% This is macro package used by OpTeX, see http://petr.olsak.net/optex
% math.opm, Petr Olšák <petr@olsak.net>, 2022
% This file can serve as an template for other package files
% See end of the file for more information

\_def\_math_version {0.23, 2026-02-15}
\_codedecl \replacemissingchars {Doing math more comfortably <\_math_version>}
\_namespace{math}

   \_doc
   The `math` package provides options, they can be declared using
   the \`\mathsetup``{<options>}` macro. For example `\mathsetup {vert, dots}`.
   If you create your own package with options, provide a similar
   `\<pkg>set` macro. The \`\.kv` macro is similar to \OpTeX's `\kv`, but
   with specific `pkg:math` dictionary.
   \_cod

\_def\.mathsetup #1{%
   \_edef\.restorekvdict{\_kvdict{\_the\_kvdict}}%
   \_kvdict{pkg:math}%
      \_nokvx {\_opwarning{\_the\_kvdict: unknown option "##1", ignored}}%
      \_kvx {vert}     {\.smartvert}%     sets | as math active, to do better |x| or ||x||
      \_kvx {dots}     {\.smartdots}%     \dots behaves like \ldots or \cdots
      \_kvx {interval} {\_let\_=\.interval}% enables \_<0,1)
      \_kvx {rmsbsp}   {\.rmsbsp}%        activates x_[text] and x^[text]
      \_kvx {ibrackets}{\.ibrackets}%     intelligent brackets
      \_kvx {multiprimes} {\.multiprimes}% enables multi-prime symbols in script, scriptsizes
      \_kvx {flexipa}  {\.flexipa}%       flexible partial symbol
      \_kvx {mstyle}   {\.mstyle{##1}}%   sets mstyle=TeX or ISO or french or upright
      \_kvx {bstyle}   {\.bstyle{##1}}%   sets bstyle=TeX or ISO or upright or OpTeX
      \_kvx {bfserif}  {\.bfserif}%       \bf, \bi select fonts with serifs
      \_kvx {rmchars}  {\.rmchars{##1}}%  does \.rmchars{<list>}
      \_kvx {vargreek} {\.vargreek{##1}}% does \.vargreek{<list>}
      \_kvx {text}     {\.dotext{##1}}%   does \.dotext{<list>}
      \_kvx {enablefic}{\.enablefic}%     enables final italic correction
      \_readkv{#1}%
   \.restorekvdict
}
\_def\.kv #1{\_trycs{_kv:pkg:math:#1}{\_kvunknown}}% for accessing values given by \mathsetup

\_nspublic \mathsetup ;
\_newpublic \_let\mathset = \.mathsetup  % for backward compatibility

   \_doc
   \`\bigp`, \`\bbigp`, \`\Bigp`, \`\biggp`, \`\Biggp`, \`\autop`, \`\normalp` are inspired from
   \tricklink[bigp]{0094}
   \_cod

\_def\.bigp #1{\.fparam{#1}\_bigl\_bigr}
\_def\.bbigp #1{\.fparam{#1}\_bbigl\_bbigr}
\_def\.Bigp #1{\.fparam{#1}\_Bigl\_Bigr}
\_def\.biggp#1{\.fparam{#1}\_biggl\_biggr}
\_def\.Biggp#1{\.fparam{#1}\_Biggl\_Biggr}
\_def\.autop#1{\.fparam{#1}\_left\_right}
\_def\.normalp#1{\.fparam{#1}\_relax\_relax}
\_def\.fparam#1#2#3{%
   \_isequal .{#1}\_iffalse #1\_fi
   \_let\.bigleft=#2\_let\.bigright=#3\_nospacefuturelet\.next\.fparamA}
\_def\.fparamA{%
   \_casesof \.next
   (        {\.fparamB()}%
   [        {\.fparamB[]}%
   \{       {\.fparamB\{\}}%
   \_bgroup {\_def\.lparen{\{}\_def\.rparen{\}}\.fparamC}%
   \_finc   {}%
}
\_def\.fparamB#1#2{%
   \_def\.lparen{#1}\_def\.rparen{#2}%
   \_def\.next#1##1#2{\_trick_ensurebalanced#1#2\.fparamC{##1}}%
   \.next
}
\_def\.fparamC#1{%
   \_ifx\.bigleft\_left \_mathopen{}\_bgroup\_fi
   \.bigleft\.lparen{#1}\.bigright\.rparen
   \_ifx\.bigright\_right \_egroup\_fi
}
\_nspublic \bigp \bbigp \Bigp \biggp \Biggp \autop \normalp ;

   \_doc
   We need macro \`\.ensurebalanced``<open-b><close-b><macro>` for balancing nested parentheses from
   \tricklink[balancing]{0043}. We use `trick` namespace for these macros.
   \_cod

\_resetnamespace{trick}
   \_def\.ensurebalanced#1#2#3{\_immediateassigned{%
      \_def\.balopen{#1}\_def\.balclose{#2}\_let\.balaction=#3%
      \_def\.readnextbal##1##2#2{\.ensurebalancedA{##1#2##2}}}%
      \.ensurebalancedA}
   \_def\.ensurebalancedA#1{\.isbalanced#1%
      \_iftrue\_afterfi{\.balaction{#1}}\_else\_afterfi{\.readnextbal{#1}}\_fi}
   \_def\.isbalanced#1\_iftrue{\_immediateassignment\_tmpnum=0 \.isbalancedA#1{\.isbalanced}}
   \_def\.isbalancedA#1#{\.countbalanced#1\.isbalanced \.isbalancedB}
   \_def\.isbalancedB#1{%
      \_ifx\.isbalanced#1\_afterfi{\_cs{ifnum}\_tmpnum=0 }\_else\_ea\.isbalancedA\_fi}
   \_def\.countbalanced#1{\_ea\_ifx\.balopen #1\_immediateassignment\_incr\_tmpnum\_fi
                          \_ea\_ifx\.balclose#1\_immediateassignment\_decr\_tmpnum\_fi
                          \_ifx\.isbalanced#1\_else\_ea\.countbalanced\_fi}
\_resetnamespace{math}

   \_doc
   \`\smartdots` re-sets `\dots` to `\.dots`.
   The `\.dots` lets `\.next` using `\futurelet` and checks the `\.next`:
   It it is declared by `\_chardef` then `\.mchar` is the real Unicode character
   with `\chardef`ed code.
   If `\.next` is a real Unicode character then `\.mchar` includes it. This
   is done by the expandable \o`\cstochar` macro provided by \OpTeX/.
   If `\.next` is something else (i.e.\ `\.mchar` is empty) then print
   \o`\ldots` else print \o`\cdots` for Op, Bin, Rel, Open, Close math
   classes of the `\.next` math object or prints \o`\ldots` in other cases.
   \_cod

\_def\.smartdots {\_let\dots=\.dots}
\_def\.dots{\_relax \_ifmmode \_ea\.specdots \_else \_dots \_fi}
\_def\.specdots{\_futurelet\.next\.specdotsA}
\_def\.specdotsA{%
   \.ischardef\.next\_iftrue \_edef\.mchar{\_Uchar\.next}%
   \_else \_edef\.mchar{\_cstochar\.next}%
   \_fi
   \_ifx\.mchar\_empty \_ldots
   \_else \_Umathcharnumdef\.next=\_Umathcode\_ea`\.mchar \_relax
      \_ifcase \.readclass\.next
         \_ldots\_or \_cdots\_or \_cdots\_or \_cdots\_or \_cdots\_or \_cdots \_else \_ldots \_fi
   \_fi
}
\_def\.ischardef #1\_iftrue {\_ea\.ischardefA\_meaning#1\_fin}
\_def\.ischardefA #1#2#3#4#5#6\_fin {\_def\.tmpa{#1#2#3#4#5}\_ifx\.tmpa\.stringchar}
\_edef\.stringchar{\_string\char}
\_def\.readclass#1{\_ea\.readclassA\_meaning#1\_fin}
\_def\.readclassA#1"#2"#3\_fin{#2}

\_nspublic \smartdots ;

   \_doc
   The macro \`\.interval` reads following tokens until the `)` or `>` is found in the input
   queue and replaces \code{<} to `\langle` and `>` to rangle. The reading and replacing
   process saves the tokens to the `\intevalL` macro only and finally this macro is launched.
   \_cod

\_def\.interval{\_def\.intervalL{}\.intervalA}
\_def\.intervalA{\_nospacefuturelet\.next\.intervalB}
\_def\.intervalB{\_ifx\.next\_bgroup \_ea\.intervalC \_else \_ea\.intervalD \_fi}
\_def\.intervalC#1{\_addto\.intervalL{{#1}}\.intervalA}
\_def\.intervalD#1{\_casesof #1
   < {\_addto\.intervalL{\langle}\.intervalA}
   > {\_addto\.intervalL{\rangle}\.intervalL}
   ) {\_addto\.intervalL{)}\.intervalL}
   \_finc {\_addto\.intervalL{#1}\.intervalA}%
}

   \_doc
   \`\smartvert` sets `|` as math-active character and declares it
   equal to `\.autovert` macro. This macro checks two variants: there
   is single `|` or there is double `||`. It runs \`\.autovertA` or
   \`\.autoVertA`. These macros find the closing `|` or `||` and use
   `|` or `‖` in context of `\left`, `\right`. The \`\singlevert`
   is declared here if a user want to use a single vertical bar.
   \_cod

