mismath (17jun24)

git-svn-id: svn://tug.org/texlive/trunk@71549 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 421 insertions, 286 deletions

diff --git a/Master/texmf-dist/source/latex/mismath/mismath.dtx b/Master/texmf-dist/source/latex/mismath/mismath.dtx
index f3fd2168bca..c2d10d32afb 100644
--- a/Master/texmf-dist/source/latex/mismath/mismath.dtx
+++ b/Master/texmf-dist/source/latex/mismath/mismath.dtx
@@ -20,7 +20,7 @@
 %<*package> 
 \NeedsTeXFormat{LaTeX2e}[2005/12/01]
 \ProvidesPackage{mismath}   
-    [2024/05/04 v3.0 .dtx Miscellaneous mathematical macros]
+    [2024/06/16 v3.1 .dtx Miscellaneous mathematical macros]
 %</package>
 %<*driver>
 \documentclass{ltxdoc}
@@ -34,13 +34,16 @@
 \usepackage{multicol}
 \usepackage{sectsty}
 \usepackage{xcolor}
-\usepackage{spacingtricks}
+\usepackage[pifont]{spacingtricks}
 \usepackage{array}
 \usepackage{metalogo} % for logos of XeLaTeX et LuaLaTeX
 
 \definecolor{darkbrown}{rgb}{0.5,0.1,0.1}
 \allsectionsfont{\color{darkbrown}}
 
+% Next command is used for showing original Latin Modern \i and \j in text mode:
+%\DeclareTextFontCommand{\extrafont}{\fontfamily{lmr}\selectfont} % useless with fourier
+
 % The following commands provide several shapes for pi
 \DeclareFontEncoding{LGR}{}{}
 \def\pilmr{\text{\usefont{LGR}{lmr}{m}{n}\symbol{112}}}
@@ -62,15 +65,13 @@
 \def\pipx{\text{\usefont{U}{pxmia}{m}{it}\symbol{"19}}}
 \def\pitx{\text{\usefont{U}{txmia}{m}{it}\symbol{"19}}}
 
-% Next command is used for showing original Latin Modern \i and \j in text mode:
-%\DeclareTextFontCommand{\extrafont}{\fontfamily{lmr}\selectfont} % useless with fourier
+\let\updelta\otherdelta
 
 \DisableCrossrefs         
 %\CodelineIndex
 %\RecordChanges
 
 \usepackage{hyperref}
-\let\C\relax % "\C already defined" with hyperref when compiling with xelatex or lualatex
 \hypersetup{%
     colorlinks, 
     linkcolor=blue,
@@ -87,7 +88,7 @@
 %</driver>
 % \fi
 %
-% \CheckSum{845}
+% \CheckSum{854}
 %
 % \CharacterTable
 %  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
@@ -105,157 +106,13 @@
 %   Grave accent  \`     Left brace    \{     Vertical bar  \|
 %   Right brace   \}     Tilde         \~}
 %
-% \changes{v0.1}{2011/12/27}{First personal version}
-%
-% \changes{v1.0}{2019/04/11}{
-%    - Initial published version: creating dtx and ins files}
-%
-% \changes{v1.1}{2019/04/20}{
-%    - Some forgotten french 'et' -> 'and', citecolor=blue,
-%    - changing the default font for pinumber Euler -> Symbol}
-%
-% \changes{v1.2}{2019/04/27}{
-%    - Works fine with beamer now, 
-%    - AtBeginDocument for enumber, inumber, jnumber, 
-%    - creating general mm@operator macro, 
-%    - using mathup instead of mathrm
-%    - added mathtools package, 
-%    - font definition Roman -> up, 
-%    - changes in documentation, 
-%    - replacing the PEroman macro by PEupright}
-%
-% \changes{v1.3}{2019/05/08}{
-%    - Using bslash in the internal mm@warning macro, 
-%    - loading of mathfixs package
-%    - Many corrections in documentation}
-%
-% \changes{v1.4}{2019/05/22}{
-%    - Changing font definition up -> UpSh, due to incompatibility with unicode-math}
-%
-% \changes{v1.5}{2019/05/30}{
-%    - A solution for using mul with frac -> braces, 
-%    - addition of paren macro}
-% \changes{v1.5}{2019/06/22}{
-%    - Small corrections in documentation}
-%
-% \changes{v1.6}{2019/09/06}{
-%    - Removing mathfixs package, problems with fractions}
-%
-% \changes{v1.7}{2019/12/27}{
-%    - Adding a table of contents to the documentation}
-%
-% \changes{v1.8}{2020/11/15}{
-%    - Incompatibility mentioned when using `i' with accent in beamer titles -> use \^i, 
-%    - small changes in documentation}
-%
-% \changes{v1.9}{2020/10/17}{
-%    - UpSh replaced by "operators" font in math mode, 
-%    - PackageWarning `command exist' replaced by PackageWarningNoLine,
-%    - medspace replaced by thickspace in the lfrac command,
-%    - changing font in documentation, lmodern -> Palatino (mathpazo)}
-%
-% \changes{v1.10}{2020/10/25}{\
-%    - pinumber command code adapted to avoid incompatibility with the new frenchmath, 
-%    - default option (in upgreek) changed from Symbol to Euler.}
-%
-% \changes{v2.0}{2022/11/11}{
-%    - pinumber command has been enhanced to use other Greek letters packages,
-%        (and LGR encoding pi by default), it is no longer compatible with the older, 
-%    - paren command has been removed, 
-%    - hvect and hlbar have been slightly modified (phantom t instead of phantom h),
-%    - several changes in the documentation, 
-%    - now using the Charter font in the doc (with the package mathdesign)}
-%
-% \changes{v2.1}{2022/12/26}{
-%    - Improved management of square brackets with the ibrackets package,
-%    - new macros codim, sinc, var, eqdef*, 
-%    - removing the systematic warning for paren command,
-%    - a small change in norm command -> bars in small size,
-%    - several changes in documentation}
-%
-% \changes{v2.2}{2023/01/06}{
-%    - Loading of ibrackets package is now optional, due to an error
-%        when using DeclarePairedDelimiter with square brackets.}
-%
-% \changes{v2.3}{2023/02/09}{
-%    - Introducing keyval options for enumber, inumber, jnumber, PEupright
-%        (corresponding old commands are maintained for now),
-%    - and also for ibrackets, boldvect and arrowvect
-%    - Documentation update}
-%
-% \changes{v2.4}{2023/02/18}{
-%    - New powerful macros MathUp, MathIt and also MathNumbers, MathProba, MathNormal,
-%    - keyval options are no longer useful and have been deleted,
-%    - loading package ifthen has been forgotten in v2.3 (causing possible errors),
-%    - no more incompatibility when using `i' with accent in beamer titles}
-%
-% \changes{v2.5}{2023/02/23}{
-%    - Unification of the code of MathUp and MathIt,
-%    - a powerful macro `apply' is used in MathNormal to act on a list,
-%    - a new `tensor' command,
-%    - small changes in the documentation}
-%
-% \changes{v2.6}{2023/03/01}{
-%    - A bug correction in mm@macro
-%    - incompatibility of \C macro solved, when using babel with Russian
-%        (thanks to Murray Eisenberg for this bug report on TeX StackExchange)
-%    - mathrm added in macro eqdef* (useful if italicized Greek uppercase Delta)
-%    - Tiny changes in the documentation}
-%
-% \changes{v2.7}{2023/03/05}{
-%    - Macros for sets of numbers (\R, \C,...) now available only in math mode
-%        (following remarks by David Carlisle and Enrico Gregorio)
-%    - special (not generic) warning when loading babel with russian
-%        (\C will not be defined in that case)}
-%
-% \changes{v2.8}{2023/07/26}{
-%    - Some small changes in the documentation
-%    - New macro `onlymathC' designed for using '\C' when Russian language is loaded}
-%
-% \changes{v2.9}{2023/12/19}{
-%    - New option decimalcomma
-%    - Some small changes in the documentation}
-%
-% \changes{v2.10}{2024/02/20}{
-%    - Better compatibility with unicode-math: 
-%        for the options ibrackets, decimalcomma and the commands MathUp, MathIt
-%    - Explicit error message when using mathcols without loading the multicol package} 
-%
-% \changes{v2.11}{2024/02/26}{
-%    - Enhancements of the pinumber macro with keyval options:
-%        * no necessity to load a Greek letters package
-%        * improvements of compatibility with unicode-math
-%    - Now using the Adobe Utopia font with the package fourier}
-%
-% \changes{v2.12}{2024/02/29}{
-%    - The xparse package has been removed by mistake in v2.11,
-%        this may cause some compatibility problems;
-%        it is loaded again by mismath
-%    - Improvements to make pinumber work perfectly with unicode-math
-%    - Small corrections in the doc}
-%
-% \changes{v3.0}{2024/03/15}{
-%    - Rewriting of the pinumber command including the pifonts macro
-%    - Presenting other lgrmath values for pinumber in the doc
-%    - The \C macro is now in AtBeginDocument
-%    - amsmath isn't loaded anymore because mathtools loads it
-%    - Bug fix with options decimalcomma and ibrackets
-%    - New option 'nofunction' to lighten the package loading
-%    - Addition of coker and Res in standard operator names
-%    - New option 'classicReIm' to deactivate Im and Re redefinition
-%    - New option 'otherReIm' to provide an alternative writing with cmsy font
-%    - Removal of the PEupright command
-%    - Additional space in the lfrac macro increased from \: (5mu) to 7mu 
-%    - New optional parameter for adjusting the space in lfrac
-%    - Changing the vphantom in hvect, hvec and lbar from `t' to `A', looks better}
-%
 % \GetFileInfo{mismath.sty}
 %
 % \title{Miscellaneous mathematical macros \\The \textsf{mismath} package\thanks{This document
 % corresponds to \textsf{mismath}~\fileversion, dated \filedate. 
