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authorKarl Berry <karl@freefriends.org>2013-04-09 16:31:58 +0000
committerKarl Berry <karl@freefriends.org>2013-04-09 16:31:58 +0000
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tree2bc872d6369d464c590c9a071de5274beca219c7 /Master/texmf-dist/doc/latex/tcolorbox/tcolorbox.doc.theorems.tex
parent92897266fb13289d7ef1da636a65bd9c444864f3 (diff)
tcolorbox (9apr13)
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+% !TeX root = tcolorbox.tex
+% include file of tcolorbox.tex (manual of the LaTeX package tcolorbox)
+\clearpage
+\section{Library 'theorems'}\label{sec:theorems}
+The library is loaded by a package option or inside the preamble by:
+\begin{dispListing}
+\tcbuselibrary{theorems}
+\end{dispListing}
+This also loads the package |amsmath|.
+
+\subsection{Macros of the Library}
+
+\begin{docCommand}{tcbmaketheorem}{\marg{name}\marg{display name}\marg{options}\marg{counter}\marg{prefix}}
+ Creates a new environment \meta{name} based on |tcolorbox| to frame a
+ (mathematical) theorem. The \meta{display name} is used in the title line
+ with a number, e.\,g. \mbox{\flqq Theorem 5.1\frqq}.
+ The \meta{options} are given to the underlying |tcolorbox| to control
+ the appearance.
+ The \meta{counter} is used for automatic numbering.
+ The new environment \meta{name} takes one optional and two mandatory
+ parameters. The optional parameter supplements the options and should be
+ used only in rare cases.
+ The first mandatory parameter is the title text for the theorem and
+ the second mandatory parameter is a \meta{marker}. The theorem is
+ automatically labeled with \meta{prefix}|:|\meta{marker}.
+\begin{dispExample}
+\tcbmaketheorem{theo}{My Theorem}{colback=green!5,colframe=green!35!black,
+ fonttitle=\bfseries}{texercise}{th}
+
+\begin{theo}{This is my title}{theoexample}
+ This is the text of the theorem. As can be seen, the counter \texttt{texercise}
+ is reused. The theorem is numbered with \ref{th:theoexample} and is
+ given on page \pageref{th:theoexample}.
+\end{theo}
+\end{dispExample}
+\end{docCommand}
+
+
+\begin{docCommand}{tcboxmath}{\oarg{options}\marg{mathematical box content}}
+ Creates a \refEnv{tcolorbox} which is fitted to the width of the given
+ \meta{mathematical box content}. This box is intended to be applied as
+ part of a larger formula and may be used as replacement for the |\boxed|
+ macro of |amsmath|.
+
+\begin{dispExample}
+\begin{equation}
+\tcbset{fonttitle=\scriptsize}
+\tcboxmath[colback=LightBlue!25!white,colframe=blue]{ a^2 = 16 }
+\quad \Rightarrow \quad
+\tcboxmath[colback=Salmon!25!white,colframe=red,title=Implication]%
+ { a = 4 ~\vee~ a=-4. }
+\end{equation}
+\end{dispExample}
+\end{docCommand}
+
+\clearpage
+\begin{docCommand}{tcbhighmath}{\oarg{options}\marg{mathematical box content}}
+ This is a special case of the \refCom{tcboxmath} macro which uses
+ the style \refKey{/tcb/highlight math}.
+ It is intended to provide context sensitive highlighting of formula parts.
+ The color settings via \refKey{/tcb/highlight math style} may be different
+ inside theorems or other colored areas and outside.
+
+\begin{dispExample}
+\tcbset{myformula/.style={colback=yellow!10!white,colframe=red!50!black,
+ highlight math style={colback=LightBlue!50!white,colframe=Navy}}}
+
+\begin{align}
+ \tcbhighmath{\sum\limits_{n=1}^{\infty} \frac{1}{n}} &= \infty.\\
+ \int x^2 ~\text{d}x &= \frac13 x^3 + c.
+\end{align}
+
+\begin{tcolorbox}[ams align,myformula]
+ \tcbhighmath{\sum\limits_{n=1}^{\infty} \frac{1}{n}} &= \infty.\\
+ \int x^2 ~\text{d}x &= \frac13 x^3 + c.
