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diff --git a/macros/latex/contrib/physics2/physics2-legacy.tex b/macros/latex/contrib/physics2/physics2-legacy.tex new file mode 100644 index 0000000000..fe3dcb1ce2 --- /dev/null +++ b/macros/latex/contrib/physics2/physics2-legacy.tex @@ -0,0 +1,544 @@ +%% ****************************************************** +%% * This work may be distributed and/or modified under * +%% * the conditions of the LaTeX Project Public License * +%% * http://www.latex-project.org/lppl.txt * +%% * either version 1.3c of this license or any later * +%% * version. * +%% ****************************************************** +\documentclass[11pt,letterpaper]{article} +\usepackage{amsmath} +\usepackage{unicode-math} +\setmainfont{Libertinus Serif} +\setsansfont{Libertinus Sans} +\setmonofont{NotoSansMono}[ + Scale=MatchLowercase, + Extension=.ttf, + UprightFont=*-Light, + BoldFont=*-Medium +] +\setmathfont{Libertinus Math} +\usepackage{physics2} +\usephysicsmodule{ab} +\usephysicsmodule{ab.legacy,nabla.legacy} +\usephysicsmodule{op.legacy,qtext.legacy} +\usephysicsmodule{ab.braket} +\usephysicsmodule{diagmat} +\usephysicsmodule[showleft=3,showtop=3]{xmat} +\usepackage{derivative} +\input{phy2docdef.tex} +\title{\pkg{physics2} manual for the legacy \pkg{physics} users} +\begin{document} +\maketitle + +\begin{abstract} +This short document describes \pkg*{physics2} package for those who are +used to the \pkg*{physics} package. This document is only a simple reference +manual for: +\begin{itemize} +\item Frequent users of the legacy \pkg{physics} package; +\item Those who have to maintain a document written with \pkg{physics}; +\item Users who failed to use \pkg*{unicode-math} with \pkg{physics}. +\end{itemize} +It seems no reason for any other user to read \emph{this} document instead of +the \href{./physics2.pdf}{package documentation} of \pkg{physics2}, +because this document cannot describe the package in detail. + +In this document, the modules of \pkg{physics2} will be introduced in +the same order as the \pkg{physics} documentation. +\end{abstract} + +\section*{Contents} +\begin{multicols}{2} +\contentsonly +\end{multicols} +\ifnum\value{page}=1 \vfil\clearpage\fi + +\section{Before you start} +\subsection{Legacy problems with \pkg{physics} package} +\label{subsec:physics-legacy-problems} +The \pkg{physics} package provides \cs{qty} command for automatic-sizing +braces. The \cs{qty} command would cause conflict with the \pkg{siunitx} +package, which provides a unified method to typeset numbers and units +correctly. + +Besides, after you loaded \pkg{physics}, when you type \cs{homework} you +will get Maxwell equations and Schrödinger equation. The \cs{homework} +command is ``declared'' in \texttt{physics.sty} but it was not described +in the documentation. That is, if you have defined \cs{homework} before +loading \pkg{physics} package, \pkg{physics} would overwrite the definition +``silently''. + +The vector-notation part of \pkg{physics} uses \pkg*{amsmath}'s (more exactly, +\texttt{amsbsy.sty}'s) \cs{boldsymbol} command to generate bold vectors. +Commands for cross/dot product are defined with \cs{boldsymbol}. +\cs{boldsymbol} uses \cs{mathversion}, a \LaTeXe\ kernel command that works +well with traditional TFM-based fonts but fails when using \pkg{unicode-math}. + +In the definition of \cs{imat}, \cs{xmat}, \cs{dmat} and \cs{admat} commands +from \pkg{physics}, there is a \cs{newtoks} command which allocates a token +list register and two \cs{newcount} commands allocating two count registers. +Every time