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algebra.sty
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algebra.sty
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\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{algebra}[2024/00/00 v0.01 (G Sokolov)]
\PackageInfo{algebra}{Some algebraic notation}
\RequirePackage{amsmath}
\RequirePackage{amssymb}
\newcommand{\abs}[1]{\lvert#1\rvert}
\newcommand{\norm}[1]{\lVert#1\rVert}
\newcommand{\slfrac}[3][\big]{#2#1/#3}
\newcommand{\ceiling}[1]{\left\lceil#1\right\rceil}
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor}
\newcommand{\arr}[1]{\overrightarrow{#1\phantom{|}}}
\renewcommand{\v}[1]{\boldsymbol{\mathbf{#1}}}
\renewcommand{\vec}[1]{\langle #1 \rangle}
\newcommand{\bigvec}[1]{\big\langle #1 \big\rangle}
\newcommand{\Bigvec}[1]{\Big\langle #1 \Big\rangle}
\newcommand{\Biggvec}[1]{\Bigg\langle #1 \Bigg\rangle}
\newcommand{\point}[1]{(#1)}
\newcommand{\dotp}{\boldsymbol{\cdot}}
\newcommand{\crossp}{\times}
\newcommand{\partialwrt}[1]{\frac{\partial}{\partial #1}}
\newcommand{\ppartialwrt}[2]{\frac{\partial^2}{\partial #1 \, \partial #2}}
\newcommand{\pppartialwrt}[3]{\frac{\partial^3}{\partial #1 \, \partial #2 \, \partial #3}}
\newcommand{\partialof}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\ppartialof}[3]{\frac{\partial^2 #1}{\partial #2 \, \partial #3}}
\newcommand{\pppartialof}[4]{\frac{\partial^3 #1}{\partial #2 \, \partial #3 \, \partial #4}}
\newcommand{\crossvec}[3][ccc]{%
\begin{vmatrix}
\begin{array}{#1}
\,\v{i} & \v{j} & \v{k}\, \\
\,#2\, \\
\,#3\, \\
\end{array}
\end{vmatrix}}
% ~~ Linear algebra ~~
\DeclareMathOperator{\Det}{\mathsf{det}} % Determinant.
\DeclareMathOperator{\Ker}{\mathsf{Ker}} % Kernel.
\DeclareMathOperator{\Col}{\mathsf{Col}} % Column space.
\DeclareMathOperator{\Image}{\mathsf{Image}} % Image.
\DeclareMathOperator{\Rank}{\mathsf{rank}} % Rank.
\DeclareMathOperator{\Null}{\mathsf{Nul}} % Null space.
\DeclareMathOperator{\Span}{\mathsf{span}} % Span.
\DeclareMathOperator{\Dim}{\mathsf{dim}} % Dimensions.
\DeclareMathOperator{\Proj}{\mathsf{Proj}} % Projection.
\DeclareMathOperator{\vProj}{\mathsf{Proj}} % Vector projection.
\DeclareMathOperator{\curl}{curl} % Curl.
\DeclareMathOperator{\dvg}{div} % Divergence.
\DeclareMathOperator{\grad}{grad} % Gradient.
% ~~ Misc ~~
\newcommand{\One}{\mathchoice{\rm 1\mskip-4.2mu l}{\rm 1\mskip-4.2mu l}{\rm 1\mskip-4.6mu l}{\rm 1\mskip-5.2mu l}}