+\end{tcolorbox}
+\end{dispExample}
+\end{docCommand}
+
+
+\clearpage
+\subsection{Option Keys of the Library}
+
+
+\begin{docTcbKey}{theorem}{=\marg{display name}\marg{counter}\marg{title}\marg{marker}}{no default}
+ This key is internally used by \refCom{tcbmaketheorem}, but can be used
+ directly in a |tcolorbox| for a more flexible approach.
+ The \meta{display name} is used together with the increased \meta{counter} value
+ and the \meta{title} for the title line of the box. Additionally, a
+ |\label| with the given \meta{marker} is created.
+\begin{dispExample}
+\begin{tcolorbox}[colback=green!10,colframe=green!50!black,arc=4mm,
+ theorem={Test}{texercise}{Direct usage}{myMarker}]
+Here, we see the test \ref{myMarker}.
+\end{tcolorbox}
+\end{dispExample}
+For a common appearance inside the document, the key |theorem| should not be
+used directly as in the example above, but as part of a new environment
+created by hand or using \refCom{tcbmaketheorem}.
+\end{docTcbKey}
+
+
+\begin{docTcbKey}{highlight math}{}{style, no value}
+ Predefined style which is used for \refCom{tcbhighmath}.
+ It can be changed comfortable with \refKey{/tcb/highlight math style}.
+\end{docTcbKey}
+
+
+\begin{docTcbKey}{highlight math style}{=\meta{style definition}}{style, no default}
+ Changes the definition for \refKey{/tcb/highlight math} to the given
+ \meta{style definition}. See \refCom{tcbhighmath} for an example.
+\end{docTcbKey}
+
+\begin{docTcbKey}{math upper}{}{style, no value}
+ Sets the upper part to mathematical mode with font |\displaystyle|.
+\end{docTcbKey}
+
+\begin{docTcbKey}{math lower}{}{style, no value}
+ Sets the lower part to mathematical mode with font |\displaystyle|.
+\end{docTcbKey}
+
+\begin{docTcbKey}{math}{}{style, no value}
+ Sets the upper part \emph{and} lower part to mathematical mode with font |\displaystyle|.
+\begin{dispExample}
+\begin{tcolorbox}[math,colback=yellow!10!white,colframe=red!50!black]
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+
+\clearpage
+\begin{marker}
+ The following styles are only tested to work with the original |amsmath| environments.
+ If e.g. the |equation| environment is redefined as |gather|, then
+ \refKey{/tcb/ams equation} should / could not be used. Obviously, you are encouraged
+ to use \refKey{/tcb/ams gather} in this case.
+\end{marker}
+
+\begin{docTcbKey}{ams equation upper}{}{style, no value}
+ Adds an |amsmath| |equation| environment to the begin and to the end
+ if the upper part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams equation lower}{}{style, no value}
+ Adds an |amsmath| |equation| environment to the begin and to the end
+ if the lower part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams equation}{}{style, no value}
+ Adds an |amsmath| |equation| environment to the begin and to the end
+ if the upper \emph{and} lower part.
+\begin{dispExample}
+\begin{tcolorbox}[ams equation,colback=yellow!10!white,colframe=red!50!black]
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams equation* upper}{}{style, no value}
+ Adds an |amsmath| |equation*| environment to the begin and to the end
+ if the upper part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams equation* lower}{}{style, no value}
+ Adds an |amsmath| |equation*| environment to the begin and to the end
+ if the lower part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams equation*}{}{style, no value}
+ Adds an |amsmath| |equation*| environment to the begin and to the end
+ if the upper \emph{and} lower part.
+\begin{dispExample}
+\begin{tcolorbox}[ams equation*,colback=yellow!10!white,colframe=red!50!black]
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+\clearpage
+\begin{docTcbKey}{ams align upper}{}{style, no value}
+ Adds an |amsmath| |align| environment to the begin and to the end
+ if the upper part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams align lower}{}{style, no value}
+ Adds an |amsmath| |align| environment to the begin and to the end
+ if the lower part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams align}{}{style, no value}
+ Adds an |amsmath| |align| environment to the begin and to the end
+ if the upper \emph{and} lower part.
