%D \module
%D   [       file=math-ali,
%D        version=2008.10.20,
%D          title=\CONTEXT\ Math Macros,
%D       subtitle=Math Alignments,
%D         author={Hans Hagen, Taco Hoekwater \& Aditya Mahajan},
%D           date=\currentdate,
%D      copyright={PRAGMA ADE \& \CONTEXT\ Development Team}]
%C
%C This module is part of the \CONTEXT\ macro||package and is
%C therefore copyrighted by \PRAGMA. See mreadme.pdf for
%C details.

\writestatus{loading}{ConTeXt Math Macros / Math Alignments}

\unprotect

\registerctxluafile{math-ali}{autosuffix}

%D The code here has been moved from other files. Beware: the \MKII\ and \MKIV\ code
%D is not gathered in files with the same name. In the meantime this code has been
%D adapted to \MKIV\ but more is possible. The code is somewhat complicated by the
%D fact that alignments are tricky with rspect to tagging.

% export:
%
% alignment : ok
% cases     :
% matrix    : ok
% substack  :

%D \macros
%D   {definemathalignment, setupmathalignment, startmathalignment}
%D
%D Modules may provide additional alignment features. The following kind of plain
%D mechanisms are provided by the core.

\newtoks\t_math_align_a
\newtoks\t_math_align_b
\newtoks\t_math_align_c

\newskip\d_math_eqalign_distance
\newskip\d_math_eqalign_rulethickness

\protected\def\math_eqalign_distance
  {\relax
   \ifdim\d_math_eqalign_distance>\zeropoint
   % \hskip\d_math_eqalign_distance
     \tabskip\d_math_eqalign_distance
   \fi
   \mathalignmentparameter\c!separator
   \relax}

\mutable\def\displayopenupvalue{.25\bodyfontsize}

\def\math_build_eqalign
  {\scratchtoks\emptytoks
   \d_math_eqalign_distance\mathalignmentparameter\c!distance\relax
   \scratchcounterone\mathalignmentparameter\c!m
   \scratchcountertwo\mathalignmentparameter\c!n
   \etoksapp\scratchtoks{\the\t_math_align_a}%
   \scratchcounter\plusone
   \dorecurse{\numexpr\scratchcounterone*\scratchcountertwo-\plusone\relax}
     {\ifnum\scratchcounter=\scratchcountertwo
        \scratchcounter\plusone
        \etoksapp\scratchtoks{\math_eqalign_distance}%
        \etoksapp\scratchtoks{\global\c_math_eqalign_column\zerocount}%
      \else
        \advance\scratchcounter\plusone
      \fi
      \etoksapp\scratchtoks{\the\t_math_align_b}}%
   \etoksapp\scratchtoks{\the\t_math_align_c}}

\def\math_math_in_eqalign#1%
  {\startforceddisplaymath
   \tabskip\zeropoint
   \everycr\emptytoks
   {{}#1{}}%
   \stopforceddisplaymath}

\def\math_text_in_eqalign#1%
  {\startimath
   \tabskip\zeropoint
   \everycr\emptytoks
   #1%
   \stopimath}

\permanent\protected\def\eqalign#1% why no halign here, probably because of displaywidth
  {\emptyhbox % why no \dontleavehmode
   \mskip\thinmuskip
   \vcenter
     {\math_openup\displayopenupvalue % was: \openup\jot
      \mathsurround\zeropoint
      \ialign{%
        \strut
        \hfil
        \startforceddisplaymath{\aligncontent}\stopforceddisplaymath
        \aligntab
        \startforceddisplaymath{{}\aligncontent{}}\stopforceddisplaymath
        \hfil\crcr
        #1\crcr}%
     }%
   \mskip\thinmuskip}

% preamble is scanned for tabskips so we need the span to prevent an error message

