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%%% filename = "thmtest.tex",
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%%% 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)",
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%%% 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.",
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% Option test file, will be created during the first LaTeX run;
% this facility is not available when using an AMS document class.
% Removed for LaTeXML testing
%\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}
% for LaTeXML testing
\date{none}
\usepackage{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}
\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}