physics.sty

\ProvidesPackage{physics}
% physics 1.3
% This material is subject to the LaTeX Project Public License.
% See http://www.ctan.org/tex-archive/help/Catalogue/licenses.lppl.html for the details of that license.
%
% Handy commands for physicists including macros for vectors, calculus, matrices, and bra-ket (Dirac) notation
% Requires xparse package, which comes bundled with l3packages and l3kernel
% This package loads amsmath, which comes standard with most latex distributions
% The commands defined in this package will silently overwrite previous commands with the same name, if such commands exist
%
% Created by Sergio C. de la Barrera
% Updated on December 12, 2012
% Uploaded on December 20, 2012

\RequirePackage{xparse}
\RequirePackage{amsmath}

% Options
\DeclareOption{trig}{\let\trigopt = 1}
\DeclareOption{notrig}{\let\trigopt = 0}
\DeclareOption{uprightdiff}{\def\diffd{\mathrm{d}}} % Upright differentials
\DeclareOption{italicdiff}{\def\diffd{d}} % Italic differentials
\DeclareOption{bolddel}{\DeclareDocumentCommand\vnabla{}{\boldsymbol\nabla}} % Vector bold \nabla symbol
\DeclareOption{arrowdel}{\DeclareDocumentCommand\vnabla{}{\vec{\boldsymbol\nabla}}} % Vector arrow \nabla symbol
\ExecuteOptions{trig,uprightdiff,bolddel}
\ProcessOptions\relax

% Symbols
\ProvideDocumentCommand\varE{}{\mathcal{E}} % Curly 'E'
\ProvideDocumentCommand\ordersymbol{}{\mathcal{O}} % Order symbol --> O(x^2)
\ProvideDocumentCommand\lparen{}{(} % Left parenthesis
\ProvideDocumentCommand\rparen{}{)} % Right parenthesis

% Brackets and braces
\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}}


\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\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

\DeclareDocumentCommand\spmqty{m}{\pqty{\begin{smallmatrix}#1\end{smallmatrix}}}
\DeclareDocumentCommand\sPmqty{m}{\left\lgroup\begin{smallmatrix}#1\end{smallmatrix}\right\rgroup}
\DeclareDocumentCommand\sbmqty{m}{\bqty{\begin{smallmatrix}#1\end{smallmatrix}}}
\DeclareDocumentCommand\svmqty{m}{\vqty{\begin{smallmatrix}#1\end{smallmatrix}}}
\DeclareDocumentCommand\smallmatrixquantity{ s g o d() d|| }
{
	\mathord{
	\IfNoValueTF{#2}
	{
		\IfNoValueTF{#3}
		{
			\IfNoValueTF{#4}
			{
				\IfNoValueTF{#5}
				{()}
				{\svmqty{#5}}
			}
			{
				\IfBooleanTF{#1}
				{\sPmqty{#4}}
				{\spmqty{#4}}
				\IfNoValueTF{#5}{}{|#5|}
			}
		}
		{\sbmqty{#3} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
	}
	{\begin{smallmatrix}#2\end{smallmatrix} \IfNoValueTF{#3}{}{[#3]} \IfNoValueTF{#4}{}{(#4)} \IfNoValueTF{#5}{}{|#5|}}
	}
}
\DeclareDocumentCommand\smqty{}{\smallmatrixquantity} % Shorthand for \smallmatrixquantity
\DeclareDocumentCommand\smallmatrixdeterminant{m}{\svmqty{#1}} % Small matrix determinant
\DeclareDocumentCommand\smdet{}{\smallmatrixdeterminant} % Shorthand for small matrix determinant

\DeclareDocumentCommand\argopen{s}{\IfBooleanTF{#1}{\mathopen{}\mathclose\bgroup}{\mathopen{}\mathclose\bgroup\left}} % Special open grouping for argument of a function
\DeclareDocumentCommand\argclose{s}{\IfBooleanTF{#1}{\egroup}{\aftergroup\egroup\right}} % Special close grouping for argument of a function

\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\fbraces{ s t\big t\Big t\bigg t\Bigg m m m m }
{ % Function braces with automatic and manual sizing
	#8
	\IfBooleanTF{#1}
	{\argopen#6\smash{#9}\argclose#7\vphantom{#9}}
	{
		\IfBooleanTF{#2}{\argopen*\bigl#6{#9}\argclose*\bigr#7}{
			\IfBooleanTF{#3}{\argopen*\Bigl#6{#9}\argclose*\Bigr#7}{
				\IfBooleanTF{#4}{\argopen*\biggl#6{#9}\argclose*\biggr#7}{
					\IfBooleanTF{#5}
					{\argopen*\Biggl#6{#9}\argclose*\Biggr#7}
					{\argopen#6{#9}\argclose#7}
				}
			}
		}
	}
}