\setnewconstant\eqalignmode\plusone

% use zeroskipplusfill

\def\math_prepare_r_eqalign_no
  {\t_math_align_a
     {\strut
      \tabskip\zeropoint
      \aligncontent % for picking up the number
      \aligntab
      \math_first_in_eqalign
      \hfil
      \math_left_of_eqalign
      \span
      \math_math_in_eqalign{\aligncontent}%
      \math_right_of_eqalign
      \tabskip\zeropoint}%
   \t_math_align_b
     {\aligntab
      \math_next_in_eqalign
      \math_left_of_eqalign
      \span
      \math_math_in_eqalign{\aligncontent}%
      \math_right_of_eqalign
      \tabskip\zeropoint}%
   \ifnum\mathraggedstatus=\plusone
     \t_math_align_c
       {\hfil
        \aligntab
        \span
        \math_text_in_eqalign{\aligncontent}%
        \tabskip\zeropoint}%
   \orelse\ifnum\mathraggedstatus=\plusthree
     \t_math_align_c
       {\hfil
        \tabskip\zeropoint\s!plus 1\s!fill
        \aligntab
        \span
        \math_text_in_eqalign{\aligncontent}%
        \tabskip\zeropoint}%
   \else
     \t_math_align_c
       {\hfil
        \tabskip\centering
        \aligntab
        \span
        \llap{\math_text_in_eqalign{\aligncontent}}%
        \tabskip\zeropoint}%
   \fi
   \math_build_eqalign
   \the\mathdisplayaligntweaks
   \tabskip\centering}

\def\math_prepare_l_eqalign_no  % \checkeddisplaymath
  {\t_math_align_a
     {\strut
      \tabskip\zeropoint
      \aligncontent % for picking up the number
      \aligntab
      \math_first_in_eqalign
      \hfil
      \math_left_of_eqalign
      \span
      \math_math_in_eqalign{\aligncontent}%
      \math_right_of_eqalign
      \tabskip\zeropoint}%
   \t_math_align_b
     {\aligntab
      \math_next_in_eqalign
      \math_left_of_eqalign
      \span
      \math_math_in_eqalign{\aligncontent}%
      \math_right_of_eqalign
      \tabskip\zeropoint}%
   \ifnum\mathraggedstatus=\plusone
     \t_math_align_c
       {\hfil
        \aligntab
        \kern-\displaywidth
        \span
        \rlap{\math_text_in_eqalign{\aligncontent}}
        \tabskip\displaywidth}%
   \orelse\ifnum\mathraggedstatus=\plusthree
     \t_math_align_c
       {\hfil
        \tabskip\zeropoint\s!plus 1\s!fill
        \aligntab
        \kern-\displaywidth
        \span
        \math_rlap{\math_text_in_eqalign{\aligncontent}}%
        \tabskip\displaywidth}%
   \else
     \t_math_align_c
       {\hfil
        \tabskip\centering
        \aligntab
        \kern-\displaywidth
        \span
        \rlap{\math_text_in_eqalign{\aligncontent}}%
        \tabskip\displaywidth}%
   \fi
   \math_build_eqalign
   \the\mathdisplayaligntweaks
   \tabskip\centering}

\def\math_halign_checked
  {\halign \ifcase\eqalignmode \or to \checkeddisplaywidth \fi}

\def\math_both_eqalign_no_normal#1#2%
  {\ifmmode
     \the\mathdisplayaligntweaks
     \vcenter\bgroup
     \enforced\let\math_finish_eqalign_no\egroup
   \else
     \enforced\let\math_finish_eqalign_no\relax
   \fi
   #1%
   \math_halign_checked\expandafter\bgroup\the\scratchtoks\crcr#2\crcr\egroup
   \math_finish_eqalign_no}

\installcorenamespace {mathalignlocation}

\defcsname\??mathalignlocation\v!top   \endcsname{\let\math_alignment_halign_method\halign\tpack}
\defcsname\??mathalignlocation\v!bottom\endcsname{\let\math_alignment_halign_method\halign\vpack}
\defcsname\??mathalignlocation\v!center\endcsname{\let\math_alignment_halign_method\halign\vcenter}

\let\math_alignment_halign_method\relax

\def\math_both_eqalign_no_aligned#1%
  {\let\math_alignment_halign_method\math_halign_checked
   \ifmmode
     \the\mathdisplayaligntweaks
     \global\mathnumberstatus\plusone
     \ifcase\mathraggedstatus
       \def\math_finish_eqalign_no{\crcr\egroup}%
     \else % we're in a mathbox
       \ifcsname\??mathalignlocation\mathalignmentparameter\c!location\endcsname
         \lastnamedcs % top|bottom|center as suggested by HM
       \else
         \vcenter
       \fi
       \bgroup
       \def\math_finish_eqalign_no{\crcr\egroup\egroup}%
     \fi
   \fi
   #1%
   \math_alignment_halign_method\expandafter\bgroup\the\scratchtoks\crcr}