\_newpublic\_mathchardef \singlevert=\_mathcode`|
\_def\.autovert {\_isnextchar|{\.autoVertA}{\.autovertA}}
\_def\.autovertA #1|{\_mathopen{}\_mathclose{\_left|#1\_right|}}
\_def\.autoVertA|#1||{\_mathopen{}\_mathclose{\_left‖#1\_right‖}}
\_bgroup \_lccode`\~=`\| \_lowercase{\_egroup
   \_def\.smartvert{\_let~=\.autovert \_mathcode`|="8000 }}

\_nspublic \smartvert ;

   \_doc
   \`\rmsbsp` activates `^` and `_` so they check the next character.
   If it is `[` then `\mathbox` is used for subscript or superscript, else
   normal behavior of subscript or superscript is kept.
   \_cod

\_def\.rmsbsp{%
   \_adef ^{\_isnextchar[{\.rmsp}{\_sp}}
   \_adef _{\_isnextchar[{\.rmsb}{\_sb}}
   \_def\.rmsp[##1]{\_sp{\_mathbox{##1}}}
   \_def\.rmsb[##1]{\_sb{\_mathbox{##1}}}
   \_catcode `\^=12   \_catcode`\_=11
   \_mathcode`_="8000 \_mathcode`^="8000
   % because ^ has different catcode, we need to re-define \_primes in order to work f'^2:
   \_def\_primes{\_prime\_isnextchar'{\_primesA}{\_ea\_isnextchar\_string^{\_primesB}{\_egroup}}}
}
\_nspublic \rmsbsp ;

   \_doc
   The control sequences \`\N`, \`\Z`, \`\Q`, \`\R`, \`\C`
   \`\sgn`, \`\argmin`, \`\argmax`, \`\grad`, \`\rank`, \`\tr`, \`\diag`, \`\Span`,
   \`\Rng`, \`\Null`, \`\Ker`, \`\Res`, \`\tg`, \`\cotg`, \`\arctg`, \`\arccotg`,
   \`\frac`, \`\dfrac`, \`\tfrac`, \`\.`
   are defined directly in the user space by \o`\_newpublic`.
   The \`\.pdef` is a shortcut for `\protected\def`.
   \_cod

\_def\.pdef{\_protected\_def}

\_newpublic\.pdef \N {{\_bbchar N}}
\_newpublic\.pdef \Z {{\_bbchar Z}}
\_newpublic\.pdef \Q {{\_bbchar Q}}
\_newpublic\.pdef \R {{\_bbchar R}}
\_newpublic\.pdef \C {{\_bbchar C}}

\_newpublic\.pdef \sgn     {\_mathop{\_rm sgn}\_nolimits}
\_newpublic\.pdef \argmin  {\_mathop{\_rm argmin}}
\_newpublic\.pdef \argmax  {\_mathop{\_rm argmax}}
\_newpublic\.pdef \grad    {\_mathop{\_rm grad}\_nolimits}
\_newpublic\.pdef \rank    {\_mathop{\_rm rank}\_nolimits}
\_newpublic\.pdef \tr      {\_mathop{\_rm tr}\_nolimits}
\_newpublic\.pdef \diag    {\_mathop{\_rm diag}\_nolimits}
\_newpublic\.pdef \Span    {\_mathop{\_rm Span}\_nolimits}
\_newpublic\.pdef \Rng     {\_mathop{\_rm Rng}\_nolimits}
\_newpublic\.pdef \Null    {\_mathop{\_rm Null}\_nolimits}
\_newpublic\.pdef \Ker     {\_mathop{\_rm Ker}\_nolimits}
\_newpublic\.pdef \Res     {\_mathop{\_rm Res}\_nolimits}
\_newpublic\.pdef \tg      {\_mathop{\_rm tg}\_nolimits}
\_newpublic\.pdef \cotg    {\_mathop{\_rm cotg}\_nolimits}
\_newpublic\.pdef \arctg   {\_mathop{\_rm arctg}\_nolimits}
\_newpublic\.pdef \arccotg {\_mathop{\_rm arccotg}\_nolimits}

\_newpublic\.pdef \frac  #1#2{{{#1}\_over#2}}
\_newpublic\.pdef \dfrac #1#2{{\_displaystyle{{#1}\_over#2}}}
\_newpublic\.pdef \tfrac #1#2{{\_textstyle{{#1}\_over#2}}}

\_newpublic\.pdef \.#1{{\_bf#1}}

   \_doc
   \`\multiprimes` sets {\def\\{\kern-3.8pt}{\tt '},
   {\tt '\\'}, {\tt '\\'\\'}, {\tt '\\'\\'\\'}}
   as active characters. It enables to use them naturally
   in script and script-script sizes.
   These special characters defined here are probably invisible
   in the following code in `math-doc.pdf`.
   \_cod

\_def\.multiprimes{\.unionly\multiprimes{%
   \_adef ′{^′}\_adef ″{^″} \_adef ‴{^‴} \_adef ⁗{^⁗}}}
\_nspublic \multiprimes ;

   \_doc
   \`\eqsystem``{<equations>}` saves its parameter to `\.tmpb`
   and does a collection of `\_replstring`s. It replaces all spaces by `&`
   (but ignores the optional first and last space), it removes spaces before `\cr`,
   it precedes `\mathord` before all `-`
   (but not if the minus is alone in the column) and runs `\halign`.
   The \n`\baselineskip` is enlarged by \O`\openup`\`\eqskip`.
   Each item adds 0.5\`\eqsep` around it and \`\eqfil` to the left side and
   `\hfil` to the right side.
   \_cod

\_protected \_optdef\.eqsystem[]#1{\_vcenter{%
   \_def\.tmpb{\.bb#1\.bb}\_replstring\.tmpb{ }{&}%
   \_replstring\.tmpb{\.bb&}{}\_replstring\.tmpb{&\.bb}{}\_replstring\.tmpb{&\cr}{\cr}%
   \_replstring\.tmpb{-}{\_mathord-}\_replstring\.tmpb{&\_mathord-&}{&-&}%
   \_let ~=\_relax
   \_the\_opt \_relax \_openup\.eqskip
   \_halign{&\_the\.eqfil\_kern.5\.eqsep$\_displaystyle{{}##{}}$\_kern.5\.eqsep\_hfil\_cr
            \.tmpb\_crcr}%
}}
\_let\.bb=\_empty
\_newdimen\.eqskip
\_newdimen\.eqsep
\_newtoks\.eqfil   \.eqfil={\_hfill}
\_nspublic \eqsystem \eqskip \eqsep \eqfil ;

   \_doc
   The \`\toright` and  \`\toleft` macros are based on the
   \o`\setpos` and \o`\posx` macros. The printing point is shifted by `\posx`
   to the left (i.e.\ to the left boundary of the sheet) and then it is shifted
   to the desired space by `\kern\hoffset+\hsize`.
   This idea is moved from \tricklink[torighteq]{0028}.
   \_cod

\_newcount \.tomarginno
\_def\.toright #1{\_incr\.tomarginno {\_setpos[_math_tr:\_the\.tomarginno]%
   \_rlap{\_kern-\_posx[_math_tr:\_the\.tomarginno]\_kern\_hoffset\_kern\_hsize\_llap{#1}}}}
\_def\.toleft #1{\_incr\.tomarginno {\_setpos[_math_tr:\_the\.tomarginno]%
   \_rlap{\_kern-\_posx[_math_tr:\_the\.tomarginno]\_kern\_hoffset\_rlap{#1}}}}

\_nspublic \toright \toleft ;

   \_doc
   The \`\subeqmark` works because the internal \O`\_thednum`
   is re-defined. The \`\.dnumpost` is added here. If you want to use another format
   for \O`\_thednum` then you have to add the \^`\.dnumpost` to it too.
   \_cod

\_def \_thednum    {(\_the\_dnum \.dnumpost)}
\_def\.dnumpost{}
\_def\.subeqmark #1{\_def\.dnumpost{#1}\_lowercase{\_ifx a#1}\_else \_decr\_dnum\_fi \_eqmark}

\_nspublic \subeqmark ;

   \_doc
   \`\ibrackets` is implemented analogically as in the \LaTeX/ package `ibrackets`.
   I.e.\ the `[` and `]` are math active and they are set as `\mathord` by defualt,
   but they are `\mathopen` if the `+` or `-` follows.
   \_cod

\_def\.ibrackets{\.unionly\ibrackets{%
   \_mathchardef\.openbracket\_mathcode`[
   \_mathchardef\.closebracket\_mathcode`]
   \_mathcode`[="8000 \_mathcode`]="8000
   {\_global\_adef[{\_futurelet\.next\.openbr}%
    \_global\_adef]{\_futurelet\.next\.closebr}}%
}}
\_def\.openbr{\.setbracket \.openbracket}
\_def\.closebr{\.setbracket \.closebracket}
\_def\.setbracket{\_ifx\.next+\_mathopen\_else \_ifx\.next-\_mathopen\_else \_mathord\_fi\_fi}

\_nspublic \ibrackets ;

