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