%
% Various commands I find useful when writing TeX notes.
%

% TODO
%
% o Fix \SPAN
% o Fix \iff

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}


% ``3.6 Theorem'' instead of ``Theorem 3.6''
%\swapnumbers

\theoremstyle{break}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}

\theoremstyle{remark}
\newtheorem{prob}{Problem}

\theoremstyle{theorem}
\newtheorem{exProb}{Problem}

\theoremstyle{definition}
\newtheorem*{defn}{Definition} % * means no numbering
\newtheorem{exmp}[theorem]{Example}

\newcommand{\emm}{\ensuremath}

\newcommand{\txt}[1]{~\textrm{#1}~}
\newcommand{\fdns}{\txt{f.d.n.s.}}
\newcommand{\fdss}{\txt{f.d.s.s.}}
\newcommand{\stt}{\txt{s.t.}}
\newcommand{\as}{\txt{as}}
\newcommand{\some}{\txt{some}}
\newcommand{\aand}{\txt{and}}

\newcommand{\fa}{\emm{~\forall~}}
\newcommand{\te}{\emm{~\exists~}}
\newcommand{\teu}{\emm{~\exists !~}}

\newcommand{\lrabs}[1]{\emm{\left|#1\right|}}
\newcommand{\lrnorm}[1]{\emm{\left\|#1\right\|}}
\newcommand{\lrparen}[1]{\emm{\left(#1\right)}}
\newcommand{\lrbrace}[1]{\emm{\left\{#1\right\}}}
\newcommand{\lrbrack}[1]{\emm{\left[#1\right]}}
\newcommand{\lrang}[1]{\emm{\left<#1\right>}}
\newcommand{\ip}[1]{\lrang{#1}}

\newcommand{\inv}[1]{\emm{#1^{\scriptscriptstyle -1}}}
\newcommand{\adj}[1]{\emm{#1^{\scriptscriptstyle \times}}}

\newcommand{\SPAN}[1]{\emm{\textrm{span}\lrparen{#1}}}

\newcommand{\al}{\emm{\alpha}}
\newcommand{\be}{\emm{\beta}}
\newcommand{\ga}{\emm{\gamma}}
\newcommand{\tht}{\emm{\theta}}
\newcommand{\ve}{\emm{\varepsilon}}
\newcommand{\de}{\emm{\delta}}
\newcommand{\sa}{\emm{\sigma}}

\newcommand{\Rimpl}{\emm{\Rightarrow}}
\newcommand{\Limpl}{\emm{\Leftarrow}}
\newcommand{\LRimpl}{\emm{\Leftrightarrow}}
\renewcommand{\iff}{\txt{iff}}

\newcommand{\BF}[1]{{\bf #1}}
\newcommand{\IT}[1]{{\it #1}}
\newcommand{\UL}[1]{\underline{#1}}
\newcommand{\OL}[1]{\overline{#1}}

\newcommand{\dom}[1]{\emm{\mathcal{D}\lrparen{#1}}}
\newcommand{\rg}[1]{\emm{\mathcal{R}\lrparen{#1}}}
\newcommand{\nty}[1]{\emm{\mathcal{N}\lrparen{#1}}}
\newcommand{\ddt}[1]{\emm{\frac{d}{dt} #1}}
\newcommand{\bb}[1]{\emm{\mathbb{#1}}}
\newcommand{\Ell}{\emm{\mathcal{L}}}

\newcommand{\into}{\buildrel\textrm{into}\over\longrightarrow}
\newcommand{\onto}{\buildrel\textrm{onto}\over\longrightarrow}
\newcommand{\bij}{\buildrel\textrm{bij}\over\leftrightarrow}
\newcommand{\wto}{\buildrel\textrm{w}\over\longrightarrow}
\newcommand{\wsto}{\buildrel\textrm{\emm{w^*}}\over\longrightarrow}

\newcommand{\eref}[1]{(\ref{#1})}
\newcommand{\thref}[1]{{\rm Theorem \ref{#1}}}
\newcommand{\dref}[1]{{\rm Definition \ref{#1}}}
\newcommand{\pref}[1]{{\rm (\ref{#1})}}           % \pref{blah} -> (n)

\DeclareMathOperator{\var}{Var}