\DeclareDocumentCommand\absolutevalue{ l m }{\braces#1{\lvert}{\rvert}{#2}} % Absolute value/complex modulus
\DeclareDocumentCommand\abs{}{\absolutevalue} % Shorthand for \absolutevalue
\DeclareDocumentCommand\norm{ l m }{\braces#1{\lVert}{\rVert}{#2}} % Norm
\DeclareDocumentCommand\order{ l m }{\fbraces#1{\lparen}{\rparen}{\ordersymbol}{#2}} % Order notation -> O(x^2)

\DeclareDocumentCommand\evaluated{ s g d[| d(| }
{ % Vertical evaluation bar
	\IfNoValueTF{#2}
	{
		\IfNoValueTF{#3}
		{
			\IfNoValueTF{#4}
				{\argopen.\vphantom{\int}\argclose\rvert}
				{\IfBooleanTF{#1}{\vphantom{#4}}{}\left(\IfBooleanTF{#1}{\smash{#4}}{#4}\vphantom{\int}\right\rvert}
		}
		{\IfBooleanTF{#1}{\vphantom{#3}}{}\left[\IfBooleanTF{#1}{\smash{#3}}{#3}\vphantom{\int}\right\rvert \IfNoValueTF{#4}{}{(#4|}}
	}
	{\IfBooleanTF{#1}{\vphantom{#2}}{}\left.\IfBooleanTF{#1}{\smash{#2}}{#2}\vphantom{\int}\right\rvert \IfNoValueTF{#3}{}{[#3|} \IfNoValueTF{#4}{}{(#4|}}
}
\DeclareDocumentCommand\eval{}{\evaluated} % Shorthand for evaluated

\DeclareDocumentCommand\poissonbracket{ l m m }{\braces#1{\lbrace}{\rbrace}{#2,#3}} % Poisson bracket [same as anti-commutator]
\DeclareDocumentCommand\pb{}{\poissonbracket} % Shorthand for \poissonbracket

% Commutators
\DeclareDocumentCommand\commutator{ l m m }{\braces#1{\lbrack}{\rbrack}{#2,#3}} % Commutator
\DeclareDocumentCommand\comm{}{\commutator} % Shorthand for \commutator
\DeclareDocumentCommand\anticommutator{ l m m }{\braces#1{\lbrace}{\rbrace}{#2,#3}} % Anticommutator [same as Poisson bracket]
\DeclareDocumentCommand\acommutator{}{\anticommutator} % Shorthand for \anticommutator
\DeclareDocumentCommand\acomm{}{\anticommutator} % Shorthand for \anticommutator

% Vector notation
\DeclareDocumentCommand\vectorbold{ s m }{\IfBooleanTF{#1}{\boldsymbol{#2}}{\mathbf{#2}}} % Vector bold [star for Greek and italic Roman]
\DeclareDocumentCommand\vb{}{\vectorbold} % Shorthand for \vectorbold

\DeclareDocumentCommand\vectorarrow{ s m }{\IfBooleanTF{#1}{\vec{\boldsymbol{#2}}}{\vec{\mathbf{#2}}}} % Vector arrow + bold [star for Greek and italic Roman]
\DeclareDocumentCommand\va{}{\vectorarrow} % Shorthand for \vectorarrow

\DeclareDocumentCommand\vectorunit{ s m }{\IfBooleanTF{#1}{\boldsymbol{\hat{#2}}}{\mathbf{\hat{#2}}}} % Unit vector [star for Greek and italic Roman]
\DeclareDocumentCommand\vu{}{\vectorunit} % Shorthand for \vectorunit

\DeclareDocumentCommand\dotproduct{}{\boldsymbol\cdot} % Vector dot product symbol
\DeclareDocumentCommand\vdot{}{\dotproduct} % Shorthand for \dotproduct [note that the command sequence \dp is protected]

\DeclareDocumentCommand\crossproduct{}{\boldsymbol\times} % Vector cross product symbol
\DeclareDocumentCommand\cross{}{\crossproduct} % Shorthand for \crossproduct
\DeclareDocumentCommand\cp{}{\crossproduct} % Shorthand for \crossproduct

\DeclareDocumentCommand\gradient{ g o d() }{ % Gradient
	\IfNoValueTF{#1}{
		\IfNoValueTF{#2}{
			\IfNoValueTF{#3}{\vnabla}{\fbraces{\lparen}{\rparen}{\vnabla}{#3}}
			}
			{\fbraces{\lbrack}{\rbrack}{\vnabla}{#2} \IfNoValueTF{#3}{}{(#3)}}
		}
		{\vnabla #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
	}
\DeclareDocumentCommand\grad{}{\gradient} % Shorthand for \gradient

