%LaTeX package providing some shorthands and quick commands, tailored to certain unspecified fields of maths.
%Not checked for conflicts with other packages.
%Mostly for personal use.
%Will not always be backwards compatible, although every effort will be made so that this is so.
%Written by Adam Walsh
%Version 1.0 (will not upgrade version numbers for minor command editions)

\ProvidesPackage{fancycom}[2018/02/03 v1.0 Fancy maths common commands package]

\RequirePackage{amsfonts}
\RequirePackage{amsthm}
\RequirePackage{amsmath}
\RequirePackage{amssymb}

\RequirePackage{mathtools}

\RequirePackage{calc}
\RequirePackage{textcomp}
\RequirePackage[nointegrals]{wasysym}
\RequirePackage{xparse}

%\RequirePackage{mathrsfs}
\RequirePackage[mathscr]{euscript}

\RequirePackage{tikz-cd}

%Textual shortcuts/aids
    \newcommand{\mbb}[1]{\mathbb{#1}} %Emblacken your symbols!
    \newcommand{\mbf}[1]{\mathbf{#1}} %Embolden your symbols!
    \newcommand{\mfk}[1]{\mathfrak{#1}} %Enfraken your symbols!
    \newcommand{\bsl}{\backslash} %Backslash
    \newcommand{\cndall}{\,\,\,\forall} %forall given as condition
    \newcommand{\st}{\,\mid\,}  %Such that symbol. : is also used.
    \newcommand{\what}[1]{& \qquad &\begin{sloppy}\textit{\small\mbox{#1}\small}\end{sloppy}} %Little comment for an align block. Memento of 2007.

%Basic symbol extensions
    \def\bA{\mathbb{A}}
    \def\bF{\mathbb{F}}
    \def\bN{\mathbb{N}}
    \def\bR{\mathbb{R}}
    \def\bZ{\mathbb{Z}}
    \def\bQ{\mathbb{Q}}
    \def\bC{\mathbb{C}}
    \def\bO{\mathbb{O}}
    \def\bP{\mathbb{P}}
    \def\bS{\mathbb{S}}
    \def\fR{\mathfrak{R}}
    \def\fZ{\mathfrak{Z}}
    \def\fQ{\mathfrak{Q}}
    \def\fC{\mathfrak{C}}
    \def\fO{\mathfrak{O}}
    \def\sC{\mathscr{C}}
    \def\sD{\mathscr{D}}
    \def\sP{\mathscr{P}}
    \def\sF{\mathscr{F}}
    \def\sH{\mathscr{H}}
    \def\sM{\mathscr{M}}
    \def\sT{\mathscr{T}}
    \def\cA{\mathcal{A}}
    \def\cB{\mathcal{B}}
    \def\cO{\mathcal{O}}
    \def\cF{\mathcal{F}}
    \def\cG{\mathcal{G}}
    \def\cC{\mathcal{C}}
    \def\cD{\mathcal{D}}
    \def\cT{\mathcal{T}}
    \def\cP{\mathcal{P}}
    \def\cS{\mathcal{S}}
    
    \def\bfz{\mathbf{0}}
    
    \def\fkp{\mathfrak{p}}
    \def\fkq{\mathfrak{q}}
    \def\fkm{\mathfrak{m}}


%Symbol abbreviations
    \def\lm{\lambda}
    \def\eps{\epsilon}
    \def\veps{\varepsilon}
    \def\vphi{\varphi}
    
    \def\ot{\otimes}
    \def\ptl{\partial}
    \def\bdry{\partial}

    \def\nin{\not\in}
    
    \newcommand{\isom}{\cong} %Isomorphism
    \newcommand{\ceq}{\coloneqq} %Defined to be equal to
    \newcommand{\eqc}{\eqqcolon} %Equal to be defined to
    \newcommand{\ra}{\rangle} %Right angle bracket
    \newcommand{\la}{\langle} %Left angle bracket
    \newcommand{\wto}{\rightharpoonup} %Weak convergence, or just an arrow with the bottom half missing
    \renewcommand{\to}{\longrightarrow} %A long right arrow, for functions and such
    \newcommand{\lmto}{\longmapsto} %A right arrow with a vertical tail, for mapping definitions
    \newcommand{\llim}{\lim\limits} %limit set up so that it always writes the limits underneath