   \_doc
   \`\flexipa` (or \`\flexiblepartial`) runs
   \~`\partialsymbolvars` `{it}`\,`{rm}`\,`{bfsans}`\,`{it}`\,`{bfitsans}`.
   The \`\partialsymbolvars` macro adds two tokens `\.partialvar \m<var>partial`
   to `\_mit`, `\_marm`, `\_mabf`, `\_mait`, `\_mabi` macros.
   The \`\.partialvar` macro sets appropriate
   `\_Umathcode` of the `\.partialchar` to the code given by the parameter
   `\m<var>partial`. Five macros
   \`\mbfpartial`, \`\mitpartial`, \`\mbfitpartial`, \`\mbfsanspartial`, \`\mbfitsanspartial`
   are declared in the macro file `unimath-table.opm`.
   The math character \`\mrmpartial` (for upright variant) is declared here.
   \_cod

\_chardef\.partialchar="2202
\_Umathchardef\.mrmpartial=0 1 \.partialchar
\_def\.partialvar #1{\_Umathcode \.partialchar 0 1
                                 \_ifx#1\.mrmpartial \.partialchar \_else\_ea`#1 \_fi
}
\_def\.inadd#1#2{\_ea\.inaddA#1{#2}#1}
\_def\.inaddA\_inmath#1#2#3{\_protected\_def#3{\_inmath{#1#2}}}

\_def\.partialsymbolvars #1#2#3#4#5{%
   \_ifx\_ncharrmA\_undefined \_opwarning{\_string\flexipa: Unicode math must be loaded first}%
   \_else
      \_def\.tmp{\_ea\_addto \_ea\_mit  \_ea {\_ea\.partialvar \_csname m#1partial\_endcsname}}%
      \_ifx\_mit\mit \.tmp \_let\mit=\_mit \_else \.tmp \_fi
      \_ea\.inadd \_ea\_marm \_ea {\_ea\.partialvar \_csname m#2partial\_endcsname}%
      \_ea\.inadd \_ea\_mabf \_ea {\_ea\.partialvar \_csname m#3partial\_endcsname}%
      \_ea\.inadd \_ea\_mait \_ea {\_ea\.partialvar \_csname m#4partial\_endcsname}%
      \_ea\.inadd \_ea\_mabi \_ea {\_ea\.partialvar \_csname m#5partial\_endcsname}%
      \_mit
   \_fi
}
\_def\.flexipa{\.unionly\flexipa{\.partialsymbolvars {it}{rm}{bfsans}{it}{bfitsans}}}
\_newpublic \_let \flexiblepartial=\.flexipa
\_nspublic \flexipa \partialsymbolvars \mrmpartial ;

   \_doc
   The options `mstyle`, resp. `bstyle` run \`\.mstyle`, resp. \`\.bstyle`
   and these macros set required shapes of math variables. This can be done
   only when Unicode-math is loaded already. This is a reason why
   \`\.unionly``{<text>}{<code>}` is used: it runs <code> only when
   Unicode-math is loaded, otherwise it prints a warning.
   \_cod

\_def\.mstyle #1{\.unionly{mstyle}{\_lowercase{\_cs{_math_mstyle_#1}}}}
\_def\.bstyle #1{\.unionly{bstyle}{\_lowercase{\_cs{_math_bstyle_#1}}}}

\_def\.mstyle_tex {%
   \_protected\_def\_mit {\_itvariables \_rmdigits \_itgreek \_rmGreek}\_mit
}
\_def\.mstyle_iso {%
   \_protected\_def\_mit {\_itvariables \_rmdigits \_itgreek \_itGreek}\_mit
}
\_def\.mstyle_french {%
   \_protected\_def\_mit {\_umathrange{A-Z}71\_ncharrmA \_umathrange{a-z}71\_ncharita
                          \_rmdigits \_rmgreek \_rmGreek}%
   \_mit
}
\_def\.mstyle_upright {%
   \_protected\_def\_mit {\_rmvariables \_rmdigits \_rmgreek \_rmGreek}\_mit
}
\_def\.bstyle_tex {%
   \_protected\_def\_mabf {\_inmath{\_bfvariables\_bigreek\_bfGreek\_bfdigits}}%
   \_protected\_def\_mabi {\_inmath{\_bivariables\_bigreek\_bfGreek\_bidigits}}%
}
\_def\.bstyle_optex {%
   \_protected\_def\_mabf {\_inmath{\_bsansvariables \_bsansgreek \_bsansGreek \_bsansdigits}}%
   \_protected\_def\_mabi {\_inmath{\_bisansvariables \_bisansgreek \_bsansGreek \_bsansdigits}}%
}
\_def\.bstyle_iso {%
   \_protected\_def\_mabf {\_inmath{\_bivariables\_bigreek\_biGreek\_bfdigits}}%
   \_protected\_def\_mabi {\_inmath{\_bivariables\_bigreek\_bfGreek\_bidigits}}%
}
\_def\.bstyle_upright {%
   \_protected\_def\_mabf {\_inmath{\_bfvariables\_bfgreek\_bfGreek\_bfdigits}}%
   \_protected\_def\_mabi {\_inmath{\_bivariables\_bigreek\_biGreek\_bidigits}}%
}
\_def\.unionly #1{\_ifx\_rmvariables\_undefined
   \_opwarning{pkg:math: \_string#1 ignored: Unicode-math must be loaded}%
   \_ea\_ignoreit \_else \_ea\_useit \_fi
}

   \_doc
   \`\bfserif` re-defines internal \OpTeX/ \O`\_mabf` and \O`\_mabi` macros.
   \_cod

\_def\.bfserif{\.unionly\bfserif{%
   \_protected\_def\_mabf {\_inmath{\_bfvariables\_bfgreek\_bfGreek\_bfdigits}}%
   \_protected\_def\_mabi {\_inmath{\_bivariables\_bigreek\_bfGreek\_bfdigits}}%
}}

\_nspublic \bfserif ;

   \_doc
   \`\rmchars``{<list>}` is implemented using \O`\foreach`. The list is
   expanded first because we want to expand control sequences like `\alpha`
   to a real character $\_rmgreek \alpha$.\nl
   \`\vargreek``{<list>}` is implemented using \O`\foreach`. The
   parameter is not expanded because we want to keep control sequences like
   `\alpha` unchanged.
   \_cod

\_def\.rmchars#1{\.unionly\rmchars{\_ea\_foreach\_expanded{#1}\_do{\_ifx,##1\_else\.rmchar##1\_fi}}}
\_def\.rmchar#1{\_Umathcode`#1=0 1 `#1 }

\_def\.vargreek#1{\_foreach#1\_do{\_ifx,##1\_else \.vargreekchar##1\_fi}}
\_def\.vargreekchar#1{%
   \_ifcsname var\_csstring#1\_endcsname \_slet{\_csstring#1}{var\_csstring#1}%
   \_else \_opwarning{\_string\vargreek: the \_bslash var\_csstring#1\_space doesn't exists}%
   \_fi
}
\_nspublic \rmchars \vargreek ;

   \_doc
   \`\textvariables`, \`\textdigits`, \`\textmoremath` initialize
   new two families 5, 6 using `\.textmathini` and sets `\mathcode`s
   of given characters to these families.
   Moreover, `\textvariables` adds `\fam` register setting to `\rm` and `\it`
   selectors and re-set Greek variables to use only math font (because we
   are not sure if Greek letters are in the current text fonts).\nl
   \`\.dotext``{<list of words>}` runs `\.text<word>` for each <word> in the list.
   It is used when the option `text={<list of words>}` is used.
   \_cod

\_def\.textmathini{%
   \_fontdef\.mathrm{\_rm}\_fontdef\.mathit{\_it}%
   \_fontdef\.mathbf{\_bf}\_fontdef\.mathbi{\_bi}%
   \_addto\_normalmath{%
      \_setmathfamily    5 \.mathrm
      \_setmathfamily    6 \.mathit
   }%
   \_addto\_boldmath{%
      \_setmathfamily    5 \.mathbf
      \_setmathfamily    6 \.mathbi
   }%
   \_normalmath
   \_let\.textmathini=\_relax
}
\_def\.textvariables {\.unionly\textvariables {%
   \.textmathini \_mathcodes 6 {7{\_Urange a-z \_Urange A-Z}}%
   \_def\_marm {\_fam5 }\_def\_mait{\_itGreek \_fam6 }%
   \_protected\_def\_itgreek    {\_umathrangegreek01\_greekita}%
   \_protected\_def\_rmgreek    {\_umathrangegreek01\_greekrma}%
   \_protected\_def\_itGreek    {\_umathrangeGREEK01\_greekitA}
   \_protected\_def\_rmGreek    {\_umathrangeGREEK01\_greekrmA}
   \_itgreek \_rmGreek
}}
\_def\.textdigits    {\.unionly\textdigits{\.textmathini \_mathcodes 5 {7{\_Urange 0-9}}}}
\_def\.textmoremath  {\.unionly\textmoremath{%
   \.textmathini
   \_mathcodes 5 {5{!?} 2{*+-} 3{=<>} 6{,:;} 0{./|} 4{([\{} 5{\})]}}%
   \_Umathcode `- = 2 5 "2212  % hyphen behaves like minus in math mode
}}
\_def\.dotext#1{\_foreach #1 \_do
   ##1 {\_trycs{_math_text##1}{\_opwarning{text option: "##1" unknown}}}}

\_nspublic \textvariables \textdigits \textmoremath ;