\DeclareDocumentCommand\divergence{ g o d() }{ % Divergence
	\IfNoValueTF{#1}{
		\IfNoValueTF{#2}{
			\IfNoValueTF{#3}{\vnabla \vdot}{\vnabla \vdot \quantity(#3)}
			}
			{\vnabla \vdot \quantity[#2] \IfNoValueTF{#3}{}{(#3)}}
		}
		{\vnabla \vdot #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
	}
\let\divisionsymbol\div % Rename \div [division symbol] in order to free up control sequence for \divergence
\let\div\relax
\DeclareDocumentCommand\div{}{\divergence} % Shorthand for \divergence

\DeclareDocumentCommand\curl{ g o d() }{ % Curl
	\IfNoValueTF{#1}{
		\IfNoValueTF{#2}{
			\IfNoValueTF{#3}{\vnabla \cross}{\vnabla \cross \quantity(#3)}
			}
			{\vnabla \cross \quantity[#2] \IfNoValueTF{#3}{}{(#3)}}
		}
		{\vnabla \cross #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
	}

\DeclareDocumentCommand\laplacian{ g o d() }{ % Laplacian
	\IfNoValueTF{#1}{
		\IfNoValueTF{#2}{
			\IfNoValueTF{#3}{\nabla^2}{\fbraces{\lparen}{\rparen}{\nabla^2}{#3}}
			}
			{\fbraces{\lbrack}{\rbrack}{\nabla^2}{#2} \IfNoValueTF{#3}{}{(#3)}}
		}
		{\nabla^2 #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}}
	}

% Operators
\DeclareMathOperator{\trace}{tr} % Trace of a matrix
\DeclareMathOperator{\Trace}{Tr} % Trace of a matrix (alternate)
\DeclareMathOperator{\rank}{rank} % Rank of a matrix
\DeclareMathOperator{\erf}{erf} % Gauss error function
\DeclareMathOperator{\Residue}{Res} % Residue
\DeclareDocumentCommand\principalvalue{g}{\IfNoValueTF{#1}{\mathcal{P}}{\mathcal{P}\mathord{#1}}}
\DeclareDocumentCommand\pv{}{\principalvalue}
\DeclareDocumentCommand\PV{g}{\IfNoValueTF{#1}{\mathrm{P.V.}}{\mathrm{P.V.}\mathord{#1}}}
\let\real\Re \DeclareDocumentCommand\Re{g}{\IfNoValueTF{#1}{\operatorname{Re}}{\fbraces{\lbrace}{\rbrace}{\operatorname{Re}}{#1}}}
\let\imaginary\Im \DeclareDocumentCommand\Im{g}{\IfNoValueTF{#1}{\operatorname{Im}}{\fbraces{\lbrace}{\rbrace}{\operatorname{Im}}{#1}}}
\DeclareDocumentCommand\opbraces{ m g o d() }
{
	\IfNoValueTF{#2}
	{
		\IfNoValueTF{#3}
			{
				\IfNoValueTF{#4}
				{#1}
				{\fbraces{\lparen}{\rparen}{#1}{#4}}
			}
			{
				\fbraces{\lbrack}{\rbrack}{#1}{#3}
				\IfNoValueTF{#4}{}{(#4)}
			}
	}
	{
		\fbraces{\lbrace}{\rbrace}{#1}{#2}
		\IfNoValueTF{#3}{}{[#3]}
		\IfNoValueTF{#4}{}{(#4)}
	}
}
\DeclareDocumentCommand\trigbraces{ m o d() }
{
	\IfNoValueTF{#3}
	{#1 \IfNoValueTF{#2}{}{[#2]}}
	{#1 \IfNoValueTF{#2}{}{^{#2}} \argopen(#3\argclose)}
}

% Trig function and operator redefinitions
\ifx\trigopt 1
	\let\sine\sin \DeclareDocumentCommand\sin{}{\trigbraces{\sine}}
	\let\cosine\cos \DeclareDocumentCommand\cos{}{\trigbraces{\cosine}}
	\let\tangent\tan \DeclareDocumentCommand\tan{}{\trigbraces{\tangent}}
	\let\cosecant\csc \DeclareDocumentCommand\csc{}{\trigbraces{\cosecant}}
	\let\secant\sec \DeclareDocumentCommand\sec{}{\trigbraces{\secant}}
	\let\cotangent\cot \DeclareDocumentCommand\cot{}{\trigbraces{\cotangent}}
	
	\let\arcsine\arcsin \DeclareDocumentCommand\arcsin{}{\trigbraces{\arcsine}}
	\let\arccosine\arccos \DeclareDocumentCommand\arccos{}{\trigbraces{\arccosine}}
	\let\arctangent\arctan \DeclareDocumentCommand\arctan{}{\trigbraces{\arctangent}}
	\DeclareMathOperator{\arccosecant}{arccsc}
	\DeclareDocumentCommand\arccsc{}{\trigbraces{\arccosecant}}
	\DeclareMathOperator{\arcsecant}{arcsec}
	\DeclareDocumentCommand\arcsec{}{\trigbraces{\arcsecant}}
	\DeclareMathOperator{\arccotangent}{arccot}
	\DeclareDocumentCommand\arccot{}{\trigbraces{\arccotangent}}

