632 lines
22 KiB
TeX
632 lines
22 KiB
TeX
\documentclass[full]{l3doc}
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\usepackage{mkessler-todo}
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\title{%
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The \pkg{groupthm} package \\
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Theorem Groups and Families
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}
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\author{%
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Maximilian Keßler
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}
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\date{Released 2022-01-17}
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\NewDocumentCommand{\kw}{m}
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{%
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\texttt{#1}%
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}
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\NewDocumentCommand{\vocab}{m}
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{%
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\emph{#1}%
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}
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\begin{document}
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\maketitle
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\begin{documentation}
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\tableofcontents
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A central thing in \LaTeX is the usage of \enquote{theorems}.
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With \enquote{theorems} we actually mean \enquote{environments} that typically
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have a title, some style applied to their contents and are numbered throughout
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the document, often later referenced by number and / or name.
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Mechanisms for generating such environments are packages like
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\pkg{amsthm}, \pkg{ntheorem}, \pkg{thmtools}.
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While the mechanism in \pkg{thmtools} are pretty versatile and suffice
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for almost all needs, it is pretty time-consuming to largely change
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the behavior of environments, or have small variants of these.
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This package aims at both providing a versatile mechanism, \meta{theorem group}s,
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to structure theorems into groups that can subsequently easily altered,
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as well as a mechanism for easily generating \meta{theorem families}.
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As the author is of the opinion that of the mentioned theorem controlling packages
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\pkg{thmtools} provides the most versatile interface, the \pkg{groupthm}
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will be working on top of \pkg{thmtools} and use this as a backend for declaring
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the \meta{theorem}s themselves.
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Thus, any styles supported by \pkg{thmtools} will be supported by \pkg{groupthm}
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as well, by passing them to \pkg{thmtools}.
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\section{Concepts}
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\subsection{Theorem groups}
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\label{sec:theorem-groups}
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A \meta{theorem group} is some named group holding some properties for
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the \meta{theorem}s that are contained in this group.
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Each \meta{theorem} can, when declared, be part of arbitrarily many \meta{theorem group}s,
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and will be subject to the styles these groups defined.
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This enables to group similar \meta{theorem}s and alter them at a late stage of
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document development in a unique manner, by only having to change the
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definition of the \meta{theorem group}, and not all \meta{theorem}s separately.
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The properties. such a \meta{theorem group} can hold are as follows
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\begin{description}
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\item[\kw{prename}] A prefix (any \meta{token list}) that will be inserted
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before the theorem name of each member of this \meta{theorem group}.
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\item[\kw{postname}] A suffix (any \meta{token list}) that will be
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inserted before the theorem name for each member of this \meta{theorem group}.
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This could be e.g.~some \enquote{$\star$} appended to the name to indicate
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variants of environments.
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\item[\kw{mapname}] A \meta{function} (some macro that takes exactly one argument)
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that is applied to the \kw{name}.
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\item[\kw{thmtools}] A \meta{clist} of key-value pairs that are passed to the underlying
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\pkg{thmtools} backend of the \meta{theorem}.
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This allows e.g.~to set the \kw{topskip} of a certain class of \meta{theorem}s.
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\end{description}
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The most versatile key here is certainly the \kw{thmtools} key,
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providing the most customization to an end user (like you).
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As mentioned, each \meta{theorem} can be member of arbitrary many \meta{theorem group}s,
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and will posses their corresponding properties.
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To adjust finer controlling of these \meta{theorem group}s, \meta{theorem group}s can inherit from each other, and \meta{theorem group}s are subject to a hierarchy that controls precedence in case
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of conflicting properties of different \meta{theorem group}s a \meta{theorem} may be part of.
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This hierarchy can of course be controlled by the user.
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\subsection{Grouped theorems}
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A \meta{grouped theorem} is just a theorem that is a member of
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a given set of groups (possibly empty).
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It behaves just a regular theorem, except that by changing the definition of
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its theorem groups, we can alter its behavior.
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It is the core concept of the \pkg{groupthm} package.
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For brevity, we will often talk about \enquote{theorems},
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although in fact we mean \enquote{grouped theorems}.
