math.sty

% Define custom commands with complex argument specifications
\usepackage{xparse}

% ---- Commands for brackets ----

% Curly brackets
\newcommand{\bc}[1]{\left\lbrace #1 \right\rbrace} 

% Parentheses
\newcommand{\bp}[1]{\left( #1 \right)} 

% Parentheses for function argument
\newcommand{\of}[1]{{\left( #1 \right)}}

% Square brackets
\newcommand{\bs}[1]{\left[ #1 \right]} 

% Angle brackets
\newcommand{\ba}[1]{\left< #1 \right>} 

% Absolute valuec in display
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}

% Absolute value in text
\newcommand{\absx}[1]{\lvert #1 \rvert}

% Norm in display
\newcommand{\norm}[1]{\left\lVert #1 \right\rVert}

% Norm in text
\newcommand{\normx}[1]{\lVert #1 \rVert}

% Floor in display
\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor}

% Floor in text
\newcommand{\floorx}[1]{\lfloor #1 \rfloor}

% Ceiling  in display
\newcommand{\ceil}[1]{\left\lceil #1 \right\rceil}

% Ceiling in text
\newcommand{\ceilx}[1]{\lceil #1 \rceil}

% ---- Commands for functions and operators ----

% Logarithm
\let\oldln\ln
\RenewDocumentCommand{\ln}{g}{%
\IfNoValueTF{#1}{\oldln}%
{\,{\oldln}\of{#1}}}

% Exponential
\let\oldexp\exp
\RenewDocumentCommand{\exp}{g}{%
\IfNoValueTF{#1}{\oldexp}%
{\,{\oldexp}\of{#1}}}

% Indicator
\NewDocumentCommand{\ind}{g}{%
\IfNoValueTF{#1}{\operatorname{\mathbb{1}}}%
{\,\mathbb{1}\of{#1}}}

% Trace
\NewDocumentCommand{\tr}{g}{%
\IfNoValueTF{#1}{\operatorname{tr}}%
{\,{\operatorname{tr}}\of{#1}}}

% Variance
\NewDocumentCommand{\var}{o g}{%
\IfNoValueTF{#2}{\operatorname{var}\IfValueT{#1}{_{#1}}}%
{\,{\operatorname{var}\IfValueT{#1}{_{#1}}}\of{#2}}}

% Covariance
\NewDocumentCommand{\cov}{o g}{%
\IfNoValueTF{#2}{\operatorname{cov}\IfValueT{#1}{_{#1}}}%
{\,{\operatorname{cov}\IfValueT{#1}{_{#1}}}\of{#2}}}

% Correlation
\NewDocumentCommand{\corr}{o g}{%
\IfNoValueTF{#2}{\operatorname{corr}\IfValueT{#1}{_{#1}}}%
{\,{\operatorname{corr}\IfValueT{#1}{_{#1}}}\of{#2}}}

% Standard deviation
\NewDocumentCommand{\sd}{o g}{%
\IfNoValueTF{#2}{\operatorname{sd}\IfValueT{#1}{_{#1}}}%
{\,{\operatorname{sd}\IfValueT{#1}{_{#1}}}\of{#2}}}

% Standard error
\NewDocumentCommand{\se}{o g}{%
\IfNoValueTF{#2}{\operatorname{se}\IfValueT{#1}{_{#1}}}%
{\,{\operatorname{se}\IfValueT{#1}{_{#1}}}\of{#2}}}

% Maximum
\let\oldmax\max
\RenewDocumentCommand{\max}{o g}{%
\IfNoValueTF{#2}{\oldmax\IfValueT{#1}{_{#1}}}%
{\,{\oldmax\IfValueT{#1}{_{#1}}}\of{#2}}}

% Supremum
\let\oldsup\sup
\RenewDocumentCommand{\sup}{o g}{%
\IfNoValueTF{#2}{\oldsup\IfValueT{#1}{_{#1}}}%
{\,{\oldsup\IfValueT{#1}{_{#1}}}\of{#2}}}

% Minimum
\let\oldmin\min
\RenewDocumentCommand{\min}{o g}{%
\IfNoValueTF{#2}{\oldmin\IfValueT{#1}{_{#1}}}%
{\,{\oldmin\IfValueT{#1}{_{#1}}}\of{#2}}}

% Infimum
\let\oldinf\inf
\RenewDocumentCommand{\inf}{o g}{%
\IfNoValueTF{#2}{\oldinf\IfValueT{#1}{_{#1}}}%
{\,{\oldinf\IfValueT{#1}{_{#1}}}\of{#2}}}

% Arg functions
\DeclareMathOperator*{\argmax}{argmax}
\DeclareMathOperator*{\argmin}{argmin}

% Expectation
\NewDocumentCommand{\E}{o g}{%
\IfNoValueTF{#2}{\operatorname{\mathbb{E}}\IfValueT{#1}{_{#1}}}%
{\,{\operatorname{\mathbb{E}}\IfValueT{#1}{_{#1}}}\of{#2}}}

% Probability
\RenewDocumentCommand{\P}{o g}{%
\IfNoValueTF{#2}{\operatorname{\mathbb{P}}\IfValueT{#1}{_{#1}}}%
{\,{\operatorname{\mathbb{P}}\IfValueT{#1}{_{#1}}}\of{#2}}}

% ---- Commands for derivatives ----

% Ordinary derivative in display
\NewDocumentCommand{\od}{o g g}{%
\frac{d\IfValueT{#1}{^{#1}} #2}{d #3\IfValueT{#1}{^{#1}}}}

% Ordinary derivative in text
\NewDocumentCommand{\odx}{o g g}{%
d\IfValueT{#1}{^{#1}} #2/d #3\IfValueT{#1}{^{#1}}}

