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Diffstat (limited to 'Master/texmf-dist/tex/latex/physics/physics.sty')
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1 files changed, 545 insertions, 135 deletions
diff --git a/Master/texmf-dist/tex/latex/physics/physics.sty b/Master/texmf-dist/tex/latex/physics/physics.sty index 36c23bf66bc..2eafc4940e5 100644 --- a/Master/texmf-dist/tex/latex/physics/physics.sty +++ b/Master/texmf-dist/tex/latex/physics/physics.sty @@ -1,94 +1,206 @@ \ProvidesPackage{physics} -% physics 1.20 +% 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, and bra-ket (Dirac) notation +% 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 October 31, 2012 -% Uploaded on November 1, 2012 +% 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{ t\big t\Big t\bigg t\Bigg g o d() d|| }{ % Flexible automatic bracketing of an expression in () or [] or {} or || +\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} - } + {\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\lvert{#8}\rtag\rvert} } - {\ltag[#6\rtag] \IfNoValueTF{#7}{}{(#7)} \IfNoValueTF{#8}{}{|#8|}} + {\ltag(#7\rtag) \IfNoValueTF{#8}{}{|#8|}} } - {\ltag\lbrace#5\rtag\rbrace \IfNoValueTF{#6}{}{[#6]} \IfNoValueTF{#7}{}{(#7)} \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\absolutevalue{ t\big t\Big t\bigg t\Bigg m }{ % Absolute value/complex modulus - \IfBooleanTF{#1}{\quantity\big|#5|}{ - \IfBooleanTF{#2}{\quantity\Big|#5|}{ - \IfBooleanTF{#3}{\quantity\bigg|#5|}{ - \IfBooleanTF{#4}{\quantity\Bigg|#5|}{\quantity|#5|} +\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\abs{}{\absolutevalue} % Shorthand for \absolutevalue +\DeclareDocumentCommand\mqty{}{\matrixquantity} % Shorthand for \matrixquantity +\DeclareDocumentCommand\matrixdeterminant{m}{\vmqty{#1}} % Matrix determinant +\DeclareDocumentCommand\mdet{}{\matrixdeterminant} % Shorthand for matrix determinant -\DeclareDocumentCommand\norm{ t\big t\Big t\bigg t\Bigg m }{ % Norm - \IfBooleanTF{#1}{\bigl\lVert{#5}\bigr\rVert}{ - \IfBooleanTF{#2}{\Bigl\lVert{#5}\Bigr\rVert}{ - \IfBooleanTF{#3}{\biggl\lVert{#5}\biggr\rVert}{ - \IfBooleanTF{#4}{\Biggl\lVert{#5}\Biggr\rVert}{\left\lVert{#5}\right\rVert} +\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\order{ t\big t\Big t\bigg t\Bigg m }{ % Order symbol -> O(x^2) - \IfBooleanTF{#1}{\mathcal{O}\IfNoValueTF{#5}{}{\!\quantity\big(#5)}}{ - \IfBooleanTF{#2}{\mathcal{O}\IfNoValueTF{#5}{}{\!\quantity\Big(#5)}}{ - \IfBooleanTF{#3}{\mathcal{O}\IfNoValueTF{#5}{}{\!\quantity\bigg(#5)}}{ - \IfBooleanTF{#4}{\mathcal{O}\IfNoValueTF{#5}{}{\!\quantity\Bigg(#5)}}{\mathcal{O}\IfNoValueTF{#5}{}{\!\quantity(#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\evaluated{ g d() }{ % Vertical evaluation bar or parentheses - \IfNoValueTF{#1}{ - \IfNoValueTF{#2} - {\rvert} - {\quantity(#2)} + +\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} + } + } } - {\left.