	\DeclareMathOperator{\asine}{asin}
	\DeclareDocumentCommand\asin{}{\trigbraces{\asine}}
	\DeclareMathOperator{\acosine}{acos}
	\DeclareDocumentCommand\acos{}{\trigbraces{\acosine}}
	\DeclareMathOperator{\atangent}{atan}
	\DeclareDocumentCommand\atan{}{\trigbraces{\atangent}}
	\DeclareMathOperator{\acosecant}{acsc}
	\DeclareDocumentCommand\acsc{}{\trigbraces{\acosecant}}
	\DeclareMathOperator{\asecant}{asec}
	\DeclareDocumentCommand\asec{}{\trigbraces{\asecant}}
	\DeclareMathOperator{\acotangent}{acot}
	\DeclareDocumentCommand\acot{}{\trigbraces{\acotangent}}
	
	\let\hypsine\sinh \DeclareDocumentCommand\sinh{}{\trigbraces{\hypsine}}
	\let\hypcosine\cosh \DeclareDocumentCommand\cosh{}{\trigbraces{\hypcosine}}
	\let\hyptangent\tanh \DeclareDocumentCommand\tanh{}{\trigbraces{\hyptangent}}
	\DeclareMathOperator{\hypcosecant}{csch}
	\DeclareDocumentCommand\csch{}{\trigbraces{\hypcosecant}}
	\DeclareMathOperator{\hypsecant}{sech}
	\DeclareDocumentCommand\sech{}{\trigbraces{\hypsecant}}
	\let\hypcotangent\coth \DeclareDocumentCommand\coth{}{\trigbraces{\hypcotangent}}
	
	\let\exponential\exp \DeclareDocumentCommand\exp{}{\opbraces{\exponential}}
	\let\logarithm\log \DeclareDocumentCommand\log{}{\trigbraces{\logarithm}}
	\let\naturallogarithm\ln \DeclareDocumentCommand\ln{}{\trigbraces{\naturallogarithm}}
	\let\determinant\det \DeclareDocumentCommand\det{}{\opbraces{\determinant}}
	\let\Probability\Pr \DeclareDocumentCommand\Pr{}{\opbraces{\Probability}}
	\DeclareDocumentCommand\tr{}{\opbraces{\trace}}
	\DeclareDocumentCommand\Tr{}{\opbraces{\Trace}}
	\DeclareDocumentCommand\Res{}{\opbraces{\Residue}}
\else
	\DeclareMathOperator{\arccsc}{arccsc}
	\DeclareMathOperator{\arcsec}{arcsec}
	\DeclareMathOperator{\arccot}{arccot}
	
	\DeclareMathOperator{\asin}{asin}
	\DeclareMathOperator{\acos}{acos}
	\DeclareMathOperator{\atan}{atan}
	\DeclareMathOperator{\acsc}{acsc}
	\DeclareMathOperator{\asec}{asec}
	\DeclareMathOperator{\acot}{acot}
	
	\DeclareMathOperator{\csch}{csch}
	\DeclareMathOperator{\sech}{sech}
	
	\DeclareDocumentCommand\tr{}{\trace}
	\DeclareDocumentCommand\Tr{}{\Trace}
	\DeclareDocumentCommand\Res{}{\Residue}
\fi

% 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}

% Derivatives
\DeclareDocumentCommand\differential{ o g d() }{ % Differential 'd'
	% o: optional n for nth differential
	% g: optional argument for readability and to control spacing
	% d: long-form as in d(cos x)
	\IfNoValueTF{#2}{
		\IfNoValueTF{#3}
			{\diffd\IfNoValueTF{#1}{}{^{#1}}}
			{\mathinner{\diffd\IfNoValueTF{#1}{}{^{#1}}\argopen(#3\argclose)}}
		}
		{\mathinner{\diffd\IfNoValueTF{#1}{}{^{#1}}#2} \IfNoValueTF{#3}{}{(#3)}}
	}
\DeclareDocumentCommand\dd{}{\differential} % Shorthand for \differential

\DeclareDocumentCommand\derivative{ s o m g d() }
{ % Total derivative
	% s: star for \flatfrac flat derivative
	% o: optional n for nth derivative
	% m: mandatory (x in df/dx)
	% g: optional (f in df/dx)
	% d: long-form d/dx(...)
	\IfBooleanTF{#1}
	{\let\fractype\flatfrac}
	{\let\fractype\frac}
	\IfNoValueTF{#4}
	{
		\IfNoValueTF{#5}
		{\fractype{\diffd \IfNoValueTF{#2}{}{^{#2}}}{\diffd #3\IfNoValueTF{#2}{}{^{#2}}}}
		{\fractype{\diffd \IfNoValueTF{#2}{}{^{#2}}}{\diffd #3\IfNoValueTF{#2}{}{^{#2}}} \argopen(#5\argclose)}
	}
	{\fractype{\diffd \IfNoValueTF{#2}{}{^{#2}} #3}{\diffd #4\IfNoValueTF{#2}{}{^{#2}}}}
}
\DeclareDocumentCommand\dv{}{\derivative} % Shorthand for \derivative

