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diff --git a/Master/texmf-doc/doc/english/amslatex-primer/amshelp.tex b/Master/texmf-doc/doc/english/amslatex-primer/amshelp.tex deleted file mode 100644 index 5235334a9c4..00000000000 --- a/Master/texmf-doc/doc/english/amslatex-primer/amshelp.tex +++ /dev/null @@ -1,1689 +0,0 @@ -%%% amshelp.tex -%%% This is an AMS-LaTeX file - -%%% Copyright (c) 2000 Philip S. Hirschhorn -% -% This document may be distributed and/or modified under the -% conditions of the LaTeX Project Public License, either version 1.2 -% of this license or (at your option) any later version. -% The latest version of this license is in -% http://www.latex-project.org/lppl.txt -% and version 1.2 or later is part of all distributions of LaTeX -% version 1999/12/01 or later. -% - - -%%% Philip Hirschhorn -%%% Department of Mathematics -%%% Wellesley College -%%% Wellesley, MA 02481 -%%% psh@poincare.wellesley.edu -%%% psh@math.mit.edu - - -%%% This is an attempt to explain how to get up and running with -%%% AmS-LaTeX, if you've already got some familiarity with either -%%% TeX or AMS-TeX or LaTeX. - - - - -\newcommand{\filedate}{August 10, 2000} -\newcommand{\fileversion}{Version 2.0} - -%--------------------------------------------------------------------- -\documentclass[12pt]{amsart} -%\documentclass{amsart} -\usepackage{amscd} - - -\newcommand{\tensor}{\otimes} -\newcommand{\homotopic}{\simeq} -\newcommand{\homeq}{\cong} -\newcommand{\iso}{\approx} -\newcommand{\ho}{\operatorname{Ho}} - - - - -\newcommand{\C}{{\cal C}} -\newcommand{\M}{{\cal M}} -\newcommand{\W}{{\cal W}} - - -\newenvironment{technical}{\begingroup \small}{\endgroup} - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- - -\numberwithin{equation}{section} - - -% Theorem environments - -\theoremstyle{plain} %% This is the default, anyway -\newtheorem{thm}[equation]{Theorem} -\newtheorem{cor}[equation]{Corollary} -\newtheorem{lem}[equation]{Lemma} -\newtheorem{prop}[equation]{Proposition} - - -\theoremstyle{definition} -\newtheorem{defn}[equation]{Definition} - -\theoremstyle{remark} -\newtheorem{rem}[equation]{Remark} -\newtheorem{ex}[equation]{Example} -\newtheorem{notation}[equation]{Notation} -\newtheorem{terminology}[equation]{Terminology} - - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- - -\begin{document} - - -\title[Running \AmS-\LaTeX] -{Getting up and running\\ -with \AmS-\LaTeX} - -\author{Philip S. Hirschhorn} - -\address{Department of Mathematics\\ - Wellesley College\\ - Wellesley, Massachusetts 02481} - -\email{psh@math.mit.edu} - - -\date{\filedate, \fileversion} - - -\begin{abstract} - This is an attempt to tell you enough about \LaTeX{} and - \AmS-\LaTeX{} so that you can get started with it \emph{without} - having to read the book. -\end{abstract} - -\maketitle - - - - -\tableofcontents -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Introduction} - -This is an attempt to get you up and running with \AmS-\LaTeX{} with -the least possible pain. These instructions won't be a substitute for -the User's Guide, but they may get you started quickly enough so that -you'll only need to refer to the guide occasionally, which should -eliminate most of the pain. - -The current version of \AmS-\LaTeX{} (version 1.2) is really just an -optional package for the new standard \LaTeX. \AmS-\LaTeX{} provides -the document classes \verb"amsart" and \verb"amsbook" (see -Section~\ref{sec:DocClsCom}) to replace the standard document classes -\verb"article" and \verb"book", and an optional package \verb"amsmath" -that can be used with the standard \LaTeX{} document classes. Thus, -using \AmS-\LaTeX{} is really using a variety of \LaTeX. If you're -new to \LaTeX{}, and these last few sentences made no sense to you at -all, don't worry about it. You don't have to know what the standard -\LaTeX{} document classes are in order to use the \AmS-\LaTeX{} -replacements for them. - - -I'll be assuming that you have at least some experience with either -plain \TeX, \AmS-\TeX{} or \LaTeX, and I'll try to tell you what you -need to know so that you can get started with \AmS-\LaTeX{} -\emph{without} actually reading the \LaTeX{} User's -Guide~\cite{latex}, or even taking much of a look at the \AmS-\LaTeX{} -User's Guide~\cite{amslatexusersguide}. - - -If you've never used \emph{any} version of \TeX, then I recommend -``The not so short introduction to \LaTeXe{}'', by Tobias Oetiker, -Hubert Partl, Irene Hyna, and Elisabeth Schlegl \cite{NotShort}. This -is intended for those with no knowledge of \TeX{} or \LaTeX, and -concisely gives a description of what a \LaTeX{} document looks like -and how you type text and simple mathematics in a \LaTeX{} document. - -I've also given you a template file \verb"template.tex", which is an -attempt to give you enough to mostly fake your way through an -\AmS-\LaTeX{} file, \emph{almost} without even reading these -instructions. I've included the text of that file in these -instructions as Section~\ref{sec:template}, so you might want to take a -look at that now, and then just use the table of contents of these -instructions to get more information on whatever in that file -confuses you. - -In case you haven't guessed, these instructions were printed using -\AmS-\LaTeX, so you can get some idea what it all looks like. - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Basic \LaTeX{} stuff} -\label{sec:basicstuff} - -In this section, we'll describe the three commands that have to be -part of any \LaTeX{} document: \verb"\documentclass", -\verb"\begin{document}", and \verb"\end{document}". The complete -explanation of these can be found in the \LaTeX{} User's -Guide~\cite{latex} or in \emph{The not so short introduction to - \LaTeXe}~\cite{NotShort}. We'll also explain how to begin a new -section or subsection of the paper, and how \LaTeX{} manages to get -the cross-references right (which is also the explanation of why you -need to run a file through \LaTeX{} \emph{twice} to be sure that all -the cross-references are correct). - - -\subsection{The \texttt{documentclass} command} -\label{sec:DocClsCom} - -Before you type anything that actually appears in the paper, you must -include a \verb"\documentclass" command. It's easiest to just put the -\verb"\documentclass" command at the very beginning of the file, -possibly with a few lines of comments before it. - -It's actually the choice of document class that determines whether -you're using \AmS-\LaTeX{} or just plain old \LaTeX. There are two -document classes that