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author | Norbert Preining <norbert@preining.info> | 2023-02-07 03:01:21 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2023-02-07 03:01:21 +0000 |
commit | 9c37af35b32c30471236254cae8f82b9a8a6c44e (patch) | |
tree | 0a2d186179ce08317b05014d51f9aed825f276dd /macros/latex/contrib/physics2/doc/physics2.tex | |
parent | 30803eebab6e94772482c1690e47cd17917875f5 (diff) |
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diff --git a/macros/latex/contrib/physics2/doc/physics2.tex b/macros/latex/contrib/physics2/doc/physics2.tex new file mode 100644 index 0000000000..043e262853 --- /dev/null +++ b/macros/latex/contrib/physics2/doc/physics2.tex @@ -0,0 +1,567 @@ +%% ****************************************************** +%% * 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{Noto Sans Mono}[Scale=MatchLowercase] +\setmathfont{Libertinus Math} +\usepackage{physics2} +\usephysicsmodule{ab,ab.braket} +\usephysicsmodule{diagmat} +\usephysicsmodule{doubleprod} +\usephysicsmodule[showleft=3,showtop=3]{xmat} +\usephysicsmodule{ab.legacy,nabla.legacy,op.legacy,qtext.legacy,bm-um.legacy} +\input{phy2docdef.tex} +\externaldocument[lega-]{physics2-legacy} +\title{The \pkg{physics2} package} +\begin{document} +\maketitle + +\begin{abstract} +This is the document for \pkg{physics2} package, which defines commands for +typesetting math formulae faster and more simply. \pkg{physics2} is a +modularized package, each module provides its own function. + +This document describes the \pkg{physics2} package in more detail. +But if you are a user of the legacy \pkg{physics} package, you can click +\hyperref{./physics2-legacy.pdf}{}{}{here} to see the documention for +\pkg{physics} users before you start. If you never used \pkg{physics} package +before, just read \emph{this} documentation. +\end{abstract} + +\tableofcontents + +\section{Introduction} +\subsection{The purpose of this package} +This package aims to provide a bundle of commands for typesetting math faster +in different modules. The commands provided by \pkg{physics2} and its different +modules are designed to be short and easy to memorize. + +\subsection{Packages required} +The \pkg{physics2} package itself only requires the \pkg*{keyval} package, which +is part of the \pkg*{latex-graphics} bundle. Almost every \LaTeX\ distribution +will include this bundle. + +Different modules of \pkg{physics2} might require different packages. It will +be explained in the following sections that which module requires which package. + +The \pkg{physics2} package requires \LaTeXe\ kernel released after 2020/10. +Please make sure that your \LaTeX\ distribution is not too old. + +\subsection{Loading the \pkg{physics2} package} +Just like loading any package, write +\begin{Verbatim} +\usepackage{physics2} +\end{Verbatim} +in the preamble to load the \pkg{physics2} package. In this version, +\pkg{physics2} doesn't provide a package option. + +However, \pkg{physics2} itself only provides very few functions. Actually, it +just provides a method to load modules. You need to load different modules of +\pkg{physics2} to have different kinds of functions applied to your document. + +\subsection{Loading a module of \pkg{physics2}} +You can load a module of \pkg{physics2} only \emph{after} you write +\verb|\usepackage{physics2}| in the preamble. Load a \pkg{physics2} module +like this: +\begin{center} +\cs{usephysicsmodule}\marg{module} +\end{center} +The usage of \cs{usephysicsmodule} is similar to \cs{usepackage}, so you can +load more than one modules in one line. For example, +\begin{Verbatim} +\usephysicsmodule{ab,ab.braket} +\end{Verbatim} +This line loads the \modu{ab} and \modu{ab.braket} modules. + +You can also load \emph{one} module with options. The options of a +\pkg{physics2} module can be a comma-separated key-value list. For example, +\begin{Verbatim} +\usephysicsmodule[tightbraces=true]{ab} +\usephysicsmodule{ab.braket,doubleprod} +\end{Verbatim} +These two lines load the \modu{ab} module with option +\opt{tightbraces\:=\:true} and load \modu{ab.braket} and \modu{doubleprod} +modules. + +\pardanger +The \modu{common} module will be loaded automatically when you load the +\pkg{physics2} package and \emph{only} the \modu{common} module will be +loaded automatically. Any other module should be loaded manually by writing +\cs{usephysicsmodule}\marg{module} after you loaded \pkg{physics2} in the +preamble. + +The following sections introduce all the user-level modules of \pkg{physics2}. +View back to the table of contents to see the names of user-level modules. + +\section{Modules of \pkg{physics2}} +\subsection{The automatically loaded \modu{common} module} +The \modu{common} module provides the following commands: + +\cs{delopen} and \cs{delclose}, followed by a math delimiter. They can be +regarded as abbreviations of ``open delimiter'' and ``close delimiter''. If +you had heard of the \pkg*{mleftright} package. You can regard \cs{delopen} +and \cs{delclose} as a simpler version of \cs{mleft} and \cs{mright}. +For example, +\begin{example} +\[ 0 \left(\frac12\right) 3 \] +\[ 0 \delopen(\frac12\delclose) 3 \] +\end{example} + +\cs{biggg} and \cs{Biggg}, followed by a math delimiter. They are even bigger +than \cs{Bigg}. \cs{biggg} and \cs{Biggg} may be useful when you need to write +something really tall in math mode, but most OpenType math font do not support +\cs{langle} (or U+27E8) and \cs{rangle} (or U+27E9) in this large size. Take +an example, +\begin{example} +\[\Biggg(\biggg(\Bigg(\bigg(\Big(\big(( +)\big)\Big)\bigg)\Bigg)\biggg)\Biggg)\] +\end{example} +\cs{bigggl}, \cs{bigggm}, \cs{bigggr}, \cs{Bigggl}, \cs{Bigggm} and \cs{Bigggr} +are also supported. + +\subsection{The \modu{ab} module --- automatic braces} +This module provides the command \cs{ab}. The \cs{ab} command, as a shorthand +of ``automatic braces'', would specify the size of the following pair of +delimiters. The delimiters after \cs{ab} 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, it's illegal to write an ``\verb|\ab(|'' without a ``\verb|)|''; +it's also illegal to write \verb|\ab=foo=|. Take some correct examples: +\begin{example} +\[ \ab ( \frac12 ) \quad + \ab [ \frac12 ] \quad + \ab\{ \frac12 \} \] +\end{example} +You can also write a command from \cs{big} to \cs{Biggg} between \cs{ab} +and the first delimiter, which means to specify the size of delimiters manually. +Also, you can write a star (\opt{*}) between \cs{ab} and the first delimiter, +to prevent \cs{ab} from setting the size of delimiters. For example, +\begin{example} +\[ \ab <\frac12> \quad + \ab\biggg|\frac12| \quad + \ab* \|\frac12\| \] +\end{example} +\pardanger +Always remember, do not put an \cs{ab} separately at the end of math mode like +\verb|$\ab$|, because \cs{ab} will try to absorb the following math shift +character (\verb|$|) as its argument. + +The \modu{ab} module also provides \texttt{\textbackslash}$X$\texttt{ab} +commands, where $X$ can be \opt{p}, \opt{b}, \opt{B}, \opt{a}, \opt{v} and +\opt{V}. These commands take a normal argument but not an argument delimited +with paired delimiters. For example, +\begin{example} +\def\0{\frac12} +\[ \pab{\0} \bab{\0} \Bab{\0} \] +\[ \aab{\0} \vab{\0} \Vab{\0} \] +\end{example} +After \texttt{\textbackslash}$X$\texttt{ab} can be a ``biggg'' command or a +star. For example, +\begin{example} +\def\0{\frac12} +\[ \pab\Big{\0} \quad \bab*{\0} \] +\end{example} + +\paragraph{The options of \modu{ab} module} +\opt{tightbraces}, a bool type key, whose default value is \opt{true}, +influences whether thin skips are reserved around the paired delimiters. +It only works with the automatically sized delimiters. + +\subsection{The \modu{ab.braket} module --- Dirac bra-ket notation} +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. + +Next, the \modu{braket} module will be introduced. Please notice that +\modu{braket} is conflict with \modu{ab.braket}, they cannot be used together. + +\subsection{The \modu{braket} module --- Dirac bra-ket notation} +\begingroup +\makeatletter\def\phy@requiremodule#1{}% +\def\PackageWarning#1#2{}% +\input phy-braket.sty\makeatother +Please notice that this module is conflict with the \modu{ab.braket} module. +Don't use them together. + +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 sqare 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{The \modu{diagmat} module --- simple diagonal matrices} +This module provides \cs{diagmat} command: +\begin{center} +\cs{diagmat}\opt{[empty\:=\:}\meta{empty entry}\opt{]}\marg{diag} +\end{center} +where \meta{diag} is the diagonal of the diagonal matrix. The entries should +be separated by commas. The \opt{empty} option is optional, with default value +\opt{0}. For example, +\begin{example} +\[ + \diagmat { 1, 2, 3 } +\] +\end{example} +\cs{pdiagmat}, \cs{bdiagmat}, \cs{Bdiagmat}, \cs{vdiagmat} and \cs{Vdiagmat} +are also available. Prefixes like \opt{p}, \opt{b}, \opt{B} have the same +meaning as the \opt{p}, \opt{b}, \opt{B} in \pkg{amsmath}'s \opt{pmatrix}, +\opt{bmatrix} and \opt{Bmatrix}. For example, +\begin{example} +\[ + \pdiagmat [ empty = {} ] + { a, b, c, d } +\] +\end{example} +This module requires \pkg{amsmath}. + +\paragraph{The options of \modu{diagmat} module} +You can set the default value of \cs{diagmat}'s empty entries in the module +option like this: +\begin{Verbatim} +\usephysicsmodule[empty={\cdot}]{diagmat} +\end{Verbatim} + +\subsection{The \modu{doubleprod} module --- tensors' double product operator} +Take an example of this module: +\begin{example} +$ A \doublecross B \doubledot C $ +\end{example} +\cs{doublecross} and \cs{doubledot} are regarded as binary operators by \TeX. + +\paragraph{The options of \modu{doubleprod} module} +You can control the scale of ``$\times$'' and ``$\cdot$'' in \cs{doublecross} +and \cs{doubledot} in module option. For example, +\begin{Verbatim} +\usephysicsmodule[crossscale=0.75,dotscale=1.2]{doubleprod} +\end{Verbatim} +The default values of \opt{crossscale} and \opt{dotscale} are \opt{0.8} and +\opt{1}. You can also control the distances between the two ``$\times$''s and +``$\cdot$''s through the \opt{crossopenup} and \opt{dotopenup} options. +For example, +\begin{Verbatim} +\usephysicsmodule[crossopenup=.05,dotopenup=.25]{doubleprod} +\end{Verbatim} +The default values of \opt{crossopenup} and \opt{dotopenup} are \opt{0.02} +and \opt{0.2}. The value stands for the multiple of current font size. +Moreover, you can change the symbols produced by \cs{doublecross} and +\cs{doubledot} by setting \opt{crosssymbol} and \opt{dotsymbol} in module +option. + +\subsection{The \modu{xmat} module --- matrices with formatted entries} +The \modu{xmat} module provides \cs{xmat} command for matrices with formatted +entries: +\begin{center} +\cs{xmat}\oarg{options}\marg{entry}\marg{rows shown}\marg{cols shown} +\end{center} +If \meta{rows shown} and \meta{cols shown} are digits, the value of them +must be less at least 2 than the value of \pkg{amsmath}'s \opt{MaxMatrixCols} +counter. For example, +\begin{example} +\[ + \xmat{a}{2}{3} +\] +\end{example} +\cs{pxmat}, \cs{bxmat}, \cs{Bxmat}, \cs{vxmat} and \cs{Vxmat} are also +available. The meaning of \opt{p} and so on is the same as the \opt{p} +in \opt{pmatrix} of \pkg{amsmath}. For example, +\begin{example} +\[ + \pxmat{M}{3}{3} +\] +\end{example} +If \meta{rows shown} and \meta{cols shown} contain non-digit characters, +extra dots will be added. For example, +\begin{example} +\[ + \bxmat[showleft=3,showtop=2] + {X}{m}{n} +\] +\end{example} +In this example we used the \opt{showleft} and \opt{showtop} options. The +default value of them is the value of \opt{MaxMatrixCols} minus 2. You can +also set them in the module option like this: +\begin{Verbatim} +\usephysicsmodule[showtop=3,showleft=3]{xmat} +\end{Verbatim} +Then every \cs{xmat} with non-digital \meta{rows shown} and \meta{cols shown} +will have 2 top-most rows and 3 left-most columns shown. This will also +influence ``\cs{xmat}''s with digital \meta{rows shown} and \meta{cols shown} +when \meta{rows shown} and \meta{cols shown} are larger than the values +corresponding to \opt{showtop} and \opt{showleft}. For example, +\begin{example} +% \usephysicsmodule +% [showtop=3,showleft=3]{xmat} +\[ \pxmat{A}{8}{8} \] +\end{example} +However, when \meta{rows shown} and \meta{cols shown} are 1 greater than +\meta{showtop} and \meta{showleft}, for example, \meta{rows shown}$\:=4$ and +\meta{cols shown}$\:=4$ in last example's settings, \cs{xmat} will still add +the extra dots: +\begin{example} +% \usephysicsmodule +% [showtop=3,showleft=3]{xmat} +\[ \pxmat{A}{4}{4} \] +\end{example} +In such situations, we need to specify \opt{showtop} and \opt{showleft} +manually. For example, +\begin{example} +% \usephysicsmodule +% [showtop=3,showleft=3]{xmat} +\[ \pxmat[showtop=4,showleft=4] + {A}{4}{4} \] +\end{example} + +The \cs{xmat} command provides the \opt{format} option, which allows users +to use a new entry format. For example, +\begin{example} +\[ + \xmat [showleft=2,showtop=2, + format=\texttt{#1[#2][#3]}] + {x}{m}{n} +\] +\end{example} +In