% Holden's fractions and parens
\newcommand{\af}[2]{\ab{\fc{#1}{#2}}}
\newcommand{\rc}[1]{\frac{1}{#1}}
\newcommand{\prc}[1]{\pa{\rc{#1}}}
\newcommand{\ff}[2]{\left\lfloor\frac{#1}{#2}\right\rfloor}
\newcommand{\cf}[2]{\left\lceil\frac{#1}{#2}\rceil\rfloor}
\newcommand{\fc}[2]{\frac{#1}{#2}}
\newcommand{\sfc}[2]{\sqrt{\frac{#1}{#2}}}
\newcommand{\pf}[2]{\pa{\frac{#1}{#2}}}

%Brackets
\newcommand{\ab}[1]{\left| {#1} \right|}
\newcommand{\an}[1]{\left\langle {#1}\right\rangle}
\newcommand{\ba}[1]{\left[ {#1} \right]}
\newcommand{\bc}[1]{\left\{ {#1} \right\}}
\newcommand{\ce}[1]{\left\lceil {#1}\right\rceil}
\newcommand{\fl}[1]{\left\lfloor {#1}\right\rfloor}
\newcommand{\pa}[1]{\left( {#1} \right)}
\newcommand{\pat}[1]{\left( \text{#1} \right)}
\newcommand{\ve}[1]{\left\Vert {#1}\right\Vert}
\newcommand{\nv}[1]{\frac{#1}{\left\Vert {#1}\right\Vert}}
\newcommand{\nvl}[2]{\frac{#1}{\left\Vert {#1}\right\Vert_{#2}}}
\newcommand{\vvt}[1]{{#1}{#1}^\top}
\newcommand{\pvvt}[1]{\pa{#1}\pa{#1}^\top}
\newcommand{\vtv}[1]{{#1}^\top{#1}}
\newcommand{\pvtv}[1]{\pa{#1}^\top\pa{#1}}
\newcommand{\rb}[1]{\left.{#1}\right|}
\newcommand{\ad}[0]{|\cdot|}
\newcommand{\ved}[0]{\ve{\cdot}}
\newcommand{\set}[2]{\left\{{#1}:{#2}\right\}}
\newcommand{\sett}[2]{\left\{\left.{#1}\right|{#2}\right\}}

\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}%Partial derivatives
\newcommand{\dd}[2]{\frac{d #1}{d #2}}
\newcommand{\pdd}[1]{\frac{\partial}{\partial #1}}
\newcommand{\ddd}[1]{\frac{d}{d #1}}
\newcommand{\ddt}[2]{\frac{d^2 #1}{d {#2}^2}}
\newcommand{\pl}[0]{\partial}
\newcommand{\nb}[0]{\nabla}
\newcommand{\dy}{\,dy}
\newcommand{\dx}{\,dx}

\newcommand{\al}[0]{\alpha}
\newcommand{\be}[0]{\beta}
\newcommand{\ga}[0]{\gamma}
\newcommand{\Ga}[0]{\Gamma}
\newcommand{\de}[0]{\delta}
\newcommand{\De}[0]{\Delta}
\newcommand{\ep}[0]{\varepsilon}
\newcommand{\eph}[0]{\frac{\varepsilon}{2}}
\newcommand{\ept}[0]{\frac{\varepsilon}{3}}
\newcommand{\ka}[0]{\kappa}
\newcommand{\la}[0]{\lambda}
\newcommand{\La}[0]{\Lambda}
\newcommand{\ph}[0]{\varphi}
\newcommand{\Ph}[0]{\Phi}
\newcommand{\rh}[0]{\rho}
\newcommand{\te}[0]{\theta}
\newcommand{\Te}[0]{\Theta}
\newcommand{\vte}[0]{\vartheta}
\newcommand{\om}[0]{\omega}
\newcommand{\Om}[0]{\Omega}
\newcommand{\si}[0]{\sigma}
\newcommand{\Si}[0]{\Sigma}
\newcommand{\ze}[0]{\zeta}

\newcommand{\Var}[0]{\operatorname{Var}}
\newcommand{\Cov}[0]{\operatorname{Cov}}
\newcommand{\Tr}[0]{\operatorname{Tr}}

\newcommand{\sumo}[2]{\sum_{#1=1}^{#2}}
\newcommand{\sumz}[2]{\sum_{#1=0}^{#2}}
\newcommand{\prodo}[2]{\prod_{#1=1}^{#2}}
\newcommand{\prodz}[2]{\prod_{#1=0}^{#2}}

\newcommand{\ub}[2]{\underbrace{#1}_{#2}}

\newcommand{\iy}[0]{\infty}

%\newcommand{\esc}[0]{\ep_{\textup{score}}}

\newcommand{\redd}[1]{{\color{red}#1}}

\newcommand{\wh}{\widehat}
\newcommand{\wt}{\widetilde}
\renewcommand{\top}{\intercal}

\newcommand{\quo}[0]{q^{\rightarrow}}