mymath.sty

%this file contains helpful macros for setting math-heavy homeworks.
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\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{mymath}[2014/10/23 Common math macros]
%----------------------------------------------------------------------------------------------------
%REQUIREMENTS
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\RequirePackage{mathtools}
\RequirePackage{amssymb}
\RequirePackage{amsthm}
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%MATH STUFF
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%common fields/sets used
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\newcommand{\E}{\ensuremath{\mathbb{E}}}
\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
\newcommand{\Com}{\ensuremath{\mathbb{C}}}
\newcommand{\C}{\Com}
\newcommand{\N}{\ensuremath{\mathbb{N}}}
\newcommand{\Q}{\ensuremath{\mathbb{Q}}}

\newcommand{\zmod}[1]{\ensuremath{\Z/#1\Z}}

\newcommand{\Sym}{\ensuremath{\mathbb{S}}}
\newcommand{\Sp}{\ensuremath{\mathbb{S}^+}}
\newcommand{\Spp}{\ensuremath{\mathbb{S}^{++}}}

% Set-theory stuff
\newcommand{\B}{\mathcal{B}} % Borel Set 
\renewcommand{\P}{\mathcal{P}} % Powerset - replaces "paragraph" mark
\newcommand{\A}{\mathcal{A}} % Family
\renewcommand{\S}{\mathcal{S}} % Sigma Algebra - replaces "section" mark
\newcommand{\T}{\mathcal{T}} % Sigma Algebra (2)
\newcommand{\D}{\mathcal{D}} % Random curly D.


%finite field - provide order as argument.
\newcommand{\F}[1]{\ensuremath{\mathbb{F}_#1}}

\newcommand{\GL}{\ensuremath{\mathrm{GL}}}

%operators
\DeclareMathOperator{\spn}{span}
\DeclareMathOperator{\trace}{trace}
%\DeclareMathOperator{\dim}{dim}
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\Img}{Im}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Erf}{\mathcal{E}rf}
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
\newcommand{\ip}[2]{\left<#1, #2\right>}

%modifiers
\newcommand*\conj[1]{\overline{#1}}

%symbols
\newcommand{\Chi}{\chi}

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%TEXT STUFF
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%common text used in mathmode.
\newcommand{\st}{\ensuremath{\text{ s.t. }}}
\newcommand{\divs}{\ensuremath{\text{ divides }}}

%for align environments
%justifying a step
%TODO: right-align this?
\newcommand{\note}[1]{
  \ensuremath{\qquad\text{#1}}
}

%proofs
%TODO: Write own theorem style - not so much vertical space, maybe boxes?
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[theorem]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}{Proposition}[section]
\newtheorem{example}{Example}[section]

\newtheorem*{defn}{Defn}
\renewcommand\qedsymbol{$\blacksquare$}