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\subsection{Theorem families}
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Often, one needs some small \meta{theorem variant}s of some \meta{theorem}, the most typical
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example being \vocab{starred} version of \meta{theorem}s that are not numbered
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in contrast to their counterparts.
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\begin{verbatim}
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\begin{theorem}
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This theorem is numbered.
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\end{theorem}
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\begin{theorem*}
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This theorem is not numbered.
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Probably because we do not want a reference to it.
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\end{theorem*}
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\end{verbatim}
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\todo{insert code example output}
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\pkg{groupthm} extends this idea and provides a versatile mechanism to define a
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\meta{theorem family}, which is based on some \meta{theorem name} and
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parses additional arguments / syntax to control the \meta{theorem groups}
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that this environment is a part of.
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So, in addition the name of a \meta{theorem}, the corresponding environment will
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accept some options and toggle the membership of certain \meta{theorem groups},
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thus further customizing its appearance.
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This can lead e.g.~to usages like the following:
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\begin{verbatim}
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\begin{theorem}*
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This theorem has a visual * at its name.
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\end{theorem}
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\end{verbatim}
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\todo{code}
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Providing this consists of two parts:
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declaring the \meta{theorem family} by listing the groups that can be toggled
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by this \meta{theorem family}, and declaring the actual option parsing
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of the \meta{theorem family}, which then controls the membership in these groups
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(and of course prior to this the definition of the desired \meta{theorem group}s).
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\subsection{General notions}
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In many cases, there are a number of variants of some command,
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call it for example \cs{Foo}.
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Then the documentation will look like
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%
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\begin{function}{\NewFoo, \RenewFoo, \ProvideFoo, \DeclareFoo}
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Defines some \kw{foo} \ldots
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\end{function}
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%
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and will not mention anything about the variants.
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This follows some general naming convention that also \pkg{xparse} uses,
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and is the following:
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\begin{description}
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\item[\cs{NewFoo}]
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Defines \kw{foo} if not defined already.
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This emits an error in case it has been defined yet.
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\item[\cs{RenewFoo}]
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Redefines \kw{foo} if defined already.
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This emits an error in case it has \emph{not} been defined yet.
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\item[\cs{ProvideFoo}]
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Defines \kw{foo} if it is not defined already.
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This does not emit an error if \kw{foo} is already defined
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(and has no effect in this case).
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\item[\cs{DeclareFoo}]
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Defines \kw{foo} in disregard of any
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existing definitions. Any old definition will be overwritten (if present).
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\end{description}
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%
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The documentation margin will list all variants that are available,
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they follow their respective conventions.
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\begin{texnote}
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The \pkg{thmtools} package, unfortunately, dose not follow this convention,
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as its \cs{declaretheorem} command actually behaves like a \cs{newtheorem}.
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The reason for this is that \pkg{amsthm} already defines \cs{newtheorem}.
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Thus, actually, calls to \cs{NewGroupedTheorem} will have an underlying
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\cs{declaretheorem}, but you do not have to bother with this.
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\end{texnote}
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\section{Theorem groups}
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\subsection{Defining theorem groups}
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\begin{function}{\NewTheoremGroup, \RenewTheoremGroup, \ProvideTheoremGroup, \DeclareTheoremGroup}
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\begin{syntax}
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\cs{NewTheoremGroup}[\meta{keys}]\{\meta{theorem group}\}
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\end{syntax}
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This introduces a new \meta{theorem group} with the given name.
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The \meta{keys} available are the same as introduced in \autoref{sec:theorem-groups}:
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\begin{description}
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\item
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\kw{prename} = \meta{token list}.
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Insert the \meta{token list} in front of the theorem name.
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\item
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\kw{postname} = \meta{token list}.
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Insert the \meta{token list} after the theorem name.
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\item
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\kw{mapname} = \meta{function}.
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Apply this \meta{function} to the theorem name.
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\item
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\kw{thmtools} = $\{$\meta{clist}$\}$.
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Pass these options to \pkg{thmtools}.