   \_doc
   \`\mathselector` `\sequence {<fontspec-A>} {<fontspec-B>} {<factor>} {<ffeatures>}`
   declares `\sequence` as a new math selector of the math family `\sequence_fam`.
   If such family is declared already then new setting is ignored.
   The font is set by \o`\fontdef` and then its name without size clause and without font features
   is saved to `\.mselF` using `\.mselA`. The line
   `\_loadmathfamily <fam> {{<fontname>:<ffeatures>}}` is saved to \o`\_normalmath`
   and analogical line is saved to \o`\_boldmath`.
   Finally, if the declared `\sequence` is in `\rm`,`\it`,`\bf`,`\bi`,`\tt` then
   `\_marm`, `\_mait`, etc.\ is defined else `\sequence` is defined.
   It guarantees that the re-declaration of `\rm`, `\it`, etc.\ affects their
   behavior only in math mode.
   \_cod

\_def\.mathselector #1#2#3#4#5{\.unionly\mathselector{%
   \_ifcsname \_csstring#1_fam\_endcsname
      \_opwarning{\_string#1 already defined as \_string\mathselector, ignored}%
   \_else
      \_ea\_newfam \_csname \_csstring#1_fam\_endcsname
      \_ifx^#4^\_else \_sxdef{_mfactor:\_the\_numexpr\_cs{\_csstring#1_fam}}{#4}\_fi
      \_ifx^#5^\_def\.mselFF{mode=base;script=latn}\_else \_def\.mselFF{#5}\_fi
      \_fontdef\.mselF{#2}\_ea\.mselA \_fontname\.mselF :\_relax
      \_edef\.tmp{\_noexpand \_loadmathfamily \_cs{\_csstring#1_fam}{{\.mselF:\.mselFF;}} }%
      \_global \_ea\_aheadto \_ea\_normalmath \_ea{\.tmp}%
      \_normalmath
      \_ifx^#3^\_addto\.mselFF{;embolden=1.7}%
      \_else \_fontdef\.mselF{#3}\_ea\.mselA \_fontname\.mselF :\_relax \_fi
      \_edef\.tmp{\_noexpand \_loadmathfamily \_cs{\_csstring#1_fam}{{\.mselF:\.mselFF;}} }%
      \_global \_ea\_aheadto \_ea\_boldmath \_ea{\.tmp}%
      \_isinlist{\rm\it\bf\bi\tt}#1\_iftrue
         \_ea\.mselB \_csname _ma\_csstring#1\_ea\_endcsname \_csname \_csstring#1_fam\_endcsname
      \_else \_ea\.mselB \_ea#1\_csname \_csstring#1_fam\_endcsname
   \_fi\_fi
}}
\_def\.mselA #1:#2\_relax{\_def\.mselF{#1}}
\_def\.mselB #1#2{\_gdef#1{\_inmath{\_rmvariables \_rmdigits \_rmgreek \_rmGreek \_fam#2}}}

\_nspublic \mathselector ;

   \_doc
   \`\replacemissingchars``<family>` defines `\UnicodeMathSymbol` and reads
   `unimath-table.opm`, i.e.\ it does for each math character following
   if the character is missing in main math font and if it is present in
   added font and if it is not already replaced character then apply new math
   code or `\Umathaccent` definition. Its name is added to `\.alist` or
   `\.clist`. The new codes are declared by `\matchars<family>{<expanded>\clist}`.
   The `\.rlist` is the list of characters already replaced. They are not
   replaced again if a new `\replacemissingchars` is used.
   \_cod

\_def\.rlist{\sqrt\cuberoot\fourthroot} % they cannot be replaced by \mathchars
\_def\.replacemissingchars#1{\.unionly\replacemissingchars{%
   \_def\.alist{}\_def\.clist{}
   \_def\UnicodeMathSymbol##1##2##3##4{%
      \_iffontchar\_textfont1##1 \_else     % not in main math font
         \_iffontchar\_textfont#1 ##1       % is presnet in added font
            \_isinlist\.rlist{##2}\_iffalse % not already replaced
               \_ifx##3\_mathaccent
                  \_protected\_def##2{\_Umathaccent fixed 7 #1 ##1 }%
                  \_addto\.alist{##2}%
               \_else
                  \_addto\.clist{##2}%
      \_fi\_fi\_fi\_fi
   }
   \_input unimath-table.opm
   \_wlog{^^J\_string\replacemissingchars: From \_string\fam=\_string#1 is printed now:^^J%
         CHARACTERS: \_unexpanded\_ea{\.clist}^^JACCENTS: \_unexpanded\_ea{\.alist}^^J}%
   \_def\.tmp{\_mathchars #1}\_ea\.tmp\_ea{\.clist}%
   \_ea\_addto \_ea\.rlist \_ea{\.clist}\_ea\_addto \_ea\.rlist \_ea{\.alist}%
   \_def\.alist{}\_def\.clist{}\_let\UnicodeMathSymbol=\_undefined
}}
\_nspublic \replacemissingchars ;

   \_doc
   \`\scriptspaces``{<s-rel>}{<s-bin>}{<ss-rel>}{<ss-bin>}`
   sets internal \LuaTeX/ registers represented by
   appropriate primitives, see section 7.5 in the \LuaTeX/ manual.
   \_cod

\_def\.scriptspaces #1#2#3#4{%
   \_Umathordrelspacing\_scriptstyle=\.orzeromu{#1}\_relax
   \_Umathrelordspacing\_scriptstyle=\.orzeromu{#1}\_relax
   \_Umathrelopspacing \_scriptstyle=\.orzeromu{#1}\_relax
   \_Umathordrelspacing\_crampedscriptstyle=\.orzeromu{#1}\_relax
   \_Umathrelordspacing\_crampedscriptstyle=\.orzeromu{#1}\_relax
   \_Umathrelopspacing \_crampedscriptstyle=\.orzeromu{#1}\_relax
   \_Umathordbinspacing\_scriptstyle=\.orzeromu{#2}\_relax
   \_Umathbinordspacing\_scriptstyle=\.orzeromu{#2}\_relax
   \_Umathbinopspacing \_scriptstyle=\.orzeromu{#2}\_relax
   \_Umathordbinspacing\_crampedscriptstyle=\.orzeromu{#2}\_relax
   \_Umathbinordspacing\_crampedscriptstyle=\.orzeromu{#2}\_relax
   \_Umathbinopspacing \_crampedscriptstyle=\.orzeromu{#2}\_relax
   \_Umathordrelspacing\_scriptscriptstyle=\.orzeromu{#3}\_relax
   \_Umathrelordspacing\_scriptscriptstyle=\.orzeromu{#3}\_relax
   \_Umathrelopspacing \_scriptscriptstyle=\.orzeromu{#3}\_relax
   \_Umathordrelspacing\_crampedscriptscriptstyle=\.orzeromu{#3}\_relax
   \_Umathrelordspacing\_crampedscriptscriptstyle=\.orzeromu{#3}\_relax
   \_Umathrelopspacing \_crampedscriptscriptstyle=\.orzeromu{#3}\_relax
   \_Umathordbinspacing\_scriptscriptstyle=\.orzeromu{#4}\_relax
   \_Umathbinordspacing\_scriptscriptstyle=\.orzeromu{#4}\_relax
   \_Umathbinopspacing \_scriptscriptstyle=\.orzeromu{#4}\_relax
   \_Umathordbinspacing\_crampedscriptscriptstyle=\.orzeromu{#4}\_relax
   \_Umathbinordspacing\_crampedscriptscriptstyle=\.orzeromu{#4}\_relax
   \_Umathbinopspacing \_crampedscriptscriptstyle=\.orzeromu{#4}\_relax
}
\_def\.orzeromu#1{\_ifx^#1^0mu\_else#1\_fi}

\_nspublic \scriptspaces ;

   \_doc
   \`\mathclap``{<formula>}`, \`\mathrlap``{<formula>}`, and \`\mathllap``{<formula>}`
   are based on the \OpTeX/ macros \O`\mathstyles` and \O`\currstyle`.
   \_cod

\_def\.mathclap#1{\_mathstyles{\_hbox to0pt{\_hss$\_currstyle#1$\_hss}}}
\_def\.mathrlap#1{\_mathstyles{\_rlap{$\_currstyle#1$}}}
\_def\.mathllap#1{\_mathstyles{\_llap{$\_currstyle#1$}}}

\_nspublic \mathclap \mathrlap \mathllap ;

   \_doc
   \`\enablefic` enables final italic correction. The relevant lua function is
   registered to `mlist_to_hlist` callback and \`\finalitalcorr` is set to one.
   \_cod

\_newcount \.finalitalcorr
\_ifnum\_luatexversion > 123
   \_def\.enablefic{%
      \_opwarning{\_noexpand\enablefic is obsolete, LuaTeX v>1.23 fixes this issue}%
   }
\_else
\_directlua{
define_lua_command("\_pkglabel _enablefic", function()
    lua.get_functions_table()[optex.registernumber("\_pkglabel _enablefic")] = function() 
        % add the function to the callback only once
        return tex.setcount("\_pkglabel _finalitalcorr", 1)
    end
    tex.setcount("\_pkglabel _finalitalcorr", 1)
    luatexbase.add_to_callback("post_mlist_to_hlist_filter", function(head, style)
        if style~="text" or tex.count.\_pkglabel _finalitalcorr<=0 then
            return true
        end
        local last = node.tail(head)
        if last.id ~= node.id("glyph") then return true end % last is glyph
        local k = font.fonts[last.font].characters[last.char].italic
        if not k or k<=0 then return true end
        local kn = node.new("kern", 3)
        kn.kern = k
        head = node.insert_after(head, n, kn) % kern node is inserted
        return head
    end, "italcorr after math") end)}
\_fi
\_nspublic \enablefic \finalitalcorr ;


\_endnamespace
\_endcode

\sec Summary

This package provides various extensions usable for math typesetting. Mostly
of them are inspired from
\ulink[http://petr.olsak.net/optex/optex-tricks.html]{\OpTeX/ tricks} www page.