+\begin{dispExample}
+\begin{tcolorbox}[ams align,colback=yellow!10!white,colframe=red!50!black]
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} &= \infty.\\
+ \int x^2 ~\text{d}x &= \frac13 x^3 + c.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams align* upper}{}{style, no value}
+ Adds an |amsmath| |align*| environment to the begin and to the end
+ if the upper part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams align* lower}{}{style, no value}
+ Adds an |amsmath| |align*| environment to the begin and to the end
+ if the lower part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams align*}{}{style, no value}
+ Adds an |amsmath| |align*| environment to the begin and to the end
+ if the upper \emph{and} lower part.
+\begin{dispExample}
+\begin{tcolorbox}[ams align*,colback=yellow!10!white,colframe=red!50!black]
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} &= \infty.\\
+ \int x^2 ~\text{d}x &= \frac13 x^3 + c.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+\clearpage
+\begin{docTcbKey}{ams gather upper}{}{style, no value}
+ Adds an |amsmath| |gather| environment to the begin and to the end
+ if the upper part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams gather lower}{}{style, no value}
+ Adds an |amsmath| |gather| environment to the begin and to the end
+ if the lower part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams gather}{}{style, no value}
+ Adds an |amsmath| |gather| environment to the begin and to the end
+ if the upper \emph{and} lower part.
+\begin{dispExample}
+\begin{tcolorbox}[ams gather,colback=yellow!10!white,colframe=red!50!black]
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.\\
+ \int x^2 ~\text{d}x = \frac13 x^3 + c.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams gather* upper}{}{style, no value}
+ Adds an |amsmath| |gather*| environment to the begin and to the end
+ if the upper part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams gather* lower}{}{style, no value}
+ Adds an |amsmath| |gather*| environment to the begin and to the end
+ if the lower part.
+\end{docTcbKey}
+
+\begin{docTcbKey}{ams gather*}{}{style, no value}
+ Adds an |amsmath| |gather*| environment to the begin and to the end
+ if the upper \emph{and} lower part.
+\begin{dispExample}
+\begin{tcolorbox}[ams gather*,colback=yellow!10!white,colframe=red!50!black]
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.\\
+ \int x^2 ~\text{d}x = \frac13 x^3 + c.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+
+\clearpage
+\begin{docTcbKey}{ams nodisplayskip upper}{}{style, no value}
+ Neutralizes the |\abovedisplayskip| of a following |align| or |gather|
+ environment for the upper part. Note that the text content has to
+ start with such a formula.
+\end{docTcbKey}
+
+
+\begin{docTcbKey}{ams nodisplayskip lower}{}{style, no value}
+ Neutralizes the |\abovedisplayskip| of a following |align| or |gather|
+ environment for the lower part. Note that the text content has to
+ start with such a formula.
+\end{docTcbKey}
+
+
+\begin{docTcbKey}{ams nodisplayskip}{}{style, no value}
+ Neutralizes the |\abovedisplayskip| of a following |align| or |gather|
+ environment for the upper part \emph{and} lower part.
+ Note that the text content has to start with such a formula.
+\begin{dispExample}
+\begin{tcolorbox}[ams nodisplayskip,colback=yellow!10!white,colframe=red!50!black]
+ \begin{gather}
+ \sum\limits_{n=1}^{\infty} \frac{1}{n} = \infty.\\
+ \int x^2 ~\text{d}x = \frac13 x^3 + c.
+ \end{gather}
+ And now for something completely different.
+\end{tcolorbox}
+\end{dispExample}
+\end{docTcbKey}
+
+
+%
+\clearpage
+\subsection{Examples for Definitions and Theorems}
+In the following, the application of \refCom{tcbmaketheorem}
+to highlight mathematical definitions, theorems, or the like is demonstrated.
+
+At first, additional |tcb| keys are created for the appearance of
+the colored boxes. It is assumed that theorems and corollaries should be
+identically colored.
+All following environments are numbered with a common counter, but this
+can be changed easily. Here, the counter output is supplemented by
+the section number.
+
+\begin{dispListing}
+%\newcounter{mytheorem}[section] % preamble
+\def\themytheorem{\thesection.\arabic{mytheorem}}
+
+\tcbset{
+ defstyle/.style={fonttitle=\bfseries\upshape, fontupper=\slshape,
+ arc=0mm, colback=blue!5!white,colframe=blue!75!black},
+ theostyle/.style={fonttitle=\bfseries\upshape, fontupper=\slshape,
+ colback=red!10!white,colframe=red!75!black},
+}
+\end{dispListing}
+\tcbusetemp
+
+By \refCom{tcbmaketheorem}, commonly numbered theorem environments are
+created now. |defstyle| and |theostyle| are used for the appearance.