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\end{description}
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For uniqueness of the given options, the \meta{clist} given to the \kw{thmtools} key
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has to be surrounded by a pair of braces.
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\begin{texnote}
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The \kw{mapname} is expected to be a function of \cs{fun:n}.
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It is subject to an \kw{x}-type expansion prior to being passed further to \pkg{thmtools}.
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\end{texnote}
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\end{function}
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\subsection{Controlling theorem group precedence}
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\begin{function}{\DeclareTheoremGroupRule}
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\begin{syntax}
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\cs{DeclareTheoremGroupRule}[\meta{keyname}]%
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\{\meta{theorem group 1}\}\{\meta{relation}\}\{\meta{theorem group 2}\}
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\end{syntax}
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This declares some relation between the two theorem groups,
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controlling their order of application in case a theorem is member
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of both groups.
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The \meta{keyname} can be one of \kw{prename}, \kw{postname}, \kw{mapname}, \kw{thmtools}.
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If present, it declares the corresponding relation only for this subkey.
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This can lead to \meta{theorem group 1} overwriting \meta{theorem group 2} when given
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contradictory \pkg{thmtools} options, but the \kw{prename} of \meta{theorem group 1}
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being applied after the one of \meta{theorem group 2}.
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When the \meta{keyname} is not given, this applies to all keywords.
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\begin{texnote}
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The \meta{keyname} is just passed to the corresponding argument
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of the \kw{lthooks} package.
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If the option argument is not present, \kw{??} is used, this has the described effect.
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\end{texnote}
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The behavior of the relations is based on the \cs{DeclareHookRule} command
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from the \pkg{xparse} package, and all respective keys are in fact available,
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but typically not needed, so the reader of this manual is referred to the
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\todoref{lthooks} packages documentation for a list of the full keys.
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For us, the following list will suffice:
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\begin{description}
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\item[\kw{higher} or \kw{after} or \kw{\string>}]
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\meta{theorem group 1} takes precedence over \meta{theorem group 2}.
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Its \kw{prename} is applied after the one of \meta{theorem group 2}.
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\item[\kw{lower} or \kw{before} or \kw{\string<}]
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\meta{theorem group 2} takes precedence over \meta{theorem group 1}.
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Its \kw{prename} is applied after the one of \meta{theorem group 1}.
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\end{description}
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\begin{texnote}
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The \meta{relation} is first stripped,
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then checked if it matches either \kw{higher} or \kw{lower}
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and in this case replaced by the corresponding \pkg{lthooks} variant
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of the relation.
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The rest is passed as is to \pkg{lthooks} and thus subject to the usual
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normalization process of \pkg{lthooks}.
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\end{texnote}
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\end{function}
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\subsection{Inheritance of theorem groups}
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\begin{function}{\AddTheoremGroupParent}
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\begin{syntax}
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\cs{AddTheoremGroupParent}\{\meta{theorem group 1}\}\{\meta{theorem group 2}\}
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\end{syntax}
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Declares \meta{theorem group 1} to \enquote{inherit} all properties
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of \meta{theorem group 2}.
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In other words, \meta{theorem group 2} is a parent of \meta{theorem group 1}
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in a usual inheritance graph.
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The definitions of the groups themselves are unchanged,
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but each new theorem defined with \meta{theorem group 1} will also
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have the properties of \meta{theorem group 2}.
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Inheritance is transitive, when defining a new theorem, we just flatten out the
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inheritance graph and apply all properties.
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Inheritance is subject to the usual theorem group hierarchies as discussed in \todoref.
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This can even yield to situations, where \meta{theorem group 1} inherits
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from \meta{theorem group 2}, but \meta{theorem group 2} overwrites
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\meta{theorem group 1}.
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\end{function}
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\subsection{Appending to theorem groups}
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\begin{function}{\AppendToTheoremGroup}
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\begin{syntax}
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\cs{AppendToTheoremGroup}[\meta{keys}]\{\meta{theorem group}\}
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\end{syntax}
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Adds the properties given as \meta{keys} to the theorem group.
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The syntax for the \meta{keys} is the same as in \cs{NewTheoremGroup}.
