%%% ==================================================================== %%% @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}