%Function constructors
    \newcommand{\func}[3]{#1\colon#2\to #3} %Generic function definition without mapping
    \newcommand{\mfunc}[3]{#1\colon#2\mapsto #3} %Generic function definition with only mapping
    \newcommand{\afunc}[3]{#1\colon#2&\to #3} %Generic function with alignment on arrow
    \newcommand{\vfunc}[5]{\func{#1}{#2}{#3},\quad#4\longmapsto #5} %Generic function definition with mapping
    \newcommand{\vafunc}[5]{\afunc{#1}{#2}{#3}\\#4&\longmapsto #5} %Generic function over two lines aligned on arrow


%More complex operator constructors
    \DeclareDocumentCommand\amod{ m g g }
    {%
      \IfNoValueTF{#2}
      {%
        \pmod{#1}
      }{%
        \IfNoValueTF{#3}
        {%
          {#1}\pmod{#2}
        }{%
          {#1} \,\equiv\, #2\pmod{#3}
        }
      }
    }

    \DeclareDocumentCommand\ppp{ m g }
    {%
      \IfNoValueTF{#2}
      {%
        \frac{\partial}{\partial #1}
      }{%
        \frac{\partial #1}{\partial #2}
      }
    }

    \newcommand{\pp}[1]{\frac{\partial}{\partial #1}}


%For theorems and proofs

    \newtheorem{Theorem}{Theorem}
    \newtheorem{Proposition}{Proposition}
    \newtheorem{Conjecture}[Theorem]{Conjecture}
    \newtheorem{Lemma}[Theorem]{Lemma}
    \newtheorem{Corollary}[Theorem]{Corollary}

\theoremstyle{remark}
    \newtheorem{Example}{Example}
    \newtheorem{Note}{Note}
    \newtheorem{Question}{Question}
    \newtheorem{Remark}{Remark}

\theoremstyle{definition}
    \newtheorem{Result}[Theorem]{Result}
    \newtheorem{Definition}[Theorem]{Definition}
    %Shorthands
    \DeclareDocumentCommand\sdef{m}{\begin{Definition}#1\end{Definition}}
    \DeclareDocumentCommand\sex{m}{\begin{Example}#1\end{Example}}
    \DeclareDocumentCommand\snote{m}{\begin{Note}#1\end{Note}}
    \DeclareDocumentCommand\slem{m}{\begin{Lemma}#1\end{Lemma}}
    \DeclareDocumentCommand\sresult{m}{\begin{Result}#1\end{Result}}
    \DeclareDocumentCommand\sres{m}{\begin{Result}#1\end{Result}}
    \DeclareDocumentCommand\sques{m}{\begin{Question}#1\end{Question}}
    \DeclareDocumentCommand\srem{m}{\begin{Remark}#1\end{Remark}}



%Mathematical Operators
    \DeclareMathOperator{\Ell}{Ell} %Elliptic genera
    \DeclareMathOperator{\id}{id}
    \DeclareMathOperator{\Id}{id}
    \DeclareMathOperator{\Set}{\mathscr{S}et}
    \DeclareMathOperator{\Hom}{\mathscr{H}om}
    \DeclareMathOperator{\Top}{\mathscr{T}op}
    \DeclareMathOperator{\Mod}{\mathbf{Mod}}
    \DeclareMathOperator{\Comm}{\mathbf{Comm}}
    \DeclareMathOperator{\Grp}{\mathbf{Grp}}
    \DeclareMathOperator{\GL}{GL}
    \DeclareMathOperator{\Obj}{Obj}
    \DeclareMathOperator{\Spec}{Spec}
    \DeclareMathOperator{\Specm}{Specm}
    \DeclareMathOperator{\Min}{min}
    \DeclareMathOperator{\Ker}{Ker}
    \DeclareMathOperator{\im}{Im}
    \DeclareMathOperator{\CoIm}{CoIm}
    \DeclareMathOperator{\CoKer}{CoKer}
    \DeclareMathOperator{\Der}{Der}
    \DeclareMathOperator{\End}{End}
    
