From 1e45d661b659c3025746d3a41119300ab90d1dcd Mon Sep 17 00:00:00 2001
From: Norbert Preining <norbert@preining.info>
Date: Fri, 28 Jul 2023 03:01:08 +0000
Subject: CTAN sync 202307280301

---
 macros/latex/contrib/mismath/mismath.dtx | 846 +++++++++++++++++--------------
 1 file changed, 458 insertions(+), 388 deletions(-)

(limited to 'macros/latex/contrib/mismath/mismath.dtx')

diff --git a/macros/latex/contrib/mismath/mismath.dtx b/macros/latex/contrib/mismath/mismath.dtx
index f8224c848f..108f3e1b75 100644
--- a/macros/latex/contrib/mismath/mismath.dtx
+++ b/macros/latex/contrib/mismath/mismath.dtx
@@ -20,7 +20,7 @@
 %<*package> 
 \NeedsTeXFormat{LaTeX2e}[2005/12/01]
 \ProvidesPackage{mismath}   
-    [2023/03/05 v2.7 .dtx mismath file]
+    [2023/07/27 v2.8 .dtx mismath file]
 %</package>
 %<*driver>
 \documentclass{ltxdoc}
@@ -69,7 +69,7 @@
 %</driver>
 % \fi
 %
-% \CheckSum{618}
+% \CheckSum{624}
 %
 % \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
@@ -193,13 +193,17 @@
 %    - 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}
+%
 % \GetFileInfo{mismath.sty}
 %
 % \title{\textsf{mismath}\\ Miscellaneous mathematical macros\thanks{This document
 % corresponds to \textsf{mismath}~\fileversion, dated \filedate. 
 % Thanks to François Bastouil for help in English translation.}}
 % \author{Antoine Missier \\ \texttt{antoine.missier@ac-toulouse.fr}}
-% \date{March 5, 2023}
+% \date{July 27, 2023}
 %
 % \maketitle
 % \tableofcontents
@@ -210,67 +214,68 @@
 % superseded by ISO~80000-2:2009, mathematical constants $\e$, $\i$, $\pi$ 
 % should be typeset in roman (upright shape) and not in italic (sloping shape) like
 % variables (see~\cite{TYPMA}~\cite{NIST}~\cite{SI}~\cite{ICTNS}).
-% This package provides some tools to achieve this (automatically).
+% This package provides some tools to achieve this automatically.
 %
 % \medskip
-% Even if it is recommended to typeset vectors names 
+% Even though it is recommended to typeset vectors names 
 % in bold italic style~\cite{NIST}~\cite{ICTNS}, 
 % they are often represented with arrows 
-% (particularly in school documents or in physics). 
-% To draw pretty arrows above vectors, we use the \textsf{esvect} package 
-% by Eddie Saudrais~\cite{VECT} 
-% and we provide a few more macros related to vectors with arrows, 
-% in particular to improve the typesetting of the norm: $\norm{\vect{AB}}$ 
+% (especially in school documents or in physics). 
+% To draw visually appealing arrows above vectors, we use the \textsf{esvect} package 
+% by Eddie Saudrais~\cite{VECT}.
+% Additionally we provide a few more macros related to vectors with arrows, 
+% particularly to enhance the typesetting of the norm: $\norm{\vect{AB}}$ 
 % instead of \LaTeX\ version $\lVert\vect{AB}\rVert$ which is not vertically adjusted,
-% or worse $\left\Vert \vect{AB} \right\Vert$ (and even ugly with Latin Modern font family).
+% or worse $\left\Vert \vect{AB} \right\Vert$.
 % 
 % \smallskip
-% The package also provides other macros for:
+% The package also offers other macros for:
 % \begin{itemize}
 % \item tensors,
-% \item some standard operator names,
+% \item some common operator names,
 % \item a few useful aliases,
-% \item improving some spacing in mathematical formulas,
+% \item enhancing spacing in mathematical formulas,
 % \item systems of equations and small matrices,
-% \item displaymath in double columns for long calculation.
+% \item displaymath in double columns for lengthy calculations.
 % \end{itemize}
 %
-% To avoid incompatibility,
-% most of our macros will be defined only 
-% if there is not another command with the same name in the packages loaded 
+% 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 produced and the \textsf{mismath} definition 
-% will simply be ignored. To keep the \textsf{mismath} command or the other one, use 
-% |\let\|\meta{command}|\relax|, before loading \textsf{mismath}, or after.
-% If the other one is defined with |\AtBeginDocument|, do the same for 
+% a warning message will be displayed and the \textsf{mismath} definition 
+% will be ignored. If you wish to keep the existing command or the \textsf{mismath} command,
+% you can use |\let\|\meta{command}|\relax|, before loading \textsf{mismath}, or after.
+% If the other command is defined with |\AtBeginDocument|, you should do the same for 
 % |\let\|\meta{command}|\relax| and for loading mismath.
 %
 % \medskip
 % \DescribeEnv{\oarg{options}}
-% The \textsf{amsmath} package is loaded by \textsf{mismath} without option.
-% For using \textsf{amsmath} with options (see~\cite{AMS}),
-% these options can be added when calling \textsf{mismath}, or 
-% \textsf{amsmath} can be loaded 
-% with the required options before \textsf{mismath}.
+% The \textsf{mismath} package loads the \textsf{amsmath} package without any options.
+% If you want to use \textsf{amsmath} with specific options (refer to~\cite{AMS}),
+% you can include these options when calling \textsf{mismath}, or 
+% you can load \textsf{amsmath} 
+% with the desired options before loading \textsf{mismath}.
 %
 % \medskip
-% \textsf{mismath} loads also the package 
-% \textsf{mathtools} by Morten Høgholm and Lars Madsen~\cite{TOOL}. 
-% It provides many useful macros and improvements of \textsf{amsmath} package.
+% In addition \textsf{mismath} loads the \textsf{mathtools} package 
+% by Morten Høgholm and Lars Madsen~\cite{TOOL}. 
+% This package offers numerous helpful macros and improvements of the \textsf{amsmath} package.
 %
 % \medskip
-% A recommendation, seldom observed, is to typeset uppercase Greek letters in italic shape 
-% like other variables~\cite{ICTNS}. This is automatically done with the packages 
-% \textsf{fixmath} by Walter Schmidt~\cite{FIXM},
+% A recommendation, although rarely followed, is to typeset uppercase 
+% Greek letters in italic shape,
+% similar to other variables~\cite{ICTNS}. This can be automatically achieved with packages 
+% such as \textsf{fixmath} by Walter Schmidt~\cite{FIXM},
 % \textsf{isomath} by Günter Milde~\cite{ISOM} 
 % or \textsf{pm-isomath} by Claudio Beccari~\cite{PMISO} and optionally with many others
-% (for instance \textsf{mathpazo} or \textsf{mathptmx} with the option \texttt{slantedGreek}),
-% but this feature is not implemented here because this rule is conflicting 
-% to the one used in France where all mathematics capitals 
-% have to be typeset in upright shape
-% \footnote{The \textsf{frenchmath} package~\cite{FR} 
-% takes this rule into account.}.
-% The choice of loading or not one of these packages remains thus to the user.
+% (such as \textsf{mathpazo} or \textsf{mathptmx} with the option \texttt{slantedGreek}).
+% However this feature is not implemented here due to a conflicting rule in France,
+% where all capital letters in mathematics
+% are required to be typeset in upright shape
+% \footnote{By using the \textsf{frenchmath} package~\cite{FR}, 
+% you can ensure that the recommended french rule is followed in your document.}.
+% The decision to load any of these packages is left to the user's discretion.
 %
 % \section{Usage}
 %
@@ -278,154 +283,165 @@
 %
 % \DescribeMacro{\mathup} 
 % As for classic functions identifiers, \emph{predefined} mathematical constants
-% should be typeset in upright shape (generally in roman family), 
-% even if this practice is not really common and tedious
-% to respect. First we provide the |\mathup| macro, which is better than |\mathrm| 
-% \footnote{\texttt{\bslash mathup}
-% is based on \texttt{\bslash operatorfont} 
-% (from \textsf{amsopn} package, automatically loaded by \textsf{amsmath}).
-% The \textsf{beamer} 
-% package uses a default sans serif math font, but \texttt{\bslash mathrm}
-% produces a font with serif in \textsf{beamer}. Therefore
-% using \texttt{\bslash mathup} is better than \texttt{\bslash mathrm}.},
-% to set any math text in upright shape, so on can write
+% should be typeset in upright shape (typically in roman family), 
+% even though this practice is not very common and can be tedious
+% to adhere to. A first solution is to use the |\mathup| macro, 
+% which is superior to |\mathrm|
+% \footnote{The \texttt{\bslash mathup} macro is based on \texttt{\bslash operatorfont}, 
+% which comes from the
+% \textsf{amsopn} package, automatically loaded by \textsf{amsmath}. 
