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