The following macros are defined in this package:
\begitems
* \~`\bigp`, \~`\bbigp`, \~`\Bigp`, \~`\biggp`, \~`\Biggp`, \~`\autop`, \~`\normalp`
  gives better controlling of sizes of parentheses.
* \~`\smartdots` declares `\dots` macro more intelligent.
  \~`\smartvert` declares \"`|`" for better spacing.
* \~`\rmsbsp` activates roman subscripts and superscripts in `[...]`.
* There are many common math macros for sets or for operators, for example
  \~`\R` or \~`\sgn`.
* \~`\eqsystem` enables to write systems of equations comfortably,
* \~`\toright`, \~`\toleft` puts the \o`\eqmark` to desired position,
  \~`\subeqmark` prints the given suffix as a part of the equation mark.
* \~`\scriptspaces` sets more spaces around rel, bin in script and scripscript styles.
* \~`\ibrackets` sets `[` and `]` as intelligent brackets.
* \~`\multiprimes` sets double, triple, quadruple primes as active.
* \~`\flexipa` enables flexible partial symbol.
* \~`\bfserif` sets `\bf` and `\bi` for math typesetting as for bold-serif, bold-italic-serif.
* \~`\rmchars` sets selected characters printed as `\rm`,
  \~`\vargreek` sets Greek leters to their variants.
* \~`\textvariables`, \~`\textdigits`, \~`\textmoremath`
  enables characters from used text font in math mode
  (variables, digits, more characters).
* \~`\mathselector` declares a new math alphabet using text fonts.
* \~`\replacemissingchars` allows to re-declare all characters missing in math font
  for printing them from additional math font.
* \~`\enablefic` enables final italic correction of inline-math lists.
\enditems

Following options are provided by the `math` package. You can set them by
\^`\mathsetup``{<options>}` after `\load[math]`, for example
`\mathsetup{dots, vert, vargreek={\epsilon,\rho}}`. The options are:
\begitems
* `dots` sets more intelligent `\dots`, the same as \~`\smartdots`.
* `interval` sets `\_` as prefix of intervals, see section~\ref[interval].
* `vert` sets more intelligent `|`, the same as \~`\smartvert`.
* `rmsbsp` sets roman sub/supscripts in `[...]`, the same as \~`\rmsbsp`.
* `ibrackets` sets intelligent brackets, the same as \~`\ibrackets`.
* `multiprimes` sets double, triple, quadruple primes as active.
* `flexipa` enables flexible partial symbol, the same as \~`\flexipa`.
* `mstyle=<style>`, `bstyle=<style>` are math styles explained in section~\ref[mstyle].
* `bfserif` sets bold-serif, bold-italic-serif, the same as \~`\bfserif`.
* `rmchars={<list>}` sets `\rm` for selected characters, the same as \~`\rmchars`,
   see section~\ref[rmchars].
* `vargreek={<list>}` sets variants for Greek letetters, the same as \~`\vargreek`,
   see section~\ref[rmchars].
* `text={<list>}` sets \~`\textvariables`, \~`\textdigits`, or \~`\textmoremath`,
  see section~\ref[textvars],
* `enablefic` enables final italic correction of inline-math lists, does
  \~`\enablefic`.
\enditems

This package is not definitive. I plan to add more features in new versions
if needed. Moreover, this package gives an example for package writers how
to write their own packages, see section~\ref[pkgtemplate].

\sec Controlled sizes of parentheses

If you write `$f(x(y+z))$` then the outer parentheses should be bigger.
Classical Plain \TeX/ provides macros \O`\bigl`, \O`\bigr`, etc., they can
be used in this manner: `$f\bigl(x(y+z)\bigr)$`. But the source file looks
bad with such markup. Better is to say that parentheses have to be bigger
using a single prefix before functional symbol, i.e. `$\bigp f(x(y+z))$`.
This should be print the same as previous example with \O`\bigl`, \O`\bigr`.

The prefixes \^`\bigp` (big pair), \^`\bbigp` (bbig pair), \^`\Bigp` (Big pair),
\^`\biggp` (bigg pair) and \^`\Biggp` (Bigg pair) are provided,
they can be used before a functional symbol. The scaled parentheses
surrounding the functional parameter can be (...) or [...] or `\{`...`\}` or
\{...\}. I.e.\ `\Bigp\Gamma [x]` is the same as `\Gamma \Bigl[x\bigr]`.
Moreover, the functional parameter gets its own \TeX/ group, so
`\Bigp G(a\over2)` results to `G\Bigl({a\over2}\bigr)`.
There are two more prefixes \^`\autop` and \^`\normalp`. First one applies
`\left`, `\right` to the parentheses of the parameter, second one keeps
the parentheses unscaled. If you want to scale the parentheses without
preceding functional symbol then use dot instead this symbol, for example
`\Bigp.(a)` is equal to `\Bigl(a\Bigr)`.

Examples:
\begtt
$$
  \displaylines{
  \biggp F (1+\Bigp g (1+\bbigp f(1+\bigp f(1+f(x))))) \cr
  f(x(y+z)),\quad  \bigp f(x(y+z)),\quad \autop f (a\over b)\cr
  \Bigp f(a\over b+c),\quad \Bigp f(x^2\over2),\quad \Bigp.(a\over b)
  }
$$
\endtt
gives:
$$
  \displaylines{
  \biggp F (1+\Bigp g (1+\bbigp f(1+\bigp f(1+f(x))))) \cr
  f(x(y+z)),\quad  \bigp f(x(y+z)),\quad \autop f (a\over b)\cr
  \Bigp f(a\over b+c),\quad \Bigp f(x^2\over2),\quad \Bigp.(a\over b)
  }
$$

\sec Intelligent `\dots` like in AMS\TeX

AMS\TeX/ provides \o`\dots` macro which works depending on the context. If it is surrounded
by symbols like $+$, $-$, $=$ then it works like \o`\cdots`, if it is surrounded by
comma or similar symbols then it works like \o`\ldots`.
This package keeps \o`\dots` unchanged but it is changed (and behaves as
mentioned above) after the \^`\smartdots` declaration.

\smartdots
You can try this after the \^`\smartdots` declaration:
\medskip

`$a_1, a_2, \dots, a_n$    ` prints $a_1, a_2, \dots, a_n$,

`$a_1 + a_2 + \dots + a_n$ ` prints $a_1 + a_2 + \dots + a_n$,


\sec[interval] Creating intervals more comfortable

Several math books uses `\langle`, `\rangle` for denoting the interval boundary
if the boundary number is element of the interval too. For example  `$\langle 0,1)$`
is printed as $\langle 0,1)$ and it
means an interval from zero to one, zero is element of the interval but one
isn't. The \TeX/ source of such math books looks badly because we cannot mark
them like \code{$<0,1)$} because it prints $\string<0,1)$ but we want $\langle 0,1)$.

This package creates the \^`\.interval` macro which can be set to be equal to `\_`
(using the `interval` option). Then `\_`  can be used just before the interval
as a prefix. The \code{<} or `>` are automatically replaced by `\langle`, `\rangle`
if `\_` is prefixed. So, you can write \code{$\\_<0,1)$} or `$\_(0,1>$` or \code{$\\_<0,1>$}
or `$\_(0,1)$` in order to get $\langle0,1)$ or $(0,1\rangle$ or $\langle0,1\rangle$
or $(0,1)$. The source with such intervals looks better.

Note that `interval` option does `\let\_=`\^`\.interval`, so the original
meaning of the `\_` control sequence (from plain \TeX/) is re-defined.
The `\_` control sequence can be used for this purpose because
the next token is `(` or \code{<}, i.e. it is non-letter.


\sec Using vertical bars with better spacing

The character \"`|`" is declared with Ord class by default in Plain \TeX/,
but we are using it typically in the context `$|x|$`. It means there should
be Open and Close classes. This example gives correct result but try to use
`$|-1|$` which gives bad spacing: $|-1|$.
And `$||x||$` gives bad result too.

When you declare \^`\smartvert`, these problems are solved. Moreover, the
\"`|`" or \"`||`" are expected to be always in pairs and they are scaled by
`\left` and `\right` primitives automatically. If you don't want to use it
in a pair, use \^`\singlevert` or `\big|`, or `\Big|` etc. Compare
the result of `$|\sum a_n|+||x||$`:
$$
  \eqalign{
     |\sum a_n|+||x|| &\quad \hbox{if \scantextokens{`\smartvert`} isn't initialized,}\cr
     \smartvert
     |\sum a_n|+||x|| &\quad \hbox{if \scantextokens{`\smartvert`} is initialized.}
  }
$$


\sec Roman subscript and superscript in `[...]`

When you declare \^`\rmsbsp`, then you can write `x_[text]` or `x^[text]`
and it is equivalent to `x_{\mathbox{text}}` or `x^{\mathbox{text}}`.