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\end{function}
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\subsection{Default theorem groups}
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There are a number of theorem groups that \pkg{group them} will initially declare
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and that have certain special treatment in some places.
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\begin{function}{all}
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Every declared grouped theorem is a member of this group.
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Initially, this group has no effect (i.e.~an empty property list).
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It can be redefined by the user to alter the behavior of all grouped theorems
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in a unified way.
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It is the lowest theorem group in the hierarchy by default.
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\end{function}
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\begin{function}{starred}
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This is group that shall represent the standard variant of theorems that
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are called with a \enquote{*} in the environment name.
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Theorems of this group are not numbered.
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The user should not add theorems to this group by hand,
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as this is handled in a unified way by default.
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\todoref{}
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It is the highest theorem group in the hierarchy by default,
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except for \cs{unnumbered},
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with which it has no relation.
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\end{function}
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\addtocounter{footnote}{-1}
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\begin{function}{unnumbered}
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Theorems in this group are not numbered.
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It is the highest theorem group in the hierarchy by default,
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except for \cs{starred},
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with which it has no relation.
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\end{function}
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The reason for the two groups \kw{starred} and \kw{unnumbered}
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to both exist is that the \kw{starred} group is \emph{meant} to be applied
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to theorems that were called with a \enquote{*} in their name (thus the name),
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whereas the \enquote{unnumbered} group \emph{means} that the environment
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is 'just unnumbered'.
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This has two reasons:
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First, this enables more fine-tuning of the behavior of the theorems in post-processing
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of a document.
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Second, more importantly, this distinguishes semantically between the environments
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\kw{theorem} and \kw{theorem*}, even if \kw{theorem} is in the \kw{unnumbered} group.
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So assuming that \kw{theorem} is member of the \kw{unnumbered} group, both calls
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\begin{verbatim}
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\begin{theorem}
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This is not numbered.
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\end{theorem}
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\begin{theorem*}
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This is not numbered.
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\end{theorem*}
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\end{verbatim}
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are defined and will produce the same result by default, but we could still
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change the definition of the \kw{starred} group later to do anything we want.
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\begin{texnote}
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The mentioned hierarchies are kept intact for newly defined theorem groups,
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i.e.~for each new such group, two theorem group rules are created.
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\end{texnote}
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\section{Grouped Theorems}
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\subsection{Defining grouped theorems}
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\begin{function}{\NewGroupedTheorem, \ProvideGroupedTheorem}
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\begin{syntax}
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\cs{NewGroupedTheorem}[\meta{keys}]\{\meta{theorem name}\}
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\end{syntax}
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This defines \meta{theorem name} as a new theorem environment.
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Its properties can be set by the following keys:
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\begin{description}
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\item
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\kw{name} $=$ \meta{displayed name}.
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If given, this is the displayed name of the environment in the document.
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If not present, the \meta{theorem name} is also used as the \meta{displayed name}
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in capitalized form.
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\item
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\kw{group} $=$ \{\meta{clist}\}
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Makes this theorem a member of the listed groups.
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It will inherit all respective properties of these groups.
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If groups are present more than one time, this has no (additional) effect.
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\item
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\kw{thmtools} = \{\meta{clist}\}
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Passes these option to the \pkg{thmtools} environment that is declared internally.
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\end{description}
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\end{function}
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\begin{function}{\NewGroupedTheorem*,\ProvideGroupedTheorem*}
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\begin{syntax}
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\cs{NewGroupedTheorem*}[\meta{keys}]\{\meta{theorem name}\}
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\end{syntax}
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Behaves the same as \cs{NewGroupedTheorem},
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but also adds the theorem to the default \kw{unnumbered} group,
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thus resulting in the environment not being numbered.
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This is thus equivalent to using \cs{NewGroupedTheorem} and adding the
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\kw{unnumbered} group.
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\end{function}
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\begin{function}{\NewTheorem, \ProvideTheorem}
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\begin{syntax}
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\cs{NewTheorem}[\meta{keys}]\{\meta{theorem name}\}
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\end{syntax}
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This behaves essentially the same as \cs{NewGroupedTheorem},
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but will define two grouped theorems, namely \meta{theorem name} and \meta{theorem name*}.
