \qedsymbol, is automatically appended at the end of +a \env{proof} environment. To substitute a different end-of-proof +symbol, use \cn{renewcommand} to redefine the command \cn{qedsymbol}. +For a long proof done as a subsection or section instead of with the +\env{proof} environment, you can obtain the symbol and the usual +amount of preceding space by using \cn{qed}. + +Placement of the QED symbol can be problematic if the last part of +a \env{proof} environment is a displayed equation or list environment +or something of that nature. In that case put a \cn{qedhere} command at +the place where the QED symbol should appear, for example, +\begin{verbatim} +\begin{proof} +... +\begin{equation} +G(t)=L\gamma!\,t^{-\gamma}+t^{-\delta}\eta(t) \qedhere +\end{equation} +\end{proof} +\end{verbatim} +When used with the \pkg{amsmath} package, version 2 or later, \cn{qedhere} +will position the QED symbol flush right; with earlier versions, the +symbol will be spaced a quad away from the end of the text or display. + +If \cn{qedhere} produces an error message in an equation, try using +\verb'\mbox{\qedhere}' instead. + +\begin{thebibliography}{[AF]} + +\bibitem[AF]{AF} AMS Author FAQ, +\texttt{http://www.ams.org/authors/author-faq.html} + +\end{thebibliography} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/changes.pdf b/Master/texmf-dist/doc/latex/amslatex/changes.pdf Binary files differnew file mode 100644 index 00000000000..c74e7bc063f --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/changes.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xa.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xa.tex new file mode 100644 index 00000000000..d6930f7cbf1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/cite-xa.tex @@ -0,0 +1,221 @@ +\documentclass{article} +\usepackage[author-year]{amsrefs} + +\newcommand{\latin}{\emph} + +\begin{document} + +\title{Evolutionary walks through a land plant morphospace} +\author{Karl J. Niklas} +\def\jinfo{Journal of Experimental Botany, Vol. 50, No. 330, pp. 39-52, + January 1999, \copyright\ Oxford University Press 1999} + +\maketitle +\section{Introduction} + +Wright's protocol has been successfully recast in terms of spatial +domains containing all (or at least many) of the conceivable +morphological variants (`morphospaces' \latin{sensu} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Thomas and Reif, 1993). +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\ocite{TR93}). +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +In this paper, I review the construction of a morphospace for early land +plants +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%(Niklas and Kerchner, 1984; Niklas, 1997a, b) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\cites{NK84,N97-adaptive-walks,N97-effects} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +and show how it can be used \ldots. + +\ldots\ horizontally cantilevered branches impose the largest bending +moments on subtending branches +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%(Niklas, 1992, 1994a). +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\cites{N92,N94-allometry}. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\ldots\ This definition removes the sharp dichotomy said to exist +between `object' and `process' complexity (i.e. the number of different +parts in an organic system versus the number of different interactions +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%among them; McShea, 1996). +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +among them \cite{M96}). +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\ldots\ fossil record for Devonian and Carboniferous vascular land +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%plants (Niklas et al., 1980, 1983; Gensel and Andrews, 1984). +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +plants \cites{NTK80,NTK83,GA84}. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{bibsection} +\begin{biblist} + +\bib*{HSW80}{collection}{ + editor={Hecht, M.}, + editor={Steere, W.}, + editor={Wallace, B.}, + date={1980}, + title={Evolutionary biology}, + publisher={Plenum Publishing}, + address={New York}, +} + +\bib{fn95}{article}{ + author={Farnsworth, K. D.}, + author={Niklas, K. J.}, + date={1995}, + title={Theories of optimization, form and function in branching + architectures in plants}, + journal={Functional Ecology}, + volume={9}, + pages={355\ndash 363}, +} + +\typeout{} +\typeout{ [Testing some of the amsrefs warning messages ...]} + +\bib{GMW81}{book}{ + author={Gill, P. E.}, + author={Murray, W.} + author={Wright, M. H.}, + date={1981}, + title={Practical optimization}, + publisher={Academic Press}, + address={London}, +} + +\bib{GA84}{book}{ + author={Gensel, P. G.}, + author={Andrews, H. N.}, + date={1984}, + title={Plant life in the Devonian}, + publisher={Praeger Press}, + address={New York}, +} + +\bib{M96}{article}{ + author={McShea, D. W.}, + date={1996}, + title={Metazoan complexity and evolution: is there a trend}, + journal={Evolution}, + volume={50}, + pages={477\ndash 492}, +} + +\bib{MWWW73}{book}{ + author={Meredith, D. D.}, + author={Wong, K. W.}, + author={Woodhead, R. W.}, + author={Wortman, R. H.}, + date={1973}, + title={Design and planning of engineering systems}, + publisher={Prentice-Hall}, + address={Englewood Cliffs, New Jersey}, +} + +\bib{N92}{book}{ + author={Niklas, K. J.}, + date={1992}, + title={Plant biomechanics: an engineering approach to plant form and + function}, + publisher={University of Chicago Press}, + address={Illinois}, +} + +\bib{N94-allometry}{book}{ + author={Niklas, K. J.}, + date={1994}, + title={Plant allometry: the scaling of form and process}, + publisher={University of Chicago Press}, + address={Illinois}, +} + +\bib{N94-simulation}{article}{ + author={Niklas, K. J.}, + date={1994}, + title={Simulation of organic shape: the roles of phenomenology and + mechanism}, + journal={Journal of Morphology}, + volume={219}, + pages={243\ndash 246}, +} + +\bib{N97-adaptive-walks}{article}{ + author={Niklas, K. J.}, + date={1997}, + title={Adaptive walks through fitness landscapes for early vascular + land plants}, + journal={American Journal of Botany}, + volume={84}, + pages={16\ndash 25}, +} + +\bib{N97-effects}{article}{ + author={Niklas, K. J.}, + date={1997}, + title={Effects of hypothetical developmental barriers and abrupt + environmental changes on adaptive walks in a computer-generated + domain for early vascular land plants}, + journal={Paleobiology}, + volume={23}, + pages={63\ndash 76}, +} + +\bib{NK84}{article}{ + author={Niklas, K. J.}, + author={Kerchner, V.}, + date={1984}, + title={Mechanical and photosynthetic constraints on the evolution of + plant shape}, + journal={Paleobiology}, + volume={10}, + pages={79\ndash 101}, +} + +\bib{NTK80}{article}{ + author={Niklas, K. J.}, + author={Tiffney, B. H.}, + author={Knoll, A. H.}, + date={1980}, + title={Apparent changes in the diversity of fossil plants: a + preliminary assessment}, + xref={HSW80}, + volume={12}, + pages={1\ndash 89}, +} + +\bib{NTK83}{article}{ + author={Niklas, K. J.}, + author={Tiffney, B. H.}, + author={Knoll, A. H.}, + date={1983}, + title={Patterns in vascular land plant diversification}, + journal={Nature}, + volume={303}, + pages={614\ndash 616}, +} + +\bib{TR93}{article}{ + author={Thomas, R. D. K.}, + author={Reif, W.-E.}, + % This is just to show what the warning looks like for an empty field: + author={}, + date={1993}, + title={The skeleton space: a finite set of organic designs}, + journal={Evolution}, + volume={47}, + pages={341\ndash 360}, +} + +\end{biblist} +\end{bibsection} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xb.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xb.tex new file mode 100644 index 00000000000..ab6265a6cec --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/cite-xb.tex @@ -0,0 +1,143 @@ +\documentclass{amsart} +\usepackage{amsrefs} + +%\usepackage{dual} % not released yet, needs more work +%\setlength{\dualindent}{-2em} + +\newenvironment{dual}{% + \par\medskip + \trivlist\item[]% +}{% + \endtrivlist +} + +\newcommand{\backup}{% + \vspace*{-\baselineskip}\vspace*{-\medskipamount}\nopagebreak +} + +\newtheorem{thm}{Theorem}[section] + +\begin{document} +\title{Citation tests} +\author{Michael Downes} + + The following examples are derived from + \emph{Homology manifold bordism} by Heather Johnston and Andrew + Ranicki (Trans.\ Amer.\ Math.\ Soc.\ \textbf{352} no 11 (2000), PII: S + 0002-9947(00)02630-1). + +\bigskip \noindent \rule{\columnwidth}{0.5pt}\par + +\setcounter{section}{3} +\begin{dual} +The results of Johnston \cite{Jo} on homology +manifolds are extended here. It is not +possible to investigate transversality by +geometric methods---as in \cite{Jo} we employ +bordism and surgery instead. +\end{dual} + +%Kirby and Siebenmann \cite{KS} (III,\S 1), +\begin{dual} +The proof of transversality is indirect, +relying heavily on surgery theory\mdash see +Kirby and Siebenmann \cite{KS}*{III, \S 1}, +Marin \cite{M} and Quinn \cite{Q3}. We shall +use the formulation in terms of topological +block bundles of Rourke and Sanderson +\cite{RS}. +\end{dual} + +\begin{dual} +$Q$ is a codimension $q$ subspace by Theorem +4.9 of Rourke and Sanderson \cite{RS}. +(Hughes, Taylor and Williams \cite{HTW} +obtained a topological regular neighborhood +theorem for arbitrary submanifolds \dots.) +\end{dual} + +%Wall \cite{Wa} (Chapter 11) obtained a +\begin{dual} +Wall \cite{Wa}*{Chapter 11} obtained a +codimension $q$ splitting obstruction \dots. +\end{dual} + +\begin{dual} +\dots\ following the work of Cohen \cite{Co} +on $PL$ manifold transversality. +\end{dual} + +\begin{dual} +In this case each inverse image is +automatically a $PL$ submanifold of +codimension $\sigma$ (Cohen \cite{Co}), so +there is no need to use $s$-cobordisms. +\end{dual} + +%Quinn (\cite{Q2}, 1.1) proved that \dots +\begin{dual} +Quinn \cite{Q2}*{1.1} proved that \dots +\end{dual} + +\begin{dual}\backup +\begin{thm}[The additive structure of + homology manifold bordism, Johnston + \cite{Jo}] +\dots +\end{thm} +\end{dual} + +\begin{dual} +For $m\geq 5$ the Novikov-Wall surgery theory +for topological manifolds gives an exact +sequence (Wall \cite{Wa}*{Chapter 10}. +\end{dual} + +\begin{dual} +The surgery theory of topological manifolds +was extended to homology manifolds in Quinn +\cites{Q1,Q2} and Bryant, Ferry, Mio +and Weinberger \cite{BFMW}. +\end{dual} + +\begin{dual} +The 4-periodic obstruction is equivalent to +an $m$-dimensional homology manifold, by +\cite{BFMW}. +\end{dual} + +\begin{dual} +Thus, the surgery exact sequence of +\cite{BFMW} does not follow Wall \cite{Wa} in +relating homology manifold structures and +normal invariants. +\end{dual} + +\begin{dual} +\dots\ the canonical $TOP$ reduction +(\cite{FP}) of the Spivak normal fibration of +$M$ \dots +\end{dual} + +\begin{dual}\backup +\begin{thm}[Johnston \cite{Jo}] +\dots +\end{thm} +\end{dual} + +\begin{dual} +Actually \cite{Jo}*{(5.2)} is for $m\geq 7$, +but we can improve to $m\geq 6$ by a slight +variation of the proof as described below. +\end{dual} + +\begin{dual} +(This type of surgery on a Poincar\'e space +is in the tradition of Lowell Jones +\cite{Jn}.) +\end{dual} + +\bibliographystyle{amsxport} +\bibliography{jr} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xh.brf b/Master/texmf-dist/doc/latex/amslatex/cite-xh.brf new file mode 100644 index 00000000000..217558e24ab --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/cite-xh.brf @@ -0,0 +1,24 @@ +\backcite {Jo}{{1}{4}{section.1}} +\backcite {Jo}{{1}{4}{section.1}} +\backcite {KS}{{1}{4}{section.1}} +\backcite {M}{{1}{4}{section.1}} +\backcite {Q3}{{1}{4}{section.1}} +\backcite {RS}{{1}{4}{section.1}} +\backcite {RS}{{1}{4}{section.1}} +\backcite {HTW}{{1}{4}{section.1}} +\backcite {Wa}{{1}{4}{section.1}} +\backcite {Co}{{1}{4}{section.1}} +\backcite {Co}{{1}{4}{section.1}} +\backcite {Q2}{{1}{4}{section.1}} +\backcite {Jo}{{2}{4.1}{thm.2}} +\backcite {Wa}{{2}{4}{thm.2}} +\backcite {Q1}{{2}{4}{thm.2}} +\backcite {Q2}{{2}{4}{thm.2}} +\backcite {BFMW}{{2}{4}{thm.2}} +\backcite {BFMW}{{2}{4}{thm.2}} +\backcite {BFMW}{{2}{4}{thm.2}} +\backcite {Wa}{{2}{4}{thm.2}} +\backcite {FP}{{2}{4}{thm.2}} +\backcite {Jo}{{2}{4.2}{thm.3}} +\backcite {Jo}{{2}{4}{thm.3}} +\backcite {Jn}{{2}{4}{thm.3}} diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xh.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xh.tex new file mode 100644 index 00000000000..e6bc80cc6aa --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/cite-xh.tex @@ -0,0 +1,154 @@ +%&pdfelatex +%% This is intended to be a working example of using the amsrefs +%% backrefs option in conjunction with hyperref. It works for me using +%% pdflatex [mjd,2002-01-03]. Cf testbib.tex in the hyperref distrib. +%% +%% This is pdfTeX, Version 3.14159-14h-released-20010417 (Web2C 7.3.3.1) +%% (format=pdflatex 2001.12.21) +%% Package: hyperref 2000/01/22 v6.69c Hypertext links for LaTeX + +\documentclass{article} +\usepackage{times} +\usepackage[colorlinks,citecolor=red,pagebackref,hypertexnames=false]{hyperref} +\usepackage[backrefs]{amsrefs} + +\newenvironment{dual}{% + \par\medskip + \trivlist\item[]% +}{% + \endtrivlist +} + +\newcommand{\backup}{% + \vspace*{-\baselineskip}\vspace*{-\medskipamount}\nopagebreak +} + +\newtheorem{thm}{Theorem}[section] + +\providecommand{\MR}{} + +\begin{document} +\title{Testing amsrefs with the hyperref package} +\author{MJD} +\maketitle + + The following examples are derived from + \emph{Homology manifold bordism} by Heather Johnston and Andrew + Ranicki (Trans.\ Amer.\ Math.\ Soc.\ \textbf{352} no 11 (2000), PII: S + 0002-9947(00)02630-1). + +\setcounter{section}{3} +\section{Homology manifold bordism} + +\begin{dual} +The results of Johnston \cite{Jo} on homology +manifolds are extended here. It is not +possible to investigate transversality by +geometric methods---as in \cite{Jo} we employ +bordism and surgery instead. +\end{dual} + +%Kirby and Siebenmann \cite{KS} (III,\S 1), +\begin{dual} +The proof of transversality is indirect, +relying heavily on surgery theory\mdash see +Kirby and Siebenmann \cite{KS}*{III, \S 1}, +Marin \cite{M} and Quinn \cite{Q3}. We shall +use the formulation in terms of topological +block bundles of Rourke and Sanderson +\cite{RS}. +\end{dual} + +\begin{dual} +$Q$ is a codimension $q$ subspace by Theorem +4.9 of Rourke and Sanderson \cite{RS}. +(Hughes, Taylor and Williams \cite{HTW} +obtained a topological regular neighborhood +theorem for arbitrary submanifolds \dots.) +\end{dual} + +%Wall \cite{Wa} (Chapter 11) obtained a +\begin{dual} +Wall \cite{Wa}*{Chapter 11} obtained a +codimension $q$ splitting obstruction \dots. +\end{dual} + +\begin{dual} +\dots\ following the work of Cohen \cite{Co} +on $PL$ manifold transversality. +\end{dual} + +\begin{dual} +In this case each inverse image is +automatically a $PL$ submanifold of +codimension $\sigma$ (Cohen \cite{Co}), so +there is no need to use $s$-cobordisms. +\end{dual} + +%Quinn (\cite{Q2}, 1.1) proved that \dots +\begin{dual} +Quinn \cite{Q2}*{1.1} proved that \dots +\end{dual} + +\begin{dual}\backup +\begin{thm}[The additive structure of + homology manifold bordism, Johnston + \cite{Jo}] +\dots +\end{thm} +\end{dual} + +\begin{dual} +For $m\geq 5$ the Novikov-Wall surgery theory +for topological manifolds gives an exact +sequence (Wall \cite{Wa}*{Chapter 10}. +\end{dual} + +\begin{dual} +The surgery theory of topological manifolds +was extended to homology manifolds in Quinn +\cites{Q1,Q2} and Bryant, Ferry, Mio +and Weinberger \cite{BFMW}. +\end{dual} + +\begin{dual} +The 4-periodic obstruction is equivalent to +an $m$-dimensional homology manifold, by +\cite{BFMW}. +\end{dual} + +\begin{dual} +Thus, the surgery exact sequence of +\cite{BFMW} does not follow Wall \cite{Wa} in +relating homology manifold structures and +normal invariants. +\end{dual} + +\begin{dual} +\dots\ the canonical $TOP$ reduction +(\cite{FP}) of the Spivak normal fibration of +$M$ \dots +\end{dual} + +\begin{dual}\backup +\begin{thm}[Johnston \cite{Jo}] +\dots +\end{thm} +\end{dual} + +\begin{dual} +Actually \cite{Jo}*{(5.2)} is for $m\geq 7$, +but we can improve to $m\geq 6$ by a slight +variation of the proof as described below. +\end{dual} + +\begin{dual} +(This type of surgery on a Poincar\'e space +is in the tradition of Lowell Jones +\cite{Jn}.) +\end{dual} + +\bibliographystyle{amsxport} +\bibliography{jr} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xs.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xs.tex new file mode 100644 index 00000000000..15167b3b9f1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/cite-xs.tex @@ -0,0 +1,19 @@ +\documentclass{amsart} +\usepackage{amsrefs} + +\begin{document} + +\section{Introduction} + +A single cite \cite{MR1451594} +and a multiple \cites{Weyl,Gould,Rob,MR95f:17013,Ser77}. +And then with an option in the middle: +\citelist{\cite{Rob} \cite{Gould} \cite{MR95f:17013}*{Chapter 18}}. + +\begin{bibsection} +\begin{biblist} +\bibselect{gktest} +\end{biblist} +\end{bibsection} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/classes/00readme.txt b/Master/texmf-dist/doc/latex/amslatex/classes/00readme.txt new file mode 100644 index 00000000000..3422ab571fb --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/classes/00readme.txt @@ -0,0 +1,145 @@ +00readme.txt for AMS document classes amsart/book/proc 2.0 [2004/08/06] + +See manifest.txt for a list of all the files in the distribution. + +See install.txt for installation instructions. + +The document classes amsart, amsbook, amsproc and related packages are +provided by the American Mathematical Society for authors to use with +LaTeX. They produce the overall layout and appearance of AMS +publications. + +In order to use an AMS document class you need to have TeX software +installed first. TeX is not an AMS product. If you need information on +getting TeX see one of the following: + + http://www.tug.org/ + http://www.ams.org/tex/tex-resources.html + +Documentation for the AMS document classes is found in + + instr-l.pdf + diffs-c.txt + amsthdoc.pdf + thmtest.tex + thmtest.pdf + +which are included in the collection. Additional documentation can be +found in the amsclass FAQ: + + http://www.ams.org/tex/amsclass-faq.html + +The recommended procedure for making a custom document class based on an +AMS class is to make a copy of the relevant .cls file using a different +name and edit the copy---e.g., copy amsbook.cls to mybook.cls. (In +general we advise against using \LoadClass, unless the base class is +frozen or changes to the base class are under your control.) + +For technical support: + + American Mathematical Society + Technical Support + Publications Technical Group + P. O. Box 6248 + Providence, RI 02940-6248 + Phone: 800-321-4AMS (321-4267) (USA/Canada) or 401-455-4080 + tech-support@ams.org + +======================================================================== +RECENT CHANGES + +---ams-c1.ins 2.20 2004/08/03 +Added amsmidx package. + +---amsclass.dtx 2.20 2004/08/06 +1. Added facility for additional line(s) in copyright block. +2. Corrected handling of section heading with no title. +3. Got rid of spurious "Appendix" in t-of-c in \backmatter. +4. Changed MR number formatting to use new style as on MathSciNet. +5. Created commands for various style elements and substituted them + for hard-coded values to simplify building derived classes. +6. Added sectioning and otherwise cleaned up commentary. + +---amsclass.faq - 2004/08/06 +Removed from distribution; replaced by on-line FAQ at +http://www.ams.org/tex/amsclass-faq.html + +---amsdtx.dtx 2.06 2004/08/06 +1. Reworked indexing commands for compatibility with doc.sty. +2. Added option environment for enhanced indexing. +3. Improved formatting. + +---amsthdoc.tex 2.20 2004/08/03 +1. Substantially rewritten for clarity. +2. Added documentation for \newtheoremstyle. + +---instr-l.tex 2.20 2004/08/05 +Substantially rewritten for clarity and to add instructions for new +features; see note on amsclass.dtx regarding features. + +---mrabbrev.bib - 2004/08/05 +Removed from distribution; this is now available separately from +http://www.ams.org/tools/mrabbrev.bib + +---thmtest.tex 2.01 2004/08/02 +1. Corrected counter for theorems with switched headers. +2. Added section headings for clarity. +3. Added example ending with a display and \qedhere. + +---upref.dtx 2.01 2004/07/29 +1. Added code to make package work with hyperref. +2. Improved documentation. + +---amsclass.dtx 2.14 2004/04/26 (not released) +1. Incorporated pending changes left by Michael Downes: + - Added trap in headings in case \thanks was set within \author, + and added \thanks@warning. + - Cleaned up and completed unfinished documentation. +2. Added braces in \uppercasenonmath to limit scope. +3. Added \contrib mechanism to handle "non-author" authors. +4. Segregated definitions of administrative footnotes to permit easier + customization for AMS journals. +5. Added explicit \bibliofont to permit easy change for special uses. +6. Changed MR number formatting to correspond to new access numbers + used by MathSciNet. +7. Added \@citestyle and \citeform to simplify font changes in citations. +8. Added OT1 defaults for \DH, \dh, \DJ, \dj, required for author names. +9. Added \markleft to permit changing of only left running head + +---amsclass.dtx 2.13 2002/12/04 (not released) +1. Fixed handling of theorem head punctuation with \swapnumbers. +2. Changed \proofname to \providecommand in case it's already defined. +3. Made \small, \Small, etc., robust. +4. Better spacing in \l@figure to prevent overprinting of figure number. +5. Changed handling of author names to prevent internal line breaks. +6. Added \@noparitemfalse in \dth@everypar to prevent weird results in + certain (rare) kinds of usage. +7. Some other cosmetic changes. + +---amsthdoc.tex 2.02 2000/06/06 +Use article class instead of amsldoc (which is overkill). + +---amsldoc.cls - 2000/06/06 +Removed from distribution, no longer needed by amsthdoc. + +---amsclass.dtx 2.07 2000/06/05 +Guard against \\ in argument of \author. + +---amsclass.dtx 2.06 2000/06/02 +Avoid using \@elt in qed stack because LaTeX output routine falls over +if triggered when something else is using \@elt. + +---amsclass.dtx 2.05 2000/05/16 +1. Added \indexintro. +2. Fixed erroneous init for thm@preskip, thm@postskip. + +---amsclass.dtx 2.04 2000/03/10 +\newtoks fix for old versions of LaTeX. Added some commentary about \cal. + +---amsclass.dtx 2.03 2000/01/17 +1. Removed dependency on amsgen package. +2. Added a warning about graphics for the draft option. +3. Improved qedhere handling for article/amsthm combination. + +---amsclass.dtx 2.02 2000/01/17 +Some fixes for the fleqn/qedhere case. diff --git a/Master/texmf-dist/doc/latex/amslatex/classes/install.txt b/Master/texmf-dist/doc/latex/amslatex/classes/install.txt new file mode 100644 index 00000000000..87fedfdc25c --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/classes/install.txt @@ -0,0 +1,106 @@ +install.txt for amscls 2.20 [2004/08/05] + +If you have a relatively up-do-date TeX system that complies with the +TeX Directory Structure (TDS) standard, installing according to the +instructions in section I below is the easiest method. See + + http://www.tug.org/tds/tds.pdf + +for details on the TDS standard. If your TeX system does not comply +with the TDS standard, please contact the manufacturer of your TeX +system for details on how to install third-party TeX packages. + +The first step is to identify the TEXMF folder that contains files used +by LaTeX. To do this, look for the file article.cls. If you find, e.g., + + /usr/local/share/texmf/tex/latex/base/article.cls + +then we will define TEXMF to mean /usr/local/share/texmf (everything +up to the /tex/latex/base part). On a Windows system the file location +will probably be something like + + c:\sw\texmf\tex\latex\base\article.cls + +Then we define TEXMF to mean c:\sw\texmf. In the following +instructions, wherever you see "TEXMF" substitute the folder name +determined in this way. + +If this terminology does not make sense to you, seek assistance from +a friend or colleague, or from the company that you bought your TeX +system from, or contact us at + + tech-support@ams.org + 800-321-4AMS (321-4267) (USA/Canada) + 401-455-4080 + +======================================================================== +I. Installing the easy way. + +1. Download the following archive file: + + ftp://ftp.ams.org/pub/tex/amscls.zip + +2. View the following files to assess the effects of the upgrade on +your system: + + 00readme.txt + install.txt (this file) + diffs-c.txt + +3. Backup the old version of AMS-LaTeX, preferably by moving it out of the +TEXMF tree. + +4. Extract files fromthe .zip archive using your favorite unzip tool, setting +the extraction target directory to the texmf root directory. + +5. To check the end result, you should find that you now have amsmath.sty +in the following location + + TEXMF/tex/latex/amscls/amsart.cls + +Some TeX systems also use a database to keep track of TeX input files. If +this database is not updated, your TeX system might not find the newly +installed files. Consult your system's documentation to determine how +to update this database. + +6. Some files will appear in both the source area and another area. +This is because the source form and the in-use form are identical. +As distributed, the files in the source/latex/amscls area comprise a +complete copy of the distribution from which all the other files can +be regenerated if need be. If you need to conserve disk space, you +could delete the files in the source area, since they are not needed +for normal use. + +======================================================================== +II. Installing the not-so-easy way. + +Download ftp://ftp.ams.org/pub/tex/amscls.zip. + +Make the following directories, if not already present: + + TEXMF/source/latex/amscls + TEXMF/tex/latex/amscls + TEXMF/doc/latex/amscls + +Backup your old AMS-LaTeX files if they are installed, preferably moving them +out of the TEXMF tree. + +Create a temporary directory and generate documentation files (these assume +a UNIX TeX installation): + + - make directory /tmp/amscls + - unzip -d /tmp/amscls amscls.zip + - cd /tmp/amscls + - Run latex on the file ams-c1.ins to produce .cls and .sty files + - Run latex on *.tex + - [optional] Run latex on *.dtx (technical documentation) + - move *.dvi, *.pdf, *.tex to TEXMF/doc/latex/amscls + - [optional] move *.dtx to TEXMF/doc/latex/amscls + - [optional] convert .dvi to .ps or .pdf + - move *.sty and *.cls to TEXMF/tex/latex/amscls + - delete /tmp/amscls + +Some TeX systems also use a database to keep track of TeX input files. If +this database is not updated, your TeX system might not find the newly +installed files. Consult your system's documentation to determine how to +update this database. diff --git a/Master/texmf-dist/doc/latex/amslatex/classes/manifest.txt b/Master/texmf-dist/doc/latex/amslatex/classes/manifest.txt new file mode 100644 index 00000000000..9cc4cd958e7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/classes/manifest.txt @@ -0,0 +1,41 @@ + +texmf/bibtex/bst/ams/ + amsalpha.bst + amsplain.bst + +texmf/doc/latex/amscls/ + amsart.template + amsbook.template + amsproc.template + amsthdoc.pdf + diffs-c.txt + instr-l.pdf + thmtest.pdf + +texmf/source/latex/amscls/ + 00readme.txt + ams-c1.ins + amsalpha.bst + amsart.template + amsbook.template + amsclass.dtx + amsdtx.dtx + amsmidx.dtx + amsplain.bst + amsproc.template + amsthdoc.tex + diffs-c.txt + install.txt + instr-l.tex + manifest.txt + thmtest.tex + upref.dtx + +texmf/tex/latex/amscls/ + amsart.cls + amsbook.cls + amsdtx.cls + amsmidx.sty + amsproc.cls + amsthm.sty + upref.sty diff --git a/Master/texmf-dist/doc/latex/amslatex/diffs-c.txt b/Master/texmf-dist/doc/latex/amslatex/diffs-c.txt new file mode 100644 index 00000000000..55a1c98793e --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/diffs-c.txt @@ -0,0 +1,319 @@ +diffs-c.txt [2004/08/06] + +History of changes for AMS document classes, the amsthm package, and +other packages distributed in this collection. + +======================================================================== +Differences in amsthm 2.20 (August 2004) + +---Added a fallback definition for \swappedhead@plain (used in + amsthm.sty 1.x). + +---For \proofname, changed from \newcommand to \providecommand in case + it's already defined. + +---Improved the handling of \qed when the [fleqn] option is used. + +---Avoid using \@elt in qed stack because LaTeX output routine falls + over if triggered when something else is using \@elt. + +======================================================================== +Differences in amsart/amsbook/amsproc 2.20 (August 2004) + +---Removed dependency on amsgen package. + +---Added warning message about graphics when draft option is used. + +---Added a check for \ifhmode when adding punctuation, and provided + \nopunct for omitting punctuation when not wanted. + +---Made \small, \Small, etc., robust in case they are used in a + \caption. + +---Changed handling of author names to prevent line breaks within + names. + +---For author URLs, made ~ a printable character. + +---amsart, amsproc: Defined \@logofont and \@copyinsfont and moved font + instructions out of \set@logo and \@setcopyright, to simplify style + changes in derivative classes. + +---Added \copyins to \@reinserts so that it would be included in the + page length calculation when a float is input on the first page + +!! This change may affect line breaks and page breaks. + +---Added provision for an extra line following the copyright line with + \@extracrline (for use in derivative classes). + +---amsart, amsproc: Added \contrib (similar to \author) to handle names + of persons who provided, e.g., an introduction or appendix. Usage: + \contrib[with Appendix 1 by]{John Smith} + \contrib[and Appendix 2 by]{Henry Moore} + \contrib{Roger Williams} + This will be set as part of the author block: + ...[authors]..., with Appendix 1 by John Smith, and Appendix 2 + by Henry Moore and Roger Williams + Contributors are ignored when generating running heads. + +---Added \thanks@warning in case \thanks is included in \author. + +---Added \markleft to permit easy changes to left running head only. + +---Defined \@cleartopmattertags and moved commands to do this out of + \maketitle. + +---Added OT1 defaults for \DH, \dh, \DJ, \dj (ordinarily in T1 only). + +---Added braces to limit scope of \uppercasenonmath. + +---Segregated definition of administrative footnotes (\@adminfootnotes) + to permit easier customization for derivative document styles. + +---amsart: When subsection has no title, made number bold. + +---Fixed the handling of theorem head punctuation when \swapnumbers is + used. Used \thm@headsep instead of \labelsep for theorem heads. + +---Provided \@citestyle and \citeform to simplify change of font used + in citation. + +---Provided \bibliofont to allow author to make change. + +---Provided \@bibtitlestyle, \@defaultbiblabelstyle and + \@indextitlestyle to simplify style changes. + +---Changed output format of \MR to recognize change in format of + MathSciNet reference numbers; output is now all lightface instead + of having a bold volume number. + +!! This change will result in a change of appearance. + +---Reset \chaptername with \backmatter to avoid spurious "Appendix" in + t-of-c. + +---Added \indexintro to allow a block of text at the top of an index. + +---Made index ragged right and suppressed hyphenation. + +---Added \seeonly = "see" to get around unfortunate use of \see for + "see also"; added \seealso (from makeindex) for compatibility with + material originally set with a LaTeX document class. + +======================================================================== +Differences in upref 2.0 (July 2004) + +---Package will now work with hyperref, regardless of package input + order. + +======================================================================== +======================================================================== +Differences in amsthm 2.0 (November 1999) + +---Allow line breaks in theorem headings (added \deferred@thm@head and + related code). + +---Make \end{proof} force end of paragraph so following text is + indented (oversight in version 1.2). + +!! This change may affect line breaks and page breaks. + +---Added \qedhere command for flush-right QED symbol in displayed + equations. + +---Added amsthdoc.tex documentation file (taken from amsldoc.tex). + +---Merged amsthm.dtx into amsclass.dtx. + +======================================================================== +Differences in amsart/amsbook/amsproc 2.0 (November 1999) + +---Corrected erroneous default style for labelenumi (should be parens + instead of period); increase list left margins slightly. + +!! To revert to former style: \renewcommand{\labelenumi}{\theenumi.