 % Thanks to François Bastouil for initial help in English translation.}}
 % \author{Antoine Missier \\ \texttt{antoine.missier@ac-toulouse.fr}}
-% \date{May 04, 2024}
+% \date{June 16, 2024}
 %
 % \maketitle
 % \tableofcontents
@@ -292,8 +149,7 @@
 % \item displaymath in double columns for lengthy calculations with short expressions.
 % \end{itemize}
 %
-% To avoid compatibility issues,
-% most of our macros will only be defined 
+% To avoid compatibility issues, most of our macros will only be defined 
 % if there isn't already a command with the same name in the packages loaded 
 % before \textsf{mismath}. If a macro is already defined,
 % a warning message will be displayed and the \textsf{mismath} definition 
@@ -302,16 +158,19 @@
 %
 % \medskip
 % \DescribeEnv{\oarg{options}}
-% The \textsf{mismath} package loads the \textsf{mathtools}  
+% The \textsf{mismath} package loads the \textsf{mleftright}
+% \footnote{The \textsf{mleftright} package defines variants \texttt{\string \mleft} 
+% and \texttt{\string \mright} of \texttt{\string left} and \texttt{\string \right}.} 
+% package by Heiko Oberdiek~\cite{MLR} and also \textsf{mathtools}  
 % \footnote{The \textsf{mathtools} package offers numerous helpful macros and improvements 
 % of the \textsf{amsmath} package.}
-% package by Morten Høgholm and Lars Madsen~\cite{TOOL} which in turn loads
-% the \textsf{amsmath} package~\cite{AMS}.
+% by Morten Høgholm and Lars Madsen~\cite{TOOL} which in turn loads
+% the \mbox{\textsf{amsmath}} package~\cite{AMS}.
 % If you want to use \mbox{\textsf{amsmath}} or \textsf{mathtools} with specific options,
 % you can include these options as options of \mbox{\textsf{mismath}}, or 
 % you can load \textsf{amsmath} or \textsf{mathtools}
 % with the desired options before loading \mbox{\textsf{mismath}}.
-% When using the package \textsf{unicode-math}~\cite{UNIC}, \textsf{mismath} 
+% When using the package \mbox{\textsf{unicode-math}}~\cite{UNIC}, \textsf{mismath} 
 % should be loaded before \textsf{unicode-math}, just like \textsf{amsmath}.
 %
 % \medskip
@@ -364,7 +223,7 @@
 % or imaginary number $\i$, with |\mathup{e}| or |\mathup{i}|, 
 % the package provides the |\e| command for Euler's number 
 % and |\i| or |\j| for imaginary numbers.
-% Let us notice that |\i| and |\j| already exist in LaTeX. In LR (left-to-right) mode, 
+% Let us notice that |\i| and |\j| already exist in \LaTeX. In LR (left-to-right) mode, 
 % they produce \mbox{`\i,\ \j'} without the dot,  
 % allowing you to place accents on them. 
 % However, in mathematical mode, they produce the warning 
@@ -376,7 +235,7 @@
 % \medskip
 % \DescribeMacro{\MathUp} 
 % Indeed, typing a lot of backslashes for constants like $\e$, $\i$, or $\j$
-% in a document with numerous formulas can become tiresome. 
+% in a document with numerous formulas using them can become tiresome. 
 % To alleviate this, the package proposes another solution 
 % with the macro |\MathUp|\marg{char}.
 % For example, when |\MathUp{e}| is called, any subsequent occurrence of $\e$
@@ -420,7 +279,7 @@
 % These three commands, used until version 2.2 but only functioning within the preamble, 
 % serve now as aliases for the commands |\MathUp{e}|, |\MathUp{i}| or |\MathUp{j}|, 
 % so they can be used anywhere 
-% in the document or preamble and has an inverse switches with |\MathIt|. 
+% in the document or preamble and has an inverse switch with |\MathIt|. 
 % 
 % \medskip
 % \DescribeMacro{\pinumber[\meta{option}]}
@@ -452,7 +311,7 @@
 % which allows the use of any Greek LGR-encoded font in math mode,
 % an idea taken up in \textsf{mathgreeks}~\cite{MGREEK}.
 % Also note \textsf{newtxmath}~\cite{NTX} which has several font options.
-% These packages provide commands like |\uppi| (\textsf{upgreek}), 
+% These packages provide commands like |\uppi| (\textsf{upgreek}, \textsf{mathgreeks}), 
 % |\piup| (\textsf{mathdesign}, \textsf{kpfonts}, \textsf{lgrmath}), 
 % |\otherpi| (\textsf{fourier}), etc.
 % \footnote{They have also options to typeset all the Greek lowercase 
@@ -461,7 +320,7 @@
 % In this case, |\pinumber| must be called in the preamble 
 % with an optional argument being the name of the command, \emph{without the backslash},
 % giving access to the upright pi:
-% piup, uppi, otherpi\ldots
+% \texttt{piup}, \texttt{uppi}, \texttt{otherpi}\ldots
 % However, installing such a Greek letters package will modify 
 % all the other Greek letter glyphs.
 % ^^A even if, except for pi, they will be in italics. 
@@ -482,7 +341,7 @@
 % providing the same glyph.
 % The following table summarizes the available options.
 % When a key is given without a value, |\pinumber| will choose a default value
-% specified in the following text (depending on the key).
+% specified in the text list following the table.
 %
 % \begin{center}
 % \setlength{\extrarowheight}{1pt}
@@ -556,18 +415,18 @@
 % (based on Palatino),
 % \texttt{txfonts} (based on Times)
 % are booleans whose default value is \texttt{true} (when called).
-% The \texttt{txfonts} option yields the same glyph than \texttt{lgrmath=txr}.
+% The \texttt{txfonts} key yields the same glyph than \texttt{lgrmath=txr}.
 %
 % \end{itemize}
 % \end{enumerate}
 % 
-% The \textsf{unicode-math} package~\cite{UNIC} provides |\uppi|, and you can use
+% The \textsf{unicode-math} package~\cite{UNIC} provides |\uppi|, so you can use
 % |\pinumber[uppi]| to produce automatic upright pi in the selected math font,
-% but |\pinumber[uppi]| must be called \emph{after} \mbox{\textsf{unicode-math}},
-% and a math font must have been explicitly chosen with |\setmathfont|.