\DeclareDocumentCommand\partialderivative{ s o m g g d() }
{ % Partial derivative
	% s: star for \flatfrac flat derivative
	% o: optional n for nth derivative
	% m: mandatory (x in df/dx)
	% g: optional (f in df/dx)
	% g: optional (y in d^2f/dxdy)
	% d: long-form d/dx(...)
	\IfBooleanTF{#1}
	{\let\fractype\flatfrac}
	{\let\fractype\frac}
	\IfNoValueTF{#4}
	{
		\IfNoValueTF{#6}
		{\fractype{\partial \IfNoValueTF{#2}{}{^{#2}}}{\partial #3\IfNoValueTF{#2}{}{^{#2}}}}
		{\fractype{\partial \IfNoValueTF{#2}{}{^{#2}}}{\partial #3\IfNoValueTF{#2}{}{^{#2}}} \argopen(#6\argclose)}
	}
	{
		\IfNoValueTF{#5}
		{\fractype{\partial \IfNoValueTF{#2}{}{^{#2}} #3}{\partial #4\IfNoValueTF{#2}{}{^{#2}}}}
		{\fractype{\partial^2 #3}{\partial #4 \partial #5}}
	}
}
\DeclareDocumentCommand\pderivative{}{\partialderivative} % Shorthand for \partialderivative
\DeclareDocumentCommand\pdv{}{\partialderivative} % Shorthand for \partialderivative

\DeclareDocumentCommand\variation{ o g d() }{ % Functional variation
	% o: optional n for nth differential
	% g: optional argument for readability and to control spacing
	% d: long-form as in d(F(g))
	\IfNoValueTF{#2}{
		\IfNoValueTF{#3}
			{\delta \IfNoValueTF{#1}{}{^{#1}}}
			{\mathinner{\delta \IfNoValueTF{#1}{}{^{#1}}\argopen(#3\argclose)}}
		}
		{\mathinner{\delta \IfNoValueTF{#1}{}{^{#1}}#2} \IfNoValueTF{#3}{}{(#3)}}
	}
\DeclareDocumentCommand\var{}{\variation} % Shorthand for \variation

\DeclareDocumentCommand\functionalderivative{ s o m g d() }
{ % Functional derivative
	% s: star for \flatfrac flat derivative
	% o: optional n for nth derivative
	% m: mandatory (g in dF/dg)
	% g: optional (F in dF/dg)
	% d: long-form d/dx(...)
	\IfBooleanTF{#1}
	{\let\fractype\flatfrac}
	{\let\fractype\frac}
	\IfNoValueTF{#4}
	{
		\IfNoValueTF{#5}
		{\fractype{\variation \IfNoValueTF{#2}{}{^{#2}}}{\variation #3\IfNoValueTF{#2}{}{^{#2}}}}
		{\fractype{\variation \IfNoValueTF{#2}{}{^{#2}}}{\variation #3\IfNoValueTF{#2}{}{^{#2}}} \argopen(#5\argclose)}
	}
	{\fractype{\variation \IfNoValueTF{#2}{}{^{#2}} #3}{\variation #4\IfNoValueTF{#2}{}{^{#2}}}}
}
\DeclareDocumentCommand\fderivative{}{\functionalderivative} % Shorthand for \functionalderivative
\DeclareDocumentCommand\fdv{}{\functionalderivative} % Shorthand for \functionalderivative

% Bra-ket notation
\DeclareDocumentCommand\bra{ s m t\ket s g }
{ % Bra
	\IfBooleanTF{#3}
	{ % Contraction
		\IfBooleanTF{#1}
		{ % Bra has a star: no resize
			\IfNoValueTF{#5}
			{\braket*{#2}{} \IfBooleanTF{#4}{*}{}}
			{\braket*{#2}{#5}}
		}
		{
			\IfBooleanTF{#4}
			{ % Ket has a star: no resize
				\IfNoValueTF{#5}
				{\braket{#2}{} *}
				{\braket*{#2}{#5}}
			}
			{\braket{#2}{\IfNoValueTF{#5}{}{#5}}} % Neither term is starred: auto sizing
		}
	}
	{ % No contraction
		\IfBooleanTF{#1}
		{\vphantom{#2}\left\langle\smash{#2}\right\rvert}
		{\left\langle{#2}\right\rvert}
		\IfBooleanTF{#4}{*}{}
		\IfNoValueTF{#5}{}{#5}
	}
}

