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- % Style helpers for use in Math M413
- \usepackage[leqno]{amsmath}
- \usepackage{amsfonts}
- \usepackage{amssymb}
- \usepackage{amsthm}
- \usepackage{latexsym}
- \numberwithin{equation}{section}
- \DeclareMathOperator{\suchthat}{s.t.}
- \DeclareMathOperator{\st}{\;|\;}
- \DeclareMathOperator{\lub}{lub}
- \DeclareMathOperator{\glb}{glb}
- \DeclareMathOperator{\C}{C}
- \DeclareMathOperator{\Rl}{R_L}
- \DeclareMathOperator{\Rm}{R_M}
- \DeclareMathOperator{\Poly}{\mathcal{P}}
- \DeclareMathOperator{\NPoly}{\mathcal{NP}}
- \DeclareMathOperator{\outdegree}{out-degree}
- \DeclareMathOperator{\indegree}{in-degree}
- % Abbreviations for Commonly used sets
- \newcommand{\field}[1]{\mathbb{#1}}
- \newcommand{\Q}{\field{Q}} % Rational numbers
- \newcommand{\N}{\field{N}} % Natural numbers
- \newcommand{\R}{\field{R}} % Real numbers
- \newcommand{\Z}{\field{Z}} % Integers
- \newcommand{\Zp}{\field{Z}^+} % Positive Integers
- % Theorem declarations
- \theoremstyle{plain}
- \newtheorem{theorem}{Theorem}[section]
- \newtheorem{lemma}{Lemma}[section]
- \newtheorem{correllary}{Correllary}[section]
- \newtheorem{proposition}{Proposition}[section]
- \theoremstyle{definition}
- \newtheorem{definition}{Definition}[section]
- \newtheorem{example}{Example}[section]
- \theoremstyle{remark}
- \newtheorem*{remark}{Remark}
- \newtheorem*{note}{Note}
- \newtheorem{case}{Case}
- % Meaningful abbreviations, etc
- \newcommand{\onlyif}{\Rightarrow}
- \newcommand{\thus}{\Longrightarrow}
- \newcommand{\contradicts}{\rightarrow\leftarrow}
- \newcommand{\Union}{\bigcup}
- \newcommand{\union}{\cup}
- \newcommand{\Intersect}{\bigcap}
- \newcommand{\intersect}{\cap}
- \newcommand{\setdiff}{\setminus}
- \newcommand{\divides}{|}
- \newcommand{\Land}{\;\bigwedge\;}
- \newcommand{\Lor}{\;\bigvee\;}
- \newcommand{\floor}[1]{\lfloor#1\rfloor}
- \newcommand{\inverse}[1]{\ensuremath\frac{1}{#1}}
- \newcommand{\abs}[1]{\ensuremath \lvert#1\rvert}
- \newcommand{\norm}[1]{\ensuremath \lVert#1\rVert}
- \newcommand{\inner}[2]{\ensuremath #1 \cdot #2}
- \newcommand{\cross}{\times}
- \newcommand{\setcomplement}[1]{\overline{#1}}
- \newcommand{\emptystring}{\epsilon}
- \newcommand{\concat}[2]{#1 \cdot #2}
- \newcommand{\pair}[2]{\langle #1, #2 \rangle}
- \newcommand{\closure}[1]{#1^*}
- \newcommand{\strlen}[1]{\abs{#1}}
- \newcommand{\produce}{\rightarrow}
- \newcommand{\derive}{\Rightarrow}
- \newcommand{\derives}{\stackrel{*}{\Rightarrow}}
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