+% In \textsf{beamer}, the default math font is sans serif, 
+% but \texttt{\bslash mathrm} produces a font with serifs, which might not match the 
+% overall style of the presentation. Hence, using \texttt{\bslash mathup} is indeed 
+% a better choice in \textsf{beamer} presentations to ensure that mathematical 
+% constants are typeset in upright shape and consistent 
+% with the default sans serif math font.},
+% for setting any math text in upright shape. For example you can use
 % |\mathup{e}| to get the Euler's number.
 %
 % \medskip
 % \DescribeMacro{\e} \DescribeMacro{\i}  \DescribeMacro{\j} 
-% To avoid to stuff a document that contains many $\e$ or $\i$ constants 
-% with |\mathup{e}| or |\mathup{i}|,
-% the package provides |\e| command for Euler's number
-% and |\i| or |\j| for imaginary numbers. 
-% Let's notice that |\i| and |\j| already exist in \LaTeX: 
-% using in LR mode, they produce `\extrafont{\i,\ \j}' without the point, 
-% so you can place accents on them, and in mathematical mode they produce 
-% ``\texttt{LaTeX Warning: Command \bslash i invalid in math mode on input line} \meta{line}''. 
-% The new definition of |\i| and |\j| concerns only the mathematical mode.
+% To avoid cluttering a document that contains many occurrences of Euler's number (e) 
+% or imaginary numbers (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, 
+% they produce `\extrafont{\i,\ \j}' without the dot, allowing you to place accents on them. 
+% However, in mathematical mode, they produce the warning 
+% ``\texttt{LaTeX Warning: Command \bslash i invalid in math mode on input line}
+% \meta{line}''. 
+% With the new definition provided by the package, |\i| and |\j| will be redefined 
+% specifically for mathematical mode.
 %
 % \medskip
 % \DescribeMacro{\MathUp} 
-% Nevertheless, it can be tiresome to type a lot of backslashes
-% for these constants, in a document 
-% with many formulas containing $\e$, $\i$ or $\j$.
-% So a way is proposed here to free of it with the macro
-% |\MathUp|\marg{char}.
-% For instance when |\MathUp{e}| is called,
-% any future occurrence of $\e$ will then automatically be set in roman,
-% without the need to type |\e|. 
-% The effect is global or local if used inside an environment or braces.
-% This macro can also be called in the preamble for applying 
-% from the beginning of the document.
-% Thanks to this powerful macro, you can bring a document up to the standards afterwards.
-% In fact |\MathUp| can apply to any valid but single character (we will see another
-% use of it with probability in section \ref{operators}).
+% Indeed, typing a lot of backslashes for constants like $\e$, $\i$, or $\j$
+% in a document with numerous formulas can become tiresome. 
+% To alleviate this, the package proposes a powerful solution with the macro |\MathUp|\marg{char}.
+% For example, when |\MathUp{e}| is called, any subsequent occurrence of $\e$
+% will automatically be set in roman (upright shape), 
+% without the need to type |\e| explicitly. The effect of this macro 
+% can be either global or local, depending on whether it is used outside or inside an
+% environment or braces.
+% Furthermore, you can call this macro in the preamble to apply the change 
+% from the beginning of the document. This powerful feature allows you 
+% to bring a document up to the standards effortlessly. 
+% In fact, |\MathUp| can be applied to any valid single character, 
+% offering flexibility for various use cases (another use of it with probability 
+% will be presented in section \ref{operators}).
 %
 % \medskip
 % \DescribeMacro{\MathIt}
-% When there are other $\mathit{e}$, $\mathit{i}$ or $j$ as variables,
-% you can still get italicized
-% $\mathit{e}$, $\mathit{i}$ or $\mathit{j}$ with \LaTeX\ commands
-% |\mathit| or |\mathnormal|, useful for a single use.
-% But you can also use the inverse switch |\MathIt|\marg{char},
-% with a global effect, or a local one if used inside an environment or braces.
-% As |\MathUp|, it can be used for any single character.
+% When there are other occurrences of $\mathit{e}$, $\mathit{i}$ or $j$ as variables, 
+% you can still obtain italicized $\mathit{e}$, $\mathit{i}$ or $\mathit{j}$ using \LaTeX\
+% commands |\mathit| or |\mathnormal|, which are useful for a single use. 
+% However, you also have the option to use the inverse switch |\MathIt|\marg{char},
+% which has a global effect when used outside environments or braces, 
+% or a local effect when used inside them. 
+% Similar to |\MathUp|, |\MathIt| can be applied to any single character.
 %
 % \medskip
 % \DescribeMacro{\MathNumbers} \DescribeMacro{\MathNormal}
-% These macros allow to set upright or normal typesetting for several letters
-% in a single command, \eg
-% |\MathNumbers{e,i}| is equivalent to |\MathUp{e}\MathUp{i}|.
-% In |\MathNumbers| the comma separator can be changed or deleted.
-% This macro has no effect on other letters than e, i or j.
-% On the other hand |\MathNormal| can be used for probability also 
-% (see section \ref{operators})
-% and can take any comma separated list argument.
+% These macros enable you to set upright or normal (italic) typesetting 
+% for multiple letters in a single command. 
+% For instance, |\MathNumbers{e,i}| is equivalent to |\MathUp{e}\MathUp{i}|.
+% In |\MathNumbers|, the comma separator between letters can be modified 
+% or removed as needed. In fact, this macro only affects the letters e, i, or j; 
+% it has no effect on other characters.
+% On the other hand, |\MathNormal| can be utilized for probability as well 
+% (refer to section \ref{operators}), and it accepts any comma-separated list of arguments.
+% This means you can apply the normal italic math mode typesetting to various letters 
+% at once using |\MathNormal|.
 % 
 % \medskip
 % \DescribeMacro{\pinumber[\meta{command}]}
 % The mathematical constant $\pi$  should also be typeset in upright shape 
-% (see~\cite{TYPMA}, \cite{NIST}, \cite{ICTNS}), which differs from italicized $\itpi$. 
-% This recommendation is even less observed than the one concerning  
-% $\e$ and $\i$~\cite{TYPMA}.
-% Several packages allow to typeset mathematical Greek letters in upright shape, 
-% let us mention \textsf{upgreek}~\cite{GREEK}, \textsf{mathdesign}~\cite{DESIGN} 
-% (used here), \textsf{kpfonts}~\cite{KPF}, \textsf{fourier}~\cite{FOUR},
+% (see~\cite{TYPMA}, \cite{NIST}, \cite{ICTNS}), which is different from italicized $\itpi$. 
+% However, this recommendation is even less commonly followed compared to the one 
+% concerning  $\e$ and $\i$~\cite{TYPMA}.
+% Several packages enable the typesetting of mathematical Greek letters in upright shape. 
+% Notably, let us mention \textsf{upgreek}~\cite{GREEK}, \textsf{mathdesign}~\cite{DESIGN} 
+% (used in the present document), \mbox{\textsf{kpfonts}}~\cite{KPF}, \textsf{fourier}~\cite{FOUR},
 % \textsf{libertinust1math},
 % \textsf{pxgreeks}, \textsf{txgreeks}, \textsf{libgreek}, etc.
-% A special mention for \textsf{lgrmath} of Jean-François Burnol~\cite{LGR}
-% which allow to use, in math mode, any Greek LGR-encoded font.
+% A special mention goes to \textsf{lgrmath} of Jean-François Burnol~\cite{LGR}
+% which allows the use of any Greek LGR-encoded font in math mode. 
 % These packages provide commands like |\uppi| (\textsf{upgreek}), 
 % |\piup| (\textsf{mathdesign}, \textsf{kpfonts}, \textsf{lgrmath}), 
 % |\otherpi| (\textsf{fourier}), etc.
 % \footnote{They also have options to typeset all the Greek lowercase 
 % letters in upright shape by default, but this in not our goal here.}
-% To preserve default sloped lowercase Greek letters except for pi, and to
-% avoid typing a lot of |\uppi| or |\piup|, we provide the 
+% To preserve default italic style for lowercase Greek letters,
+% with the exception of pi, and to
+% avoid the need to type a lot of |\uppi| or |\piup|, we offer the 
 % macro |\pinumber|[\meta{command}].
-% It redefines |\pi| to match
-% the optional command  name given (without backslash), for instance |piup|, 
-% assuming the appropriate package has been loaded before. 
