seastaralgebras.sty

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{seastaralgebras}[2023/09/14 Seastaralgebras LaTeX package]

% required packages
\RequirePackage[english]{babel}
\RequirePackage{mathtools}
\RequirePackage{enumitem}
\RequirePackage{framed}
\RequirePackage{amsthm}
\RequirePackage{thmtools}
\RequirePackage{amssymb}
\RequirePackage{amsmath}
\RequirePackage{verbatim}
\RequirePackage{lmodern}
\RequirePackage{tabularx}
\RequirePackage{hyperref}



% general commands

\newcommand{\bb}[1]{\mathbb{#1}}
\newcommand{\bba}{\bb A}
\newcommand{\bbb}{\bb B}
\newcommand{\bbc}{\bb C}
\newcommand{\bbd}{\bb D}
\newcommand{\bbe}{\bb E}
\newcommand{\bbf}{\bb F}
\newcommand{\bbg}{\bb G}
\newcommand{\bbh}{\bb H}
\newcommand{\bbi}{\bb I}
\newcommand{\bbj}{\bb J}
\newcommand{\bbk}{\bb K}
\newcommand{\bbl}{\bb L}
\newcommand{\bbm}{\bb M}
\newcommand{\bbn}{\bb N}
\newcommand{\bbo}{\bb O}
\newcommand{\bbp}{\bb P}
\newcommand{\bbq}{\bb Q}
\newcommand{\bbr}{\bb R}
\newcommand{\bbs}{\bb S}
\newcommand{\bbt}{\bb T}
\newcommand{\bbu}{\bb U}
\newcommand{\bbv}{\bb V}
\newcommand{\bbw}{\bb W}
\newcommand{\bbx}{\bb X}
\newcommand{\bby}{\bb Y}
\newcommand{\bbz}{\bb Z}

\newcommand{\ccal}[1]{\mathcal{#1}}
\newcommand{\cla}{\ccal A}
\newcommand{\clb}{\ccal B}
\newcommand{\clc}{\ccal C}
\newcommand{\cld}{\ccal D}
\newcommand{\cle}{\ccal E}
\newcommand{\clf}{\ccal F}
\newcommand{\clg}{\ccal G}
\newcommand{\clh}{\ccal H}
\newcommand{\cli}{\ccal I}
\newcommand{\clj}{\ccal J}
\newcommand{\clk}{\ccal K}
\newcommand{\cll}{\ccal L}
\newcommand{\clm}{\ccal M}
\newcommand{\cln}{\ccal N}
\newcommand{\clo}{\ccal O}
\newcommand{\clp}{\ccal P}
\newcommand{\clq}{\ccal Q}
\newcommand{\clr}{\ccal R}
\newcommand{\cls}{\ccal S}
\newcommand{\clt}{\ccal T}
\newcommand{\clu}{\ccal U}
\newcommand{\clv}{\ccal V}
\newcommand{\clw}{\ccal W}
\newcommand{\clx}{\ccal X}
\newcommand{\cly}{\ccal Y}
\newcommand{\clz}{\ccal Z}


\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\DeclarePairedDelimiter{\inprod}{\langle}{\rangle}
\DeclarePairedDelimiter{\set}{\{}{\}}
\DeclarePairedDelimiter{\paren}{(}{)}
\DeclarePairedDelimiter{\cl}{[}{]}
\DeclarePairedDelimiter{\clop}{[}{)}
\DeclarePairedDelimiter{\opcl}{(}{]}


\renewcommand{\vec}[1]{\text{\textbf{#1}}}
\newcommand{\eps}{\varepsilon}
\newcommand{\cnj}[1]{\overline{#1}}
\newcommand{\sth}{\mid}
\newcommand{\cmpl}[1]{#1^\mathrm{C}}
\newcommand{\prm}[1]{#1^\prime}
\newcommand{\dprm}[1]{#1^{\prime\prime}}
\newcommand{\card}{\operatorname{card}}
\newcommand{\continuum}{\mathfrak{c}}

\newcommand{\id}{\operatorname{Id}}


% algebra commands

\newcommand{\vspan}[1]{\operatorname{span}(#1)}
\newcommand{\image}{\operatorname{im}}
\renewcommand{\ker}{\operatorname{ker}}
\newcommand{\gen}[1]{\langle #1 \rangle}
\newcommand{\lcm}[1]{\operatorname{lcm}[#1]}
\renewcommand{\gcd}[1]{\operatorname{gcd}(#1)}
\newcommand{\aut}{\operatorname{aut}}
\newcommand{\End}{\operatorname{end}}
\newcommand{\ann}{\operatorname{ann}}
\newcommand{\tor}{\operatorname{tor}}
\renewcommand{\hom}{\operatorname{Hom}}
\newcommand{\rank}{\operatorname{rank}}
\newcommand{\pmat}[1]{\begin{pmatrix} #1 \end{pmatrix}}
\newcommand{\vmat}[1]{\begin{vmatrix} #1 \end{vmatrix}}


