307 lines
11 KiB
TeX
307 lines
11 KiB
TeX
%LaTeX package providing some shorthands and quick commands, tailored to certain unspecified fields of maths.
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%Not checked for conflicts with other packages.
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%Mostly for personal use.
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%Will not always be backwards compatible, although every effort will be made so that this is so.
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%Written by Adam Walsh
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%Version 1.0 (will not upgrade version numbers for minor command editions)
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\ProvidesPackage{fancycom}[2018/02/03 v1.0 Fancy maths common commands package]
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\RequirePackage{amsfonts}
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\RequirePackage{amsthm}
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\RequirePackage{amsmath}
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\RequirePackage{amssymb}
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\RequirePackage{mathtools}
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\RequirePackage{calc}
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\RequirePackage{textcomp}
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\RequirePackage[nointegrals]{wasysym}
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\RequirePackage{xparse}
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%\RequirePackage{mathrsfs}
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\RequirePackage[mathscr]{euscript}
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\RequirePackage{tikz-cd}
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%Textual shortcuts/aids
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\newcommand{\mbb}[1]{\mathbb{#1}} %Emblacken your symbols!
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\newcommand{\mbf}[1]{\mathbf{#1}} %Embolden your symbols!
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\newcommand{\mfk}[1]{\mathfrak{#1}} %Enfraken your symbols!
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\newcommand{\bsl}{\backslash} %Backslash
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\newcommand{\cndall}{\,\,\,\forall} %forall given as condition
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\newcommand{\st}{\,\mid\,} %Such that symbol. : is also used.
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\newcommand{\what}[1]{& \qquad &\begin{sloppy}\textit{\small\mbox{#1}\small}\end{sloppy}} %Little comment for an align block. Memento of 2007.
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%Basic symbol extensions
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\def\bA{\mathbb{A}}
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\def\bF{\mathbb{F}}
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\def\bN{\mathbb{N}}
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\def\bR{\mathbb{R}}
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\def\bZ{\mathbb{Z}}
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\def\bQ{\mathbb{Q}}
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\def\bC{\mathbb{C}}
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\def\bO{\mathbb{O}}
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\def\bP{\mathbb{P}}
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\def\bS{\mathbb{S}}
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\def\fR{\mathfrak{R}}
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\def\fZ{\mathfrak{Z}}
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\def\fQ{\mathfrak{Q}}
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\def\fC{\mathfrak{C}}
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\def\fO{\mathfrak{O}}
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\def\sC{\mathscr{C}}
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\def\sD{\mathscr{D}}
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\def\sP{\mathscr{P}}
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\def\sF{\mathscr{F}}
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\def\sH{\mathscr{H}}
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\def\sM{\mathscr{M}}
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\def\sT{\mathscr{T}}
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\def\cA{\mathcal{A}}
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\def\cB{\mathcal{B}}
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\def\cO{\mathcal{O}}
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\def\cF{\mathcal{F}}
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\def\cG{\mathcal{G}}
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\def\cC{\mathcal{C}}
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\def\cD{\mathcal{D}}
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\def\cT{\mathcal{T}}
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\def\cP{\mathcal{P}}
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\def\cS{\mathcal{S}}
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\def\bfz{\mathbf{0}}
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\def\fkp{\mathfrak{p}}
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\def\fkq{\mathfrak{q}}
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\def\fkm{\mathfrak{m}}
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%Symbol abbreviations
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\def\lm{\lambda}
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\def\eps{\epsilon}
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\def\veps{\varepsilon}
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\def\vphi{\varphi}
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\def\ot{\otimes}
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\def\ptl{\partial}
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\def\bdry{\partial}
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\def\nin{\not\in}