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The \meta{theorem name*} environment has the same properties as the \meta{theorem name},
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but will be member of the \kw{starred} theorem group.
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It is thus not recommended to call \cs{NewTheorem}
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with an actual \enquote{*} in the environment name, since both environments
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will be generated.
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\end{function}
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\begin{function}{\NewTheorem*, \ProvideTheorem*}
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\begin{syntax}
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\cs{NewTheorem}[\meta{keys}]\{\meta{theorem name}\}
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\end{syntax}
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Combines the behavior of \cs{NewGroupedTheorem*} and \cs{NewTheorem}, thus
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declaring \meta{theorem} to (additionally) be member of the \kw{unnumbered}
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and \meta{theorem*} to (additionally) be member of the \kw{starred} group.
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As mentioned in \todoref, by default both environments will behave the same.
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\end{function}
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\subsection{Defining families of grouped theorems}
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\begin{function}{\NewGroupedTheoremFamily, \ProvideGroupedTheoremFamily}
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\begin{syntax}
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\cs{NewTheoremFamily}[\meta{keys}]\{\meta{theorem name}\}
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\end{syntax}
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Defines a family of grouped theorems.
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The \meta{keys} accept the same arguments as the \cs{NewGroupedTheorem} macro.
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However, for each \emph{subset} of the given groups,
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a grouped theorem is defined.
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These grouped theorems are not meant to be accessed directly (but could),
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so we omit their actual (internal) names here.
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To call these, some \kw{GroupedTheoremFamilyOptions} have to specified,
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see \cs{NewGroupedTheoremFamilyOptions}.
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\end{function}
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\begin{function}{\NewGroupedTheoremFamily*, \ProvideGroupedTheoremFamily*}
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Behaves the same as \cs{NewGroupedTheoremFamily}, but also adds each variant
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to the default \kw{unnumbered} group, thus resulting in the environments not being
|
|
numbered.
|
|
|
|
This is \emph{almost} equivalent to calling \cs{NewGroupedTheoremFamily}
|
|
with the \kw{unnumbered} group being present, as it does not generate the variants
|
|
where the \kw{unnumbered} group is not present.
|
|
\end{function}
|
|
|
|
\begin{function}{\NewTheoremFamily, \ProvideTheoremFamily}
|
|
This behaves essentially the same as \cs{NewGroupedTheoremFamily},
|
|
but will add the \kw{starred} group to the list of groups and also generate variants
|
|
for these.
|
|
|
|
It is thus not recommended to call \cs{NewTheoremFamily} with the \kw{starred}
|
|
group explicitly given, since this is added anyways.
|
|
\end{function}
|
|
|
|
\begin{function}{\NewTheoremFamily*, \ProvideTheoremFamily*}
|
|
Combines the behavior of \cs{NewGroupedTheoremFamily*} and \cs{NewTheoremFamily}, thus
|
|
declaring all variants to (additionally) be member of the \kw{unnumbered}
|
|
group, and also generates definitions with and without the \kw{starred} group.
|
|
|
|
As mentioned in \todoref, by default both environments will behave the same.
|
|
\end{function}
|
|
|
|
|
|
\begin{function}{\AddTheoremToGroup}
|
|
\begin{syntax}
|
|
\cs{AddTheoremToGroup}\{\meta{theorem group}\}
|
|
\end{syntax}
|
|
|
|
Means that the current invocation of a theorem family should
|
|
call the theorem variant with the given group.
|
|
|
|
Can only be used in the body of \cs{NewGroupedTheoremFamilyOptions} or similarly.
|
|
\end{function}
|
|
|
|
\begin{function}
|
|
{
|
|
\NewGroupedTheoremFamilyOptions, \RenewGroupedTheoremFamilyOptions,
|
|
\ProvideGroupedTheoremFamilyOptions, \DeclareGroupedTheoremFamilyOptions
|
|
}
|
|
\begin{syntax}
|
|
\cs{NewGroupedTheoremFamilyOptions}\{\meta{theorem name}\}\{\meta{argument specifiation}\}%
|
|
\{\meta{selection body}\}
|
|
\end{syntax}
|
|
|
|
Defines a new environment with options, given by \meta{theorem name}.