} + +---amsart: For "swapped" theorem heads (numbers shifted to the left + margin) the number font was changed to lightface to match subsection + numbers. This is an AMS journal style requirement---old behavior was + incorrect. + +!! This change may affect line breaks and page breaks. + +---Overfull \vbox messages for every other page: increased headheight + +---Added openany option for amsbook + +---Moved erroneously placed \endgroup in \curraddr, \email and \urladdr + +---Added a year option to \subjclass (default to 1991 for backward + compatibility). + +---For \cleardoublepage, use \pagestyle{empty} for blank pages. + +---Empty argument of \thanks: do nothing instead of printing an empty + footnote. + +---Clear up contradictory font size commands for abstract; always + \Small, + +---Omit final punctuation for \section{} head containing only a number. + +---Added \contentsnamefont to make changes easier. + +---Read a .cfg file. + +---Changed \parindent\z@ to \@parboxrestore in \@serieslogo to avoid + side effects depending on context of pagebreaks. + +---Use \protect instead of \@nx in \@secmark. + +---Moved \thispagestyle{firstpage} closer to beginning of \maketitle to + assure that the logo will be set on the first page if long abstract + breaks to second page (for derivative classes that don't box the + abstract). + +---Added support for paragraph, subparagraph. + +---In \partrunhead, added \ignorespaces, \unskip. + +---In \@starttoc, set \parskip to zero. + +---In \indexchap, rearranged commands to fix vertical spacing for + title; wrong \baselineskip was being used, resulting in title 6pt + too low. + +---Footnote failure in minipage: Changed \@makefnmark so that it + doesn't use math mode. + +---Added figure* and table* environments + +---Revised \@cflci to do the right thing with drop folio at the end of + a two-column page. + +---Incorporate amsthm package by direct embedding instead of + \RequirePackage. + +---Added missing default definition for \MRhref. + +---Use \MakeTextUppercase if available to handle latin-1 characters in + author names. + +---amsbook: Print keywords and date info on title-page obverse if + given. + +---Added various features for AMS in-house use: \dateposted, e-only + option, \Mc, etc. + +======================================================================== +Differences in amsart/amsbook/amsproc 1.2 (January 1995) + +---Documentation + +The documentation for the AMS documentclasses, formerly contained in +amslatex.tex, is now found in instr-l.tex in the amslatex/classes area. +This is a copy of the file instr-l.tex that is found in the author-info +area of e-math.ams.org. That area contains additional information +pertaining specifically to the submission of LaTeX or AmS-TeX documents +to AMS publications. + +---New documentclass "amsproc". + +A document class amsproc has been added for books that consist of a +collection of articles, such as the proceedings of a conference. + +---Different placement of "abstract" environment. + +The abstract should now be entered *before* the \maketitle command. +This provides maximum control over the position and vertical spacing +when printing the abstract information at different places, as required +by different AMS publications---for example, in some publications the +abstract may be required to fall between certain other elements in the +beginning section of a document, or it may be postponed to the end of +the document, or it might even be omitted entirely. If an abstract is +entered after \maketitle, it will still be printed, but with a warning +(and possibly in the wrong place or with wrong spacing). + +---Treatment of the @ character. + +As the AMS document classes automatically load the amsmath package, all +changes for amsmath 1.2 affect the AMS classes also. Note in particular +that the @ character is no longer a special command prefix, so to +produce a printed @ in an e-mail address you should now write simply +@ instead of @@. + +---The nonbreaking dash commands @-, @--, @--- are no longer available +because @ as a special command prefix has disappeared. An alternative +\nobreakdash command is provided in the amsmath package. + +---Added "nomath" option. + +The AMS document classes now take an option nomath that suppresses +the automatic loading of the amsmath package. This is sometimes helpful +in converting a pre-existing document to AMS style if you only want to +do a quick conversion without attempting to deal with any of the math. + +---Theorem handling. + +Theorem setup is now handled by the amsthm package instead of the +"theorem" package. \theorembodyfont, \theoremheaderfont, etc are not +used any more. See amsldoc.tex and thmtest.tex for details. + +---The old environments pf, pf* are superseded by a single proof +environment. It takes an optional argument to specify an alternative +heading text. + +If you are converting an older document to run with \documentclass +instead of \documentstyle, here is how you could provide +backward-compatible definitions for pf and pf*: + + \newenvironment{pf}{\proof[\proofname]}{\endproof} + \newenvironment{pf*}[1]{\proof[#1]}{\endproof} + +---\small now produces 9pt text; \tiny now produces 6pt text + +Formerly \small produced the same typesize as \footnotesize (8pt). Now +they produce different sizes, normally 9 and 8 respectively. Also the +range of typesize-changing commands is filled out to include, below +\normalsize, the following: \small, \Small, \SMALL, \tiny, \Tiny. +\footnotesize and \scriptsize are retained as synonyms of \Small and +\SMALL respectively. As it stands \tiny no longer produces the same +typesize as it did before (now 6 instead of 5), except in compatibility +mode. This might affect some existing documents if they are updated to +use \documentclass instead of \documentstyle. Similarly, \large now +produces 11pt if the base size is 10pt, where formerly it produced +12pt. + +New commands \larger and \smaller are provided for changing the +typesize relative to the current size. These commands take an optional +integer argument to specify how many steps to go up or down: \larger[2] +means go up two sizes, and \larger without an optional argument is the +same as \larger[1]. The list of sizes is a standard progression of +type sizes and associated linespacing values as defined by the +documentclass. If you need finer control over type size or linespacing, +consult the LaTeX documentation about the \fontsize command. + +---Extra documentclass options 8pt, 9pt, 11pt, 12pt + +---The \qed symbol is now an open square + +The \qed symbol is no longer a filled black square, but an open square, +and it is positioned at the right margin, instead of at a fixed +horizontal distance from the preceding text. If the \qed command is +used inside a displayed equation, however, it will be placed at a fixed +distance from the preceding material (correct placement in this case is +limited by some technical difficulties). + +---The command \rom was renamed to \upn. + +The command \rom, for making numbers and punctuation roman/upright in +italic text, has been renamed \upn ``upright punctuation or number''. +It will in most cases suffice to leave this refinement undone until a +document is sent to a publisher for final typesetting, and furthermore, +certain publications at the AMS now use special in-house italic fonts +that have upright numbers and punctuation built in, making the use of +\upn unnecessary even then. For general preprint-type use, this +refinement is one that most users probably won't care to bother with. + +======================================================================== diff --git a/Master/texmf-dist/doc/latex/amslatex/diffs-m.txt b/Master/texmf-dist/doc/latex/amslatex/diffs-m.txt new file mode 100644 index 00000000000..0bfa0ff69d4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/diffs-m.txt @@ -0,0 +1,552 @@ +diffs-m.txt [1999/12/15] American Mathematical Society + +This is a synopsis of the principal differences between various versions +of the amsmath package and its companion packages. + +A synopsis of changes in the "AMS-LaTeX" distribution is included at the +end of this file. See also diffs-c.txt in the amslatex/classes area. + +Those upgrading from version 1.2 to version 2.0 will probably be +interested in the question: + + After I upgrade will anything fail in my pre-existing documents? + +Certain of the bug fixes have the potential to affect the output of +existing documents in the following ways: + +---Vertical spacing for some displayed equations will change because +"abovedisplayshortskip" is now applied when possible. + +---Incorrect horizontal spacing for certain math constructs will change, +e.g., for \iint\nolimits or a subscript on a double-accented letter. + +---The default subscript placement in displayed formulas for \varinjlim, +\varprojlim, \varliminf, \varlimsup is now below rather than to the +side. To get the old behavior, add \nolimits---e.g., +\varliminf\nolimits_{...}. + +---Ellipsis dots in text (\ldots or \dots) will now behave the same as +in standard LaTeX; the surrounding space may therefore change. + +During regression testing we found some errors cropping up in documents +from incorrect usage that had not been caught with version 1.2. Although +these errors are relatively rare, documents containing such usage will +need to be corrected before they will run properly with version 2.0: + +---Use of two mutually exclusive display structures for the same +display. In this example the outer \[ \] are redundant: + + \[ + \begin{align*} + ... + \end{align*} + \] + +---Inadequate argument markup for math accents: + + \hat \mathcal{C} + +This should have been written with braces surrounding the argument of +the \hat command: \hat{\mathcal{C}}. + +For documents where error messages crop up after the upgrade, there are +various possible approaches, including: + +(a) Change instances of incorrect usage (if applicable). + +(b) Put a copy of amsmath.sty version 1.2 into the home directory of the +document. Then it should continue to work the same as before. + +(c) Use the snapshot package in combination with a shell script to +arrange that version 1.2 of amsmath is found instead of 2.0 when +processing the document. See ftp://ftp.ams.org/pub/tex/snapshot.*. This +approach requires a certain amount of technical knowledge. + +(d) Downgrade to version 1.2 again. + +======================================================================== +Changes in amsmath 2.0 [November 1999] + +---The AMS-LaTeX User's Guide (amsldoc.tex) has been turned into the + AMSmath User's Guide by moving the amsthm documentation into a + separate file (amsthdoc.tex) in the amslatex/classes area. + +---Restored normal use of "shortskip" spacing in single equations. + +[!! NOTE: This means that page breaks may change in existing documents.] + +---Restored normal use of available shrink around binary operators in + single equations. + +---Fixed poor subscript placement for double-accented letters. Math +accent handling was reworked in the process in such a way that the +capitalized forms of the math accent commands are no longer necessary. +\hat{\hat{X}} will do proper alignment of the second accent. \Hat et +cetera are retained for compabitility reasons. (Thanks to Javier Bezos +for donating some code from his accents package.) + +[!! NOTE: Improper math accent use will now produce wrong output.] + +Suppose that we have \boldH defined in the preamble as +\newcommand{\boldH}{\mathbf{H}}. Then the following examples illustrate +recommended usage. + + \hat{\mathbf{H}} OK + \hat{\boldH} OK + \hat\boldH Works OK, but deprecated by the LaTeX book + \hat\mathbf{H} Not OK! Output will be incorrect. + +Since the output will be wrong, amsmath gives an error message when the +last variant is detected. + +---The following kinds of mixed structures worked by happenstance with + amsmath 1.2, although they should have produced an error message. + With amsmath 2.0 they will produce an error or warning message. + + [!! NOTE: Potential error messages] + + % Outer \[ \] is redundant + + \[ + \begin{align*} + ... + \end{align*} + \] + + % Outer \begin{equation*} ... \end{equation*} is redundant + + \begin{equation*}\begin{alignat*}{2} + ... + \end{alignat*} + \end{equation*} + + % No printed material is allowed between \begin{equation} and + % \begin{split}: + + \begin{equation*}\left \{ + \begin{split} + ... + \end{split}\right . + \end{equation*} + +---diff12.tex is replaced by diffs-m.txt and diffs-c.txt, with the + latter moving to the amslatex/classes area. + +---Added an "?" option which gives some information about the available + documentation. + +---The amsmath definitions for matrix, pmatrix, and cases are + incompatible with the plain-TeX syntax for \pmatrix, \matrix, and + \cases, which are used occasionally by some authors in LaTeX + documents. In version 2.0 the error messages resulting from the + plain-TeX syntax have been made more intelligible. + +---If you need the boldsymbol facilities of the amsbsy package, use of + the "bm" (boldmath) package is recommended instead for new documents. + The amsbsy package is retained for compatibility with existing + documents. If you have a recent version of LaTeX (1998 or newer) you + already have the bm package; otherwise you may need to get it from + CTAN. (It is not an AMS package.) + +---\iint\nolimits: Fixed poor placement of subscript (also \iiint, +\idotsint, etc). + +---\varinjlim, \varprojlim, \varliminf, \varlimsup: Default to +\displaylimits instead of nolimits. + +---Fixed alignedat so that it doesn't take the first token of its + contents and try to interpret it as a number. + +---Leave text version of \dots and \ldots unchanged. + +---Changed \numberwithin so it no longer assumes previous definition of + \thesomething contained no prefixes. + +---\mathbf{\Gamma}: Leave cap Greek letters alone instead of converting + them from variable (fam 7) to fixed (fam 0). \mathbf{\gamma} still + fails---but that's a math font problem. + +---\mathindent is aliased to \@mathmargin so that when the fleqn option + is used, users can reset it as the LaTeX book advertises. + +---With the showkeys package: Corrected loss of marginal notes when +labels occurred inside an align environment. + +---Carried over some tweaks (\bmod, \right/leftarrowfill) from the 1996 + version of plain.tex. + +---Adjusted spacing of overarrow@ and underarrow@ to allow more room for + larger cmsy arrowheads. + +---Corrected spurious "overfull \hbox" warnings for \xrightarrow. + +---Corrected poor spacing for \xleftarrow. + +---Removed the \leavevmode in \smash which caused trouble for some + applications (e.g., the crop package) that expected the original + LaTeX definition. + +---Changed \def to \newcommand/\newenvironment where appropriate. + +---Use \sqrtsign instead of \@@sqrt (but include a backward + compatibility hack for the latter). + +---Left brace in \env{cases} environment would fail to work in + certain circumstances: Fix by using \lbrace instead of \{. + +---Use \ignorespacesafterend where applicable instead of + \global\@ignoretrue. + +---Protected commands in the definition of \theequation were + incorrectly expanded by the subequations environment when copying + the definition to \theparentequation: Fix by using \protected@edef. + +---Spurious extra space following punctuation at that end of a display: + In \math@cr, \math@cr@@, etc, use \iffalse{\fi instead of simply { to + keep an unwanted mathord atom from being added at the end of the + current math list; added \endmultline@math to work around a similar + sort of problem specific to the `multline' environment. + +---Various wrong results or no effect for \displaybreak inside "align", + "alignat", etc. Resetting \dspbrk@level in the \everycr of + \@display@init cleared most of these up. + +---Changed \displaybreak to issue an error message if enclosed in boxing + environment that will keep it from having any effect. + +---Turned off \displaybreak during the measuring phase of multline. + +---Fixed some numbering problems with multline and multline* and error + for use of \tag. + +---Use \@gtempa instead of \@tempa where assigned globally (standard + save stack precaution). + +---Save and restore \column@ to keep aligned from screwing up the column + counting of a parent align environment. Made \column@ assignments + uniformly global, except in a couple of places where the risk of side + effects seemed too great. + +---Error recovery for misspelled '\end{multline}' was not very helpful. + Improve \collect@body along lines suggested by Hellström. + +---Fixed up certain number placement problems with align + +---Add \alignsafe@testopt to work around a LaTeX bug: when a nested + alignment environment that takes an optional argument has an empty + first cell (i.e., begins with an &) LaTeX's optional argument + scanning screws up the alignment state. + +---Add `mathdisplay' environment (internal use) to correct several + problems of \[ \] and the `equation' environment arising from the + previous implementation as a degenerate case of `gather'. + +---It is possible now to use \eeq as an abbreviation for \end{equation} +(one of the consequences of the preceding change). But still not \eal +for \end{align} or certain other display structures. + +---Reorganize `split' internal calling sequence to go along with the use + of `mathdisplay' in \[ \] and `equation'. + +---Suppression of LaTeX error messages during measuring phase made + primitive TeX errors harder to understand; stop suppressing. (As a + result, users will sometimes get redundant error messages now.) + Remove obsolete Sb, Sp environments again. + +---The file amsintx.dtx was removed from the distribution pending + further development. + +---Remove the \ifinany@ switch, use \spread@equation instead to achieve + the same ends. + +---Remove unbracefonts@ function, no longer needed after changes in + math accent handling. + +---Got rid of the special trap for '^x that had been carried over from +AMS-TeX. + +---Made \overline, \doteq, \longrightarrow, etc, robust. + +---Changed \relbar to use \std@minus---otherwise \underleftrightarrow +works poorly in a \DeclareMathOperator definition. + +---Use \new@ifnextchar in matrix, pmatrix, cases so that \\<newline>[x] +doesn't trigger an error. + +---Bug fix for nested use of \label inside minipage inside equation. + +---Add minalignsep after every second column in aligned, for consistency +with align. + +======================================================================== +Changes in amsmath 1.2 [January 1995] + +---Name change; relation to the "amsfonts" package + +In version 1.1 of AMS-LaTeX, the name of this package was "amstex". The +new name is "amsmath". The amstex package automatically invoked the +amsfonts package as well; the amsmath package does not. + +---Adapted for LaTeX2e + +Old method of invocation: + + \documentstyle[amstex]{article}% LaTeX 2.09 + +New method of invocation: + + \documentclass{article} + \usepackage{amsmath} + +---Handling of options intlim, nosumlim, nonamelm, righttag, ctagsplt + +Old usage: + + \documentstyle[amstex,righttag,intlim] + +New usage: + + \usepackage[reqno,intlimits]{amsmath} + +Several option names were changed (mainly, they are no longer restricted +to eight characters): + + intlim -> intlimits + nosumlim -> nosumlimits + nonamelm -> nonamelimits + righttag -> reqno [for consistency with "leqno"] + ctagsplt -> centertags + +---Character @ is no longer used as a special command prefix + +Certain commands in the amstex pkg started with "@" instead of "\". This +special usage has been discontinued, except for the amscd package, and +then only within the CD environment. Practically speaking, this means +primarily that it is no longer necessary to use doubled @@ to get a +single printed @ character (e.g., in e-mail addresses). + +---The @, and @! micro-spacing commands are no longer provided + +As a consequence of the @ character change, "@," and "@!" are no longer +recognized spacing commands. An \mspace command is provided that can be +used instead; see the AMSmath User's Guide. + +---Extensible arrow commands @>>> and @<<< + +The commands @>>> and @<<< are no longer available [except in the CD +environment of the amscd package]; alternative commands \xleftarrow and +\xrightarrow are provided by the amsmath package. The sub and +superscripts are given through an optional resp. mandatory argument, for +example + + X\xleftarrow{b}Y % superscript "b" only + X\xrightarrow[\alpha]{\beta}Y % sub alpha, sup beta + +---The command \bold has been superseded by the command \mathbf, as the +latter is now the standard name provided by LaTeX for this purpose. + +---The commands \newsymbol, \frak, \Bbb are no longer available because +the amsfonts package is not loaded by amsmath. In any case those +commands now have new names---\frak -> \mathfrak, \Bbb -> \mathbb, etc. +See the amsfonts documentation for further details. + +---The amsmath package provides \lvert and \rvert to use for vert-bar +symbols when they act as delimiters (compare \langle, \rangle for +angle-bracket delimiters). Commands \lVert and \rVert are likewise +provided instead of \| for paired-delimiter use of the double-vert +symbol. Use of | and \| for paired delimiters can lead to incorrect +spacing in rare cases. Further discussion is found in the AMS-LaTeX +user's guide (amsldoc.tex). + +---The ~ command is now left unchanged by amsmath; the change +that makes it remove a redundant preceding or following space character +is now done only by AMS documentclasses (in version 1.1 this was done by +the amstex package). + +---The following rarely used commands are removed to the amsxtra +package: \accentedsymbol, \sphat, \spcheck, \sptilde, \spdot, \spddot, +\spdddot, \spbreve, \@))), \@(((. + +---The six generalized fraction commands \over, \overwithdelims, \atop, +\atopwithdelims, \above, \abovewithdelims are deprecated and produce +warning messages. Their functionality can be obtained through \frac, +\binom, and \genfrac instead. See amsldoc.tex and technote.tex for +further details. + +---The \fracwithdelims command is gone, as \genfrac provides +equivalent functionality (and a little more). + +---The optional argument of \frac that allowed changing the thickness of +the fraction line is gone. That functionality is now provided only +through \genfrac: the need to change the line thickness is so rare in +practice that it seems better not to burden the ubiquitous \frac command +with the somewhat time-consuming look-ahead process required for an +optional argument. I.e., this change will contribute in a small way to +making your documents run faster. + +---The commands \lcfrac and \rcfrac for left or right alignment of +continued fraction numerators are gone; they are replaced by an optional +argument of the \cfrac command. + +---A new command \DeclareMathOperator is provided for defining new +operator names: + +\DeclareMathOperator{\Tr}{Tr} +\DeclareMathOperator*{\xlim}{x-lim} + +The * form makes the operator name produce limit-style sub and +superscripts, like \max or \lim. This is now the preferred method, +instead of using the old command \operatorname (which is, however, +retained for now). The command \operatornamewithlimits has been renamed +\operatorname*. These commands now can also be obtained through a +separate package amsopn, so it's not necessary to load the entire +amsmath package just to get that feature. + +---Environments "Sb", "Sp" retired. + +The environments Sb and Sp for multiline subscripts have been replaced +by a single command \substack, used as follows: + +\sum_{\substack{first line\\second line}} + +This command can be used equally well in a subscript or superscript, and +provides better vertical positioning (as compared to Sb, Sp) if a +multiline subscript is placed on the side, as perhaps for an integral. +There is also a slightly generalized alternative, an environment +subarray that allows you to specify either centering or left alignment +for the contents: + +\sum_{\begin{subarray}{l}first line\\second line\end{subarray}} + +---New command \nobreakdash + +A command \nobreakdash is provided to suppress the possibility of a +linebreak after the following hyphen or dash. For example, if you write +"$p$\nobreakdash-adic" then a linebreak will never be taken between the +hyphen and the "adic". + +---The placement of equation numbers has been substantially improved for +align, gather, and split. Numbers will now never overlap on top of the +equation body (as far as we can ascertain), and they are much less +likely to be shifted up or down unnecessarily when there is actually +adequate space to leave the number in the normal place. In a few +remaining cases, an equation number will be shifted unnecessarily +because technical complications make accurate measurement of the +available room too difficult; for those cases a \raisetag command is +provided that allows you to manually adjust the vertical position of the +equation number. + +---The [xx]align[at] family of environments has been thoroughly revised: +now the xalignat environment is gone, as its function has been merged +into the align environment (it's no longer necessary to specify how many +side-by-side structures, as was required for xalignat, because align +automatically handles any number of them). Similarly, the xxalignat +environment has been replaced by an environment flalign that doesn't +require you to specify how many side-by-side structures will be needed. +Certain numbering problems (presence of an equation number when it +should be absent, or vice versa) have also been cleared up. + +(Thanks to David M. Jones for his substantial [volunteer] work behind +this change and the preceding one.) + +---The alignedat environment was changed to take two arguments rather +than one: a mandatory argument (as formerly) specifying the number of +align structures, and a new optional one specifying the placement of the +environment (parallel to the optional argument of aligned). However, +aligned is simpler to use, allowing any number of aligned structures +automatically, and therefore the use of alignedat is deprecated. + +---The seldom-used command \oldnos is gone; if you need it, you should +consult the LaTeX documentation on using fonts (e.g., fntguide.tex) to +find out how to construct an equivalent command. + +---A new subequations environment causes all numbered equation +environments within its scope to be numbered (4.9a) (4.9b) (4.9c) etc., +if the preceding numbered equation was 4.8. A \label command immediately +after \begin{subequations} will produce a \ref of the parent number +`4.9', not `4.9a'. The counters used by the subequations environment are +parentequation and equation and standard uses of \addtocounter, +\setcounter, etc., are possible with those counter names. + +---The amsmath package (unlike amstex) respects the setting provided by +the documentclass for putting equation numbers on the right or the left. +[Technical note: a documentclass that has leqno as the default should +explicitly pass that option to the amsmath package with +\PassOptionsToPackage in order for it to be effective.] + +---The fleqn option for left-aligned instead of centered equations is +now supported (thanks to David M. Jones). + +************************************************************************ +The remainder of this file discusses some changes that do not directly +pertain to the amsmath package but to the parent distribution known as +"AMS-LaTeX". + +======================================================================== +Changes in AMS-LaTeX 2.0 + +---The AMS-LaTeX User's Guide (amsldoc.tex) is split up into amsldoc.tex +and amsthdoc.tex, with the latter moving into the "classes" area. + +---The file amslatex.faq was split into amsmath.faq and amsclass.faq. + +---The file amslatex.bug was done away with; most of the information was +merged into diffs-m.txt, diffs-c.txt, amsmath.faq, and amsclass.faq. + +======================================================================== +Changes in AMS-LaTeX 1.2 + +---Adapted for LaTeX2e + +AMS-LaTeX 1.0 and 1.1 were designed to work with LaTeX 2.09, which +became obsolete in 1994 with the appearance of "LaTeX2e". AMS-LaTeX 1.2 +has been extensively adapted to take advantage of various features of +LaTeX2e. It is no longer a separate TeX format---i.e., it does not need +to be invoked by a separate "amslatex" command. + +---LaTeX 2.09 font commands (\bf, \it, etc) + +Pre-existing documents will for the most part continue to work fine +without requiring any changes. However, depending on the installation +options used for your copy of AMS-LaTeX 1.1 you may need to update the +options list of the \documentstyle command by adding newlfont, for +example: + + \documentstyle[newlfont]{amsart} + +---The packages amsfonts, amssymb were moved to the AMSFonts +distribution. They used to be included in the AMS-LaTeX distribution for +pragmatic reasons but their natural home is with the AMSFonts +distribution. + +---Package amstex renamed to amsmath + +The amstex package has been renamed amsmath. The old name `amstex' came +from the fact that version 1.0 was a more or less straight port into +LaTeX of selected portions from the macro package AmS-TeX written by +Michael Spivak, but the historical origins of the package are likely of +less interest to the general usership---especially looking to the +future---than a straightforward declaration in the name `amsmath' of the +sort of features that are provided. + +Another important reason for the name change was to make possible some +progress that would be out of the question (because of the impact on +existing documents) if the name `amstex' were retained. For example, +unlike amstex, amsmath doesn't automatically load the amsfonts package, +as that package was moved out to the AMSFonts distribution as described +above. If this change were not accompanied by a name change, many +existing documents would have to be updated by hand (adding +\usepackage{amsfonts}) in order to run without error. A frozen version +of amstex.sty is provided for processing pre-existing documents; it +won't have active maintainence henceforth except for bug fixes. For new +documents, authors should use the amsmath package. + +Therefore, "\usepackage{amstex}" is incorrect usage---do not rely on the +1994 edition of `The LaTeX Companion' in this respect (unless you obtain +the errata for Chapter 8; see +http://ctan.tug.org/info/compan-rev/ch8.pdf). + +---New documentclass amsproc + +A new documentclass amsproc was added for collections of articles, such as +the proceedings of a conference. diff --git a/Master/texmf-dist/doc/latex/amslatex/exercise.thm b/Master/texmf-dist/doc/latex/amslatex/exercise.thm new file mode 100644 index 00000000000..93929b3beb0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/exercise.thm @@ -0,0 +1,8 @@ +%% LaTeX2e file `exercise.thm' +%% generated by the `filecontents' environment +%% from source `thmtest' on 2005/02/14. +%% +\def\th@exercise{% + \normalfont % body font + \thm@headpunct{:}% +} diff --git a/Master/texmf-dist/doc/latex/amslatex/gktest.ltb b/Master/texmf-dist/doc/latex/amslatex/gktest.ltb new file mode 100644 index 00000000000..4236749372b --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/gktest.ltb @@ -0,0 +1,440 @@ +\documentclass{amsbook} +\usepackage{amsrefs} +\providecommand{\cyr}{} +\providecommand{\cprime}{\textprime} +\providecommand{\germ}{\mathfrak } + +\begin{document} +\begin{bibdiv} +\begin{biblist} + +\bib{MR58:27738}{book}{ + author={Andrews, G.~E.}, + title={The theory of partitions}, + publisher={Encyclopedia of Mathematics and its Applications, Vol. 2, + Addison-Wesley, Mass.-London-Amsterdam}, + date={1976}, +} + +\bib{MR90b:82001}{book}{ + author={Baxter, R.~J.}, + title={Exactly solved models in statistical mechanics}, + publisher={Academic Press Inc.}, + address={London}, + date={1989}, + ISBN={0-12-083182-1}, +} + +\bib{MR1451594}{article}{ + author={Benkart, G.}, + author={Kang, S.-J.}, + author={Melville, D.}, + title={Quantized enveloping algebras for Borcherds superalgebras}, + date={1998}, + ISSN={0002-9947}, + journal={Trans. Amer. Math. Soc.}, + volume={350}, + number={8}, + pages={3297\ndash 3319}, +} + +\bib{MR95d:17023}{article}{ + author={Benkart, G.}, + author={Kang, S.-J.}, + author={Misra, K.~C.}, + title={Indefinite Kac-Moody algebras of classical type}, + date={1994}, + ISSN={0001-8708}, + journal={Adv. Math.}, + volume={105}, + number={1}, + pages={76\ndash 110}, +} + +\bib{MR93d:17017}{article}{ + author={Chari, V.}, + author={Pressley, A.}, + title={Quantum affine algebras}, + date={1991}, + ISSN={0010-3616}, + journal={Comm. Math. Phys.}, + volume={142}, + number={2}, + pages={261\ndash 283}, +} + +\bib{MR26:2519}{book}{ + author={Curtis, Charles~W.}, + author={Reiner, Irving}, + title={Representation theory of finite groups and associative algebras}, + publisher={Interscience Publishers, a division of John Wiley \& Sons, New + York-London}, + date={1962}, + review={\MR{26 \#2519}}, +} + +\bib{Dr86}{incollection}{ + author={Drinfel$'$d, V.~G.}, + title={Quantum Groups}, + date={1987}, +conference={ + title={Proceedings of the International Congress of Mathematicians}, + address={Berkeley}, + date={1986} +}, + publisher={American Mathematical Society, Providence}, + pages={798\ndash 820}, +} + +\bib{MR94d:17032}{article}{ + author={Feingold, A.