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\newcommand{\isom}{\cong} %Isomorphism
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\newcommand{\ceq}{\coloneqq} %Defined to be equal to
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\newcommand{\eqc}{\eqqcolon} %Equal to be defined to
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\newcommand{\ra}{\rangle} %Right angle bracket
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\newcommand{\la}{\langle} %Left angle bracket
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\newcommand{\wto}{\rightharpoonup} %Weak convergence, or just an arrow with the bottom half missing
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\renewcommand{\to}{\longrightarrow} %A long right arrow, for functions and such
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\newcommand{\lmto}{\longmapsto} %A right arrow with a vertical tail, for mapping definitions
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\newcommand{\llim}{\lim\limits} %limit set up so that it always writes the limits underneath
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%Function constructors
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\newcommand{\func}[3]{#1\colon#2\to #3} %Generic function definition without mapping
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\newcommand{\mfunc}[3]{#1\colon#2\mapsto #3} %Generic function definition with only mapping
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\newcommand{\afunc}[3]{#1\colon#2&\to #3} %Generic function with alignment on arrow
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\newcommand{\vfunc}[5]{\func{#1}{#2}{#3},\quad#4\longmapsto #5} %Generic function definition with mapping
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\newcommand{\vafunc}[5]{\afunc{#1}{#2}{#3}\\#4&\longmapsto #5} %Generic function over two lines aligned on arrow
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%More complex operator constructors
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\DeclareDocumentCommand\amod{ m g g }
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{%
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\IfNoValueTF{#2}
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{%
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\pmod{#1}
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}{%
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\IfNoValueTF{#3}
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{%
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{#1}\pmod{#2}
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}{%
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{#1} \,\equiv\, #2\pmod{#3}
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}
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}
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}
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\DeclareDocumentCommand\ppp{ m g }
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{%
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\IfNoValueTF{#2}
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{%
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\frac{\partial}{\partial #1}
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}{%
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\frac{\partial #1}{\partial #2}
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}
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}
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\newcommand{\pp}[1]{\frac{\partial}{\partial #1}}
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%For theorems and proofs
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\newtheorem{Theorem}{Theorem}
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\newtheorem{Proposition}{Proposition}
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\newtheorem{Conjecture}[Theorem]{Conjecture}
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\newtheorem{Lemma}[Theorem]{Lemma}
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\newtheorem{Corollary}[Theorem]{Corollary}
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\theoremstyle{remark}
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\newtheorem{Example}{Example}
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\newtheorem{Note}{Note}
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\newtheorem{Question}{Question}
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\newtheorem{Remark}{Remark}
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\theoremstyle{definition}
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\newtheorem{Result}[Theorem]{Result}
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\newtheorem{Definition}[Theorem]{Definition}
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%Shorthands
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\DeclareDocumentCommand\sdef{m}{\begin{Definition}#1\end{Definition}}
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\DeclareDocumentCommand\sex{m}{\begin{Example}#1\end{Example}}
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\DeclareDocumentCommand\snote{m}{\begin{Note}#1\end{Note}}
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\DeclareDocumentCommand\slem{m}{\begin{Lemma}#1\end{Lemma}}
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\DeclareDocumentCommand\sresult{m}{\begin{Result}#1\end{Result}}
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\DeclareDocumentCommand\sres{m}{\begin{Result}#1\end{Result}}
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\DeclareDocumentCommand\sques{m}{\begin{Question}#1\end{Question}}
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\DeclareDocumentCommand\srem{m}{\begin{Remark}#1\end{Remark}}
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%Mathematical Operators
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\DeclareMathOperator{\Ell}{Ell} %Elliptic genera
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\DeclareMathOperator{\id}{id}
