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-%%
-%% This is file `PJLmath.sty',
-%% generated with the docstrip utility.
-
-%% Copyright (C) 2021 by Jinwen XU
-%%
-%% This is part of the ProjLib Toolkit.
-%%
-%% This work may be distributed and/or modified under the conditions of the
-%% LaTeX Project Public License, either version 1.3c of this license or (at
-%% your option) any later version. The latest version of this license is in
-%%
-%% http://www.latex-project.org/lppl.txt
-%%
-%% and version 1.3c or later is part of all distributions of LaTeX version
-%% 2005/12/01 or later.
-%%
-\NeedsTeXFormat{LaTeX2e}[2020-10-01]
-\ProvidesPackage{PJLmath}
- [2021/12/16 Useful math macros and shortcuts]
-\RequirePackage{kvoptions}
-\RequirePackage{etoolbox}
-\RequirePackage{mathtools}
-\RequirePackage{mathrsfs}
-\@ifpackageloaded{unicode-math}{}{\RequirePackage{amssymb}}
-
-%%================================
-%% Shorthands
-%%================================
-\providecommand{\N}{\ensuremath{\mathbb{N}}}
-\providecommand{\Z}{\ensuremath{\mathbb{Z}}}
-\providecommand{\Q}{\ensuremath{\mathbb{Q}}}
-\providecommand{\R}{\ensuremath{\mathbb{R}}}
-\providecommand{\C}{\ensuremath{\mathbb{C}}}
-\providecommand{\F}{\ensuremath{\mathbb{F}}}
-\providecommand{\A}{\ensuremath{\mathbb{A}}}
-
-\providecommand{\bb}[1]{\ensuremath{\mathbb{#1}}}
-\providecommand{\bbA}{\ensuremath{\mathbb{A}}}
-\providecommand{\bbB}{\ensuremath{\mathbb{B}}}
-\providecommand{\bbC}{\ensuremath{\mathbb{C}}}
-\providecommand{\bbD}{\ensuremath{\mathbb{D}}}
-\providecommand{\bbE}{\ensuremath{\mathbb{E}}}
-\providecommand{\bbF}{\ensuremath{\mathbb{F}}}
-\providecommand{\bbG}{\ensuremath{\mathbb{G}}}
-\providecommand{\bbH}{\ensuremath{\mathbb{H}}}
-\providecommand{\bbI}{\ensuremath{\mathbb{I}}}
-\providecommand{\bbJ}{\ensuremath{\mathbb{J}}}
-\providecommand{\bbK}{\ensuremath{\mathbb{K}}}
-\providecommand{\bbL}{\ensuremath{\mathbb{L}}}
-\providecommand{\bbM}{\ensuremath{\mathbb{M}}}
-\providecommand{\bbN}{\ensuremath{\mathbb{N}}}
-\providecommand{\bbO}{\ensuremath{\mathbb{O}}}
-\providecommand{\bbP}{\ensuremath{\mathbb{P}}}
-\providecommand{\bbQ}{\ensuremath{\mathbb{Q}}}
-\providecommand{\bbR}{\ensuremath{\mathbb{R}}}
-\providecommand{\bbS}{\ensuremath{\mathbb{S}}}
-\providecommand{\bbT}{\ensuremath{\mathbb{T}}}
-\providecommand{\bbU}{\ensuremath{\mathbb{U}}}
-\providecommand{\bbV}{\ensuremath{\mathbb{V}}}
-\providecommand{\bbW}{\ensuremath{\mathbb{W}}}
-\providecommand{\bbX}{\ensuremath{\mathbb{X}}}
-\providecommand{\bbY}{\ensuremath{\mathbb{Y}}}
-\providecommand{\bbZ}{\ensuremath{\mathbb{Z}}}
-
-\providecommand{\mc}[1]{\ensuremath{\mathcal{#1}}}
-\providecommand{\mcA}{\ensuremath{\mathcal{A}}}
-\providecommand{\mcB}{\ensuremath{\mathcal{B}}}
-\providecommand{\mcC}{\ensuremath{\mathcal{C}}}
-\providecommand{\mcD}{\ensuremath{\mathcal{D}}}
-\providecommand{\mcE}{\ensuremath{\mathcal{E}}}