+% This macro redefines |\pi| to match
+% the optional command  name provided (without a backslash), such as |piup|, 
+% assuming that the appropriate package has been loaded beforehand. 
 %
-% By calling preliminary |\MathNumbers{ei}\pinumber[piup]| 
-% (and with the \textsf{mathdesign} package loaded)
-% you can get for instance:
+% By using the preliminary code |\MathNumbers{ei}\pinumber[piup]| 
+% (assuming the \textsf{mathdesign} package is loaded)
+% you can achieve the following result:
 % \begin{center}
-% |$e^{i\pi} = -1$| \quad yields \quad   $\e^{i\pi}=-1$.
+% |$e^{i\pi} = -1$| \quad which yields \quad   $\e^{i\pi}=-1$.
 % \end{center}
 %
-% When calling |\pinumber| without argument
-% it defines |\pi| with the default LGR font encoding of Greek letters
-% to produce $\mypi$. In that case the appropriate option \texttt{LGR}
-% for the \textsf{fontenc} package will be automatically loaded,
-% provided that the command is called in the preamble (first). 
-% The pi character will look the same as the one supplied with
+% When you call |\pinumber| without any argument,
+% it defines |\pi| using the default LGR font encoding for Greek letters,
+% resulting in the character $\mypi$. In this case the appropriate option \texttt{LGR}
+% for the \textsf{fontenc} package will be automatically loaded
+% if the |\pinumber| command is called in the preamble (at least the first time it is used). 
+% The pi character obtained with this setting will look the same as the one provided by
 % Günter Milde's \textsf{textalpha} package~\cite{ALPHA}.
-% This $\mypi$ is particularly suitable
+% This $\mypi$ character is particularly well-suited
 % for use with the default Computer Modern or Latin Modern font family
-% \footnote{This default $\mypi$ doesn't fit well with many text fonts, 
-% more bold than Computer Modern;
-% the \textsf{upgreek} package~\cite{GREEK} provides often a better $\uppi$
-% (with the \texttt{Symbol} option using Adobe Symbol font) 
-% that fits well with several text fonts, for instance Times.}.
+% \footnote{This default $\mypi$ character may not always fit well with various text fonts, 
+% especially those that are bolder or different from the default Computer Modern font.
+% The \textsf{upgreek} package~\cite{GREEK} provides a better $\uppi$ character 
+% with the Symbol option, utilizing the Adobe Symbol font. This $\uppi$ character 
+% matches well with several text fonts, such as Times.}.
 %
 % \medskip
 % \DescribeMacro{\itpi}
-% When activating |\pinumber|, the original italic $\itpi$ 
-% is still available with |\itpi|.
+% When you activate |\pinumber|, the original italic $\itpi$ 
+% is still accessible using |\itpi|.
 %
 % \DescribeMacro{\pinormal}
-% In fact |\pinumber| acts as a switch and there is also an inverse switch, 
-% |\pinormal|, that can be called anywhere.
+% In fact |\pinumber| acts as a switch, enabling the upright $\pi$.
+% Additionally, there is an inverse switch, 
+% |\pinormal|, which you can call anywhere to revert to the original behavior
+% of the |\pi| command (italic $\itpi$).
 %
 % \subsection{Vectors (and tensors)}
 %
 % \DescribeMacro{\vect}
 % By default, the |\vect| command
-% \footnote{As for many macros of this package, 
-% the definition will take effect only if this macro is not defined before 
-% by another package.},
+% \footnote{The definition of most macros in this package, 
+% will only take effect if the macro has not been previously
+% defined by another package. This ensures compatibility and avoids conflicts 
+% when using the \textsf{mismath} package with other \LaTeX\ packages.},
 % produces vectors with arrows
-% (thanks to the \textsf{esvect} package of Eddie Saudrais
+% (thanks to the \textsf{esvect} package by Eddie Saudrais
 % \footnote{\textsf{esvect} provides the \texttt{\bslash vv} macro 
 % used by \texttt{\bslash vect}.})
 % which are more elegant than those produced by \LaTeX's |\overrightarrow| command.
 % The \textsf{esvect} package has an optional argument 
-% (one letter between \texttt{a} and \texttt{h}) defining 
-% the required type of arrow (see~\cite{VECT}).
+% (a single letter between \texttt{a} and \texttt{h}) to define 
+% the desired type of arrow (see~\cite{VECT}).
 % In \textsf{mismath}, \textsf{esvect} is loaded with the option \texttt{b}:
 % |\vect{AB}| gives $\vect{AB}$.
-% To choose another type of arrow, \textsf{esvect} must be called 
-% with the required option \emph{before} \textsf{mismath}, 
-% \eg |\usepackage[d]{esvect}|
-% will give the arrows produced by default in~\cite{VECT}.
+% If you wish to use a different type of arrow, you must call \textsf{esvect}
+% with the appropriate option \emph{before} loading \textsf{mismath}.  
+% For example, using |\usepackage[d]{esvect}|
+% will provide the arrows produced by default in~\cite{VECT}.
 %
 % \medskip 
 % \DescribeMacro{\boldvect}
-% The |\vect| macro allow to typeset vector's names using bold italic
-% (according to ISO recommendation~\cite{NIST}~\cite{SI}) rather than arrows. 
-% For this, calling |\boldvect| will modify the behavior of |\vect|,
-% globally or locally, depending on where |\boldvect| 
-% is placed:\\[1ex]
+% 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|
+% locally or globally, depending on its placement in the document (inside or outside
+% a group or an environment):\\[1ex]
 % \begin{minipage}{8cm}
 % \begin{verbatim} 
 %\[ \boldvect \vect{v}
@@ -438,44 +454,49 @@
 %
 % \DescribeMacro{\boldvectcommand}
 % By default |\boldvect| uses the |\boldsymbol| command
-% \footnote{\texttt{\bslash mathbf} gives upright bold font, 
-% even if used in combination with \texttt{\bslash mathit}.}
-% from \textsf{amsbsy} package, loaded by \textsf{amsmath}.
-% But other packages producing bold italic can be preferred, \eg
-% |\mathbold| from \textsf{fixmath}
-% package or |\mathbfit| from \textsf{isomath}
-% or \texttt{\bslash bm} from \textsf{bm} package.
-% For that, redefine |\boldvectcommand|, for instance, after loading \textsf{fixmath}: 
+% \footnote{\texttt{\bslash mathbf} produces upright bold font, 
+% even when used in combination with \texttt{\bslash mathit}.}
+% from the \textsf{amsbsy} package, which is automatically loaded by \textsf{amsmath}.
+% However, you may prefer other packages that produce bold italic fonts, 
+% such as \textsf{fixmath} with the |\mathbold| command,
+% \textsf{isomath} with |\mathbfit| 
+% or \textsf{bm} with the \texttt{\bslash bm} command.
+% To use an alternative command, redefine |\boldvectcommand|, 
+% for instance after loading \textsf{fixmath}: 
 % \begin{center} |\renewcommand\boldvectcommand{\mathbold}|. \end{center}
 %
-% According to ISO rules, symbols for matrices are also in bold italic,
-% so you can use the same |\boldvectcommand| or create another alias.
+% According to ISO rules, symbols for matrices are also in bold italic.
+% Therefore you can use the same |\boldvectcommand| or create another alias.
 %
 % \medskip
 % \DescribeMacro{\arrowvect}
-% At any moment, you can get back to the default behavior with the inverse switch
+% At any moment, you can revert to the default behavior using the inverse switch
 % |\arrowvect|. 
-% These switches can be placed anywhere: 
-% inside mathematical mode or inside an environment (with local effect) or outside 
-% (with global effect).
+% These switches can be placed anywhere, whether
+% inside mathematical mode or within an environment (with a local effect) or outside 
+% (with a global effect).
 %
 % \medskip
 % \DescribeMacro{\hvect}
 % When vectors with arrows are typeset side by side,
-% arrows can be set up a bit higher (with a vertical phantom box containing $t$) 
-% to avoid inelegant effects:
+% the arrows can be set up slightly higher using |\hvect|
+% (which places a vertical phantom box containing ``$t$'') 
+% to avoid inelegant effects. For example, writing
 % \begin{itemize}
 % \item $\vect{AB}=\hvect{u}+ \vect{AC}$, obtained with |\hvect{u}|,
 % is better than $\vect{AB}=\vect{u}+ \vect{AC}$;
 % \item $\hvect{a} \cdot \vect{b}=0$, obtained with |\hvect{a}|,
 % is better thant $\vect{a} \cdot \vect{b}=0$.
 % \end{itemize}
-% The |\boldvect| and |\arrowvect| switches have the same effect on |\hvect| than on |\vect|,
-% and so have \texttt{boldvect} and \texttt{arrowvect} options.