\def\math_rlap#1%
  {\setbox\scratchbox\hbox{#1}%
   \ifdim\wd\scratchbox>\d_math_number_correction
     \global\d_math_number_correction\wd\scratchbox
   \fi
   \box\scratchbox
   \global\mathnumberstatus\plustwo}

\def\math_handle_eqalign_no_r_normal {\math_both_eqalign_no_normal \math_prepare_r_eqalign_no}
\def\math_handle_eqalign_no_l_normal {\math_both_eqalign_no_normal \math_prepare_l_eqalign_no}
\def\math_handle_eqalign_no_r_aligned{\math_both_eqalign_no_aligned\math_prepare_r_eqalign_no}
\def\math_handle_eqalign_no_l_aligned{\math_both_eqalign_no_aligned\math_prepare_l_eqalign_no}
\def\math_finish_eqalign_no          {\crcr\egroup}

\aliased\let\reqalignno\relax % just in case someone used that
\aliased\let\leqalignno\relax % just in case someone used that
\aliased\let\eqalignno \relax % just in case someone used that

%D Here we implement the user interface part. We start with basic math alignments:

\newcount      \c_math_eqalign_column
\newcount      \c_math_eqalign_row
\newconditional\c_math_eqalign_first

\newtoks \everymathalignment
\newtoks \everymathalignmentdone

\permanent\tolerant\protected\def\math_alignment_NN[#1]#*[#2]%
  {\aligntab
   \strc_formulas_place_number_nested{#1}{#2}}

\permanent\tolerant\protected\def\math_alignment_NR[#1]#*[#2]%
  {\aligntab
   \dostoptagged % finish cell
   \strc_formulas_place_number_nested{#1}{#2}%
   \math_number_right_of_eqalign
   \global\settrue\c_math_eqalign_first
   \crcr
   \noalign{\dostoptagged}} % finish row

\permanent\protected\def\math_alignment_NC
  {\relax
   \ifconditional\c_math_eqalign_first
     \ifx\p_math_alignment_number\v!auto
       \strc_formulas_place_number_nested{+}{}%
     \fi
     \global\setfalse\c_math_eqalign_first
   \fi
   \math_number_left_of_eqalign
   \aligntab}

\permanent\protected\def\math_alignment_EQ
  {\NC=}

\noaligned\tolerant\protected\def\math_common_TB[#1]%
  {\noalign{\blank[#1]}}

\installmacrostack\NC % maybe more to shared table definitions
\installmacrostack\NN % maybe more to shared table definitions
\installmacrostack\EQ % maybe more to shared table definitions
\installmacrostack\NR % maybe more to shared table definitions
\installmacrostack\BC % maybe more to shared table definitions
\installmacrostack\EC % maybe more to shared table definitions
\installmacrostack\TB % maybe more to shared table definitions

\appendtoks
    \push_macro_NC
    \push_macro_NN
    \push_macro_EQ
    \push_macro_NR
    \push_macro_TB
    \enforced\let\NC\math_alignment_NC
    \enforced\let\NN\math_alignment_NN
    \enforced\let\EQ\math_alignment_EQ
    \enforced\let\NR\math_alignment_NR
    \enforced\let\TB\math_common_TB
    \global\settrue\c_math_eqalign_first
\to \everymathalignment

\appendtoks
    \pop_macro_TB
    \pop_macro_NR
    \pop_macro_EQ
    \pop_macro_NN
    \pop_macro_NC
\to \everymathalignmentdone

\let\math_alignment_snap_start\relax
\let\math_alignment_snap_stop \relax

% % experimental:
%
% \def\math_alignment_snap_start
%   {\ifgridsnapping
%      \edef\p_math_alignment_grid{\mathalignmentparameter\c!grid}%
%      \ifx\p_math_alignment_grid\v!no\else
%        \snaptogrid[\p_math_alignment_grid]\vbox\bgroup
%      \fi
%    \fi}
%
% \def\math_alignment_snap_stop
%   {\ifgridsnapping
%      \ifx\p_math_alignment_grid\v!no\else
%        \egroup
%      \fi
%    \fi}
%
% % doesn't work well, so:

\let\math_alignment_snap_start\relax
\let\math_alignment_snap_stop \relax

% end of experimental

\newconditional\c_math_alignment_auto_number

% \begingroup not permitted ($$...assignments...\halign... ).. check in luametatex