~J.}, + author={Frenkel, I.~B.}, + author={Ries, J.~F.~X.}, + title={Representations of hyperbolic Kac-Moody algebras}, + date={1993}, + ISSN={0021-8693}, + journal={J. Algebra}, + volume={156}, + number={2}, + pages={433\ndash 453}, +} + +\bib{MR84f:17004}{article}{ + author={Frenkel, I.~B.}, + author={Kac, V.~G.}, + title={Basic representations of affine Lie algebras and dual resonance + models}, + date={1981}, + ISSN={0020-9910}, + journal={Invent. Math.}, + volume={62}, + number={1}, + pages={23\ndash 66}, +} + +\bib{Gould}{article}{ + author={Gould, M.~D.}, + author={Zhang, R.~B.}, + author={Bracken, A.~J.}, + title={Quantum double construction for graded Hopf algebras}, + date={1993}, + journal={Bull. Austral. Math. Soc.}, + volume={47}, + pages={353\ndash 375}, +} + +\bib{MR1633090}{article}{ + author={Hong, J.}, + author={Kang, S.-J.}, + author={Miwa, T.}, + author={Weston, R.}, + title={Mixing of ground states in vertex models}, + date={1998}, + ISSN={0305-4470}, + journal={J. Phys. A}, + volume={31}, + number={28}, + pages={L515\ndash L525}, +} + +\bib{Jac1}{book}{ + author={Jacobson, N.}, + title={Basic algebra II}, + publisher={W. H. Freeman and Company}, + address={San Francisco}, + date={1980}, + ISBN={0-7167-1079-X (v. 2)}, +} + +\bib{MR98k:17037}{article}{ + author={Jeong, K.}, + author={Kang, S.-J.}, + author={Lee, H.}, + title={Lie-admissible algebras and Kac-Moody algebras}, + date={1997}, + ISSN={0021-8693}, + journal={J. Algebra}, + volume={197}, + number={2}, + pages={492\ndash 505}, +} + +\bib{Joseph}{book}{ + author={Joseph, A.}, + title={Quantum groups and their primitive ideals}, + publisher={Springer-Verlag}, + address={Berlin}, + date={1995}, + ISBN={3-540-57057-8}, +} + +\bib{Kac90}{book}{ + author={Kac, V.~G.}, + title={Infinite dimensional Lie algebras}, + edition={3}, + publisher={Cambridge University Press}, + address={Cambridge}, + date={1990}, + ISBN={0-521-37215-1; 0-521-46693-8}, +} + +\bib{KMW}{incollection}{ + author={Kac, V.~G.}, + author={Moody, R.~V.}, + author={Wakimoto, M.}, + title={On ${E}\sb {10}$}, + date={1988}, +conference={ + title={Differential geometrical methods in theoretical physics}, + address={Como}, + date={1987} +}, + publisher={Kluwer Acad. Publ.}, + address={Dordrecht}, + pages={109\ndash 128}, +} + +\bib{Ka93-1}{article}{ + author={Kang, S.-J.}, + title={Root multiplicities of the hyperbolic Kac-Moody Lie algebra + $HA\sp{(1)}\sb 1$}, + date={1993}, + ISSN={0021-8693}, + journal={J. Algebra}, + volume={160}, + number={2}, + pages={492\ndash 523}, +} + +\bib{MR94d:17033}{article}{ + author={Kang, S.-J.}, + title={On the hyperbolic Kac-Moody Lie algebra $HA\sb 1\sp + {(1)}$}, + date={1994}, + ISSN={0002-9947}, + journal={Trans. Amer. Math. Soc.}, + volume={341}, + number={2}, + pages={623\ndash 638}, +} + +\bib{MR97e:17041}{incollection}{ + author={Kang, S.-J.}, + title={Root multiplicities of graded Lie algebras}, + date={1996}, +conference={ + title={Lie algebras and their representations}, + address={Seoul}, + date={1995}, +}, + publisher={Amer. Math. Soc.}, + address={Providence, RI}, + pages={161\ndash 176}, +} + +\bib{MR1641035}{article}{ + author={Kang, S.-J.}, + author={Kashiwara, M.}, + title={Quantized affine algebras and crystals with core}, + date={1998}, + ISSN={0010-3616}, + journal={Comm. Math. Phys.}, + volume={195}, + number={3}, + pages={725\ndash 740}, +} + +\bib{MR93g:17027}{article}{ + author={Kang, S.-J.}, + author={Kashiwara, M.}, + author={Misra, K.~C.}, + author={Miwa, T.}, + author={Nakashima, T.}, + author={Nakayashiki, A.}, + title={Vertex models and crystals}, + date={1992}, + ISSN={0764-4442}, + journal={C. R. Acad. Sci. Paris S\'er. I Math.}, + volume={315}, + number={4}, + pages={375\ndash 380}, +} + +\bib{MR1464137}{article}{ + author={Kang, S.-J.}, + author={Kim, M.-H.}, + title={Borcherds superalgebras and a monstrous Lie superalgebra}, + date={1997}, + ISSN={0025-5831}, + journal={Math. Ann.}, + volume={307}, + number={4}, + pages={677\ndash 694}, +} + +\bib{MR95f:17013}{article}{ + author={Kang, S.-J.}, + author={Misra, K.~C.}, + title={Crystal bases and tensor product decompositions of $U\sb q(G\sb + 2)$-modules}, + date={1994}, + ISSN={0021-8693}, + journal={J. Algebra}, + volume={163}, + number={3}, + pages={675\ndash 691}, +} + +\bib{Kash90}{article}{ + author={Kashiwara, M.}, + title={Crystalizing the $q$-analogue of universal enveloping algebras}, + date={1990}, + journal={Comm. Math. Phys.}, + volume={133}, + pages={249\ndash 260}, +} + +\bib{Keng82}{book}{ + author={Keng, H.~L.}, + title={Introduction to number theory}, + publisher={Springer-Verlag}, + date={1982}, +} + +\bib{Wang}{article}{ + author={Li, W.~L.}, + title={Classification of generalized Cartan matrices of hyperbolic + type}, + date={1988}, + journal={Chinese Ann. Math. Ser. B}, + volume={9}, + number={1}, + pages={68\ndash 77}, +} + +\bib{MR98a:20041}{incollection}{ + author={Littelmann, P.}, + title={An effective method to classify nilpotent orbits}, + date={1996}, +conference={ + title={Algorithms in algebraic geometry and applications}, + address={Santander}, + year={1994} +}, + publisher={Birkh\"auser}, + address={Basel}, + pages={255\ndash 269}, +} + +\bib{MR2000d:17019}{article}{ + author={Littelmann, P.}, + title={Bases canoniques et applications}, + date={1998}, + ISSN={0303-1179}, + journal={Ast\'erisque}, + number={252}, + pages={Exp.\ No.\ 847, 5, 287\ndash 306}, + note={S\'eminaire Bourbaki. Vol.\ 1997/98}, +} + +\bib{MR92d:16032}{article}{ + author={Littelmann, P.}, + author={Procesi, C.}, + title={On the Poincar\'e series of the invariants of binary forms}, + date={1990}, + ISSN={0021-8693}, + journal={J. Algebra}, + volume={133}, + number={2}, + pages={490\ndash 499}, +} + +\bib{MR92g:20067}{incollection}{ + author={Littelmann, Peter}, + title={Good filtrations, decomposition rules and standard monomial + theory}, + date={1991}, +conference={ + title={Computational aspects of Lie group representations and + related topics}, + address={Amsterdam}, + date={1990} +}, + publisher={Math. Centrum Centrum Wisk. Inform.}, + address={Amsterdam}, + pages={89\ndash 106}, +} + +\bib{MR92b:14027}{incollection}{ + author={Littelmann, Peter}, + author={Procesi, Claudio}, + title={Equivariant cohomology of wonderful compactifications}, + date={1990}, +conference={ + title={Operator algebras, unitary representations, enveloping + algebras, and invariant theory}, + address={Paris}, + date={1989} +}, + publisher={Birkh\"auser Boston}, + address={Boston, MA}, + pages={219\ndash 262}, +} + +\bib{MR94m:17016}{book}{ + author={Lusztig, G.}, + title={Introduction to quantum groups}, + publisher={Birkh\"auser Boston Inc.}, + address={Boston, MA}, + date={1993}, + ISBN={0-8176-3712-5}, +} + +\bib{Nak96}{article}{ + author={Nakayashiki, A.}, + title={Fusion of the $q$-vertex operators and its applications + to solvable vertex models}, + date={1996}, + ISSN={0010-3616}, + journal={Commun. Math. Phys.}, + volume={177}, + number={2}, + pages={27\ndash 62}, +} + +\bib{Rob}{article}{ + author={Robinson, D.}, + title={On representations of the symmetric group}, + date={1938}, + journal={Amer. J. Math.}, + volume={60}, + pages={745\ndash 760}, +} + +\bib{Ser77}{book}{ + author={Serre, J.-P.}, + title={Linear representations of finite groups}, + publisher={Springer-Verlag}, + date={1977}, +} + +\bib{Weyl}{book}{ + author={Weyl, H.}, + title={Classical groups}, + edition={2}, + publisher={Princeton University Press}, + date={1946}, +} + +\bib{Young4}{article}{ + author={Young, A.}, + title={On quantitative substitutional analysis IV}, + date={1929}, + journal={Proc. Lond. Math. Soc. (2)}, + volume={31}, + pages={253\ndash 272}, +} + +\end{biblist} +\end{bibdiv} +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/install.txt b/Master/texmf-dist/doc/latex/amslatex/install.txt new file mode 100644 index 00000000000..e03f5411a1e --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/install.txt @@ -0,0 +1,69 @@ +install.txt for amsrefs 2.0 [2004-06-30] + +Preliminary note: The normal destination directory for amsrefs.sty in a +standard TDS structure would be texmf/tex/latex/amscls (see step 3 +below). In the future, the amsrefs package will be integrated more +thoroughly into the amscls distribution, but the current release has to +be provided in the form of a separate distribution for those who already +have the amscls distrib but not amsrefs. + +------------------------------------------------------------------------ +The first step is to identify the primary location for LaTeX input files +on your system. Typical examples are + + /usr/local/share/texmf/tex/latex... (Unix) + + C:\SWP30\TCITeX\TeX\LaTeX... (Windows) + +We define "ROOT" to mean everything preceding the "/tex/latex" part. In +the second example, this would be "C:\SWP30\TCITeX". ROOT will normally +end in "texmf"; if it doesn't you may need to consult the documentation +for your TeX system to find out what to use. In the following +instructions, wherever you see ROOT substitute the actual directory or +folder name that is used on your system. + +If this terminology doesn't make sense to you, seek assistance from +a friend or colleague, or from the company that you bought your TeX +system from, or contact us at + + tech-support@ams.org + 800-321-4AMS (321-4267) (USA/Canada) + 401-455-4080 + +If you have multiple texmf trees (as discussed, for example, in the +teTeX documentation), you may want to install amsrefs using the +TEXMFLOCAL tree as the value of ROOT. In due course when you upgrade to +a newer TeX system, we expect that you will find amsrefs already +incorporated into the TEXMFMAIN tree as part of the tex/latex/amscls +area, at which point you will no longer need the copy in your TEXMFLOCAL +tree. + +------------------------------------------------------------------------ +1. Download the following archive file: + + ftp://ftp.ams.org/pub/tex/amsrefs.zip + +2. Extract files using the texmf root directory as the destination. Some +typical examples: + +WinZip: Click on "Extract" and then in the "Extract to" box, enter + c:\sw\texmf (or whatever ROOT is on your system) + +unzip: unzip amsrefs.zip -d ROOT + +3. Please note that although the source files for amsrefs unpack into +the ROOT/source/latex/amsrefs area at the present time [2001-12-28], the +other files unpack into .../latex/amscls because that is the natural +location for them. + +To check the end result, you should find that you now have amsrefs.sty +in the following location (substituting \ or : for / if appropriate): + + ROOT/tex/latex/amscls/amsrefs.sty + +If you have a teTeX system you may need to rerun mktexlsr [known in +earlier versions of teTeX as "texhash"]. + +For a MikTeX system the command would be "initexmf -u", or look for +"Refresh the Filename Database" in the MikTeX menus (this may be +somewhat version-dependent). diff --git a/Master/texmf-dist/doc/latex/amslatex/instr-l.pdf b/Master/texmf-dist/doc/latex/amslatex/instr-l.pdf Binary files differnew file mode 100644 index 00000000000..76fabaa0e54 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/instr-l.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/instr-l.tex b/Master/texmf-dist/doc/latex/amslatex/instr-l.tex new file mode 100644 index 00000000000..30aa283237b --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/instr-l.tex @@ -0,0 +1,1233 @@ +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "instr-l.tex", +%%% version = "2.20", +%%% date = "2004/08/06", +%%% time = "16:17:21 EDT", +%%% checksum = "60855 1233 6587 50183", +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1994, 2004 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Publications Technical Group, +%%% 201 Charles Street, +%%% Providence, RI 02904, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% codetable = "ISO/ASCII", +%%% keywords = "latex, AMS, amslatex, ams-latex, author instructions", +%%% supported = "yes", +%%% abstract = "These are instructions for preparing documents for +%%% submission to the AMS, using amsmath and AMS LaTeX +%%% document classes.", +%%% docstring = "The checksum field above contains a CRC-16 checksum +%%% as the first value, followed by the equivalent of +%%% the standard UNIX wc (word count) utility output of +%%% lines, words, and characters. This is produced by +%%% Robert Solovay's checksum utility.", +%%% } +%%% ==================================================================== +\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX) +[1995/06/01]% LaTeX date must be June 1995 or later +\documentclass{amsart} + +\hyphenation{man-u-script man-u-scripts over-view pre-par-ing which-ever} + +%% Define macros for text substitution and for presentation of examples +\newcommand{\AMS}{American Mathematical Society} +\def\latex/{{\protect\LaTeX}} +\def\latexe/{{\protect\LaTeXe}} +\def\amslatex/{{\protect\AmS-\protect\LaTeX}} +\def\tex/{{\protect\TeX}} +\def\amstex/{{\protect\AmS-\protect\TeX}} +\def\bibtex/{{Bib\protect\TeX}} +\def\makeindx/{\textit{MakeIndex}} + +\newcommand{\filnam}[1]{\mbox{\texttt{\ignorespaces#1\unskip}}} +\let\fn=\filnam +\let\cls=\filnam +\let\env=\filnam +\let\pkg=\filnam +\def\opt#1{\filnam{[#1]}} + +%% For this manual, add a section number to the references header, and +%% include that section header in the contents list. +\makeatletter +\def\thebibliography#1{\section\refname + \normalfont\small\labelsep .5em\relax + \list{\@arabic\c@enumiv.}{\settowidth\labelwidth{#1.}% + \leftmargin\labelwidth \advance\leftmargin\labelsep + \usecounter{enumiv}}% + \sloppy \clubpenalty4000\relax \widowpenalty\clubpenalty + \sfcode`\.\@m} +% +%% Turn off series logo and copyright note +\let\serieslogo@\relax +\let\@setcopyright\relax + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Table of contents customizations + +\let\tocori=\tableofcontents +\def\tableofcontents{\tocori + \skip@\lastskip \vskip-\lastskip + \addtocontents{toc}{\protect\tocpatch}% + \vskip\skip@ \relax} + +\def\tocsection#1#2#3{% + \indentlabel{\@ifnotempty{#2}{\tocnbox{\hss#1 #2.\quad}}}#3} +\let\tocnbox=\hbox +\def\tocpatch{% + \@xp\let\csname r@tocindent2\@xp\endcsname\csname r@tocindent1\endcsname + \def\tocnbox{\hbox to\@tempdima}} +%% In this document, subsections are unnumbered, but we want an indent +%% to be used. +\def\tocsubsection#1#2#3{\hbox to\leftskip{}#3} +\def\l@subsection{\@tocline{2}{0pt}{.5pc}{}{}} +\makeatother + +\newdimen\exindent +\exindent=3\parindent +%% Add a high penalty to discourage line breaks within an example +%% without absolutely prohibiting them. +{\obeylines + \gdef^^M{\par\penalty9999 }% + \gdef\beginexample#1{\medskip\bgroup % + \def\(##1){\makebox[0pt]{\normalfont\mdseries##1}}% + \def~{\char`\~}\def\\{\char`\\}% + \normalfont\ttfamily\frenchspacing % + \parindent=0pt#1\leftskip=\exindent\obeylines} +}% end \obeylines +\def\endexample{\endgraf\egroup\medskip} +\newdimen\exboxwidth +\exboxwidth=3in +\def\exbox#1#2{\noindent \hangindent=\exboxwidth + \makebox[0pt][r]{\null\normalfont\mdseries#1\unskip\enspace}% + \makebox[\exboxwidth][l]{\normalfont\ttfamily\ignorespaces#2}% + \normalfont\mdseries\ignorespaces} + +\newcommand\cn[1]{\mbox{\def\\{\char`\\}% + \normalfont\ttfamily\\\ignorespaces#1\unskip}} +\let\ttcs=\cn +\newcommand\ttcsb[2]{% + \mbox{\def\\{\char`\\}% + \normalfont\ttfamily + \\begin\{\ignorespaces#1\unskip\}\ignorespaces#2\unskip}} +\newcommand\ttcse[1]{\mbox{\def\\{\char`\\}% + \normalfont\ttfamily\\end\{\ignorespaces#1\unskip\}}} +\def\{{\char`\{\relax} +\def\}{\char`\}\relax} + +%% Provide a meta-command facility; provide an alternate escape +%% character so it can be used within the verbatim environment. + +\catcode`\|=0 +\begingroup \catcode`\>=13 % in LaTeX2e verbatim env makes > active +\gdef\?#1>{{\normalfont$\langle$\textup{#1}$\rangle$}} +\gdef\0{\relax} +\endgroup +\def\<#1>{{\normalfont$\langle$\textup{#1}$\rangle$}} +\newcommand{\Dimen}{\<dimen>} +\newcommand{\tab}{\textsc{tab}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% Provide a dummy titlepage, saving maketitle for the article title. +%% Table of contents goes onto the inside front cover. + +\def\instrversion{2.20} +\def\instrdate{August 2004} + +\begin{document} + +\thispagestyle{empty} +\vspace*{1.5in} +\begin{center} + {\huge\bfseries Instructions\\[2pt] for Preparation\\[2pt] + of Papers\\[2pt] and Monographs + \par\vspace{\baselineskip} + \amslatex/ + \par} + \vspace{3\baselineskip} + \Large + Version \instrversion\\[4pt] \instrdate +\end{center} +\newpage + +\thispagestyle{empty} +\tableofcontents +\newpage + +\setcounter{page}{1} + +\title [ELECTRONIC MANUSCRIPTS: \amslatex/] + {Instructions for Preparation\\ + of Papers and Monographs: \amslatex/} +\dedicatory{% + \mbox{\normalfont\mdseries\small Version \instrversion: \instrdate}} + +\maketitle + +\section{Introduction} + +This manual is directed mainly to authors preparing material for +publication by the AMS, using \amslatex/ document classes. As such, +it deals with the AMS publishing style. Since these document classes +are also used by authors who are not submitting items to the AMS, +the manual also covers topics of more general relevance. However, it +assumes familiarity with standard \latex/ techniques and conventions, +and contains only material specific to AMS packages. + +Links to information useful in preparing manuscripts and graphics +can be found on the AMS Author Resource Center web page \cite{ARC}\@. +That information supplements this manual, and we recommend that you +review it. + +The AMS produces three major types of publications: journals (both +print and electronic), proceedings volumes, and monographs. There +is a core AMS document class for each: \cls{amsart}, \cls{amsproc} +and \cls{amsbook}, respectively. For most journals or book series, +there is a specific author package, based on one of the core classes. +If the specific publication is known, the appropriate author package +should be obtained from the AMS web server \cite{AP} and used for +preparation of manuscripts. In addition, there is a separate package +for editors of proceedings volumes \cite{EP}, with facilities for +preparing material that does not fit into the normal ``article'' +category. + +If the specific publication is not known, an appropriate generic AMS +document class can be used: + +\begin{itemize} +\item \pkg{gen-j-l} for journal articles (based on \pkg{amsart}) +\item \pkg{gen-p-l} for articles in book proceedings (based on \pkg{amsproc}) +\item \pkg{gen-m-l} for monographs (based on \pkg{amsbook}) +\end{itemize} + +The tagging of elements in a manuscript---title, author(s), section +headings, theorems, etc.--- is consistent through all author packages. +Thus a manuscript prepared using the appropriate generic document +class can be modified trivially to use the specific package, simply by +updating the \cn{documentclass} statement. For example, to specify +the \textit{Contemporary Mathematics} proceedings series: +\begin{verbatim} +\documentclass{conm-p-l} +\end{verbatim} + +Each author package contains an electronic version of this manual, +class files, sample documents, and a \texttt{README} file that +contains information about each of the files in the package. + +When an AMS author package is used, both \latex/ and a recent version +of \amslatex/ must be installed on the computer being used for +manuscript preparation. The AMS Author Resource Center web page +\cite{ARC} has a link to download the most recent version of +\amslatex/. The version number appears at the top of the file +\pkg{amsmath.sty} (and other files in the collection), and is also +reported in the log file of a \latex/ run; make sure you have +version 2.0 or later. + +\section{Article preparation} + +We first address articles intended for journals and proceedings. +Monographs are addressed in a separate section (see +page~\pageref{s:mono}). + +\subsection*{Starting a new article}\label{ss:newamsart} +%% +Individual articles generally have the following structure: +\begin{itemize} +\item \verb+\documentclass{...}+ +\item preamble (for document-specific customizations) +\item \verb+\begin{document}+ +\item top matter information +\item \verb+\maketitle+ (to set the top matter) +\item article body +\item reference list +\item \verb+\end{document}+ +\end{itemize} +A detailed template file (included in each package) provides +a complete set of commands for the article top matter, and the +instructions for using them. The most efficient way to start a +new article is to make a copy of the template and fill it in. + + +\section{The preamble} + +The area between the \verb+\documentclass+ statement and the line +\verb+\begin{document}+ is referred to as the ``preamble''. This is +the place to load external packages and define document-specific +commands. + +Available \cn{documentclass} options are described in the file +\filnam{amsclass.dtx}. Process this file with \latex/ to obtain a +version with human-readable documentation. One option does need to +be mentioned here: \opt{psamsfonts}; include this option as +\begin{verbatim} +\documentclass[psamsfonts]{...} +\end{verbatim} +to ensure correct sizing of fonts in environments other than normal text. + +\subsection*{Packages} +%% +The AMS document classes incorporate the code for the AMS theorem +(\pkg{amsthm}) package and automatically load the \pkg{amsmath} +package. It is not necessary to request either one explicitly. +The user guides for these packages \cite{ATP,AMP} contain the details, +which will not be repeated here. The \pkg{amsfonts} package is loaded +as well, unless the \opt{noamsfonts} option is specified; see the +AMSFonts User's Guide \cite{AFG} for the features provided. + +Not all publicly available packages are compatible with the AMS +document classes. For this reason, we mention some that are: +\begin{itemize} +\item \pkg{amssymb} provides names for additional symbols from the + AMS symbol fonts; see \cite{AFG} for details. +\item \pkg{amsmidx} supports multiple indexes for a book; see + page~\pageref{ss:indexing}. +\item \pkg{graphicx} is part of the \latex/ suite, preferred for + inclusion of graphics. +\item \pkg{longtable} facilitates tables longer than one page. +\item \pkg{upref} forces cross-references with \cn{ref} to roman; + see ``Roman type'', page~\pageref{ss:roman}. +\item \pkg{xypic} is recommended for creating commutative diagrams. +\end{itemize} + +There are several packages that cause particular problems for AMS +production. Their use should be avoided if possible: +\begin{itemize} +\item \pkg{psfrag}, for applying labels externally to included graphics, + may result in a PostScript that can't be converted properly to PDF. +\item \pkg{epsfig} has been superseded by \pkg{graphicx}. +\end{itemize} + +Don't load any packages that aren't actually needed. + + +\subsection*{New commands} +%% +Place all definitions for new commands in the preamble. This includes +instructions to access fonts that are not already defined in the AMS +document classes or \pkg{amsmath}, such as a new math alphabet (see +\cite{AMP}). + +Always use \cn{newcommand}; this will let you know if the name you +have chosen has already been used. Do not redefine any command from +\latex/, \pkg{amsmath}, or any AMS document class, as this could cause +problems in AMS production. New definitions may be used to provide +shorthand forms for mathematical expressions that are used frequently, +but do not use new definitions for text; for articles posted on-line, +this will prevent indexing software from identifying relevant +references. + +Use commands and environments provided by the AMS document classes +and standard packages whenever applicable---for example, you should +use the AMS \env{proof} environment rather than define your own +alternative. + +When the file is complete, remove any commands that haven't been used. + + +\section{Top matter}\label{s:topmatter} + +The top matter associated with an article includes information that +would appear in a bibliographic reference to the paper, plus additional +information about the author(s), subject classifications, key words, +acknowledgments of support, and the abstract. + + +\subsection*{Summary of tags and elements} +%% +Table 1 lists the top matter commands provided by \amslatex/ +version 2.0 and later. Not every tag is necessary for each paper. +The table shows which tags are necessary and which are optional. +Requirements for monographs are somewhat different and are described +later. The template file included in every author package contains +all the necessary tags and instructions for using them. + +\begin{table}[ht] +\caption{Top matter tags} +\begin{minipage}{\textwidth} +\begin{verbatim} +\documentclass{amsart} +|?preamble commands, such as |ttcs|bgroup|0newcommand|egroup, etc.> + +\begin{document} +\end{verbatim} +\begin{center} +\begin{tabular}{lcc} +\ & \multicolumn{2}{c}{Required by}\\ +\ & Journals & Books \\ +\verb+\title[...]{...}+ & yes\rlap{${}^1$} & yes\rlap{${}^1$} \\ + +\verb+\author[...]{...}+ & yes\rlap{${}^1$} & yes\rlap{${}^1$} \\ +\verb+\contrib[...]{...}+ & no\rlap{${}^2$} & --- \\ +\verb+\address{...}+ & yes & yes \\ +\verb+\curraddr{...}+ & no & no \\ +\verb+\email{...}+ & no & no \\ +\verb+\urladdr{...}+ & no & no \\ +\verb+\dedicatory{...}+ & no & no \\ +\verb+\date{...}+ & ---\rlap{${}^3$} & --- \\ +\verb+\thanks{...}+ & no & no \\ +\verb+\translator{...}+ & ---\rlap{${}^3$} & ---\rlap{${}^3$} \\ +\verb+\keywords{...}+ & no & no \\ +\verb+\subjclass[2000]{...}+ & yes & yes \\ +\verb+\begin{abstract}...\end{abstract}+ & yes\rlap{${}^4$} & no \\ +\verb+\maketitle+ & yes & yes \\ +\end{tabular} +\end{center} +\vspace*{1pc} + +{\Small +${}^1$ If no short form is needed, omit the brackets. + +${}^2$ For contributors, see details on page~\pageref{ss:contrib}. + +${}^3$ If this is necessary, it will be filled in by the AMS staff. + +${}^4$ For the \textit{Journal of the American Mathematical Society}, +abstracts are optional. +\par +} +\end{minipage} +\vspace{.25\baselineskip} +\hrule width \textwidth +\vspace{.5\baselineskip} +\end{table} + +\subsection*{Title} +%% +For AMS journal articles, capitalize only the first word and proper +nouns in the title. For articles in an AMS proceedings volume, +capitalize the first and last words of the title and all nouns, +pronouns, adjectives, adverbs, and verbs. Articles, conjunctions, and +prepositions should be lowercased unless they are the first or last +word of the title. These rules should be followed even if the +publication in which the article appears has another style. The style +for the particular publication will be generated automatically when +the article is processed at the AMS. + +A multiline title may be left for \latex/ to break, or a desired break +may be indicated by \cn{\\}. + +Unless the title is very short, provide a form of the title suitable +for use in running heads. This should be entered in brackets between the +tag \cn{title} and the full title: +\verb+\title[+short title\verb+]{+full title\verb+}+. +Do not use author-defined macros in the title. + +\subsection*{Author information}\label{ss:authorinfo} +%% +Enter the name(s) of the author(s) with the tag \cn{author}, using +standard capitalization for proper names. Use a separate \cn{author} +command for each author. Names will be combined by \latex/ according +to the dictates of the document class. See also ``contributors'', +below. + +If the author name(s) cannot fit in the space available for the running +head, enter a shortened form for each name in [brackets] +between the tag \cn{author} and the full name. Acceptable shortened +forms use initials for all but the surname(s). For example, +\begin{verbatim} +\author[J. Smith]{Joseph Smith} +\end{verbatim} +If the list of shortened author names is still too long for the running +head (including a reasonable space for the page number), it can be +shortened as in the following example, as a last resort: +\begin{trivlist} +\item\relax +\verb+\markleft{J. SMITH ET AL.}+ +\end{trivlist} + +\noindent +Note that \cn{markleft} is available only for \amslatex/ versions 2.20 +and later; it is not a basic \latex/ command. +Data provided with \cn{markleft\{\}} \emph{must} be in all capital letters +(except for included math). Place \cn{markleft\{\}} before the first +\cn{author} in your file. + +For each author you should provide one or more addresses. Tag them +as follows, grouping them in this order by author: +\begin{verbatim} +\address{...} |rm address where the research was carried out |tt +\curraddr{...} |rm current address, if different from the research address |tt +\email{...} |rm address for electronic mail |tt +\urladdr{...} |rm URL address (optional) +\end{verbatim} +Do \emph{not} include any addresses within the scope of an +\cn{author\{\}} command (this is different from basic \latex/). +Do not use abbreviations in addresses. + +The main address should be divided by \cn{\\} into segments that +correspond to address lines for use on an envelope. When typeset, the +lines will be strung together separated by commas, but the division by +\cn{\\} will be useful to a person preparing an envelope to return +proofs. + +Addresses are considered part of the top matter, but in AMS articles +they are ordinarily printed at the end of the article following the +bibliography (this is different from basic \latex/). Suitable labels +will indicate the current, e-mail, and URL addresses, typically +\textit{Current address}:, \textit{E-mail address}:, \textit{URL}:, +respectively. + +If \texttt{\textasciitilde} is needed in a URL address, enter it +directly as \texttt{\textasciitilde} if you are using \amslatex/ +version 2.20 or later; otherwise, see the Author FAQ \cite{AF} +for instructions. + +\subsection*{Contributors + {\mdseries (new with version 2.20)}}\label{ss:contrib} +%% +Contributors are much like authors, but are responsible for only +a portion of an article, e.g., an appendix or auxiliary tables. +The bracketed portion is not optional; it gives the exact text that +will be printed to indicate the nature of the contribution: +\begin{verbatim} +\contrib[with an appendix by]{William Rogers} +\end{verbatim} +Multiple contributors and contributions are input like this: +\begin{verbatim} +\contrib[with Appendix A by]{William Rogers} +\contrib[]{Henry Taylor} +\contrib[and Appendix B by]{John Henderson} +\end{verbatim} +Note the empty brackets on the second line. Multiple contributors +indicated in this way will be combined and ``andified'' appropriately. +Contributors will not be included in running heads. Addresses provided +for contributors will be treated the same as for regular authors. + +\subsection*{Dedication} +%% +Use the tag \cn{dedicatory} for such things as ``Dedicated to +Professor X on the occasion of his eightieth birthday.'' If the +dedication is longer than one line, you may indicate a break with +\cn{\\}. + +\subsection*{Acknowledgments of support and other first-page footnotes} +%% +Use the command \cn{thanks} to acknowledge grants and other kinds of +support or for other general information not covered by one of the +more specific commands such as \cn{keywords} or \cn{subjclass}. Enter +\cn{thanks} immediately following the address(es) for the relevant +author, \emph{not} within the scope of the \cn{author\{\}} command +(this is different from basic \latex/). Like \cn{address}, \cn{thanks} +can appear more than once in the top matter. Each occurrence will be +printed as an unnumbered footnote at the bottom of the first page of +the article. + +\subsection*{Subject information} +%% +Subject classifications and key words, like acknowledg-\linebreak ments, are +part of the top matter and appear as unnumbered footnotes at the bottom of +the first page. + +Subject classifications may be primary (the major topic(s) of the +paper) or secondary (subject areas covered by ancillary results, +motivation or origin of problems discussed, intended or potential +field of application, or other significant aspects worthy of notice). +At least one primary subject classification is \textbf{required}. +Additional primaries and secondaries are optional. + +\begin{samepage} +These classifications are entered as +\begin{verbatim} +\subjclass[2000]{Primary |?primary class>; Secondary |?secondary classes>} +\end{verbatim} +(Omitting \texttt{[2000]} will cause the 1991 Subject Classification +to be cited.) +\end{samepage} + +To determine the classifications, use the 2000 Mathematics Subject +Classification scheme that appears in annual indexes of \textit{Mathematical +Reviews} beginning in 1999. It can also be accessed on the Web at URL: +\texttt{http://www.ams.org/msc/} or obtained in printed form from +Customer Services. +Please use the full number; the two-digit code from the Contents of +\textit{Mathematical Reviews} is \textbf{not} sufficient. + +Key words are not required but may be provided by an author if desired. +They should be tagged as \cn{keywords\{...\}}. + +\subsection*{Abstract} +%% +With an AMS document class, place the abstract before \cn{maketitle}, +contrary to the practice with the basic \latex/ document classes. +This is necessary to ensure that the abstract can always be printed in +the proper location and style. If the abstract is given after +\cn{maketitle}, it will be printed in place and generate a warning +message. + +Input the abstract text between \verb+\begin{abstract}...