-% You can also use the \texttt{fontspec} key option to obtain pi in any font 
-% that is supported by \mbox{\textsf{unicode-math}} \eg
-% |\pinumber[fontspec=STIX Two Math]|.
+% but a math font must have been explicitly chosen with |\setmathfont|.
+% You can also use the \texttt{fontspec} key option,
+% \eg |\pinumber[fontspec=STIX Two Math]|,
+% to obtain pi in any font 
+% that is supported by \textsf{unicode-math}.
 %
 % For other fonts, it can be quite complicated to make Greek letters packages 
 % work with \textsf{unicode-math}. In any case, such a package must be loaded 
@@ -616,7 +475,7 @@
 % \DescribeMacro{\boldvect}
 % The |\vect| macro allows vector names to be typeset using bold italic font,
 % as recommended by ISO~\cite{NIST}~\cite{SI}, instead of using arrows. 
-% By using the |\boldvect| command, you can modify the behavior of |\vect|
+% To achieve this, call the |\boldvect| command, it will modify the behavior of |\vect|
 % locally or globally, depending on its placement in the document (inside or outside
 % a group or an environment):\\[2ex]
 % \begin{minipage}{8cm}
@@ -639,16 +498,16 @@
 % \textsf{isomath} with |\mathbfit| 
 % or \textsf{bm} with the |\bm| command;
 % \textsf{unicode-math} provides the |\symbfit| command.
-% To use an alternative command instead of |\boldsymbol| in \textsf{mismath}, 
+% To use an alternative command instead of |\boldsymbol| in \mbox{\textsf{mismath}}, 
 % redefine |\boldvectcommand|, 
-% for instance after loading \textsf{fixmath}:
+% for instance if \textsf{fixmath} is loaded:
 %
 % \medskip
 % \centeredline{|\renewcommand\boldvectcommand{\mathbold}|}
 %
 % \medskip
 % According to ISO rules, symbols for matrices are also in bold italic.
-% Therefore you can use the same |\boldvect| command or create another alias.
+% Therefore you can also use |\vect| with |\boldvect| for matrices, or create another alias.
 %
 % \medskip
 % \DescribeMacro{\arrowvect}
@@ -663,7 +522,7 @@
 % When vectors with arrows are typeset side by side,
 % the arrows can be set up slightly higher using |\hvect|
 % (which places a vertical phantom box containing `$A$') 
-% to avoid inelegant effects. For example, writing
+% to prevent inelegant effects. For example, writing
 % \begin{itemize}
 % \item $\vect{AB}=\hvect{u} + \vect{AC}$, obtained with |\hvect{u}|,
 % looks better than $\vect{AB}=\vect{u}+ \vect{AC}$;
@@ -696,7 +555,7 @@
 % for adaptive delimiters. Unfortunately, these delimiters 
 % are always vertically centered, relatively to the mathematical center line, 
 % whereas vectors with arrows are asymmetric objects.
-% The code |$\norm{\vec{h}}$| raises a smaller double bar to produce $\norm{\vec{h}}$
+% The code |$\norm{\vec{h}}$| raises the double bar to produce $\norm{\vec{h}}$
 % instead of $\Vert\vec{h}\Vert$ or $\left\Vert \vec{h} \right\Vert$.
 % Let's notice that the height of the bars don't adjust to content, 
 % but however to context: main text, subscripts or exponents, 
@@ -745,6 +604,27 @@
 % The command |\di| can also represent the \emph{distance}, hence its name:
 % \[\di(u, \cmmathcal{H}) = \frac{\abs{\langle u,v\rangle}}{\lVert v \rVert}.\]
 %
+% \DescribeMacro{\opDelta} \DescribeMacro{\opdelta}
+% Two other `difference' operators allow for expressing variations ($\opDelta$)
+% or small variations ($\opdelta$). 
+% They are obtained using the |\opDelta| and |\opdelta| commands.
+% \begin{align*}
+% \opDelta f \approx \opDelta h = f'(x_0) \opDelta x &&
+% \frac{\opdelta T}{T}=\frac{1}{2}\frac{\opdelta l}{l} &&
+% h= \opdelta x\opdelta y
+% \end{align*}
+%
+% Like |\di|, these operators use specific spacing and are typeset using 
+% the upright Greek letters given by |\updelta| and |\upDelta|.
+% By default |\upDelta| is an alias for |\Delta| (which is supposed to be in upright shape);
+% |\updelta| is not provided by \textsf{mismath} but can be obtained with 
+% other packages such as \textsf{mathgreeks}~\cite{MGREEK}, 
+% \mbox{\textsf{unicode-math}}~\cite{UNIC}, 
+% or as an alias for the upright delta provided by other fonts
+% \footnote{With \textsf{fourier} (without the \texttt{upright} option) we have used 
+% \texttt{\string\let\string\updelta\string\otherdelta}.}.
+%
+% \pagebreak
 % \DescribeMacro{\P} \DescribeMacro{\E}
 % To refer to probability
 % \footnote{\LaTeX\ provides also \texttt{\string \Pr} which gives $\Pr$.}
@@ -754,7 +634,7 @@
 %
 % \medskip
 % \DescribeMacro{\Par}
-% The |\P| command already existed to refer to the end of paragraph symbol \Par\ 
+% The |\P| command already existed to refer to the `end of paragraph' symbol (\Par)
 % and has been redefined, but this symbol can still be obtained with |\Par|.
 %
 % \medskip
@@ -762,17 +642,16 @@
 % Variance is generally denoted by $\var$ or $\Var$ (see the following table),
 % but some authors prefer to use $\V$, which can be produced using |\V|.
 %
-% \pagebreak
 % \DescribeMacro{\MathProba}\DescribeMacro{\MathNormal}
 % As for $\e$, $\i$ or $\j$, you can use |\MathUp{P}|, |\MathUp{E}| 
 % or |\MathUp{V}| to avoid typing many |\P|, |\E| or |\V|. 
 % However you can also achieve this in a single command with |\MathProba|, 
 % for example |\MathProba{PE}|. We get the inverse toggle with
-% |\MathIt| for any individual letter or |\MathNormal| for a list.
+% |\MathIt| for any individual letter or |\MathNormal| for a comma-separated list.
 %
 % \medskip
 % \DescribeMacro{\probastyle}
-% Some authors use ``outline'' font shape to represent probability, expectation 
+% Some authors use double-struck font shape to represent probability, expectation 
 % and variance: $\mathbb{P}, \mathbb{E}, \mathbb{V}$.
 % The |\probastyle| macro sets the appearance of |\P|, |\E| and |\V|.
 % For instance |\renewcommand\probastyle{\mathbb}|
@@ -780,7 +659,7 @@
 % in which it is used.}
 % brings the double-struck letters.
 % The |\mathbb| command is provided by \textsf{amsfonts} package
-% (which needs to be called in the preamble), but also by other complete math font
+% (which needs to be loaded in the preamble), but also by other complete math font
 % packages such as \textsf{mathdesign}, \textsf{kpfonts}, \textsf{fourier}, 
 % \textsf{unicode-math}\ldots
 % \hypertarget{nofunction}{}
@@ -829,8 +708,8 @@
 %
 % \DescribeMacro{[nofunction]}
 % Some may find that the definition of all these operators and functions is not useful 
-% for their needs. So, the above definitions (on this page)
-% can be disabled with the \texttt{nofunction} option.
+% for their needs. So, the definitions of standard operators and functions in both
+% previous tables can be disabled with the \texttt{nofunction} option.
 % \hypertarget{classicReIm}{}
 %
 % \medskip
@@ -841,7 +720,6 @@
 % Nevertheless, it is still possible to obtain the old symbols 
 % with |\oldRe| and |\oldIm|.