\DeclareDocumentCommand\ket{ s m }
{ % Ket
	\IfBooleanTF{#1}
	{\vphantom{#2}\left\lvert\smash{#2}\right\rangle} % No resize
	{\left\lvert{#2}\right\rangle} % Auto sizing
}

\DeclareDocumentCommand\innerproduct{ s m g }
{ % Inner product
	\IfBooleanTF{#1}
	{ % No resize
		\IfNoValueTF{#3}
		{\vphantom{#2}\left\langle\smash{#2}\middle\vert\smash{#2}\right\rangle}
		{\vphantom{#2#3}\left\langle\smash{#2}\middle\vert\smash{#3}\right\rangle}
	}
	{ % Auto resize
		\IfNoValueTF{#3}
		{\left\langle{#2}\middle\vert{#2}\right\rangle}
		{\left\langle{#2}\middle\vert{#3}\right\rangle}
	}
}
\DeclareDocumentCommand\braket{}{\innerproduct} % Alternative for \innerproduct
\DeclareDocumentCommand\ip{}{\innerproduct} % Shorthand for \innerproduct
	
\DeclareDocumentCommand\outerproduct{ s m g }
{ % Dyad
	\IfBooleanTF{#1}
	{ % No resize
		\IfNoValueTF{#3}
		{\vphantom{#2}\left\lvert\smash{#2}\middle\rangle\!\middle\langle\smash{#2}\right\rvert}
		{\vphantom{#2#3}\left\lvert\smash{#2}\middle\rangle\!\middle\langle\smash{#3}\right\rvert}
	}
	{ % Auto resize
		\IfNoValueTF{#3}
		{\left\lvert{#2}\middle\rangle\!\middle\langle{#2}\right\rvert}
		{\left\lvert{#2}\middle\rangle\!\middle\langle{#3}\right\rvert}
	}
}
\DeclareDocumentCommand\dyad{}{\outerproduct} % Alternative for \outerproduct
\DeclareDocumentCommand\op{}{\dyad} % Shorthand for \outerproduct
\DeclareDocumentCommand\ketbra{}{\dyad} % Alternative for \outerproduct

\DeclareDocumentCommand\expectationvalue{ s s m g }
{ % Expectation value
	\IfNoValueTF{#4}
	{
		\IfBooleanTF{#1}
		{\vphantom{#3}\left\langle\smash{#3}\right\rangle} % Starred implicit form: no resizing
		{\left\langle{#3}\right\rangle} % Normal implicit form: auto sizing
	}
	{
		\IfBooleanTF{#1}
		{
			\IfBooleanTF{#2}
			{\left\langle{#4}\middle\vert{#3}\middle\vert{#4}\right\rangle} % Double starred explicit form: total auto sizing
			{\vphantom{#3#4}\left\langle\smash{#4}\middle\vert\smash{#3}\middle\vert\smash{#4}\right\rangle} % Starred explicit form: no resizing
		}
		{\vphantom{#3}\left\langle{#4}\middle\vert\smash{#3}\middle\vert{#4}\right\rangle} % Normal explicit form: only resize based on bra/ket arguments
	}
}
\DeclareDocumentCommand\expval{}{\expectationvalue} % Shorthand for \expectationvalue
\DeclareDocumentCommand\ev{}{\expectationvalue} % Shorthand for \expectationvalue
\DeclareDocumentCommand\vev{ m }{\expectationvalue{#1}{0}} % Vacuum expectation value

\DeclareDocumentCommand\matrixelement{ s s m m m }
{ % Matrix element
	\IfBooleanTF{#1}
	{
		\IfBooleanTF{#2}
		{\left\langle{#3}\middle\vert{#4}\middle\vert{#5}\right\rangle} % Double starred: total resizing
		{\vphantom{#3#4#5}\left\langle\smash{#3}\middle\vert\smash{#4}\middle\vert\smash{#5}\right\rangle} % Starred: no resizing
	}
	{\vphantom{#4}\left\langle{#3}\middle\vert\smash{#4}\middle\vert{#5}\right\rangle} % Normal: only resize based on bra/ket arguments
}
\DeclareDocumentCommand\matrixel{}{\matrixelement} % Shorthand for \matrixelement
\DeclareDocumentCommand\mel{}{\matrixelement} % Shorthand for \matrixelement

