diff --git a/main.tex b/main.tex index 641875d..456147f 100644 --- a/main.tex +++ b/main.tex @@ -15,10 +15,10 @@ For errata and more stuff, see \url{https://sarielhp.org/book/} \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 \[\left( \floor{\sqrt{d}}+1 \right)^d \leq |P|\leq \left( \ceil{\sqrt{d}}+1 \right)^d. \] -\end{oneshot} +\end{exercise} hmm... the first exercise in this book is wrong. See \url{https://sarielhp.org/book/errata.pdf}. The stated lowerbound is actually an upperbound. \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 $d$. \end{proof} -\begin{oneshot}{1.2} +\begin{exercise} Compute clustering radius -\end{oneshot} +\end{exercise} \end{document} diff --git a/xenotes.sty b/xenotes.sty index e513212..e3c5023 100644 --- a/xenotes.sty +++ b/xenotes.sty @@ -26,12 +26,14 @@ \setCJKsansfont{Source Han Serif SC} \setCJKmonofont{Source Han Serif SC} \RequirePackage[charter]{mathdesign} % math font only for serif mode +\RequirePackage{amsmath} +\RequirePackage{eucal} +\RequirePackage{microtype} \fi % \setCJKmainfont{SourceHanSerifSC-Regular.otf}[BoldFont={SourceHanSerifSC-Bold.otf}, ItalicFont=SourceHanSerifSC-Regular.otf] \RequirePackage[margin=1in]{geometry} -\RequirePackage{amsmath} \RequirePackage[dvipsnames]{xcolor} \RequirePackage[colorlinks=true,urlcolor=Blue,citecolor=Green,linkcolor=BrickRed,unicode]{hyperref} @@ -43,8 +45,6 @@ \RequirePackage{graphicx} % essentials -% \RequirePackage{microtype} -\RequirePackage{eucal} \RequirePackage[nocompress]{cite} % other convenient stuff \RequirePackage{enumerate} %\usepackage{pgf,tikz} @@ -57,18 +57,21 @@ \newaliascnt{corollary}{theorem} \newaliascnt{conjecture}{theorem} \newaliascnt{proposition}{theorem} +\newaliascnt{exercise}{theorem} \newtheorem{lemma}{Lemma}[section] \newtheorem{corollary}{Corollary}[section] \newtheorem{conjecture}{Conjecture}[section] \newtheorem{proposition}{Proposition}[section] \newtheorem{problem}{Problem} +\newtheorem{exercise}{Ex}[section] \newcommand{\lemmaautorefname}{Lemma} \newcommand{\corollaryautorefname}{Corollary} \newcommand{\conjectureautorefname}{Conjecture} \newcommand{\propositionautorefname}{Proposition} \newcommand{\problemautorefname}{Problem} +\newcommand{\exerciseautorefname}{Exercise} \newenvironment{definition}[1][Definition]{\begin{trivlist} \item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}