% \definemathmatrix
%   [pmatrix]
%   [matrix:parentheses]
% % [align=1:right]
%   [align=all:right]
% % [align=2:right]
% % [align={1:left,2:middle,3:right}]

\permanent\tolerant\protected\def\math_alignment_start[#1]#*[#2]%
  {\edef\currentmathalignment{#1}%
   \ifarguments\or\or
     \setupmathalignment[#1][#2]% bad! ungrouped
   \fi
   \math_alignment_snap_start
   \the\everymathalignment
   \c_math_eqalign_row   \zerocount
   \c_math_eqalign_column\zerocount
   \edef\p_math_alignment_number{\mathalignmentparameter\c!number}%
   \processcommacommand
     [\mathalignmentparameter\c!align]%
     {\advance\c_math_eqalign_column\plusone\math_eqalign_set_column}% takes argument
   \global\c_math_eqalign_column\plusone
   \dostarttagged\t!math\empty
   \dostarttagged\t!mtable\currentmathalignment
   \numberedeqalign}

\def\math_alignment_stop % can be protected
  {\math_finish_eqalign_no
   \dostoptagged
   \dostoptagged
   \the\everymathalignmentdone
   \math_alignment_snap_stop}

\installcorenamespace{mathalignment}
\installcorenamespace{mathalignmentvariant}

\installcommandhandler \??mathalignment {mathalignment} \??mathalignment

\appendtoks
    \frozen\protected\instance\edefcsname\e!start\currentmathalignment\endcsname{\math_alignment_start[\currentmathalignment]}%
    \noaligned\frozen\protected\instance \defcsname\e!stop \currentmathalignment\endcsname{\math_alignment_stop}% can this be protected now?
\to \everydefinemathalignment

% to be tested
%
% \appendtoks
%               \frozen\instance\protected\defcsname\e!start\currentmathalignment\endcsname{\math_alignment_start[\currentmathalignment]}%
%     \noaligned\frozen\instance\protected\defcsname\e!stop \currentmathalignment\endcsname{\math_alignment_stop}%
% \to \everydefinemathalignment

\setupmathalignment
  [\c!n=2,
   \c!m=1,
   \c!distance=\emwidth,
   \c!grid=\v!math]

\definemathalignment[align]            % default case (this is what amstex users expect)
\definemathalignment[\v!mathalignment] % prefered case (this is cleaner, less clashing)

% special case.. in case one mistypes ..

\ifdefined \startalignment

    \pushoverloadmode

    \aliased\let\align_math_normal_start\startalign
    \aliased\let\align_math_normal_stop \stopalign

    \aliased\let\align_text_normal_start\startalignment
    \aliased\let\align_text_normal_stop \stopalignment

    \permanent\overloaded\protected\def\startalign
      {\ifmmode
         \enforced\let\stopalign\align_math_normal_stop % cannot be a protected def ... lookahead in align
         \expandafter\align_math_normal_start
       \orelse\ifinformula
         \enforced\let\stopalign\align_math_normal_stop
         \expandafter\align_math_normal_start
       \else
         \enforced\let\stopalign\align_text_normal_stop
         \expandafter\align_text_normal_start
       \fi}

    \aliased\let\stopalign\relax

    \permanent\overloaded\protected\def\startalignment
      {\ifmmode
         \enforced\let\stopalignment\align_math_normal_stop % cannot be a protected def ... lookahead in align
         \expandafter\align_math_normal_start
       \orelse\ifinformula
         \enforced\let\stopalignment\align_math_normal_stop % cannot be a protected def ... lookahead in align
         \expandafter\align_math_normal_start
       \else
         \enforced\let\stopalignment\align_text_normal_stop
         \expandafter\align_text_normal_start
       \fi}

    \aliased\let\stopalignment\relax

    \pushoverloadmode

\fi

%

\permanent\protected\def\numberedeqalign
  {\doifelse{\formulaparameter\c!location}\v!left
     \math_handle_eqalign_no_l_aligned
     \math_handle_eqalign_no_r_aligned}

\def\math_first_in_eqalign
  {\global\c_math_eqalign_column\plusone
   \global\advance\c_math_eqalign_row\plusone
   \dostarttagged\t!mtablerow \empty
   \dostarttagged\t!mtablecell\empty}

\def\math_next_in_eqalign
  {\global\advance\c_math_eqalign_column\plusone
   \dostoptagged % finish cell
   \dostarttagged\t!mtablecell\empty}