    
% Brackets and braces
    \DeclareDocumentCommand\braces{}{{\ifnum\z@=`}\fi\@braces}
    \DeclareDocumentCommand\@braces{ s t\big t\Big t\bigg t\Bigg m m m }
    { % General braces with automatic and manual sizing
    	\IfBooleanTF{#1}
    	{\left#6\smash{#8}\right#7\vphantom{#8}}
    	{
    		\IfBooleanTF{#2}{\bigl#6{#8}\bigr#7}{
    			\IfBooleanTF{#3}{\Bigl#6{#8}\Bigr#7}{
    				\IfBooleanTF{#4}{\biggl#6{#8}\biggr#7}{
    					\IfBooleanTF{#5}{\Biggl#6{#8}\Biggr#7}{\left#6{#8}\right#7}
    				}
    			}
    		}
    	}
    	\ifnum\z@=`{\fi}
    }


    \DeclareDocumentCommand\quantity{}{{\ifnum\z@=`}\fi\@quantity}
    \DeclareDocumentCommand\@quantity{ t\big t\Big t\bigg t\Bigg g o d() d|| }
    { % Flexible automatic bracketing of an expression in () or [] or {} or ||
    	% Handles manual override of sizing
    	\IfBooleanTF{#1}{\let\ltag\bigl \let\rtag\bigr}{
    		\IfBooleanTF{#2}{\let\ltag\Bigl \let\rtag\Bigr}{
    			\IfBooleanTF{#3}{\let\ltag\biggl \let\rtag\biggr}{
    				\IfBooleanTF{#4}
    				{\let\ltag\Biggl \let\rtag\Biggr}
    				{\let\ltag\left \let\rtag\right}
    			}
    		}
    	}
    	% Handles actual bracketing
    	\IfNoValueTF{#5}{
    		\IfNoValueTF{#6}{
    			\IfNoValueTF{#7}{
    				\IfNoValueTF{#8}
    				{()}
    				{\ltag\lvert{#8}\rtag\rvert}
    			}
    			{\ltag(#7\rtag) \IfNoValueTF{#8}{}{|#8|}}
    		}
    		{\ltag[#6\rtag] \IfNoValueTF{#7}{}{(#7)} \IfNoValueTF{#8}{}{|#8|}}
    	}
    	{\ltag\lbrace#5\rtag\rbrace  \IfNoValueTF{#6}{}{[#6]} \IfNoValueTF{#7}{}{(#7)} \IfNoValueTF{#8}{}{|#8|}}
    	\ifnum\z@=`{\fi}
    }
    \DeclareDocumentCommand\qty{}{\quantity} % Shorthand for \quantity
    \DeclareDocumentCommand\pqty{ l m }{\braces#1{\lparen}{\rparen}{#2}}
    \DeclareDocumentCommand\bqty{ l m }{\braces#1{\lbrack}{\rbrack}{#2}}
    \DeclareDocumentCommand\Bqty{ l m }{\braces#1{\lbrace}{\rbrace}{#2}}
    \DeclareDocumentCommand\vqty{ l m }{\braces#1{\lvert}{\rvert}{#2}}