you write a command like \cs{imat} in your document, then one token +list register and two count registers will be wasted. What's even worse is +that, if you wrote really too many matrix commands from \pkg{physics} (for +example, 32767 \cs{imat}s in \hologo{LuaLaTeX}), there'd be no room for a new +\cs{count}. + +\pkg{physics} integrated all the functions in one file (\texttt{physics.sty}), +that is, you cannot load one of the total seven parts of functions; you have +to load the seven parts altogether, even included the extra \cs{homework} +command we mentioned in the first paragraph. + +Moreover, the code of \texttt{physics.sty} ``abuses'' the \texttt{g}-type +arguments of \pkg*{xparse} package. Therefore the syntax of \pkg{physics} package +looks kind of weird. See \href{https://tex.stackexchange.com/questions/% +470819/macros-dv-and-pdv-eat-the-subsequent-parenthesis-argument/470842#470842}% +{here} for more. + +\subsection{Loading \pkg{physics2}} +The \pkg{physics2} package includes different modules, among which every module +focuses on one single function. + +Write the following line in the preamble to load \pkg{physics2}: +\begin{Verbatim} +\usepackage{physics2} +\end{Verbatim} +But this is not enough. \pkg{physics2} contains different modules. +If you want to load any module of \pkg{physics2}, write this line after loading +\pkg{physics2} package: +\begin{displayed} +\cs{usephysicsmodule}\marg{module list} +\end{displayed} +For example, ``\verb|\usephysicsmodule{ab,doubleprod}|'' loads the \modu{ab} +module and the \modu{doubleprod} module. + +You can also load a module with options: +\begin{displayed} +\cs{usephysicsmodule}\oarg{option list}\marg{module} +\end{displayed} +For example, ``\verb|\usephysicsmodule[legacy]{ab}|'' loads \modu{ab} with the +option ``\opt{legacy}''. + +\pardanger Attention, if you used any font package in your document, remember +that \pkg{physics2} requires to be loaded \emph{after} font packages. + + +\section{List of commands} +\subsection{Automatic bracing}\label{subsec:ab-and-legacy} +As mentioned in \S\ref{subsec:physics-legacy-problems}, the \cs{qty} command +from \pkg{physics} would cause conflicts with \pkg{siunitx}. The command for +automatic braces in \pkg{physics2} is \cs{ab}, a shorthand for +{\bfseries a}utomatic {\bfseries b}races. + +The \cs{ab} command requires the \modu{ab} module, so don't forget to write +\verb|\usephysicsmodule{ab}| in the preamble after you loaded \pkg{physics2}. +Always remember, \emph{do not put an \cs{ab} separately in the end of a math +formula}. Take some examples: +\begin{example} +\[ \ab ( \frac12 ) \quad + \ab [ \frac12 ] \quad + \ab\{ \frac12 \} \] +\end{example} +\cs{ab} can modify a delimiter-braced subformula. But the delimiters should +not be out of the range described by the following chart: +\begin{center} +\begin{tabular}{c@{\hskip2em}l@{\hskip2em}c} +\opt{(},\quad\opt{)} && \\ +\opt{[},\quad\opt{]} && \\ +\cs{\{},\quad\cs{\}} &or& \cs{lbrace},\quad\cs{rbrace} \\ +\opt{<},\quad\opt{>} &or& \cs{langle},\quad\cs{rangle} \\ +\opt{|},\quad\opt{|} &or& \cs{vert},\quad\cs{vert} \\ + \cs{|},\quad\cs{|} &or& \cs{Vert},\quad\cs{Vert} +\end{tabular} +\end{center} +For example, \verb|$\ab{foo}$| and \verb|$\ab(foo]$| are illegal, but +\verb|$\ab\{foo\}$| and \verb|$\ab(foo)$| are okay; \verb|$\ab([)$| +is okay but \verb|$\ab(()$| is illegal. + +\pardanger Attention, if you want to delimit a subformula with ``\{'' and +``\}'', you can only write \verb|\{|, \verb|\}| or \cs{lbrace}, \cs{rbrace} +around it. \verb|{| and \verb|}| are not supported in \modu{ab} module. + +Between \cs{ab} and the first delimiter can be a ``biggg'' command, that is, +from \cs{big} to \cs{Bigg}. Actually, you can also write \cs{biggg} and +\cs{Biggg} because \pkg{physics2} defines these after you load it. For example, +\begin{example} +\[ \ab\Big \| \frac12 \| \quad + \ab\Bigg < \frac12 > \quad + \ab\Biggg| \frac12 | \] +\end{example} +Between \cs{ab} and the first delimiter can also be a star (\opt{*}), which +means ``use the default size of delimiters''. But in this situation, you +needn't use the \cs{ab} command at all. + +The \pkg{physics} package provides commands like \cs{pqty}, \cs{bqty}. In +the \modu{ab} module of \pkg{physics2}, these commands have changed to +\cs{pab}, \cs{bab}, etc. The following example shows all the +\texttt{\textbackslash}$X$\texttt{ab} commands in \modu{ab} module: +\begin{example} +\def\0{\frac12} +\[ \pab{\0} \quad \bab{\0} + \quad \Bab{\0} \] +\[ \aab{\0} \quad \vab{\0} + \quad \Vab{\0} \] +\end{example} +\texttt{\textbackslash$X$ab} can take an optional star and an optional \oarg{biggg} +argument. For example, +\begin{example} +\def\0{\frac12} +\[ \pab[Big]{\0} \quad \bab*{\0} \] +\end{example} + +\pkg{physics} also provides the following commands: +\begin{Verbatim}[fontsize=\small] +\abs \norm \eval \order \comm \acomm \pb +\end{Verbatim} +\pardanger These commands are not originally supported by \pkg{physics2}, but +the first four commands can be used through the \modu{ab.legacy} module of +\pkg{physics2}: +\begin{Verbatim} +\usephysicsmodule{ab.legacy} +\end{Verbatim} +For example, +\begin{example} +\def\0{\frac12} +\[ \abs{\0} \quad \abs[big]{\0} + \quad \abs*{\0} \] +\end{example} +Users of the legacy \pkg{physics} package should notice that the syntax of +\cs{eval} has been changed. The \modu{ab.legacy} module abandoned the +\verb"\eval(foo|"-like syntax. The new \cs{eval}'s syntax is just like other +commands in this module. There are also two variants of \cs{eval} --- \cs{peval} +and \cs{beval}. For example, +\begin{example} +\def\0{1+\frac12x} +\[ \eval{\0}_a^b \quad + \peval*{\0}_a^b \quad + \beval[big]{\0}_a^b \] +\end{example} +The \cs{comm}, \cs{acomm} and \cs{pb} (Poisson bracket) are not supported. +But you can write like \verb|\ab[foo,baz]| or \verb|\bab{foo,baz}| instead. + +By the way, you can set the ``order'' symbol in \modu{ab.legacy} through +the \opt{order} option like this: +\begin{Verbatim} +\usephysicsmodule[order=O]{ab.legacy} +\end{Verbatim} +Then \verb|$\order(N)$| yields $O(N)$. + +\subsection{Vector notation} +Unfortunately, there is not a plan for \pkg{physics2} to support this part +of \pkg{physics} completely, but the rest of this section will show some +methods to maintain the document written with \pkg{physics}. + +The \cs{vb}(\opt{*}), \cs{va}(\opt{*}) and \cs{vu}(\opt{*}) are not supported +in any module of \pkg{physics2}. But these commands can be defined by copying +the following lines below and pasting them in the preamble: +\begin{Verbatim}[fontsize=\small] +\makeatletter +\newcommand\vb{\@ifstar\boldsymbol\mathbf} +\newcommand\va[1]{\@ifstar{\vec{#1}}{\vec{\mathrm{#1}}}} +\newcommand\vu[1]{% + \@ifstar{\hat{\boldsymbol{#1}}}{\hat{\mathbf{#1}}}} +\makeatother +\end{Verbatim} +The \cs{boldsymbol} command requires the \pkg*{amsmath} or \pkg*{bm} package. +If you prefer to use \pkg{bm}, you can also use the \cs{bm} command. +What's more, if you tried the commands above, you might find that, +the result of \cs{va} above is different from that of \pkg{physics}. +This is because, if you choose to present a vector in bold, there's almost +no need to