% \def\math_left_of_eqalign
%   {\ifcsname\??mathalignmentvariant\number\c_math_eqalign_column\endcsname
%      \ifcase\lastnamedcs \or \relax \or \hfill \or \hfill \fi
%    \fi}

% \def\math_right_of_eqalign
%   {\ifcsname\??mathalignmentvariant\number\c_math_eqalign_column\endcsname
%      \ifcase\lastnamedcs \or \hfill \or \relax \or \hfill \fi
%    \fi}

\def\math_left_of_eqalign
  {\ifcsname\??mathalignmentvariant\number\c_math_eqalign_column\endcsname
     \ifcase\lastnamedcs \or \relax \or \hfill \or \hfill \fi
   \orelse\ifcsname\??mathalignmentvariant\number\zerocount\endcsname
     \ifcase\lastnamedcs \or \relax \or \hfill \or \hfill \fi
   \fi}

\def\math_right_of_eqalign
  {\ifcsname\??mathalignmentvariant\number\c_math_eqalign_column\endcsname
     \ifcase\lastnamedcs \or \hfill \or \relax \or \hfill \fi
   \orelse\ifcsname\??mathalignmentvariant\number\zerocount\endcsname
     \ifcase\lastnamedcs \or \hfill \or \relax \or \hfill \fi
   \fi}

\newconditional\c_math_alignment_local_number % not used but when true puts in front (todo)

\def\math_number_right_of_eqalign
  {\ifcase\wd\b_strc_formulas_number\else
     \ifconditional\c_math_alignment_local_number
       \ifcase\c_strc_math_number_location\or\or
         \box\b_strc_formulas_number
       \fi
     \else
       \box\b_strc_formulas_number
     \fi
   \fi}

\def\math_number_left_of_eqalign
  {\ifcase\wd\b_strc_formulas_number\else
     \ifconditional\c_math_alignment_local_number
       \ifcase\c_strc_math_number_location\or
         \box\b_strc_formulas_number
       \fi
     \fi
   \fi}

% \def\math_eqalign_set_column#1% we could just add to the preamble (as with other alignments)
%   {\expandafter\chardef\csname\??mathalignmentvariant\number\c_math_eqalign_column\expandafter\expandafter\expandafter\endcsname
%      \ifcsname\??mathalignmentvariant#1\endcsname\lastnamedcs\else\zerocount\fi\relax}

% \def\math_eqalign_set_column_indeed[#1:#2:#3]% we don't really check for all (so * will do too) ... yet
%   {\expandafter\chardef\csname\??mathalignmentvariant\number
%      \ifcstok{#2}\emptytoks\c_math_eqalign_column\orelse\ifchknum#1\or#1\else\zerocount\fi
%    \endcsname
%    \ifcsname\??mathalignmentvariant#2\endcsname\lastnamedcs\else\zerocount\fi\relax}

\def\math_eqalign_set_column_indeed[#1:#2:#3]% we don't really check for all (so * will do too) ... yet
  {\ifcstok{#2}\emptytoks
     % current counter
   \orelse\ifchknum#1\or
     \c_math_eqalign_column#1\relax
   \else
     \c_math_eqalign_column\zerocount
   \fi
   \chardef\csname\??mathalignmentvariant\number\c_math_eqalign_column\endcsname
   \ifcsname\??mathalignmentvariant#2\endcsname\lastnamedcs\else\zerocount\fi\relax}

\def\math_eqalign_set_column#1%
  {\normalexpanded{\math_eqalign_set_column_indeed[#1::]}}

\letcsname\??mathalignmentvariant\v!normal\endcsname\zerocount
\letcsname\??mathalignmentvariant\v!left  \endcsname\plusone
\letcsname\??mathalignmentvariant\v!right \endcsname\plustwo
\letcsname\??mathalignmentvariant\v!middle\endcsname\plusthree

\permanent\protected\def\math_align_NR_generic[#1][#2]%
  {\strc_formulas_place_number_nested{#1}{#2}\crcr}

%D \starttyping
%D \placeformula[eqn0]\startformula \startalign[n=1] a\NR       \stopalign \stopformula See \in[eqn0]
%D \placeformula[eqn1]\startformula \startalign[n=1] a\NR       \stopalign \stopformula See \in[eqn1]
%D \placeformula      \startformula \startalign[n=1] a\NR[eqn2] \stopalign \stopformula See \in[eqn2]
%D \placeformula[eqn3]\startformula \startalign[n=1] a\NR[+]    \stopalign \stopformula See \in[eqn3]
%D \stoptyping