 %
-% \medskip
 % \DescribeMacro{[otherReIm]}
 % An alternative notation $\Re$, $\Im$ is provided by invoking the \texttt{otherReIm}
 % package option,
@@ -874,9 +752,9 @@
 % \DescribeMacro{\mathset}
 % The |\mathset| command enables you to change the behavior 
 % of all these macros in a global way. 
-% By default, |\mathset| is an alias for |\mathbf|, but if you prefer outline letters, 
-% you can simply use |\renewcommand\mathset{\mathbb}| (with local effect when
-% inside an environment or a pair of curly braces).
+% By default, |\mathset| is an alias for |\mathbf|, but if you prefer double-struck letters, 
+% you can simply use |\renewcommand\mathset{\mathbb}| (with local effect within
+% an environment or a pair of curly braces).
 %
 % \smallskip
 % \DescribeMacro{\onlymathC}
@@ -894,7 +772,7 @@
 %
 % \medskip
 % Symbols with limits behave differently for in-line formulas or for displayed equations. 
-% In the latter case, ``limits'' are placed under or above the symbol 
+% In the latter case, `limits' are placed under or above the symbol 
 % whereas for in-line math mode, 
 % they are placed on the right, as a subscript or exponent. Compare:
 % $\zeta(s)=\sum_{n=1}^{\infty    }\frac{1}{n^s}$ with
@@ -905,9 +783,9 @@
 % With in-line math mode, displaymath can be forced with |\displaystyle|
 % or its alias |\ds|. However, when using these commands, all the rest of the current
 % mathematical environment will be set in displaymath mode 
-% (as shown in the previous example, where the fraction will be expanded).
+% (as shown in the previous example, where the fraction is expanded).
 % To limit the display style effect to the affected symbol only, 
-% similar the the  \textsf{amsmath} command |\dfrac|, 
+% similar to the  \textsf{amsmath} command |\dfrac|, 
 % we can use the following macros:
 % |\dlim|, |\dsum|, |\dprod|, |\dcup|, |\dcap|.
 % So 
@@ -969,13 +847,16 @@
 % \DescribeMacro{\iif}
 % |\iif| is an alias for ``\iif'', to be used in text mode.
 %
+% \medskip
+% \DescribeMacro{\then} 
+% This macro produces the symbol $\Longrightarrow$ surrounded by large spaces,
+% like the standard macro |\iff| does it with $\Longleftrightarrow$.
+% It's just an alias for the \textsf{amsmath} |\implies| macro.
+%
 % \subsection{Improved spacing in mathematical formulas}
 %
-% \DescribeMacro{\then} 
-% The |\then| macro produces the symbol $\Longrightarrow$ surrounded by large spaces
-% just like the standard macro |\iff| does it with $\Longleftrightarrow$.
-% Similarly, the |\txt|, \DescribeMacro{\txt}
-% based on the |\text| macro from the \textsf{amstext} package
+% \DescribeMacro{\txt}
+% The |\txt| macro, based on |\text| from the \textsf{amstext} package
 % (loaded by \textsf{amsmath}),
 % leaves em quad spaces (|\quad|) around the text. See the following example:
 % \begin{center}
@@ -988,76 +869,82 @@
 % The multiplication symbol obtained with |\times| produces the same spacing as addition
 % or subtraction operators, whereas division obtained with $/$ is closer to its operands.
 % This actually hides the priority of multiplication over $+$ and $-$.
-% That's why we provide the |\mul| macro, behaving like $/$ 
-% (ordinary symbol) and leaving less space around than |\times|:
+% That's why we provide the |\mul| macro, to avoid the large space surrounding |\times|:
 % \begin{center}
 % $\lambda+\alpha \mul b-\beta \mul c$, obtained with |\mul|,
 % looks better than $\lambda+\alpha \times b-\beta \times c$.
 % \end{center}
 %
-% When using |\mul| before a function name or around a |\left...\right| structure, 
-% the space may be too large on one side of |\mul|.
-% To ensure the same amount of space on both sides, 
-% you can use thin negative spaces |\!| 
-% or enclose the function or structure with braces:
+% Using |\mul| before a function name works also fine (since v3.1) without the need 
+% of curly braces to avoid the additional space before the operator name:
+% |$x\mul\sin x$| yields $x\mul{\sin x}$.
+%
+% \medskip
+% When using a |\left| \ldots |\right| structure, 
+% \TeX\ sets additional surrounding space in some situations.
+% The \textsf{mleftright}~\cite{MLR} package, loaded by \textsf{mismath},
+% offers the variants |\mleft| and |\mright|
+% to address these spacing issues of inner formulas.
+% It also provides the |\mleftright| macro that redefines |\left| as |\mleft|
+% and |\right| as |\mright|.
+% 
 % \begin{center}
-% $x\mul{\sin x}$, obtained with |x\mul{\sin x}|, is slightly better than $x\mul\sin x$;\\[1ex]
-% |$\sin\!{\left( \frac{\pi}{3} \right)} \mul 2$|\\
-% yields $\sin\!{\left(\frac{\pi}{3}\right)}\mul 2$, which looks better than
-% $\sin\left(\frac{\pi}{3}\right)\mul 2$. 
+% Compare $\sin\left(\frac{\pi}{3}\right)\mul 2$ with
+% $\sin\mleft(\frac{\pi}{3}\mright)\mul 2$ obtained with
+% |$\sin\mleft(\frac{\pi}{3}\mright)}\mul 2$|.
 % \end{center}
-% The negative thin space after the function name is not related to |\mul|,
-% but to the  ``excessive'' spaces around the |\left... \right| structure.
 %
-% \medskip
 % \DescribeMacro{\pow}
 % In the same way, when typesetting an exponent after a closing \emph{big} 
 % parenthesis produced by |\right)|,
 % the exponent appears to be a little to far from the parenthesis.
 % To address this issue, the |\pow|\marg{expr}\marg{pow} command is provided
 % \footnote{This macro gives bad results with \emph{normal-sized} parenthesis.},
-% which sets the positioning of the exponent \meta{pow}
+% which places \meta{expr} in a pair of parenthesis and
+% sets the positioning of the exponent \meta{pow}
 % slightly closer to the right parenthesis.
 % Compare:
 % \[ \e^a =\lim_{n \to +\infty}\pow{1+\frac{a}{n}}{n} 
 % \txt{obtained with \texttt{\string \pow}, rather than} 
 % \e^a =\lim_{n \to +\infty}\left(1+\frac{a}{n}\right)^{n}.\]
 %
-% \DescribeMacro{\abs}
-% The correct typesetting of absolute value (or modular for a complex number) is achieved
-% using |\lvert| \ldots |\rvert|, rather than $\mid$, as the latter doesn't maintain 
-% proper spacing in some situations (when a sign follows the open delimiter).
-% For bars whose height has to adapt to the content, 
-% we can use |\left\vert| \ldots |\right\vert| or, more simply, 
-% the |\abs|\{\ldots\} command, which is equivalent
+% \DescribeMacro{\abs} \DeleteShortVerb{\|}
+% The \cs{abs} command typesets the absolute value while properly managing the spacing, 
+% which \texttt{|}\ldots\texttt{|} does not. Compare $\abs{-x}$, 
+% obtained with \cs{abs}, to $|-x|$ without. 
+% Using the delimiters \cs{lvert} and \cs{rvert} presents another issue when 
+% the absolute value follows a function name; \eg \verb@\ln\lvert x\rvert@ yields 
+% $\ln \lvert x\rvert$
+% instead of $\ln\abs{x}$ (with \verb@\ln\abs{x}@). 
+% Moreover, with \cs{abs}, the size of the delimiters adapts to the content
 % \footnote{We could also define \texttt{\string \abs} 
 % using \texttt{\string \DeclarePairedDelimiter} 
 % from the \mbox{\textsf{mathtools}} package~\cite{TOOL}.}.
+% \MakeShortVerb{\|}
 %
 % \medskip
 % \DescribeMacro{\lfrac}
 % The |\lfrac| macro behaves like |\frac|
-% but with thicker spaces around the arguments,
-% making the corresponding fraction bar slightly longer. See the following examples:
+% but with additional spacing around the arguments,
+% making the corresponding fraction bar slightly longer. 