%Matrix constructors
\DeclareDocumentCommand\pmqty{m}{\begin{pmatrix}#1\end{pmatrix}}
\DeclareDocumentCommand\Pmqty{m}{\left\lgroup\begin{matrix}#1\end{matrix}\right\rgroup}
\DeclareDocumentCommand\bmqty{m}{\begin{bmatrix}#1\end{bmatrix}}
\DeclareDocumentCommand\Bmqty{m}{\begin{Bmatrix}#1\end{Bmatrix}}
\DeclareDocumentCommand\sbmqty{m}{\left[\begin{smallmatrix}#1\end{smallmatrix}\right]}
\DeclareDocumentCommand\vmqty{m}{\begin{vmatrix}#1\end{vmatrix}}
\DeclareDocumentCommand\matrixquantity{}{{\ifnum\z@=`}\fi\@matrixquantity}
\DeclareDocumentCommand\@matrixquantity{ s g o d() d|| }
{
	\mathord{
	\IfNoValueTF{#2}
	{
		\IfNoValueTF{#3}
		{
			\IfNoValueTF{#4}
			{
				\IfNoValueTF{#5}
				{()}
				{\vmqty{#5}}
			}
			{
				\IfBooleanTF{#1}
				{\Pmqty{#4}}
				{\pmqty{#4}}
				\IfNoValueTF{#5}{}{|#5|}
			}
		}
		{\bmqty{#3} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
	}
	{\begin{matrix}#2\end{matrix} \IfNoValueTF{#3}{}{[#3]} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
	}
	\ifnum\z@=`{\fi}
}
\DeclareDocumentCommand\mqty{}{\matrixquantity} % Shorthand for \matrixquantity
\DeclareDocumentCommand\matrixdeterminant{m}{\vmqty{#1}} % Matrix determinant
\DeclareDocumentCommand\mdet{}{\matrixdeterminant} % Shorthand for matrix determinant


% Quick quad text (math-mode text with \quad spacing)
    \DeclareDocumentCommand\qqtext{ s m }{\IfBooleanTF{#1}{}{\quad}\text{#2}\quad}
    \DeclareDocumentCommand\qq{}{\qqtext}
    
    \DeclareDocumentCommand\qcomma{}{,\quad}
    \DeclareDocumentCommand\qc{}{\qcomma}
    
    \DeclareDocumentCommand\qif{s}{\IfBooleanTF{#1}{}{\quad}\text{if}\quad}
    \DeclareDocumentCommand\qthen{s}{\IfBooleanTF{#1}{}{\quad}\text{then}\quad}
    \DeclareDocumentCommand\qelse{s}{\IfBooleanTF{#1}{}{\quad}\text{else}\quad}
    \DeclareDocumentCommand\qotherwise{s}{\IfBooleanTF{#1}{}{\quad}\text{otherwise}\quad}
    \DeclareDocumentCommand\qunless{s}{\IfBooleanTF{#1}{}{\quad}\text{unless}\quad}
    \DeclareDocumentCommand\qgiven{s}{\IfBooleanTF{#1}{}{\quad}\text{given}\quad}
    \DeclareDocumentCommand\qusing{s}{\IfBooleanTF{#1}{}{\quad}\text{using}\quad}
    \DeclareDocumentCommand\qassume{s}{\IfBooleanTF{#1}{}{\quad}\text{assume}\quad}
    \DeclareDocumentCommand\qsince{s}{\IfBooleanTF{#1}{}{\quad}\text{since}\quad}
    \DeclareDocumentCommand\qlet{s}{\IfBooleanTF{#1}{}{\quad}\text{let}\quad}
    \DeclareDocumentCommand\qfor{s}{\IfBooleanTF{#1}{}{\quad}\text{for}\quad}
    \DeclareDocumentCommand\qall{s}{\IfBooleanTF{#1}{}{\quad}\text{all}\quad}
    \DeclareDocumentCommand\qeven{s}{\IfBooleanTF{#1}{}{\quad}\text{even}\quad}
    \DeclareDocumentCommand\qodd{s}{\IfBooleanTF{#1}{}{\quad}\text{odd}\quad}
    \DeclareDocumentCommand\qinteger{s}{\IfBooleanTF{#1}{}{\quad}\text{integer}\quad}
    \DeclareDocumentCommand\qand{s}{\IfBooleanTF{#1}{}{\quad}\text{and}\quad}
    \DeclareDocumentCommand\qor{s}{\IfBooleanTF{#1}{}{\quad}\text{or}\quad}
    \DeclareDocumentCommand\qas{s}{\IfBooleanTF{#1}{}{\quad}\text{as}\quad}
    \DeclareDocumentCommand\qin{s}{\IfBooleanTF{#1}{}{\quad}\text{in}\quad}
    \DeclareDocumentCommand\qcc{s}{\IfBooleanTF{#1}{}{\quad}\text{c.c.}\quad}