are a part of \AmS-\LaTeX: \verb"amsart" and -\verb"amsbook". There is also the \verb"amsmath" package that can be -used with the standard \LaTeX{} \verb"article" document class. I'll -only be discussing the \verb"amsart" document class here. For the -others, see the \AmS-\LaTeX{} User's Guide~\cite{amslatexusersguide}. - - -The simplest version of the \verb"documentclass" command is -\begin{center} -\verb"\documentclass{amsart}" -\end{center} -This will give you the default type size, which is 10~point type. If -you'd like to use 12~point type, then you should include the optional -argument \verb"[12pt]"; this makes the command -\begin{center} -\verb"\documentclass[12pt]{amsart}" -\end{center} - - -There are at least two optional packages that might be of interest. -The first is for when you want to include the macros that make it -easier to draw commutative diagrams. (These aren't included -automatically, since they take up a lot of memory, and not everyone -wants to use them.) If you want 10~point type and you want to use the -commutative diagram macros, then the commands to use are -\begin{center} - \begin{tabular}{l} - \verb"\documentclass{amsart}"\\ - \verb"\usepackage{amscd}" - \end{tabular} -\end{center} -If you want 12~point type and you want to use the commutative -diagram macros, then the commands are -\begin{center} - \begin{tabular}{l} - \verb"\documentclass[12pt]{amsart}"\\ - \verb"\usepackage{amscd}" - \end{tabular} -\end{center} - - -The other optional package is for use when you want to use some of the -special symbols contained in the \AmS-Fonts package. (These are the -fonts \verb"msam" and \verb"msbm".) If you want the standard names -for these symbols to be defined for your use, then you need to use the -optional package \verb"amssymb". Thus, to use the default 10~point -type and have the special symbols defined, use the commands -\begin{center} - \begin{tabular}{l} - \verb"\documentclass{amsart}"\\ - \verb"\usepackage{amssymb}" - \end{tabular} -\end{center} -If you want to use 12~point type, the commutative diagram macros, and -special symbols from the \AmS-Fonts collection, then use the commands -\begin{center} - \begin{tabular}{l} - \verb"\documentclass[12pt]{amsart}"\\ - \verb"\usepackage{amssymb}" - \end{tabular} -\end{center} -This document uses both of these packages, and so we used the commands -\begin{center} - \begin{tabular}{l} - \verb"\documentclass[12pt]{amsart}"\\ - \verb"\usepackage{amscd}"\\ - \verb"\usepackage{amssymb}" - \end{tabular} -\end{center} - -%--------------------------------------------------------------------- - -\subsection{\texttt{begin\{document\}} and \texttt{end\{document\}}} - -Everything that is to appear in the document must appear in between -the \verb"\begin{document}" and \verb"\end{document}" commands. There -are no optional arguments for these commands, so they always look the -same. Anything following the \verb"\end{document}" command is -ignored. You \emph{are} allowed to have macro definitions (i.e., -newcommands; see Section~\ref{sec:definitions}) before the -\verb"\begin{document}", and that's actually a good place for them, - but that's about all. - -%--------------------------------------------------------------------- -\subsection{Sections and subsections} -\label{sec:sections} - -To begin a new section, you give the command -\begin{center} -\verb"\section{Section name}" -\end{center} -To begin the present section, I gave the command -\begin{center} -\verb"\section{Basic \LaTeX{} stuff}" -\end{center} -A section number is supplied automatically. If you want to be able to -make reference to that section, then you need to \emph{label} it. -Since I wanted to be able to demonstrate the cross-reference commands, -I actually began this section with the lines -\begin{center} - \begin{tabular}{l} - \verb"\section{Basic \LaTeX{} stuff}"\\ - \verb"\label{sec:basicstuff}" - \end{tabular} -\end{center} -This allows me to say ``\verb"Section~\ref{sec:basicstuff}"'' and have -it printed as Section~\ref{sec:basicstuff}. - -To begin a new subsection, you give the command -\begin{center} -\verb"\subsection{Subsection name}" -\end{center} -To begin the present subsection, I gave the command -\begin{center} -\verb"\subsection{Sections and subsections}" -\end{center} -A subsection number is supplied automatically. If you want to be able -to make reference to that subsection, then you need to \emph{label} -it. This subsection was begun with the lines -\begin{center} - \begin{tabular}{l} - \verb"\subsection{Sections and subsections}"\\ - \verb"\label{sec:sections}" - \end{tabular} -\end{center} -so if we say ``\verb"Section~\ref{sec:sections}",'' it is printed as -Section~\ref{sec:sections}. - -Labels always take the number of the smallest enclosing structure. -Thus, a \verb"\label" command that's inside a section but \emph{not} -inside a subsection or Theorem or anything else will take the value of -the section counter, while a \verb"\label" command that's inside the -statement of a Theorem will take the value of that Theorem number. -For more information on this, see Section~\ref{sec:xreferences}. - -%-------------------------------------------------------------------- -\subsubsection{Yes, there are subsubsections too} - -I began this subsubsection with the command -\begin{center} -\verb"\subsubsection{Yes, there are subsubsections too}" -\end{center} -I refuse to even experiment to see if there are subsubsubsections. - - - -%-------------------------------------------------------------------- -\subsubsection*{Sections without numbers} - -I began this subsubsection with the command -\begin{center} -\verb"\subsubsection*{Sections without numbers}" -\end{center} -and got a subsubsection that wasn't numbered. If you give the command -\begin{center} -\verb"\section*{A Section Title}" -\end{center} -then you'll begin a new section that will not have a number. - - - -%--------------------------------------------------------------------- -\subsection{Italics \emph{for emphasis}} - -If you want to use italics to emphasize a word or two, the \LaTeX{} -convention is not to switch explicitly to italics, but rather to use -the command \verb"\emph" (which means \emph{emphasize}). This command -works just like a font change command, except that it switches you -\emph{into} italics if the current font is upright, and switches you -\emph{out of} italics if the current font is italics. - -For example, if you type -\begin{center} -\verb"The whole is \emph{more} than the sum of its parts." -\end{center} -you'll