-\providecommand{\mcF}{\ensuremath{\mathcal{F}}}
-\providecommand{\mcG}{\ensuremath{\mathcal{G}}}
-\providecommand{\mcH}{\ensuremath{\mathcal{H}}}
-\providecommand{\mcI}{\ensuremath{\mathcal{I}}}
-\providecommand{\mcJ}{\ensuremath{\mathcal{J}}}
-\providecommand{\mcK}{\ensuremath{\mathcal{K}}}
-\providecommand{\mcL}{\ensuremath{\mathcal{L}}}
-\providecommand{\mcM}{\ensuremath{\mathcal{M}}}
-\providecommand{\mcN}{\ensuremath{\mathcal{N}}}
-\providecommand{\mcO}{\ensuremath{\mathcal{O}}}
-\providecommand{\mcP}{\ensuremath{\mathcal{P}}}
-\providecommand{\mcQ}{\ensuremath{\mathcal{Q}}}
-\providecommand{\mcR}{\ensuremath{\mathcal{R}}}
-\providecommand{\mcS}{\ensuremath{\mathcal{S}}}
-\providecommand{\mcT}{\ensuremath{\mathcal{T}}}
-\providecommand{\mcU}{\ensuremath{\mathcal{U}}}
-\providecommand{\mcV}{\ensuremath{\mathcal{V}}}
-\providecommand{\mcW}{\ensuremath{\mathcal{W}}}
-\providecommand{\mcX}{\ensuremath{\mathcal{X}}}
-\providecommand{\mcY}{\ensuremath{\mathcal{Y}}}
-\providecommand{\mcZ}{\ensuremath{\mathcal{Z}}}
-
-\providecommand{\cal}[1]{\ensuremath{\mathcal{#1}}}
-\providecommand{\calA}{\ensuremath{\mathcal{A}}}
-\providecommand{\calB}{\ensuremath{\mathcal{B}}}
-\providecommand{\calC}{\ensuremath{\mathcal{C}}}
-\providecommand{\calD}{\ensuremath{\mathcal{D}}}
-\providecommand{\calE}{\ensuremath{\mathcal{E}}}
-\providecommand{\calF}{\ensuremath{\mathcal{F}}}
-\providecommand{\calG}{\ensuremath{\mathcal{G}}}
-\providecommand{\calH}{\ensuremath{\mathcal{H}}}
-\providecommand{\calI}{\ensuremath{\mathcal{I}}}
-\providecommand{\calJ}{\ensuremath{\mathcal{J}}}
-\providecommand{\calK}{\ensuremath{\mathcal{K}}}
-\providecommand{\calL}{\ensuremath{\mathcal{L}}}
-\providecommand{\calM}{\ensuremath{\mathcal{M}}}
-\providecommand{\calN}{\ensuremath{\mathcal{N}}}
-\providecommand{\calO}{\ensuremath{\mathcal{O}}}
-\providecommand{\calP}{\ensuremath{\mathcal{P}}}
-\providecommand{\calQ}{\ensuremath{\mathcal{Q}}}
-\providecommand{\calR}{\ensuremath{\mathcal{R}}}
-\providecommand{\calS}{\ensuremath{\mathcal{S}}}
-\providecommand{\calT}{\ensuremath{\mathcal{T}}}
-\providecommand{\calU}{\ensuremath{\mathcal{U}}}
-\providecommand{\calV}{\ensuremath{\mathcal{V}}}
-\providecommand{\calW}{\ensuremath{\mathcal{W}}}
-\providecommand{\calX}{\ensuremath{\mathcal{X}}}
-\providecommand{\calY}{\ensuremath{\mathcal{Y}}}
-\providecommand{\calZ}{\ensuremath{\mathcal{Z}}}
-
-\providecommand{\mf}[1]{\ensuremath{\mathfrak{#1}}}
-\providecommand{\mfa}{\ensuremath{\mathfrak{a}}}
-\providecommand{\mfb}{\ensuremath{\mathfrak{b}}}
-\providecommand{\mfc}{\ensuremath{\mathfrak{c}}}
-\providecommand{\mfd}{\ensuremath{\mathfrak{d}}}
-\providecommand{\mfe}{\ensuremath{\mathfrak{e}}}
-\providecommand{\mff}{\ensuremath{\mathfrak{f}}}
-\providecommand{\mfg}{\ensuremath{\mathfrak{g}}}
-\providecommand{\mfh}{\ensuremath{\mathfrak{h}}}