%D \startbuffer
%D \placeformula \startformula \eqalignno {
%D  a &= b & \formulanumber \cr
%D  c &= d \cr
%D    &= e \cr
%D    &= f & \formulanumber
%D } \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula \startalign
%D \NC  a \EQ b \NR[+]
%D \NC  c \EQ d \NR
%D \NC    \EQ f \NR[for:demo-a-1]
%D \NC    \EQ g \NR[for:demo-a-2][a]
%D \NC    \EQ h \NR[for:demo-a-3][b]
%D \NC    \EQ i \NR
%D \stopalign \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula \startalign
%D \NC a \EQ b \NR[+]
%D \NC c \EQ d \NR
%D \NC   \EQ f \NR
%D \NC   \EQ g \NR
%D \NC   \EQ h \NR
%D \NC   \EQ i \NR[+]
%D \stopalign \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula \startalign
%D \NC  a \NC \eq  b \NR[+]
%D \NC  c \NC \neq d \NR
%D \NC    \NC \neq f \NR[for:demo-b-1]
%D \NC    \NC \geq g \NR[for:demo-b-2][a]
%D \NC    \NC \leq h \NR[for:demo-b-3][b]
%D \NC    \NC \neq i \NR
%D \stopalign \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula \startalign[n=3,align={left,middle,right}]
%D \NC       l \NC = \NC r     \NR
%D \NC    left \NC = \NC right \NR
%D \stopalign \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula \startalign[n=3,align={right,middle,left}]
%D \NC       l \NC = \NC r     \NR
%D \NC    left \NC = \NC right \NR
%D \stopalign \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula \startalign[n=3,align={middle,middle,middle}]
%D \NC       l \NC = \NC r     \NR
%D \NC    left \NC = \NC right \NR
%D \stopalign \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula
%D \startformula
%D     \startalign[n=3,align={middle,middle,middle}]
%D         \NC a  \NC = \NC b  \NR[+]
%D         \NC 2a \NC = \NC 2b \NR
%D     \stopalign
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula
%D \startformulas
%D     \setupmathalignment[n=3,align={middle,middle,middle}]%
%D     \startformula
%D         \startalign
%D             \NC a  \NC = \NC b  \NR[+]
%D             \NC 2a \NC = \NC 2b \NR
%D         \stopalign
%D     \stopformula
%D     \startformula
%D         \startalign
%D             \NC a  \NC = \NC b  \NR[+]
%D             \NC 2a \NC = \NC 2b \NR
%D         \stopalign
%D     \stopformula
%D \stopformulas
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula
%D \startformulas
%D     \dorecurse{5}{\startformula
%D         \startalign[n=3,align={middle,middle,middle}]
%D             \NC a  \NC = \NC b  \NR[+]
%D             \NC 2a \NC = \NC 2b \NR
%D         \stopalign
%D     \stopformula}
%D \stopformulas
%D \stopbuffer
%D
%D \typebuffer \getbuffer

%D \macros
%D   {definemathcases, setupmathcases, startmathcases}
%D
%D Another wish \unknown

\installcorenamespace{mathcases}

\installcommandhandler \??mathcases {mathcases} \??mathcases

\setupmathcases
  [\c!distance=\emwidth,
   \c!strut=\v!yes, % new
  %\c!numberdistance=2.5\emwidth,
   \c!numberdistance=\zeropoint, % pending an extension wrt placement (Aditya/Hans)
   \c!left={\left\{\mskip\thinmuskip},
   \c!right={\right.}]

\appendtoks
    \frozen\instance\protected\edefcsname\e!start\currentmathcases\endcsname{\math_cases_start[\currentmathcases]}%
    \frozen\instance          \defcsname \e!stop \currentmathcases\endcsname{\math_cases_stop}%
\to \everydefinemathcases

