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author | Karl Berry <karl@freefriends.org> | 2013-04-09 16:31:58 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2013-04-09 16:31:58 +0000 |
commit | d6730e96b1acc94ef3a26f9079e57099be823dff (patch) | |
tree | 2bc872d6369d464c590c9a071de5274beca219c7 /Master/texmf-dist/doc/latex/tcolorbox/tcolorbox.doc.theorems.tex | |
parent | 92897266fb13289d7ef1da636a65bd9c444864f3 (diff) |
tcolorbox (9apr13)
git-svn-id: svn://tug.org/texlive/trunk@29788 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/tcolorbox/tcolorbox.doc.theorems.tex')
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diff --git a/Master/texmf-dist/doc/latex/tcolorbox/tcolorbox.doc.theorems.tex b/Master/texmf-dist/doc/latex/tcolorbox/tcolorbox.doc.theorems.tex new file mode 100644 index 00000000000..c890a8a6223 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tcolorbox/tcolorbox.doc.theorems.tex @@ -0,0 +1,404 @@ +% !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} + + + |