My LaTeX macros

gistfile1.txt

\DeclarePairedDelimiter{\norm}{||}{||_1}
\providecommand{\floor}[1]{\left \lfloor #1 \right \rfloor }
\newcommand{\shortexactseq}[5]{#1\to #2 \hookrightarrow #3 \twoheadrightarrow #4 \to #5}
\newcommand{\rad}[1]{\sqrt{#1}}
\newcommand{\set}[1]{\left\{ #1 \right\}}
\newcommand{\gen}[1]{\langle #1 \rangle}
\newcommand{\restr}[1]{|_{#1}}
\newcommand{\sepdeg}[2]{[{#1}:{#2}]_{\rm sep}}

\renewcommand{\Pr}{\mathbb{P}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\A}{\mathbb{A}}
\newcommand{\I}{\mathcal{I}}
\newcommand{\B}{\mathcal{B}}
\newcommand{\Tor}{\text{Tor }}
\newcommand{\rank}{\text{rank }}
\newcommand{\vspan}{\text{span }}
\newcommand{\vdim}{\text{dim }}
\newcommand{\sign}{\text{sgn }}
\newcommand{\Ann}{\text{Ann }}
\newcommand{\fker}{\text{ker }}
\newcommand{\tC}{\Tilde{C}}
\newcommand{\n}{\hat{n}}
\newcommand{\ff}{\text{Frac}}
\renewcommand{\Im}{\text{Im}}
\newcommand{\lcm}{\text{lcm}}
\newcommand{\orb}{\text{orb}}
\newcommand{\stab}{\text{stab}}
\newcommand{\id}{\text{id}}
\newcommand{\isoarrow}{\xrightarrow{\sim}}
\newcommand{\iso}{\cong}
\newcommand{\semidirect}{\rtimes}

\newcommand{\Sol}{{\bf Solution.} }