{#1}\right\rvert \IfNoValueTF{#2}{}{(#2)}} } +} + +\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{ m m }{{\left\lbrace{#1},{#2}\right\rbrace}} % Poisson bracket [same as anti-commutator] + +\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{ m m }{\left[{#1},{#2}\right]} % Commutator +\DeclareDocumentCommand\commutator{ l m m }{\braces#1{\lbrack}{\rbrack}{#2,#3}} % Commutator \DeclareDocumentCommand\comm{}{\commutator} % Shorthand for \commutator - -\DeclareDocumentCommand\anticommutator{ m m }{\left\lbrace{#1},{#2}\right\rbrace} % Anticommutator [same as Poisson bracket] +\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 @@ -109,13 +221,12 @@ \DeclareDocumentCommand\cross{}{\crossproduct} % Shorthand for \crossproduct \DeclareDocumentCommand\cp{}{\crossproduct} % Shorthand for \crossproduct -\DeclareDocumentCommand\vnabla{}{\boldsymbol\nabla} % Vector bold \nabla symbol \DeclareDocumentCommand\gradient{ g o d() }{ % Gradient \IfNoValueTF{#1}{ \IfNoValueTF{#2}{ - \IfNoValueTF{#3}{\vnabla}{\vnabla\!\quantity(#3)} + \IfNoValueTF{#3}{\vnabla}{\fbraces{\lparen}{\rparen}{\vnabla}{#3}} } - {\vnabla\!\quantity[#2] \IfNoValueTF{#3}{}{(#3)}} + {\fbraces{\lbrack}{\rbrack}{\vnabla}{#2} \IfNoValueTF{#3}{}{(#3)}} } {\vnabla #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}} } @@ -147,44 +258,120 @@ \DeclareDocumentCommand\laplacian{ g o d() }{ % Laplacian \IfNoValueTF{#1}{ \IfNoValueTF{#2}{ - \IfNoValueTF{#3}{\nabla^2}{\nabla^2\!\quantity(#3)} + \IfNoValueTF{#3}{\nabla^2}{\fbraces{\lparen}{\rparen}{\nabla^2}{#3}} } - {\nabla^2\!\quantity[#2] \IfNoValueTF{#3}{}{(#3)}} + {\fbraces{\lbrack}{\rbrack}{\nabla^2}{#2} \IfNoValueTF{#3}{}{(#3)}} } {\nabla^2 #1 \IfNoValueTF{#2}{}{[#2]} \IfNoValueTF{#3}{}{(#3)}} } % Operators -\let\sine\sin -\let\cosine\cos -\let\tangent\tan -\let\cosecant\csc -\let\secant\sec -\let\cotangent\cot -\let\arcsine\arcsin -\let\arccosine\arccos -\let\arctangent\arctan -\let\hypsine\sinh -\let\hypcosine\cosh -\let\hyptangent\tanh -\let\hypcotangent\coth -\DeclareDocumentCommand\sin{ o d() }{\IfNoValueTF{#2}{\sine \IfNoValueTF{#1}{}{[#1]}}{\sine \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\cos{ o d() }{\IfNoValueTF{#2}{\cosine \IfNoValueTF{#1}{}{[#1]}}{\cosine \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\tan{ o d() }{\IfNoValueTF{#2}{\tangent \IfNoValueTF{#1}{}{[#1]}}{\tangent \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\csc{ o d() }{\IfNoValueTF{#2}{\cosecant \IfNoValueTF{#1}{}{[#1]}}{\cosecant \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\sec{ o d() }{\IfNoValueTF{#2}{\secant \IfNoValueTF{#1}{}{[#1]}}{\secant \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\cot{ o d() }{\IfNoValueTF{#2}{\cotangent \IfNoValueTF{#1}{}{[#1]}}{\cotangent \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\arcsin{ o d() }{\IfNoValueTF{#2}{\arcsine \IfNoValueTF{#1}{}{[#1]}}{\arcsine \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\arccos{ o d() }{\IfNoValueTF{#2}{\arccosine \IfNoValueTF{#1}{}{[#1]}}{\arccosine \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\arctan{ o d() }{\IfNoValueTF{#2}{\arctangent \IfNoValueTF{#1}{}{[#1]}}{\arctangent \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\sinh{ o d() }{\IfNoValueTF{#2}{\hypsine \IfNoValueTF{#1}{}{[#1]}}{\hypsine \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\cosh{ o d() }{\IfNoValueTF{#2}{\hypcosine \IfNoValueTF{#1}{}{[#1]}}{\hypcosine \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\tanh{ o d() }{\IfNoValueTF{#2}{\hyptangent \IfNoValueTF{#1}{}{[#1]}}{\hyptangent \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} -\DeclareDocumentCommand\coth{ o d() }{\IfNoValueTF{#2}{\hypcotangent \IfNoValueTF{#1}{}{[#1]}}{\hypcotangent \IfNoValueTF{#1}{}{^{#1}} \!