get -\begin{center} -The whole is \emph{more} than the sum of its parts. -\end{center} -but if you type -\begin{verbatim} -\begin{thm} - The whole is \emph{more} than the sum of its parts. -\end{thm} -\end{verbatim} -you'll get -\begin{thm} - The whole is \emph{more} than the sum of its parts. -\end{thm} - - -\subsubsection*{Note} - -The \verb"\emph" command is a recent addition to \LaTeX, and it has -the feature that it automatically inserts an italic correction where -needed. If you don't know what an italic correction is, you can -safely ignore this paragraph (but I will at least mention that all -those ``\verb"\/"'' commands frequently seen in \TeX{} (and older -\LaTeX) documents are all inserting italic corrections; the point of -this paragraph is that, with the current version of \LaTeX, you don't -have to do that anymore). - - - -%--------------------------------------------------------------------- -\subsection{Once is never enough} - -This is an explanation of how \LaTeX{} manages to fill in -cross-references to parts of the file it hasn't processed yet, and -what those \verb".aux" and \verb".toc" files are. - - -\subsubsection*{Cross-References} - -Every time \LaTeX{} processes your file, it writes an \emph{auxiliary} -file. Since the file containing these instructions is called -\verb"amshelp.tex", the auxiliary file is called \verb"amshelp.aux". -The auxiliary file contains the definitions of all the keys used for -cross-references. When \LaTeX{} begins to process your file, it first -looks for an \verb".aux" file, and reads it in if it exists. Of -course, this is the \verb".aux" file that was produced the \emph{last} -time that your file was processed, so the Theorem numbers, Section -numbers, etc., are all the ones from the last time the file was -processed. - -The very first time that \LaTeX{} processes your file, there is no -\verb".aux" file, and so \LaTeX{} gives \emph{lots} of warning -messages about undefined labels, or whatever. Ignore all of this. -The \emph{next} time that you run \LaTeX, there \emph{will} be an -\verb".aux" file, and all the references will be filled in. (Yes, it -is possible, at least in theory, for some page number to change every -time you run \LaTeX{} on your file, even without any changes in the -source file, but this isn't very likely.) - -\subsubsection*{The Table of Contents} - -If you give the command \verb"\tableofcontents", then \LaTeX{} will -try to write a table of contents, including the page numbers of the -sections. Obviously, \LaTeX{} can't know those page numbers or -section titles yet, so as \LaTeX{} processes your file, it writes a -\verb".toc" file containing the information it needs. (The -\verb".toc" file for these instructions is \verb"amshelp.toc".) Once -again, \LaTeX{} is always using the information from the \emph{last} -time that it processed your file. - -If you \emph{do} include a table of contents in your document, and if -the table of contents takes up at least a page or so of space, then -you might have to run \LaTeX{} \emph{three} times in order to get all -of the cross-references right. The reason for this is that the first -time you run \LaTeX{} there isn't any \verb".toc" file listing the -section titles, and so the table of contents has nothing in it. The -second time you run \LaTeX{} you'll get a table of contents that lists -the page numbers for the sections from the last time you ran \LaTeX, -when the table of contents took up no space at all. Unfortunately, -during this second run, the table of contents will be created, and -will take up enough space to change the page numbers of the sections -from what they were during the first run. Only during the -\emph{third} run will the correct page numbers be written into the -table of contents. Since this doesn't change the amount of space that -the table of contents occupies, this version will be correct. - -\subsubsection*{How do I know when everything is correct?} - -After processing your file, \LaTeX{} checks whether all the -cross-reference numbers that it read from the \verb".aux" file are -correct. If any of them are incorrect, it prints a warning on the -screen at the very end of the run advising you that labels may have -changed, and that you should run \LaTeX{} again to get the -cross-references right. Unfortunately, \LaTeX{} doesn't seem to check -that the table of contents entries are correct, so if you change the -name of a section in a way that doesn't make any page references -incorrect, you won't be warned to run \LaTeX{} again. - - - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Title, Author, and the \texttt{maketitle} command} - -This stuff should go right after the \verb"\begin{document}" command. - I'll give a quick sketch here, which is probably all you'll ever - need, but the full explanation is given in \emph{Instructions for - preparation of papers and monographs: \AmS-\LaTeX} \cite{instr-l}. - If you are already familiar with \LaTeX, then you should be warned - that this part is slightly different from what you do when using the - standard \LaTeX{} \verb"article" documentclass. - -%--------------------------------------------------------------------- - -\subsection{The title} -You announce the title with the -command -\begin{center} -\verb"\title[Optional running title]{Actual title}" -\end{center} -These instructions used the title command -\begin{center} - \begin{tabular}{l} - \verb"\title[Running \AmS-\LaTeX]"\\ - \verb"{Getting up and running\\"\\ - \verb"with \AmS-\LaTeX}" - \end{tabular} -\end{center} -Notice that you indicate line breaks in the title with a double -backslash. If I had decided to let the \emph{full} title be printed -in the head of the odd numbered pages, I would have used the command -\begin{center} - \begin{tabular}{l} - \verb"\title{Getting up and running\\"\\ - \verb"with \AmS-\LaTeX}" - \end{tabular} -\end{center} - - - -%--------------------------------------------------------------------- -\subsection{The author, and the author's address} - - -The author is specified with an \verb"author" command: -\begin{center} -\verb"\author{Author's name}" -\end{center} -These directions used the command -\verb"\author{Philip S. Hirschhorn}". -The author's address is given in an address command, with double -backslashes to indicate line breaks. These instructions used the -command -\begin{center} - \begin{tabular}{l} - \verb"\address{Department of Mathematics\\"\\ - \verb"Wellesley College\\"\\ - \verb"Wellesley, Massachusetts 02481}" - \end{tabular} -\end{center} -If