\end{abstract}+. +It may comprise multiple paragraphs and include displayed material if +appropriate. The length of the abstract depends primarily on the +length of the paper itself and on the difficulty of summarizing the +material. An upper limit of about 150 words for short papers and 300 +words for long papers is suggested. Do not use author-defined macros +or \cn{ref} in the abstract. + + +\section{Document body (all document classes)} + +\subsection*{Linking for the Web} +%% +All AMS primary journals are posted on-line. Electronic +manuscripts prepared in \latex/ for any AMS journal should be tagged +for maximum linking on the Web. For use of \cn{label}, \cn{ref}, +and \cn{cite}, see \cite{LC}; for \cn{eqref}, see \cite{AMP}. + +\subsection*{Headings} +%% +Four levels of headings are provided to permit logical sectioning of +a manuscript. These headings are applicable to individual articles +and to chapters of a monograph. (Headings specific to monographs are +listed under \textit{Monograph formatting}.) + +\begin{verbatim} +\specialsection{...} +\section[...]{...} +\subsection[...]{...} +\subsubsection[...]{...} +\end{verbatim} + +\cn{specialsection} is for long articles that need extra divisions +(e.g., parts) at a level above the \cn{section} level. + +Explicit line breaks are obtained by \verb+\\+ in first-level section +headings. + +Any heading may be given a label to allow references to be made to it, +by including a \cn{label\{...\}} command with a unique identifier +directly \emph{after} the heading. References are made using the +command \cn{ref\{...\}} and the same identifier. For example, +\begin{verbatim} +\section{Monograph formatting} +\label{s:mono} +\end{verbatim} +will establish a label for this section that can be referred to with +\cn{ref\{s:mono\}}. Cross references of +this sort will require \latex/ to be run at least twice for proper +resolution. A warning at the end of the \latex/ run, ``Cross +references may have changed\dots\unskip'', should be heeded in this regard. + + +\subsection*{Mathematical text} +%% +For instructions on preparing mathematical text, refer to +\cite{AMP} and \cite{ML}. See also ``Roman type'', below. + +\subsection*{Lists} +%% +Follow usual \latex/ conventions for producing list environments. + +\subsection*{Theorems, lemmas, and other proclamations} +%% +See the manual \textit{Using the \pkg{amsthm} package} \cite{ATP} +for details. Theorem environments following AMS style with respect to +punctuation, spacing and paragraphing are defined in the AMS document +classes. This is incompatible with the \latex/ \pkg{theorem} package, +which cannot be used with the AMS document classes. + +Three different theorem styles are provided by AMS document classes: +\cls{plain}, \cls{definition}, and \cls{remark}. By referring to these +styles and using the \cn{newtheorem} command, you can build a +complement of theorem environments appropriate for any paper or +monograph. All \cn{newtheorem} specifications should be included in +the preamble; a starter set is included in the template for every +AMS author package. + +Theorem support is also available separately in the \pkg{amsthm} package +for users of document classes other than those from the AMS. + +\subsection*{Equations} +%% +Check displayed equations carefully, making sure they are broken and +aligned following the guidelines in \cite[pp. 44--48]{MIT}. + +\subsection*{Roman type}\label{ss:roman} +%% +Numbers, punctuation, (parentheses), [brackets], +$\lbrace$braces$\rbrace$, and symbols used as labels should always be +set in roman type. This is true even within the statement of a theorem, +which is ordinarily set in italic type. + +Be careful to distinguish between roman elements that are mathematical +in nature (e.g., ``a group of class 2''), and those that are part of +the text (e.g., a label or a year). Mathematical expressions, no matter +how short or insignificant, should be coded as math, by enclosing them +within dollar signs \verb+$...$+ or \verb+\(...\)+. Roman text elements +should be coded as \cn{textup\{...\}} in potentially nonroman +environments such as theorems. + +Abbreviated forms of mathematical terms are also usually set in roman +type to distinguish them from mathematical variables or constants. +Use the control sequences for common mathematical functions and +operators like \verb+log+ and \verb+lim+; use \cn{DeclareMathOperator} +to add additional operator names (see \cite[\S5]{AMP}). + +The style of reference citations, though publication-dependent, is +usually roman. To ensure consistency and support linking for the Web, +\textbf{always} use the standard \latex/ \cn{cite} command when citing +a reference. Internal references with the \cn{ref} command are not +automatically roman in non-roman environments, but can be forced by +using the \pkg{upref} package (part of the \amslatex/ collection). + +\subsection*{Exercises} +%% +Exercises are produced using the \env{xca} and \env{xcb} environments. +\env{xca} may be used in any publication, but must be defined in +the document preamble with \cn{theoremstyle\{definition\}} and the +\cn{newtheorem} command; it is used for exercises that occur within a +section. \env{xcb} is defined only for monographs and is used for +exercises that occur at the end of a chapter. + +\subsection*{Indexing facilities} +\label{ss:indexing} +%% +The tags needed for \makeindx/ are already included in AMS document +classes. Do not include the \pkg{makeidx} package, but do put the +command \cn{makeindex} in the preamble to launch a single index. +See \cite[chapter 11]{LC} and \cite[chapter 11]{GL} for use of +\makeindx/. + +A package for multiple indexes, \pkg{amsmidx}, is included in the +\amslatex/ collection beginning with version 2.20. Unlike other +multiple-index packages, \pkg{amsmidx} is compatible with the AMS +document classes. To use this package, put these commands into the +preamble: +\begin{verbatim} +\usepackage{amsmidx} +\makeindex{|?name of first index file>} +\makeindex{|?name of second index file>} +\end{verbatim} +To identify index entries in the text: +\begin{verbatim} +\index{|?name of index file>}{|?index term>} +\end{verbatim} +In the backmatter, where the indexes are to appear: +\begin{verbatim} +\Printindex{|?name of first index file>}{|?title of first index>} +\Printindex{|?name of second index file>}{|?title of second index>} +\end{verbatim} +Note the capitalization of the \cn{Printindex} command. + +\section{Floating objects: Figures and tables} + +Figures and tables are usually handled as floating inserts. Such +items are often so large that fitting them into the document at the +point of reference may cause problems with pagination. Placing such +items into a floating insert allows them to be repositioned +automatically by \latex/ as required for good pagination. + +A floating insert generally contains one of these possibilities: +\begin{itemize} +\item \latex/ code that produces an object such as a table or + commutative diagram; +\item a command to incorporate an item produced by another application + (most often an Encapsulated PostScript (EPS) file produced by a + graphics utility; see \textit{Electronic graphics}, + page~\pageref{ss:electronicgraphics}). +\end{itemize} + +If a figure is described by \latex/ code (e.g., using \pkg{xypic} or +the \env{picture} environment), it should be included directly in the +file. + +\subsection*{Placement} +%% +Floats should +\begin{enumerate} +\item be numbered consistently throughout the paper (figures and tables + are numbered separately), +\item be placed at the top or bottom of the page, +\item have an in-text reference, and +\item definitely appear within the same section as their first text + reference. +\end{enumerate} + +A figure or table should not precede its first text reference unless +they both appear on the same page spread. When a figure or table is +an integral part of text, it may appear unnumbered in place in the +middle of text. + +Figures and tables should be allowed to float according to the \latex/ +defaults preset by the document class. If you are submitting a file +that will be processed at the AMS (this applies to all journal +articles), you could introduce major problems with pagination if you +hard-set your figures and tables by using the \verb+[h!]+ option. +Production problems will be avoided when you use the appropriate +author package class file and avoid using figure or table options. +For electronic manuscripts, the final placement of inserts will be +determined by the AMS editorial staff, on the basis of the most +appropriate page layout. + +\subsection*{Captions} +%% +Captions for floating inserts are usually positioned above a table and +below a figure. The following is the general structure used to specify +a figure insert, with a caption at the bottom: +\begin{verbatim} +\begin{figure} +\includegraphics{|?file name of |tt.eps|rm| file>}|quad|rm or|tt|quad|?code for the insertion> +\caption{|?caption text>} +\label{|?reference label>}|quad|rm (optional)|tt +\end{figure} +\end{verbatim} + +This is the general structure for a table insert, with a caption at +the top: +\begin{verbatim} +\begin{table} +\caption{|?caption text>} +\label{|?reference label>}|quad|rm (optional)|tt +|?code for the insertion body> +\end{table} +\end{verbatim} + +Caption headings (e.g., ``\textsc{Table 3.1.}''\ or +``\textsc{Figure 7.}'')\ will be supplied automatically. The +\<caption text> is any appropriate descriptive text, and may be +omitted if no descriptive text is desired. (The style of the caption +differs from the basic \latex/ caption style.) A reference label +should usually be associated with the caption, and must be given +\emph{after} the caption. A reference in text to the figure or table +has the form \cn{ref\{\<reference label>\}}. + +\latex/ packages for captions may appear to work with the AMS document +classes, but the caption style doesn't usually match the AMS style. + +\subsection*{Electronic graphics}\label{ss:electronicgraphics} +%% +Graphics created by applications other than \latex/ may be submitted +to the AMS in an electronic format. This includes output from +graphics applications as well as scanned photographs or other +computer-generated images. The AMS requires such graphics in +Encapsulated PostScript (EPS) format. + +Use the \pkg{graphicx} package (part of the \pkg{graphics} bundle +of \latex/) to embed references to EPS graphics directly in a \latex/ +file; see the manual, \filnam{grfguide.tex} \cite{GB}. Another +valuable reference is the manual ``Using EPS Graphics in \latexe/ +Documents'' \cite{EG}. + +Other packages are not recommended, as there are numerous areas of +incompatibility which may result in the need for manual intervention, +delaying processing and increasing the cost. + +The EPS files will not be physically included in the \latex/ file. +You must submit a separate file for each graphic along with the \latex/ +document. No matter what method is used to produce a graphic, it is +necessary to provide a paper copy to the AMS for verification. Double +check to make sure the electronic and paper versions are the same. + +\subsection*{Compatibility requirements for graphics} +There are two important requirements that must be observed when +embedding graphics. + +\emph{Omit path names} for the included files. Instead of +\begin{verbatim} +\includegraphics*{/usr/joe/book/figures/fig1.ps} +\end{verbatim} +use just the name of the file: +\begin{verbatim} +\includegraphics*{fig1.ps} +\end{verbatim} +The easiest way to do this is to place the graphics files in the +same directory as the file(s) being {\TeX}ed. + +Do not use the \cn{graphicspath\{\<directory list>\}} command to +establish a path. This will result in the path being included in +the DVI file, which will be impossible to process at the AMS\@. +It may be possible to specify a path using one of the environments +recognized by the {\TeX} engine (\fn{TEXINPUTS}, for example); +instructions for setting these environments should be in the +documentation for your system. + +Graphics commands must be compatible with the \textit{dvips} output +driver. This is particularly important if you are submitting a DVI +file for a camera-ready publication. The method is specific to the +graphics package you are using; a typical method is to use a file +\filnam{graphics.cfg} containing the line \cn{ExecuteOptions\{dvips\}} +when you run \latex/ to create the DVI or PostScript file to send to +the AMS. + +\subsection*{Technical requirements for graphics} +%% +If you scale a figure before submitting it, remember that line weights +also scale. The lightest line weight that will reproduce clearly at +high resolution is 0.5pt after scaling. Do \emph{not} specify +``hairline'' weight, as this will be nearly invisible at high +resolution and will disappear in the printing process. If a rule line +is screened, its weight should be no less than 1 point \emph{after} +scaling. + +Graded line weights should increase in increments of at least 0.5pt. +Increments less than this are insufficiently distinguishable at high +resolution. + +Screened fills should be screened not less than 15\% (less will print +as white) and not greater than 85\% (greater will print as black). + +Ideally, text included in graphics files should be font outlines +rather than bitmaps, because the AMS typesets its publications on a +high-resolution imagesetter, not a laser printer. Text or lines in +graphics which are 300dpi bitmaps (which look fine in the +laser-printed output of your article) may appear poor in quality next +to the high-resolution text of AMS publications. If bitmaps of +characters are part of bitmapped line art files, output will be +satisfactory if the bitmapped characters are at 1200dpi. + +\subsection*{Color graphics} +%% +AMS publications are ordinarily printed in black and white. +Use of color requires explicit permission from the AMS. + +Color figures should have the resolution of at least 266 pixels per +inch when printed at 100\%, and must also be suitable for printing +as grayscale. The files must be in EPS format + + +\section{Bibliographic references} +%% +\subsection*{Using \protect\bibtex/ to prepare a bibliography}% +An author may find it convenient to maintain a file of references in +\bibtex/ form, as described in \textit{The \latex/ Companion} +\cite[Section 13.2]{LC}. Two \bibtex/ styles are provided: + +\begingroup +\exindent=2\parindent +\beginexample{\exboxwidth=1.05in} +\exbox{}{amsplain.bst} will produce numeric labels; preferred for articles; +\exbox{}{amsalpha.bst} will produce labels constructed from the % + author name(s)\newline and year of publication. +\endexample +\endgroup + +\noindent +Both will translate references in a \bibtex/ input (\filnam{.bib}) +file to \latex/ input in a \filnam{.bbl} file in the form appropriate +for AMS publications, including all necessary formatting instructions. +This method of preparing bibliographies is therefore recommended. + +To access a \bibtex/ bibliography in a paper or monograph, include these +instructions in the appropriate place in the input file: +\begin{verbatim} +\bibliographystyle{|?style>}|qquad|rm(|tt|0amsplain |rm or|tt amsalpha|rm)|tt +\bibliography{|?name of bibliography |bgroup|tt.bib|egroup| file>} +\end{verbatim} + +Running \bibtex/ on the \filnam{.bib} file will produce a \filnam{.bbl} +file. The \filnam{.bib} file may have any name the author finds convenient; +however, the \filnam{.bbl} file must have the same name as the source file +for a monograph from which it is input, so it may be necessary for the +author to rename it. For an article, after the bibliography has been +completed (including processing by \bibtex/), the contents of the +\filnam{.bbl} file should be inserted into the main article input file, +replacing the \cn{bibliographystyle} and \cn{bibliography} statements. + +Items in the bibliography are usually ordered alphabetically by author. +\bibtex/ processing may alter this order, especially if the +\filnam{amsalpha} style is used. + +All categories of bibliographic entries listed in +\cite[Table 13.1]{LC} are supported in the two AMS \bibtex/ styles. +In addition to the fields listed in Table 13.1, a \verb+language+ +field is provided for use in identifying the original language of an +item whose title has been translated. + +The \pkg{harvard} package (available from CTAN) provides an +author-year style that is compatible with the AMS document classes. +This should ordinarily be used only for monographs on historical +topics. + +Standard abbreviations for periodicals should be obtained from +\cite{ASMR}\@. + +\subsection*{Preparing a bibliography without \protect\bibtex/} +%% +The references section of a paper is contained between the commands +\begin{verbatim} +\begin{thebibliography}{|?model label>} +\end{thebibliography} +\end{verbatim} +This environment is resolved as an unnumbered section in an article +or an unnumbered chapter in a monograph, following AMS publication +specifications. The indentation for the labels is set to an +appropriate width using the model given with the \cn{begin} command. +Thus the widest label in the bibliography should be used as the model; +for example, \verb+99+ will provide space for a 2-digit numeric label. + +For the proper order of reference elements and use of fonts and +punctuation, look at an issue or volume in the journal or book series +for which your document is intended and follow the examples you see +there. More examples are given in \cite{MIT}. + +\subsubsection*{Reference input} +%% +Begin each item with the command \cn{bibitem\{\<bibitem label>\}}. +The \latex/ default is to number references automatically; however, +other labels may be used by inserting an optional key argument in +square brackets between the command and the internal label: +\begin{verbatim} +\bibitem[ABC]{Arno1994} +\end{verbatim} +The item label and the key need not be identical. Whatever appears +within the \verb+[ ]+ is what prints; whatever is within the curly +braces is used for linking and must not include any math or special +characters. + +Give at least one full name; initials and last name is an acceptable +form. If a subsequent reference is by the same author(s), use +\cn{bysame} instead of the name(s). + +For examples, refer to \cite{MIT}. + + +\section{Monograph formatting}\label{s:mono} + +A monograph is a long work by a single author or co-authors on a +single subject. Each chapter should be prepared as a separate file, +as should the bibliography. In addition, a ``driver'' file should be +used to input all the others. These files should be given meaningful +names, so that when they are transmitted to the AMS, there will be no +question about which file represents which chapter. For example, a +monograph by author Grey might be composed of files named +\filnam{grey.tex} (the driver file), \filnam{grey-ch1.tex}, +\filnam{grey-ch2.tex}, \dots, \filnam{grey-ch12.tex}, +\filnam{grey-appa.tex}, etc., and \filnam{grey-bib.tex}. +If the author name is a common one, please include something to make +it unique, such as first initials. + +Information that identifies the author(s), the subject matter of the +monograph, acknowledgments of support, and so forth, will appear in the +front matter of the book. Place this information in the driver file, +and use the tags shown below. Most of these are the same as the tags +associated with the top matter of an article; see the \textit{Top +matter} section (page~\pageref{s:topmatter}) for explanations and an +indication of which tags are required. + +\subsection*{Starting a new monograph}\label{s:newamsbook} +%% +The driver file for a monograph is generally made up of the following: +\begin{itemize} +\item \verb+\documentclass{...}+ +\item preamble (where extra definitions might go) +\item \verb+\begin{document}+ +\item \verb+\frontmatter+ +\item title page and copyright page information +\item \verb+\maketitle+ (to set the title page and copyright page; see note) +\item \verb+\include+ files (e.g., preface, introduction) +\item \verb+\mainmatter+ +\item \verb+\include+ files (e.g., main chapters, appendices) +\item \verb+\backmatter+ +\item commands for bibliography, index +\item \verb+\end{document}+ +\end{itemize} + +\noindent +Note: The title and copyright pages are for information only, so that +a printed copy can be associated with the correct author(s). The final +copy will be prepared at the AMS. + +For a typical driver file, see the template for \cls{amsbook}, included +in the \amslatex/ collection. + +Instructions for preparing a dedication page are given in the AMS +Author FAQ \cite{AF}. + +The table of contents will be produced automatically from a +\filnam{.toc} file produced anew in each run of \latex/. Since there is +no \filnam{.toc} before the first run, the body of the table of contents +will be empty on the first run. It is AMS style to include only +first-level heads, chapter titles, and part titles in the table of +contents. + +Chapters in AMS book series start on right-hand (odd-numbered) pages. +Blank pages will be provided as necessary at the end of earlier material +to accomplish this. + + +\subsection*{Chapter titles} +%% +Chapter titles should be capitalized as follows: the first and last +words of the title and all nouns, pronouns, adjectives, adverbs, and +verbs should be capitalized. Articles, conjunctions, and prepositions +should be lowercased unless they are the first or last word of the title. + +There are three common variations of the chapter title. The form with +a chapter number is most common: +\begin{verbatim} +\chapter{Matrix Algebras} +\end{verbatim} + +The second variation is an appendix, where the word ``Appendix'' +replaces the word ``Chapter''. Use the command \cn{appendix} before +the first \cn{chapter} command in a sequence of appendix chapters. +\begin{verbatim} +\appendix +\chapter{Poisson Integral} +\end{verbatim} +In addition to ``Appendix'', the counter will produce letters ``A'', +``B'', ``C'', etc.,\ instead of numbers. + +The third variation is used for an element such as a preface or +introduction, which has no pretitle text at all. For this, use the +\cn{chapter*} command: +\begin{verbatim} +\chapter*{Preface} +\end{verbatim} +Unlike the \latex/ \cls{book} class, the AMS document classes will +place entries for unnumbered chapters in the table of contents, as +required by AMS style. + +\subsection*{Monograph running heads} +%% +The chapter title is used for the left running head and section +headings for the right running head. The chapter title repeats if +there are no sections. If the text of a section heading is too long +to fit as a running head, use the square-bracket option to specify a +shortened form for use in the running heads: + +\begin{verbatim} +\section[Fourier coefficients of periodic functions] + {Fourier coefficients of continuous periodic functions + of bounded entropy norm} +\end{verbatim} + +If the chapter title is too long to fit as a running head, a shortened +form can be supplied in a similar way. Full chapter titles and section +headings will be used in the table of contents (this is different from +basic \latex/). + +\subsection*{Numbering of figures and tables} +%% +The preferred AMS style for numbering figures and tables is to start +numbering from 1 within each chapter, and to include both the chapter +and element number in the printed caption heading. For example, the +first figure in Chapter 5 would be numbered ``\textsc{Figure} 5.1''. +The \cls{amsbook} document class resets figure and table numbers +automatically, but does not include the chapter number in the printed +caption. To add the chapter number, place these lines in the preamble +of the driver file: +\begin{verbatim} +\numberwithin{figure}{chapter} +\numberwithin{table}{chapter} +\end{verbatim} + + +\section{Getting help} + +Many questions raised by authors are answered in the AMS Author FAQ +\cite{AF}. Please check that before asking for assistance. + +If you encounter difficulties in preparing or submitting your +manuscript in electronic form after it has been accepted for +publication by the appropriate editorial board, you can ask for help +from the \AMS\ at: + +\penalty-100 +\begin{samepage} +\beginexample{\normalfont\mdseries} +Technical Support +Publications Technical Group +201 Charles Street +Providence, RI 02904-2294 +\vspace{3pt} +Phone: 800-321-4267, ext.\ 4080 \quad or \quad 401-455-4080 +E-mail: {\texttt{tech-support@ams.org}} +\endexample +\end{samepage} + +\noindent +Please supply the name of the journal or book series, the editor's +name if the manuscript is for a proceedings volume, and a concise +explanation of the problem. + + +\begin{thebibliography}{[ASMR]} + +\bibitem[AF]{AF} AMS Author FAQ, +\texttt{http://www.ams.org/authors/author-faq.html} + +\bibitem[AFG]{AFG} \textit{AMSFonts{} version~\textup{2.2d} user's guide}, +Amer. Math. Soc., Providence, RI, 2002. +PDF file linked from \texttt{http://www.ams.org/tex/amsfonts.html} + +\bibitem[AMP]{AMP} \textit{User's guide for the \pkg{amsmath} package +\textup{(}version~\textup{2.0)}}, Amer. Math. Soc., Providence, RI, 2004. +PDF file linked from \texttt{http://www.ams.org/tex/amslatex.html} + +\bibitem[AP]{AP} Author packages for publishing with the AMS,\\ +\texttt{http://www.ams.org/tex/author-info.html} + +\bibitem[ARC]{ARC} AMS Author Resource Center, +\texttt{http://www.ams.org/authors/} + +\bibitem[ASMR]{ASMR} \textit{Abbreviations of names of serials reviewed in +Mathematical Reviews}, Amer. Math. Soc., Providence, RI, +revised annually; searchable on-line at\\ +\texttt{http://www.ams.org/msnhtml/serials-list/annser\_frames.html}. + +\bibitem[ATP]{ATP} \textit{Using the \pkg{amsthm} package, +version~\textup{2.0}}, Amer. Math. Soc., Providence, RI, 2004.\\ +PDF file linked from \texttt{http://www.ams.org/tex/amslatex.html} + +\bibitem[EG]{EG} Keith Reckdahl, ``Using EPS graphics in \latexe/ +documents'', available in electronic form as \texttt{info/epslatex.ps} +or \filnam{.pdf} from\newline +\texttt{http://www.ctan.org/tex-archive/} + +\bibitem[EP]{EP} Guide to AMS editor's package, +\texttt{http://www.ams.org/authors/editpkg.html} + +\bibitem[GB]{GB} David Carlisle, ``Packages in the `graphics' bundle'', +available in electronic form as +\filnam{macros/latex/required/graphics/grfguide.tex} or \filnam{.ps} +from\\ \texttt{http://www.ctan.org/tex-archive/} + +\bibitem[GL]{GL} Helmut Kopka and Patrick Daly, \textit{A Guide to + \latex/}, 4th ed., Addison-Wesley, Reading, MA, 2004. + +\bibitem[HBW]{HBW} Nicholas J. Higham, \textit{Handbook of Writing for +the Mathematical Sciences}, 2nd ed., SIAM, Philadelphia, PA, 1998. + +\bibitem[HWM]{HWM} +Norman E. Steenrod, Paul R. Halmos, Menahem M. Schiffer, and Jean A. +Dieudonn\'e, \textit{How to Write Mathematics}, 5th printing 1995, +Amer. Math. Soc., Providence, RI, 1973. + +\bibitem[Joy]{Joy} M. D. Spivak, \textit{The Joy of \tex/}, +2nd revised ed., Amer. Math. Soc., Providence, RI, 1990. + +\bibitem[LC]{LC} Frank Mittelbach and Michel Goossens, with +Johannes Braams, David Carlisle and Chris Rowley, +\textit{The \latex/ Companion}, 2nd ed., Addison-Wesley Co., +Reading, MA, 2004. + +\bibitem[LGC]{LGC} Michel Goossens, Sebastian Rahtz, and Frank Mittelbach, +\textit{The \latex/ graphics Companion}, Addison-Wesley Co., Reading, +MA, 1997. + +\bibitem[MIT]{MIT} Ellen E. Swanson, updated by Arlene O'Sean and +Antoinette Schleyer, \textit{Mathematics into Type}, +Updated ed., Amer. Math. Soc., Providence, RI, 1999. + +\bibitem[ML]{ML} George Gr\"{a}tzer, \textit{Math into \latex/}, +3rd ed., Birkh\"{a}user, Boston, MA/Springer Verlag, NY, 2000. + +\bibitem[MSC]{MSC} \textit{\textup{2000} Mathematics subject classification}, +Amer. Math. Soc., Providence, RI, 1999; searchable on-line at +\texttt{http://www.ams.org/msc/}. + +\end{thebibliography} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/manifest.txt b/Master/texmf-dist/doc/latex/amslatex/manifest.txt new file mode 100644 index 00000000000..ffeebfacf43 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/manifest.txt @@ -0,0 +1,56 @@ + +texmf/bibtex/bst/ams/ + amsra.bst + amsrn.bst + amsrs.bst + amsru.bst + amsry.bst + +texmf/doc/latex/amscls/ + amsrdoc.pdf + amsrefs.faq + amsrefs.pdf + changes.pdf + cite-xa.tex + cite-xb.tex + cite-xh.tex + cite-xs.tex + gktest.ltb + jr.bib + mathscinet.pdf + textcmds.pdf + +texmf/source/latex/amsrefs/ + 00readme.txt + ams-r1.ins + amsrdoc.pdf + amsrefs.dtx + amsrefs.faq + amsrefs.pdf + amsxport.dtx + changes.pdf + cite-xa.tex + cite-xb.tex + cite-xh.tex + cite-xs.tex + gktest.ltb + ifoption.dtx + install.txt + jr.bib + manifest.txt + mathscinet.dtx + mathscinet.pdf + pcatcode.dtx + rkeyval.dtx + textcmds.dtx + textcmds.pdf + +texmf/tex/latex/amscls/ + amsrbeta.sty + amsrefs.sty + ifoption.sty + mathscinet.sty + pcatcode.sty + rkeyval.sty + rkvbeta.sty + textcmds.sty diff --git a/Master/texmf-dist/doc/latex/amslatex/math/00readme.txt b/Master/texmf-dist/doc/latex/amslatex/math/00readme.txt new file mode 100644 index 00000000000..080ed622537 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/math/00readme.txt @@ -0,0 +1,123 @@ +00readme.txt for amsmath 2.0 [2004/08/06] American Mathematical Society + +See manifest.txt for a list of all the files in the distribution. + +See install.txt for installation instructions. [Installing from an +archive file such as ftp://ftp.ams.org/pub/tex/amsmath.zip is +recommended.] + +The amsmath package is an extension package for LaTeX that provides +additional features to facilitate mathematical typesetting. It has been +developed by the American Mathematical Society and released for general +use as a service to the mathematical community. A number of smaller +auxiliary packages are also distributed with the amsmath package. + +In order to use amsmath you need to have TeX installed first. TeX is not +an AMS product. For information on getting TeX see one of the following: + + http://www.tug.org/ + http://www.ams.org/tex/tex-resources.html + +The primary documentation for amsmath is in + + amsldoc.pdf + +Additional documentation files include: + + diffs-m.txt + subeqn.pdf + technote.pdf + testmath.pdf + +which are included in the collection. Additional documentation can be +found in the amsmath FAQ: + + http://www.ams.org/tex/amsmath-faq.html + +For technical support: + + American Mathematical Society + Technical Support + Publications Technical Group + P. O. Box 6248 + Providence, RI 02940-6248 + Phone: 800-321-4AMS (321-4267) (USA/Canada) or 401-455-4080 + tech-support@ams.org + +For submitting bug reports, however, users are encouraged to use the +standard LaTeX bug reporting system: Issue the command + + latex latexbug.tex + +and follow the resulting instructions (selecting the "amslatex" category +when the list of possible categories is shown). + +======================================================================== +RECENT CHANGES (REVERSE ORDER) + +---amsmath.faq - 2004/08/06 +Removed from distribution; replaced by on-line FAQ at +http://www.ams.org/tex/amsmath-faq.html + +---amsmath.dtx 2.13 2000/07/18: + +After the numbering patches in 2.11, \notag failed in certain +circumstances: introduce some more auxiliary functions to sort things +out, and redefine \nonumber. + +---amstext.dtx 2.01 2000/06/29: + +Use \f@size instead of \tf@size because they are not necessarily the +same and the former is better for putting a few words into a display. + +---amsmath.dtx 2.12 2000/06/06: + +Fix transposed lines in 2.11 patch. + +---amsdtx.dtx - 2000/06/02: + +Move to the amscls distribution. + +---amsmath.dtx 2.11 2000/06/02: + +Prevent "Arithmetic overflow" error by guarding against divide-by-zero +in \x@calc@shift@lc (align environment). + +---amsmath.dtx 2.10 2000/05/25: + +Clear up error message for \allowdisplaybreaks[0]. + +Make mathdisplay re-entrant by introducing mathdisplay@stack, to +clear up numbering problems in unusual circumstances such as \[ \] +nested inside minipage inside equation. + +---amsmath.dtx 2.09 2000/04/21: + +Ensure good catcodes for " etc. + +---amsmath.dtx 2.08 2000/03/16: + +Fixed erroneous tag placement on split with fleqn/tbtags options. + +---amsmath.dtx 2.07 2000/03/15: + +Add \reset@strutbox@ to deal with the following bug: After +$...\mbox{\Huge $...$}...