+% This adjustment ensures a more visually pleasing appearance when vectors 
+% with arrows are combined in an equation.
+% The |\boldvect| and |\arrowvect| switches have the same effect on |\hvect| 
+% as they do on |\vect|.
 %
 % \DescribeMacro{\hvec}
 % In a similar way, |\hvec| raises the little arrow produced by
-% the \LaTeX\ command |\vec| (from height of $t$ letter):
+% the \LaTeX\ command |\vec|, to the height of the letter ``$t$''
+% (but |\boldvect| have no effect here):
 % \begin{itemize}
 % \item $\mathcal{P}=\vec{f}\cdot\hvec{v}$, obtained with |\hvec{v}|,
 % is better than $\mathcal{P}=\vec{f}\cdot\vec{v}$.
@@ -484,36 +505,39 @@
 % \end{itemize}
 %
 % \DescribeMacro{\norm}
-% The norm of a vector is classically produced by the delimiters |\lVert| and |\rVert|
-% (rather than \texttt{\bslash}$\mid$) or |\left\Vert| and |\right\Vert| 
-% for delimiters adapting to the content. Unfortunately, these delimiters 
+% The norm of a vector is conventionally represented using the delimiters |\lVert| and |\rVert|
+% (or \texttt{\bslash}$\mid$ unless a plus (+) or minus (-) sign follows the opening delimiter)
+% or |\left\Vert| and |\right\Vert| 
+% for adaptive delimiters. Unfortunately, these delimiters 
 % are always vertically centered, relatively to the middle of the base line, 
 % whereas vectors with arrows are asymmetric objects.
 % The code |$\norm{\vec{h}}$| raises a smaller double bar to produce $\norm{\vec{h}}$
 % instead of $\left\Vert \vec{h} \right\Vert$.
 % Let's notice that the height of the bars don't adjust to content, 
 % but however to context: main text, subscripts or exponents, 
-% \eg $\e^{\norm{\vec{h}}}$.
+% \eg $\e^{\norm{\vec{h}}}$. 
+% This macro is useful only for arguments of special height, such as $\vec{h}$ or $\vect{AB}$
+% and may give bad results in other situations.
 %
 % \medskip
 % \DescribeMacro{\mathbfsfit}\DescribeMacro{\tensor}
-% For tensors symbols, ISO rules recommend to use
+% For tensors symbols, ISO rules recommend using
 % sans serif bold italic, but there
-% is no such math alphabet in \TeX\ default mathematical style.
-% \textsf{mismath} defines this alphabet 
-% (assuming the font encoding and package you use permits it), 
+% is no such math alphabet in the default \TeX\  mathematical style.
+% However, the \textsf{mismath} package defines this alphabet 
+% (assuming the font encoding and package you use permits it) 
 % and provides the macro |\mathbfsfit| or its alias |\tensor|.
-% So |\tensor{T}| produces $\tensor{T}$.
+% By using |\tensor{T}| you can produce $\tensor{T}$.
 %
 % \subsection{Standard operator names}\label{operators}
 %
 % \DescribeMacro{\di}
-% The \emph{differential} operator should be typeset in upright shape and not in
-% italic, to make it different from variables 
+% The \emph{differential} operator should be typeset in upright shape, not in
+% italics, to distinguish it from variables 
 % (as mentioned in \cite{TYPMA}~\cite{NIST}~\cite{ICTNS}~\cite{LSHORT}).
-% For this, we provide the |\di| command.
-% See the following examples (notice the thin spaces before the d, 
-% as for classic function's names): \\
+% To achieve this, we provide the |\di| command.
+% Take a look at the following examples (notice the thin spaces before the d, 
+% just like with classic function's names): \\
 % \begin{minipage}[t]{7cm}
 % \begin{verbatim} 
 %\[ \iint xy\di x\di y \]
@@ -533,15 +557,15 @@
 % \[m\frac{\di^2x}{\di t^2}+h\frac{\di x}{\di t}+kx=0\]
 % \end{minipage}
 %
-% This command can also stand for \emph{distance} (hence its name):
-% \[\lambda\di(A,\mathcal{F})+\mu\di(B,\mathcal{H}).\]
+% This command can also represent \emph{distance} (hence its name):
+% \[\lambda\di(A, \mathcal{F})+\mu\di(B, \mathcal{H}).\]
 %
 % \DescribeMacro{\P} \DescribeMacro{\E}
 % To refer to probability
 % \footnote{\LaTeX\ provides also \texttt{\bslash Pr} which gives $\Pr$.}
-% and expectation the proper use is to typeset capital letters $\P$, $\E$ 
-% in roman as for any standard function identifier.
-% This is obtained with |\P| and |\E|.
+% and expectation the proper use is to typeset the capital letters $\P$, $\E$ 
+% in roman just like any standard function identifier.
+% This can be achieved with |\P| and |\E| commands.
 %
 % \DescribeMacro{\Par}
 % The |\P| command already existed to refer to the end of paragraph symbol \Par\ 
@@ -550,29 +574,29 @@
 % \medskip
 % \DescribeMacro{\V}
 % Variance is generally denoted by $\var$ or $\Var$ (see table below),
-% but some authors prefer to use $\V$, produced by |\V|.
+% but some authors prefer to use $\V$, which can be produced using |\V|.
 %
 % \DescribeMacro{\MathProba}\DescribeMacro{\MathNormal}
 % In the same way as for $\e$, $\i$ or $\j$, you can use |\MathUp{P}|, |\MathUp{E}| 
 % or |\MathUp{V}| to avoid typing many |\P|, |\E| or |\V|. 
-% But you can also do that in a single command with |\MathProba|, 
-% for example |\MathProba{P,E}| and we get the inverse switch with
+% However you can also achieve this in a single command with |\MathProba|, 
+% for example |\MathProba{P,E}|. We get the inverse switch with
 % |\MathIt| for any individual letter or |\MathNormal| for a list.
 %
 % \medskip
 % \DescribeMacro{\probastyle}
-% Some authors use ``blackboard bold'' font
-% 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}|
-% \footnote{As for \texttt{\bslash boldvect} and \texttt{\bslash arrowvect},
-% effect is local to the container environment.}
+% Some authors use ``blackboard bold'' font 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}|
+% \footnote{The effect of this redefinition is global or local to the container environment 
+% in which it is used.}
 % brings the previous ``openwork'' letters.
-% |\mathbb| comes from \textsf{amsfonts} package
-% (loaded by \textsf{amssymb} 
-% but also available standalone)
-% which has to be called in the preamble.
+% The |\mathbb| command comes from \textsf{amsfonts} package
+% (loaded by \textsf{amssymb} but also available standalone)
+% which needs to be called in the preamble.
 %
+% \medskip
 % The following standard operator names are defined in \textsf{mismath}:
 % \begin{center}
 % \begin{tabular}{rlrlrl}
@@ -594,27 +618,29 @@
 % $\boldvect \grad, \curl, \rot$.
 % For the variance, the covariance and the identity function, 
 % two notations are proposed, with or without a first capital letter, 
-% because they are both very common.
+% because both are very common.
 % On the other hand, `$\im$' stands for the image of a linear transformation 
 % (like `$\ker$' for the kernel)
 % whereas `$\Im$' is the imaginary part of a complex number.
-% Notice that |\div| already exist ($\div$) and |\span| is a \TeX\ primitive
+% Please note that |\div| already exists ($\div$) and |\span| is a \TeX\ primitive
 % (used in |\multicolumn|);
-% they haven't been redefined, therefore the macros |\divg| (divergence) 
-% and |\spa| (span of a set of vectors) ;
-% |\Z| is used for the set of integers (see \ref{aliases}), therefore we used |\Zu|,
+% they haven't been redefined. Therefore the provided macros are called |\divg| (divergence) 
+% and |\spa| (span of a set of vectors).
+% Furthermore |\Z| is used to denote the set of integers (see \ref{aliases}), 
+% which is why we used |\Zu|,
 % to designate the center of a group: $\Zu(G)$ (from German Zentrum).
 %
 %\medskip
 % \DescribeMacro{\oldRe} \DescribeMacro{\oldIm}
-% The |\Re| and |\Im| macros already existed, to refer to real and imaginary part 
+% The |\Re| and |\Im| macros already existed to refer to real and imaginary part 
 % of a complex number, producing outdated symbols $\oldRe$ and $\oldIm$.
-% They have been redefined according to actual use, as mentioned in the above table, 
-% but it's still possible to get the old symbols with |\oldRe| and |\oldIm|.
+% However, they have been redefined according to current usage, 
+% as mentioned in the above table. Nevertheless,
+% it is still possible to obtain the old symbols with |\oldRe| and |\oldIm|.