% Partial derivative in display
\NewDocumentCommand{\pd}{o g g g}{%
\IfNoValueTF{#4}{\frac{\partial\IfValueT{#1}{^{#1}} #2}{\partial #3\IfValueT{#1}{^{#1}}}}%
{\left.\frac{\partial\IfValueT{#1}{^{#1}} #2}{\partial #3\IfValueT{#1}{^{#1}}}\right\vert_{#4}}}

% Partial derivative in text
\NewDocumentCommand{\pdx}{o g g g}{%
\IfNoValueTF{#4}{\partial\IfValueT{#1}{^{#1}} #2/\partial #3\IfValueT{#1}{^{#1}}}%
{\left.\partial\IfValueT{#1}{^{#1}} #2/\partial #3\IfValueT{#1}{^{#1}}\right\vert_{#4}}}

% Ordinary elasticity in display
\renewcommand{\oe}[2]{\frac{d\ln{#1}}{d\ln{#2}}}

% Ordinary elasticity in text
\newcommand{\oex}[2]{d\ln(#1)/d\ln(#2)}

% Partial elasticity in display
\NewDocumentCommand{\pe}{g g g}{%
\IfNoValueTF{#3}{\frac{\partial\ln{#1}}{\partial\ln{#2}}}%
{\left.\frac{\partial\ln{#1}}{\partial\ln{#2}}\right\vert_{#3}}}

% Partial elasticity in text
\NewDocumentCommand{\pex}{g g g}{%
\IfNoValueTF{#3}{\partial\ln(#1)/\partial\ln(#2)}%
{\left.\partial\ln(#1)/\partial\ln(#2)\right\vert_{#3}}}

% ---- Commands for logical relations ----

% Equivalence
\renewcommand{\iff}{\Leftrightarrow}

% Implication
\renewcommand{\implies}{\Rightarrow}

% ---- Commands for statistical relations ----

% Independent and identically distributed variables
\newcommand{\iid}{\overset{iid}{\sim}}

% Almost sure convergence
\newcommand{\asto}{\overset{as}{\to}}

% Convergence in probability
\newcommand{\pto}{\overset{p}{\to}}

% Convergence in distribution
\newcommand{\dto}{\overset{d}{\to}}

% Essential (to be used with \inf and \sup)
\DeclareMathOperator*{\ess}{ess}

% ---- Commands for accents ----

% Create custom accents for symbols in math mode
\usepackage{accents}

% Underbar
\newcommand{\ubar}[1]{\underaccent{\bar}{#1}}

% Underline
\newcommand{\ul}[1]{\underline{#1}}

% Arrow
\newcommand{\oa}[1]{\overrightarrow{#1}}

% Overline
\newcommand{\ol}[1]{\overline{#1}}

% Wide hat
\newcommand{\wh}[1]{\widehat{#1}}

% Wide tilde
\newcommand{\wt}[1]{\widetilde{#1}}

% ---- Commands for complex numbers ----

% Real part
\renewcommand{\Re}{\operatorname{Re}}

% Imaginary part
\renewcommand{\Im}{\operatorname{Im}}


% ---- Commands for blackboard letters ----

\def\R{\mathbb{R}}
\def\N{\mathbb{N}}
\def\Z{\mathbb{Z}}
\def\Q{\mathbb{Q}}
\def\C{\mathbb{C}}


% ---- Commands for Greek letters ----

\def\a{\alpha}
\def\b{\beta}
\def\c{\chi}
\def\d{\delta}
\def\D{\Delta}
\def\uD{\upDelta}
\def\e{\epsilon}
\def\ve{\varepsilon}
\def\f{\phi}
\def\vf{\varphi}
\def\F{\Phi}
\def\g{\gamma}
\def\G{\Gamma}
\def\h{\eta}
\def\i{\iota}
\def\k{\kappa}
\def\l{\lambda}
\def\L{\Lambda}
\def\m{\mu}
\def\n{\nu}
\def\o{\omega}
\def\O{\Omega}
\def\vp{\varpi}
\def\p{\psi}
\def\r{\rho}
\def\s{\sigma}
\def\S{\Sigma}
\def\t{\theta}
\def\vt{\vartheta}
\def\T{\Theta}
\def\u{\upsilon}
\def\U{\Upsilon}
\def\x{\xi}
\def\X{\Xi}
\def\z{\zeta}

% ---- Commands for caligraphic letters ----

\newcommand{\Ac}{\mathcal{A}}
\newcommand{\Bc}{\mathcal{B}}
\newcommand{\Cc}{\mathcal{C}}
\newcommand{\Dc}{\mathcal{D}}
\newcommand{\Ec}{\mathcal{E}}
\newcommand{\Fc}{\mathcal{F}}
\newcommand{\Gc}{\mathcal{G}}
\newcommand{\Hc}{\mathcal{H}}
\newcommand{\Ic}{\mathcal{I}}
\newcommand{\Jc}{\mathcal{J}}
\newcommand{\Kc}{\mathcal{K}}
\newcommand{\Lc}{\mathcal{L}}
\newcommand{\Mc}{\mathcal{M}}
\newcommand{\Nc}{\mathcal{N}}
\newcommand{\Oc}{\mathcal{O}}
\newcommand{\Pc}{\mathcal{P}}
\newcommand{\Qc}{\mathcal{Q}}
\newcommand{\Rc}{\mathcal{R}}
\newcommand{\Sc}{\mathcal{S}}
\newcommand{\Tc}{\mathcal{T}}
\newcommand{\Uc}{\mathcal{U}}
\newcommand{\Vc}{\mathcal{V}}
\newcommand{\Wc}{\mathcal{W}}
\newcommand{\Xc}{\mathcal{X}}
\newcommand{\Yc}{\mathcal{Y}}
\newcommand{\Zc}{\mathcal{Z}}