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\DeclareMathOperator{\Id}{id}
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\DeclareMathOperator{\Set}{\mathscr{S}et}
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\DeclareMathOperator{\Hom}{\mathscr{H}om}
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\DeclareMathOperator{\Top}{\mathscr{T}op}
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\DeclareMathOperator{\Mod}{\mathbf{Mod}}
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\DeclareMathOperator{\Comm}{\mathbf{Comm}}
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\DeclareMathOperator{\Grp}{\mathbf{Grp}}
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\DeclareMathOperator{\GL}{GL}
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\DeclareMathOperator{\Obj}{Obj}
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\DeclareMathOperator{\Spec}{Spec}
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\DeclareMathOperator{\Specm}{Specm}
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\DeclareMathOperator{\Min}{min}
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\DeclareMathOperator{\Ker}{Ker}
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\DeclareMathOperator{\im}{Im}
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\DeclareMathOperator{\CoIm}{CoIm}
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\DeclareMathOperator{\CoKer}{CoKer}
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\DeclareMathOperator{\Der}{Der}
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\DeclareMathOperator{\End}{End}
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% Brackets and braces
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\DeclareDocumentCommand\braces{}{{\ifnum\z@=`}\fi\@braces}
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\DeclareDocumentCommand\@braces{ s t\big t\Big t\bigg t\Bigg m m m }
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{ % General braces with automatic and manual sizing
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\IfBooleanTF{#1}
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{\left#6\smash{#8}\right#7\vphantom{#8}}
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{
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\IfBooleanTF{#2}{\bigl#6{#8}\bigr#7}{
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\IfBooleanTF{#3}{\Bigl#6{#8}\Bigr#7}{
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\IfBooleanTF{#4}{\biggl#6{#8}\biggr#7}{
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\IfBooleanTF{#5}{\Biggl#6{#8}\Biggr#7}{\left#6{#8}\right#7}
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}
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}
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}
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}
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\ifnum\z@=`{\fi}
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}
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\DeclareDocumentCommand\quantity{}{{\ifnum\z@=`}\fi\@quantity}
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\DeclareDocumentCommand\@quantity{ t\big t\Big t\bigg t\Bigg g o d() d|| }
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{ % Flexible automatic bracketing of an expression in () or [] or {} or ||
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% Handles manual override of sizing
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\IfBooleanTF{#1}{\let\ltag\bigl \let\rtag\bigr}{
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\IfBooleanTF{#2}{\let\ltag\Bigl \let\rtag\Bigr}{
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\IfBooleanTF{#3}{\let\ltag\biggl \let\rtag\biggr}{
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\IfBooleanTF{#4}
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{\let\ltag\Biggl \let\rtag\Biggr}
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{\let\ltag\left \let\rtag\right}
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}
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}
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}
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% Handles actual bracketing
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\IfNoValueTF{#5}{
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\IfNoValueTF{#6}{
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\IfNoValueTF{#7}{
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\IfNoValueTF{#8}
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{()}
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{\ltag\lvert{#8}\rtag\rvert}
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}
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{\ltag(#7\rtag) \IfNoValueTF{#8}{}{|#8|}}
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}
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{\ltag[#6\rtag] \IfNoValueTF{#7}{}{(#7)} \IfNoValueTF{#8}{}{|#8|}}
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}
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{\ltag\lbrace#5\rtag\rbrace \IfNoValueTF{#6}{}{[#6]} \IfNoValueTF{#7}{}{(#7)} \IfNoValueTF{#8}{}{|#8|}}
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\ifnum\z@=`{\fi}
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}
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\DeclareDocumentCommand\qty{}{\quantity} % Shorthand for \quantity
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\DeclareDocumentCommand\pqty{ l m }{\braces#1{\lparen}{\rparen}{#2}}
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\DeclareDocumentCommand\bqty{ l m }{\braces#1{\lbrack}{\rbrack}{#2}}
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\DeclareDocumentCommand\Bqty{ l m }{\braces#1{\lbrace}{\rbrace}{#2}}
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\DeclareDocumentCommand\vqty{ l m }{\braces#1{\lvert}{\rvert}{#2}}
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%Matrix constructors
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\DeclareDocumentCommand\pmqty{m}{\begin{pmatrix}#1\end{pmatrix}}