+% This macro has an optional parameter |\lfrac|\oarg{space}\marg{num}\marg{denom}
+% to adjust the length of the fraction bar. The optional \meta{space} argument must be given
+% with \emph{math units} (\texttt{mu}); 
+% the default value is \texttt{7mu} (equivalent to |\:\,|).
+% See the following examples;
+% the last one is obtained with |\lfrac[4mu]{1}{\sqrt{x}}|.
 % \[ \lbar{Z} = \lfrac{\lbar{z_1-z_2}}{\lbar{z_1+z_2}} \qquad
 %  u(x)= \lfrac{\frac{1-2x}{5}}{x^2+1} \qquad
 % y'+xy=\lfrac[4mu]{1}{\sqrt{x}}
 % \]
-%
-% This macro has an optional parameter |\lfrac|\oarg{space}\marg{num}\marg{denom}
-% to adjust the length of the fraction bar. The optional \meta{space} argument must be given
-% in \emph{math units} (\texttt{mu}); 
-% the default value is \texttt{7mu} (equivalent to |\:\,|),
-% \texttt{4mu} in the last example.
 % \hypertarget{ibrackets}{}
 %
-% \medskip
 % \DescribeMacro{[ibrackets]}
 % Open intervals are commonly represented with parenthesis, \eg $(0, +\infty)$,
 % but sometimes square brackets are used, especially in French mathematics: $]0, +\infty[$.
-% In that specific case, the space around the square brackets is often inappropriate, 
+% In that case, the space around the square brackets is generally inappropriate, 
 % as in the expression $x \in \mathclose{]} 0, +\infty[$.
-% To address this issue, we have redefined the brackets in the \textsf{ibrackets}
+% To address this issue, we have redefined the brackets in the \mbox{\textsf{ibrackets}}
 % package~\cite{BRACKET}.
 % This one can be optionally
 % loaded by \textsf{mismath} using the \texttt{ibrackets} package option.
@@ -1107,7 +994,7 @@
 % However, in the math mode of \LaTeX, the comma is always, by default, 
 % treated as a punctuation symbol and therefore is followed by a space. 
 % This is appropriate in intervals: |$[a,b]$| results in $[a,b]$,
-% but is not appropriate for numbers where the comma represents the decimal separator. 
+% but not for numbers where the comma represents the decimal separator. 
 % For example, |$12,5$| is displayed as $12, 5$ instead of $12{,}5$.
 %
 % Two very convenient packages allow handling the decimal comma in math mode:
@@ -1143,15 +1030,15 @@
 % \DescribeMacro{\systemsep}
 % This first example could also have been achieved using the \texttt{cases} environment
 % from the \textsf{amsmath} package, although \texttt{cases} places mathematical expressions 
-% closer to the bracket.
-% The |\systemsep| length allows you to adjust the gap between 
-% the bracket and the expressions. 
+% closer to the curly brace.
+% The |\systemsep| length allows to adjust the gap between 
+% the bracket and the math expressions. 
 % By default, the gap is set to |\medspace|. You can reduce this gap by redefining 
-% the command, \eg: |\renewcommand{\systemsep}{\thinspace}|.
-% Alternatively you can increase the gap using |\thickspace| 
-% and the same spacing as of the \texttt{cases} environment 
-% is obtained with |\renewcommand\systemsep}{}|.
-% The |\systemsep| command allows for greater flexibility in adjusting the spacing 
+% the command, \eg |\renewcommand{\systemsep}{\thinspace}|.
+% Alternatively you can increase the gap using |\thickspace|;
+% the same spacing as of the \texttt{cases} environment 
+% being obtained with |\renewcommand\systemsep}{}|.
+% So the |\systemsep| command allows for greater flexibility in adjusting the spacing 
 % within the \texttt{system} environment.
 %
 % \medskip
@@ -1179,7 +1066,7 @@
 % The default spacing between the lines of a \texttt{system} environment has been slightly 
 % enlarged compared to the one used in \texttt{array} environments (using a factor of 1.2). 
 % This can be adjusted by using
-% |\renewcommand{\systemstretch}|\marg{stretch}, where \meta{stretch} is the desired value
+% |\renewcommand{\systemstretch}|\marg{stretch}, where \meta{stretch} is the desired factor
 % for the spacing. You can place this command 
 % inside the current mathematical environment for a local change, or outside 
 % for a global change. The default value for is 1.2.
@@ -1241,7 +1128,7 @@
 % as shown in the following example.
 % However, to use this feature, the \textsf{multicol} package must be loaded in the preamble.
 % The \texttt{mathcols} environment activates mathematical mode
-% in display style and uses an \texttt{aligned} environment.
+% in display style and uses the \texttt{aligned} environment (from \textsf{amsmath}).
 % \begin{mathcols}
 %           & \frac{1}{2 \mul {\pow{\frac{1}{4}}{n}} + 1} \geq 0.999 \\
 %     \iff\ & 1 \geq 1.998  \pow{\frac{1}{4}}{n} + 0.999 \\
@@ -1293,6 +1180,7 @@
 % \end{tabular}
 % \end{center}
 % \StopEventually{}
+%
 % \section{Implementation}
 %
 % We load certain packages conditionally to avoid 'option clash' errors in cases
@@ -1314,6 +1202,7 @@
 %\@ifpackageloaded{amsmath}{}{\RequirePackage{amsmath}}
 \@ifpackageloaded{mathtools}{}{\RequirePackage{mathtools}}
 \@ifpackageloaded{esvect}{}{\RequirePackage[b]{esvect}}
+\RequirePackage{mleftright}
 \RequirePackage{ifthen}
 \RequirePackage{xparse} % provides \NewDocumentCommand, now in LaTeX3
 \RequirePackage{xspace} % for \iif command
@@ -1369,7 +1258,7 @@
 % \DescribeMacro{\mm@warning} \DescribeMacro{\mm@macro} \DescribeMacro{\mm@operator} 
 % The next three internal macros serve as meta commands for
 % conditionally defining macros while providing a warning message if the macro already exists.
-% These macros can be useful in other packages as well.
+%
 % \medskip
 %    \begin{macrocode}
 \newcommand\mm@warning[1]{
@@ -1395,7 +1284,7 @@
 % This command also works fine with other sans serif fonts like \textsf{cmbright}.
 %
 % Moreover for \textsf{beamer}, which changes the default font family (to sans serif),
-% |\e|, |\i|, |\j| have no effect without |\AtBeginDocument|.
+% |\e|, |\i|, |\j| have no effect without |\AtBeginDocument| and
 % |\AtBeginDocument| is also necessary to redefine |\i| when calling 
 % the \textsf{hyperref} package which overwrites the |\i| definition.
 % \medskip
@@ -1411,15 +1300,15 @@
 %    \end{macrocode}
 %
 % \DescribeMacro{\MathFamily}
-% The following macros |\MathUp| and |\MathIt| are switches that transform 
+% The following macros |\MathUp| and |\MathIt| are toggles that transform 
 % any chosen letter in math mode to roman or italic style. 
-% These switches can be used anywhere in the document or preamble.
+% These switches can be used anywhere in the document or the preamble.
 % They are based on the generic macro |\MathFamily|.
 % To obtain a letter in roman style instead of italic, we need to change the 
 % mathcode digit that represents the font family: 1 to 0.
 %
 % For example, except for \LuaLaTeX, mathcode of the `e' letter is:
-% `e="7165 (decimal 29029), with the second digit `1' indicating ``italic'' style.
+% e="7165 (decimal 29029), with the second digit `1' indicating ``italic'' style.
 % To get a roman `e', we need to change its mathcode to "7065.
 %
 % When used in the preamble, we call |\MathFamily| by |\AtBeginDocument|
@@ -1531,7 +1420,7 @@
 % Let its author, Petr Ol\v{s}ák, be thanked.