the author's current address is different from the address at which -the research was carried out, then you can specify the current address -with the command \verb"\curraddr". For example, you might say -\begin{center} - \begin{tabular}{l} - \verb"\curraddr{Department of Mechanics\\"\\ - \verb"Brake and Wheel Bearing Division\\"\\ - \verb"Serene Service Center\\"\\ - \verb"Salem, Massachusetts 02139}" - \end{tabular} -\end{center} -You can also include an email address, with the \verb"\email" -command. These instructions used the command -\begin{center} - \verb"\email{psh@math.mit.edu}" -\end{center} -To acknowledge support, use the command \verb"\thanks", e.g., -\begin{center} - \verb"\thanks{Supported in part by NSF grant 3.14159}" -\end{center} -This will be printed as a footnote on the first page. - - - - - -\subsubsection*{Multiple authors} - -If there are several authors, then each one should have a separate -\verb"\author" command, with each individual's address (and current -address, and email address) following that individual's \verb"\author" -command, in its own \verb"\address" command (and \verb"\curraddr" -command, and \verb"\email" command). If there \emph{are} several -authors, and their combined names are too long for the running head on -the even numbered pages, you can give an optional argument to each -\verb"\author" command to supply a shortened form to use in the -running head. (It's apparently a convention that the running head in -a multiple author paper should have only initials for the first and -middle names, but I don't think that I was invited to that -convention.) - - -%--------------------------------------------------------------------- - -\subsection{The date} - -This is pretty straightforward: -\begin{center} -\verb"\date{Whatever date you please}" -\end{center} -To have the date of processing used, use the command -\verb"\date{\today}". - -%--------------------------------------------------------------------- -\subsection{\texttt{maketitle}} - - -After you've given all of the commands mentioned in this section, you -can give the command \verb"\maketitle". The exact arrangement is -determined by the document class. In particular, the \verb"amsart" -document class puts the author's address at the \emph{end} of the -paper. If you \emph{don't} give the command \verb"\maketitle", a -title won't be made. - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Theorems, Propositions, Lemmas, etc.} - -The instructions in this section assume that you're using the -\verb"newtheorem" commands that I put in the file -\verb"template.tex". - -\subsection{Stating theorems, propositions, etc.} - -To state a theorem, you do the following: -\begin{verbatim} -\begin{thm} -The square of the hypotenuse of a right triangle -is equal to the sum of the squares of the two -adjacent sides. -\end{thm} -\end{verbatim} -If you do that, you'll get the following: -\begin{thm} -\label{pythagthm} -The square of the hypotenuse of a right triangle -is equal to the sum of the squares of the two -adjacent sides. -\end{thm} -If you thought that it was only a proposition, you'd use -\begin{verbatim} -\begin{prop} -The square of the hypotenuse of a right triangle -is equal to the sum of the squares of the two -adjacent sides. -\end{prop} -\end{verbatim} -and you'd get -\begin{prop} -The square of the hypotenuse of a right triangle -is equal to the sum of the squares of the two -adjacent sides. -\end{prop} - -If you think it's a theorem again, but you'd like to make reference to -it in some other part of the paper, you have to choose a \emph{key} -with which you'll refer to it, and then \emph{label} the theorem. If -you want to use the key \emph{pythagthm}, then it would look like the -following: -\begin{verbatim} -\begin{thm} -\label{pythagthm} -The square of the hypotenuse of a right triangle -is equal to the sum of the squares of the two -adjacent sides. -\end{thm} -\end{verbatim} -If you later give the command \verb"\ref{pythagthm}", then that -command will expand to the \emph{number} that was assigned to that -theorem (in this case, \ref{pythagthm}). For more explanation of -cross-references, see Section~\ref{sec:xreferences}. - -If you'd like to state a theorem and give a \emph{name} to it, then -you can add an optional argument to the \verb"\begin{thm}" command. -If you type -\begin{verbatim} -\begin{thm}[Pythagorus] -The square of the hypotenuse of a right triangle -is equal to the sum of the squares of the two -adjacent sides. -\end{thm} -\end{verbatim} -you'll get -\begin{thm}[Pythagorus] -The square of the hypotenuse of a right triangle -is equal to the sum of the squares of the two -adjacent sides. -\end{thm} - - -\subsubsection*{Summary of environments provided in the template} - -All of the following structures are numbered in the same sequence, -in the form SectionNumber.Number. Equations (i.e., displayed -formulas, whether they are equations or not) will be numbered in the -same sequence. - -$$ -\begin{tabular}{c@{\hspace{4em}}l@{\hspace{4em}}c} - -\multicolumn{3}{c}{Theorem Environments}\\*[8pt] - -\hspace{1em}Name& Printed Form& Body font\\*[6pt] - -\texttt{thm}& \textbf{Theorem}& Italic\\ -\texttt{cor}& \textbf{Corollary}& Italic\\ -\texttt{lem}& \textbf{Lemma}& Italic\\ -\texttt{prop}& \textbf{Proposition}& Italic\\ -\texttt{defn}& \textbf{Definition}& Normal\\ -\texttt{rem}& \textit{Remark}& Normal\\ -\texttt{ex}& \textit{Example}& Normal\\ -\texttt{notation}& \textit{Notation}& Normal\\ -\texttt{terminology}& \textit{Terminology}& Normal\\*[3pt] -\end{tabular} -$$ - -For full details, see the beginning of the template file (reproduced -here in Section~\ref{sec:template}), after the comment ``The Theorem -Environments.'' - - - -%--------------------------------------------------------------------- -\subsection{Proofs} - -To give a proof, you do the following: -\begin{verbatim} -\begin{proof} -As any fool can plainly see, it's true! -\end{proof} -\end{verbatim} -and you'll get the following: -\begin{proof} -As any fool can plainly see, it's true! -\end{proof} -If the theorem said that a condition was both necessary and sufficient -for something, and you want to prove each part separately, -you can do the following: -\begin{verbatim} -\begin{proof}[Proof (sufficiency)] -Well, it's \emph{obviously} sufficient! -\end{proof} -\end{verbatim} -and you'll get -\begin{proof}[Proof (sufficiency)] -Well, it's \emph{obviously} sufficient! -\end{proof} -that is, the \verb"proof" environment allows you to use an optional -second