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\DeclareDocumentCommand\Pmqty{m}{\left\lgroup\begin{matrix}#1\end{matrix}\right\rgroup}
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\DeclareDocumentCommand\bmqty{m}{\begin{bmatrix}#1\end{bmatrix}}
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\DeclareDocumentCommand\Bmqty{m}{\begin{Bmatrix}#1\end{Bmatrix}}
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\DeclareDocumentCommand\sbmqty{m}{\left[\begin{smallmatrix}#1\end{smallmatrix}\right]}
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\DeclareDocumentCommand\vmqty{m}{\begin{vmatrix}#1\end{vmatrix}}
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\DeclareDocumentCommand\matrixquantity{}{{\ifnum\z@=`}\fi\@matrixquantity}
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\DeclareDocumentCommand\@matrixquantity{ s g o d() d|| }
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{
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\mathord{
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\IfNoValueTF{#2}
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{
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\IfNoValueTF{#3}
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{
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\IfNoValueTF{#4}
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{
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\IfNoValueTF{#5}
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{()}
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{\vmqty{#5}}
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}
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{
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\IfBooleanTF{#1}
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{\Pmqty{#4}}
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{\pmqty{#4}}
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\IfNoValueTF{#5}{}{|#5|}
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}
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}
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{\bmqty{#3} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
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}
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{\begin{matrix}#2\end{matrix} \IfNoValueTF{#3}{}{[#3]} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
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}
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\ifnum\z@=`{\fi}
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}
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\DeclareDocumentCommand\mqty{}{\matrixquantity} % Shorthand for \matrixquantity
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\DeclareDocumentCommand\matrixdeterminant{m}{\vmqty{#1}} % Matrix determinant
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\DeclareDocumentCommand\mdet{}{\matrixdeterminant} % Shorthand for matrix determinant
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% Quick quad text (math-mode text with \quad spacing)
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\DeclareDocumentCommand\qqtext{ s m }{\IfBooleanTF{#1}{}{\quad}\text{#2}\quad}
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\DeclareDocumentCommand\qq{}{\qqtext}
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\DeclareDocumentCommand\qcomma{}{,\quad}
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\DeclareDocumentCommand\qc{}{\qcomma}
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\DeclareDocumentCommand\qif{s}{\IfBooleanTF{#1}{}{\quad}\text{if}\quad}
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\DeclareDocumentCommand\qthen{s}{\IfBooleanTF{#1}{}{\quad}\text{then}\quad}
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\DeclareDocumentCommand\qelse{s}{\IfBooleanTF{#1}{}{\quad}\text{else}\quad}
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\DeclareDocumentCommand\qotherwise{s}{\IfBooleanTF{#1}{}{\quad}\text{otherwise}\quad}
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\DeclareDocumentCommand\qunless{s}{\IfBooleanTF{#1}{}{\quad}\text{unless}\quad}
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\DeclareDocumentCommand\qgiven{s}{\IfBooleanTF{#1}{}{\quad}\text{given}\quad}
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\DeclareDocumentCommand\qusing{s}{\IfBooleanTF{#1}{}{\quad}\text{using}\quad}
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\DeclareDocumentCommand\qassume{s}{\IfBooleanTF{#1}{}{\quad}\text{assume}\quad}
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\DeclareDocumentCommand\qsince{s}{\IfBooleanTF{#1}{}{\quad}\text{since}\quad}
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\DeclareDocumentCommand\qlet{s}{\IfBooleanTF{#1}{}{\quad}\text{let}\quad}
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\DeclareDocumentCommand\qfor{s}{\IfBooleanTF{#1}{}{\quad}\text{for}\quad}
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\DeclareDocumentCommand\qall{s}{\IfBooleanTF{#1}{}{\quad}\text{all}\quad}
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\DeclareDocumentCommand\qeven{s}{\IfBooleanTF{#1}{}{\quad}\text{even}\quad}
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\DeclareDocumentCommand\qodd{s}{\IfBooleanTF{#1}{}{\quad}\text{odd}\quad}
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\DeclareDocumentCommand\qinteger{s}{\IfBooleanTF{#1}{}{\quad}\text{integer}\quad}
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\DeclareDocumentCommand\qand{s}{\IfBooleanTF{#1}{}{\quad}\text{and}\quad}
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\DeclareDocumentCommand\qor{s}{\IfBooleanTF{#1}{}{\quad}\text{or}\quad}
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\DeclareDocumentCommand\qas{s}{\IfBooleanTF{#1}{}{\quad}\text{as}\quad}
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\DeclareDocumentCommand\qin{s}{\IfBooleanTF{#1}{}{\quad}\text{in}\quad}
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\DeclareDocumentCommand\qcc{s}{\IfBooleanTF{#1}{}{\quad}\text{c.c.}\quad}
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