$, line spacing is wrong in a following +"gather" or other environment that uses \strut@. + +Patch to fix bug with intlimits option: too much space in the middle of +\iint. + +Overhaul math accents again to fix a couple of bugs reported by Thimm. + +---amsmath.dtx 2.06 2000/03/10: + +Change \MathAccent to \mathaccentV so \DeclareMathAccent won't give an +error when redefining an accent. + +---amsmath.dtx 2.05 2000/01/06: + +Fixed incorrect placement of fleqn/reqno equation numbers inside +indented lists (displaywidth < columnwidth). Changed the +multline/fleqn/leqno indent to match mathmargin when possible instead of +always just using multlinetaggap. diff --git a/Master/texmf-dist/doc/latex/amslatex/math/amsdtx.cls b/Master/texmf-dist/doc/latex/amslatex/math/amsdtx.cls new file mode 100644 index 00000000000..96a50814c8f --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/math/amsdtx.cls @@ -0,0 +1,517 @@ +%% +%% This is file `amsdtx.cls', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% amsdtx.dtx (with options: `amsdtx') +%% +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "amsdtx.dtx", +%%% version = "2.06", +%%% date = "2004/08/06", +%%% time = "12:18:49 EDT", +%%% checksum = "19929 1192 3506 39423", +%%% author = "Michael J. Downes, updated by David M. Jones", +%%% copyright = "Copyright 1996, 1999, 2004 +%%% American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Publications Technical Group, +%%% 201 Charles Street, +%%% Providence, RI 02904, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% codetable = "ISO/ASCII", +%%% keywords = "latex, amslatex, ams-latex, user documentation", +%%% supported = "yes", +%%% abstract = "This is the source for two document classes, amsdtx +%%% and amsldoc, used to produce AMS user documentation +%%% or technical documentation.", +%%% docstring = "The checksum field above contains a CRC-16 +%%% checksum as the first value, followed by the +%%% equivalent of the standard UNIX wc (word +%%% count) utility output of lines, words, and +%%% characters. This is produced by Robert +%%% Solovay's checksum utility.", +%%% } +%%% ==================================================================== +\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX) +[1995/06/01]% LaTeX date must be June 1995 or later +\ProvidesClass{amsdtx}[2004/08/06 v2.06] +\DeclareOption*{\PassOptionsToClass{\CurrentOption}{book}} +\ProcessOptions +\LoadClass{book} +\IfFileExists{url.sty}{% + \RequirePackage{url}\relax + \@gobble +}{% + \@firstofone +} +{ + \DeclareRobustCommand{\url}[1]{% + \def\@tempa{#1}% + \texttt{\urlsetup $\expandafter\strip@prefix\meaning\@tempa$}% + }% + \def\urlsetup{% + \check@mathfonts \textfont\@ne\the\font \textfont\z@\the\font + \urlfix +\urlfix\=\urlfix\:\urlfix\-\urlfix\.\urlfix\,\urlfix\;% + \urlbreak\&\urlbreak\/\urlbreak\?% + }% + \def\urlbreak#1{% + \mathcode`#1="8000 + \begingroup \lccode`\~=`#1 \lowercase{\endgroup \edef~}% + {\mathchar\number`#1\penalty\hyphenpenalty}% + }% + \def\urlfix#1{% + \mathcode`#1=`#1\relax + }% +} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\providecommand{\qq}[1]{\textquotedblleft#1\/\textquotedblright} +\providecommand{\mdash}{\textemdash\penalty\exhyphenpenalty} +\providecommand{\ndash}{\textendash\penalty\exhyphenpenalty} +\let\@xp\expandafter +\newcommand*{\autoindex}[1]{% + \index{#1\ifcodeline@index\encapchar usage\fi}% +} +\newcommand{\ntt}{\normalfont\ttfamily} +\newcommand*{\indexcs}[1]{% + \@xp\@xp\@xp\@indexcs\@xp\@nobslash\string#1\@nil +} +\def\@indexcs#1\@nil{% + \autoindex{#1\actualchar + \string\verb\quotechar*\verbatimchar + \@xp\@bothoftwo\string\ #1\@empty + \verbatimchar + }% +} +\def\@bothoftwo#1#2{#1#2} +\def\category@index#1#2{% + {\ntt#2}% + \@category@index{#1}{#2}% +} +\def\@category@index#1#2{% + \autoindex{% + #2\actualchar\string\texttt{#2}% + \ifx\@nil#1\@nil\else\space#1\fi + }% +} +\chardef\bslchar=`\\ % p. 424, TeXbook +\newcommand{\addbslash}{\expandafter\@addbslash\string} +\def\@addbslash#1{\bslchar\@nobslash#1} +\newcommand{\nobslash}{\expandafter\@nobslash\string} +\def\@nobslash#1{\ifnum`#1=\bslchar\else#1\fi} +\def\@boxorbreak{% + \leavevmode + \ifmmode\hbox\else\ifdim\lastskip=\z@\penalty9999 \fi\fi +} +\DeclareRobustCommand{\cs}[1]{% + \@boxorbreak{% + \ntt + \addbslash#1\@empty + \@xp\@xp\@xp\@indexcs\@xp\@nobslash\string#1\@nil + }% +} +\let\cn\cs +\DeclareRobustCommand{\cls}{\category@index{class}} +\DeclareRobustCommand{\pkg}{\category@index{package}} +\DeclareRobustCommand{\opt}{\category@index{option}} +\DeclareRobustCommand{\env}[1]{{\ntt#1}\SpecialEnvIndex{#1}} +\DeclareRobustCommand{\fn}{\category@index{}} +\DeclareRobustCommand{\bst}{\category@index{\string\BibTeX{} style}} +\DeclareRobustCommand{\cnt}{\category@index{counter}} +\DeclareRobustCommand{\fnt}{\category@index{font}} +\def\allowtthyphens{\begingroup + \fontencoding{OT1}\fontfamily{cmtt}% + \expandafter\let\csname OT1+cmtt\endcsname\relax + \try@load@fontshape + \endgroup + \expandafter\let\csname OT1+cmtt\endcsname\@empty +} +\hfuzz2pc +\vbadness9999 \hbadness5000 +\def\AmS{{\protect\usefont{OMS}{cmsy}{m}{n}% + A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}} +\def\latex/{{\protect\LaTeX}} +\def\amslatex/{{\protect\AmS-\protect\LaTeX}} +\def\tex/{{\protect\TeX}} +\def\amstex/{{\protect\AmS-\protect\TeX}} +\def\bibtex/{{Bib\protect\TeX}} +\def\makeindx/{MakeIndex} +\def\xypic/{XY\mbox{-}pic} +\newcommand{\Textures}{\textit{Textures}} +\def\<#1>{\textit{$\langle$#1\/$\rangle$}} +\def\@listi{% + \leftmargin\leftmargini + \topsep 3\p@ \@plus2\p@ \@minus\p@ + \parsep \p@ \@plus\p@ \itemsep\parsep +} +\let\@listI\@listi +\@listi +\def\@listii{% + \leftmargin\leftmarginii + \labelwidth\leftmarginii \advance\labelwidth-\labelsep + \topsep\p@\@plus\p@ \@minus\p@ + \parsep\z@skip \itemsep\z@skip +} +\def\@listiii{% + \leftmargin\leftmarginiii + \labelwidth\leftmarginiii \advance\labelwidth-\labelsep + \topsep\z@skip \parsep\z@skip \itemsep\z@skip +} +\newenvironment{histnote}{% + \trivlist\item[\hspace{\labelsep}\bfseries Historical Note:]% +}{% + \endtrivlist +} +\def\@starttoc#1{\begingroup + \let\autoindex\@gobble + \makeatletter + \@input{\jobname.#1}\if@filesw + \expandafter\newwrite\csname tf@#1\endcsname + \immediate\openout + \csname tf@#1\endcsname \jobname.#1\relax + \fi \global\@nobreakfalse \endgroup} +\newcommand*{\secref}[1]{\S\ref{#1}} +\newcommand{\qc}[1]{}% check for prior definition +\edef\qc#1{\noexpand\protect\expandafter\noexpand\csname qc \endcsname + \noexpand\protect#1} +\@namedef{qc }#1#2{\begingroup\ntt + \ifx\ #2\char`\ \else\escapechar\m@ne\string#2\fi\endgroup} +\DeclareRobustCommand{\qcat}{\qc\@}% +\DeclareRobustCommand{\qcamp}{\qc\&}% +\DeclareRobustCommand{\qcbang}{\qc\!}% +\DeclareRobustCommand{\arg}[1]{{\ntt\##1}} +\def\ncn#1{{\let\index\@gobble\cn{#1}}} + +\DeclareRobustCommand{\cnbang}{% + \ncn{\!}\index{"!@{\ntt\bslchar\qcbang}}} +\DeclareRobustCommand{\cnat}{% + \ncn{\!}\index{"@@{\ntt\bslchar\qcat}}} +\def\5{\penalty500 } +\newcommand{\errexa}{\par\noindent\textit{Example}:\ } +\newcommand{\errexpl}{\par\noindent\textit{Explanation}:\ } +\renewcommand\chapter{\par \@afterindentfalse + \secdef\@chapter\@schapter} +\def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \refstepcounter{chapter}% + \typeout{\@chapapp\space\thechapter.}% + \addcontentsline{toc}{chapter}% + {\protect\numberline{\thechapter}#1}% + \else + \addcontentsline{toc}{chapter}{#1}\fi + \else + \addcontentsline{toc}{chapter}{#1} + \fi + \chaptermark{#1}% + \addtocontents{lof}{\protect\addvspace{10\p@}}% + \addtocontents{lot}{\protect\addvspace{10\p@}}% + \if@twocolumn + \@topnewpage[\@makechapterhead{#2}]% + \else + \@makechapterhead{#2}% + \@afterheading + \fi} +\def\@makechapterhead#1{% + \vspace{1.5\baselineskip}% + {\parindent \z@ \raggedright \reset@font + \ifnum \c@secnumdepth >\m@ne + \large\bfseries \@chapapp\space\thechapter + \par\nobreak + \vskip.5\baselineskip\relax + \fi + #1\par\nobreak + \vskip\baselineskip + }} +\def\@schapter#1{\if@twocolumn + \@topnewpage[\@makeschapterhead{#1}]% + \else + \@makeschapterhead{#1}% + \@afterheading + \fi} +\def\@makeschapterhead#1{% + \vspace*{1.5\baselineskip}% + {\parindent \z@ \raggedright + \reset@font + \large \bfseries #1\par\nobreak + \vskip\baselineskip + }} +\def\@removefromreset#1#2{\let\@tempb\@elt + \expandafter\let\expandafter\@tempa\csname c@#1\endcsname + \def\@elt##1{\expandafter\ifx\csname c@##1\endcsname\@tempa\else + \noexpand\@elt{##1}\fi}% + \expandafter\edef\csname cl@#2\endcsname{\csname cl@#2\endcsname}% + \let\@elt\@tempb} +\@removefromreset{footnote}{chapter} +\def\ps@headings{% + \let\@oddfoot\@empty\let\@evenfoot\@empty + \def\@evenhead{\thepage\hfil{\footnotesize\leftmark{}{}}}% + \def\@oddhead{{\footnotesize\rightmark{}{}}\hfil\thepage}% + \let\@mkboth\markboth + \def\chaptermark##1{% + \markboth {\uppercase{\ifnum \c@secnumdepth >\m@ne + \if@mainmatter + \@chapapp\ \thechapter. \ \fi + \fi + ##1}}{}}% + \def\sectionmark##1{% + \markright {\uppercase{\ifnum \c@secnumdepth >\z@ + \thesection. \ \fi + ##1}}}} +\renewcommand\maketitle{\par + \begingroup + \renewcommand\thefootnote{\fnsymbol{footnote}}% + \def\@makefnmark{\hbox to\z@{$\m@th^{\@thefnmark}$\hss}}% + \long\def\@makefntext##1{\parindent 1em\noindent + \hbox to1.8em{\hss$\m@th^{\@thefnmark}$}##1}% + \if@twocolumn + \ifnum \col@number=\@ne + \@maketitle + \else + \twocolumn[\@maketitle]% + \fi + \else + \newpage + \global\@topnum\z@ % Prevents figures from going at top of page. + \@maketitle + \fi + \thispagestyle{plain}\@thanks + \endgroup + \setcounter{footnote}{0}% + \let\thanks\relax + \let\maketitle\relax\let\@maketitle\relax + \gdef\@thanks{}\gdef\@author{}\gdef\@title{}} +\def\@maketitle{% + \newpage + \null + \vskip 2em% + \begin{center}% + {\LARGE \@title \par}% + \vskip 1.5em% + {\large + \lineskip .5em% + \begin{tabular}[t]{c}% + \@author + \end{tabular}\par}% + \vskip 1em% + {\large \@date}% + \end{center}% + \par + \uppercase\expandafter{\expandafter\toks@\expandafter{\@title}}% + \edef\@tempa{\noexpand\markboth{\the\toks@}{\the\toks@}}% + \@tempa + \vskip 1.5em} +\renewcommand\tableofcontents{% + \if@twocolumn + \@restonecoltrue\onecolumn + \else + \@restonecolfalse + \fi + \subsection*{\contentsname}% + \@starttoc{toc}% + \if@restonecol\twocolumn\fi + } +\renewcommand\section{\@startsection {section}{1}{\z@}% + {-.6\baselineskip \@plus -3\p@}% + {.4\baselineskip} + {\reset@font\Large\bfseries}} +\renewcommand\subsection{\@startsection{subsection}{2}{\z@}% + {-.3\baselineskip\@plus -2\p@}% + {.2\baselineskip}% + {\reset@font\large\bfseries}} +\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}% + {-.2\baselineskip\@plus -2\p@}% + {.2\baselineskip}% + {\reset@font\normalsize\bfseries}} +\renewenvironment{theindex}{% + \if@twocolumn \@restonecolfalse \else \@restonecoltrue \fi + \columnseprule \z@ \columnsep 35\p@ + \let\autoindex\@gobble + \twocolumn[\section*{\indexname}]% + \addcontentsline{toc}{chapter}{\indexname}% + \@mkboth{\uppercase{\indexname}}{\uppercase{\indexname}}% + \thispagestyle{plain}\parindent\z@ + \parskip\z@ \@plus .3\p@\relax + \let\item\@idxitem +}{% + \if@restonecol\onecolumn\else\clearpage\fi +} +\renewcommand{\thesection}{\arabic{section}} +\long\def\@makecaption#1#2{% + \addvspace\abovecaptionskip + \begingroup + \countdef\@parcycles=8 % local count register + \@parcycles\z@ + \@setpar{\advance\@parcycles\@ne \ifnum\@parcycles>999 + \@@par\@parcycles\z@\fi + \ifhmode \unskip\hskip\parfillskip\penalty-\@M\fi}% + \@hangfrom{\textbf{#1.} }\vadjust{\penalty\m@ne}#2% + \endgroup + \ifhmode\unpenalty\fi\par + \ifnum\lastpenalty=\m@ne % only one line in the caption + \unpenalty \setbox\@tempboxa\lastbox + \nointerlineskip + \hbox to\hsize{\hfill\unhbox\@tempboxa\unskip\hfill}% + \fi + \nobreak\vskip\belowcaptionskip +} +\renewenvironment{table}{% + \belowcaptionskip\abovecaptionskip \abovecaptionskip\z@skip + \@float{table}% +}{% + \end@float +} +\renewenvironment{table*}{% + \belowcaptionskip\abovecaptionskip \abovecaptionskip\z@skip + \@dblfloat{table}% +}{% + \end@dblfloat +} +\setcounter{topnumber}{4}\setcounter{bottomnumber}{4} +\setcounter{totalnumber}{4}\setcounter{dbltopnumber}{4} +\renewcommand{\topfraction}{.97}\renewcommand{\bottomfraction}{.97} +\renewcommand{\textfraction}{.03}\renewcommand{\floatpagefraction}{.9} +\renewcommand{\dbltopfraction}{.97} +\renewcommand{\dblfloatpagefraction}{.9} +\setlength{\floatsep}{8pt plus6pt} +\setlength{\textfloatsep}{10pt plus8pt} +\setlength{\intextsep}{8pt plus6pt} +\setlength{\dblfloatsep}{8pt plus6pt} +\setlength{\dbltextfloatsep}{10pt plus8pt} +\setlength{\@fptop}{0pt}\setlength{\@fpsep}{8pt}% +\setlength{\@fpbot}{0pt plus 1fil} +\setlength{\@dblfptop}{0pt}\setlength{\@dblfpsep}{8pt}% +\setlength{\@dblfpbot}{0pt plus 1fil} + +\pagestyle{headings} +\newcommand{\arrayargpatch}{% + \let\@oldarray\@array + \edef\@array[##1]##2{\catcode\number`\|=\number\catcode`\| + \catcode\number`\@=\number\catcode`\@ \relax + \let\noexpand\@array\noexpand\@oldarray + \noexpand\@array[##1]{##2}}% + \catcode`\|=12 \catcode`\@=12 \relax +} +\newenvironment{ctab}{% + \par\topsep\medskipamount + \trivlist\centering + \item[]% + \arrayargpatch + \begin{tabular}% +}{% + \end{tabular}% + \endtrivlist +} +\RequirePackage{doc} +\def\AltMacroFont{\MacroFont} +\def\SpecialMainEnvIndex#1{% + \@bsphack + \special@index{% + #1\actualchar\string\texttt{#1} environment\encapchar main% + }% + \special@index{% + environments:\levelchar#1% + \actualchar\string\texttt{#1}% + \encapchar main}% + \@esphack +} +\def\SpecialEnvIndex#1{% + \@bsphack + \index{#1\actualchar\string\texttt{#1} environment\encapchar usage}% + \index{% + environments:\levelchar#1% + \actualchar\string\texttt{#1}% + \encapchar usage}% + \@esphack +} +\def\DescribeOption{% + \leavevmode + \@bsphack + \begingroup + \MakePrivateLetters + \Describe@Option +} +\def\Describe@Option#1{% + \endgroup + \marginpar{\raggedleft\PrintDescribeOption{#1}}% + \SpecialOptionIndex{#1}% + \@esphack + \ignorespaces +} +\def\PrintDescribeOption#1{\strut \MacroFont #1\ } +\def\option{% + \let\SpecialMainEnvIndex\SpecialMainOptionIndex +\begingroup + \catcode`\\12 + \MakePrivateLetters \m@cro@ \iffalse} +\def\SpecialMainOptionIndex#1{% + \@bsphack + \special@index{#1\actualchar\string\texttt{#1} option\encapchar main}% + \@esphack +} +\def\SpecialOptionIndex{\@category@index{option}} +\def\hDocInput#1{\MakePercentIgnore + \begingroup + \begingroup \lccode`\~=`\@ + \lowercase{\endgroup\long\def ~}##1##{% + \catcode`\==12 \skipfileheader{##1}}% + \catcode`\@=\active \catcode`\==14 % comment + \def\filename{#1}% + \@@input#1 \MakePercentComment} +\def\skipfileheader#1#2 {\endgroup + \hGetFileInfo#2 version = "??" date = "??"\@nil + \begingroup\catcode`\==9 \catcode`\ =9 \futurelet\0\endgroup +} +\long\def\hGetFileInfo#1 version = "#2"#3 date = "#4"#5\@nil{% + \def\fileversion{#2}\def\filedate{#4}} +\DoNotIndex{\@xp,\@nx,\@empty,\newcommand,\renewcommand} +\DoNotIndex{\newenvironment,\renewenvironment,\providecommand} +\DoNotIndex{\if,\fi,\ifnum,\fi,\@let@token,\futurelet,\fsa@n} +\DoNotIndex{\ignorespaces,\@tempcnta,\@tempcntb,\count@} +\DoNotIndex{\toks@,\@ne,\advance} +\DoNotIndex{\!,\/,\?,\@,\^,\_} +\DoNotIndex{\@@par,\@M,\@auxout,\@bsphack,\@esphack,\@depth,\@ehc} +\DoNotIndex{\@for,\@flushglue,\@gobble,\@gobbletwo,\@height,\@idxitem} +\DoNotIndex{\@ifnextchar,\@ifstar,\@ifundefined,\@input,\@latexerr} +\DoNotIndex{\@makeschapterhead,\@namedef,\@nameuse,\@nil} +\DoNotIndex{\@nobreakfalse,\@restonecolfalse,\@restonecoltrue} +\DoNotIndex{\@tempa,\@tempb,\@tempc,\@tempf,\@temptokena,\@themark,\@width} +\DoNotIndex{\active,\aindex,\baselineskip,\begin,\begingroup,\box} +\DoNotIndex{\c@page,\catcode,\chapter,\char,\chardef,\closeout} +\DoNotIndex{\CodelineIndex,\sp,\sb,\label,\leavevmode,\mark} +\DoNotIndex{\mark,\newinsert,\newwrite,\newtoks,\xdef} +\DoNotIndex{\columnsep,\columnseprule,\columnwidth,\csname,\def} +\DoNotIndex{\dimen,\do,\DocInput,\documentstyle,\edef,\em} +\DoNotIndex{\EnableCrossrefs,\end,\endcsname,\endgroup,\endinput} +\DoNotIndex{\everypar,\expandafter,\filedate,\fileversion} +\DoNotIndex{\footnotesize,\gdef,\global,\glossary,\hangindent} +\DoNotIndex{\if@filesw,\else,\fi} +\DoNotIndex{\if@nobreak,\if@twocolumn,\if@twoside,\fi,\fi,\fi} +\DoNotIndex{\hsize,\hskip} +\DoNotIndex{\ifhmode,\ifmmode,\ifodd,\ifvmode,\ifx,\fi,\fi,\fi,\fi,\fi} +\DoNotIndex{\ifcase,\ifdim,\ifeof,\iffalse,\iftrue,\fi,\fi,\fi,\fi,\fi} +\DoNotIndex{\ifcat,\fi} +\DoNotIndex{\immediate,\insert,\item,\jobname,\long} +\DoNotIndex{\let,\lineskip,\marginparsep,\marginparwidth,\maxdimen} +\DoNotIndex{\makeatletter,\noexpand,\openout,\protect,\rlap} +\DoNotIndex{\min,\newpage,\nobreak,\normalbaselineskip} +\DoNotIndex{\normallineskip,\p@,\par,\parfillskip,\parindent,\parskip} +\DoNotIndex{\penalty,\relax,\section,\sin,\sloppy,\space,\string} +\DoNotIndex{\tableofcontents,\the,\thepage,\thispagestyle,\toks,\tt} +\DoNotIndex{\twocolumn,\uppercase,\vbox,\vrule,\vskip,\vss} +\DoNotIndex{\write,\z@,\z@skip} +\endinput +%% +%% End of file `amsdtx.cls'. diff --git a/Master/texmf-dist/doc/latex/amslatex/math/install.txt b/Master/texmf-dist/doc/latex/amslatex/math/install.txt new file mode 100644 index 00000000000..fb4b835f282 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/math/install.txt @@ -0,0 +1,108 @@ +install.txt for amsmath 2.16 [2004/08/05] + +If you have a relatively up-do-date TeX system that complies with the +TeX Directory Structure (TDS) standard, installing according to the +instructions in section I below is the easiest method. See + + http://www.tug.org/tds/tds.pdf + +for details on the TDS standard. If your TeX system does not comply +with the TDS standard, please contact the manufactuer of your TeX +system for details on how to install third-party TeX packages. + +The first step is to identify the TEXMF folder that contains files used +by LaTeX. To do this, look for the file article.cls. If you find, e.g., + + /usr/local/share/texmf/tex/latex/base/article.cls + +then we will define TEXMF to mean /usr/local/share/texmf (everything +up to the /tex/latex/base part). On a Windows system the file location +will probably be something like + + c:\sw\texmf\tex\latex\base\article.cls + +Then we define TEXMF to mean c:\sw\texmf. In the following instructions, +wherever you see "TEXMF" substitute the folder name determined in this +way. + +If this terminology does not make sense to you, seek assistance from +a friend or colleague, or from the company that you bought your TeX +system from, or contact us at + + tech-support@ams.org + 800-321-4AMS (321-4267) (USA/Canada) + 401-455-4080 + +======================================================================== +I. Installing the easy way. + +1. Download the following archive file: + + ftp://ftp.ams.org/pub/tex/amsmath.zip + +2. View the following files to assess the effects of the upgrade on +your system: + + 00readme.txt + install.txt (this file) + diffs-m.txt + +3. Backup the old version of AMS-LaTeX, preferably by moving it out of the +TEXMF tree. + +4. Extract files from the .zip archive using your favorite unzip tool, +setting the extraction target directory to the texmf root directory. + +5. To check the end result, you should find that you now have amsmath.sty +in the following location + + TEXMF/tex/latex/amsmath/amsmath.sty + +Some TeX systems also use a database to keep track of TeX input files. +If this database is not updated, your TeX system might not find the +newly installed files. Consult your TeX system's documentation to +determine how to update this database. + +6. Some files will appear in both the source area and another area. +This is because the source form and the in-use form are identical. +As distributed, the files in the source/latex/ams* areas comprise a +complete copy of the distribution from which all the other files can +be regenerated if need be. If you need to conserve disk space, you +could delete the files in the source area, since they are not needed +for normal use. + +======================================================================== +II. Installing the not-so-easy way. + +Download ftp://ftp.ams.org/pub/tex/amsmath.zip. + +Make the following directories, if not already present: + + TEXMF/source/latex/amsmath + TEXMF/tex/latex/amsmath + TEXMF/doc/latex/amsmath + +Backup your old AMS-LaTeX files if they are installed, preferably moving them +out of the TEXMF tree. + +******** revise -- pdf file amsldoc will be included in distrib + +Create a temporary directory and generate documentation files (these assume +a UNIX TeX installation): + + - make directory /tmp/amsmath + - unzip -d /tmp/amscls amsmath.zip + - cd /tmp/amsmath + - Run latex on the file ams-m1.ins to produce .cls and .sty files + - Run latex on *.tex + - [optional] Run latex on *.dtx (technical documentation) + - move *.dvi, *.pdf, *.tex to TEXMF/doc/latex/amsmath + - [optional] move *.dtx to TEXMF/doc/latex/amsmath + - [optional] convert .dvi to .ps or .pdf + - move *.sty and *.cls to TEXMF/tex/latex/amsmath + - delete /tmp/amsmath + +Some TeX systems also use a database to keep track of TeX input files. +If this database is not updated, your TeX system might not find the +newly installed files. Consult your system's documentation to determine +how to update this database. diff --git a/Master/texmf-dist/doc/latex/amslatex/math/manifest.txt b/Master/texmf-dist/doc/latex/amslatex/math/manifest.txt new file mode 100644 index 00000000000..2ea274a32d7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/math/manifest.txt @@ -0,0 +1,38 @@ + +texmf/doc/latex/amsmath/ + amsldoc.pdf + diffs-m.txt + subeqn.pdf + technote.pdf + testmath.pdf + +texmf/source/latex/amsmath/ + 00readme.txt + ams-m1.ins + amsbsy.dtx + amscd.dtx + amsdtx.cls + amsgen.dtx + amsldoc.cls + amsldoc.tex + amsmath.dtx + amsopn.dtx + amstex.sty + amstext.dtx + amsxtra.dtx + diffs-m.txt + install.txt + manifest.txt + subeqn.tex + technote.tex + testmath.tex + +texmf/tex/latex/amsmath/ + amsbsy.sty + amscd.sty + amsgen.sty + amsmath.sty + amsopn.sty + amstex.sty + amstext.sty + amsxtra.sty diff --git a/Master/texmf-dist/doc/latex/amslatex/mathscinet.pdf b/Master/texmf-dist/doc/latex/amslatex/mathscinet.pdf Binary files differnew file mode 100644 index 00000000000..2392932a506 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/mathscinet.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/other/amsmidx.sty b/Master/texmf-dist/doc/latex/amslatex/other/amsmidx.sty new file mode 100644 index 00000000000..9fd19b0a06e --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/other/amsmidx.sty @@ -0,0 +1,82 @@ +% amsmidx.sty +% 2001/09/26 +% preliminary version +% +% Package for use with AMS document classes to produce multiple indexes +% +% Adapted from multind.sty (version 1.1b, 31 August 1991), by F.W. Long + +% Modified \makeindex and \index commands to allow multiple indexes +% The first argument of \makeindex and \index is the index file name. +% These commands now work more like \@starttoc and \addcontentsline. +% \index is no longer defined inside \makeindex but determines whether +% the appropriate file is defined before writing to it. + +\def\makeindex#1{\begingroup + \makeatletter + \if@filesw \expandafter\newwrite\csname #1@idxfile\endcsname + \expandafter\immediate\openout \csname #1@idxfile\endcsname #1.idx\relax + \typeout{Writing index file #1.idx }\fi \endgroup} + +\def\index#1{\@bsphack + \begingroup + \def\protect##1{\string##1\space}\@sanitize + \@wrindex{#1}} + +% \@wrindex now checks that the appropriate file is defined. + +\def\@wrindex#1#2{\let\thepage\relax + \xdef\@gtempa{\@ifundefined{#1@idxfile}{}{% + \expandafter\write\csname #1@idxfile\endcsname + {\string\indexentry{#2}{\thepage}}}}% + \endgroup\@gtempa + \if@nobreak \ifvmode\nobreak\fi\fi + \@esphack} + +% Modified \printindex command to accept the name of an index file. + +\renewcommand{\printindex}[1]{\@input{#1.ind}} + +% Alternate command with new name: +% \Printindex locally modifies some formatting commands for an improved +% appearance, sets the index title and reads in the requested index file. +% #1 = file name, #2 = index title + +\newcommand\Printindex[2]{% + \begingroup + \cleardoublepage + \def\indexname{#2}% + \raggedright + \hyphenpenalty=10000 + \renewcommand{\seename}{see~also} + \renewcommand{\subitem}{\par\hangindent 3em\hspace*{1em}} + \@input{#1.ind}% + \endgroup +} + +\endinput + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Instructions for using amsmidx.sty + +Put these commands in the preamble: + + \usepackage{amsmidx} + \makeindex{filename-a} + \makeindex{filename-b} + +To identify the index entries in the text: + + \index{filename-a}{index term} + \index{filename-b}{index term} + +In the backmatter, where the indexes are to appear: + + \Printindex{filename-a}{First Index} + \Printindex{filename-b}{Second Index} + +Two files of index terms, filename-a.idx and filename-b.idx, will be +generated. To sort the index terms, process the two .idx files +separately with Makeindex; this will create the files filename-a.ind +and filename-b.ind, which will in turn be input by \Printindex. diff --git a/Master/texmf-dist/doc/latex/amslatex/subeqn.pdf b/Master/texmf-dist/doc/latex/amslatex/subeqn.pdf Binary files differnew file mode 100644 index 00000000000..a2aa7a40fd2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/subeqn.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/subeqn.tex b/Master/texmf-dist/doc/latex/amslatex/subeqn.tex new file mode 100644 index 00000000000..d0fa7d9b023 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/subeqn.tex @@ -0,0 +1,202 @@ +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "subeqn.tex", +%%% version = "1.2c", +%%% date = "1999/11/29", +%%% time = "14:49:29 EST", +%%% checksum = "29866 202 668 6426", +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1999 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Electronic Products and Services, +%%% P. O. Box 6248, +%%% Providence, RI 02940, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% supported = "yes", +%%% keywords = "latex, amslatex, ams-latex, amstex", +%%% abstract = "This is part of the AMS-\LaTeX{} distribution. +%%% It is a sample document illustrating the use of +%%% the subequations environment and the effect of +%%% the fleqn option.", +%%% docstring = "The checksum field above contains a CRC-16 +%%% checksum as the first value, followed by the +%%% equivalent of the standard UNIX wc (word +%%% count) utility output of lines, words, and +%%% characters. This is produced by Robert +%%% Solovay's checksum utility.", +%%% } +%%% ==================================================================== +\documentclass[fleqn]{article} + +\title{Test of subequations environment} +\author{mjd} + +\usepackage{amsmath} +\numberwithin{equation}{section} + +\newcommand{\env}[1]{{\normalfont\texttt{#1}}} + +\AtEndDocument{\multipasswarning} +\newcommand{\multipasswarning}{% + \clearpage + \typeout{% + **********************************************************************} + \typeout{% + Note: This document needs to run through LaTeX three times, instead of} + \typeout{% + the usual two, to resolve indirect cross-references.} + \typeout{% + **********************************************************************} +} + +\makeatletter +% Omit the warning message if three passes have been completed (on +% first pass \ref{check} is undefined and it is set to 0; on second +% pass \ref{check} is 0 and set to 1; on third pass it is 1). +\def\checkref{\begingroup + \@ifundefined{r@check}{\def\@currentlabel{0}}{\def\@currentlabel{1}}% + \ifnum1=0\expandafter\@firstoftwo\r@check\relax + \global\let\multipasswarning\relax + \fi + \label{check}% + \endgroup} +\makeatother + +\begin{document} +\section{Prime equation numbers} + +First an equation. +\begin{equation}\label{e:previous} +A=B +\end{equation} +That was equation \eqref{e:previous}. + +Then the same, with a prime on the number.\checkref +\begin{equation} +\tag{\ref{e:previous}$'$}\label{e:prevprime} +C=D +\end{equation} +And that was equation \eqref{e:prevprime}. + +Notice, by the way, that when a \verb"\ref" occurs inside a \verb"\tag", +and that \verb"\tag" is then \verb"\label"'d, a \verb"\ref" for the the +second \verb"\label" requires \emph{three} runs of \LaTeX{} in order to +get the proper value. (If you run through the logic of \LaTeX{}'s +cross-referencing mechanisms as they apply in this case, you will see +that this is necessary.) + +\section{Subnumbered equations} + +Here is a,b,c sub-numbering. +\begin{subequations} +\begin{eqnarray} +A&=&B\\ +D&=&C \label{e:middle}\\ +E&=&F +\end{eqnarray} +\end{subequations} +That was produced with the \env{eqnarray} environment; the middle line +was labeled as \eqref{e:middle}. + +An equation following the end of the \verb"subequations" environment +should revert to normal numbering: +\begin{equation}\label{e:check} +H<K +\end{equation} +A check on the labeling: that was equation~\eqref{e:check}. + +The sub-numbered equations can be spread out through the text, like +this: +\begin{subequations} +\begin{equation} +A=B +\end{equation} +The \verb"subequations" environment can span arbitrary text between +subsidiary equations. The only restriction is that if there are any +numbered equations inside the \verb"subequations" environment that break +out of the subequation numbering sequence, they would have to be handled +specially. +\begin{equation} +D=C \label{e:newmiddle} +\end{equation} +More arbitrary text. +\begin{equation} +E=F +\end{equation} +\end{subequations} +Label check: the middle one was \eqref{e:newmiddle} + +A final equation for a numbering check. +\begin{equation}\label{e:final} +G=H +\end{equation} +That equation was labeled as \eqref{e:final}. + +\section{Tests of \env{align}, \env{gather}, and other +AMS-\protect\LaTeX{} environments} + +The \env{align} environment: +\begin{subequations} +\begin{align} +\label{align:a}A+B&=B+A\\ +\label{align:b}C&=D+E\\ +\label{align:c}E&=F +\end{align} +\end{subequations} +Label check: that was \eqref{align:a}, \eqref{align:b}, and +\eqref{align:c}. + +The \env{align} environment again: +\begin{subequations} +\begin{align} +\label{xalign:a}A+B&=B& B&=B+A\\ +\label{xalign:b}C&=D+E& C\oplus D&=E\\ +\label{xalign:c}E&=F& E'&=F' +\end{align} +\end{subequations} +Label check: that was \eqref{xalign:a}, \eqref{xalign:b}, and +\eqref{xalign:c}. + +The \env{gather} environment. For the third line we refer to one of the +numbers in the first \env{align} structure. +\begin{subequations} +\begin{gather} +\label{gather:a}A+B=B\\ +\label{gather:b}C=D+E\\ +\tag{\ref{align:c}$'$}\label{gather:c}E=F +\end{gather} +\end{subequations} +Label check: that was \eqref{gather:a}, +\eqref{gather:b}, and +\eqref{gather:c}. + +The next \env{subequations} environment encompasses two separate +equations. A \env{split} environment: +\begin{subequations} +\begin{equation} +\label{split:x} +\begin{split} +A&=B+C+F\\ +&=G +\end{split} +\end{equation} +and a \env{multline} environment: +\begin{multline}\label{multline:x} +A[B]C[D]E[F]G[[H[I]J[K]L[M]N]]=\\ +H[I]J[K]L[M]N[O]P[Q]R[S]T[U]V[W]X[Y]Z +\end{multline} +\end{subequations} +Label check: That was \eqref{split:x} and \eqref{multline:x}. + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/technote.pdf b/Master/texmf-dist/doc/latex/amslatex/technote.pdf Binary files differnew file mode 100644 index 00000000000..11b67dfa4dc --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/technote.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/technote.tex b/Master/texmf-dist/doc/latex/amslatex/technote.tex new file mode 100644 index 00000000000..aede450621e --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/technote.tex @@ -0,0 +1,233 @@ +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "technote.tex", +%%% version = "2.0", +%%% date = "1999/11/15", +%%% time = "15:07:20 EST", +%%% checksum = "58506 233 1647 12005", +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1995, 1999 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Electronic Products and Services, +%%% P. O. Box 6248, +%%% Providence, RI 02940, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% supported = "yes", +%%% keywords = "amsmath, latex", +%%% abstract = "This is part of the AMS-\LaTeX{} distribution. It +%%% is a document discussing some technical issues in the +%%% contents and interface of AMS-\LaTeX{} packages." +%%% docstring = "The checksum field above contains a CRC-16 checksum +%%% as the first value, followed by the equivalent of +%%% the standard UNIX wc (word count) utility output of +%%% lines, words, and characters. This is produced by +%%% Robert Solovay's checksum utility.", +%%% } +%%% ==================================================================== +\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX) +[1994/12/01]% LaTeX date must December 1994 or later +\documentclass{amsdtx} + +\title{Technical notes on the \pkg{amsmath} package} +\author{American Mathematical Society\\Michael Downes} +\date{1999/10/29} + +\markboth + {Technical notes on the \pkg{amsmath} package} + {Technical notes on the \pkg{amsmath} package} +\renewcommand{\sectionmark}[1]{} + +\providecommand{\etc}[1]{etc.} + +\providecommand{\begend}[1]{% + {\ntt \symbol{92}begin\symbol{123}#1\symbol{125}} + \ldots\ {\ntt\symbol{92}end\symbol{123}#1\symbol{125}}% +} + +\MakeShortVerb{\|} + +\begin{document} +\maketitle + +\section{Introduction} + +These notes are miscellaneous remarks on some technical questions +applicable to version 2.0 of \amslatex/. + +\section{Deprecated and disallowed commands} + +Certain commands that were in the \pkg{amstex} package (the predecessor, +in \amslatex/ 1.0 and 1.1, of the \pkg{amsmath} package) were moved into +\pkg{amsxtra} because they seemed to be little-used relics: +\cn{accentedsymbol}, \qq{sup accents} (\cn{sptilde}, \cn{sphat}, etc.). + +Certain other commands\mdash e.g., \cn{over}, \cn{pmatrix}, and +\cn{cases}\mdash are changed by the \pkg{amsmath} package to produce +warning messages or error messages, depending on their history; these +are discussed in more detail in the following sections. + +\section{Why do \cn{matrix}, \cn{pmatrix}, and \cn{cases} stop working +when I add the \pkg{amsmath} package?