-\providecommand{\mfi}{\ensuremath{\mathfrak{i}}}
-\providecommand{\mfj}{\ensuremath{\mathfrak{j}}}
-\providecommand{\mfk}{\ensuremath{\mathfrak{k}}}
-\providecommand{\mfl}{\ensuremath{\mathfrak{l}}}
-\providecommand{\mfm}{\ensuremath{\mathfrak{m}}}
-\providecommand{\mfn}{\ensuremath{\mathfrak{n}}}
-\providecommand{\mfo}{\ensuremath{\mathfrak{o}}}
-\providecommand{\mfp}{\ensuremath{\mathfrak{p}}}
-\providecommand{\mfq}{\ensuremath{\mathfrak{q}}}
-\providecommand{\mfr}{\ensuremath{\mathfrak{r}}}
-\providecommand{\mfs}{\ensuremath{\mathfrak{s}}}
-\providecommand{\mft}{\ensuremath{\mathfrak{t}}}
-\providecommand{\mfu}{\ensuremath{\mathfrak{u}}}
-\providecommand{\mfv}{\ensuremath{\mathfrak{v}}}
-\providecommand{\mfw}{\ensuremath{\mathfrak{w}}}
-\providecommand{\mfx}{\ensuremath{\mathfrak{x}}}
-\providecommand{\mfy}{\ensuremath{\mathfrak{y}}}
-\providecommand{\mfz}{\ensuremath{\mathfrak{z}}}
-\providecommand{\mfA}{\ensuremath{\mathfrak{A}}}
-\providecommand{\mfB}{\ensuremath{\mathfrak{B}}}
-\providecommand{\mfC}{\ensuremath{\mathfrak{C}}}
-\providecommand{\mfD}{\ensuremath{\mathfrak{D}}}
-\providecommand{\mfE}{\ensuremath{\mathfrak{E}}}
-\providecommand{\mfF}{\ensuremath{\mathfrak{F}}}
-\providecommand{\mfG}{\ensuremath{\mathfrak{G}}}
-\providecommand{\mfH}{\ensuremath{\mathfrak{H}}}
-\providecommand{\mfI}{\ensuremath{\mathfrak{I}}}
-\providecommand{\mfJ}{\ensuremath{\mathfrak{J}}}
-\providecommand{\mfK}{\ensuremath{\mathfrak{K}}}
-\providecommand{\mfL}{\ensuremath{\mathfrak{L}}}
-\providecommand{\mfM}{\ensuremath{\mathfrak{M}}}
-\providecommand{\mfN}{\ensuremath{\mathfrak{N}}}
-\providecommand{\mfO}{\ensuremath{\mathfrak{O}}}
-\providecommand{\mfP}{\ensuremath{\mathfrak{P}}}
-\providecommand{\mfQ}{\ensuremath{\mathfrak{Q}}}
-\providecommand{\mfR}{\ensuremath{\mathfrak{R}}}
-\providecommand{\mfS}{\ensuremath{\mathfrak{S}}}
-\providecommand{\mfT}{\ensuremath{\mathfrak{T}}}
-\providecommand{\mfU}{\ensuremath{\mathfrak{U}}}
-\providecommand{\mfV}{\ensuremath{\mathfrak{V}}}
-\providecommand{\mfW}{\ensuremath{\mathfrak{W}}}
-\providecommand{\mfX}{\ensuremath{\mathfrak{X}}}
-\providecommand{\mfY}{\ensuremath{\mathfrak{Y}}}
-\providecommand{\mfZ}{\ensuremath{\mathfrak{Z}}}
-
-\providecommand{\frak}[1]{\ensuremath{\mathfrak{#1}}}
-\providecommand{\fraka}{\ensuremath{\mathfrak{a}}}
-\providecommand{\frakb}{\ensuremath{\mathfrak{b}}}
-\providecommand{\frakc}{\ensuremath{\mathfrak{c}}}
-\providecommand{\frakd}{\ensuremath{\mathfrak{d}}}
-\providecommand{\frake}{\ensuremath{\mathfrak{e}}}
-\providecommand{\frakf}{\ensuremath{\mathfrak{f}}}
-\providecommand{\frakg}{\ensuremath{\mathfrak{g}}}
-\providecommand{\frakh}{\ensuremath{\mathfrak{h}}}
-\providecommand{\fraki}{\ensuremath{\mathfrak{i}}}
-\providecommand{\frakj}{\ensuremath{\mathfrak{j}}}
-\providecommand{\frakk}{\ensuremath{\mathfrak{k}}}
-\providecommand{\frakl}{\ensuremath{\mathfrak{l}}}
