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exercise env
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Yu Cong
2025-08-05 09:37:45 +08:00
parent 66dacb1dfc
commit edb9aaaa43
2 changed files with 10 additions and 7 deletions
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8
main.tex
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@@ -15,10 +15,10 @@
For errata and more stuff, see \url{https://sarielhp.org/book/} For errata and more stuff, see \url{https://sarielhp.org/book/}
\section{Grid} \section{Grid}
\begin{oneshot}{1.1} \begin{exercise}\label{ex1.1}
Let $P$ be a max cardinality point set contained in the $d$-dimensional unit hypercube such that the smallest distance of point pairs in $P$ is 1. Prove that Let $P$ be a max cardinality point set contained in the $d$-dimensional unit hypercube such that the smallest distance of point pairs in $P$ is 1. Prove that
\[\left( \floor{\sqrt{d}}+1 \right)^d \leq |P|\leq \left( \ceil{\sqrt{d}}+1 \right)^d. \] \[\left( \floor{\sqrt{d}}+1 \right)^d \leq |P|\leq \left( \ceil{\sqrt{d}}+1 \right)^d. \]
\end{oneshot} \end{exercise}
hmm... the first exercise in this book is wrong. See \url{https://sarielhp.org/book/errata.pdf}. hmm... the first exercise in this book is wrong. See \url{https://sarielhp.org/book/errata.pdf}.
The stated lowerbound is actually an upperbound. The stated lowerbound is actually an upperbound.
\begin{proof} \begin{proof}
@@ -36,9 +36,9 @@ n &\geq 1/\vol(1b^d)\\
The last line is greater than $(\sqrt{d}/5)^d$ for large enough $d$. The last line is greater than $(\sqrt{d}/5)^d$ for large enough $d$.
\end{proof} \end{proof}
\begin{oneshot}{1.2} \begin{exercise}
Compute clustering radius Compute clustering radius
\end{oneshot} \end{exercise}
\end{document} \end{document}

9
xenotes.sty
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@@ -26,12 +26,14 @@
\setCJKsansfont{Source Han Serif SC} \setCJKsansfont{Source Han Serif SC}
\setCJKmonofont{Source Han Serif SC} \setCJKmonofont{Source Han Serif SC}
\RequirePackage[charter]{mathdesign} % math font only for serif mode \RequirePackage[charter]{mathdesign} % math font only for serif mode
\RequirePackage{amsmath}
\RequirePackage{eucal}
\RequirePackage{microtype}
\fi \fi
% \setCJKmainfont{SourceHanSerifSC-Regular.otf}[BoldFont={SourceHanSerifSC-Bold.otf}, ItalicFont=SourceHanSerifSC-Regular.otf] % \setCJKmainfont{SourceHanSerifSC-Regular.otf}[BoldFont={SourceHanSerifSC-Bold.otf}, ItalicFont=SourceHanSerifSC-Regular.otf]
\RequirePackage[margin=1in]{geometry} \RequirePackage[margin=1in]{geometry}
\RequirePackage{amsmath}
\RequirePackage[dvipsnames]{xcolor} \RequirePackage[dvipsnames]{xcolor}
\RequirePackage[colorlinks=true,urlcolor=Blue,citecolor=Green,linkcolor=BrickRed,unicode]{hyperref} \RequirePackage[colorlinks=true,urlcolor=Blue,citecolor=Green,linkcolor=BrickRed,unicode]{hyperref}
@@ -43,8 +45,6 @@
\RequirePackage{graphicx} % essentials \RequirePackage{graphicx} % essentials
% \RequirePackage{microtype}
\RequirePackage{eucal}
\RequirePackage[nocompress]{cite} % other convenient stuff \RequirePackage[nocompress]{cite} % other convenient stuff
\RequirePackage{enumerate} \RequirePackage{enumerate}
%\usepackage{pgf,tikz} %\usepackage{pgf,tikz}
@@ -57,18 +57,21 @@
\newaliascnt{corollary}{theorem} \newaliascnt{corollary}{theorem}
\newaliascnt{conjecture}{theorem} \newaliascnt{conjecture}{theorem}
\newaliascnt{proposition}{theorem} \newaliascnt{proposition}{theorem}
\newaliascnt{exercise}{theorem}
\newtheorem{lemma}{Lemma}[section] \newtheorem{lemma}{Lemma}[section]
\newtheorem{corollary}{Corollary}[section] \newtheorem{corollary}{Corollary}[section]
\newtheorem{conjecture}{Conjecture}[section] \newtheorem{conjecture}{Conjecture}[section]
\newtheorem{proposition}{Proposition}[section] \newtheorem{proposition}{Proposition}[section]
\newtheorem{problem}{Problem} \newtheorem{problem}{Problem}
\newtheorem{exercise}{Ex}[section]
\newcommand{\lemmaautorefname}{Lemma} \newcommand{\lemmaautorefname}{Lemma}
\newcommand{\corollaryautorefname}{Corollary} \newcommand{\corollaryautorefname}{Corollary}
\newcommand{\conjectureautorefname}{Conjecture} \newcommand{\conjectureautorefname}{Conjecture}
\newcommand{\propositionautorefname}{Proposition} \newcommand{\propositionautorefname}{Proposition}
\newcommand{\problemautorefname}{Problem} \newcommand{\problemautorefname}{Problem}
\newcommand{\exerciseautorefname}{Exercise}
\newenvironment{definition}[1][Definition]{\begin{trivlist} \newenvironment{definition}[1][Definition]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}} \item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}