} + +If you used the \fn{plain.tex} versions of \cn{matrix}, \cn{pmatrix}, or +\cn{cases} in a document and then later converted the document to use +the \pkg{amsmath} package (or one of the AMS documentclasses, which +automatically call the \pkg{amsmath} package internally), the instances +of those commands will produce error messages. The problem is that when +\latex/ was originally created, it adopted most of its mathematics +features straight from \fn{plain.tex}. But in the case of \cn{matrix}, +\cn{pmatrix}, \cn{cases} this was a mistake\mdash the \fn{plain.tex} +syntax for them is decidedly non-\latex/ in style, for example the fact +that they use \cs{cr} instead of \cn{\\} to mark line breaks, and they +don't use \cn{begin} and \cn{end}. In basic \latex/ this mistake will be +perpetuated at least until \latex/3 appears, in order to avoid breaking +existing documents. But no existing documents that were written with the +\pkg{amsmath} package have that syntactic problem, as \pkg{amsmath} +provides proper \latex/-syntax versions of \cn{matrix} and the others. +The possibility of optionally allowing the \fn{plain.tex} variants to +make document conversion easier seems ill-advised since those variants +are so blatantly wrong in a \latex/ context. The \env{array} environment +ought to have been used instead. + +\section{Why do \cn{over}, \cn{atop}, \cn{above} [\dots{\ntt withdelims}] + give a warning when I add the \pkg{amsmath} package?} + +Using the six generalized fraction commands \cn{over}, +\cn{overwithdelims}, \cn{atop}, \cn{atopwithdelims}, \cn{above}, +\cn{abovewithdelims} is not really a good idea in \latex/, for reasons +explained below. I construe \latex/'s provision of \cs{frac}, and the +lack of any mention in the \latex/ book of the primitive fraction +commands, as an implicit injunction against their use, although I don't +think Lamport actually spent a lot of time pondering the issue, and the +basic \latex/ version of \cn{frac} provides access only to \cn{over}, +not to \cn{atop}, \cn{above}, or the \verb'withdelims' variants. The +\pkg{amsmath} package, however, provides a \cn{genfrac} command that +gives user-level access to all six of the generalized fraction +primitives in a way that conforms to the syntactic conventions followed +by all other \latex/ commands. + +Not only is the unusual syntax of the \tex/ primitives rather out of +place in \latex/, but furthermore that syntax seems to be responsible +for one of the most significant flaws in \tex/'s mathematical +typesetting capabilities: the fact that the current mathstyle at any +given point in a math formula cannot be determined until the end of the +formula, because of the possibility that a following generalized +fraction command will change the mathstyle of the \emph{preceding} +material. To cite two of the worst side effects: \cn{mathchoice} must +actually typeset all four of its arguments, instead of being able to +immediately select only one; and, were it possible to always know the +current math style at a given point, math font selection would be +greatly simplified and the upper limit of 16 different math font +\cn{fam}s would never be a problem as \cn{text,script[script]font} +assignments for any \cn{fam} could take immediate effect and therefore +could be changed arbitrarily often within a single formula. More +concretely, math font selection difficulties are responsible for many of +the more convoluted passages in the source code of \latex/'s NFSS (that +does font loading on demand) and of the \pkg{amsmath} package, and by +extension it has historically been responsible for significant delays in +making new features available to end users and for making those features +more prone to bugs. + +There are additional bad consequences following from the syntax of those +generalized fraction commands that only become evident when you do some +writing of nontrivial macros for math use. For example, as things +currently stand you cannot measure the size of any object in math +without going through \cn{mathchoice} and \emph{leaving and reentering +math mode} via \verb'\hbox{$' (which then introduces complications +regarding \cn{everymath} and \cn{mathsurround}). And it seems that +uncertainty about the current mathstyle is the only barrier to allowing +the use of mu units with \cn{vrule}, to make vertical struts in +constructing compound symbols or notation. And so on and so forth. + +\section{The \opt{fleqn} option and \cn{mathindent}} + +Strictly speaking, the \pkg{amsmath} package doesn't use \cn{mathindent} +to control the left indent of displayed equations when the \opt{fleqn} +option is in effect: it uses an internal parameter \cs{@mathmargin} +instead. However, for compatibility with existing \latex/ documentation, +\pkg{amsmath} turns \cn{mathindent} into an alias for \cs{@mathmargin}. +There is a small risk here: In the plain \latex/ implementation, +\cn{mathindent} is a dimen register, but with \pkg{amsmath} +\cs{@mathmargin} is a skip register and, by association, so is +\cn{mathindent}. If any package or documentclass uses \cn{mathindent} in +a way that depends on it being a dimen register, when used in +conjunction with the \pkg{amsmath} package it may be vulnerable to a +well-known pitfall having to do with the primitive \tex/ lookahead for a +\texttt{plus} or \texttt{minus} key word. However if the standard +\latex/ commands \cn{setlength} and \cn{addtolength} are used to modify +\cn{mathindent} then this problem will not arise. + +\section{Why can't I use abbreviations for \protect\begend{align}?} + +Authors often like to use abbreviations such as |\beq| |\eeq| for +|\begin{equation}| |\end{equation}|. For some environments defined by +the \pkg{amsmath} package, such as \env{align}, \env{gather}, +\env{multline}, and others of the same general type, this does not work: +An attempt to define |\bal| |\eal| as shorthand for |\begin{align}| +|\end{align}| will fail with a puzzling error message. This has to do +with unfortunately nontrivial technical complications: the given +environments must read their contents as a delimited macro argument +because they do multipass processing of the contents using algorithms +inherited from Spivak's \fn{amstex.tex}. The obvious +solution\mdash substitution of different algorithms that do box shuffling +instead of token shuffling for the multipass calculations\mdash would +require rewriting these display environments from the ground up; while +that is a worthy goal, it was beyond the original scope of the +\amslatex/ project. Work is under way on an auxiliary package called +\pkg{breqn} that addresses not only this problem but a number of others; +at the time of this writing, however [September 1999] it has only +progressed as far as a beta release. + +Some workarounds: +\begin{itemize} +\item |\def\bal#1\eal{\begin{align}#1\end{align}}| +\item Define |\newcommand{\env}[2]{\begin{#1}#2\end{#1}}| and then use + |\env{align}{...}| +\end{itemize} + +\section{The \pkg{upref} package} + +The reason for splitting out the \pkg{upref} package instead of +automatically incorporating it in the \cls{amsart} and \cls{amsbook} +classes is this: It involves low-level surgery on an important \latex/ +command. This means that if ever this command changes in the future (as +it did between versions 2.09 and 2e of \latex/) we have a maintenance +problem. And the benefit that \pkg{upref} provides is something that +most end users don't care much about. + +\section{The \pkg{amsintx} package} + +After a very preliminary trial release the \pkg{amsintx} package was +withdrawn to await further development. It is still considered a worthy +project but has simply not yet made it to the head of the priority queue +in the AMS \latex/ development program, as it has had to contend with a +number of other equally worthy projects for development time. + +\section{Hyphenation in the documentation} + +Hyphenation was allowed for certain long command names in +\fn{amsldoc.tex}; this presented technical difficulties because \latex/ +normally deactivates hyphenation for tt fonts. The method chosen to +reinstate hyphenation was to turn off the encoding-specific function +\cs{OT1+cmtt} that disables the \cs{hyphenchar} for tt fonts; see the +definition of \cn{allowtthyphens} in \fn{amsdtx.dtx}. Then a list of all +tt words in the document was gathered (from the \fn{.idx} file, produced +by the \cn{cn}, \cn{fn}, \cn{pkg}, etc. commands) and \cn{showhyphens} +was applied to this list. The result was another list in the resulting +\tex/ log, containing those words in a form suitable for the argument of +\cn{hyphenation}. That list was then edited by hand to overrule +undesirable hyphenations; words with acceptable hyphenations were +dropped from the list, as they don't need to be repeated there. + +\end{document} diff --git a/Master/texmf-dist/doc/latex/amslatex/testmath.pdf b/Master/texmf-dist/doc/latex/amslatex/testmath.pdf Binary files differnew file mode 100644 index 00000000000..9d638a0b796 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/testmath.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/testmath.tex b/Master/texmf-dist/doc/latex/amslatex/testmath.tex new file mode 100644 index 00000000000..069944ee9d0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/testmath.tex @@ -0,0 +1,2342 @@ +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "testmath.tex", +%%% version = "2.0", +%%% date = "1999/11/15", +%%% time = "15:09:17 EST", +%%% checksum = "07762 2342 7811 82371", +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1995, 1999 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Electronic Products and Services, +%%% P. O. Box 6248, +%%% Providence, RI 02940, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% codetable = "ISO/ASCII", +%%% keywords = "latex, amsmath, examples, documentation", +%%% supported = "yes", +%%% abstract = "This is a test file containing extensive examples of +%%% mathematical constructs supported by the amsmath +%%% package.", +%%% docstring = "The checksum field above contains a CRC-16 +%%% checksum as the first value, followed by the +%%% equivalent of the standard UNIX wc (word +%%% count) utility output of lines, words, and +%%% characters. This is produced by Robert +%%% Solovay's checksum utility.", +%%% } +%%% ==================================================================== +\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX) +[1994/12/01]% LaTeX date must December 1994 or later +\documentclass[draft]{article} +\pagestyle{headings} + +\title{Sample Paper for the \pkg{amsmath} Package\\ +File name: \fn{testmath.tex}} +\author{American Mathematical Society} +\date{Version 2.0, 1999/11/15} + +\usepackage{amsmath,amsthm} + +% Some definitions useful in producing this sort of documentation: +\chardef\bslash=`\\ % p. 424, TeXbook +% Normalized (nonbold, nonitalic) tt font, to avoid font +% substitution warning messages if tt is used inside section +% headings and other places where odd font combinations might +% result. +\newcommand{\ntt}{\normalfont\ttfamily} +% command name +\newcommand{\cn}[1]{{\protect\ntt\bslash#1}} +% LaTeX package name +\newcommand{\pkg}[1]{{\protect\ntt#1}} +% File name +\newcommand{\fn}[1]{{\protect\ntt#1}} +% environment name +\newcommand{\env}[1]{{\protect\ntt#1}} +\hfuzz1pc % Don't bother to report overfull boxes if overage is < 1pc + +% Theorem environments + +%% \theoremstyle{plain} %% This is the default +\newtheorem{thm}{Theorem}[section] +\newtheorem{cor}[thm]{Corollary} +\newtheorem{lem}[thm]{Lemma} +\newtheorem{prop}[thm]{Proposition} +\newtheorem{ax}{Axiom} + +\theoremstyle{definition} +\newtheorem{defn}{Definition}[section] + +\theoremstyle{remark} +\newtheorem{rem}{Remark}[section] +\newtheorem*{notation}{Notation} + +%\numberwithin{equation}{section} + +\newcommand{\thmref}[1]{Theorem~\ref{#1}} +\newcommand{\secref}[1]{\S\ref{#1}} +\newcommand{\lemref}[1]{Lemma~\ref{#1}} + +\newcommand{\bysame}{\mbox{\rule{3em}{.4pt}}\,} + +% Math definitions + +\newcommand{\A}{\mathcal{A}} +\newcommand{\B}{\mathcal{B}} +\newcommand{\st}{\sigma} +\newcommand{\XcY}{{(X,Y)}} +\newcommand{\SX}{{S_X}} +\newcommand{\SY}{{S_Y}} +\newcommand{\SXY}{{S_{X,Y}}} +\newcommand{\SXgYy}{{S_{X|Y}(y)}} +\newcommand{\Cw}[1]{{\hat C_#1(X|Y)}} +\newcommand{\G}{{G(X|Y)}} +\newcommand{\PY}{{P_{\mathcal{Y}}}} +\newcommand{\X}{\mathcal{X}} +\newcommand{\wt}{\widetilde} +\newcommand{\wh}{\widehat} + +\DeclareMathOperator{\per}{per} +\DeclareMathOperator{\cov}{cov} +\DeclareMathOperator{\non}{non} +\DeclareMathOperator{\cf}{cf} +\DeclareMathOperator{\add}{add} +\DeclareMathOperator{\Cham}{Cham} +\DeclareMathOperator{\IM}{Im} +\DeclareMathOperator{\esssup}{ess\,sup} +\DeclareMathOperator{\meas}{meas} +\DeclareMathOperator{\seg}{seg} + +% \interval is used to provide better spacing after a [ that +% is used as a closing delimiter. +\newcommand{\interval}[1]{\mathinner{#1}} + +% Notation for an expression evaluated at a particular condition. The +% optional argument can be used to override automatic sizing of the +% right vert bar, e.g. \eval[\biggr]{...}_{...} +\newcommand{\eval}[2][\right]{\relax + \ifx#1\right\relax \left.\fi#2#1\rvert} + +% Enclose the argument in vert-bar delimiters: +\newcommand{\envert}[1]{\left\lvert#1\right\rvert} +\let\abs=\envert + +% Enclose the argument in double-vert-bar delimiters: +\newcommand{\enVert}[1]{\left\lVert#1\right\rVert} +\let\norm=\enVert + +\begin{document} +\maketitle +\markboth{Sample paper for the {\protect\ntt\lowercase{amsmath}} package} +{Sample paper for the {\protect\ntt\lowercase{amsmath}} package} +\renewcommand{\sectionmark}[1]{} + +\section{Introduction} + +This paper contains examples of various features from \AmS-\LaTeX{}. + +\section{Enumeration of Hamiltonian paths in a graph} + +Let $\mathbf{A}=(a_{ij})$ be the adjacency matrix of graph $G$. The +corresponding Kirchhoff matrix $\mathbf{K}=(k_{ij})$ is obtained from +$\mathbf{A}$ by replacing in $-\mathbf{A}$ each diagonal entry by the +degree of its corresponding vertex; i.e., the $i$th diagonal entry is +identified with the degree of the $i$th vertex. It is well known that +\begin{equation} +\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$}, +\quad i=1,\dots,n +\end{equation} +where $\mathbf{K}(i|i)$ is the $i$th principal submatrix of +$\mathbf{K}$. +\begin{verbatim} +\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$}, +\end{verbatim} + +Let $C_{i(j)}$ be the set of graphs obtained from $G$ by attaching edge +$(v_iv_j)$ to each spanning tree of $G$. Denote by $C_i=\bigcup_j +C_{i(j)}$. It is obvious that the collection of Hamiltonian cycles is a +subset of $C_i$. Note that the cardinality of $C_i$ is $k_{ii}\det +\mathbf{K}(i|i)$. Let $\wh X=\{\hat x_1,\dots,\hat x_n\}$. +\begin{verbatim} +$\wh X=\{\hat x_1,\dots,\hat x_n\}$ +\end{verbatim} +Define multiplication for the elements of $\wh X$ by +\begin{equation}\label{multdef} +\hat x_i\hat x_j=\hat x_j\hat x_i,\quad \hat x^2_i=0,\quad +i,j=1,\dots,n. +\end{equation} +Let $\hat k_{ij}=k_{ij}\hat x_j$ and $\hat k_{ij}=-\sum_{j\not=i} \hat +k_{ij}$. Then the number of Hamiltonian cycles $H_c$ is given by the +relation \cite{liuchow:formalsum} +\begin{equation}\label{H-cycles} +\biggl(\prod^n_{\,j=1}\hat x_j\biggr)H_c=\frac{1}{2}\hat k_{ij}\det +\wh{\mathbf{K}}(i|i),\qquad i=1,\dots,n. +\end{equation} +The task here is to express \eqref{H-cycles} +in a form free of any $\hat x_i$, +$i=1,\dots,n$. The result also leads to the resolution of enumeration of +Hamiltonian paths in a graph. + +It is well known that the enumeration of Hamiltonian cycles and paths in +a complete graph $K_n$ and in a complete bipartite graph $K_{n_1n_2}$ +can only be found from \textit{first combinatorial principles} +\cite{hapa:graphenum}. One wonders if there exists a formula which can +be used very efficiently to produce $K_n$ and $K_{n_1n_2}$. Recently, +using Lagrangian methods, Goulden and Jackson have shown that $H_c$ can +be expressed in terms of the determinant and permanent of the adjacency +matrix \cite{gouja:lagrmeth}. However, the formula of Goulden and +Jackson determines neither $K_n$ nor $K_{n_1n_2}$ effectively. In this +paper, using an algebraic method, we parametrize the adjacency matrix. +The resulting formula also involves the determinant and permanent, but +it can easily be applied to $K_n$ and $K_{n_1n_2}$. In addition, we +eliminate the permanent from $H_c$ and show that $H_c$ can be +represented by a determinantal function of multivariables, each variable +with domain $\{0,1\}$. Furthermore, we show that $H_c$ can be written by +number of spanning trees of subgraphs. Finally, we apply the formulas to +a complete multigraph $K_{n_1\dots n_p}$. + +The conditions $a_{ij}=a_{ji}$, $i,j=1,\dots,n$, are not required in +this paper. All formulas can be extended to a digraph simply by +multiplying $H_c$ by 2. + +\section{Main Theorem} +\label{s:mt} + +\begin{notation} For $p,q\in P$ and $n\in\omega$ we write +$(q,n)\le(p,n)$ if $q\le p$ and $A_{q,n}=A_{p,n}$. +\begin{verbatim} +\begin{notation} For $p,q\in P$ and $n\in\omega$ +... +\end{notation} +\end{verbatim} +\end{notation} + +Let $\mathbf{B}=(b_{ij})$ be an $n\times n$ matrix. Let $\mathbf{n}=\{1, +\dots,n\}$. Using the properties of \eqref{multdef}, it is readily seen +that + +\begin{lem}\label{lem-per} +\begin{equation} +\prod_{i\in\mathbf{n}} +\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat x_i\biggr) +=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)\per \mathbf{B} +\end{equation} +where $\per \mathbf{B}$ is the permanent of $\mathbf{B}$. +\end{lem} + +Let $\wh Y=\{\hat y_1,\dots,\hat y_n\}$. Define multiplication +for the elements of $\wh Y$ by +\begin{equation} +\hat y_i\hat y_j+\hat y_j\hat y_i=0,\quad i,j=1,\dots,n. +\end{equation} +Then, it follows that +\begin{lem}\label{lem-det} +\begin{equation}\label{detprod} +\prod_{i\in\mathbf{n}} +\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat y_j\biggr) +=\biggl(\prod_{\,i\in\mathbf{n}}\hat y_i\biggr)\det\mathbf{B}. +\end{equation} +\end{lem} + +Note that all basic properties of determinants are direct consequences +of Lemma ~\ref{lem-det}. Write +\begin{equation}\label{sum-bij} +\sum_{j\in\mathbf{n}}b_{ij}\hat y_j=\sum_{j\in\mathbf{n}}b^{(\lambda)} +_{ij}\hat y_j+(b_{ii}-\lambda_i)\hat y_i\hat y +\end{equation} +where +\begin{equation} +b^{(\lambda)}_{ii}=\lambda_i,\quad b^{(\lambda)}_{ij}=b_{ij}, +\quad i\not=j. +\end{equation} +Let $\mathbf{B}^{(\lambda)}=(b^{(\lambda)}_{ij})$. By \eqref{detprod} +and \eqref{sum-bij}, it is +straightforward to show the following +result: +\begin{thm}\label{thm-main} +\begin{equation}\label{detB} +\det\mathbf{B}= +\sum^n_{l =0}\sum_{I_l \subseteq n} +\prod_{i\in I_l}(b_{ii}-\lambda_i) +\det\mathbf{B}^{(\lambda)}(I_l |I_l ), +\end{equation} +where $I_l =\{i_1,\dots,i_l \}$ and $\mathbf{B}^{(\lambda)}(I_l |I_l )$ +is the principal submatrix obtained from $\mathbf{B}^{(\lambda)}$ +by deleting its $i_1,\dots,i_l $ rows and columns. +\end{thm} + +\begin{rem} +Let $\mathbf{M}$ be an $n\times n$ matrix. The convention +$\mathbf{M}(\mathbf{n}|\mathbf{n})=1$ has been used in \eqref{detB} and +hereafter. +\end{rem} + +Before proceeding with our discussion, we pause to note that +\thmref{thm-main} yields immediately a fundamental formula which can be +used to compute the coefficients of a characteristic polynomial +\cite{mami:matrixth}: +\begin{cor}\label{BI} +Write $\det(\mathbf{B}-x\mathbf{I})=\sum^n_{l =0}(-1) +^l b_l x^l $. Then +\begin{equation}\label{bl-sum} +b_l =\sum_{I_l \subseteq\mathbf{n}}\det\mathbf{B}(I_l |I_l ). +\end{equation} +\end{cor} +Let +\begin{equation} +\mathbf{K}(t,t_1,\dots,t_n) +=\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\ +-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\ +\hdotsfor[2]{4}\\ +-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}, +\end{equation} +\begin{verbatim} +\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\ +-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\ +\hdotsfor[2]{4}\\ +-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix} +\end{verbatim} +where +\begin{equation} +D_i=\sum_{j\in\mathbf{n}}a_{ij}t_j,\quad i=1,\dots,n. +\end{equation} + +Set +\begin{equation*} +D(t_1,\dots,t_n)=\frac{\delta}{\delta t}\eval{\det\mathbf{K}(t,t_1,\dots,t_n) +}_{t=1}. +\end{equation*} +Then +\begin{equation}\label{sum-Di} +D(t_1,\dots,t_n) +=\sum_{i\in\mathbf{n}}D_i\det\mathbf{K}(t=1,t_1,\dots,t_n; i|i), +\end{equation} +where $\mathbf{K}(t=1,t_1,\dots,t_n; i|i)$ is the $i$th principal +submatrix of $\mathbf{K}(t=1,t_1,\dots,t_n)$. + +Theorem ~\ref{thm-main} leads to +\begin{equation}\label{detK1} +\det\mathbf{K}(t_1,t_1,\dots,t_n) +=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}t^{n-\envert{I}} +\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A} +^{(\lambda t)}(\overline{I}|\overline I). +\end{equation} +Note that +\begin{equation}\label{detK2} +\det\mathbf{K}(t=1,t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}} +\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A} +^{(\lambda)}(\overline{I}|\overline{I})=0. +\end{equation} + +Let $t_i=\hat x_i,i=1,\dots,n$. Lemma ~\ref{lem-per} yields +\begin{multline} +\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr) +\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\ +=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr) +\sum_{I\subseteq\mathbf{n}-\{l \}} +(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I) +\det\mathbf{A}^{(\lambda)} +(\overline I\cup\{l \}|\overline I\cup\{l \}). +\label{sum-ali} +\end{multline} +\begin{verbatim} +\begin{multline} +\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr) +\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\ +=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr) +\sum_{I\subseteq\mathbf{n}-\{l \}} +(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I) +\det\mathbf{A}^{(\lambda)} +(\overline I\cup\{l \}|\overline I\cup\{l \}). +\label{sum-ali} +\end{multline} +\end{verbatim} + +By \eqref{H-cycles}, \eqref{detprod}, and \eqref{sum-bij}, we have +\begin{prop}\label{prop:eg} +\begin{equation} +H_c=\frac1{2n}\sum^n_{l =0}(-1)^{l} +D_{l}, +\end{equation} +where +\begin{equation}\label{delta-l} +D_{l}=\eval[2]{\sum_{I_{l}\subseteq \mathbf{n}} +D(t_1,\dots,t_n)}_{t_i=\left\{\begin{smallmatrix} +0,& \text{if }i\in I_{l}\quad\\% \quad added for centering +1,& \text{otherwise}\end{smallmatrix}\right.\;,\;\; i=1,\dots,n}. +\end{equation} +\end{prop} + +\section{Application} +\label{lincomp} + +We consider here the applications of Theorems~\ref{th-info-ow-ow} and +~\ref{th-weak-ske-owf} to a complete +multipartite graph $K_{n_1\dots n_p}$. It can be shown that the +number of spanning trees of $K_{n_1\dots n_p}$ +may be written +\begin{equation}\label{e:st} +T=n^{p-2}\prod^p_{i=1} +(n-n_i)^{n_i-1} +\end{equation} +where +\begin{equation} +n=n_1+\dots+n_p. +\end{equation} + +It follows from Theorems~\ref{th-info-ow-ow} and +~\ref{th-weak-ske-owf} that +\begin{equation}\label{e:barwq} +\begin{split} +H_c&=\frac1{2n} +\sum^n_{{l}=0}(-1)^{l}(n-{l})^{p-2} +\sum_{l _1+\dots+l _p=l}\prod^p_{i=1} +\binom{n_i}{l _i}\\ +&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot +\biggl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\biggr].\end{split} +\end{equation} +\begin{verbatim} +... \binom{n_i}{l _i}\\ +\end{verbatim} +and +\begin{equation}\label{joe} +\begin{split} +H_c&=\frac12\sum^{n-1}_{l =0} +(-1)^{l}(n-l )^{p-2} +\sum_{l _1+\dots+l _p=l} +\prod^p_{i=1}\binom{n_i}{l _i}\\ +&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i} +\left(1-\frac{l _p}{n_p}\right) +[(n-l )-(n_p-l _p)]. +\end{split} +\end{equation} + +The enumeration of $H_c$ in a $K_{n_1\dotsm n_p}$ graph can also be +carried out by Theorem ~\ref{thm-H-param} or ~\ref{thm-asym} +together with the algebraic method of \eqref{multdef}. +Some elegant representations may be obtained. For example, $H_c$ in +a $K_{n_1n_2n_3}$ graph may be written +\begin{equation}\label{j:mark} +\begin{split} +H_c=& +\frac{n_1!\,n_2!\,n_3!} +{n_1+n_2+n_3}\sum_i\left[\binom{n_1}{i} +\binom{n_2}{n_3-n_1+i}\binom{n_3}{n_3-n_2+i}\right.\\ +&+\left.\binom{n_1-1}{i} +\binom{n_2-1}{n_3-n_1+i} +\binom{n_3-1}{n_3-n_2+i}\right].\end{split} +\end{equation} + +\section{Secret Key Exchanges} +\label{SKE} + +Modern cryptography is fundamentally concerned with the problem of +secure private communication. A Secret Key Exchange is a protocol +where Alice and Bob, having no secret information in common to start, +are able to agree on a common secret key, conversing over a public +channel. The notion of a Secret Key Exchange protocol was first +introduced in the seminal paper of Diffie and Hellman +\cite{dihe:newdir}. \cite{dihe:newdir} presented a concrete +implementation of a Secret Key Exchange protocol, dependent on a +specific assumption (a variant on the discrete log), specially +tailored to yield Secret Key Exchange. Secret Key Exchange is of +course trivial if trapdoor permutations exist. However, there is no +known implementation based on a weaker general assumption. + +The concept of an informationally one-way function was introduced +in \cite{imlelu:oneway}. We give only an informal definition here: + +\begin{defn} A polynomial time +computable function $f = \{f_k\}$ is informationally +one-way if there is no probabilistic polynomial time algorithm which +(with probability of the form $1 - k^{-e}$ for some $e > 0$) +returns on input $y \in \{0,1\}^{k}$ a random element of $f^{-1}(y)$. +\end{defn} +In the non-uniform setting \cite{imlelu:oneway} show that these are not +weaker than one-way functions: +\begin{thm}[\cite{imlelu:oneway} (non-uniform)] +\label{th-info-ow-ow} +The existence of informationally one-way functions +implies the existence of one-way functions. +\end{thm} +We will stick to the convention introduced above of saying +``non-uniform'' before the theorem statement when the theorem +makes use of non-uniformity. It should be understood that +if nothing is said then the result holds for both the uniform and +the non-uniform models. + +It now follows from \thmref{th-info-ow-ow} that + +\begin{thm}[non-uniform]\label{th-weak-ske-owf} Weak SKE +implies the existence of a one-way function. +\end{thm} + +More recently, the polynomial-time, interior point algorithms for linear +programming have been extended to the case of convex quadratic programs +\cite{moad:quadpro,ye:intalg}, certain linear complementarity problems +\cite{komiyo:lincomp,miyoki:lincomp}, and the nonlinear complementarity +problem \cite{komiyo:unipfunc}. The connection between these algorithms +and the classical Newton method for nonlinear equations is well +explained in \cite{komiyo:lincomp}. + +\section{Review} +\label{computation} + +We begin our discussion with the following definition: + +\begin{defn} + +A function $H\colon \Re^n \to \Re^n$ is said to be +\emph{B-differentiable} at the point $z$ if (i)~$H$ is Lipschitz +continuous in a neighborhood of $z$, and (ii)~ there exists a positive +homogeneous function $BH(z)\colon \Re^n \to \Re^n$, called the +\emph{B-derivative} of $H$ at $z$, such that +\[ \lim_{v \to 0} \frac{H(z+v) - H(z) - BH(z)v}{\enVert{v}} = 0. \] +The function $H$ is \textit{B-differentiable in set $S$} if it is +B-differentiable at every point in $S$. The B-derivative $BH(z)$ is said +to be \textit{strong} if +\[ \lim_{(v,v') \to (0,0)} \frac{H(z+v) - H(z+v') - BH(z)(v + -v')}{\enVert{v - v'}} = 0. \] +\end{defn} + + +\begin{lem}\label{limbog} There exists a smooth function $\psi_0(z)$ +defined for $\abs{z}>1-2a$ satisfying the following properties\textup{:} +\begin{enumerate} +\renewcommand{\labelenumi}{(\roman{enumi})} +\item $\psi_0(z)$ is bounded above and below by positive constants +$c_1\leq \psi_0(z)\leq c_2$. +\item If $\abs{z}>1$, then $\psi_0(z)=1$. +\item For all $z$ in the domain of $\psi_0$, $\Delta_0\ln \psi_0\geq 0$. +\item If $1-2a<\abs{z}<1-a$, then $\Delta_0\ln \psi_0\geq +c_3>0$. +\end{enumerate} +\end{lem} + +\begin{proof} +We choose $\psi_0(z)$ to be a radial function depending only on $r=\abs{z}$. +Let $h(r)\geq 0$ be a suitable smooth function satisfying $h(r)\geq c_3$ +for $1-2a<\abs{z}<1-a$, and $h(r)=0$ for $\abs{z}>1-\tfrac a2$. The radial +Laplacian +\[\Delta_0\ln\psi_0(r)=\left(\frac {d^2}{dr^2}+\frac +1r\frac d{dr}\right)\ln\psi_0(r)\] +has smooth coefficients for $r>1-2a$. Therefore, we may +apply the existence and uniqueness theory for ordinary differential +equations. Simply let $\ln \psi_0(r)$ be the solution of the differential +equation +\[\left(\frac{d^2}{dr^2}+\frac 1r\frac d{dr}\right)\ln \psi_0(r)=h(r)\] +with initial conditions given by $\ln \psi_0(1)=0$ and +$\ln\psi_0'(1)=0$. + +Next, let $D_\nu$ be a finite collection of pairwise disjoint disks, +all of which are contained in the unit disk centered at the origin in +$C$. We assume that $D_\nu=\{z\mid \abs{z-z_\nu}<\delta\}$. Suppose that +$D_\nu(a)$ denotes the smaller concentric disk $D_\nu(a)=\{z\mid +\abs{z-z_\nu}\leq (1-2a)\delta\}$. We define a smooth weight function +$\Phi_0(z)$ for $z\in C-\bigcup_\nu D_\nu(a)$ by setting $\Phi_ +0(z)=1$ when $z\notin \bigcup_\nu D_\nu$ and $\Phi_ +0(z)=\psi_0((z-z_\nu)/\delta)$ when $z$ is an element of $D_\nu$. It +follows from \lemref{limbog} that $\Phi_ 0$ satisfies the properties: +\begin{enumerate} +\renewcommand{\labelenumi}{(\roman{enumi})} +\item \label{boundab}$\Phi_ 0(z)$ is bounded above and below by +positive constants $c_1\leq \Phi_ 0(z)\leq c_2$. +\item \label{d:over}$\Delta_0\ln\Phi_ 0\geq 0$ for all +$z\in C-\bigcup_\nu D_\nu(a)$, +the domain where the function $\Phi_ 0$ is defined. +\item \label{d:ad}$\Delta_0\ln\Phi_ 0\geq c_3\delta^{-2}$ +when $(1-2a)\delta<\abs{z-z_\nu}<(1-a)\delta$. +\end{enumerate} +Let $A_\nu$ denote the annulus $A_\nu=\{(1-2a)\delta<\abs{z-z_\nu}<(1-a) +\delta \}$, and set $A=\bigcup_\nu A_\nu$. The +properties (\ref{d:over}) and (\ref{d:ad}) of $\Phi_ 0$ +may be summarized as $\Delta_0\ln \Phi_ 0\geq c_3\delta^{-2}\chi_A$, +where $\chi _A$ is the characteristic function of $A$. +\end{proof} + +Suppose that $\alpha$ is a nonnegative real constant. We apply +Proposition~\ref{prop:eg} with $\Phi(z)=\Phi_ 0(z) e^{\alpha\abs{z}^2}$. If +$u\in C^\infty_0(R^2-\bigcup_\nu D_\nu(a))$, assume that $\mathcal{D}$ +is a bounded domain containing the support of $u$ and $A\subset +\mathcal{D}\subset R^2-\bigcup_\nu D_\nu(a)$. A calculation gives +\[\int_{\mathcal{D}}\abs{\overline\partial u}^2\Phi_ 0(z) e^{\alpha\abs{z}^2} +\geq c_4\alpha\int_{\mathcal{D}}\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2} ++c_5\delta^{-2}\int_ A\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}.\] + +The boundedness, property (\ref{boundab}) of $\Phi_ 0$, then yields +\[\int_{\mathcal{D}}\abs{\overline\partial u}^2e^{\alpha\abs{z}^2}\geq c_6\alpha +\int_{\mathcal{D}}\abs{u}^2e^{\alpha\abs{z}^2} ++c_7\delta^{-2}\int_ A\abs{u}^2e^{\alpha\abs{z}^2}.\] + +Let $B(X)$ be the set of blocks of $\Lambda_{X}$ +and let $b(X) = \abs{B(X)}$. If $\phi \in Q_{X}$ then +$\phi$ is constant on the blocks of $\Lambda_{X}$. +\begin{equation}\label{far-d} + P_{X} = \{ \phi \in M \mid \Lambda_{\phi} = \Lambda_{X} \}, +\qquad +Q_{X} = \{\phi \in M \mid \Lambda_{\phi} \geq \Lambda_{X} \}. +\end{equation} +If $\Lambda_{\phi} \geq \Lambda_{X}$ then +$\Lambda_{\phi} = \Lambda_{Y}$ for some $Y \geq X$ so that +\[ Q_{X} = \bigcup_{Y \geq X} P_{Y}. \] +Thus by M\"obius inversion +\[ \abs{P_{Y}}= \sum_{X\geq Y} \mu (Y,X)\abs{Q_{X}}.\] +Thus there is a bijection from $Q_{X}$ to $W^{B(X)}$. +In particular $\abs{Q_{X}} = w^{b(X)}$. + +Next note that $b(X)=\dim X$. We see this by choosing a +basis for $X$ consisting of vectors $v^{k}$ defined by +\[v^{k}_{i}= +\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\ +0 &\text{otherwise.} \end{cases} +\] +\begin{verbatim} +\[v^{k}_{i}= +\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\ +0 &\text{otherwise.} \end{cases} +\] +\end{verbatim} + +\begin{lem}\label{p0201} +Let $\A$ be an arrangement. Then +\[ \chi (\A,t) = \sum_{\B \subseteq \A} +(-1)^{\abs{\B}} t^{\dim T(\B)}. \] +\end{lem} + +In order to compute $R''$ recall the definition +of $S(X,Y)$ from \lemref{lem-per}. Since $H \in \B$, +$\A_{H} \subseteq \B$. Thus if $T(\B) = Y$ then +$\B \in S(H,Y)$. Let $L'' = L(\A'')$. Then +\begin{equation}\label{E_SXgYy} +\begin{split} +R''&= \sum_{H\in \B \subseteq \A} (-1)^{\abs{\B}} +t^{\dim T(\B)}\\ +&= \sum_{Y \in L''} \sum_{\B \in S(H,Y)} +(-1)^{\abs{\B}}t^{\dim Y} \\ +&= -\sum_{Y \in L''} \sum_{\B \in S(H,Y)} (-1)^ +{\abs{\B - \A_{H}}} t^{\dim Y} \\ +&= -\sum_{Y \in L''} \mu (H,Y)t^{\dim Y} \\ +&= -\chi (\A '',t). +\end{split} +\end{equation} + +\begin{cor}\label{tripleA} +Let $(\A,\A',\A'')$ be a triple of arrangements. Then +\[ \pi (\A,t) = \pi (\A',t) + t \pi (\A'',t). \] +\end{cor} + +\begin{defn} +Let $(\A,\A',\A'')$ be a triple with respect to +the hyperplane $H \in \A$. Call $H$ a \textit{separator} +if $T(\A) \not\in L(\A')$. +\end{defn} + +\begin{cor}\label{nsep} +Let $(\A,\A',\A'')$ be a triple with respect to $H \in \A$. +\begin{enumerate} +\renewcommand{\labelenumi}{(\roman{enumi})} +\item +If $H$ is a separator then +\[ \mu (\A) = - \mu (\A'') \] +and hence +\[ \abs{\mu (\A)} = \abs{ \mu (\A'')}. \] + +\item If $H$ is not a separator then +\[\mu (\A) = \mu (\A') - \mu (\A'') \] +and +\[ \abs{\mu (\A)} = \abs{\mu (\A')} + \abs{\mu (\A'')}. \] +\end{enumerate} +\end{cor} + +\begin{proof} +It follows from \thmref{th-info-ow-ow} that $\pi(\A,t)$ +has leading term +\[(-1)^{r(\A)}\mu (\A)t^{r(\A)}.