 % This macro allows to accomplish tasks that
 % usual loop instructions like |\@for| or |\foreach| cannot achieve due to
-% errors like ``!~Improper alphabetic constant''.
+% errors like ``\texttt{!~Improper alphabetic constant}''.
 % For instance, if you try |\def\letter{A} \MathUp{\letter}| it will fail
 % because the control sequence |\letter| is not strictly
 % equivalent here to the single character `A'.
@@ -1549,11 +1438,11 @@
 
 %    \end{macrocode}
 %
-% The following commands were used until version 2.2 but still work.
-% They were intended to set some letters in upright shape
-% in math mode, but only worked in the preamble.
-% This is now managed by the more powerful |\MathUp| command, and
-% the old commands are maintained but as alias for |\MathUp|.
+% The following commands were used originally (until version 2.2)
+% to set the math letters e, i or j in upright shape,
+% but only worked in the preamble.
+% This is now managed by the more powerful |\MathUp| command, but
+% the old commands are maintained as alias for |\MathUp|. 
 % \medskip
 %
 %    \begin{macrocode}
@@ -1564,7 +1453,7 @@
 %    \end{macrocode}
 %
 % Obtaining an upright Greek letter $\pi$ must be handled differently. 
-% The switches are called |\pinumber| and |\pinormal| 
+% The toggles are called |\pinumber| and |\pinormal| 
 % and can be used anywhere in the document.
 %
 % But |\pinumber| must be called first in the preamble with an optional argument.
@@ -1573,11 +1462,11 @@
 % Compatibility with \textsf{unicode-math} is a bit tricky!
 % When given without an argument in the preamble, 
 % |\pinumber| uses an LGR font encoding called \texttt{lmr}.
-% A new feature (v2.11) is to use |\pinumber| with a keyval option to 
+% A new feature (v2.11) for |\pinumber| is provided with keyval options to 
 % use many other Greek pi letters without loading
 % a whole package, thus without altering the other (italic) Greek letters. 
 % We achieve this with |\DeclareSymbolFont| and |\DeclareMathSymbol|.
-% We just have to know the ``name'' of the desired symbol font.
+% We just have to know the `name' of the desired symbol font.
 % 
 % \medskip
 %    \begin{macrocode}
@@ -1722,28 +1611,28 @@
 
 %    \end{macrocode}
 % When |\pinumber|\oarg{keyval} has been called, you can also get 
-% some other mathematical constants using Greek letters, 
+% some other mathematical constants using Greek letters in the same font (\texttt{mmupgr}) 
 % \eg $\othergamma$, the Euler-Mascheroni constant:
 % \begin{verbatim}
 % \let\gamma\relax
 % \DeclareMathSymbol{\gamma}{\mathord}{mmupgr}{"0D}
 % \end{verbatim}
 % \vspace{-2ex}
-% If \textsf{unicode-math} is used, you must put these commands in
+% If \textsf{unicode-math} is used, you must put these commands inside
 % |\AtBeginDocument|.
 % The hexadecimal code |"0D| depends on the option passed to |\pinumber|
-% in the preamble (see the command |\pifonts| above and search in package docs). \\
+% in the preamble (see the command |\pifonts| above and search in package docs).
 % And to get the golden ratio $\othervarphi$:
 % \begin{verbatim}
-% \let\phi\relax
+% \let\varphi\relax
 % \DeclareMathSymbol{\varphi}{\mathord}{mmupgr}{"27}
 % \end{verbatim}
 % \vspace{-2ex}
-% To preserve the original $\gamma$ or $\varphi$, 
+% I you want to preserve the original $\gamma$ or $\varphi$, 
 % you can define |\upgamma| or |\upvarphi| instead.
 %
 % \medskip
-% And now the commands for vectors and tensors.
+% Commands for vectors and tensors follow.
 % \medskip
 %    \begin{macrocode}
 \newboolean{arrowvect}
@@ -1774,9 +1663,48 @@
 \newcommand{\tensor}{\mathbfsfit} % isomath uses \mathsfbfit
 
 %    \end{macrocode}
+%
+% `Operators', as for example common function names, are generally defined 
+% using the |\DeclareMathOperator| command or |\operatorname| for occasional use. 
+% Operators are then typeset in roman (upright) shape and with appropriate thin space 
+% before and after the operator name.
+% However, for the `differential' operator d, no space should be left after it 
+% to obtain, for example, `$\di x$' instead of `$\operatorname{d} x$'.
+%
+% \medskip
+% Two other operators, suggested by `quark67', representing differences 
+% or variations are defined by the macros |\opDelta| and |\opdelta|. 
+% They use the Greek letters $\upDelta$ and $\updelta$ with appropriate spacing, 
+% similar to |\di|. 
+% By default |\upDelta| will be an alias for |\Delta|.
+% Generally, the uppercase Delta is upright 
+% unless a package is loaded to change this, but the lowercase delta 
+% is italic by default. 
+%
+% To use the |\opdelta| macro, it is therefore necessary 
+% to load a package that provides the lowercase delta in upright shape, 
+% such as \textsf{mathgreeks} or \textsf{unicode-math},
+% or you can use the same symbol font \texttt{mmupgr} as seen above for the upright pi 
+% (if |\pinumber|\oarg{keyval} has been called previously).
+% So you could get the upright delta with:
+% \begin{verbatim}
+% \DeclareMathSymbol{\updelta}{\mathord}{mmupgr}{"0E}
+% \end{verbatim} \vspace{-2ex}
+% The hexadecimal code |"0E| depends on the option passed to |\pinumber|.
+% If you have loaded a package that provides upright shapes of Delta and delta, 
+% it may be necessary to create new aliases for |\upDelta| or |\updelta|,
+% \eg |\let\updelta\|\meta{mydelta}.
+%    \begin{macrocode}
+\mm@macro{di}{\operatorname{d}\mathopen{}}
+\mm@macro{upDelta}{\Delta}
+\mm@macro{opDelta}{\operatorname{\upDelta}\mathopen{}}
+\mm@macro{opdelta}{\operatorname{\updelta}\mathopen{}}
 
+%    \end{macrocode}
+% For the field of probability, we provide the macros |\P|, |\E|, and |\V|, 
+% which are defined as operators. They are typeset in normal roman font, 
+% but can be changed to double-struck style (or another style) if desired.
 %    \begin{macrocode}
-\mm@macro{di}{\mathop{}\!\mathup{d}}
 \newcommand\probastyle{}
 \let\Par\P % end of paragraph symbol
 \renewcommand{\P}{\operatorname{\probastyle{P}}}
@@ -1790,7 +1718,7 @@
 }
 
 %    \end{macrocode}
-% Classic identifiers are presented below. They will be defined only
+% Classic operators or function identifiers are presented below. They will be defined only
 % if the option \texttt{nofunction} has not been activated.
 % \medskip
 %    \begin{macrocode}
@@ -1840,13 +1768,13 @@
 %
 % The |\mathcal| alphabet, from the original Computer Modern font family,
 % is used here to produce $\Re$, $\Im$ and $\bigO$.
-% Several font packages redefines this alphabet producing glyphs that may seem less 
+% Several font packages redefine this alphabet producing glyphs that may seem less 
 % suitable for the commands below.
 % We have therefore retained the original |\cmmathcal| math alphabet, 
 % which can be used for other letters.
 % If \textsf{unicode-math} is called, it will redefine the commands |\Re| and |\Im|
-% in |\AtBeginDocument|, hence the use of `|\AtEndPreamble{\AtBeginDocument{|'
-% to ensure that the \textsf{mismath} redefinition occur after the actions 
+% in |\AtBeginDocument|, hence the use of |\AtEndPreamble{\AtBeginDocument{|\ldots
+% to ensure that the \textsf{mismath} redefinitions occur after the actions 
 % of \textsf{unicode-math}.
 %
 %    \begin{macrocode}
@@ -1880,24 +1808,23 @@
 %    \end{macrocode}
 % And finally we present the remaining macros.
 %
-% With Cyrillic languages, the command |\C| may already be defined but only for text mode.