% Matrix macros
\DeclareDocumentCommand\identitymatrix{m}
{
	{
		\newtoks\matrixtoks
		\global\matrixtoks = {}
		\newcount\rowcount
		\newcount\colcount
		\loop
		\colcount = 0
		\advance \rowcount by 1
		{
			\loop
			\advance \colcount by 1
			\edef\addtoks
			{
				\ifnum \colcount = 1 \else & \fi
				\ifnum \colcount = \rowcount 1 \else 0 \fi
			}
			\global\matrixtoks = \expandafter{\the\expandafter\matrixtoks\addtoks}
			\ifnum \colcount < #1
			\repeat
		}
		\ifnum \rowcount < #1
			\global\matrixtoks = \expandafter{\the\matrixtoks \\ }
			\repeat
	}
	\the\matrixtoks
}
\DeclareDocumentCommand\imat{}{\identitymatrix}

\DeclareDocumentCommand\xmatrix{ s m m m }
{
	{
		\newtoks\matrixtoks
		\global\matrixtoks = {}
		\newcount\rowcount
		\newcount\colcount
		\loop
		\colcount = 0
		\advance \rowcount by 1
		{
			\loop
			\advance \colcount by 1
			\edef\addtoks{\ifnum \colcount = 1 \else & \fi #2 \IfBooleanTF{#1}{_{\ifnum #3 > 1 \the\rowcount \fi \ifnum #4 > 1 \the\colcount \fi}}{}}
			\global\matrixtoks = \expandafter{\the\expandafter\matrixtoks\addtoks}
			\ifnum \colcount < #4
			\repeat
		}
		\ifnum \rowcount < #3
			\global\matrixtoks = \expandafter{\the\matrixtoks \\ }
			\repeat
	}
	\the\matrixtoks
}
\DeclareDocumentCommand\xmat{}{\xmatrix}

\DeclareDocumentCommand\zeromatrix{ m g }{\IfNoValueTF{#2}{\xmatrix{0}{#1}{#1}}{\xmatrix{0}{#1}{#2}}}
\DeclareDocumentCommand\zmat{}{\zeromatrix}

\DeclareDocumentCommand\paulixmatrix{}{0&1\\1&0}
\DeclareDocumentCommand\pauliymatrix{}{0&-i\\i&0}
\DeclareDocumentCommand\paulizmatrix{}{1&0\\0&-1}
\DeclareDocumentCommand\paulimatrix{m}
{
	\let\argin=#1
	\ifx\argin 0 \identitymatrix{2} \else
	\ifx\argin 1 \paulixmatrix \else
	\ifx\argin 2 \pauliymatrix \else
	\ifx\argin 3 \paulizmatrix \else
	\ifx\argin x \paulixmatrix \else
	\ifx\argin y \pauliymatrix \else
	\ifx\argin z \paulizmatrix \fi\fi\fi\fi\fi\fi\fi
}
\DeclareDocumentCommand\pmat{}{\paulimatrix}

\DeclareDocumentCommand\diagonalmatrix{O{} >{\SplitList{,}}m }{\@dmat{#1}#2}
\DeclareDocumentCommand\@dmat{mmggggggg}
{
	\newtoks\matrixtoks
	\global\matrixtoks = {}
	\IfNoValueTF{#3}
	{#2}
	{
		\IfNoValueTF{#4}
		{\global\matrixtoks = \expandafter{\mqty{#2}&#1\\#1&\mqty{#3}}}
		{
			\IfNoValueTF{#5}
			{\global\matrixtoks = \expandafter{\mqty{#2}&#1&#1\\#1&\mqty{#3}&#1\\#1&#1&\mqty{#4}}}
			{
				\IfNoValueTF{#6}
				{\global\matrixtoks = \expandafter{\mqty{#2}&#1&#1&#1\\#1&\mqty{#3}&#1&#1\\#1&#1&\mqty{#4}&#1\\#1&#1&#1&\mqty{#5}}}
				{
					\IfNoValueTF{#7}
					{\global\matrixtoks = \expandafter{\mqty{#2}&#1&#1&#1&#1\\#1&\mqty{#3}&#1&#1&#1\\#1&#1&\mqty{#4}&#1&#1\\#1&#1&#1&\mqty{#5}&#1\\#1&#1&#1&#1&\mqty{#6}}}
					{
						\IfNoValueTF{#8}
						{\global\matrixtoks = \expandafter{\mqty{#2}&#1&#1&#1&#1&#1\\#1&\mqty{#3}&#1&#1&#1&#1\\#1&#1&\mqty{#4}&#1&#1&#1\\#1&#1&#1&\mqty{#5}&#1&#1\\#1&#1&#1&#1&\mqty{#6}&#1\\#1&#1&#1&#1&#1&\mqty{#7}}}
						{
							\IfNoValueTF{#9}
							{\global\matrixtoks = \expandafter{\mqty{#2}&#1&#1&#1&#1&#1&#1\\#1&\mqty{#3}&#1&#1&#1&#1&#1\\#1&#1&\mqty{#4}&#1&#1&#1&#1\\#1&#1&#1&\mqty{#5}&#1&#1&#1\\#1&#1&#1&#1&\mqty{#6}&#1&#1\\#1&#1&#1&#1&#1&\mqty{#7}&#1\\#1&#1&#1&#1&#1&#1&\mqty{#8}}}
							{\global\matrixtoks = \expandafter{\mqty{#2}&#1&#1&#1&#1&#1&#1&#1\\#1&\mqty{#3}&#1&#1&#1&#1&#1&#1\\#1&#1&\mqty{#4}&#1&#1&#1&#1&#1\\#1&#1&#1&\mqty{#5}&#1&#1&#1&#1\\#1&#1&#1&#1&\mqty{#6}&#1&#1&#1\\#1&#1&#1&#1&#1&\mqty{#7}&#1&#1\\#1&#1&#1&#1&#1&#1&\mqty{#8}&#1\\#1&#1&#1&#1&#1&#1&#1&\mqty{#9}}}
						}
					}
				}
			}
		}
	}
	\the\matrixtoks
}
\DeclareDocumentCommand\dmat{}{\diagonalmatrix}