\sec Basic and typical macros for sets, functions etc.

These typical macros are defined in `math.opm`:
\^`\N` for $\N$, \^`\Z` for $\Z$, \^`\Q` for $\Q$, \^`\R` for $\R$, \^`\C` for $\C$,
\^`\sgn`, \^`\argmin`, \^`\argmax`, \^`\grad`, \^`\rank`, \^`\tr`, \^`\diag`, \^`\Span`, \^`\Rng`,
\^`\Null`, \^`\Ker`, \^`\Res`, \^`\tg`, \^`\cotg`, \^`\arctg`, \^`\arccotg`.

I hate the \^`\frac`, \^`\dfrac` and \^`\tfrac` macros defined in \LaTeX/
but someone may want to use them. This package defines them.
But I note: usage of `$1\over2$` for $1\over2$
is much more understandable than \LaTeX's `$\frac12$`.

The vectors and matrices are usually printed by `{\bf A}{\bf x}`.
The package provides a shortcut `\.<letter>` to do the same, so user can write
`\.A\.x` for multiplication of a matrix $\.A$ by a vector $\.x$.
We strictly don't recommend usage of `\.`, `\v`, `\=`, etc.\ for accents, so
`math.opm` can define `\.` differently than the classical meaning \"dotaccent".


\sec System of equations printed by `\eqsystem`

The \^`\eqsystem``{<equations>}` enables to write systems of equations more
comfortably. The equations are separated by `\cr` and the aligned columns
are separated by space. For example:
\begtt
$$
  \eqsystem{  x +  y - 2z = 10 \cr
             2x - 7y +  z = 13 \cr
             -x +  y ~  ~ = -5 }
$$
\endtt
prints
$$
  \eqsystem{  x +  y - 2z = 10 \cr
             2x - 7y +  z = 13 \cr
             -x +  y ~  ~ = -5 }
$$
Note that empty columns have to be filled by `~` mark.
There are columns for variables (possibly multiplied by a constant) and for
binary operators `+` and `-` or relations `=`, `>` etc. or constants. Each column
is aligned to right. The number of columns is unlimited (we have 7 columns in
the example above). All given equations are packed to the `\vcenter` box.

The spaces between lines are enlarged by the value of \^`\eqskip`
and the horizontal spaces between columns are enlaged by \^`\eqsep`.
Both registers are set to 0\,pt by default.

The \^`\eqfil` register is \"left filler" applied to each item in the \^`\eqsystem` columns.
Its default is `\eqfil={\hfill}`. The right filler is hardwired and it is `\hfil`.
This makes columns aligned to right by default. For example, when you set
`\eqfil={\hfil}` then you have columns centered.

The \^`\eqsystem` macro allows optional parameter which is processed inside
group before printing equations. You can do local settings here, for example
`\eqsystem[\eqskip=2pt \eqsep=5pt]{...}`.


\sec Equation marks in atypical cases

We may want to put equation marks `\eqmark` in more lines in display mode when we
are using macros not designed for such case. For example in the lines of
the `\cases` macro:

\begtt
$$ f(x) = \cases{0 & for $x<0$\toright\eqmark \cr
                 1 & otherwise\toright\eqmark } $$
\endtt
This puts the equation marks to the right margin in each line generated by
the `\cases` macro.
$$ f(x) = \cases{0 & for $x\string<0$\toright\eqmark \cr
                 1 & otherwise\toright\eqmark }
$$
The \^`\toright`\o`\eqmark` is used here. Analogically,
\^`\toleft`\o`\eqmark` puts the equation mark to the left margin.
The position of these marks are correct after second or more \TeX/ run
because \TeX/ needs to read data from its previous run in this case.

Sometimes we want to declare a bunch of equations with the same numeric
equation marks but with different suffixes, for example (1.1a), (1.1b). We
provide the macro \^`\subeqmark``<suffix>` here.
If `<suffix>` is `a` or `A` then \^`\subeqmark` starts a new bunch of
equations with the next number. Following `\subeqmark b`, `\subeqmark c`,
etc.\ use the same equation number, they differ only by given suffixes:
You can put `[<label>]` after `<suffix>` for referencing purposes.
Example:

\begtt
$$ \eqsystem[\eqskip=3pt]{
     x + 2y + 3z = 600 \toright{\subeqmark a}\cr
   12x +  y - 3z = -7  \toright{\subeqmark b[label]}\cr
    4x -  y + 5z =  5  \toright{\subeqmark c}\cr }
$$
The equation~\ref[label] has negative right side. Moreover, it applies
$$
  a^2 + b^2 = c^2. \eqmark
$$
\endtt
prints
$$ \eqsystem[\eqskip=3pt]{
     x + 2y + 3z = 600 \toright{\subeqmark a}\cr
   12x +  y - 3z = -7  \toright{\subeqmark b[label]}\cr
    4x -  y + 5z =  5  \toright{\subeqmark c}\cr
  }
$$
The equation~\ref[label] has negative right side. Moreover, it applies
$$
  a^2 + b^2 = c^2. \eqmark
$$

\sec Setting more spaces in script styles

Classical \TeX/ puts \n`\thickmuskip` around relations and \n`\medmuskip` around
binary operators only in \n`\textstyle` and \n`\displaystyle`. These spaces are
missing in \n`\scripstyle` and \n`\scriptscriptstyle`. It means that we get, for
example
$$
  \sum_{i=j+1}^\infty a_i
$$
The formula $i=k+1$ has no spaces here, so it looks unattractive. \LuaTeX/
provides better control of all such spaces, so `math.opm` declares the macro
\^`\scriptspaces``{<s-rel>}{<s-bin>}{<ss-rel>}{<ss-bin>}` for setting
these spaces. <s-rel> is \"muskip" value used around relations in \n`\scriptstyle`,
<s-bin> is \"muskip" used around binary operators in \n`\scriptstyle` and the
last two parameters gives these spacing in \n`\scriptscriptstyle`.
If a parameter is empty, it means that it has zero value.
For example after `\scriptspaces {2mu}{1.3mu}{}{}`
the formula mentioned above looks like
$$
  \scriptspaces {2mu}{1.3mu}{}{}
  \sum_{i=j+1}^\infty a_i
$$
It looks better, doesn't it?

\sec[mstyle] `\bf` and `\bi` shapes, math styles

\OpTeX/ sets `\bf` and `\bi` math selectors as sans serif, because this
follows the old traditional math typesetting of vectors and matrices.
But Knuth's \TeX/ has another default behavior:`\bf` and `\bi` select serifed
shapes. So, many people consider it as a standard. You can declare \^`\bfserif` if
you want serifed `\bf` and `\bi` math letters.

Moreover, this package provides `mstyle=<style>` and `bstyle=<style>` options.
The `mstyle` option can be `TeX`, `ISO`, `french` or `upright` and `bstyle`
option can be `TeX`, `OpTeX`, `ISO`, `upright`. The `mstyle` and `bstyle`
options set the upright/italic versions of math Latin/Greek variables in the same
manner as `math-style` and `bold-style` options (from \LaTeX's
`unicode-math`) do it. The `bstyle=OpTeX` sets sans serif bold variables,
which is default in \OpTeX.

\sec[rmchars] Selected upright letters and variants for Greek letters

Some mathematicians claim that the letters $e$, $i$ and $\pi$ in meaning
\"a constant" should be printed in upright form. \TeX/ prints all variables in
math italic, but this package enables to set exceptions for some letters.
For example after \^`\rmchars``{e, i, \pi}`, all occurrences of these three letters
in math mode will be set in upright shape. If you set this, then the
well-known math identity `$e^{i\pi}=-1$` looks like this:
$$
  {\rm e}^{\rm i\muppi} = -1, \qquad \hbox{compare with:}\quad e^{i\pi} = -1.
$$
The syntax is \^`\rmchars``{<list>}`, where <list> is a list of characters
separated by (optional) commas. The character is `a` to `z` or `A` to `Z` or
`\alpha` to `\omega`.

If you set a character by `\rmchars` globally and you want to print it in italic
locally then use `\mit`, for example `{\mit e}` prints $e$.

Several Greek letters have their variant shape:
`\epsilon`~$\epsilon$, `\varepsilon`~$\varepsilon$,
`\sigma`~$\sigma$, `\varsigma`~$\varsigma$,
`\phi`~$\phi$, `\varphi`~$\varphi$,
`\theta`~$\theta$, `\vartheta`~$\vartheta$,
`\pi`~$\pi$, `\varpi`~$\varpi$,
`\kappa`~$\kappa$, `\varkappa`~$\varkappa$,
`\rho`~$\rho$, `\varrho`~$\varrho$,
`\Theta`~$\Theta$, `\varTheta`~$\varTheta$.
Maybe, there is a tradition of usage variant shapes instead of standard ones
in your mathematics field. Then you can use
\^`\vargreek``{<list>}`, where <list> includes the list of no-var control
sequences for these letters (separated by optional comma).
For example `\vargreek{\epsilon \phi \rho}` causes that `\epsilon` is
printed as $\varepsilon$, `\phi` as $\varphi$ and `\rho` as $\varrho$.

If you want to declare a Greek letter by both `\vargreek` and `\rmchars`,
use `\rmchars` first.