\quantity(#2)}} - -\DeclareMathOperator{\tr}{tr} % Trace and partial trace [w/subscript] +\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} @@ -221,43 +408,56 @@ % d: long-form as in d(cos x) \IfNoValueTF{#2}{ \IfNoValueTF{#3} - {\mathrm{d}\IfNoValueTF{#1}{}{^{#1}}} - {\mathrm{d}\IfNoValueTF{#1}{}{^{#1}}\!\quantity(#3)} + {\diffd\IfNoValueTF{#1}{}{^{#1}}} + {\mathinner{\diffd\IfNoValueTF{#1}{}{^{#1}}\argopen(#3\argclose)}} } - {\mathrm{d}\IfNoValueTF{#1}{}{^{#1}} #2 \,} + {\mathinner{\diffd\IfNoValueTF{#1}{}{^{#1}}#2} \IfNoValueTF{#3}{}{(#3)}} } \DeclareDocumentCommand\dd{}{\differential} % Shorthand for \differential -\DeclareDocumentCommand\derivative{ o m g d() }{ % Total derivative +\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(...) - \IfNoValueTF{#3}{ - \IfNoValueTF{#4} - {\frac{\dd \IfNoValueTF{#1}{}{^{#1}}}{\dd #2\IfNoValueTF{#1}{}{^{#1}}}} - {\frac{\dd \IfNoValueTF{#1}{}{^{#1}}}{\dd #2\IfNoValueTF{#1}{}{^{#1}}} \!\quantity(#4)} - } - {\frac{\dd \IfNoValueTF{#1}{}{^{#1}} #2}{\dd #3\IfNoValueTF{#1}{}{^{#1}}}} + \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{ o m g g d() }{ % Partial 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(...) - \IfNoValueTF{#3}{ + \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} - {\frac{\partial \IfNoValueTF{#1}{}{^{#1}}}{\partial #2\IfNoValueTF{#1}{}{^{#1}}}} - {\frac{\partial \IfNoValueTF{#1}{}{^{#1}}}{\partial #2\IfNoValueTF{#1}{}{^{#1}}} \!\quantity(#5)} - }{ - \IfNoValueTF{#4} - {\frac{\partial \IfNoValueTF{#1}{}{^{#1}} #2}{\partial #3\IfNoValueTF{#1}{}{^{#1}}}} - {\frac{\partial^2 #2}{\partial #3 \partial #4}} - } + {\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 @@ -268,80 +468,290 @@ \IfNoValueTF{#2}{ \IfNoValueTF{#3} {\delta \IfNoValueTF{#1}{}{^{#1}}} - {\delta \IfNoValueTF{#1}{}{^{#1}}\!\quantity(#3)} + {\mathinner{\delta \IfNoValueTF{#1}{}{^{#1}}\argopen(#3\argclose)}} } - {\delta \IfNoValueTF{#1}{}{^{#1}} #2 \,} + {\mathinner{\delta \IfNoValueTF{#1}{}{^{#1}}#2} \IfNoValueTF{#3}{}{(#3)}} } \DeclareDocumentCommand\var{}{\variation} % Shorthand for \variation -\DeclareDocumentCommand\functionalderivative{ o m g d() }{ % Functional derivative +\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(...) - \IfNoValueTF{#3}{ - \IfNoValueTF{#4} - {\frac{\variation \IfNoValueTF{#1}{}{^{#1}}}{\variation #2\IfNoValueTF{#1}{}{^{#1}}}} - {\frac{\variation \IfNoValueTF{#1}{}{^{#1}}}{\variation #2\IfNoValueTF{#1}{}{^{#1}}} \!