put a \cs{vec} ($\vec{\mskip9mu}$) sign above it. + +However, the method above may not work well with \pkg*{unicode-math} +because there are so many OpenType math fonts without a bold version. +When using \pkg{unicode-math}, it's recommended to use \cs{symbf} and +\cs{symbfit} for a separate vector. For example, \verb|$\symbf{0}$| yields +$\symbf{0}$, and \verb|$\symbfit{A}$| yields $\symbfit{A}$. + +The \cs{vdot} and \cs{cross} commands are not supported in any module +of \pkg{physics2}. Actually, there is no need to use a bold ``$\cdot$'' +or ``$\times$'' for the products of two vectors. Using \cs{cdot} and +\cs{times} is enough. + +The commands related to ``$\nabla$'' are supported through \modu{nabla.legacy} +module. These commands are \cs{grad}, \cs{div} and \cs{curl}. These commands +should not be put in the end of a math formula either (just like \cs{ab}). +Notice that the former \cs{div} command for a ``$\divsymbol$'' (if there +exists one) is redefined as \cs{divsymbol}. For example, +\begin{example} +% \usephysicsmodule{nabla.legacy} +\[ \grad F \quad + \grad(\frac G2) \] +\[ \div\Bigg[X] \quad + \curl*\{\frac Y2\} \] +\[ 2 \divsymbol 1 \] +\end{example} +Actually, the nabla-related commands end with \cs{ab}. Thus, the subformula +after these commands can be delimited with \verb|()|, \verb|[]| and \verb|\{\}|. + +The \modu{nabla.legacy} requires the \pkg*{fixdif} package at least +version 2.0 (file date: 2023/01/31 or after 2023/01/31). + +By the way, if you are used to writing \cs{bm} for a vector but interested in +\pkg{unicode-math}, the \modu{bm-um.legacy} module would be a passable +alternative to \pkg{bm} package. Notice that the \cs{bm} command from the +\modu{bm-um.legacy} module can only take \emph{one} letter (or \emph{one} digit) +as its argument. + +\subsection{Operators} +There's no plan for \pkg{physics2} to support this part of \pkg{physics} +completely. The syntax in this part of \pkg{physics} (such as \verb|\tan[2](x)|) +abuses \pkg*{xparse}. + +It's suggested to write like this if you used the \modu{ab} module: +\begin{Verbatim}[fontsize=\small] +$ \sin^2 \ab( \frac{\alpha}{2} ) $ +\end{Verbatim} +Rather than take the superscript as an optional argument of the command of +log-like functions. + +The \pkg{physics} package provides a bundle of commands for log-like functions +that have not been defined in the \LaTeXe\ kernel. Those log-like functions +can be used with the \modu{op.legacy} module; this module does not support +the syntax of \pkg{physics} either. For example: +\begin{example} +% \usephysicsmodule{op.legacy} +\[ \asin^2 x \quad \rank \{ A \} \] +\end{example} +The \cs{Re} and \cs{Im} commands are redefined as operators ``$\Re$'' and +``$\Im$'', while $\Resymbol$ and $\Imsymbol$ are reserved as \cs{Resymbol} and +\cs{Imsymbol}. $\Resymbol$ and $\Imsymbol$ are ordinary symbols but $\Re$ and +$\Im$ are operators. + +\subsection{Quick quad text}\label{subsec:qtext} +The \modu{qtext.legacy} module provides the \cs{q}\meta{foo} commands +for \cs{quad}-wrapped texts. These commands have the same syntax as +\pkg{physics}. For example, +\begin{example} +% \usephysicsmodule{qtext.legacy} +\[ A \qq {foo bar} B \] +\[ A \qq*{foo bar} B \] +\[ C \qcc D \qcc* E \] +\[ F \qif G \qthen H \] +\end{example} +All the commands described in \S2.4 of +\href{http://mirrors.ctan.org/macros/latex/contrib/physics/physics.pdf}% +{\textsf{physics} documentation} are supported when using \modu{qtext.legacy} +module, but I don't recommend using this module unless you are maintaining a +document written with \pkg{physics}'s \cs{q}\meta{foo} commands. + +\subsection{Derivatives} +There is no plan for \pkg{physics2} to support this part of \pkg{physics}. If +you want to typeset the differential operators on a better sense, you can try +the \pkg*{fixdif} package; if you want an easy way to type derivatives, you +can try the \pkg*{derivative} package. These two packages can be used +together. For example, +\begin{example} +% \usepackage{fixdif,derivative} +\[ \pdv{f}{x,y,z} \d x \] +Math ($\d x$) v.s.