The package provides two options `rmchars` and `vargreek`. The equation
sign must follow and then the `{<list>}` with syntax mentioned above. For example
`\mathsetup{vargreek={\epsilon,\rho}}`.

\sec[ibrackets] Intelligent brackets

Some mathematicians write open intervals like this: $\left]0,1\right[$. But
\TeX/ is not ready (by default) to set proper spaces around these symbols,
because `[` is set as `\mathopen` and `]` is set as `\mathclose` atom. When
\^`\ibrackets` is declared, then the characters `[` and `]` are more intelligent:
the spaces around then are correct in both cases: `$x\in [0,1]$` and
`$x\in ]0,1[$`. See `ibrackets` \LaTeX/ package for more detail.

\sec[multiprime] Double, triple, quadruple primes

\def\tprime{\hbox to.5em{\tt\hss'\kern-3.7pt'\kern-3.7pt'\hss}}

The single quotation character is used as derivation symbol, for example
`$f'$`. It is defined (in plain \TeX/ and in \OpTeX/ too) as a math-active
character which internally does `^\prime`. Moreover it checks if another
prime symbol follows like in this example: `$f'''$`. Then the macro does a
bit more work (we don't dive to details here). On the other hand, the double
prime (or triple or quadruple) symbols are provided in OpenType math fonts
and they are not defined as active macros. The reason is that these symbols
are shifted to the right position by default in their text-style sizes. So,
we can write `$f`\tprime`$` and we get~$f‴$. But the concept introduced by
D. Knuth works too: `$f^`\tprime`$` gives $f^‴$. The reason it works is that
the script and scriptscript style sizes of these symbols are implemented in
the OpenType font similarly like the original `\prime` symbol drawn by D.
Knuth in Computer Modern fonts (i.e. they are bigger and at the baseline).

This mixed concept provided by fonts brings into a problem: if the `f`{\tprime}
is used in script style, then we get unaccepted result. For example
`$f`\tprime`\over2$` gives $f‴\over2$. Of course, we can use `$f^`\tprime`\over2$`
but previous notation is more natural. If you are using `$f`\tprime`$` etc.
in your \TeX/ source in various sizes, you can use the option `multiprimes`
or use the \^`\multiprimes` macro. It sets the symbols for double, triple and
quadruple primes as active characters and they are defined as `^` followed
by the character. Now, the notation `$f`\tprime`$` works in all sizes, but
notation `$f^`\tprime`$` doesn't work.

\sec[flexipa] Flexible partial symbol $\partial$

Classical \TeX/ with Computer Modern fonts uses slanted `\partial` symbol
$\mitpartial$. On the other hand, default setting of Unicode math gives
upright `\partial` $\rm\partial$ but six variants of this symbol are provided:
roman (upright) \^`\mrmpartial` $\mrmpartial$, bold \^`\mbfpartial` $\mbfpartial$,
italic \^`\mitpartial` $\mitpartial$, bold italic \^`\mbfitpartial` $\mbfitpartial$,
bold sans serif \^`\mbfsanspartial` $\mbfsanspartial$, bold italic sans serif
\^`\mbfitsanspartial` $\mbfitsanspartial$.

When you declare \^`\flexipa` or \^`\flexiblepartial` or use the `flexipa`
package option, then the `\partial` symbols get italic variant as default
and behaves like others Greek symbols: it changes its variant according to
the `\rm`, `\it`, `\bf`, `\bi` selectors in math mode. You can declare what
variant of the `\partial` character will be shown at what selector. This can
be done by the \^`\partialsymbolvars`~`<default> <rm> <bf> <it> <bi>` macro.
Each of these five parameters can be `{rm}` or `{bf}` or `{it}` or `{bfit}`
or `{bfsans}` or `{bfitsans}`. For example the third parameter declares
what variant of the partial symbol is printed when `\bf` selector is used
in math mode. The `\flexipa` macro runs the following default setting:
\begtt
\partialsymbolvars {it} {rm} {bfsans} {it} {bfitsans}
\endtt
It means that default is italic variant and when `\rm` is selected then roman
(upright) variant is printed, when `\bf` is selected then bold sans serif
variant is printed etc.


\sec[textvars] Variables and digits from currently used text font

When Unicode math font is loaded then all variables and digits are printed
from it in math mode. If you are using text fonts with another visual
concept then you can see a differences when you use digits in text mode and in
math mode. You can specify \^`\textdigits` if you want to use digits from
current text `\rm` font in math and \^`\textvariables` if you want to use
variables from current text `\it` font in math.
You can set printing of
+−*/=<>\{([])\} from text `\rm` font in math by \^`\textmoremath`.
You can inspire from the \^`\textmoremath` macro and set more similar
characters from text font.

You have to load a text font family (using \o`\fontfam` for example) first and
use \^`\textdigits`, \^`\textvariables`, \^`\textmoremath` after it. This is
due to these macros reads {\em current} text \o`\rm` and \o`\it` fonts and set
them to math printing.

Note that we cannot avoid a visual incompatibility of parentheses when they
are use in the context \n`\left`, \n`\right`. These parentheses must be printed
from math font always because text font is unable to create bigger versions of
them.

The package provides the option `text={<list of words>}`, each <word> from the
<list> can be `digits` or `variables` or `moremath`. It runs corresponding macro(s)
described above. For example `\mathsetup{text=digits variables}` is equal to the
declaration of `\textdigits` `\textvariables`.

\sec Adding a new math alphabet from a text font

Each individual Unicode math font includes several math alphabets together: default
italic shape and others, which can be selected by `\rm`, `\it`, `\bf`,
`\bi`, `\tt`, `\cal`, `\frak`, `\bbchar` in math mode. For example, if you
use `\frak` in math mode, the fracture shapes from loaded Unicode math font are
used.

If you have a text font with a special alphabet, you can use it in your math formulas
by a new math selector declared by the \~`\mathselector` macro. For example:

\begtt
\fontfam[lm]
\load[math]
\font\missaali=[Missaali-Regular] % Bold fraktur
\mathselector \bfrak {\missaali} {\missaali} {} {}

Test: $a = {\frak A}, b = {\bfrak A}_{\bfrak C}$.
\endtt
This example declares a new math selector `\bfrak`. When `\bfrak` is used in math mode,
then the letters are rendered from `Missali-Regular.otf` font.

\^`\mathselector` `\sequence {<fontspec-A>} {<fontspec-B>} {<factor>} {<ffeatures>}`
declares a new font selector `\sequence` which can be used in math mode.
This selector selects a text font given by <fontspec-A> in normal math mode
and by <fontspec-B> in `\boldmath`.
If <fontspec-B> is empty then faked bold font declared by <fontspec-A>
is used for `\boldmath`. <fontspec-A> cannot be empty.

The <fontspec-A> and <fontspec-B> declare text fonts. They can be:
\begitems
* a font switch deflared by the `\font` primitive,
* an optional family selector followed by optional font modifiers
  followed by a variant selector.
  The actual font selected by this rule is configured as math selector.
\enditems

The <factor> parameter gives correction scaling factor according to the size
of the main Unicode math font. If it is empty then factor 1 is assumed.

The <ffeatures> parameter enables you to give font features used for loading
given fonts. If it is empty, then default font features
`mode=base;script=latn;` are used.

\^`\mathselector` `\sequence` declares internally a new math family with
the name `\sequence_fam`. The `\sequence` selector switches to this
family. So, the declared text fonts work in all math sizes but only for math
alphabets, Greek letters and digits, because other math symbols (+, =, etc.) are
bounded (by default) to the fixed math family 1 where Unicode math font is loaded.

Other example:
\begtt
\fontfam[lm]
\mathselector \textit {\it} {\bi} {} {}
   $AVA$         -- default italic variables from math font.\par
   $\it AVA$     -- default italic letters from math font.\par
   $\textit AVA$ -- italic letters from text font.
\endtt
You will probably see no difference between these three examples. Where is
the difference? `$AVA$` uses italic shapes from the
Unicode math font, `script=math` is specified. Italic corrections between
characters are inserted. `$\it AVA$` uses the same shapes from the same math font,
but `script=latn`. This disables italic corrections between
characters and enables kerning and ligatures. But typical Unicode math font
doesn't include tables for kerning and ligatures. So, these features
typically don't work. Finally `$\textit AVA$` uses shapes from text font like
`{\it ABC}` in text mode. If the font has data for kerning and ligatures
(which is probably true) then you get this feature in math formulas.

When you re-declare `\rm`, `\it`, `bf`, `\bi` or `\tt` by the `\mathselector` macro,
then these selectors keep their meaning used in text mode but re-define
their behavior in math mode according to the declaration. For example
`\mathselector \it {\it} {\bi} {} {}` declares new behavior of `\it` in math mode
but `\it` is unchanged in text mode.