\] +The conclusion +follows by comparing coefficients of the leading +terms on both sides of the equation in +Corollary~\ref{tripleA}. If $H$ is a separator then +$r(\A') < r(\A)$ and there is no contribution +from $\pi (\A',t)$. +\end{proof} + +The Poincar\'e polynomial of an arrangement +will appear repeatedly +in these notes. It will be shown to equal the +Poincar\'e polynomial +of the graded algebras which we are going to +associate with $\A$. It is also the Poincar\'e +polynomial of the complement $M(\A)$ for a +complex arrangement. Here we prove +that the Poincar\'e polynomial is the chamber +counting function for a real arrangement. The +complement $M(\A)$ is a disjoint union of chambers +\[M(\A) = \bigcup_{C \in \Cham(\A)} C.\] +The number +of chambers is determined by the Poincar\'e +polynomial as follows. + +\begin{thm}\label{th-realarr} +Let $\A_{\mathbf{R}}$ be a real arrangement. Then +\[ \abs{\Cham(\A_{\mathbf{R}})} = \pi (\A_{\mathbf{R}},1). \] +\end{thm} + +\begin{proof} +We check the properties required in Corollary~\ref{nsep}: +(i) follows from $\pi (\Phi_{ l},t) = 1$, and (ii) is a +consequence of Corollary~\ref{BI}. +\end{proof} + +\begin{figure} +\vspace{5cm} +\caption[]{$Q(\A_{1}) = xyz(x-z)(x+z)(y-z)(y+z)$} +\end{figure} + +\begin{figure} +\vspace{5cm} +\caption[]{$Q(\A_{2})= xyz(x+y+z)(x+y-z)(x-y+z)(x-y-z)$} +\end{figure} + + +\begin{thm} +\label{T_first_the_int} +Let $\phi$ be a protocol for a random pair $\XcY$. +If one of $\st_\phi(x',y)$ and $\st_\phi(x,y')$ is a prefix of the other +and $(x,y)\in\SXY$, then +\[ +\langle \st_j(x',y)\rangle_{j=1}^\infty +=\langle \st_j(x,y)\rangle_{j=1}^\infty +=\langle \st_j(x,y')\rangle_{j=1}^\infty . +\] +\end{thm} +\begin{proof} +We show by induction on $i$ that +\[ +\langle \st_j(x',y)\rangle_{j=1}^i +=\langle \st_j(x,y)\rangle_{j=1}^i +=\langle \st_j(x,y')\rangle_{j=1}^i. +\] +The induction hypothesis holds vacuously for $i=0$. Assume it holds for +$i-1$, in particular +$[\st_j(x',y)]_{j=1}^{i-1}=[\st_j(x,y')]_{j=1}^{i-1}$. Then one of +$[\st_j(x',y)]_{j=i}^{\infty}$ and $[\st_j(x,y')]_{j=i}^{\infty}$ is a +prefix of the other which implies that one of $\st_i(x',y)$ and +$\st_i(x,y')$ is a prefix of the other. If the $i$th message is +transmitted by $P_\X$ then, by the separate-transmissions property and +the induction hypothesis, $\st_i(x,y)=\st_i(x,y')$, hence one of +$\st_i(x,y)$ and $\st_i(x',y)$ is a prefix of the other. By the +implicit-termination property, neither $\st_i(x,y)$ nor $\st_i(x',y)$ +can be a proper prefix of the other, hence they must be the same and +$\st_i(x',y)=\st_i(x,y)=\st_i(x,y')$. If the $i$th message is +transmitted by $\PY$ then, symmetrically, $\st_i(x,y)=\st_i(x',y)$ by +the induction hypothesis and the separate-transmissions property, and, +then, $\st_i(x,y)=\st_i(x,y')$ by the implicit-termination property, +proving the induction step. +\end{proof} + +If $\phi$ is a protocol for $(X,Y)$, and $(x,y)$, $(x',y)$ are distinct +inputs in $\SXY$, then, by the correct-decision property, +$\langle\st_j(x,y)\rangle_{j=1}^\infty\ne\langle +\st_j(x',y)\rangle_{j=1}^\infty$. + +Equation~(\ref{E_SXgYy}) defined $\PY$'s ambiguity set $\SXgYy$ +to be the set of possible $X$ values when $Y=y$. +The last corollary implies that for all $y\in\SY$, +the multiset% +\footnote{A multiset allows multiplicity of elements. +Hence, $\{0,01,01\}$ is prefix free as a set, but not as a multiset.} +of codewords $\{\st_\phi(x,y):x\in\SXgYy\}$ is prefix free. + +\section{One-Way Complexity} +\label{S_Cp1} + +$\Cw1$, the one-way complexity of a random pair $\XcY$, +is the number of bits $P_\X$ must transmit in the worst case +when $\PY$ is not permitted to transmit any feedback messages. +Starting with $\SXY$, the support set of $\XcY$, we define $\G$, +the \textit{characteristic hypergraph} of $\XcY$, and show that +\[ +\Cw1=\lceil\,\log\chi(\G)\rceil\ . +\] + +Let $\XcY$ be a random pair. For each $y$ in $\SY$, the support set of +$Y$, Equation~(\ref{E_SXgYy}) defined $\SXgYy$ to be the set of possible +$x$ values when $Y=y$. The \textit{characteristic hypergraph} $\G$ of +$\XcY$ has $\SX$ as its vertex set and the hyperedge $\SXgYy$ for each +$y\in\SY$. + + +We can now prove a continuity theorem. +\begin{thm}\label{t:conl} +Let $\Omega \subset\mathbf{R}^n$ be an open set, let +$u\in BV(\Omega ;\mathbf{R}^m)$, and let +\begin{equation}\label{quts} +T^u_x=\left\{y\in\mathbf{R}^m: + y=\tilde u(x)+\left\langle \frac{Du}{\abs{Du}}(x),z +\right\rangle \text{ for some }z\in\mathbf{R}^n\right\} +\end{equation} +for every $x\in\Omega \backslash S_u$. Let $f\colon \mathbf{R}^m\to +\mathbf{R}^k$ be a Lipschitz continuous function such that $f(0)=0$, and +let $v=f(u)\colon \Omega \to \mathbf{R}^k$. Then $v\in BV(\Omega +;\mathbf{R}^k)$ and +\begin{equation} +Jv=\eval{(f(u^+)-f(u^-))\otimes \nu_u\cdot\, +\mathcal{H}_{n-1}}_{S_u}. +\end{equation} +In addition, for $\abs{\wt{D}u}$-almost every $x\in\Omega $ the +restriction of the function $f$ to $T^u_x$ is differentiable at $\tilde +u(x)$ and +\begin{equation} +\wt{D}v=\nabla (\eval{f}_{T^u_x})(\tilde u) +\frac{\wt{D}u}{\abs{\wt{D}u}}\cdot\abs{\wt{D}u}.\end{equation} +\end{thm} + +Before proving the theorem, we state without proof three elementary +remarks which will be useful in the sequel. +\begin{rem}\label{r:omb} +Let $\omega\colon \left]0,+\infty\right[\to \left]0,+\infty\right[$ +be a continuous function such that $\omega (t)\to 0$ as $t\to +0$. Then +\[\lim_{h\to 0^+}g(\omega(h))=L\Leftrightarrow\lim_{h\to +0^+}g(h)=L\] +for any function $g\colon \left]0,+\infty\right[\to \mathbf{R}$. +\end{rem} +\begin{rem}\label{r:dif} +Let $g \colon \mathbf{R}^n\to \mathbf{R}$ be a Lipschitz +continuous function and assume that +\[L(z)=\lim_{h\to 0^+}\frac{g(hz)-g(0)}h\] +exists for every $z\in\mathbf{Q}^n$ and that $L$ is a linear function of +$z$. Then $g$ is differentiable at 0. +\end{rem} +\begin{rem}\label{r:dif0} +Let $A \colon \mathbf{R}^n\to \mathbf{R}^m$ be a linear function, and +let $f \colon \mathbf{R}^m\to \mathbf{R}$ be a function. Then the +restriction of $f$ to the range of $A$ is differentiable at 0 if and +only if $f(A)\colon \mathbf{R}^n\to \mathbf{R}$ is differentiable at 0 +and +\[\nabla(\eval{f}_{\IM(A)})(0)A=\nabla (f(A))(0).\] +\end{rem} + +\begin{proof} + We begin by showing that $v\in BV(\Omega;\mathbf{R}^k)$ and +\begin{equation}\label{e:bomb} +\abs{Dv}(B)\le K\abs{Du}(B)\qquad\forall B\in\mathbf{B}(\Omega ), +\end{equation} +where $K>0$ is the Lipschitz constant of $f$. By \eqref{sum-Di} and by +the approximation result quoted in \secref{s:mt}, it is possible to find +a sequence $(u_h)\subset C^1(\Omega ;\mathbf{R}^m)$ converging to $u$ in +$L^1(\Omega ;\mathbf{R}^m)$ and such that +\[\lim_{h\to +\infty}\int_\Omega \abs{\nabla u_h}\,dx=\abs{Du}(\Omega ).\] +The functions $v_h=f(u_h)$ are locally Lipschitz continuous in $\Omega +$, and the definition of differential implies that $\abs{\nabla v_h}\le +K\abs{\nabla u_h}$ almost everywhere in $\Omega $. The lower semicontinuity +of the total variation and \eqref{sum-Di} yield +\begin{equation} +\begin{split} +\abs{Dv}(\Omega )\le\liminf_{h\to +\infty}\abs{Dv_h}(\Omega) & +=\liminf_{h\to +\infty}\int_\Omega \abs{\nabla v_h}\,dx\\ +&\le K\liminf_{h\to +\infty}\int_\Omega +\abs{\nabla u_h}\,dx=K\abs{Du}(\Omega). +\end{split}\end{equation} +Since $f(0)=0$, we have also +\[\int_\Omega \abs{v}\,dx\le K\int_\Omega \abs{u}\,dx;\] +therefore $u\in BV(\Omega ;\mathbf{R}^k)$. Repeating the same argument +for every open set $A\subset\Omega $, we get \eqref{e:bomb} for every +$B\in\mathbf{B}(\Omega)$, because $\abs{Dv}$, $\abs{Du}$ are Radon measures. To +prove \lemref{limbog}, first we observe that +\begin{equation}\label{e:SS} +S_v\subset S_u,\qquad\tilde v(x)=f(\tilde u(x))\qquad \forall x\in\Omega +\backslash S_u.\end{equation} +In fact, for every $\varepsilon >0$ we have +\[\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>\varepsilon \}\subset \{y\in +B_\rho(x): \abs{u(y)-\tilde u(x)}>\varepsilon /K\},\] +hence +\[\lim_{\rho\to 0^+}\frac{\abs{\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}> +\varepsilon \}}}{\rho^n}=0\] +whenever $x\in\Omega \backslash S_u$. By a similar argument, if $x\in +S_u$ is a point such that there exists a triplet $(u^+,u^-,\nu_u)$ +satisfying \eqref{detK1}, \eqref{detK2}, then +\[ +(v^+(x)-v^-(x))\otimes \nu_v=(f(u^+(x))-f(u^-(x)))\otimes\nu_u\quad +\text{if }x\in S_v +\] +and $f(u^-(x))=f(u^+(x))$ if $x\in S_u\backslash S_v$. Hence, by (1.8) +we get +\begin{equation*}\begin{split} +Jv(B)=\int_{B\cap S_v}(v^+-v^-)\otimes \nu_v\,d\mathcal{H}_{n-1}&= +\int_{B\cap S_v}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}\\ +&=\int_{B\cap S_u}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1} +\end{split}\end{equation*} +and \lemref{limbog} is proved. +\end{proof} + +To prove \eqref{e:SS}, it is not restrictive to assume that $k=1$. +Moreover, to simplify our notation, from now on we shall assume that +$\Omega = \mathbf{R}^n$. The proof of \eqref{e:SS} is divided into two +steps. In the first step we prove the statement in the one-dimensional +case $(n=1)$, using \thmref{th-weak-ske-owf}. In the second step we +achieve the general result using \thmref{t:conl}. + +\subsection*{Step 1} +Assume that $n=1$. Since $S_u$ is at most countable, \eqref{sum-bij} +yields that $\abs{\wt{D}v}(S_u\backslash S_v)=0$, so that +\eqref{e:st} and \eqref{e:barwq} imply that $Dv=\wt{D}v+Jv$ is +the Radon-Nikod\'ym decomposition of $Dv$ in absolutely continuous and +singular part with respect to $\abs{\wt{D} u}$. By +\thmref{th-weak-ske-owf}, we have +\begin{equation*} +\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+} +\frac{Dv(\interval{\left[t,s\right[})} +{\abs{\wt{D}u}(\interval{\left[t,s\right[})},\qquad +\frac{\wt{D}u}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+} +\frac{Du(\interval{\left[t,s\right[})} +{\abs{\wt{D}u}(\interval{\left[t,s\right[})} +\end{equation*} +$\abs{\wt{D}u}$-almost everywhere in $\mathbf{R}$. It is well known +(see, for instance, \cite[2.5.16]{ste:sint}) that every one-dimensional +function of bounded variation $w$ has a unique left continuous +representative, i.e., a function $\hat w$ such that $\hat w=w$ almost +everywhere and $\lim_{s\to t^-}\hat w(s)=\hat w(t)$ for every $t\in +\mathbf{R}$. These conditions imply +\begin{equation} +\hat u(t)=Du(\interval{\left]-\infty,t\right[}), +\qquad \hat v(t)=Dv(\interval{\left]-\infty,t\right[})\qquad +\forall t\in\mathbf{R} +\end{equation} +and +\begin{equation}\label{alimo} +\hat v(t)=f(\hat u(t))\qquad\forall t\in\mathbf{R}.\end{equation} +Let $t\in\mathbf{R}$ be such that +$\abs{\wt{D}u}(\interval{\left[t,s\right[})>0$ for every $s>t$ and +assume that the limits in \eqref{joe} exist. By \eqref{j:mark} and +\eqref{far-d} we get +\begin{equation*}\begin{split} +\frac{\hat v(s)-\hat +v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}&=\frac {f(\hat +u(s))-f(\hat u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\ +&=\frac{f(\hat u(s))-f(\hat +u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}u +}(\interval{\left[t,s\right[}))}% +{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\ +&+\frac +{f(\hat u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D} +u}(\interval{\left[t,s\right[}))-f(\hat +u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})} +\end{split}\end{equation*} +for every $s>t$. Using the Lipschitz condition on $f$ we find +{\setlength{\multlinegap}{0pt} +\begin{multline*} +\left\lvert\frac{\hat v(s)-\hat +v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})} -\frac{f(\hat +u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t) +\abs{\wt{D}u}(\interval{\left[t,s\right[}))-f(\hat +u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\right\rvert\\ +\le K\left\lvert +\frac{\hat u(s)-\hat u(t)} + {\abs{\wt{D}u}(\interval{\left[t,s\right[})} +-\frac{\wt{D}u}{\abs{ +\wt{D}u}}(t)\right\rvert.\end{multline*} +}% end of group with \multlinegap=0pt +By \eqref{e:bomb}, the function $s\to +\abs{\wt{D}u}(\interval{\left[t,s\right[})$ is continuous and +converges to 0 as $s\downarrow t$. Therefore Remark~\ref{r:omb} and the +previous inequality imply +\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0^+} +\frac{f(\hat u(t)+h\dfrac{\wt{D}u}{\abs{\wt{D}u}} +(t))-f(\hat u(t))}h\quad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}.\] +By \eqref{joe}, $\hat u(x)=\tilde u(x)$ for every +$x\in\mathbf{R}\backslash S_u$; moreover, applying the same argument to +the functions $u'(t)=u(-t)$, $v'(t)=f(u'(t))=v(-t)$, we get +\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0} +\frac{f(\tilde u(t) ++h\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t))-f(\tilde u(t))}{h} +\qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}\] +and our statement is proved. + +\subsection*{Step 2} + +Let us consider now the general case $n>1$. Let $\nu\in \mathbf{R}^n$ be +such that $\abs{\nu}=1$, and let $\pi_\nu=\{y\in\mathbf{R}^n: \langle +y,\nu\rangle =0\}$. In the following, we shall identify $\mathbf{R}^n$ +with $\pi_\nu\times\mathbf{R}$, and we shall denote by $y$ the variable +ranging in $\pi_\nu$ and by $t$ the variable ranging in $\mathbf{R}$. By +the just proven one-dimensional result, and by \thmref{thm-main}, we get +\[\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\wt{D}u_y}{\abs{ +\wt{D}u_y}}(t))-f(\tilde u(y+t\nu))}h=\frac{\wt{D}v_y}{\abs{ +\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}\] +for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. We claim that +\begin{equation} +\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle +}}(y+t\nu)=\frac{\wt{D}u_y} +{\abs{\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R} +\end{equation} +for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$. In fact, by +\eqref{sum-ali} and \eqref{delta-l} we get +\begin{multline*} +\int_{\pi_\nu}\frac{\wt{D}u_y}{\abs{\wt{D}u_y}}\cdot\abs{\wt{D}u_y +}\,d\mathcal{H}_{n-1}(y)=\int_{\pi_\nu}\wt{D}u_y\,d\mathcal{H}_{n-1}(y)\\ +=\langle \wt{D}u,\nu\rangle =\frac +{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}\cdot +\abs{\langle \wt{D}u,\nu\rangle }=\int_{\pi_\nu}\frac{ +\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }} +(y+\cdot \nu)\cdot\abs{\wt{D}u_y}\,d\mathcal{H}_{n-1}(y) +\end{multline*} +and \eqref{far-d} follows from \eqref{sum-Di}. By the same argument it +is possible to prove that +\begin{equation} +\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle +}}(y+t\nu)=\frac{\wt{D}v_y}{\abs{\wt{D}u_y}}(t)\qquad\abs{ +\wt{D}u_y}\text{-a.e. in }\mathbf{R}\end{equation} +for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. By \eqref{far-d} +and \eqref{E_SXgYy} we get +\[ +\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\langle \wt{D} +u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(y+t\nu))-f(\tilde +u(y+t\nu))}{h} +=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle +\wt{D}u,\nu\rangle }}(y+t\nu)\] +for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$, and using again +\eqref{detK1}, \eqref{detK2} we get +\[ +\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\langle +\wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde +u(x))}{h}=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu +\rangle }}(x) +\] +$\abs{\langle \wt{D}u,\nu\rangle}$-a.e. in $\mathbf{R}^n$. + +Since the function $\abs{\langle \wt{D}u,\nu\rangle }/\abs{\wt{D}u}$ +is strictly positive $\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere, +we obtain also +\begin{multline*} +\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\abs{\langle +\wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\dfrac{\langle \wt{D} +u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde u(x))}{h}\\ +=\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\frac +{\langle \wt{D}v,\nu\rangle }{\abs{\langle +\wt{D}u,\nu\rangle }}(x) +\end{multline*} +$\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere in $\mathbf{R}^n$. + +Finally, since +\begin{align*} +&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}} +\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}} +=\frac{\langle \wt{D}u,\nu\rangle }{\abs{\wt{D}u}} +=\left\langle \frac{\wt{D}u}{\abs{\wt{D}u}},\nu\right\rangle + \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n\\ +&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}} +\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}} +=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\wt{D}u}} +=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}},\nu\right\rangle + \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n +\end{align*} +and since both sides of \eqref{alimo} +are zero $\abs{\wt{D}u}$-almost everywhere +on $\abs{\langle \wt{D}u,\nu\rangle }$-negligible sets, we conclude that +\[ +\lim_{h\to 0}\frac{f\left( +\tilde u(x)+h\left\langle \dfrac{\wt{D} +u}{\abs{\wt{D}u}}(x),\nu\right\rangle \right)-f(\tilde u(x))}h +=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}}(x),\nu\right\rangle, +\] +$\abs{\wt{D}u}$-a.e. in $\mathbf{R}^n$. +Since $\nu$ is arbitrary, by Remarks \ref{r:dif} and~\ref{r:dif0} +the restriction of $f$ to +the affine space $T^u_x$ is differentiable at $\tilde u(x)$ for $\abs{\wt{D} +u}$-almost every $x\in \mathbf{R}^n$ and \eqref{quts} holds.\qed + +It follows from \eqref{sum-Di}, \eqref{detK1}, and \eqref{detK2} that +\begin{equation}\label{Dt} +D(t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I} +\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)} +(\overline I|\overline I). +\end{equation} +Let $t_i=\hat x_i$, $i=1,\dots,n$. Lemma 1 leads to +\begin{equation}\label{Dx} +D(\hat x_1,\dots,\hat x_n)=\prod_{i\in\mathbf{n}}\hat x_i +\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}\per \mathbf{A} +^{(\lambda)}(I|I)\det\mathbf{A}^{(\lambda)}(\overline I|\overline I). +\end{equation} +By \eqref{H-cycles}, \eqref{sum-Di}, and \eqref{Dx}, +we have the following result: +\begin{thm}\label{thm-H-param} +\begin{equation}\label{H-param} +H_c=\frac{1}{2n}\sum^n_{l =1}l (-1)^{l -1}A_{l} +^{(\lambda)}, +\end{equation} +where +\begin{equation}\label{A-l-lambda} +A^{(\lambda)}_l =\sum_{I_l \subseteq\mathbf{n}}\per \mathbf{A} +^{(\lambda)}(I_l |I_l )\det\mathbf{A}^{(\lambda)} +(\overline I_{l}|\overline I_l ),\abs{I_{l}}=l . +\end{equation} +\end{thm} + +It is worth noting that $A_l ^{(\lambda)}$ of \eqref{A-l-lambda} is +similar to the coefficients $b_l $ of the characteristic polynomial of +\eqref{bl-sum}. It is well known in graph theory that the coefficients +$b_l $ can be expressed as a sum over certain subgraphs. It is +interesting to see whether $A_l $, $\lambda=0$, structural properties +of a graph. + +We may call \eqref{H-param} a parametric representation of $H_c$. In +computation, the parameter $\lambda_i$ plays very important roles. The +choice of the parameter usually depends on the properties of the given +graph. For a complete graph $K_n$, let $\lambda_i=1$, $i=1,\dots,n$. +It follows from \eqref{A-l-lambda} that +\begin{equation}\label{compl-gr} +A^{(1)}_l =\begin{cases} n!,&\text{if }l =1\\ +0,&\text{otherwise}.\end{cases} +\end{equation} +By \eqref{H-param} +\begin{equation} +H_c=\frac 12(n-1)!. +\end{equation} +For a complete bipartite graph $K_{n_1n_2}$, let $\lambda_i=0$, $i=1,\dots,n$. +By \eqref{A-l-lambda}, +\begin{equation} +A_l = +\begin{cases} -n_1!n_2!\delta_{n_1n_2},&\text{if }l =2\\ +0,&\text{otherwise }.\end{cases} +\label{compl-bip-gr} +\end{equation} +Theorem ~\ref{thm-H-param} +leads to +\begin{equation} +H_c=\frac1{n_1+n_2}n_1!n_2!\delta_{n_1n_2}. +\end{equation} + +Now, we consider an asymmetrical approach. Theorem \ref{thm-main} leads to +\begin{multline} +\det\mathbf{K}(t=1,t_1,\dots,t_n;l |l )\\ +=\sum_{I\subseteq\mathbf{n}-\{l \}} +(-1)^{\abs{I}}\prod_{i\in I}t_i\prod_{j\in I} +(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)} +(\overline I\cup\{l \}|\overline I\cup\{l \}). +\end{multline} + +By \eqref{H-cycles} and \eqref{sum-ali} we have the following asymmetrical +result: +\begin{thm}\label{thm-asym} +\begin{equation} +H_c=\frac12\sum_{I\subseteq\mathbf{n}-\{l \}} +(-1)^{\abs{I}}\per\mathbf{A}^{(\lambda)}(I|I)\det +\mathbf{A}^{(\lambda)} +(\overline I\cup\{l \}|\overline I\cup\{l \}) +\end{equation} +which reduces to Goulden--Jackson's formula when $\lambda_i=0,i=1,\dots,n$ +\cite{mami:matrixth}. +\end{thm} + +\section{Various font features of the \pkg{amsmath} package} +\label{s:font} +\subsection{Bold versions of special symbols} + +In the \pkg{amsmath} package \cn{boldsymbol} is used for getting +individual bold math symbols and bold Greek letters---everything in +math except for letters of the Latin alphabet, +where you'd use \cn{mathbf}. For example, +\begin{verbatim} +A_\infty + \pi A_0 \sim +\mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+} +\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}} +\end{verbatim} +looks like this: +\[A_\infty + \pi A_0 \sim \mathbf{A}_{\boldsymbol{\infty}} +\boldsymbol{+} \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}\] + +\subsection{``Poor man's bold''} +If a bold version of a particular symbol doesn't exist in the +available fonts, +then \cn{boldsymbol} can't be used to make that symbol bold. +At the present time, this means that +\cn{boldsymbol} can't be used with symbols from +the \fn{msam} and \fn{msbm} fonts, among others. +In some cases, poor man's bold (\cn{pmb}) can be used instead +of \cn{boldsymbol}: +% Can't show example from msam or msbm because this document is +% supposed to be TeXable even if the user doesn't have +% AMSFonts. MJD 5-JUL-1990 +\[\frac{\partial x}{\partial y} +\pmb{\bigg\vert} +\frac{\partial y}{\partial z}\] +\begin{verbatim} +\[\frac{\partial x}{\partial y} +\pmb{\bigg\vert} +\frac{\partial y}{\partial z}\] +\end{verbatim} +So-called ``large operator'' symbols such as $\sum$ and $\prod$ +require an additional command, \cn{mathop}, +to produce proper spacing and limits when \cn{pmb} is used. +For further details see \textit{The \TeX book}. +\[\sum_{\substack{i<B\\\text{$i$ odd}}} +\prod_\kappa \kappa F(r_i)\qquad +\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}} +\mathop{\pmb{\prod}}_\kappa \kappa(r_i) +\] +\begin{verbatim} +\[\sum_{\substack{i<B\\\text{$i$ odd}}} +\prod_\kappa \kappa F(r_i)\qquad +\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}} +\mathop{\pmb{\prod}}_\kappa \kappa(r_i) +\] +\end{verbatim} + +\section{Compound symbols and other features} +\label{s:comp} +\subsection{Multiple integral signs} + +\cn{iint}, \cn{iiint}, and \cn{iiiint} give multiple integral signs +with the spacing between them nicely adjusted, in both text and +display style. \cn{idotsint} gives two integral signs with dots +between them. +\begin{gather} +\iint\limits_A f(x,y)\,dx\,dy\qquad\iiint\limits_A +f(x,y,z)\,dx\,dy\,dz\\ +\iiiint\limits_A +f(w,x,y,z)\,dw\,dx\,dy\,dz\qquad\idotsint\limits_A f(x_1,\dots,x_k) +\end{gather} + +\subsection{Over and under arrows} + +Some extra over and under arrow operations are provided in +the \pkg{amsmath} package. (Basic \LaTeX\ provides +\cn{overrightarrow} and \cn{overleftarrow}). +\begin{align*} +\overrightarrow{\psi_\delta(t) E_t h}& +=\underrightarrow{\psi_\delta(t) E_t h}\\ +\overleftarrow{\psi_\delta(t) E_t h}& +=\underleftarrow{\psi_\delta(t) E_t h}\\ +\overleftrightarrow{\psi_\delta(t) E_t h}& +=\underleftrightarrow{\psi_\delta(t) E_t h} +\end{align*} +\begin{verbatim} +\begin{align*} +\overrightarrow{\psi_\delta(t) E_t h}& +=\underrightarrow{\psi_\delta(t) E_t h}\\ +\overleftarrow{\psi_\delta(t) E_t h}& +=\underleftarrow{\psi_\delta(t) E_t h}\\ +\overleftrightarrow{\psi_\delta(t) E_t h}& +=\underleftrightarrow{\psi_\delta(t) E_t h} +\end{align*} +\end{verbatim} +These all scale properly in subscript sizes: +\[\int_{\overrightarrow{AB}} ax\,dx\] +\begin{verbatim} +\[\int_{\overrightarrow{AB}} ax\,dx\] +\end{verbatim} + +\subsection{Dots} + +Normally you need only type \cn{dots} for ellipsis dots in a +math formula. The main exception is when the dots +fall at the end of the formula; then you need to +specify one of \cn{dotsc} (series dots, after a comma), +\cn{dotsb} (binary dots, for binary relations or operators), +\cn{dotsm} (multiplication dots), or \cn{dotsi} (dots after +an integral). For example, the input +\begin{verbatim} +Then we have the series $A_1,A_2,\dotsc$, +the regional sum $A_1+A_2+\dotsb$, +the orthogonal product $A_1A_2\dotsm$, +and the infinite integral +\[\int_{A_1}\int_{A_2}\dotsi\]. +\end{verbatim} +produces +\begin{quotation} +Then we have the series $A_1,A_2,\dotsc$, +the regional sum $A_1+A_2+\dotsb$, +the orthogonal product $A_1A_2\dotsm$, +and the infinite integral +\[\int_{A_1}\int_{A_2}\dotsi\] +\end{quotation} + +\subsection{Accents in math} + +Double accents: +\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad +\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad +\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad +\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad +\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\] +\begin{verbatim} +\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad +\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad +\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad +\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad +\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\] +\end{verbatim} +This double accent operation is complicated +and tends to slow down the processing of a \LaTeX\ file. + + +\subsection{Dot accents} +\cn{dddot} and \cn{ddddot} are available to +produce triple and quadruple dot accents +in addition to the \cn{dot} and \cn{ddot} accents already available +in \LaTeX: +\[\dddot{Q}\qquad\ddddot{R}\] +\begin{verbatim} +\[\dddot{Q}\qquad\ddddot{R}\] +\end{verbatim} + +\subsection{Roots} + +In the \pkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust +the position of the root index of a radical: +\begin{verbatim} +\sqrt[\leftroot{-2}\uproot{2}\beta]{k} +\end{verbatim} +gives good positioning of the $\beta$: +\[\sqrt[\leftroot{-2}\uproot{2}\beta]{k}\] + +\subsection{Boxed formulas} The command \cn{boxed} puts a box around its +argument, like \cn{fbox} except that the contents are in math mode: +\begin{verbatim} +\boxed{W_t-F\subseteq V(P_i)\subseteq W_t} +\end{verbatim} +\[\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}.\] + +\subsection{Extensible arrows} +\cn{xleftarrow} and \cn{xrightarrow} produce +arrows that extend automatically to accommodate unusually wide +subscripts or superscripts. The text of the subscript or superscript +are given as an optional resp.\@ mandatory argument: +Example: +\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1] + \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\] +\begin{verbatim} +\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1] + \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\] +\end{verbatim} + +\subsection{\cn{overset}, \cn{underset}, and \cn{sideset}} +Examples: +\[\overset{*}{X}\qquad\underset{*}{X}\qquad +\overset{a}{\underset{b}{X}}\] +\begin{verbatim} +\[\overset{*}{X}\qquad\underset{*}{X}\qquad +\overset{a}{\underset{b}{X}}\] +\end{verbatim} + +The command \cn{sideset} is for a rather special +purpose: putting symbols at the subscript and superscript +corners of a large operator symbol such as $\sum$ or $\prod$, +without affecting the placement of limits. +Examples: +\[\sideset{_*^*}{_*^*}\prod_k\qquad +\sideset{}{'}\sum_{0\le i\le m} E_i\beta x +\] +\begin{verbatim} +\[\sideset{_*^*}{_*^*}\prod_k\qquad +\sideset{}{'}\sum_{0\le i\le m} E_i\beta x +\] +\end{verbatim} + +\subsection{The \cn{text} command} +The main use of the command \cn{text} is for words or phrases in a +display: +\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad +y'_k=\delta_k y_{\tau(k)}\] +\begin{verbatim} +\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad +y'_k=\delta_k y_{\tau(k)}\] +\end{verbatim} + +\subsection{Operator names} +The more common math functions such as $\log$, $\sin$, and $\lim$ +have predefined control sequences: \verb=\log=, \verb=\sin=, +\verb=\lim=. +The \pkg{amsmath} package provides \cn{DeclareMathOperator} and +\cn{DeclareMathOperator*} +for producing new function names that will have the +same typographical treatment. +Examples: +\[\norm{f}_\infty= +\esssup_{x\in R^n}\abs{f(x)}\] +\begin{verbatim} +\[\norm{f}_\infty= +\esssup_{x\in R^n}\abs{f(x)}\] +\end{verbatim} +\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\} +=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\} +\quad \forall\alpha>0.\] +\begin{verbatim} +\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\} +=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\} +\quad \forall\alpha>0.\] +\end{verbatim} +\cn{esssup} and \cn{meas} would be defined in the document preamble as +\begin{verbatim} +\DeclareMathOperator*{\esssup}{ess\,sup} +\DeclareMathOperator{\meas}{meas} +\end{verbatim} + +The following special operator names are predefined in the \pkg{amsmath} +package: \cn{varlimsup}, \cn{varliminf}, \cn{varinjlim}, and +\cn{varprojlim}. Here's what they look like in use: +\begin{align} +&\varlimsup_{n\rightarrow\infty} + \mathcal{Q}(u_n,u_n-u^{\#})\le0\\ +&\varliminf_{n\rightarrow\infty} + \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\ +&\varinjlim (m_i^\lambda\cdot)^*\le0\\ +&\varprojlim_{p\in S(A)}A_p\le0 +\end{align} +\begin{verbatim} +\begin{align} +&\varlimsup_{n\rightarrow\infty} + \mathcal{Q}(u_n,u_n-u^{\#})\le0\\ +&\varliminf_{n\rightarrow\infty} + \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\ +&\varinjlim (m_i^\lambda\cdot)^*\le0\\ +&\varprojlim_{p\in S(A)}A_p\le0 +\end{align} +\end{verbatim} + +\subsection{\cn{mod} and its relatives} +The commands \cn{mod} and \cn{pod} are variants of +\cn{pmod} preferred by some authors; \cn{mod} omits the parentheses, +whereas \cn{pod} omits the `mod' and retains the parentheses. +Examples: +\begin{align} +x&\equiv y+1\pmod{m^2}\\ +x&\equiv y+1\mod{m^2}\\ +x&\equiv y+1\pod{m^2} +\end{align} +\begin{verbatim} +\begin{align} +x&\equiv y+1\pmod{m^2}\\ +x&\equiv y+1\mod{m^2}\\ +x&\equiv y+1\pod{m^2} +\end{align} +\end{verbatim} + +\subsection{Fractions and related constructions} +\label{fracs} + +The usual notation for binomials is similar to the fraction concept, +so it has a similar command \cn{binom} with two arguments. Example: +\begin{equation} +\begin{split} +\sum_{\gamma\in\Gamma_C} I_\gamma& +=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\ +&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l} ++\dots+(-1)^k\\ +&=(2-1)^k=1 +\end{split} +\end{equation} +\begin{verbatim} +\begin{equation} +\begin{split} +[\sum_{\gamma\in\Gamma_C} I_\gamma& +=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\ +&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l} ++\dots+(-1)^k\\ +&=(2-1)^k=1 +\end{split} +\end{equation} +\end{verbatim} +There are also abbreviations +\begin{verbatim} +\dfrac \dbinom +\tfrac \tbinom +\end{verbatim} +for the commonly needed constructions +\begin{verbatim} +{\displaystyle\frac ... } {\displaystyle\binom ... } +{\textstyle\frac ... } {\textstyle\binom ... } +\end{verbatim} + +The generalized fraction command \cn{genfrac} provides full access to +the six \TeX{} fraction primitives: +\begin{align} +\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}& +\text{\cn{overwithdelims}: }& + \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\ +\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}& +\text{\cn{atopwithdelims}: }& + \genfrac{(}{)}{0pt}{}{n+1}{2}\\ +\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}& +\text{\cn{abovewithdelims}: }& + \genfrac{[}{]}{1pt}{}{n+1}{2} +\end{align} +\begin{verbatim} +\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}& +\text{\cn{overwithdelims}: }& + \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\ +\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}& +\text{\cn{atopwithdelims}: }& + \genfrac{(}{)}{0pt}{}{n+1}{2}\\ +\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}& +\text{\cn{abovewithdelims}: }& + \genfrac{[}{]}{1pt}{}{n+1}{2} +\end{verbatim} + +\subsection{Continued fractions} +The continued fraction +\begin{equation} +\cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+\dotsb +}}}}} +\end{equation} +can be obtained by typing +\begin{verbatim} +\cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+ + \cfrac{1}{\sqrt{2}+\dotsb +}}}}} +\end{verbatim} +Left or right placement of any of the numerators is accomplished by using +\cn{cfrac[l]} or \cn{cfrac[r]} instead of \cn{cfrac}. + +\subsection{Smash} + +In \pkg{amsmath} there are optional arguments \verb"t" and \verb"b" for +the plain \TeX\ command \cn{smash}, because sometimes it is advantageous +to be able to `smash' only the top or only the bottom of something while +retaining the natural depth or height. In the formula +$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$ \cn{smash}\verb=[b]= has been +used to limit the size of the radical symbol. +\begin{verbatim} +$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$ +\end{verbatim} +Without the use of \cn{smash}\verb=[b]= the formula would have appeared +thus: $X_j=(1/\sqrt{\lambda_j})X_j'$, with the radical extending to +encompass the depth of the subscript $j$. + +\subsection{The `cases' environment} +`Cases' constructions like the following can be produced using +the \env{cases} environment. +\begin{equation} +P_{r-j}= + \begin{cases} + 0& \text{if $r-j$ is odd},\\ + r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. + \end{cases} +\end{equation} +\begin{verbatim} +\begin{equation} P_{r-j}= + \begin{cases} + 0& \text{if $r-j$ is odd},\\ + r!