-\providecommand{\frakm}{\ensuremath{\mathfrak{m}}}
-\providecommand{\frakn}{\ensuremath{\mathfrak{n}}}
-\providecommand{\frako}{\ensuremath{\mathfrak{o}}}
-\providecommand{\frakp}{\ensuremath{\mathfrak{p}}}
-\providecommand{\frakq}{\ensuremath{\mathfrak{q}}}
-\providecommand{\frakr}{\ensuremath{\mathfrak{r}}}
-\providecommand{\fraks}{\ensuremath{\mathfrak{s}}}
-\providecommand{\frakt}{\ensuremath{\mathfrak{t}}}
-\providecommand{\fraku}{\ensuremath{\mathfrak{u}}}
-\providecommand{\frakv}{\ensuremath{\mathfrak{v}}}
-\providecommand{\frakw}{\ensuremath{\mathfrak{w}}}
-\providecommand{\frakx}{\ensuremath{\mathfrak{x}}}
-\providecommand{\fraky}{\ensuremath{\mathfrak{y}}}
-\providecommand{\frakz}{\ensuremath{\mathfrak{z}}}
-\providecommand{\frakA}{\ensuremath{\mathfrak{A}}}
-\providecommand{\frakB}{\ensuremath{\mathfrak{B}}}
-\providecommand{\frakC}{\ensuremath{\mathfrak{C}}}
-\providecommand{\frakD}{\ensuremath{\mathfrak{D}}}
-\providecommand{\frakE}{\ensuremath{\mathfrak{E}}}
-\providecommand{\frakF}{\ensuremath{\mathfrak{F}}}
-\providecommand{\frakG}{\ensuremath{\mathfrak{G}}}
-\providecommand{\frakH}{\ensuremath{\mathfrak{H}}}
-\providecommand{\frakI}{\ensuremath{\mathfrak{I}}}
-\providecommand{\frakJ}{\ensuremath{\mathfrak{J}}}
-\providecommand{\frakK}{\ensuremath{\mathfrak{K}}}
-\providecommand{\frakL}{\ensuremath{\mathfrak{L}}}
-\providecommand{\frakM}{\ensuremath{\mathfrak{M}}}
-\providecommand{\frakN}{\ensuremath{\mathfrak{N}}}
-\providecommand{\frakO}{\ensuremath{\mathfrak{O}}}
-\providecommand{\frakP}{\ensuremath{\mathfrak{P}}}
-\providecommand{\frakQ}{\ensuremath{\mathfrak{Q}}}
-\providecommand{\frakR}{\ensuremath{\mathfrak{R}}}
-\providecommand{\frakS}{\ensuremath{\mathfrak{S}}}
-\providecommand{\frakT}{\ensuremath{\mathfrak{T}}}
-\providecommand{\frakU}{\ensuremath{\mathfrak{U}}}
-\providecommand{\frakV}{\ensuremath{\mathfrak{V}}}
-\providecommand{\frakW}{\ensuremath{\mathfrak{W}}}
-\providecommand{\frakX}{\ensuremath{\mathfrak{X}}}
-\providecommand{\frakY}{\ensuremath{\mathfrak{Y}}}
-\providecommand{\frakZ}{\ensuremath{\mathfrak{Z}}}
-
-\providecommand{\ms}[1]{\ensuremath{\mathscr{#1}}}
-\providecommand{\msA}{\ensuremath{\mathscr{A}}}
-\providecommand{\msB}{\ensuremath{\mathscr{B}}}
-\providecommand{\msC}{\ensuremath{\mathscr{C}}}
-\providecommand{\msD}{\ensuremath{\mathscr{D}}}
-\providecommand{\msE}{\ensuremath{\mathscr{E}}}
-\providecommand{\msF}{\ensuremath{\mathscr{F}}}
-\providecommand{\msG}{\ensuremath{\mathscr{G}}}
-\providecommand{\msH}{\ensuremath{\mathscr{H}}}
-\providecommand{\msI}{\ensuremath{\mathscr{I}}}
-\providecommand{\msJ}{\ensuremath{\mathscr{J}}}
-\providecommand{\msK}{\ensuremath{\mathscr{K}}}
-\providecommand{\msL}{\ensuremath{\mathscr{L}}}
-\providecommand{\msM}{\ensuremath{\mathscr{M}}}
-\providecommand{\msN}{\ensuremath{\mathscr{N}}}
-\providecommand{\msO}{\ensuremath{\mathscr{O}}}