-% Thus, it will not be redefined by \textsf{mismath}. However, when activating
-% |\onlymathC|, you can to use our |\C| macro only for math mode,
+% With Cyrillic languages, the command |\C| may already be defined 
+% but works only in text mode.
+% Then, it will not be redefined by \textsf{mismath}. However, the command
+% |\onlymathC| allows to use our |\C| macro in math mode,
 % without interfering the definition of the text |\C| that is already defined.
 %
 % When using \XeTeX\ or \LuaTeX\ engines with the \textsf{hyperref} package,
 % |\C| will be already defined and
-% you get the message "\texttt{Command \string\C\space unavailable in encoding TU}".
+% you get the message ``\texttt{Command \string\C\space unavailable in encoding TU}''.
 % Therefore |\onlymathC| is automatically called in that case.
 % \medskip
 %    \begin{macrocode}
 \mm@macro{mathset}{\mathbf}
 \mm@macro{R}{\mathset{R}}
-\AtBeginDocument{
-    \@ifpackageloaded{hyperref}%
-        {\iftutex\onlymathC\fi}% LuaTex or XeTeX engines
-        {\mm@macro{C}{\mathset{C}}}
-}
+\mm@macro{C}{\mathset{C}}
+\AtBeginDocument{% \iftutex = LuaTex or XeTeX engines
+    \@ifpackageloaded{hyperref}{\iftutex\onlymathC\fi}{} }
 \providecommand\onlymathC{\let\oldC\C 
     \renewcommand{\C}{\TextOrMath{\oldC}{\mathset{C}}} }
 \mm@macro{N}{\mathset{N}}
@@ -1918,29 +1845,27 @@
     \providecommand*{\hlbar}[1]{\overline{\vphantom{A}#1}}}{
     \mm@warning{hlbar} }
 \newcommand\@eqdef{\stackrel{\mathup{def}}{=}}
-\newcommand\@@eqdef{\stackrel{\mathrm{\Delta}}{=}}
+\newcommand\@@eqdef{\stackrel{\upDelta}{=}}
 \mm@macro{eqdef}{\@ifstar{\@@eqdef}{\@eqdef}}
 \mm@macro{unbr}{\underbrace}
 \mm@macro{iif}{if and only if\xspace}
+\mm@macro{then}{\implies} 
 
-%    \end{macrocode}
-% Above, we have used |\mathrm| before |\Delta| in case of defining capital Greek letters
-% in italics (for example with the \textsf{fixmath} package).
-%
-% The use of |\mbox{}| ensures that the space produced by |\| in the |\then| macro 
-% is not suppressed in tables.
-% \medskip
-%    \begin{macrocode}
-\mm@macro{then}{\ \Longrightarrow \ \mbox{} } 
 \@ifundefined{txt}{
     \providecommand*{\txt}[1]{\quad\text{#1}\quad} }{
     \mm@warning{txt} }
-\mm@macro{mul}{\mathord{\times}}
+\mm@macro{mul}{\mathclose{}\mathord{\times}\mathopen{}}
 \@ifundefined{pow}{
     \providecommand*{\pow}[2]{\left( #1 \right)^{\!#2}} }{
     \mm@warning{pow} }
+%    \end{macrocode}
+% For |\abs|, the |\left...\right| structure is inserted within a pair of curly braces
+% to prevent incorrect spacing before the first delimiter when it follows a function name,
+% in cases where the package \textsf{mleftright} is used and activated.
+% This issue was pointed out by `quark67'.
+%     \begin{macrocode}
 \@ifundefined{abs}{
-    \providecommand*{\abs}[1]{\left\vert#1\right\vert} }{
+    \providecommand*{\abs}[1]{{\left\vert#1\right\vert}} }{
     \mm@warning{abs} }
 \@ifundefined{lfrac}{
     \providecommand*{\lfrac}[3][7mu]{%
@@ -1981,7 +1906,216 @@
 }   
 %    \end{macrocode}
 %
-% \begin{thebibliography}{34}
+% \pagebreak
+% \section*{Change History}
+%
+% \begin{multicols}{2}\begin{raggedright}
+% \renewcommand\changes[3]{\item[#1 \ (#2)] \mbox{}\\ #3}
+% \setlength{\compactlistindent}{-1em}
+% \begin{list}{}{\setlength\labelwidth{1.4em}\setlength{\leftmargin}{2em}
+%     \setlength{\parsep}{0pt}}
+%
+% \changes{v0.1}{2011/12/27}{First personal version.}
+%
+% \changes{v1.0}{2019/04/11}{Initial published version.}
+%
+% \changes{v1.1}{2019/04/20}{
+%    Changing the default font for \cs{pinumber} from Euler to Symbol.}
+%
+% \changes{v1.2}{2019/04/27}{
+%  \begin{compactlist}
+%    \item commands \cs{enumber}, \cs{inumber}, \cs{jnumber} in \cs{AtBeginDocument}\\
+%    \hand works fine with \textsf{beamer} now, 
+%    \item new general \cs{mm@operator} macro, 
+%    \item using \cs{mathup} instead of \cs{mathrm},
+%    \item including \textsf{mathtools}, 
+%    \item in \cs{DeclareSymbolFont} 'Roman' changed to 'up', 
+%    \item changes in the documentation, 
+%    \item replacing \cs{PEroman} by \cs{PEupright}.
+%  \end{compactlist}}
+%
+% \changes{v1.3}{2019/05/08}{
+%  \begin{compactlist}
+%    \item using \cs{bslash} in the internal \cs{mm@warning} macro
+%    to type out a control sequence whose name is given as parameter, 
+%    \item including the \textsf{mathfixs} package,
+%    \item many corrections in the documentation.
+%  \end{compactlist}}
+%
+% \changes{v1.4}{2019/05/22}{
+%    In \cs{DeclareSymbolFont} 'up' chan\-ged to 'UpSh'
+%        to prevent incompatibility with \textsf{unicode-math}.}
+%
+% \changes{v1.5}{2019/05/30}{
+%  \begin{compactlist}
+%    \item a solution for using \cs{mul} with \cs{frac} \hand use braces, 
+%    \item addition of the \cs{paren} macro.
+%  \end{compactlist}}
+%
+% \changes{v1.6}{2019/09/06}{
+%    Removing the \textsf{mathfixs} package because of problems with fractions.}
+%
+% \changes{v1.7}{2019/12/27}{
+%    Adding a table of contents to the documentation.}
+%
+% \changes{v1.8}{2020/11/15}{
+%    Small changes in the documentation, in particular
+%    an incompatibility is mentioned when using `i' with accent in \textsf{beamer} titles: 
+%        (use \texttt{\textbackslash\textasciicircum i} instead of î).}
+%
+% \changes{v1.9}{2020/10/17}{
+%  \begin{compactlist}
+%    \item in \cs{DeclareSymbolFont} 'UpSh' replaced by 'operators'
+%    \item\cs{PackageWarning} replaced by \cs{PackageWarningNoLine} for existing macros,
+%    \item \cs{thickspace}  replaces \cs{medspace} in \cs{lfrac},
+%    \item changing the documentation font: from lmodern to Palatino (\textsf{mathpazo}).
+%  \end{compactlist}}
+%
+% \changes{v1.10}{2020/10/25}{
+%    \cs{pinumber} code updated to prevent incompatibility 
+%        with the new version of the \textsf{frenchmath} package
+%        (in which the default 'upgreek' option has been changed from Symbol to Euler).}
+%
+% \changes{v2.0}{2022/11/11}{
+%  \begin{compactlist}
+%    \item enhancing \cs{pinumber} to use other Greek letters packages
+%        (it is no longer compatible with the older), 
+%    \item \cs{paren} has been removed (useless), 
+%    \item \cs{hvect} and \cs{hlbar} have been slightly modified (\cs{phantom}\texttt{\{t\}}
+%        instead of \cs{phantom}\texttt{\{h\}}),
+%    \item several changes in the documentation 
+%    (now the Charter font is used, with the \textsf{mathdesign} package).