+
+\begin{dispListing}
+\tcbmaketheorem{Definition}{Definition}{defstyle}{mytheorem}{def}
+\tcbmaketheorem{Theorem}{Theorem}{theostyle}{mytheorem}{theo}
+\tcbmaketheorem{Corollary}{Corollary}{theostyle}{mytheorem}{cor}
+\end{dispListing}
+\tcbusetemp
+
+Now, everything is prepared for the following examples.
+
+\begin{dispExample}
+The following theorem is numbered as Theorem \ref{theo:diffbarstetig} and
+referenced with the marker \texttt{theo:diffbarstetig}.\bigskip
+
+\begin{Theorem}{Differenzierbarkeit bedingt Stetigkeit, wobei diese Benennung
+ zu Testzwecken ungew\"{o}hnlich lang ist}{diffbarstetig}%
+ Eine Funktion $f:I\to\mathbb{R}$ ist in $x_0\in I$ stetig, wenn $f$ in
+ $x_0$ differenzierbar ist.
+\end{Theorem}
+\end{dispExample}
+
+
+\begin{dispExample}
+The following definition is numbered as Definition \ref{def:diffbarkeit} and
+referenced with the marker \texttt{def:diffbarkeit}.\bigskip
+
+\begin{Definition}{Differenzierbarkeit}{diffbarkeit}
+ Eine Funktion $f:~I\to\mathbb{R}$ auf einem Intervall $I$ hei\ss{}t in
+ $x_0\in I$ differenzierbar oder linear approximierbar,
+ wenn der Grenzwert
+ \begin{equation*}
+ \lim\limits_{x\to x_0}\frac{f(x)-f(x_0)}{x-x_0}=
+ \lim\limits_{h\to 0}\frac{f(x_0+h)-f(x_0)}{h}
+ \end{equation*}
+ existiert. Bei Existenz hei\ss{}t dieser Grenzwert Ableitung
+ oder Differentialquotient von $f$ in $x_0$ und man
+ schreibt f\"{u}r ihn
+ \begin{equation*}
+ f'(x_0)\quad\text{oder}\quad\frac{df}{dx}(x_0).
+ \end{equation*}
+\end{Definition}
+\end{dispExample}
+
+
+\begin{dispExample}
+The following corollary is numbered as Corollary \ref{cor:nullstellen} and
+referenced with the marker \texttt{cor:nullstellen}.\bigskip
+
+\begin{Corollary}{Nullstellenexistenz}{nullstellen}
+ Ist $f:[a,b]\to\mathbb{R}$ stetig und haben $f(a)$ und $f(b)$ entgegengesetzte
+ Vorzeichen, also $f(a)f(b)<0$, so besitzt $f$ eine Nullstelle $x_0\in]a,b[$,
+ also $f(x_0)=0$.
+\end{Corollary}
+\end{dispExample}
+
+
+\begin{dispExample}
+\begin{Theorem}[boxrule=2mm,toptitle=-1.5mm,bottomtitle=-1.5mm]{%
+ Hinreichende Bedingung f\"{u}r Wendepunkte}{wendehinreichend}%
+ $f$ sei eine auf einem Intervall $]a,b[$ dreimal stetig differenzierbare Funktion.
+ Ist $f''(x_0)=0$ in $x_0\in]a,b[$ und $f'''(x_0)\ne 0$, so ist
+ $(x_0,f(x_0))$ ein Wendepunkt von $f$.
+\end{Theorem}
+\end{dispExample}
+
+You need more attention for your theorems? Here, you are \ldots
+
+\begin{dispExample}
+% tcbuselibrary{skins} % preamble
+\begin{Theorem}[enhanced,frame style={circular glow={fill=yellow}},
+ watermark color=red!35!white,
+ watermark text={Overacting\\Fundamental Theorem}]%
+ {Fundamental Theorem of Theorems}{fundamental}%
+ \lipsum[1-2]
+\end{Theorem}
+\end{dispExample}
+
+
+