[ceph.git] / ceph / src / boost / libs / graph / doc / math.sty

% 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}}
Commit	Line	Data
7c673cae FG	1	% Style helpers for use in Math M413
	2
	3	\usepackage[leqno]{amsmath}
	4	\usepackage{amsfonts}
	5	\usepackage{amssymb}
	6	\usepackage{amsthm}
	7	\usepackage{latexsym}
	8
	9	\numberwithin{equation}{section}
	10
	11	\DeclareMathOperator{\suchthat}{s.t.}
	12	\DeclareMathOperator{\st}{\;\|\;}
	13	\DeclareMathOperator{\lub}{lub}
	14	\DeclareMathOperator{\glb}{glb}
	15	\DeclareMathOperator{\C}{C}
	16	\DeclareMathOperator{\Rl}{R_L}
	17	\DeclareMathOperator{\Rm}{R_M}
	18	\DeclareMathOperator{\Poly}{\mathcal{P}}
	19	\DeclareMathOperator{\NPoly}{\mathcal{NP}}
	20	\DeclareMathOperator{\outdegree}{out-degree}
	21	\DeclareMathOperator{\indegree}{in-degree}
	22
	23	% Abbreviations for Commonly used sets
	24	\newcommand{\field}[1]{\mathbb{#1}}
	25	\newcommand{\Q}{\field{Q}} % Rational numbers
	26	\newcommand{\N}{\field{N}} % Natural numbers
	27	\newcommand{\R}{\field{R}} % Real numbers
	28	\newcommand{\Z}{\field{Z}} % Integers
	29	\newcommand{\Zp}{\field{Z}^+} % Positive Integers
	30
	31	% Theorem declarations
	32	\theoremstyle{plain}
	33	\newtheorem{theorem}{Theorem}[section]
	34	\newtheorem{lemma}{Lemma}[section]
	35	\newtheorem{correllary}{Correllary}[section]
	36	\newtheorem{proposition}{Proposition}[section]
	37
	38	\theoremstyle{definition}
	39	\newtheorem{definition}{Definition}[section]
	40	\newtheorem{example}{Example}[section]
	41
	42	\theoremstyle{remark}
	43	\newtheorem*{remark}{Remark}
	44	\newtheorem*{note}{Note}
	45	\newtheorem{case}{Case}
	46
	47
	48	% Meaningful abbreviations, etc
	49	\newcommand{\onlyif}{\Rightarrow}
	50	\newcommand{\thus}{\Longrightarrow}
	51	\newcommand{\contradicts}{\rightarrow\leftarrow}
	52	\newcommand{\Union}{\bigcup}
	53	\newcommand{\union}{\cup}
	54	\newcommand{\Intersect}{\bigcap}
	55	\newcommand{\intersect}{\cap}
	56	\newcommand{\setdiff}{\setminus}
	57	\newcommand{\divides}{\|}
	58	\newcommand{\Land}{\;\bigwedge\;}
	59	\newcommand{\Lor}{\;\bigvee\;}
	60	\newcommand{\floor}[1]{\lfloor#1\rfloor}
	61	\newcommand{\inverse}[1]{\ensuremath\frac{1}{#1}}
	62	\newcommand{\abs}[1]{\ensuremath \lvert#1\rvert}
	63	\newcommand{\norm}[1]{\ensuremath \lVert#1\rVert}
	64	\newcommand{\inner}[2]{\ensuremath #1 \cdot #2}
65
66	\newcommand{\cross}{\times}
67	\newcommand{\setcomplement}[1]{\overline{#1}}
68	\newcommand{\emptystring}{\epsilon}
69	\newcommand{\concat}[2]{#1 \cdot #2}
70	\newcommand{\pair}[2]{\langle #1, #2 \rangle}
71	\newcommand{\closure}[1]{#1^*}
72	\newcommand{\strlen}[1]{\abs{#1}}
73
74	\newcommand{\produce}{\rightarrow}
75	\newcommand{\derive}{\Rightarrow}
76	\newcommand{\derives}{\stackrel{*}{\Rightarrow}}