+%  \end{compactlist}}
+%
+% \changes{v2.1}{2022/12/26}{
+%  \begin{compactlist}
+%    \item including the \textsf{ibrackets} package to improve 
+%    the management of square brackets,
+%    \item new macros \cs{codim}, \cs{sinc}, \cs{var}, \cs{eqdef*}, 
+%    \item removing the warning for the obsolete \cs{paren} command,
+%    \item a small change in the \cs{norm} command (bars in small size),
+%    \item several changes in documentation.
+%  \end{compactlist}}
+%
+% \changes{v2.2}{2023/01/06}{
+%    New option \texttt{ibrackets} to load the \textsf{ibrackets} package
+%    \emph{optionally} because of errors
+%    when using \cs{DeclarePairedDelimiter} with square brackets.}
+%
+% \changes{v2.3}{2023/02/09}{
+%    Introducing keyval options as an alternative to \cs{enumber}, 
+%    \cs{inumber}, \cs{jnumber}, \cs{PEupright},
+%    and also for using ibrackets, \cs{boldvect} and \cs{arrowvect}.}
+%
+% \changes{v2.4}{2023/02/18}{
+%  \begin{compactlist}
+%    \item new powerful macros \cs{MathUp}, \cs{MathIt}, 
+%    (and \cs{MathNumbers}, \cs{MathProba}, \cs{MathNormal}),
+%    \item keyval options are no longer useful and have been removed,
+%    \item loading the package \textsf{ifthen} has been forgotten in v2.3 
+%    (causing possible issues),
+%    \item no more incompatibility when using `i' with accent in \textsf{beamer} titles.
+%  \end{compactlist}}
+%
+% \changes{v2.5}{2023/02/23}{
+%  \begin{compactlist}
+%    \item unification of the code of \cs{MathUp} and \cs{MathIt},
+%    \item a new powerful macro \cs{apply} is used in \cs{MathNormal} to act on a list,
+%    \item new \cs{tensor} command.
+%  \end{compactlist}}
+%
+% \changes{v2.6}{2023/03/01}{
+%  \begin{compactlist}
+%    \item bug fix in \cs{mm@macro},
+%    \item solving incompatibility of the \cs{C} macro when using \textsf{babel} with Russian
+%        (thanks to Murray Eisenberg for this bug report on TeX StackExchange),
+%    \item \cs{mathrm} added in the macro \cs{eqdef*}.
+%  \end{compactlist}}
+%
+% \columnbreak
+% \changes{v2.7}{2023/03/05}{
+%  \begin{compactlist}
+%    \item macros for sets of numbers (\cs{R}, \cs{C}\ldots) now available only in math mode
+%        (following remarks by David Carlisle and Enrico Gregorio),
+%    \item special warning when loading \textsf{babel} with Russian
+%        (\cs{C} will not be defined in that case).
+%  \end{compactlist}}
+%
+% \changes{v2.8}{2023/07/26}{
+%    New macro \cs{onlymathC} designed for using \cs{C} in pmath mode
+%    when Russian language is loaded.}
+%
+% \changes{v2.9}{2023/12/19}{
+%    New option \texttt{decimalcomma}.}
+%
+% \changes{v2.10}{2024/02/20}{
+%  \begin{compactlist}
+%    \item better compatibility with \textsf{unicode-math}: 
+%        for the options \texttt{ibrackets}, \texttt{decimalcomma}
+%        and the commands \cs{MathUp}, \cs{MathIt},
+%    \item Explicit error message when using \texttt{mathcols}
+%        without loading the \textsf{multicol} package.
+%  \end{compactlist}} 
+%
+% \changes{v2.11}{2024/02/26}{
+%  \begin{compactlist}\setlength\compactlistindent{-0.5em}
+%    \item enhancements of the \cs{pinumber} macro with keyval options:       
+%        \begin{compactlist}[\dash]
+%        \item no necessity to load a Greek letters package,
+%        \item improvements of compatibility with \textsf{unicode-math};
+%        \end{compactlist}
+%    \item changing the font to Adobe Utopia with the package \textsf{fourier}.
+%  \end{compactlist}}
+%
+% \changes{v2.12}{2024/02/29}{
+%  \begin{compactlist}
+%    \item the \textsf{xparse} package has been removed by mistake in v2.11,
+%        causing some compatibility issues, it is loaded again by \textsf{mismath},
+%    \item improvements to make \cs{pinumber} work better with \textsf{unicode-math}.
+%  \end{compactlist}}
+%
+% \changes{v3.0}{2024/03/15}{
+%  \begin{compactlist}
+%    \item rewriting the \cs{pinumber} command with a new \cs{pifonts} macro,
+%    \item presenting other \texttt{lgrmath} values for \cs{pinumber} in the doc,
+%    \item The \cs{C} macro is now inside \cs{AtBeginDocument},
+%    \item \textsf{amsmath} isn't loaded explicitly because \textsf{mathtools} loads it,
+%    \item bug fix with options \texttt{decimalcomma} and \texttt{ibrackets},
+%    \item new option \texttt{nofunction} to lighten the package loading,
+%    \item addition of macros \cs{coker} and \cs{Res} as standard operator names,
+%    \item new option \texttt{classicReIm} to deactivate \cs{Im} and \cs{Re} redefinition,
+%    \item new option \texttt{otherReIm} to provide an alternative writing 
+%        with \texttt{cmsy} font,
+%    \item removing  the \cs{PEupright} command,
+%    \item additional space in the \cs{lfrac} macro increased from \texttt{\textbackslash:}
+%        (5mu) to 7mu,
+%    \item new optional parameter for adjusting the space in \cs{lfrac},
+%    \item changing the \cs{vphantom} argument in \cs{hvect}, \cs{hvec} and \cs{lbar} 
+%        from `t' to `A', looks better.
+%  \end{compactlist}}
+%
+% \changes{v3.1}{2024/06/16}{
+%  \begin{compactlist}\setlength\compactlistindent{-0.5em}
+%    \item adding a change history,
+%    \item bug fix with the \cs{C} macro when using \textsf{hyperref} with 
+%        \LuaTeX{} or \XeTeX{} engines,
+%    \item the $\upDelta$ produced in \cs{eqdef*} is now obtained with \cs{upDelta}
+%         (\cs{mathrm}, used before, doesn't work generally),
+%    \item several relevant suggestions and remarks by `quark67':
+%        \begin{compactlist}[\dash]
+%            \item new macros for variations \cs{opDelta} and small variations \cs{opdelta},
+%            \item redefinition of \cs{then} as an alias for \cs{implies},
+%            \item improvement of the \cs{abs} macro,
+%            \item including the \textsf{mleftright} package;
+%        \end{compactlist}
+%    \item new implementation of \cs{di},
+%    \item improvement of the \cs{mul} macro.
+%  \end{compactlist}}
+%
+% \end{list}\end{raggedright}
+% \end{multicols}
+%
+% \begin{thebibliography}{35}
 % \begin{raggedright}
 % \bibitem{TYPMA} \emph{Typesetting mathematics for science and technology according 
 % to ISO 31/XI}, Claudio Beccari, TUGboat Volume 18 (1997), No.~1.
@@ -1997,6 +2131,7 @@
 % \url{https://old.iupac.org/standing/idcns/italic-roman_dec99.pdf}.
 % \bibitem{VECT} \emph{\textsf{esvect}  -- Typesetting vectors with beautiful 
 % arrow with \LaTeXe}, Eddie Saudrais, CTAN, v1.3 2013/07/11.
+% \bibitem{MLR} \emph{The \textsf{mleftright} package}, Heiko Oberdiek, CTAN, v1.2 2019/12/03.
 % \bibitem{TOOL} \emph{The \textsf{mathtools} package}, Morten Høgholm, Lars Madsen, CTAN,
 % v1.29 2022/06/29.
 % \bibitem{AMS} \emph{\textsf{amsmath} -- \AmS\ mathmatical facilities for \LaTeX},