-\providecommand{\msP}{\ensuremath{\mathscr{P}}}
-\providecommand{\msQ}{\ensuremath{\mathscr{Q}}}
-\providecommand{\msR}{\ensuremath{\mathscr{R}}}
-\providecommand{\msS}{\ensuremath{\mathscr{S}}}
-\providecommand{\msT}{\ensuremath{\mathscr{T}}}
-\providecommand{\msU}{\ensuremath{\mathscr{U}}}
-\providecommand{\msV}{\ensuremath{\mathscr{V}}}
-\providecommand{\msW}{\ensuremath{\mathscr{W}}}
-\providecommand{\msX}{\ensuremath{\mathscr{X}}}
-\providecommand{\msY}{\ensuremath{\mathscr{Y}}}
-\providecommand{\msZ}{\ensuremath{\mathscr{Z}}}
-
-\providecommand{\scr}[1]{\ensuremath{\mathscr{#1}}}
-\providecommand{\scrA}{\ensuremath{\mathscr{A}}}
-\providecommand{\scrB}{\ensuremath{\mathscr{B}}}
-\providecommand{\scrC}{\ensuremath{\mathscr{C}}}
-\providecommand{\scrD}{\ensuremath{\mathscr{D}}}
-\providecommand{\scrE}{\ensuremath{\mathscr{E}}}
-\providecommand{\scrF}{\ensuremath{\mathscr{F}}}
-\providecommand{\scrG}{\ensuremath{\mathscr{G}}}
-\providecommand{\scrH}{\ensuremath{\mathscr{H}}}
-\providecommand{\scrI}{\ensuremath{\mathscr{I}}}
-\providecommand{\scrJ}{\ensuremath{\mathscr{J}}}
-\providecommand{\scrK}{\ensuremath{\mathscr{K}}}
-\providecommand{\scrL}{\ensuremath{\mathscr{L}}}
-\providecommand{\scrM}{\ensuremath{\mathscr{M}}}
-\providecommand{\scrN}{\ensuremath{\mathscr{N}}}
-\providecommand{\scrO}{\ensuremath{\mathscr{O}}}
-\providecommand{\scrP}{\ensuremath{\mathscr{P}}}
-\providecommand{\scrQ}{\ensuremath{\mathscr{Q}}}
-\providecommand{\scrR}{\ensuremath{\mathscr{R}}}
-\providecommand{\scrS}{\ensuremath{\mathscr{S}}}
-\providecommand{\scrT}{\ensuremath{\mathscr{T}}}
-\providecommand{\scrU}{\ensuremath{\mathscr{U}}}
-\providecommand{\scrV}{\ensuremath{\mathscr{V}}}
-\providecommand{\scrW}{\ensuremath{\mathscr{W}}}
-\providecommand{\scrX}{\ensuremath{\mathscr{X}}}
-\providecommand{\scrY}{\ensuremath{\mathscr{Y}}}
-\providecommand{\scrZ}{\ensuremath{\mathscr{Z}}}
-
-%%================================
-%% General symbols
-%%================================
-\providecommand{\abs}[1]{\lvert#1\rvert}
-\providecommand{\norm}[1]{\lVert#1\rVert}
-
-\providecommand*{\injection}{\ensuremath{\hookrightarrow}}
-\providecommand*{\surjection}{\ensuremath{\twoheadrightarrow}}
-\providecommand*{\bijection}{\ensuremath{\xrightarrow{\sim}}}
-
-%%================================
-%% Symbols for number theory
-%%================================
-\ifdefined\@@pmod\else
-\let\@@pmod\pmod
-\DeclareRobustCommand{\pmod}{\@ifstar\@pmods\@@pmod}
-\def\@pmods#1{\mkern4mu({\operator@font mod}\mkern 6mu#1)}
-\fi
-
-\providecommand{\genlegendre}[4]{%
- \genfrac{(}{)}{}{#1}{#3}{#4}%
- \if\relax\detokenize{#2}\relax\else_{\!#2}\fi%
-}
-\providecommand{\legendre}[3][]{\genlegendre{}{#1}{#2}{#3}}
-\providecommand{\dlegendre}[3][]{\genlegendre{0}{#1}{#2}{#3}}
-\providecommand{\tlegendre}[3][]{\genlegendre{1}{#1}{#2}{#3}}
-
-\endinput
-%%
-%% End of file `PJLmath.sty'.