argument that will appear in place of the word \verb"Proof". - -If the proof of Theorem~\ref{pythagthm} does not appear immediately -after its statement, you might use the following: -\begin{verbatim} -\begin{proof}[Proof of Theorem~\ref{pythagthm}] -As any fool can plainly see, it's true! -\end{proof} -\end{verbatim} -and you'd get -\begin{proof}[Proof of Theorem~\ref{pythagthm}] -As any fool can plainly see, it's true! -\end{proof} - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Cross-References} -\label{sec:xreferences} - -This section explains how to make reference to numbered sections, -theorems, equations, and bibliography items, with the correct -reference numbers filled in automatically by \LaTeX. - -%--------------------------------------------------------------------- -\subsection{References to sections, theorems and equations} -\label{sec:thmrefs} - -For each structure in the manuscript to which you'll be making -reference, you must assign a \emph{key} that you'll use to refer to -that structure. For sections, theorems and numbered equations, you -assign the key using the \verb"\label" command. This command takes -one argument, which is the \emph{key} you're assigning to the object. -The command \verb"\ref{key}" then produces the number that was -assigned to that structure. If the structure is an equation, then the -command \verb"\eqref{key}" should be used instead of the command -\verb"\ref{key}". - - -Consider the following example. -\begin{thm} -\label{homotopy} -If the maps $f\colon X \to Y$ and $g\colon X \to Y$ are homotopic, -then $f_* = g_* \colon \mathrm{H}_*X \to \mathrm{H}_*Y$. -\end{thm} - -We typed this theorem as follows. -\begin{verbatim} -\begin{thm} -\label{homotopy} -If the maps $f\colon X \to Y$ and $g\colon X \to Y$ are -homotopic, then -$f_* = g_* \colon \mathrm{H}_*X \to \mathrm{H}_*Y$. -\end{thm} -\end{verbatim} -If we now type ``\verb"see Theorem~\ref{homotopy}",'' then it will be -printed as ``see Theorem~\ref{homotopy}.'' - - - - - -\subsubsection*{So, what exactly is the label labeling?} - -We began this section by typing -\begin{center} - \begin{tabular}{l} - \verb"\section{Cross-References}"\\ - \verb"\label{sec:xreferences}" - \end{tabular} -\end{center} -and we began this subsection by typing -\begin{center} - \begin{tabular}{l} - \verb"\subsection{References to sections, theorems and equations}"\\ - \verb"\label{sec:thmrefs}" - \end{tabular} -\end{center} -The phrase ``\verb"See Section~\ref{sec:xreferences}"'' is printed as -``See Section~\ref{sec:xreferences},'' while the phrase -``\verb"See Section~\ref{sec:thmrefs}"'' is printed as ``See -Section~\ref{sec:thmrefs}.'' - - -The command \verb"\label{key}" assigns to \verb"key" the value of the -\emph{smallest enclosing structure}. That's why the command -\verb"\ref{sec:xreferences}" is printed as~\ref{sec:xreferences}, -while \verb"\ref{sec:thmrefs}" is printed as~\ref{sec:thmrefs}: the -key \verb"sec:xreferences" was defined inside of -Section~\ref{sec:xreferences} but \emph{outside} of -Section~\ref{sec:thmrefs}, while the key \verb"sec:thmrefs" was -defined \emph{inside} of Section~\ref{sec:thmrefs}. - - -\subsubsection*{References to equations} - -To make reference to a numbered equation, you assign the \emph{key} -as before, but you replace \verb"\ref" with \verb"\eqref". For -example, if you type -\begin{verbatim} -\begin{equation} -\label{additivity} -\mathrm{H}_* \bigvee_{\alpha\in A} X_\alpha \iso - \bigoplus_{\alpha\in A}\mathrm{H}_* X_\alpha -\end{equation} -\end{verbatim} -then you'll get -\begin{equation} -\label{additivity} -\mathrm{H}_* \bigvee_{\alpha\in A} X_\alpha \iso - \bigoplus_{\alpha\in A}\mathrm{H}_* X_\alpha -\end{equation} -If we now say -\begin{verbatim} -\begin{thm} -Equation~\eqref{additivity} is true for all sorts of -functors $\mathrm{H}$. -\end{thm} -\end{verbatim} -then we'll get -\begin{thm} -Equation~\eqref{additivity} is true for all sorts of -functors $\mathrm{H}$. -\end{thm} -Notice the parentheses around the equation number, and the fact that -even though the theorem is set in slanted type, the equation -number is set in an upright font. This is the advantage of using -\verb"\eqref" instead of \verb"\ref"; the command \verb"\eqref" -arranges it so that the number and surrounding parentheses are in an -upright font no matter what the surrounding font, and supplies an -italic correction if it's needed. - - -%--------------------------------------------------------------------- -\subsection{References to page numbers} - -If you want to make reference to the \emph{page} that contains a -label, rather than to the structure that is labeled, use the command -\verb"\pageref{key}". For example, if you type -\begin{verbatim} -Look at page~\pageref{homotopy} to find -Theorem~\ref{homotopy}. -\end{verbatim} -you'll get ``Look at page~\pageref{homotopy} to find -Theorem~\ref{homotopy}.'' - - - - - - - -%--------------------------------------------------------------------- -\subsection{Bibliographic references} -\label{sec:bibreferences} - - -Bibliography entries receive a \emph{key} as part of their basic -structure. Each item in the bibliography is entered as -\begin{verbatim} -\bibitem{key} The actual bibliography item goes here. -\end{verbatim} -(For more detail on this, see Section~\ref{sec:bibliography}.) - -You refer to bibliography items using the \verb"\cite" command. For -example, the bibliography of these instructions contains the entry -% -\begin{verbatim} -\bibitem{HA} -D. G. Quillen, \emph{Homotopical Algebra,} Lecture Notes in -Mathematics number 43, Springer-Verlag, Berlin, 1967. -\end{verbatim} -% -If we say ``\verb"This is the work of Quillen~\cite{HA}",'' then it -will be printed as ``This is the work of Quillen~\cite{HA}.'' Notice -that square brackets have been inserted around the bibliography item -number. - -The \verb"\cite" command takes an optional argument, which allows you -to annotate the reference. If we say -``\verb"see~\cite[Chapter I]{HA}"'', then it will be printed as -``see~\cite[Chapter I]{HA}''. - - - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Mathematics} - - -\subsection{Mathematics in running text} - -This is pretty much exactly as it is in plain \TeX, except that you -have an extra option (which you can ignore). The simplest thing is to -just enclose between dollar signs (\verb"$") any material that should -be in math mode. Thus, if you type -\begin{center} -\verb"Let $f\colon X \to Y$ be a continuous function." -\end{center} -you'll get -\begin{center} -Let $f\colon X \to Y$ be a continuous function. -\end{center} - -The only novelty that \LaTeX{} introduces is that, instead of using -a dollar sign to toggle math mode on and off, you can use -`\verb"\("' to \emph{begin} math mode, and `\verb"\)"' to \emph{end} -math mode. Thus, the example above is equivalent to typing -\begin{center} -\verb"Let \(f\colon X \to Y\) be a continuous function." -\end{center} -This provides a tiny bit more error checking, but can -otherwise be safely ignored. - - -%--------------------------------------------------------------------- -\subsection{Displayed mathematics} - -For simple displayed mathematics without an equation number, this is -very much like plain \TeX, again with extra choices that can be -ignored. If you enclose material between double dollar -signs(\verb"$$"), it will be interpreted in math mode and displayed. -Thus, if you've previously given the command -\begin{center} - \verb"\newcommand{\iso}{\approx}" -\end{center} -(see Section~\ref{sec:definitions}), and you type -\begin{verbatim} -$$ -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -$$ -\end{verbatim} -you'll get -$$ -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -$$ -The new choices are that exactly the same thing will be obtained by -either -\begin{verbatim} -\[ -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -\] -\end{verbatim} -or by -\begin{verbatim} -\begin{displaymath} -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -\end{displaymath} -\end{verbatim} -or by -\begin{verbatim} -\begin{equation*} -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -\end{equation*} -\end{verbatim} - - -If you'd like the displayed formula to be \emph{numbered}, then you -should use the \verb"equation" environment. (\LaTeX{} calls all -formula numbers \emph{equation numbers}, whether or not the -mathematics has anything to do with equations.) If you type -\begin{verbatim} -\begin{equation} -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -\end{equation} -\end{verbatim} -you'll get -\begin{equation} -\label{pi1eqn} -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -\end{equation} -(Notice that the \verb"equation" environment produces an equation -number, while the \verb"equation*" environment doesn't. This is a -standard \LaTeX ism: Adding an asterisk to the name of a numbered -\LaTeX{} environment often gives the unnumbered equivalent.) - - -If you'd like to be able to make reference to the equation number, -you need to \emph{label} the equation, using a \emph{key} that you -can use for referencing it: -\begin{verbatim} -\begin{equation} -\label{pi1eqn} -\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y -\end{equation} -\end{verbatim} -If you later type ``\verb"see formula~\eqref{pi1eqn}"'' you'll get -``see formula~\eqref{pi1eqn}.'' (For more on cross-references to -formulas, see Section~\ref{sec:thmrefs}.) - -\AmS-\LaTeX{} has several environments that make it easier to typeset -complicated multi-line displays. These are explained in the -\AmS-\LaTeX{} User's Guide~\cite{amslatexusersguide} and illustrated -in \verb"testmath.tex"~\cite[pages 29--40]{testmath}. - - - -%--------------------------------------------------------------------- -\subsection{Commutative diagrams} - -\AmS-\LaTeX{} provides the \verb"CD" environment for drawing -commutative diagrams. These only allow for \emph{rectangular} -diagrams, but they're very convenient to use. If you need diagonal -arrows, or curving arrows, or arrows that make a number of right angle -turns, I recommend the XY-Pic package, which can do all of these -things (and more). - -\textbf{Important}: To use the \verb"CD" environment, you need to load -it with the command \verb"\usepackage{amscd}". For example, the -template file gives the commands -\begin{center} - \begin{tabular}{l} - \verb"\documentclass[12pt]{amsart}"\\ - \verb"\usepackage{amscd}" - \end{tabular} -\end{center} -which select the \verb"amsart" document class with twelve point type, -and loads the macros for the \verb"CD" environment. - -\subsubsection*{A simple example} - -To produce the diagram -$$ -\begin{CD} -A @>>> B @= B\\ -@AAA @| @VVV\\ -X @<<< B @>>> Y -\end{CD} -$$ -you type -\begin{verbatim} -$$ -\begin{CD} -A @>>> B @= B\\ -@AAA @| @VVV\\ -X @<<< B @>>> Y -\end{CD} -$$ -\end{verbatim} -This illustrates several things. First of all, the \verb"CD" -environment must be inside of a displayed mathematics environment. -(Here we used the standard \verb"$$" toggle to get displayed -mathematics. If we had used, e.g., \verb"\begin{equation}" and - \verb"\end{equation}", we would have had an equation number assigned -to the display.) Right pointing arrows are obtained with \verb"@>>>", -left pointing arrows with \verb"@<<<", up pointing arrows with -\verb"@AAA", down pointing arrows with \verb"@VVV", horizontal equals -signs with \verb"@=", and vertical equals signs with \verb"@|". Every -line except the last is ended with a double backslash (\verb"\\"). - -\subsubsection*{Labeling the arrows} - -The arrows can also be labeled. For horizontal arrows, anything -between the first and second inequality sign goes above the arrow, -and anything between the second and third inequality sign goes below -it. For downward arrows, anything between the first and second -\verb"V" goes to the left, and anything between the second and third -goes to the right (and similarly for upward arrows). Thus, if you -type -\begin{verbatim} -\begin{displaymath} -\begin{CD} -\mathrm{H}_iX @>f_*>> \mathrm{H}_iY @<g_*<\iso< E_fA\\ -@V\phi VV @V\psi VV @AA\Omega A\\ -\pi_iQ @>\alpha\beta\gamma>> \pi_i(R,S) - @<<\text{A long arrow}< \prod_{k=1}^i H_kZ -\end{CD} -\end{displaymath} -\end{verbatim} -you'll get -\begin{displaymath} -\begin{CD} -\mathrm{H}_iX @>f_*>> \mathrm{H}_iY @<g_*<\iso< E_fA\\ -@V\phi VV @V\psi VV @AA\Omega A\\ -\pi_iQ @>\alpha\beta\gamma>> \pi_i(R,S) - @<<\text{A long arrow}< \prod_{k=1}^i H_kZ -\end{CD} -\end{displaymath} - - -\subsubsection*{Leaving out part of the rectangle} - -If you want to end a line in the diagram early (omitting the right -end of that line), just type the double backslash. If you want to -leave out the \emph{beginning} of a line, you type ``\verb"@."'' -(the ``at'' sign followed by a period) to denote an invisible arrow. -(It's the arrows that are the column markers in the \verb"CD" -environment.) Thus, if you type -\begin{verbatim} -\begin{displaymath} -\begin{CD} -X\\ -@VfVV\\ -Y @= Y\\ -@. @VVgV\\ - @. Z -\end{CD} -\end{displaymath} -\end{verbatim} -you'll get -\begin{displaymath} -\begin{CD} -X\\ -@VfVV\\ -Y @= Y\\ -@. @VVgV\\ - @. Z -\end{CD} -\end{displaymath} - - - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Macro definitions, a.k.a.