 %
 % \medskip
-% Some (inverse) circular or hyperbolic functions, missing
-% in \LaTeX, are also provided by \textsf{mismath}:
+% The package \textsf{mismath} also provides some (inverse) circular or hyperbolic functions, 
+% that are missing in \LaTeX:
 % \begin{center}
 % \begin{tabular}{rlrlrl}
 % |\arccot| & $\arccot$\qquad\mbox{} & |\arsinh| & $\arsinh$\qquad\mbox{} 
@@ -635,62 +661,70 @@
 % that classic sets of numbers are typeset in bold roman:
 % $\R, \C, \Z, \N, \Q$, 
 % whereas ``openwork'' letters ($\mathbb{R}, \mathbb{Z}, \ldots$) 
-% are reserved for writing at blackboard~\cite{LSHORT};
-% and likewise to designate a field: $\F$ or $\K$ (Körper in German).
-% We get these symbols with the macros
-% \footnote{The \texttt{\bslash C} macro is incompatible with \texttt{russian} option
-% of \textsf{babel}; it will not be redefined in that case.}:
+% are reserved for writing at the blackboard~\cite{LSHORT}.
+% Similarly, to designate a field we use $\F$ or $\K$ (Körper in German).
+% We get obtain these symbols with the following macros:
 % \begin{center}
 % |\R|, |\C|, |\Z|, |\N|, |\Q|, |\F|, |\K|.
 % \end{center}
 %
 % \DescribeMacro{\mathset}
-% The |\mathset| command enables to change the behavior of all these macros in a global way: 
-% by default, |\mathset| is an alias for |\mathbf|, but if you prefer openwork letters, 
-% just place |\renewcommand\mathset{\mathbb}| where you want, for instance in the preamble,
-% after loading \textsf{amsfonts} package (which provides the ``blackboard bold'' typeface,
+% 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 openwork letters, 
+% you can simply place |\renewcommand\mathset{\mathbb}| where you want, 
+% for instance in the preamble after loading the \textsf{amsfonts} package 
+% (which provides the ``blackboard bold'' typeface,
 % also loaded by \textsf{amssymb}).
 %
+% \smallskip
+% \DescribeMacro{\onlymathC}
+% The macro |\onlymathC| is designed for cases when |\C| is already defined,
+% but only in text mode (usually when loading the Russian language with \textsf{babel}
+% or \textsf{polyglossia}). The macro preserves the original definition for text mode
+% and allows you to use |\C| for the complex number set in math mode.
+% For this purpose, simply call |\onlymathC| once in the preamble or anywhere in the document.
+%
 % \medskip
 % \DescribeMacro{\ds}
-% The |\displaystyle| command being very common, the |\ds| alias is provided.
-% Not only it eases typing but also  it makes source code more readable.
+% The |\displaystyle| command is very common, so the |\ds| alias is provided.
+% Not only it eases typing but also it makes source code more readable.
 %
 % \medskip
 % Symbols with limits behave differently for in-line formulas or for displayed equations. 
-% In the latter case, ``limits'' are put under or above whereas for in-line math mode, 
-% they are placed on the right, as subscript or exponent. Compare:
+% 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
 % \[\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}.\]
 %
 % \DescribeMacro{\dlim} \DescribeMacro{\dsum} \DescribeMacro{\dprod}
 % \DescribeMacro{\dcup} \DescribeMacro{\dcap}
 % With in-line math mode, displaymath behavior can be forced with |\displaystyle|
-% or its alias |\ds|, but then, all the rest of the current mathematical 
-% environment will be set in displaymath mode too (in the previous example, 
-% the fraction will be expanded).
-% Just as the \textsf{amsmath} command |\dfrac|
-% only transforms the required fraction in display style, we can limit 
-% the display style effect to the affected symbol, by using the following macros:
+% 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).
+% To limit the display style effect to the affected symbol only, 
+% similar the the  \textsf{amsmath} command |\dfrac|, 
+% we can use the following macros:
 % |\dlim|, |\dsum|, |\dprod|, |\dcup|, |\dcap|.
 % So 
 % \begin{center}
-% |$\dlim_{x\to +\infty}\frac{1}{x}$| \quad  gives \quad  $\dlim_{x \to +\infty}\frac{1}{x}$.
+% |$\dlim_{x\to +\infty}\frac{1}{x}$| \quad  yields \quad  $\dlim_{x \to +\infty}\frac{1}{x}$.
 % \end{center}
 %
 % \DescribeMacro{\lbar} \DescribeMacro{\hlbar}
 % Large bars over expressions are obtained with |\overline|
-% or, shorter, its alias |\lbar|, to get for instance $\lbar{z_1z_2}$.
-% Such as for vectors, you can raise the bar (from the height of $h$) with
-% the |\hlbar| command, in order to correct uneven bars heights.
+% or its alias |\lbar|, to get for instance $\lbar{z_1z_2}$.
+% Similar to vectors, you can raise the bar (from the height of ``$h$'') with
+% the |\hlbar| command, to correct uneven bars heights.
 % \begin{center}
 % $\lbar{z+z'}=\hlbar{z}+\lbar{z'}$, obtained with |\hlbar{z}|,
 % is better than $\lbar{z+z'}=\lbar{z}+\lbar{z'}$.
 % \end{center}
 %
-% \pagebreak
 % \DescribeMacro{\eqdef} \DescribeMacro{\eqdef*}
-% The |\eqdef| macro writes equality symbol topped with `def'
+% The |\eqdef| macro writes the equality symbol topped with `def'
 % or with `$\scriptstyle \Delta$' for |\eqdef*|
 % (thanks to the \LaTeX\ command |\stackrel|): 
 %
@@ -718,9 +752,9 @@
 % \DescribeMacro{\unbr}
 % |\unbr| is an alias for |\underbrace|
 % \footnote{The \textsf{mathtools} package by Morten Høgholm 
-% and Lars Madsen~\cite{TOOL} provides a new improved version 
-% of \texttt{\bslash underbrace} command (as many other usefull macros);
-% it is loaded by \textsf{mismath}.}, 
+% and Lars Madsen~\cite{TOOL} provides a new and improved version 
+% of the \texttt{\bslash underbrace} command, along with many other usefull macros.
+% It is loaded by \textsf{mismath}.}, 
 % making source code more compact.\\[2ex]
 % \begin{minipage}{7.5cm}
 % \begin{verbatim}
@@ -739,22 +773,22 @@
 %
 % \DescribeMacro{\then} 
 % The |\then| macro produces the symbol $\Longrightarrow$ surrounded by large spaces
-% as the standard macro |\iff| does it with $\Longleftrightarrow$.
-% In a similar way, |\txt|, \DescribeMacro{\txt}
+% 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
 % (loaded by \textsf{amsmath}),
 % leaves em quad spaces (|\quad|) around the text. See the following example:
 % \begin{center}
-% |\[ \ln x=a \then x=\e^a \txt{rather than}| \\
+% |\[ \ln x=a \then x=\e^a, \txt{rather than}| \\
 % | \ln x=a \Longrightarrow x=\e^a \]| \\[1ex]
-% $ \ln x=a \then x=\e^a \txt{rather than}    \ln x=a \Longrightarrow x=\e^a$
+% $ \ln x=a \then x=\e^a, \txt{rather than}    \ln x=a \Longrightarrow x=\e^a$
 % \end{center}
 %
 % \DescribeMacro{\mul}
-% The multiplication symbol obtained with |\times| produces the same spacing than addition
+% 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 the multiplication on $+$ and $-$.
-% This is why we provide the |\mul| macro, behaving like $/$ 
+% 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|:
 % \begin{center}
 % $\lambda+\alpha \mul b-\beta \mul c$, obtained with |\mul|,
@@ -763,9 +797,9 @@
 %
 % 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 get the same amount of space on the two sides of |\mul|, 
+% To ensure the same amount of space on both sides of |\mul|, 
 % you can use thin negative spaces |\!| 
-% or enclose the function or the structure with braces:
+% or enclose the function or structure with braces:
 % \begin{center}
 % $x\mul{\sin x}$, obtained with |x\mul{\sin x}|, is slightly better than $x\mul\sin x$.\\[1ex]
 % |$\sin\!{\left( \frac{\pi}{3} \right)} \mul 2$| \quad gives\\
@@ -780,30 +814,31 @@
 % \DescribeMacro{\pow}
 % In the same way, when typesetting an exponent after a closing \emph{big} 
 % parenthesis produced by |\right)|,
-% the exponent is little to far from the parenthesis.