\DeclareDocumentCommand\antidiagonalmatrix{O{} >{\SplitList{,}}m }{\@admat{#1}#2}
\DeclareDocumentCommand\@admat{mmggggggg}
{
	\newtoks\matrixtoks
	\global\matrixtoks = {}
	\IfNoValueTF{#3}
	{#2}
	{
		\IfNoValueTF{#4}
		{\global\matrixtoks = \expandafter{#1&\mqty{#2}\\\mqty{#3}&#1}}
		{
			\IfNoValueTF{#5}
			{\global\matrixtoks = \expandafter{#1&#1&\mqty{#2}\\#1&\mqty{#3}&#1\\\mqty{#4}&#1&#1}}
			{
				\IfNoValueTF{#6}
				{\global\matrixtoks = \expandafter{#1&#1&#1&\mqty{#2}\\#1&#1&\mqty{#3}&#1\\#1&\mqty{#4}&#1&#1\\\mqty{#5}&#1&#1&#1}}
				{
					\IfNoValueTF{#7}
					{\global\matrixtoks = \expandafter{#1&#1&#1&#1&\mqty{#2}\\#1&#1&#1&\mqty{#3}&#1\\#1&#1&\mqty{#4}&#1&#1\\#1&\mqty{#5}&#1&#1&#1\\\mqty{#6}&#1&#1&#1&#1}}
					{
						\IfNoValueTF{#8}
						{\global\matrixtoks = \expandafter{#1&#1&#1&#1&#1&\mqty{#2}\\#1&#1&#1&#1&\mqty{#3}&#1\\#1&#1&#1&\mqty{#4}&#1&#1\\#1&#1&\mqty{#5}&#1&#1&#1\\#1&\mqty{#6}&#1&#1&#1&#1\\\mqty{#7}&#1&#1&#1&#1&#1}}
						{
							\IfNoValueTF{#9}
							{\global\matrixtoks = \expandafter{#1&#1&#1&#1&#1&#1&\mqty{#2}\\#1&#1&#1&#1&#1&\mqty{#3}&#1\\#1&#1&#1&#1&\mqty{#4}&#1&#1\\#1&#1&#1&\mqty{#5}&#1&#1&#1\\#1&#1&\mqty{#6}&#1&#1&#1&#1\\#1&\mqty{#7}&#1&#1&#1&#1&#1\\\mqty{#8}&#1&#1&#1&#1&#1&#1}}
							{\global\matrixtoks = \expandafter{#1&#1&#1&#1&#1&#1&#1&\mqty{#2}\\#1&#1&#1&#1&#1&#1&\mqty{#3}&#1\\#1&#1&#1&#1&#1&\mqty{#4}&#1&#1\\#1&#1&#1&#1&\mqty{#5}&#1&#1&#1\\#1&#1&#1&\mqty{#6}&#1&#1&#1&#1\\#1&#1&\mqty{#7}&#1&#1&#1&#1&#1\\#1&\mqty{#8}&#1&#1&#1&#1&#1&#1\\\mqty{#9}&#1&#1&#1&#1&#1&#1&#1}}
						}
					}
				}
			}
		}
	}
	\the\matrixtoks
}
\DeclareDocumentCommand\admat{}{\antidiagonalmatrix}

% Misc
\DeclareDocumentCommand\flatfrac{ m m }{\left.#1\middle\slash#2\right.}
\DeclareDocumentCommand\homework{}{ % You can try it
	\ensuremath{
	\div{\vb{E}}=\frac{\rho}{\epsilon_0} \qc
	\div{\vb{B}}=0 \qc
	\curl{\vb{E}}=-\pdv{\vb{B}}{t}\qc
	\curl{\vb{B}}=\mu_0\vb{J}+\frac{1}{c^2}\pdv{\vb{E}}{t}\qc
	H\ket{\Psi}=i\hbar\pdv{}{t}\ket{\Psi},
	\qq{all else follows.}
	}
}