\ \texttt{newcommand}} -\label{sec:definitions} - - -\LaTeX{} allows you to use the same \verb"\def" command that you use -in plain \TeX, but it's considered bad style. Instead, \LaTeX{} has -the \verb"\newcommand" and \verb"\renewcommand" commands, which do a -little error checking for you. In plain \TeX, you might use the -command -\begin{center} -\verb"\def\tensor{\otimes}" -\end{center} -but in \LaTeX, the preferred form is -\begin{center} -\verb"\newcommand{\tensor}{\otimes}" -\end{center} -The advantage of this is that \LaTeX{} will check to see if there -already is a command with the name \verb"\tensor", and give you an -error message if there is. If you know that there is a previous -definition of \verb"\tensor" but you \emph{want} to override it, -then you use the command -\begin{center} -\verb"\renewcommand{\tensor}{\otimes}" -\end{center} - - -If you want to use macros with replaceable parameters, the -\verb"newcommand" command allows this. For the equivalent of the -plain \TeX{} command -\begin{center} -\verb"\def\pushout#1#2#3{#1\cup_{#2}#3}" -\end{center} -you use the \LaTeX{} command -\begin{center} -\verb"\newcommand{\pushout}[3]{#1\cup_{#2}#3}" -\end{center} -i.e., the command name is enclosed in braces, and the number of -parameters is enclosed in square brackets. - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{Lists: \texttt{itemize, enumerate, and description}} - -There are three list making environments: \texttt{itemize}, -\texttt{enumerate}, and \texttt{description}. The \texttt{itemize} -environment just lists the items with a marker in front of each one. -If you type -% -\begin{verbatim} -\begin{itemize} -\item -This is the first item in the list, which runs on long enough to -spill over onto a second line. -\item -This is the second item in the list, which is a bit shorter. -\item -This is the last item. -\end{itemize} -\end{verbatim} -% -then you'll get -% -\begin{itemize} -\item -This is the first item in the list, which runs on long enough to -spill over onto a second line. -\item -This is the second item in the list, which is a bit shorter. -\item -This is the last item. -\end{itemize} - - - -The \texttt{enumerate} environment looks the same, except that the items -in the list are numbered. If you type -\begin{verbatim} -\begin{enumerate} -\item -This is the first item in the list, which runs on long enough to -spill over onto a second line. -\item -This is the second item in the list, which is a bit shorter. -\item -This is the last item. -\end{enumerate} -\end{verbatim} -then you'll get -\begin{enumerate} -\item -This is the first item in the list, which runs on long enough to -spill over onto a second line. -\item -This is the second item in the list, which is a bit shorter. -\item -This is the last item. -\end{enumerate} - -The \texttt{description} environment requires an extra argument for each -\verb"\item" command, which will be printed at the beginning of the -item. If you type -\begin{verbatim} -\begin{description} -\item[sedge] -A green plant, found in both wetlands and uplands. -Sedges are often confused with grasses and rushes. -\item[grass] -A green plant, found in both wetlands and uplands. -Grasses are often confused with sedges and rushes. -\item[rush] -A green plant, found in both wetlands and uplands. -Rushes are often confused with sedges and grasses -\end{description} -\end{verbatim} -you'll get -\begin{description} -\item[sedge] -A green plant, found in both wetlands and uplands. Sedges are often -confused with grasses and rushes. -\item[grass] -A green plant, found in both wetlands and uplands. Grasses are often -confused with sedges and rushes. -\item[rush] -A green plant, found in both wetlands and uplands. Rushes are often -confused with sedges and grasses -\end{description} - - -These environments can be inserted within each other, and the -\verb"enumerate" environment keeps track of what level it's at, and -numbers its items accordingly. If you type -\begin{verbatim} -\begin{enumerate} -\item I went to the dry cleaners. -\item I went to the supermarket. I bought -\begin{enumerate} -\item Bread, -\item cheese, and -\item Tabasco sauce. -\end{enumerate} -\item I went to the bank. -\end{enumerate} -\end{verbatim} -% -you'll get -% -\begin{enumerate} -\item I went to the dry cleaners. -\item I went to the supermarket. I bought -\begin{enumerate} -\item Bread, -\item cheese, and -\item Tabasco sauce. -\end{enumerate} -\item I went to the bank. -\end{enumerate} - - - - - - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{The bibliography} -\label{sec:bibliography} - -\subsection{\texttt{begin\{thebibliography\}} and - \texttt{end\{thebibliography\}}} - - -The bibliography is begun with the command -\begin{center} -\verb"\begin{thebibliography}{number}" -\end{center} -where \emph{number} is a random number that, when printed, is as -wide as the widest number of any item in the bibliography. (The only -use made of \verb"number" is that \LaTeX{} assumes that the numbers -that it will assign to the actual items in the bibliography will be -no wider (when printed) than \verb"number".) For example, if the -bibliography will contain between 10 and~19 items, you can use -\verb"\begin{thebibliography}{10}". - -After listing each item in the bibliography, you end the bibliography -with the \verb"\end{thebibliography}" command. - - -\subsection{Bibliography items} - -Each item is begun with a \verb"\bibitem" command. The format is -\begin{center} -\verb"\bibitem{key for cross-references}Item entry" -\end{center} -For example, the bibliography in these instructions contains the -entry -% -\begin{verbatim} -\bibitem{yellowmonster} -A. K. Bousfield and D. M. Kan, \emph{Homotopy Limits, -Completions and Localizations,} Lecture Notes in -Mathematics number 304, Springer-Verlag, New York, 1972. -\end{verbatim} - - -The above entry allows you to say -\begin{verbatim} -Homotopy inverse limits are discussed -in~\cite[Chapter 11]{yellowmonster}. -\end{verbatim} -and have it print as -``Homotopy inverse limits are discussed -in~\cite[Chapter 11]{yellowmonster}.'' -For more on this, see Section~\ref{sec:bibreferences}. - - - - - - - - - - - - - - - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- -\section{The template file} -\label{sec:template} - -The following is the text of the file \verb"template.tex". - -\begin{verbatim} -%%% template.tex -%%% This is a template for making up an AMS-LaTeX file -%%% Version of August 10, 2000 -%%%--------------------------------------------------------- -%%% The following commands choose 12 point type (instead -%%% of the default 10 point), allow us to use the -%%% commutative diagram macros, and define the standard -%%% names for all of the special symbols in the AMSfonts -%%% package: -\documentclass[12pt]{amsart} -\usepackage{amscd} -\usepackage{amssymb} - - - - - -%%% This part of the file (after the \documentclass command, -%%% but before the \begin{document}) is called the ``preamble''. -%%% This is a good place to put our macro definitions. - -\newcommand{\tensor}{\otimes} -\newcommand{\homotopic}{\simeq} -\newcommand{\homeq}{\cong} -\newcommand{\iso}{\approx} - -\DeclareMathOperator{\ho}{Ho} -\DeclareMathOperator*{\colim}{colim} - - - -\newcommand{\R}{\mathbb{R}} -\newcommand{\C}{\mathbb{C}} -\newcommand{\Z}{\mathbb{Z}} - -\newcommand{\M}{\mathcal{M}} -\newcommand{\W}{\mathcal{W}} - - - -\newcommand{\itilde}{\tilde{\imath}} -\newcommand{\jtilde}{\tilde{\jmath}} -\newcommand{\ihat}{\hat{\imath}} -\newcommand{\jhat}{\hat{\jmath}} - - - -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%% The Theorem environments: -%%% -%%% -%%% The following commands set it up so that: -%%% -%%% All Theorems, Corollaries, Lemmas, Propositions, Definitions, -%%% Remarks, Examples, Notations, and Terminologies will be numbered -%%% in a single sequence, and the numbering will be within each -%%% section. Displayed equations will be numbered in the same -%%% sequence. -%%% -%%% -%%% Theorems, Propositions, Lemmas, and Corollaries will have the most -%%% formal typesetting. -%%% -%%% Definitions will have the next level of formality. -%%% -%%% Remarks, Examples, Notations, and Terminologies will be the least -%%% formal. -%%% -%%% Theorem: -%%% \begin{thm} -%%% -%%% \end{thm} -%%% -%%% Corollary: -%%% \begin{cor} -%%% -%%% \end{cor} -%%% -%%% Lemma: -%%% \begin{lem} -%%% -%%% \end{lem} -%%% -%%% Proposition: -%%% \begin{prop} -%%% -%%% \end{prop} -%%% -%%% Definition: -%%% \begin{defn} -%%% -%%% \end{defn} -%%% -%%% Remark: -%%% \begin{rem} -%%% -%%% \end{rem} -%%% -%%% Example: -%%% \begin{ex} -%%% -%%% \end{ex} -%%% -%%% Notation: -%%% \begin{notation} -%%% -%%% \end{notation} -%%% -%%% Terminology: -%%% \begin{terminology} -%%% -%%% \end{terminology} -%%% -%%% Theorem environments - -% The following causes equations to be numbered within sections -\numberwithin{equation}{section} - -% We'll use the equation counter for all our theorem environments, so -% that everything will be numbered in the same sequence. - -% Theorem environments - -\theoremstyle{plain} %% This is the default, anyway -\newtheorem{thm}[equation]{Theorem} -\newtheorem{cor}[equation]{Corollary} -\newtheorem{lem}[equation]{Lemma} -\newtheorem{prop}[equation]{Proposition} - - -\theoremstyle{definition} -\newtheorem{defn}[equation]{Definition} - -\theoremstyle{remark} -\newtheorem{rem}[equation]{Remark} -\newtheorem{ex}[equation]{Example} -\newtheorem{notation}[equation]{Notation} -\newtheorem{terminology}[equation]{Terminology} - - -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -\begin{document} - -%%% In the title, use a double backslash "\\" to show a linebreak: -%%% Use one of the following two forms: -%%% \title{Text of the title} -%%% or -%%% \title[Short form for the running head]{Text of the title} -\title - - - - -\author{} - - - -%%% In the address, show linebreaks with double backslashes: -\address{} - - - - -%%% Email address is optional. -\email{} - -%%% To have the current date inserted, use \date{\today}: -\date{} - - -\maketitle - -%%% To include a table of contents, uncomment the next line: -% \tableofcontents -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%% Start the body of the paper here! E.G., maybe use: -%%% \section{Introduction} -%%% \label{sec:intro} - - - - - - - - - - - - - - - - - -%%%------------------------------------------------------------------- -%%%------------------------------------------------------------------- -%%% The number "10" that appears in the next command is a TOTALLY -%%% RANDOM NUMBER which is chosen so that if it was printed, it would -%%% be at least as wide as any number of an item in the bibliography: - -\begin{thebibliography}{10} - - - - -%%% The format of bibliography items is as in the following examples: -%%% -%%% \bibitem{yellowmonster} -%%% A. K. Bousfield and D. M. Kan, \emph{Homotopy Limits, Completions -%%% and Localizations,} Lecture Notes in Mathematics number 304, -%%% Springer-Verlag, New York, 1972. -%%% -%%% \bibitem{HA} -%%% D. G. Quillen, \emph{Homotopical Algebra,} Lecture Notes in -%%% Mathematics number 43, Springer-Verlag, Berlin, 1967. - - - - - - - - -\end{thebibliography} -\end{document} -\end{verbatim} - - - - - - - - - - - -%--------------------------------------------------------------------- -%--------------------------------------------------------------------- - -\begin{thebibliography}{10} - - -\bibitem{amslatexusersguide} - American Mathematical Society, \emph{\AmS-\LaTeX{} Version 1.2 User's - Guide,} November, 1996. This is the file \texttt{amsldoc.dvi}, - available from the AMS ftp site \texttt{e-math.ams.org}. - -\bibitem{instr-l} - American Mathematical Society, \emph{Instructions for preparation of - papers and monographs: \AmS-\LaTeX,} November, 1966. This is the - file \texttt{instr-l.dvi}, available from the AMS ftp site - \texttt{e-math.ams.org}. - -\bibitem{testmath} - American Mathematical Society, \emph{Sample paper for the amsmath - package,} November, 1996. This is the file \texttt{testmath.tex}, - available from the AMS ftp site \texttt{e-math.ams.org}. - -\bibitem{latex} - Leslie Lamport, \emph{\LaTeX{} User's Guide and Reference Manual,} - Addison-Wesley, 1986. - -\bibitem{NotShort} - Tobias Oetiker, Hubert Partl, Irene Hyna, and Elisabeth Schlegl - \emph{The not so short introduction to \LaTeXe}, available by ftp - from CTAN (the Comprehensive \TeX{} archive network), at - \verb"ftp.tex.ac.uk", \verb"ftp.dante.de", and many mirrors, under - the name \verb"lshort2e.tex" or \verb"lshort2e.dvi". - -\bibitem{yellowmonster} - A. K. Bousfield and D. M. Kan, \emph{Homotopy Limits, Completions - and Localizations,} Lecture Notes in Mathematics number 304, - Springer-Verlag, New York, 1972. - -\bibitem{HA} - D. G. Quillen, \emph{Homotopical Algebra,} Lecture Notes in - Mathematics number 43, Springer-Verlag, Berlin, 1967. - - -\end{thebibliography} -\end{document} - |