-% The command |\pow|\marg{expr}\marg{pow} sets
-% \meta{expr} between parentheses and puts the exponent \meta{pow}
+% 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, which sets
+% \meta{expr} between parentheses and adjusts the positioning of the exponent \meta{pow}
 % slightly closer to the right parenthesis
-% \footnote{This macro gives bad results with normal sized parenthesis.}. 
+% \footnote{This macro gives bad results with normal-sized parenthesis.}. 
 % Compare:
-% \[ \e^a \sim\pow{1+\frac{a}{n}}{n} \txt{may be better than} 
+% \[ \e^a \sim\pow{1+\frac{a}{n}}{n} \txt{which may be better than} 
 % \e^a \sim\left(1+\frac{a}{n}\right)^{n}.\]
 %
 % \DescribeMacro{\abs}
-% Absolute value (or modular for a complex number) should be typeset with
-% |\lvert| \ldots |\rvert| rather than $\mid$ which doesn't respect correct 
-% spaces for delimiters; for bars whose height has to adapt to content, 
-% we use |\left\vert| \ldots |\right\vert| or, more simply, 
-% the |\abs|\{\ldots\} command which is equivalent
+% 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
 % \footnote{Another solution is to define \texttt{\bslash abs} 
-% with the \texttt{\bslash DeclarePairedDelimiter} command 
+% using the \texttt{\bslash DeclarePairedDelimiter} command 
 % from the \textsf{mathtools} package~\cite{TOOL}.}.
 %
 % \medskip
 % \DescribeMacro{\lfrac}
-% This macro behaves like |\frac|
-% but with thick spaces around the arguments,
-% so the corresponding fraction bar is perceptibly a little bit longer:\\
+% The |\lfrac| macro behaves like |\frac|
+% but with thicker spaces around the arguments,
+% making the corresponding fraction bar slightly longer:\\
 % \begin{minipage}[t]{8cm}
 % \begin{verbatim}
 %\[ \lbar{Z} = 
@@ -816,18 +851,18 @@
 %
 % \medskip
 % \DescribeMacro{[ibrackets]}
-% Open intervals are usually represented with parenthesis, \eg $(0, +\infty)$,
-% but sometimes we find also
-% square brackets, for example in French mathematics.
-% In that case the space around them is often unsuitable, 
-% \eg $x \in \mathclose{]} 0, +\infty[$.
-% We have redefined brackets in the \textsf{ibrackets} package~\cite{BRACKET} 
+% 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, 
+% as in the expression $x \in \mathclose{]} 0, +\infty[$.
+% To address this issue, we have redefined the brackets in the \textsf{ibrackets}
+% package~\cite{BRACKET} 
 % which can be optionally
 % \footnote{This functionality is optional because it causes
-% error when using a command defined by 
+% errors when using a command defined by 
 % \texttt{\bslash DeclarePairedDelimiter}~\cite{TOOL} with square brackets.}
-% loaded by \textsf{mismath} with \texttt{ibrackets} package option
-% \footnote{It's the only option of the \textsf{mismath} package.}.
+% loaded by \textsf{mismath} using the \texttt{ibrackets} package option
+% \footnote{It is the only option specific to the \textsf{mismath} package.}.
 %
 % Simply type |$x\in ]-\pi,0[ \cup ]2\pi,3\pi[$| to get
 % \begin{align*} 
@@ -836,34 +871,38 @@
 % x\in \mathclose{]}-\pi, 0 \mathopen{[} \cup \mathclose{]} 2\pi, 3\pi \mathopen{[} 
 % &\mbox{\quad without \textsf{ibrackets}}.
 % \end{align*}
-% In our code, $[$ and $]$  symbols become ``active'' 
+% In our code, the symbols $[$ and $]$ 
 % and are not defined by default as delimiters. 
-% Thereby a line break could occur between the two brackets, but
+% Therefore, a line break could occur between the two brackets. However,
 % it is always possible to transform them 
-% into delimiters with |\left| and |\right|.
+% into delimiters using |\left| and |\right|.
 %
-% With \textsf{ibrackets}: a bracket becomes an ordinary character 
-% but an open delimiter when it is immediately followed by a + or - character.
-% Thus, when the left bound contains an operator sign,
+% With the \textsf{ibrackets} package, brackets are set as ``active'' characters, 
+% behaving like ordinary characters in most cases. 
+% However, when a bracket is \emph{immediately} followed by a + or - character,
+% it becomes an open delimiter.
+% Therefore, when the left bound contains an operator sign,
 % \emph{you don't have to leave a space between the first bracket and the sign},
-% otherwise, the spaces surrounding the operator will be too large:
-% \eg |$x \in ] -\infty, 0]$| yields $x \in  ] -\infty, 0]$.
-% Contrariwise, when you want to write algebra on intervals then
+% otherwise, the spaces surrounding the operator will be too large.
+% For example if you write |$x \in ] -\infty, 0]$|, it yields $x \in  ] -\infty, 0]$
+% instead of $x \in  ]-\infty, 0]$.
+% Conversely, when dealing with algebraic expressions involving intervals,
 % \emph{you must leave a blank space between the second bracket and the} +/- 
-% \emph{operations},
-% \eg |$[a, b] + [c, d]$| yields $[a, b] + [c, d]$
+% \emph{operations}.
+% For instance |$[a, b] + [c, d]$| yields $[a, b] + [c, d]$
 % but |$[a, b]+ [c, d]$| yields $[a, b]+ [c, d]$.
 %
-% Let us also mention other approaches with the |\interval| macro
+% Besides, there are other approaches, for example the |\interval| macro
 % from the \textsf{interval} package~\cite{INT},
 % or |\DeclarePairedDelimiters| from the \textsf{mathtools} package~\cite{TOOL}
 % (but the latter is incompatible with \textsf{ibrackets}
-% for brackets management).
+% for managing brackets).
 %
 % \subsection{Environments for systems of equations and small matrices}
 %
 % \DescribeEnv{system}
-% The \texttt{system} environment produces a system of equations:\\
+% The \texttt{system} environment, defined in the \textsf{mismath} package, 
+% is used to represent a system of equations:\\
 % \begin{minipage}[t]{6.5cm}
 % \begin{verbatim}
 %$\begin{system} 
@@ -877,22 +916,28 @@
 %
 % \medskip
 % \DescribeMacro{\systemsep}
-% This first example could also have been produced with \texttt{cases} environment
-% from \textsf{amsmath} package, although \texttt{cases} places mathematical expressions 
-% closer to the bracket (which makes sense considering it's use).
-% |\systemsep| enables to set the gap between the bracket and the expressions, 
-% set by default to |\medspace|. This gap may be reduced, for instance:
-% |\renewcommand{\systemsep}{\thinspace}|,
-% or enlarged with |\thickspace| (and with |\renewcommand\systemsep}{}|
-% we obtain what \texttt{cases} do).
+% 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| command allows you to adjust the gap between 
+% the bracket and the expressions. 
+% By default, the gap is set to |\medspace|. You can reduce the gap by redefining the command,
+% for instance: |\renewcommand{\systemsep}{\thinspace}|.
+% Alternatively you can increase the gap using |\thickspace| 
+% (and with |\renewcommand\systemsep}{}| you can achieve the same spacing as the
+% \texttt{cases} environment).
+% The |\systemsep| command allows for greater flexibility in adjusting the spacing 
+% within the \texttt{system} environment.
 %
 % \medskip
 % \DescribeEnv{system\oarg{coldef}}
 % By default, a system is written like an \texttt{array} environment with only one column, 
-% left aligned. The environment has an optional argument to create several columns,
-% specifying their alignment, with the same syntax than the \texttt{array} environment of
-% \LaTeX : |\begin{system}[cl]| produces a two-column system, the first one being centered, 
-% the second being left aligned, such as in the following example:\\
+% left aligned. However the \texttt{system} environment has an optional 
+% argument that allows to create systems with multiple columns,
+% specifying their alignment using the same syntax as the \texttt{array} environment in
+% \LaTeX. For instance, using |\begin{system}[cl]| will produce a two-column system, 
+% with the first column centered and
+% the second column left-aligned, as shown in the following example:\\
 % \begin{minipage}[t]{7cm}
 % \begin{verbatim}
 %$\begin{system}[cl] 
@@ -906,13 +951,16 @@
 % \end{minipage}
 %
 % \DescribeMacro{\systemstretch}
-% Default spacing between the lines of a \texttt{system} environment has been slightly 
-% enlarged compared to the one from \texttt{array} environments (from 1.2 factor). 
-% This spacing may be changed by typing |\renewcommand{\systemstretch}|\marg{stretch},
-% inside the current mathematical environment (for a local change) or outside 
-% (for a global change). By default, stretch's value is 1.2.