the value of \opt{format} key, \verb|#1| stands for the common entry, +or the first mandotary \meta{entry} argument of \cs{xmat}; \verb|#2| +stands for the row index and \verb|#3| stands for the column index. + +This module requires \pkg{amsmath}. + +\paragraph{The options of \modu{xmat} module} +Only \opt{showtop} and \opt{showleft} can be used as module options. +\opt{format} should be only used in the optional argument of the +\cs{xmat} command. + +\section{The ``legacy'' modules} +The legacy modules have similar names like \meta{module}\opt{.legacy}. Most of +them are designed to provide solutions to maintain documents written with the +legacy \pkg{physics} package. It's not suggest to use them in a new document. + +\subsection{The \modu{ab.legacy} module} +This module provides the following commands: +\begin{Verbatim}[fontsize=\small] +\abs \norm \eval \order +\end{Verbatim} +They can take a normal argument. Between these commands and their argument +can be a ``biggg'' command or a star. For example, +\begin{example} +\def\0{\frac12} +\[ \abs{\0} \quad + \norm\Big{\0} \quad + \order*{\0} \] +\end{example} +\begin{example} +\def\0{\frac12x} +\[ \eval{\0}_a^b \quad + \eval[(]{\0}_a^b \quad + \eval[[]\big{\0}_a^b \] +\end{example} +You can set the ``order'' symbol in this module through +the \opt{order} option like this: +\begin{Verbatim} +\usephysicsmodule[order=O]{ab.legacy} +\end{Verbatim} +For further information of this module, see \S\ref*{lega-subsec:ab-and-legacy} +of \hyperref{./physics2-legacy.pdf}{}{}{physics2-legacy}. + +\subsection{The \modu{bm-um.legacy} module} +If you are maintaining a document with plenty of ``\cs{bm}''s or +``\cs{boldsymbol}''s in it but want to use \pkg{unicode-math} package +simultaneously, you could take a look at this module. + +The \cs{bm} command from \pkg{bm} package uses \cs{mathversion} to support +its function, but there are few OpenType math fonts who released with a bold +version. The \modu{bm-um.legacy} module provides a \cs{bm} command too, but +this \cs{bm} can only take \emph{one} math character or a series of math +characters sharing the same category code as its argument. +If the argument was Latin letters or Greek letters, \cs{bm} would switch to +the bold italic glyphs corresponding to them (if there exists bold italic +glyphs); else \cs{bm} would switch to the bold upright glyphs. For example, +\begin{example} +$\bm{0}\bm{A}\bm{z} + \bm{\alpha}\bm{\Omega}$ +\end{example} + +\subsection{The \modu{nabla.legacy} module} +This module provides some commands related to nabla ($\nabla$). Notice that +this module requires the \pkg{fixdif} package with file date 2023/01/31 at +minimum. + +This module defines \cs{grad} and \cs{curl} and redefines \cs{div}. For example, +\begin{example} +\[ \grad V \] +\[ \div (x,y,z) \] +\[ \curl(x,y,z) \] +\end{example} +The ``$\divsymbol$'' symbol was redefined as \cs{divsymbol}. + +\subsection{The \modu{op.legacy} module} +This module provides a series of commands for log-like operators. They are +\begin{Verbatim} +\asin \acos \atan +\acsc \asec \acot +\Tr \tr \rank +\erf \Res \res +\PV \pv +\Re \Im +\end{Verbatim} +where \cs{Re} and \cs{Im} are redefined. The first four lines of commands +yield what they look like in math mode. For example, +\begin{example} +$\asin x$ \quad $\rank A$ +\end{example} +\cs{PV} yields ``$\PV$'' as an ordinary symbol and \cs{pv} yields ``$\pv$''. +For example, +\begin{example} +$\PV f(z)$ \quad $\pv f(z)$ +\end{example} +\cs{Re} and \cs{Im} are redefined as ``$\Re$'' and ``$\Im$''. $\Resymbol$ +and $\Imsymbol$ are redefined as \cs{Resymbol} and \cs{Imsymbol}, in default. + +This module \emph{does not} require \pkg{amsmath}. + +\paragraph{The options of \modu{op.legacy} module} +\opt{ReIm}, a bool key with default value \opt{true}, determines whether to +redefine \cs{Re} and \cs{Im}. If you want to reserve the definition of +\cs{Re} and \cs{Im}, you can write like this: +\begin{Verbatim} +\usephysicsmodule[ReIm=false]{op.legacy} +\end{Verbatim} + +\subsection{The \modu{qtext.legacy} module} +This module was written just to offer a method to maintain documents written +with the legacy \pkg{physics} package. See \S\ref*{lega-subsec:qtext} of +\hyperref{./physics2-legacy.pdf}{}{}{physics2-legacy} for more information. + +\end{document}
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