\,(-1)^{(r-j)/2}& \text{if $r-j$ is even}. + \end{cases} +\end{equation} +\end{verbatim} +Notice the use of \cn{text} and the embedded math. + +\subsection{Matrix} + +Here are samples of the matrix environments, +\cn{matrix}, \cn{pmatrix}, \cn{bmatrix}, \cn{Bmatrix}, \cn{vmatrix} +and \cn{Vmatrix}: +\begin{equation} +\begin{matrix} +\vartheta& \varrho\\\varphi& \varpi +\end{matrix}\quad +\begin{pmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{pmatrix}\quad +\begin{bmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{bmatrix}\quad +\begin{Bmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{Bmatrix}\quad +\begin{vmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{vmatrix}\quad +\begin{Vmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{Vmatrix} +\end{equation} +% +\begin{verbatim} +\begin{matrix} +\vartheta& \varrho\\\varphi& \varpi +\end{matrix}\quad +\begin{pmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{pmatrix}\quad +\begin{bmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{bmatrix}\quad +\begin{Bmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{Bmatrix}\quad +\begin{vmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{vmatrix}\quad +\begin{Vmatrix} +\vartheta& \varrho\\\varphi& \varpi +\end{Vmatrix} +\end{verbatim} + +To produce a small matrix suitable for use in text, use the +\env{smallmatrix} environment. +\begin{verbatim} +\begin{math} + \bigl( \begin{smallmatrix} + a&b\\ c&d + \end{smallmatrix} \bigr) +\end{math} +\end{verbatim} +To show +the effect of the matrix on the surrounding lines of +a paragraph, we put it here: \begin{math} + \bigl( \begin{smallmatrix} + a&b\\ c&d + \end{smallmatrix} \bigr) +\end{math} +and follow it with enough text to ensure that there will +be at least one full line below the matrix. + +\cn{hdotsfor}\verb"{"\textit{number}\verb"}" produces a row of dots in a matrix +spanning the given number of columns: +\[W(\Phi)= \begin{Vmatrix} +\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\ +\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}& +\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\ +\hdotsfor{5}\\ +\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}& +\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots& +\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}& +\dfrac{\varphi}{(\varphi_n,\varepsilon_n)} +\end{Vmatrix}\] +\begin{verbatim} +\[W(\Phi)= \begin{Vmatrix} +\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\ +\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}& +\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\ +\hdotsfor{5}\\ +\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}& +\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots& +\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}& +\dfrac{\varphi}{(\varphi_n,\varepsilon_n)} +\end{Vmatrix}\] +\end{verbatim} +The spacing of the dots can be varied through use of a square-bracket +option, for example, \verb"\hdotsfor[1.5]{3}". The number in square brackets +will be used as a multiplier; the normal value is 1. + +\subsection{The \cn{substack} command} + +The \cn{substack} command can be used to produce a multiline +subscript or superscript: +for example +\begin{verbatim} +\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j) +\end{verbatim} +produces a two-line subscript underneath the sum: +\begin{equation} +\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j) +\end{equation} +A slightly more generalized form is the \env{subarray} environment which +allows you to specify that each line should be left-aligned instead of +centered, as here: +\begin{equation} +\sum_{\begin{subarray}{l} + 0\le i\le m\\ 0<j<n + \end{subarray}} + P(i,j) +\end{equation} +\begin{verbatim} +\sum_{\begin{subarray}{l} + 0\le i\le m\\ 0<j<n + \end{subarray}} + P(i,j) +\end{verbatim} + + +\subsection{Big-g-g delimiters} +Here are some big delimiters, first in \cn{normalsize}: +\[\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + \biggr) +\] +\begin{verbatim} +\[\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + \biggr) +\] +\end{verbatim} +and now in \cn{Large} size: +{\Large +\[\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + \biggr) +\]} +\begin{verbatim} +{\Large +\[\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + \biggr) +\]} +\end{verbatim} + +\newpage +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\makeatletter + +%% This turns on vertical rules at the right and left margins, to +%% better illustrate the spacing for certain multiple-line equation +%% structures. +\def\@makecol{\ifvoid\footins \setbox\@outputbox\box\@cclv + \else\setbox\@outputbox + \vbox{\boxmaxdepth \maxdepth + \unvbox\@cclv\vskip\skip\footins\footnoterule\unvbox\footins}\fi + \xdef\@freelist{\@freelist\@midlist}\gdef\@midlist{}\@combinefloats + \setbox\@outputbox\hbox{\vrule width\marginrulewidth + \vbox to\@colht{\boxmaxdepth\maxdepth + \@texttop\dimen128=\dp\@outputbox\unvbox\@outputbox + \vskip-\dimen128\@textbottom}% + \vrule width\marginrulewidth}% + \global\maxdepth\@maxdepth} +\newdimen\marginrulewidth +\setlength{\marginrulewidth}{.1pt} +\makeatother + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\appendix +\section{Examples of multiple-line equation structures} +\label{s:eq} + +\textbf{\large Note: Starting on this page, vertical rules are +added at the margins so that the positioning of various display elements +with respect to the margins can be seen more clearly.} + +\subsection{Split} +The \env{split} environment is not an independent environment +but should be used inside something else such as \env{equation} +or \env{align}. + +If there is not enough room for it, the equation number for a +\env{split} will be shifted to the previous line, when equation numbers are +on the left; the number shifts down to the next line when numbers are on +the right. +\begin{equation} +\begin{split} +f_{h,\varepsilon}(x,y) +&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon} +L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\ +&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\ +&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\ +&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon} + \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)} + \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon} + L_{x,y_\varepsilon(\varepsilon s)} + \varphi(x)\,ds\biggr)\biggr]\\ +&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y), +\end{split} +\end{equation} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{equation} +\begin{split} +f_{h,\varepsilon}(x,y) +&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon} +L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\ +&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\ +&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\ +&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon} + \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)} + \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon} + L_{x,y_\varepsilon(\varepsilon s)} + \varphi(x)\,ds\biggr)\biggr]\\ +&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y), +\end{split} +\end{equation} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +Unnumbered version: +\begin{equation*} +\begin{split} +f_{h,\varepsilon}(x,y) +&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon} +L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\ +&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\ +&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\ +&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon} + \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)} + \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon} + L_{x,y_\varepsilon(\varepsilon s)} + \varphi(x)\,ds\biggr)\biggr]\\ +&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y), +\end{split} +\end{equation*} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{equation*} +\begin{split} +f_{h,\varepsilon}(x,y) +&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon} +L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\ +&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\ +&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y} + \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds + -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\ +&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon} + \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)} + \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon} + L_{x,y_\varepsilon(\varepsilon s)} + \varphi(x)\,ds\biggr)\biggr]\\ +&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y), +\end{split} +\end{equation*} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +If the option \env{centertags} is included in the options +list of the \pkg{amsmath} package, +the equation numbers for \env{split} environments will be +centered vertically on the height +of the \env{split}: +{\makeatletter\ctagsplit@true +\begin{equation} +\begin{split} + \abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)-\int_{\gamma(t)}^a + \frac{d\theta}{k(\theta,t)} + \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\ +&\le C_6\left\lvert \left\lvert f\int_\Omega\left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split} +\end{equation}}% +Some text after to test the below-display spacing. + +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +Use of \env{split} within \env{align}: +{\delimiterfactor750 +\begin{align} +\begin{split}\abs{I_1} + &=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\ +&\le C_3\left[\int_\Omega\left(\int_{a}^x + g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\ +&\quad\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k} + \left(\int_{a}^x cu_t\,d\xi\right)^2\right\} + c\Omega\right]^{1/2}\\ +&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split}\label{eq:A}\\ +\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t) + -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)} + \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\ +&\le C_6\left\lvert \left\lvert f\int_\Omega + \left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split} +\end{align}}% +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{align} +\begin{split}\abs{I_1} + &=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\ +&\le C_3\left[\int_\Omega\left(\int_{a}^x + g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\ +&\quad\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k} + \left(\int_{a}^x cu_t\,d\xi\right)^2\right\} + c\Omega\right]^{1/2}\\ +&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split}\label{eq:A}\\ +\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t) + -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)} + \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\ +&\le C_6\left\lvert \left\lvert f\int_\Omega + \left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split} +\end{align} +\end{verbatim} + +%%%%%%%%%%%%%%%%%% + +\newpage +Unnumbered \env{align}, with a number on the second \env{split}: +\begin{align*} +\begin{split}\abs{I_1}&=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\ + &\le C_3\left[\int_\Omega\left(\int_{a}^x + g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\ +&\phantom{=}\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k} + \left(\int_{a}^x cu_t\,d\xi\right)^2\right\} + c\Omega\right]^{1/2}\\ +&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split}\\ +\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t) + -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)} + \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\ +&\le C_6\left\lvert \left\lvert f\int_\Omega + \left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split}\tag{\theequation$'$} +\end{align*} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{align*} +\begin{split}\abs{I_1}&=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\ + &\le C_3\left[\int_\Omega\left(\int_{a}^x + g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\ +&\phantom{=}\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k} + \left(\int_{a}^x cu_t\,d\xi\right)^2\right\} + c\Omega\right]^{1/2}\\ +&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split}\\ +\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t) + -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)} + \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\ +&\le C_6\left\lvert \left\lvert f\int_\Omega + \left\lvert \wt{S}^{-1,0}_{a,-} + W_2(\Omega,\Gamma_l)\right\rvert\right\rvert + \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}} + (\Omega;\Gamma_r,T)\right\rvert\right\rvert. +\end{split}\tag{\theequation$'$} +\end{align*} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +\subsection{Multline} +Numbered version: +\begin{multline}\label{eq:E} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline} +To test the use of \verb=\label= and +\verb=\ref=, we refer to the number of this +equation here: (\ref{eq:E}). + +\begin{verbatim} +\begin{multline}\label{eq:E} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Unnumbered version: +\begin{multline*} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline*} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{multline*} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline*} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\iffalse % bugfix needed, error message "Multiple \tag" + % [mjd,24-Jan-1995] +\newpage +And now an ``unnumbered'' version numbered with a literal tag: +\begin{multline*}\tag*{[a]} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline*} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{multline*}\tag*{[a]} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline*} +\end{verbatim} + +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +The same display with \verb=\multlinegap= set to zero. +Notice that the space on the left in +the first line does not change, because of the equation number, while +the second line is pushed over to the right margin. +{\setlength{\multlinegap}{0pt} +\begin{multline*}\tag*{[a]} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline*}}% +Some text after to test the below-display spacing. + +\begin{verbatim} +{\setlength{\multlinegap}{0pt} +\begin{multline*}\tag*{[a]} +\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2] + -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\ + =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2 + \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy +\end{multline*}} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% +\fi % matches \iffalse above [mjd,24-Jan-1995] + +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +\subsection{Gather} +Numbered version with \verb;\notag; on the second line: +\begin{gather} +D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\ +\seg(a,r)\equiv\{z\in\mathbf{C}\colon +\Im z= \Im a,\ \abs{z-a}<r\},\notag\\ +c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C} +\colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\ +C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r). +\end{gather} +\begin{verbatim} +\begin{gather} +D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\ +\seg(a,r)\equiv\{z\in\mathbf{C}\colon +\Im z= \Im a,\ \abs{z-a}<r\},\notag\\ +c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C} +\colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\ +C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r). +\end{gather} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Unnumbered version. +\begin{gather*} +D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\ +\seg (a,r)\equiv\{z\in\mathbf{C}\colon +\Im z= \Im a,\ \abs{z-a}<r\},\\ +c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C} + \colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\ +C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r). +\end{gather*} +Some text after to test the below-display spacing. +\begin{verbatim} +\begin{gather*} +D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\ +\seg (a,r)\equiv\{z\in\mathbf{C}\colon +\Im z= \Im a,\ \abs{z-a}<r\},\\ +c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C} + \colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\ +C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r). +\end{gather*} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +\subsection{Align} +Numbered version: +\begin{align} +\gamma_x(t)&=(\cos tu+\sin tx,v),\\ +\gamma_y(t)&=(u,\cos tv+\sin ty),\\ +\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv, + -\frac\beta\alpha\sin tu+\cos tv\right). +\end{align} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{align} +\gamma_x(t)&=(\cos tu+\sin tx,v),\\ +\gamma_y(t)&=(u,\cos tv+\sin ty),\\ +\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv, + -\frac\beta\alpha\sin tu+\cos tv\right). +\end{align} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Unnumbered version: +\begin{align*} +\gamma_x(t)&=(\cos tu+\sin tx,v),\\ +\gamma_y(t)&=(u,\cos tv+\sin ty),\\ +\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv, + -\frac\beta\alpha\sin tu+\cos tv\right). +\end{align*} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{align*} +\gamma_x(t)&=(\cos tu+\sin tx,v),\\ +\gamma_y(t)&=(u,\cos tv+\sin ty),\\ +\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv, + -\frac\beta\alpha\sin tu+\cos tv\right). +\end{align*} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +A variation: +\begin{align} +x& =y && \text {by (\ref{eq:C})}\\ +x'& = y' && \text {by (\ref{eq:D})}\\ +x+x' & = y+y' && \text {by Axiom 1.} +\end{align} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{align} +x& =y && \text {by (\ref{eq:C})}\\ +x'& = y' && \text {by (\ref{eq:D})}\\ +x+x' & = y+y' && \text {by Axiom 1.} +\end{align} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +\subsection{Align and split within gather} +When using the \env{align} environment within the \env{gather} +environment, one or the other, or both, should be unnumbered (using the +\verb"*" form); numbering both the outer and inner environment would +cause a conflict. + +Automatically numbered \env{gather} with \env{split} and \env{align*}: +\begin{gather} +\begin{split} \varphi(x,z) +&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\ +&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n +\end{split}\\[6pt] +\begin{align*} +\zeta^0 &=(\xi^0)^2,\\ +\zeta^1 &=\xi^0\xi^1,\\ +\zeta^2 &=(\xi^1)^2, +\end{align*} +\end{gather} +Here the \env{split} environment gets a number from the outer +\env{gather} environment; numbers for individual lines of the +\env{align*} are suppressed because of the star. + +\begin{verbatim} +\begin{gather} +\begin{split} \varphi(x,z) +&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\ +&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n +\end{split}\\[6pt] +\begin{align*} +\zeta^0 &=(\xi^0)^2,\\ +\zeta^1 &=\xi^0\xi^1,\\ +\zeta^2 &=(\xi^1)^2, +\end{align*} +\end{gather} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +The \verb"*"-ed form of \env{gather} with the non-\verb"*"-ed form of +\env{align}. +\begin{gather*} +\begin{split} \varphi(x,z) +&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\ +&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n +\end{split}\\[6pt] +\begin{align} \zeta^0&=(\xi^0)^2,\\ +\zeta^1 &=\xi^0\xi^1,\\ +\zeta^2 &=(\xi^1)^2, +\end{align} +\end{gather*} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{gather*} +\begin{split} \varphi(x,z) +&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\ +&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n +\end{split}\\[6pt] +\begin{align} \zeta^0&=(\xi^0)^2,\\ +\zeta^1 &=\xi^0\xi^1,\\ +\zeta^2 &=(\xi^1)^2, +\end{align} +\end{gather*} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +\subsection{Alignat} +Numbered version: +\begin{alignat}{3} +V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j, + & \qquad U_i & = u_i, + \qquad \text{for $i\ne j$;}\label{eq:B}\\ +V_j & = v_j, & \qquad X_j & = x_j, + & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i. +\end{alignat} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{alignat}{3} +V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j, + & \qquad U_i & = u_i, + \qquad \text{for $i\ne j$;}\label{eq:B}\\ +V_j & = v_j, & \qquad X_j & = x_j, + & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i. +\end{alignat} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Unnumbered version: +\begin{alignat*}3 +V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j, + & \qquad U_i & = u_i, + \qquad \text{for $i\ne j$;} \\ +V_j & = v_j, & \qquad X_j & = x_j, + & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i. +\end{alignat*} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{alignat*}3 +V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j, + & \qquad U_i & = u_i, + \qquad \text{for $i\ne j$;} \\ +V_j & = v_j, & \qquad X_j & = x_j, + & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i. +\end{alignat*} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +The most common use for \env{alignat} is for things like +\begin{alignat}{2} +x& =y && \qquad \text {by (\ref{eq:A})}\label{eq:C}\\ +x'& = y' && \qquad \text {by (\ref{eq:B})}\label{eq:D}\\ +x+x' & = y+y' && \qquad \text {by Axiom 1.} +\end{alignat} +Some text after to test the below-display spacing. + +\begin{verbatim} +\begin{alignat}{2} +x& =y && \qquad \text {by (\ref{eq:A})}\label{eq:C}\\ +x'& = y' && \qquad \text {by (\ref{eq:B})}\label{eq:D}\\ +x+x' & = y+y' && \qquad \text {by Axiom 1.} +\end{alignat} +\end{verbatim} +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +\setlength{\marginrulewidth}{0pt} + +\begin{thebibliography}{10} + +\bibitem{dihe:newdir} +W.~Diffie and E.~Hellman, \emph{New directions in cryptography}, IEEE +Transactions on Information Theory \textbf{22} (1976), no.~5, 644--654. + +\bibitem{fre:cichon} +D.~H. Fremlin, \emph{Cichon's diagram}, 1983/1984, presented at the +S{\'e}minaire Initiation {\`a} l'Analyse, G. Choquet, M. Rogalski, J. +Saint Raymond, at the Universit{\'e} Pierre et Marie Curie, Paris, 23e +ann{\'e}e. + +\bibitem{gouja:lagrmeth} +I.~P. Goulden and D.~M. Jackson, \emph{The enumeration of directed +closed {E}uler trails and directed {H}amiltonian circuits by +{L}angrangian methods}, European J. Combin. \textbf{2} (1981), 131--212. + +\bibitem{hapa:graphenum} +F.~Harary and E.~M. Palmer, \emph{Graphical enumeration}, Academic +Press, 1973. + +\bibitem{imlelu:oneway} +R.~Impagliazzo, L.~Levin, and M.~Luby, \emph{Pseudo-random generation +from one-way functions}, Proc. 21st STOC (1989), ACM, New York, +pp.~12--24. + +\bibitem{komiyo:unipfunc} +M.~Kojima, S.~Mizuno, and A.~Yoshise, \emph{A new continuation method +for complementarity problems with uniform p-functions}, Tech. Report +B-194, Tokyo Inst. of Technology, Tokyo, 1987, Dept. of Information +Sciences. + +\bibitem{komiyo:lincomp} +\bysame, \emph{A polynomial-time algorithm for a class of linear +complementarity problems}, Tech. Report B-193, Tokyo Inst. of +Technology, Tokyo, 1987, Dept. of Information Sciences. + +\bibitem{liuchow:formalsum} +C.~J. Liu and Yutze Chow, \emph{On operator and formal sum methods for +graph enumeration problems}, SIAM J. Algorithms Discrete Methods +\textbf{5} (1984), 384--438. + +\bibitem{mami:matrixth} +M.~Marcus and H.~Minc, \emph{A survey of matrix theory and matrix +inequalities}, Complementary Series in Math. \textbf{14} (1964), 21--48. + +\bibitem{miyoki:lincomp} +S.~Mizuno, A.~Yoshise, and T.~Kikuchi, \emph{Practical polynomial time +algorithms for linear complementarity problems}, Tech. Report~13, Tokyo +Inst. of Technology, Tokyo, April 1988, Dept. of Industrial Engineering +and Management. + +\bibitem{moad:quadpro} +R.~D. Monteiro and I.~Adler, \emph{Interior path following primal-dual +algorithms, part {II}: Quadratic programming}, August 1987, Working +paper, Dept. of Industrial Engineering and Operations Research. + +\bibitem{ste:sint} +E.~M. Stein, \emph{Singular integrals and differentiability properties +of functions}, Princeton Univ. Press, Princeton, N.J., 1970. + +\bibitem{ye:intalg} +Y.~Ye, \emph{Interior algorithms for linear, quadratic and linearly +constrained convex programming}, Ph.D. thesis, Stanford Univ., Palo +Alto, Calif., July 1987, Dept. of Engineering--Economic Systems, +unpublished. + +\end{thebibliography} + +\end{document} +\endinput diff --git a/Master/texmf-dist/doc/latex/amslatex/textcmds.pdf b/Master/texmf-dist/doc/latex/amslatex/textcmds.pdf Binary files differnew file mode 100644 index 00000000000..5af7f0177e3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/textcmds.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/thmtest.pdf b/Master/texmf-dist/doc/latex/amslatex/thmtest.pdf Binary files differnew file mode 100644 index 00000000000..f1bbf14e5d3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/thmtest.pdf diff --git a/Master/texmf-dist/doc/latex/amslatex/thmtest.tex b/Master/texmf-dist/doc/latex/amslatex/thmtest.tex new file mode 100644 index 00000000000..21193949e83 --- /dev/null +++ b/Master/texmf-dist/doc/latex/amslatex/thmtest.tex @@ -0,0 +1,255 @@ +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "thmtest.tex", +%%% version = "2.01", +%%% date = "2004/08/02", +%%% time = "14:18:27 EDT", +%%% checksum = "26819 255 963 8277", +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1996, 2004 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Publications Technical Group, +%%% 201 Charles Street, +%%% Providence, RI 02904, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% email = "tech-support@ams.org (Internet)", +%%% codetable = "ISO/ASCII", +%%% supported = "yes", +%%% keywords = "latex, amslatex, ams-latex, theorem, proof", +%%% abstract = "This is part of the AMS-\LaTeX{} distribution. +%%% It is a sample document illustrating the use of +%%% the amsthm package.", +%%% docstring = "The checksum field above contains a CRC-16 +%%% checksum as the first value, followed by the +%%% equivalent of the standard UNIX wc (word +%%% count) utility output of lines, words, and +%%% characters. This is produced by Robert +%%% Solovay's checksum utility.", +%%% } +%%% ==================================================================== + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Option test file, will be created during the first LaTeX run; +% this facility is not available when using an AMS document class. +\begin{filecontents}{exercise.thm} +\def\th@exercise{% + \normalfont % body font + \thm@headpunct{:}% +} +\end{filecontents} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\documentclass{article} +\title{Newtheorem and theoremstyle test} +\author{Michael Downes\\updated by Barbara Beeton} + +\usepackage[exercise]{amsthm} + +\newtheorem{thm}{Theorem}[section] +\newtheorem{cor}[thm]{Corollary} +\newtheorem{prop}{Proposition} +\newtheorem{lem}[thm]{Lemma} + +\theoremstyle{remark} +\newtheorem*{rmk}{Remark} + +\theoremstyle{plain} +\newtheorem*{Ahlfors}{Ahlfors' Lemma} + +\newtheoremstyle{note}% name + {3pt}% Space above + {3pt}% Space below + {}% Body font + {}% Indent amount (empty = no indent, \parindent = para indent) + {\itshape}% Thm head font + {:}% Punctuation after thm head + {.5em}% Space after thm head: " " = normal interword space; + % \newline = linebreak + {}% Thm head spec (can be left empty, meaning `normal') + +\theoremstyle{note} +\newtheorem{note}{Note} + +\newtheoremstyle{citing}% name + {3pt}% Space above, empty = `usual value' + {3pt}% Space below + {\itshape}% Body font + {}% Indent amount (empty = no indent, \parindent = para indent) + {\bfseries}% Thm head font + {.}% Punctuation after thm head + {.5em}% Space after thm head: " " = normal interword space; + % \newline = linebreak + {\thmnote{#3}}% Thm head spec + +\theoremstyle{citing} +\newtheorem*{varthm}{}% all text supplied in the note + +\newtheoremstyle{break}% name + {9pt}% Space above, empty = `usual value' + {9pt}% Space below + {\itshape}% Body font + {}% Indent amount (empty = no indent, \parindent = para indent) + {\bfseries}% Thm head font + {.}% Punctuation after thm head + {\newline}% Space after thm head: \newline = linebreak + {}% Thm head spec + +\theoremstyle{break} +\newtheorem{bthm}{B-Theorem} + +\theoremstyle{exercise} +\newtheorem{exer}{Exercise} + +\swapnumbers +\theoremstyle{plain} +\newtheorem{thmsw}{Theorem}[section] +\newtheorem{corsw}[thmsw]{Corollary} +\newtheorem{propsw}{Proposition} +\newtheorem{lemsw}[thmsw]{Lemma} + +% Because the amsmath pkg is not used, we need to define a couple of +% commands in more primitive terms. +\let\lvert=|\let\rvert=| +\newcommand{\Ric}{\mathop{\mathrm{Ric}}\nolimits} + +% Dispel annoying problem of slightly overlong lines: +\addtolength{\textwidth}{8pt} + +\begin{document} +\maketitle + +\section{Test of standard theorem styles} + +Ahlfors' Lemma gives the principal criterion for obtaining lower bounds +on the Kobayashi metric. + +\begin{Ahlfors} +Let $ds^2 = h(z)\lvert dz\rvert^2$ be a Hermitian pseudo-metric on +$\mathbf{D}_r$, $h\in C^2(\mathbf{D}_r)$, with $\omega$ the associated +$(1,1)$-form. If $\Ric\omega\geq\omega$ on $\mathbf{D}_r$, +then $\omega\leq\omega_r$ on all of $\mathbf{D}_r$ (or equivalently, +$ds^2\leq ds_r^2$). +\end{Ahlfors} + +\begin{lem}[negatively curved families] +Let $\{ds_1^2,\dots,ds_k^2\}$ be a negatively curved family of metrics +on $\mathbf{D}_r$, with associated forms $\omega^1$, \dots, $\omega^k$. +Then $\omega^i \leq\omega_r$ for all $i$. +\end{lem} + +Then our main theorem: +\begin{thm}\label{pigspan} +Let $d_{\max}$ and $d_{\min}$ be the maximum, resp.\ minimum distance +between any two adjacent vertices of a quadrilateral $Q$. Let $\sigma$ +be the diagonal pigspan of a pig $P$ with four legs. +Then $P$ is capable of standing on the corners of $Q$ iff +\begin{equation}\label{sdq} +\sigma\geq \sqrt{d_{\max}^2+d_{\min}^2}. +\end{equation} +\end{thm} + +\begin{cor} +Admitting reflection and rotation, a three-legged pig $P$ is capable of +standing on the corners of a triangle $T$ iff (\ref{sdq}) holds. +\end{cor} + +\begin{rmk} +As two-legged pigs generally fall over, the case of a polygon of order +$2$ is uninteresting. +\end{rmk} + +\section{Custom theorem styles} + +\begin{exer} +Generalize Theorem~\ref{pigspan} to three and four dimensions. +\end{exer} + +\begin{note} +This is a test of the custom theorem style `note'. It is supposed to have +variant fonts and other differences. +\end{note} + +\begin{bthm} +Test of the `linebreak' style of theorem heading. +\end{bthm} + +This is a test of a citing theorem to cite a theorem from some other source. + +\begin{varthm}[Theorem 3.6 in \cite{thatone}] +No hyperlinking available here yet \dots\ but that's not a +bad idea for the future. +\end{varthm} + +\section{The proof environment} + +\begin{proof} +Here is a test of the proof environment. +\end{proof} + +\begin{proof}[Proof of Theorem \ref{pigspan}] +And another test. +\end{proof} + +\begin{proof}[Proof \textup(necessity\textup)] +And another. +\end{proof} + +\begin{proof}[Proof \textup(sufficiency\textup)] +And another, ending with a display: +\[ +1+1=2\,. \qedhere +\] +\end{proof} + +\section{Test of number-swapping} + +This is a repeat of the first section but with numbers in theorem heads +swapped to the left. + +Ahlfors' Lemma gives the principal criterion for obtaining lower bounds +on the Kobayashi metric. +\begin{Ahlfors} +Let $ds^2 = h(z)\lvert dz\rvert^2$ be a Hermitian pseudo-metric on +$\mathbf{D}_r$, $h\in C^2(\mathbf{D}_r)$, with $\omega$ the associated +$(1,1)$-form. If $\Ric\omega\geq\omega$ on $\mathbf{D}_r$, +then $\omega\leq\omega_r$ on all of $\mathbf{D}_r$ (or equivalently, +$ds^2\leq ds_r^2$). +\end{Ahlfors} + +\begin{lemsw}[negatively curved families] +Let $\{ds_1^2,\dots,ds_k^2\}$ be a negatively curved family of metrics +on $\mathbf{D}_r$, with associated forms $\omega^1$, \dots, $\omega^k$. +Then $\omega^i \leq\omega_r$ for all $i$. +\end{lemsw} + +Then our main theorem: +\begin{thmsw} +Let $d_{\max}$ and $d_{\min}$ be the maximum, resp.\ minimum distance +between any two adjacent vertices of a quadrilateral $Q$. Let $\sigma$ +be the diagonal pigspan of a pig $P$ with four legs. +Then $P$ is capable of standing on the corners of $Q$ iff +\begin{equation}\label{sdqsw} +\sigma\geq \sqrt{d_{\max}^2+d_{\min}^2}. +\end{equation} +\end{thmsw} + +\begin{corsw} +Admitting reflection and rotation, a three-legged pig $P$ is capable of +standing on the corners of a triangle $T$ iff (\ref{sdqsw}) holds. +\end{corsw} + +\begin{thebibliography}{99} +\bibitem{thatone} Dummy entry. +\end{thebibliography} + +\end{document} |