|
|
The \meta{argument specification} can be any valid \pkg{xparse} argument specification.
|
|
|
|
The \meta{selection body} is there to process the options of
|
|
the \meta{argument specification} and select which variant of the \meta{theorem name}
|
|
to enter.
|
|
The arguments are available as usual with \pkg{xparse} by \kw{\#1}, \kw{\#2}, \ldots
|
|
|
|
The body may also call any number of \cs{AddTheoremToGroup} calls,
|
|
which enables the corresponding groups.
|
|
|
|
When the environment is called within the document, the options are parsed
|
|
as with \pkg{xpars} and the \meta{selection body} is executed.
|
|
Immediately after, the theorem variant of \meta{theorem name} with the specified groups
|
|
by \cs{AddTheoremToGroup} is called.
|
|
|
|
At the end of the environment, the \meta{selection body} is executed again and the
|
|
called theorem variant is ended again.
|
|
|
|
The possible theorem variants that the newly declared environment will call
|
|
\emph{have to be generated subsequently} by a call to the \cs{NewGroupedTheoremFamily}
|
|
function.
|
|
|
|
\end{function}
|
|
|
|
\begin{function}
|
|
{
|
|
\NewGroupedTheoremFamilyOptions*, \RenewGroupedTheoremFamilyOptions*,
|
|
\ProvideGroupedTheoremFamilyOptions*, \DeclareGroupedTheoremFamilyOptions*
|
|
}
|
|
\begin{syntax}
|
|
\cs{NewGroupedTheoremFamilyOptions*}\{\meta{theorem name}\}\{\meta{argument specifiation}\}%
|
|
\{\meta{selection body}\}
|
|
\end{syntax}
|
|
|
|
Does the same as \cs{NewGroupedTheoremFamilyOptions},
|
|
but calls the variants with the additional \kw{unnumbered} group.
|
|
|
|
The possible theorem variants have to be generated
|
|
with the \cs{NewGroupedTheoremFamily*} command before.
|
|
|
|
\end{function}
|
|
|
|
\begin{function}
|
|
{
|
|
\NewTheoremFamilyOptions, \RenewTheoremFamilyOptions,
|
|
\ProvideTheoremFamilyOptions, \DeclareTheoremFamilyOptions
|
|
}
|
|
\begin{syntax}
|
|
\cs{NewTheoremFamilyOptions}\{\meta{theorem name}\}\{\meta{argument specifiation}\}%
|
|
\{\meta{selection body}\}
|
|
\end{syntax}
|
|
|
|
This behaves essentially the same as \cs{NewGroupedTheoremFamilyOptions},
|
|
but also declares the environment \meta{theorem name*},
|
|
which behaves the same but calls the theorem variants with the additional \kw{starred}
|
|
subgroup.
|
|
|
|
The possible theorem variants have to be generated with the \cs{NewTheoremFamily}
|
|
command before.
|
|
|
|
\end{function}
|
|
|
|
\begin{function}
|
|
{
|
|
\NewTheoremFamilyOptions*, \RenewTheoremFamilyOptions*,
|
|
\ProvideTheoremFamilyOptions*, \DeclareTheoremFamilyOptions*
|
|
}
|
|
|
|
Combines the behavior of \cs{NewGroupedTheoremFamilyOptions*} and \cs{NewTheoremFamilyOptions},
|
|
thus declaring both \meta{theorem name} and \meta{theorem name*} environments,
|
|
the latter calling the \kw{starred} variants of the theorem family,
|
|
and both of them calling \kw{unnumbered} variants of the family.
|
|
|
|
The possible theorem variants have to be generated with the \cs{NewTheoremFamily*}
|
|
command before.
|
|
|
|
\end{function}
|
|
|
|
%\section{\LaTeX3 interface}
|
|
|
|
\end{documentation}
|
|
|
|
\PrintIndex
|
|
\end{document}
|