physics2 (7feb23)

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diff --git a/Master/texmf-dist/doc/latex/physics2/README.md b/Master/texmf-dist/doc/latex/physics2/README.md
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+# The `physics2` package
+
+This package defines commands for typesetting math formulae faster and
+more simply. `physics2` is a modularized package, each module provides its
+own function while `physics2.sty` itself only provides very few functions.
+Therefore you can load modules separately after loading `physics2`.
+
+Modules of `physics2` provide the following supports:
+
+- Automatic braces;
+- Dirac bra-ket notation;
+- Easy way to typeset diagonal matrices and matrices with similar entries;
+- Double cross and double dot (binary) operators for tensors;
+
+**Welcome to pull requests
+[here](https://github.com/AlphaZTX/physics2/pulls).**
+
+## License
+
+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 (at your option) any later version.
+
+This work has the LPPL maintenance status `maintained`.
+
+The Current Maintainer of this work is
+[Zhang Tingxuan](https://www.ctan.org/author/zhang-tx).
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/physics2/phy2docdef.tex b/Master/texmf-dist/doc/latex/physics2/phy2docdef.tex
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+%% This is part of physics2 documentation.
+%% ******************************************************
+%% * 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.                                           *
+%% ******************************************************
+\makeatletter
+\usepackage[nohyperref]{doc}
+\renewcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.1em}}
+\def\contentsonly{\@starttoc{toc}}
+\usepackage{manfnt}
+\protected\def\pardanger{\ifnum\lastnodetype=1%
+  \leavevmode\hbox to \z@{\hss\dbend\hskip10pt\hskip\parindent}\else
+  \ifnum\lastnodetype=11%
+  \leavevmode\hbox to \z@{\hss\dbend\hskip10pt}%
+  \fi\fi\ignorespaces}
+\usepackage{hyperref,color,xr}
+\definecolor{pkgcolor}{RGB}{0,120,80}
+\definecolor{moducolor}{RGB}{0,0,150}
+\hypersetup{colorlinks,urlcolor=magenta,linkcolor=black,filecolor=blue,
+  pdfstartview=FitH,pdfview=FitH,pdfcreator=XeTeX output}
+\def\s@pkg#1{\texorpdfstring{\textcolor{pkgcolor}{\textsf{#1}}}{“#1”}}
+\def\@pkg#1{\texorpdfstring{\hyperref{https://www.ctan.org/pkg/#1}%
+  {}{}{\textcolor{pkgcolor}{\textsf{#1}}}}{“#1”}}
+\DeclareRobustCommand\pkg{\@ifstar\@pkg\s@pkg}
+\def\modu#1{\texorpdfstring{\textcolor{moducolor}{\textsf{#1}}}{“#1”}}
+\def\opt#1{\texorpdfstring{\texttt{#1}}{“#1”}}
+\protected\def\marg#1{\texttt\{\meta{#1}\texttt\}}
+\protected\def\oarg#1{\texttt[\meta{#1}\texttt]}
+\parindent2.4em
+\linespread{1.06}
+\usepackage{multicol,fancyvrb,verbatim,array,hologo}
+\fvset{xleftmargin=\parindent}
+\newenvironment{displayed}{\trivlist\item[]\leftskip\parindent\relax}{\endtrivlist}
+\usepackage[normalem]{ulem}
+\newcounter{example}[subsection]
+\renewcommand\theexample{\thesubsection.\arabic{example}}
+\newwrite\example@out
+\def\example@name{\jobname.example.aux}
+\long\def\example@start{\begingroup\@bsphack
+  \immediate\openout\example@out=\example@name
+  \let\do\@makeother\dospecials\catcode`\^^M\active
+  \def\verbatim@processline{\immediate\write\example@out{\the\verbatim@line}}%
+  \verbatim@start}
+\long\def\example@end{\immediate\closeout\example@out\@esphack\endgroup%
+  \trivlist\item[]\relax
+    \leavevmode\hbox to \z@{%
+      \hbox to \z@{\hss{\footnotesize[\theexample]}\hskip10pt}%
+      \hskip\parindent
+      \begin{minipage}[c]{0.55\textwidth}%
+        \small\verbatiminput{\example@name}%
+      \end{minipage}%
+      \fbox{%
+        \begin{minipage}[c]{0.5\textwidth}%
+          \normalsize\input{\example@name}%
+        \end{minipage}%
+      }%
+    \hss}%
+  \endtrivlist}
+\newenvironment{example*}[1]%
+  {\refstepcounter{example}\label{#1}\example@start}{\example@end}
+\newenvironment{example}
+  {\stepcounter{example}\example@start}{\example@end}
+\author{Zhang Tingxuan}
+\date{2023/02/07\quad Version 0.1.1\thanks{%
+  \url{https://www.github.com/AlphaZTX/physics2}}}
+\makeatother
+\endinput
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/physics2/physics2-legacy.pdf b/Master/texmf-dist/doc/latex/physics2/physics2-legacy.pdf
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diff --git a/Master/texmf-dist/doc/latex/physics2/physics2-legacy.tex b/Master/texmf-dist/doc/latex/physics2/physics2-legacy.tex
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+%% ******************************************************
+%% * 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{Latin Modern Roman}
+\setsansfont{Latin Modern Sans}
+\setmonofont{Latin Modern Mono}
+\setmathfont{Latin Modern 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 \hyperref{./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 \hyperref{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, among which,
+only the \modu{common} module would be loaded automatically by the package.
+If you want to load other modules of \pkg{physics2}, write this 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}
+Also, 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}
+
+\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 to \cs{eval}\oarg{left delimiter}\marg{subformula}.
+The \modu{ab.legacy} module abandoned the \verb"\eval(foo|"-like syntax. The
+\meta{left delimiter} argument is optional. For example,
+\begin{example}
+\def\0{\frac12x}
+\[ \eval{\0}_a^b       \quad
+   \eval[(]{\0}_a^b    \quad
+   \eval[[]\big{\0}_a^b   \]
+\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 beacuse, if you choose to present a vector in bold, it's alomost
+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 write \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 do 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 opetators.
+
+\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
+\hyperref{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 to use 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
+\hyperref{http://mirrors.ctan.org/macros/latex/contrib/fixdif/fixdif.pdf}%
+{}{}{\textsf{fixdif}} and
+\hyperref{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 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{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}
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/physics2/physics2.pdf b/Master/texmf-dist/doc/latex/physics2/physics2.pdf
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+++ b/Master/texmf-dist/doc/latex/physics2/physics2.pdf
diff --git a/Master/texmf-dist/doc/latex/physics2/physics2.tex b/Master/texmf-dist/doc/latex/physics2/physics2.tex
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+++ b/Master/texmf-dist/doc/latex/physics2/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}
\ No newline at end of file