|
|
|
|
%%% This file contains definitions of various useful macros and environments %%%
|
|
|
|
|
%%% Please add more macros here instead of cluttering other files with them. %%%
|
|
|
|
|
|
|
|
|
|
%%% Minor tweaks of style
|
|
|
|
|
|
|
|
|
|
% These macros employ a little dirty trick to convince LaTeX to typeset
|
|
|
|
|
% chapter headings sanely, without lots of empty space above them.
|
|
|
|
|
% Feel free to ignore.
|
|
|
|
|
\makeatletter
|
|
|
|
|
\def\@makechapterhead#1{
|
|
|
|
|
{\parindent \z@ \raggedright \normalfont
|
|
|
|
|
\Huge\bfseries \thechapter. #1
|
|
|
|
|
\par\nobreak
|
|
|
|
|
\vskip 20\p@
|
|
|
|
|
}}
|
|
|
|
|
\def\@makeschapterhead#1{
|
|
|
|
|
{\parindent \z@ \raggedright \normalfont
|
|
|
|
|
\Huge\bfseries #1
|
|
|
|
|
\par\nobreak
|
|
|
|
|
\vskip 20\p@
|
|
|
|
|
}}
|
|
|
|
|
\makeatother
|
|
|
|
|
|
|
|
|
|
% This macro defines a chapter, which is not numbered, but is included
|
|
|
|
|
% in the table of contents.
|
|
|
|
|
\def\chapwithtoc#1{
|
|
|
|
|
\chapter*{#1}
|
|
|
|
|
\addcontentsline{toc}{chapter}{#1}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
% Draw black "slugs" whenever a line overflows, so that we can spot it easily.
|
|
|
|
|
\overfullrule=1mm
|
|
|
|
|
|
|
|
|
|
%%% Macros for definitions, theorems, claims, examples, ... (requires amsthm package)
|
|
|
|
|
|
|
|
|
|
\theoremstyle{plain}
|
|
|
|
|
\newtheorem{thm}{Theorem}
|
|
|
|
|
\newtheorem{lemma}[thm]{Lemma}
|
|
|
|
|
\newtheorem{claim}[thm]{Claim}
|
|
|
|
|
|
|
|
|
|
\theoremstyle{plain}
|
|
|
|
|
\newtheorem{defn}{Definition}
|
|
|
|
|
|
|
|
|
|
\theoremstyle{remark}
|
|
|
|
|
\newtheorem*{cor}{Corollary}
|
|
|
|
|
\newtheorem*{rem}{Remark}
|
|
|
|
|
\newtheorem*{example}{Example}
|
|
|
|
|
|
|
|
|
|
%%% An environment for proofs
|
|
|
|
|
|
|
|
|
|
\newenvironment{myproof}{
|
|
|
|
|
\par\medskip\noindent
|
|
|
|
|
\textit{Proof}.
|
|
|
|
|
}{
|
|
|
|
|
\newline
|
|
|
|
|
\rightline{$\qedsymbol$}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
%%% An environment for typesetting of program code and input/output
|
|
|
|
|
%%% of programs. (Requires the fancyvrb package -- fancy verbatim.)
|
|
|
|
|
|
|
|
|
|
\DefineVerbatimEnvironment{code}{Verbatim}{fontsize=\small, frame=single}
|
|
|
|
|
|
|
|
|
|
%%% The field of all real and natural numbers
|
|
|
|
|
\newcommand{\R}{\mathbb{R}}
|
|
|
|
|
\newcommand{\N}{\mathbb{N}}
|
|
|
|
|
|
|
|
|
|
%%% Useful operators for statistics and probability
|
|
|
|
|
\DeclareMathOperator{\pr}{\textsf{P}}
|
|
|
|
|
\DeclareMathOperator{\E}{\textsf{E}\,}
|
|
|
|
|
\DeclareMathOperator{\var}{\textrm{var}}
|
|
|
|
|
\DeclareMathOperator{\sd}{\textrm{sd}}
|
|
|
|
|
|
|
|
|
|
%%% Transposition of a vector/matrix
|
|
|
|
|
\newcommand{\T}[1]{#1^\top}
|
|
|
|
|
|
|
|
|
|
%%% Various math goodies
|
|
|
|
|
\newcommand{\goto}{\rightarrow}
|
|
|
|
|
\newcommand{\gotop}{\stackrel{P}{\longrightarrow}}
|
|
|
|
|
\newcommand{\maon}[1]{o(n^{#1})}
|
|
|
|
|
\newcommand{\abs}[1]{\left|{#1}\right|}
|
|
|
|
|
\newcommand{\dint}{\int_0^\tau\!\!\int_0^\tau}
|
|
|
|
|
\newcommand{\isqr}[1]{\frac{1}{\sqrt{#1}}}
|
|
|
|
|
|
|
|
|
|
%%% Various table goodies
|
|
|
|
|
\newcommand{\pulrad}[1]{\raisebox{1.5ex}[0pt]{#1}}
|
|
|
|
|
\newcommand{\mc}[1]{\multicolumn{1}{c}{#1}}
|
|
|
|
|
|
|
|
|
|
% Old habbits die hard.
|
|
|
|
|
\newcommand{\uv}[1]{\enquote{#1}}
|