-% In addition we can use the end of line with a spacing option such 
-% as it has been done above with |\\[1ex]|.
+% 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
+% 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.
+% Furthermore you can also use the end of the line with a spacing option, as 
+% demonstrated above with |\\[1ex]|, to control the spacing between specific lines in
+% the system.
 %
 % Another example with |\begin{system}[rl@{\quad}l]|
 % \footnote{\texttt{@\{\ldots\}} sets inter-column space.}:
@@ -928,41 +976,45 @@
 %    \end{system}
 % \end{equation*}
 % 
-% Let's mention the \textsf{systeme} package~\cite{SYST} which deals with linear systems
-% with a lighter syntax and automatic alignments on $+$, $-$, $=$,
-% and also the \textsf{spalign} package~\cite{SPAL} which moreover produces nice alignments 
-% for matrices (with spaces and semi­colons as de­lim­iters).
+% Let's also mention the \textsf{systeme} package~\cite{SYST} which provides 
+% a lighter syntax and automatic alignments for linear systems.
+% Additionally, there is the \textsf{spalign} package~\cite{SPAL},
+% which offers a convenient and easy syntax for systems and matrices with
+% visually appealing alignments.
 %
 % \medskip
 % \DescribeEnv{spmatrix}
-% The \textsf{amsmath} package provides various environments to typeset matrices: 
-% for instance \texttt{pmatrix} surrounds the matrix with parenthesis
-% or \texttt{smallmatrix} typesets a small matrix that can even be inserted 
-% in a text line. We provide a combination of the two with \texttt{spmatrix}:\\
+% The \textsf{amsmath} package offers several environments to typeset matrices :
+% For example, the \texttt{pmatrix} environment surrounds the matrix with parenthesis,
+% and the \texttt{smallmatrix} environment creates a smaller matrix suitable for insertion 
+% within a text line. We provide a combination of the these both 
+% functionalities with the \texttt{spmatrix} environment:
 % |$\vec{u}\begin{spmatrix}-1\\2\end{spmatrix}$| yielding
 % $\vec{u}\begin{spmatrix}-1\\2\end{spmatrix}$.
 %
-% The \textsf{mathtools} package enhance \textsf{amsmath} matrices environments
-% and provides also a small matrix environment with parenthesis.
-% Furthermore, with starred version |\begin{psmallmatrix*}|\oarg{col},
+% The \textsf{mathtools} package enhances the \textsf{amsmath} matrix environments
+% and also provides a small matrix environment with parenthesis: \texttt{psmallmatrix}.
+% Moreover, with the starred version |\begin{psmallmatrix*}|\oarg{col},
 % you can choose the alignment inside the columns (\texttt{c}, \texttt{l} or \texttt{r}).
-% But sadly, the space before the left parenthesis is too narrow
-% regarding to the space inside the parenthesis.
-% Compare previous $\vec{u}\begin{spmatrix}-1\\2\end{spmatrix}$
-% with $\vec{u}\begin{psmallmatrix}-1\\2\end{psmallmatrix}$.
+% However, the space before the left parenthesis is unfortunately too narrow
+% compared to the space inside the parenthesis.
+% To illustrate this, consider the following comparison:
+% $\vec{u}\begin{spmatrix}-1\\2\end{spmatrix}$ (using \textsf{mismath}'s \texttt{spmatrix})
+% vs.\@ $\vec{u}\begin{psmallmatrix}-1\\2\end{psmallmatrix}$ 
+% (using \textsf{mathtools} \texttt{psmallmatrix}).
 %
 % \medskip
-% For typesetting  various kind of matrices, let's mention the awesome 
+% For typesetting  various kinds of matrices, let's mention the excellent 
 % \textsf{nicematrix} package by François Pantigny~\cite{NMATX}.
 %
 % \subsection{Displaymath in double columns}
 %
 % \DescribeEnv{mathcols}
-% The \texttt{mathcols} environment enables to arrange 
-% ``long'' calculation in double columns, separated with a central rule, 
+% The \texttt{mathcols} environment allows you to arrange 
+% ``long'' calculations in double columns, separated with a central rule, 
 % as shown in the following example.
-% But the \textsf{multicol} package must be loaded in the preamble.
-% It activates the mathematical mode
+% 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 with an \texttt{aligned} environment.
 % \begin{mathcols}
 %           & \frac{1}{2 \mul {\pow{\frac{1}{4}}{n}} + 1} \geq 0.999 \\
@@ -976,8 +1028,9 @@
 % \end{mathcols}
 %
 % \DescribeMacro{\changecol}
-% The |\changecol| macro causes a change of column;
-% alignment is produced using the classic delimiters |&| and |\\|.
+% The |\changecol| macro is used to switch to the next column,
+% and an alignment within the column is done using the classic delimiters 
+% |&| to separate entries and |\\| to start a new row.
 % 
 % \begin{verbatim}
 %\begin{mathcols}
@@ -995,12 +1048,14 @@
 % \vspace{-4ex}
 % \subsection{Deprecated commands}
 %
-% Here we present a summary table of deprecated commands, used until version 2.2.
-% They produce a warning message but are still working and will be maintained for now.
-% These deprecated commands
-% worked only in the preamble, globally, and there was no inverse switch.
-% Therefore they are replaced by the more powerful and more general 
-% macro |\MathUp| which can be placed anywhere and has an inverse switch |\MathIt|. 
+% Here is a summary table of the deprecated commands that were used until version 2.2.
+% These commands are still functional and will be maintained for the time being,
+% but they do produce a warning message.
+% They used to work only in the preamble, affecting the entire document globally, 
+% and lacked an inverse switch.
+% As a result, these deprecated commands are now being replaced by the more 
+% versatile and powerful |\MathUp| macro, which can be used anywhere 
+% in the document or preamble and has an inverse switch |\MathIt|. 
 %
 % \begin{center} 
 % \setlength{\extrarowheight}{1pt}
@@ -1017,16 +1072,18 @@
 % \end{center}
 %
 % \medskip
-% |\MathNumbers| may be used instead of |\MathUp| with an argument containing
+% You can also utilize|\MathNumbers| instead of |\MathUp| with an argument containing
 % all the constants you want to be typeset in roman (among `e, i, j').
-% And |\MathProba{P,E}| may be used instead of |\MathUp{P}\MathUp{E}|
-% and you can add also V in its argument to refer to variance.
+% Additionally |\MathProba{P,E}| can be used instead of |\MathUp{P}\MathUp{E}|,
+% and you can include V in its argument to refer to variance.
 %
 % \medskip
-% In version 2.3 we tried a way to replace these deprecated commands
-% by package options based on keyval. This less efficient method is abandoned.
-% And thus the command |\mismathset| is obsolete.
-% Another command, |\paren|, used before version 2.0, is no longer supported.
+% In version 2.3 we attempted to replace these deprecated commands
+% with package options based on keyval. However, we found that this method was
+% less efficient and have decided to abandon it.
+% As a result, the command |\mismathset| is now obsolete.
+% Additionally, the command, |\paren|, which was used before version 2.0, 
+% is no longer supported.
 %
 % \StopEventually{}
 % \section{Implementation}
@@ -1046,14 +1103,15 @@
 \ifmm@ibrackets\RequirePackage{ibrackets}\fi
 
 %    \end{macrocode}
-% The above conditional packages loading avoids ``option clash'' errors if these packages 
-% have been previously loaded with other options.
+% The above conditional packages loading prevents ``option clash'' errors in case
+% these packages have been previously loaded previously with different options.
 %
 % \medskip
 % \DescribeMacro{\bslash}
-% The |\bslash| macro comes from Frank Mittelbach's \textsf{doc.sty} package. 
-% It can also be used in other documents instead of |\textbackslash|
-% (which doesn't work inside warnings).
+% The |\bslash| macro originates from Frank Mittelbach's \textsf{doc.sty} package. 
+% It can be employed in other documents as an alternative to |\textbackslash|,
+% especially in situations where |\textbackslash| does not work correctly, such as
+% inside warning messages.
 %    \begin{macrocode}
 {\catcode`\|=\z@ \catcode`\\=12 |gdef|bslash{\}} % \bslash command
 
@@ -1061,9 +1119,9 @@
 %
 % \medskip
 % \DescribeMacro{\mm@warning} \DescribeMacro{\mm@macro} \DescribeMacro{\mm@operator} 
-% The three following internal macros are meta commands for
-% conditional macro definition with a warning message if the macro already exists.
-% They should be useful in other packages.
+% 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]{
@@ -1085,10 +1143,10 @@
 %
 % To produce the correct upright shape font when working 
 % with the \textsf{beamer} package, you don't have to use |\mathrm|
-% but |\mathup| (based on |\operatorfont| from the \textsf{amsopn} package).
