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diff --git a/Master/texmf-dist/source/latex/amscls/thmtest.tex b/Master/texmf-dist/source/latex/amscls/thmtest.tex new file mode 100644 index 00000000000..21193949e83 --- /dev/null +++ b/Master/texmf-dist/source/latex/amscls/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} |