diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/xsim/examples/xsim.texsx-13635.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/xsim/examples/xsim.texsx-13635.tex | 70 |
1 files changed, 70 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/xsim/examples/xsim.texsx-13635.tex b/Master/texmf-dist/doc/latex/xsim/examples/xsim.texsx-13635.tex new file mode 100644 index 00000000000..3b52ce46b24 --- /dev/null +++ b/Master/texmf-dist/doc/latex/xsim/examples/xsim.texsx-13635.tex @@ -0,0 +1,70 @@ +% https://tex.stackexchange.com/q/13635/ +\documentclass{article} +\usepackage{xsim} + +\DeclareExerciseEnvironmentTemplate{theorem:remark} + { + \par\addvspace{\baselineskip} + \noindent + \textit{% + \IfInsideSolutionF{\XSIMmixedcase{\GetExerciseName}~}% + \GetExerciseProperty{counter}}% + \GetExercisePropertyT{subtitle}{ \textup{(#1)}}% + . % + } + {\par\addvspace{\baselineskip}} + +\DeclareExerciseHeadingTemplate{exercises}{\subsection*{Exercises}} + +\xsimsetup{ + exercise/template = theorem:remark , + exercise/within = section , + exercise/the-counter = \thesection.\arabic{exercise} , + print-collection/headings = true , + print-collection/headings-template = exercises +} + +\DeclareExerciseCollection{prime numbers} +\DeclareExerciseCollection{Zeta function} + +\begin{document} + +\collectexercises{prime numbers} +\section{Prime Numbers} + +A \emph{prime number} is a positive integer other than $1$ that is only +divisible by $1$ and itself. + +\begin{exercise}[subtitle=Euclid's Theorem] + \label{ex:euclid} + Show that there are infinitely many prime numbers. +\end{exercise} + +As you will show in Exercise \ref{ex:euclid}, there are infinitely many +primes. The number of primes that are smaller than a given natural number $n$ +is denoted $\pi(n)$. + +\begin{exercise} + Find an asymptotic formula for $\pi(n)$. \emph{Hint:} You might find + Exercise \ref{ex:zeta} helpful. +\end{exercise} +\collectexercisesstop{prime numbers} + +\printcollection{prime numbers} + +\collectexercises{Zeta function} +\section{Zeta function} + +The zeta function is given by $\zeta(s) = \sum_{n=1}^\infty n^{-s}$, where $s$ +is a complex number with real part bigger than $1$. +\begin{exercise}\label{ex:zeta} + Extend $\zeta$ as far as possible and find all zeros + of the function. +\end{exercise} +For example $\zeta(2) = \frac{\pi^2}{6}$. + +\collectexercisesstop{Zeta function} + +\printcollection{Zeta function} + +\end{document} |