-% This command works also fine with other sans serif fonts like \textsf{cmbright}.
+% but rather |\mathup| (based on |\operatorfont| from the \textsf{amsopn} package).
+% This command also works fine with other sans serif fonts like \textsf{cmbright}.
 %
-% Moreover for \textsf{beamer}, which changes the family default font (sans serif)
+% Moreover for \textsf{beamer}, which changes the default font family (sans serif)
 % |\e|, |\i|, |\j| have no effect without |\AtBeginDocument|.
 % 
 % |\AtBeginDocument| is also necessary to redefine |\i| when calling 
@@ -1103,16 +1161,16 @@
 
 %    \end{macrocode}
 %
-% The following macros are switches that transform in roman vs italic any chosen letter
-% in math mode. They can be used anywhere.
-% To get a letter in roman instead of italic, we have to change the 
-% digit of mathcode that represent the family: 1 to 0.
+% The following macros are switches that transform any chosen letter in math mode
+% to roman or italic style. These switches can be used anywhere in the document or preamble.
+% 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), the second digit `1' meaning ``italic''.
-% To get a roman `e', we have to change his mathcode in "7065.
+% `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 called in the preamble, |\AtBeginDocument| is necessary 
+% When used in the preamble, it is necessary to call |\AtBeginDocument|
 % for using with the \textsf{beamer} package.
 % In the preamble, |\math@family{#1}{0}| is equivalent to \\
 % |\DeclareMathSymbol{#1}{\mathalpha}{operators}{`#1}|.
@@ -1165,15 +1223,17 @@
 \newcommand*\MathIt[1]{\MathFamily{#1}{1}}
 
 %    \end{macrocode}
-% On the same model we could also create some other macros to set any letter
-% in bold or sans serif, but unfortunately there is no family number associated by default
-% to these typefaces. It depends on the font package that is loaded and
-% it can also depend on which |\DeclareSymbolFont| is used.
+% With a similar approach we could also create additional macros to set any letter
+% in bold or sans serif. However, there is no default family number associated 
+% with these typefaces. The family number depends on the font package being loaded and
+% may vary depending on specific |\DeclareSymbolFont| used.
+% Therefore, setting letters in bold or sans serif requires additional consideration 
+% and may not have a straightforward solution.
 %
 % \medskip
-% In complement to |\MathUp| and |\MathIt|, we provide the two following commands
-% to set in roman a group of letters among `e, i, j' for mathematical constants
-% or `P, E, V' for probability operators.
+% In addition to |\MathUp| and |\MathIt|, we also offer the following two commands
+% to set a group of letters in roman typeface: one for for mathematical constants,
+% among `e, i, j', and the other for probability operators, among or `P, E, V'.
 %
 % \medskip
 %    \begin{macrocode}
@@ -1191,18 +1251,20 @@
 
 %    \end{macrocode}
 % \DescribeMacro{\apply}
-% The inverse global switch |\MathNormal| acts on any comma separated list 
-% thanks to the |\apply| macro which works as follows:
-% |\apply\macro{comma,list}| expands to |\macro{comma}\macro{list}|.
-% We could also use |\apply\MathUp{e,i,j}| instead of |\MathNumbers{e,i,j}|.
-% I found this macro on Tex RSSing.com by searching 
+% With the inverse global switch |\MathNormal|, you can apply the normal (italic) style 
+% on any comma-separated list of characters. This is achieved using
+% the |\apply| macro, for example |\apply\macro{arg1,arg2}|
+% expands to |\macro{arg1}\macro{arg2}|.
+% So using |\apply\MathUp{e,i,j}| is equivalent to |\MathUp{e}\MathUp{i}\MathUp{j}|.
+% I discovered this powerfull macro on Tex RSSing.com by searching for 
 % ``TeX How to iterate over a comma separated list?''
-% The answer was given by ``wipet'' on 2021/02/26.
-% I don't know who is wipet but I thank him for this powerful macro!
-% Unfortunately usual loop instructions like |\@for| or |\foreach| do not work
-% and produce the error message ``!~Improper alphabetic constant''.
-% Indeed |\def\letter{A} \MathUp{\letter}| fails,
-% the control sequence |\letter| is not considered as the single character `A'.
+% The answer was provided by a user named ``wipet'' on 2021/02/26.
+% I don't know who is wipet but I am grateful for his contribution,
+% as this macro allows us to accomplish the task that
+% usual loop instructions like |\@for| or |\foreach| cannot achieve due to
+% errors like ``!~Improper alphabetic constant''.
+% For instance, if you try |\def\letter{A} \MathUp{\letter}| it will fail
+% because the control sequence |\letter| is not considered as the single character `A'.
 %
 % \medskip
 %    \begin{macrocode}
@@ -1218,10 +1280,10 @@
 %    \end{macrocode}
 %
 % The following commands are deprecated but still work.
-% They were intended to set some letters in upright shape by default
-% in math mode, but worked only in the preamble.
-% This is now managed by the more powerful |\MathUp| command.
-% The old commands are maintained for now for compatibility reasons.
+% 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 for compatibility reasons.
 % \medskip
 %
 %    \begin{macrocode}
@@ -1252,11 +1314,11 @@
 
 %    \end{macrocode}
 %
-% The Greek letter pi must be managed in a different way. The switches are called
+% The Greek letter pi must be handled differently. The switches are called
 % |\pinumber| and |\pinormal|.
-% When given without argument, |\pinumber| uses the LGR font encoding.
+% When given without an argument, |\pinumber| uses the LGR font encoding.
 % A particularity of the \textsf{fontenc} package is that it can be loaded 
-% several times with different options without ``option clash'' error.
+% several times with different options without triggering an ``option clash'' error.
 % \medskip
 %    \begin{macrocode}
 \newcommand*\pinumber[1][]{
@@ -1277,16 +1339,16 @@
         \let\savedpi\pi
       \fi
     }{
-        \@ifundefined{#1}{
-            \PackageWarning{mismath}{%
-                Value #1 must be a valid
-                command name\MessageBreak for pinumber,
-                but command \bslash #1\space
-                is undefined.\MessageBreak
-                Perhaps a missing package}
-        }{\renewcommand{\pi}{%
-            \csname #1\endcsname}
-        }
+      \@ifundefined{#1}{
+          \PackageWarning{mismath}{%
+              Value #1 must be a valid
+              command name\MessageBreak for pinumber,
+              but command \bslash #1\space
+              is undefined.\MessageBreak
+              Perhaps a missing package}
+      }{\renewcommand{\pi}{%
+          \csname #1\endcsname}
+      }
     }
 } 
 
@@ -1327,7 +1389,7 @@
 
 %    \end{macrocode}
 %
-% And now all the other commands.
+% Classic identifiers are presented below.
 % \medskip
 %    \begin{macrocode}
 \mm@macro{di}{\mathop{}\!\mathup{d}}
@@ -1381,13 +1443,20 @@
 \mm@operator[bigo]{\bigo}{O}
 \mm@operator[lito]{\lito}{o}
 
+%    \end{macrocode}
+% And finally we present the remaining macros.
+%
+% With Cyrillic languages, the command |\C| may already be defined (only for text mode).
+% Thus, it will not be redefined by \textsf{mismath}. However, one may still want
+% to use our |\C| macro only for math mode without interfering the definition of 
+% the text |\C|, therefore the |\onlymathC| macro. 
+% \medskip
+%    \begin{macrocode}
 \mm@macro{mathset}{\mathbf}
 \mm@macro{R}{\mathset{R}}
-\@ifpackagewith{babel}{russian}{
-    \PackageWarningNoLine{mismath}{Option russian of babel
-    is loaded\MessageBreak    
-    Command \bslash C will not be redefined}
-    }{\mm@macro{C}{\mathset{C}}}
+\mm@macro{C}{\mathset{C}}
+\providecommand\onlymathC{\let\oldC\C 
+    \renewcommand{\C}{\TextOrMath{\oldC}{\mathset{C}}} }
 \mm@macro{N}{\mathset{N}}
 \mm@macro{Z}{\mathset{Z}}
 \mm@macro{Q}{\mathset{Q}}
@@ -1412,9 +1481,10 @@
 \mm@macro{iif}{if and only if\xspace}
 
 %    \end{macrocode}
-% We used |\mathurm| before |\Delta| in the case of defining capital Greek letters
-% in italic (for example with the \textsf{fixmath} package).
-% Without |\mbox{}|, space produced by |\| in macro |\then| would be suppressed in tables.
+% 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{} } 
-- 
cgit v1.2.3