\quantity(#4)} - } - {\frac{\variation \IfNoValueTF{#1}{}{^{#1}} #2}{\variation #3\IfNoValueTF{#1}{}{^{#1}}}} + \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{g} }{ % Bra - \IfBooleanTF{#1} - {\left\lvert{#2}\right\rangle \IfNoValueTF{#4}{}{#4}} % Complex conjugate - {\IfBooleanTF{#3}{\braket{#2}{\IfNoValueTF{#4}{}{#4}}}{\left\langle{#2}\right\rvert \IfNoValueTF{#4}{}{#4}}} % No star --- allow contraction +\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 + } } - -\DeclareDocumentCommand\ket{ s m }{ % Ket + { % 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} - {\left\langle{#2}\right\rvert} % Complex conjugate - {\left\lvert{#2}\right\rangle} % No star + {\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} } - -\DeclareDocumentCommand\innerproduct{ s m g }{ % Inner product - \IfNoValueTF{#3} - {\left\langle{#2}\vert{#2}\right\rangle} - { % Two arguments - \IfBooleanTF{#1} - {\left\langle{#3}\middle\vert{#2}\right\rangle} % Complex conjugate - {\left\langle{#2}\middle\vert{#3}\right\rangle} % No star - } + { % Auto resize + \IfNoValueTF{#3} + {\left\langle{#2}\middle\vert{#2}\right\rangle} + {\left\langle{#2}\middle\vert{#3}\right\rangle} } -\DeclareDocumentCommand\braket{}{\innerproduct} % Shorthand for \innerproduct +} +\DeclareDocumentCommand\braket{}{\innerproduct} % Alternative for \innerproduct \DeclareDocumentCommand\ip{}{\innerproduct} % Shorthand for \innerproduct -\DeclareDocumentCommand\outerproduct{ s m g }{ % Dyad - \IfNoValueTF{#3} +\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} - { % Two arguments - \IfBooleanTF{#1} - {\left\lvert{#3}\middle\rangle\!\middle\langle{#2}\right\rvert} - {\left\lvert{#2}\middle\rangle\!\middle\langle{#3}\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{ m g }{ % Expectation value - \IfNoValueTF{#2} - {\left\langle{#1}\right\rangle} - {\left\langle{#2}\middle\vert{#1}\middle\vert{#2}\right\rangle} + +\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{ m m m }{\left\langle{#1}\middle\vert{#2}\middle\vert{#3}\right\rangle} % Matrix element + +\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&\mqty{#3}}} + { + \IfNoValueTF{#5} + {\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}}} + { + \IfNoValueTF{#6} + {\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}}} + { + \IfNoValueTF{#7} + {\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}}} + { + \IfNoValueTF{#8} + {\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}}} + { + \IfNoValueTF{#9} + {\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\#1&\mqty{#8}}} + {\global\matrixtoks = \expandafter{\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\#1&\mqty{#8}\\#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}}} + { + \IfNoValueTF{#5} + {\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\\mqty{#4}}} + { + \IfNoValueTF{#6} + {\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\\mqty{#5}}} + { + \IfNoValueTF{#7} + {\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\\mqty{#6}}} + { + \IfNoValueTF{#8} + {\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\\mqty{#7}}} + { + \IfNoValueTF{#9} + {\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\\mqty{#8}}} + {\global\matrixtoks = \expandafter{#1&\mqty{#2}\\#1&\mqty{#3}\\#1&\mqty{#4}\\#1&\mqty{#5}\\#1&\mqty{#6}\\#1&\mqty{#7}\\#1&\mqty{#8}\\\mqty{#9}}} + } + } + } + } + } + } + \the\matrixtoks +} +\DeclareDocumentCommand\admat{}{\antidiagonalmatrix} + % Misc -\DeclareDocumentCommand\varE{}{\mathcal{E}} % Curly 'E' +\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 |