\sec Replacing all missing math characters from another font

If we load an additional math font by \o`\addUmathfont`, for example:
\begtt
\addUmathfont \xits {[XITSMath-Regular]}{} {[XITSMath-Bold]}{} {}
\endtt
then we can re-declare the code of arbitrary math character in such a way
that it is printed from this additional font. It can be done by \o`\mathchars`
provided by \OpTeX/, for example:
\begtt
\mathchars \xits {\leftdasharrow \updasharrow \rightdasharrow \downdasharrow}
\endtt
But this method enables to re-declare only selected characters. Maybe, you
want to re-declare {\em all} Unicode math characters which are missing in the main font.
This can be done by \^`\replacemissingchars`\,`<family>` provided by the
`math.opm`. For example
\begtt
\replacemissingchars \xits
\endtt
replaces all characters missing in the main font by characters from the
`\xits` declared by previous \o`\addUmathfont`.
The names of all replaced characters are printed in log file.
If the additional math font doesn't provide all Unicode math characters
then you can load a next additional math font using another \o`\addUmathfont` and do
\^`\replacemissingchars`\,`<family>` again. Only those characters not replaced
by previous steps are replaced.


\sec Final italic correction

{\bf Note:} {\em This issue was corrected in \LuaTeX/ version 1.24, so the
\^`\enablefic` is no longer needed. It prints only warning when \LuaTeX\,$\succeq$1.24
and does the following described feature when \LuaTeX\,$\prec$1.24. We will completely remove this
feature from future versions of math.opm package.}

Classical \TeX/ adds italic correction after each Ord atom with a single
letter from math italic font including the last one in inline-math. \LuaTeX/
and \OpTeX/ does the same only when classical `tfm` math fonts are used. When
you switch to Unicode math, the italic correction of the last glyph of the
inline-math list is lost, unfortunately. Try this:

\begtt
$T$' the italic correction after $T$ is inserted (classical fonts)

\fontfam[lm]
$T$' the italic correction after $T$ isn't inserted (Unicode fonts)
\bye
\endtt

This package provides the \^`\enablefic` command which enables the classical TeX
feature: the final italic correction of the inline-math list is automatically added.

When \^`\enablefic` (or `enablefic` option) is declared then you can control
the behavior of this feature by the \^`\finalitalcorr` register: if it is positive
then the feature is activated and if it is zero, the feature is deactivated.
The \^`\enablefic` macro sets \^`\finalitalcorr``=1`.


\sec Miscellaneous commands

I created various commands at the requests of users. They asked me to create
commands similar to ones from \LaTeX/ packages.

\^`\mathclap``{<formula>}` creates `{\hbox to0pt{\hss $<formula>$\hss}}` and
respects the math style.\nl
\^`\mathrlap``{<formula>}` and \^`\mathllap``{<formula>}` is \O`\rlap` and
\O`\llap` analogue of \^`\mathclap`.


\sec[pkgtemplate] General recommendation for writing \OpTeX/ packages

This section has nothing common with the subject of this package but this package
can serve as inspiration for another package writers. It should be a template
for another `<pkg>.opm` files. We emphasize several principles here.
The basic information can be found in
\ulink[https://petr.olsak.net/ftp/olsak/optex/optex-doc.pdf\#ref:basic-code]
{section 2.2} of the \OpTeX/ manual.
Try to run\fnote{Run it three times because Table of contents and Index are created.}
\begtt
optex -jobname math-doc '\docgen math'
\endtt
for creating this documentation. You can see (from the log file) that the
`math.opm` is read four times during this process. First one is due to
\o`\docgen`~`math`. It skips the part before \o`\_endcode` and searches the
following {`\_doc...\_cod`} pair in the file and processes it (see the end
of the file `math.opm`). The macros and main instruction about generating
toc, index, etc.\ are here. First instruction is \o`\load``[doc,math]` which
initializes `doc` mode of \OpTeX/ and loads `math.opm` secondly because we
want to show some effects provided by this package. Then there is
\o`\printdoctail`~`math.opm` which loads the `math.opm` again and prints the
documentation starting from \o`\_endcode`. Finally, there is
\o`\printdoc`~`math.opm` which prints the codes mixed by the documentation
text inside pairs {`\_doc...\_cod`}. This causes the fourth loading of the
`math.opm` file.

The first part of the `math.opm` file looks like:
\begtt \catcode`\<=13 \adef!{\string}
% Optional comments

\_def\_<pkg>_version {<version-number>, <version-date>}
\_codedecl \pkgsequence {Doing the life more comfortable !<\_<pkg>_version>}
\_namespace{<pkg>}
\endtt
The `\_<pkg>_version` macro should be declared here. The macro should expand
to version number followed by version date. User can check
the package version simply by expanding this macro after the package is
loaded. And we want to have this data only at single place of the file.
You may check the log file if the text given by \o`\_codedecl` isn't too long
and isn't broken to more lines. Keeping single line is better because users can
`grep @:` on log file in order to get information of all loaded packages
and their version numbers.

The \o`\_namespace``{<pkg>}` opens the name space used by your package where all
`\.foo` are internally transformed to `\_<pkg>_foo`. Next part of the file
includes the code itself documented in {`\_doc...\_cod`} pairs. It is
finished by \o`\_endnamespace` which finalizes the scope where `\.foo` are
transformed to `\_<pkg>_foo` and by \o`\_endcode` which does \n`\endinput` when
the macros are load. Final part of the file after \o`\_endcode` can include
more detailed documentation.

If your package requires other packages then insert
\o`\load``[<package1>,<package2>]` after \o`\_codedecl` and before the the
\o`\_namespace` command. Each package uses its own namespace, so it is
important to load these packages before your \o`\_namespace` is opened.

If you have any idea of creating a macro package, you probably start with
experimental macros in the public namespace. It means that there are
`\def\mymacro` etc. Once such a code is working, you can include it to the
macro package introduced by \o`\_namespace``{<pkg>}`. You have to go through
your code carefully sequence per sequence and insert `_` or `.` in front of
their names. The \"`_`" prefix have to be used if the sequence is a primitive or
an \OpTeX/ macro and the \"`.`" prefix if it is your macro. So, the code fragment
`\def\mymacro` have to be rewritten to `\_def\.mymacro`. If the macro
`\mymacro` is intended for end users, then export it to the
public name space after it is defined by the \o`\_nspublic` `\mymacro ;` command.

Sometimes you may want to define a macro only in public namespace. Then
use prefix \o`\_newpublic` before your declaration, see declaration of
 \^`\sgn` in this package as an example. The reason is: if
a user has defined such a macro already then the warning is printed.
The user can read this warning and declare the macro after
`\load[<pkg>]` in this case.

   \_doc
   %  optex -jobname math-doc '\docgen math'
   \load [doc,math]
   \def\opurl{http://petr.olsak.net/ftp/olsak/optex/optex-doc.pdf}
   \def\tnurl{http://petr.olsak.net/ftp/olsak/optex/tex-nutshell.pdf}
   \def\trurl{http://petr.olsak.net/optex/optex-tricks.html}
   \def\tricklink[#1]#2{\ea\ulink \ea[\trurl\##1]{\OpTeX/ trick #2}}
   \def\exlink#1#2{\ea\ulink\expanded{[#2\csstring#1]{\hbox{\tt\string#1\,}}}}
   \def\o`#1`{\exlink#1{\opurl\#cs:^}}
   \def\O`#1`{\exlink#1{\opurl\#cs:}}
   \def\n`#1`{\exlink#1{\tnurl\#cs:}}
   \outlines 0
   \tracinglostchars=0

   \tit Macros for doing math more comfortably
   \hfill Version: \_math_version \par
   \centerline{\it Petr Olšák\/\fnotemark1, 2022, 2023, 2024, 2025, 2026}
   \fnotetext{\url{https://petr.olsak.net}}

   \notoc\nonum\sec Table of contents
   \maketoc
   \printdoctail math.opm % prints the documentation written after \_endcode
   \sec Implementation
   \printdoc     math.opm % prints \_doc...\_cod parts + code before \_endcode
   \nonum\sec Index
   \begmulti 3
      \tt \makeindex      % prints index in three columns
   \endmulti
   \bye
   \_cod

\endinput

0.23  2026-02-15  \enablefic prints warning only when LuaTeX v>1.23
0.22  2025-12-22  \multiprimes introduced
0.21  2025-11-30  \rmsbsp: \_primes correction
0.20  2025-06-10  \ibrackets introduced
0.19  2025-02-14  \mathselector introduced.
0.18  2025-01-15  \enablefic modifired.
0.17  2024-12-04  \mathsetup instead \mathset, \.unionly modified
0.16  2024-10-17  \mathclap, etc.  corrected.
0.15  2024-04-28  \_ as interval prefix added.
0.14  2024-03-18  \flexipa introduced.
0.13  2024-03-06  \enablefic introduced.
0.12  2024-03-02  \rmsbsp introduced.
0.11  2023-04-15: \bbigp introduced.
0.10  2023-03-12: \mathclap etc. introduced.
0.09  2023-03-11: mstyle, bstyle options introduced.
0.08  2023-01-28: \eqsystem introduced, \eqfil added.
0.07  2023-01-23: \sgn etc. defined as \protected\def.
      2023-01-15: \replacemissingchars: bug fixed
0.06, 2023-01-14: \rmchars, \vargreek, \bfserif introduced
0.05, 2023-01-07: \mathset introduced
0.04, 2022-12-26: \casesof used in \.fparamA
                  \singlevert declared instead \_singlevert (bug fix)
0.03, 2022-12-19: \cotg, \arccotg defined,
                  \autop: \mathclose{} replaced by \bgroup...\egroup,
                  \scriptspaces: Rel-Op, Bin-Op spacing added.
0.02, 2022-11-26: \smartvert introduced
0.01, 2022-11-25: released