% topology/geometry commands

\newcommand{\closure}{\operatorname{clos}}
\newcommand{\interior}{\operatorname{int}}
\newcommand{\bd}{\partial}
\newcommand{\smooth}{C^\infty}


\newcommand{\rp}{\bbr\bbp}

\newcommand{\diff}[2]{\de{#1}_{#2}}

\newcommand{\pf}[1]{#1_\star}

\newcommand{\tfield}[2]{\mathcal{T}^{#1}_{#2}}
\newcommand{\covd}[1]{\dfrac{\mathrm{D}#1}{\mathrm{d}t}}
\newcommand{\covde}{\dfrac{\mathrm{D}}{\mathrm{d}t}}

\newcommand{\cirg}{\mathring{g}}

\newcommand{\bee}{B}

\newcommand{\base}[1]{B(#1)}
\newcommand{\bundle}[1]{E(#1)}



%analysis commands

\newcommand{\mus}{\mu^\ast}
\newcommand{\mup}{\mu_0}
\newcommand{\mut}{\mu_\ast}
\newcommand{\leb}{\mathcal{L}}
\newcommand{\de}[1]{\mathrm{d}#1}
\newcommand{\dmu}{\de{\mu}}
\newcommand{\dnu}{\de{\nu}}
\newcommand{\nup}{\nu^+}
\newcommand{\num}{\nu^-}
\newcommand{\dnup}{\de{\nup}}
\newcommand{\dnum}{\de{\num}}
\newcommand{\dmn}{\de{(\mu \times \nu)}}
\newcommand{\dmm}{\de{(\mu \times m)}}
\newcommand{\dm}{\de{m}}
\newcommand{\ds}{\de{s}}
\newcommand{\dw}{\de{w}}
\newcommand{\dcw}{\de{\cnj{w}}}
\newcommand{\dx}{\de{x}}
\newcommand{\dy}{\de{y}}
\newcommand{\dz}{\de{z}}
\newcommand{\dcz}{\de{\cnj{z}}}
\newcommand{\dt}{\de{t}}
\newcommand{\dlambda}{\de{\lambda}}
\newcommand{\borelr}{\mathcal{B}_\rr}
\newcommand{\borelc}{\mathcal{B}_\cc}
\newcommand{\nabs}{\abs{\nu}}
\newcommand{\dnabs}{\de{\nabs}}
\newcommand{\mabs}{\abs{\mu}}
\newcommand{\drho}{\de{\rho}}
\newcommand{\ccc}{\mathcal{C}}
\newcommand{\Hs}{H^\ast}
\newcommand{\nur}{\nu_r}
\newcommand{\nui}{\nu_i}
\newcommand{\dnur}{\de{\nur}}
\newcommand{\dnui}{\de{\nui}}
\newcommand{\danur}{\de{\abs{\nur}}}
\newcommand{\danui}{\de{\abs{\nui}}}

\newcommand{\dde}[2]{\dfrac{\mathrm{d} #1}{\mathrm{d} #2}}
\newcommand{\ddee}[1]{\dfrac{\mathrm{d}}{\mathrm{d} #1}}
\newcommand{\pd}[2]{\dfrac{\partial#1}{\partial#2}}
\newcommand{\pdd}[1]{\dfrac{\partial}{\partial#1}}

\newcommand{\cw}{\cnj{w}}
\newcommand{\cz}{\cnj{z}}


\newcommand{\pnorm}[2]{\norm{#1}_{#2}}
\newcommand{\limd}[2]{\lim\limits_{#1 \to #2}}
\newcommand{\liminfd}[2]{\liminf\limits_{#1 \to #2}}
\newcommand{\limsupd}[2]{\limsup\limits_{#1 \to #2}}

\newcommand{\maxm}{\operatorname{max}}
\newcommand{\str}[1]{#1^{\star}}
\newcommand{\dstr}[1]{#1^{\star\star}}
\newcommand{\weakto}{\rightharpoonup}
\newcommand{\starto}{\overset{\star}{\rightharpoonup}}