\ Text (\d x) +\end{example} +Here are the documentations of +\href{http://mirrors.ctan.org/macros/latex/contrib/fixdif/fixdif.pdf}% +{\textsf{fixdif}} and +\href{http://mirrors.ctan.org/macros/latex/contrib/derivative/derivative% +.pdf}{\textsf{derivative}}. + +\pkg{fixdif}'s commands behave better in superscripts and subscripts. + +\subsection{Dirac bra-ket notation} +There are two solutions to Dirac bra-ket in \pkg{physics2} --- \modu{ab.braket} +and \modu{braket}. These two modules are \emph{not} compatible and neither of +them supports \pkg{physics}'s syntax completely. +Click \hyperlink{para:ab.braket}{\textcolor{cyan}{here}} to see the +\modu{ab.braket} module and \hyperlink{para:braket}{\textcolor{cyan}{here}} +to see the \modu{braket} module. + +\paragraph{The \modu{ab.braket} module} +\hypertarget{para:ab.braket}{This} module provides four commands --- \cs{bra}, \cs{ket}, \cs{braket} and +\cs{ketbra}. After these commands can be a star (\opt{*}) or a ``biggg'' +command. These commands share similar syntaxes like \cs{ab}'s syntax. But, +\emph{the bra-ket commands from \modu{ab.braket} module are completely different +from \cs{ab}}. Their internal structures are different. + +The argument of \cs{bra} should be delimited with \opt{<} and \opt{|}, that is, +\begin{center} +\cs{bra} \opt{<} \meta{subformula} \opt{|} +\end{center} +For example, +\begin{example} +\[ \bra < \frac \phi 2 | \] +\[ \bra*< \frac \phi 2 | \] +\[ \bra\Big< \phi | \] +\end{example} +The argument of \cs{ket} should be delimited with \opt{|} and \opt{>}, that is, +\begin{center} +\cs{ket} \opt{|} \meta{subformula} \opt{>} +\end{center} +For example, +\begin{example} +\[ \ket | \frac \psi 2 > \] +\[ \ket*| \frac \psi 2 > \] +\[ \ket\Big| \psi > \] +\end{example} +\pardanger +If you want to write ``$>$'' and ``$<$'' for relations in the argument of +\cs{bra} and \cs{ket}, you can write \verb|\mathrel{>}| and \verb|\mathrel{<}| +(although there is almost no such need). + +The argument of \cs{braket} should be delimited with \opt{<} and \opt{>}, +that is, +\begin{center} +\cs{braket} \opt{<} \meta{subformula} \opt{>} +\end{center} +In the \meta{subformula} argument, every ``\opt{|}'' will be regarded as an +extensible vertical bar. For example, +\begin{example} +\[ \braket< \phi > \] +\[ \braket< \phi | \psi > \] +\[ \braket< \phi | A | \psi > \] +\end{example} +\begin{example} +\def\0{\frac\phi2} +\[ \braket < \0 | \psi > \] +\[ \braket* < \0 | \psi > \] +\[ \braket\Bigg< \0 | \psi > \] +\end{example} +The argument of \cs{ketbra} should be delimited with \opt{|} and \opt{|}. +In the argument, \opt{>} and \opt{<} will be regarded as extensible $\rangle$ +and $\langle$. That is, +\begin{center} +\cs{ketbra} \opt{|} \meta{subformula$_1$} \opt{>} \meta{optional} + \opt{<} \meta{subformula$_2$} \opt{|} +\end{center} +For example, +\begin{example} +\def\0{\frac\phi2} +\[ \ketbra | \0 >< \psi | \] +\[ \ketbra* | \0 >< \psi | \] +\[ \ketbra\Bigg| \0 >< \psi | \] +\end{example} +\begin{example} +\def\0{\frac\phi2} +\[ \ketbra| \0 >_x^y < \psi | \] +\end{example} +\pardanger +If you want to write ``$>$'' and ``$<$'' for relations in the argument of +\cs{braket} and \cs{ketbra}, you can write \cs{>} and \cs{<} (although there +is almost no such need). It is quite different from \verb|\mathrel{>}| or +\verb|\mathrel{<}| because in these commands' argument, \opt{>} and \opt{<} +will be redefined. + +\paragraph{The \modu{braket} module} +\begingroup +\makeatletter\def\phy@requiremodule#1{}% +\def\PackageWarning#1#2{}% +\input phy-braket.sty\makeatother +\hypertarget{para:braket}{This} module contains four commands --- \cs{bra}, +\cs{ket}, \cs{braket} and \cs{ketbra}. After these commands can be a star +(\opt{*}) or a square-bracket-delimited size option, the size option can +take the following values: +\begin{center} +\opt{big},\quad\opt{Big},\quad\opt{bigg},\quad\opt{Bigg},\quad +\opt{biggg}\quad or\quad\opt{Biggg}. +\end{center} +Star stands for ``do not size the bra-ket automatically''. + +The argument(s) of these four commands are braced with \verb|{| and \verb|}|. +\cs{bra} and \cs{ket} take one mandatory argument. For example, +\begin{example} +\def\0{\frac\phi2} +\[ \bra {\0} \quad \bra* {\0} + \quad \bra[Big] {\0} \] +\[ \ket {\0} \quad \ket* {\0} + \quad \ket[Big] {\0} \] +\end{example} +The \cs{braket} command, in default, can take two arguments. +\begin{example} +\def\0{\frac\phi2} +\[ \braket {\0} {\psi} \quad + \braket*{\0} {\psi} \quad + \braket[big] {\0} {\psi} \] +\end{example} +If you want \cs{braket} to take one or three arguments, you can write the +number of arguments in the square bracket. If you need to specify the size +of bra-ket simultaneously, you need to separate the number and the size with +a comma: +\begin{example} +\def\0{\frac\phi2} +\[ \braket [1] {\0} \quad + \braket*[1] {\0} \] +\[ \braket [3] {\0}{A}{\psi} \] +\[ \braket[3,big] {\0}{A}{\psi} + \quad + \braket[Big,3] {\0}{A}{\psi} \] +\end{example} +The \cs{ketbra} command takes two mandatory arguments. It can also take an +optional argument between the two mandatory arguments. The optional argument +will be placed between $\rangle$ and $\langle$: +\begin{example} +\def\0{\frac\phi2} +\[ \ketbra {\0} {\psi} \quad + \ketbra* {\0} {\psi} \] +\[ \ketbra [Bigg] {\0} {\psi} \] +\[ \ketbra {\0} [_x^y] {\psi} \] +\end{example} +\endgroup + +\subsection{Matrix macros} +Unfortunately, \pkg{physics2} do not support the \cs{mqty} command from +\pkg{physics}. If you are used to this command, you can write like this: +\begin{Verbatim}[fontsize=\small] +\newcommand\mqty[1]{\begin{matrix}#1\end{matrix}} +\newcommand\pmqty[1]{\begin{pmatrix}#1\end{pmatrix}} +$\ab(\mqty{foo})$ or $\pmqty{foo}$ +\end{Verbatim} +These are equal to physics's \verb|\mqty(foo)| (require \pkg{amsmath}). + +\pkg{physics2}'s \modu{diagmat} module provides \cs{diagmat} command +for diagonal matrices. For example, +\begin{example} +\[ + \diagmat { 1, 2, 3 } +\] +\end{example} +\begin{example} +\[ + \pdiagmat [ empty = {} ] + { a, b, c, d } +\] +\end{example} +\cs{pdiagmat}, \cs{bdiagmat}, \cs{Bdiagmat}, \cs{vdiagmat} and \cs{Vdiagmat} +are also available. + +\pkg{physics2}'s \modu{xmat} module provides \cs{xmat} command +for matrices with formatted entries. For example, +\begin{example} +\[ + \xmat{a}{2}{3} +\] +\end{example} +\begin{example} +% \usephysicsmodule +% [showleft=3,showtop=3]{xmat} +\[ + \pxmat{X}{m}{n} +\] +\end{example} +\begin{example} +\[ + \xmat [showleft=2,showtop=2, + format=\texttt{#1[#2][#3]}] + {x}{m}{n} +\] +\end{example} +\cs{pxmat}, \cs{bxmat}, \cs{Bxmat}, \cs{vxmat} and \cs{Vxmat} are also available. + + + + + + + + + +\end{document}
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