% \permanent\protected\def\math_cases_NC_zero
%   {\math_cases_NC}
%
% \permanent\protected\def\math_cases_MC_zero
%   {\math_cases_NC
%    \ifmmode\else
%      \startimath
%      \enforced\let\math_cases_end_math\stopimath
%    \fi}
%
% \let\math_cases_end_math\relax
%
% \permanent\protected\def\math_cases_NR_zero
%   {\unskip
%    \math_cases_end_math
%    \aligntab
%    \global\enforced\let\math_cases_NC\math_cases_NC_first
%    \dodirectdoubleempty\math_cases_NR}
%
% \permanent\protected\def\math_cases_NC_first
%   {\global\enforced\let\math_cases_NC\math_cases_NC_second}
%
% \permanent\protected\def\math_cases_NC_second
%   {\math_cases_end_math\aligntab}
%
% \let\math_cases_NR\math_align_NR_generic
%
% \installmacrostack\math_cases_NC
%
% \let\math_cases_strut\relax
%
% \permanent\tolerant\protected\def\math_cases_start[#1]#*[#2]%
%   {\begingroup
%    \edef\currentmathcases{#1}%
%    \ifarguments\or\or
%      \setupcurrentmathcases[#2]%
%    \fi
%    \edef\p_strut{\mathcasesparameter\c!strut}%
%    \ifx\p_strut\v!yes
%      \enforced\let\math_cases_strut\strut
%    \else
%      \enforced\let\math_cases_strut\relax
%    \fi
%    \mathcasesparameter\c!left
%    \vcenter\bgroup
%    \push_macro_math_cases_NC
%    \enforced\let\MC\math_cases_MC_zero
%    \enforced\let\NR\math_cases_NR_zero
%    \enforced\let\TB\math_common_TB
%    \enforced\glet\math_cases_NC\math_cases_NC_first
%    \normalbaselines
%    \mathsurround\zeropoint
%    \everycr\emptytoks
%    \tabskip\zeropoint
%    \global\c_math_eqalign_column\plusone
%    \halign\bgroup
%      \startimath
%      \mathcasesparameter\c!style
%      \aligncontent
%      \stopimath
%      \hfil
%      \aligntab
%      \hskip\mathcasesparameter\c!distance\relax
%      \pop_macro_math_cases_NC
%      \math_cases_strut % looks better
%      \aligncontent
%      \hfil
%      \aligntab
%      \hskip\mathcasesparameter\c!numberdistance\relax
%    % \let\formuladistance\!!zeropoint
%      \span\math_text_in_eqalign{\aligncontent}%
%      \crcr} % todo: number
%
% % When we have just protected we get an extra row but we can no flag
% % this as a proper alignment related command which means that uit gets
% % expanded.
%
% \noaligned\permanent\protected\def\math_cases_stop
%   {\crcr
%    \egroup
%    \pop_macro_math_cases_NC
%    \egroup
%    \mathcasesparameter\c!right
%    \endgroup}

\let\math_cases_strut\relax

\newcount\c_math_cases_nc

\def\math_cases_NC_zero
  {\ifmmode\else\startimath\fi}

\def\math_cases_NC_one
  {\ifmmode\stopimath\fi
   \aligntab
   \ifmmode\else\startimath\fi}

\def\math_cases_NC_two
  {\ifmmode\stopimath\fi}

\def\math_cases_TC_zero
  {}

\def\math_cases_TC_one
  {\ifmmode\stopimath\fi
   \aligntab}

\permanent\protected\def\math_cases_NC
  {\ifcase\c_math_cases_nc
     \expandafter\math_cases_NC_zero
   \or
     \expandafter\math_cases_NC_one
   \or
     \expandafter\math_cases_NC_zero
   \else
     % error
   \fi
   \global\advance\c_math_cases_nc\plusone}

\permanent\protected\def\math_cases_TC
  {\ifcase\c_math_cases_nc
     \expandafter\math_cases_TC_zero
   \or
     \expandafter\math_cases_TC_one
   \or
     \expandafter\math_cases_TC_two
   \else
     % error
   \fi
   \global\advance\c_math_cases_nc\plusone}

\noaligned\tolerant\permanent\protected\def\math_cases_NR[#1]#*[#2]%
  {\unskip
   \ifmmode\stopimath\fi
   \aligntab
   \global\c_math_cases_nc\zerocount
   \math_align_NR_generic[#1][#2]}

\installglobalmacrostack\c_math_cases_nc

\permanent\tolerant\protected\def\math_cases_start[#1]#*[#2]%
  {\begingroup
   \edef\currentmathcases{#1}%
   \ifarguments\or\or
     \setupcurrentmathcases[#2]%
   \fi
   \edef\p_strut{\mathcasesparameter\c!strut}%
   \ifx\p_strut\v!yes
     \enforced\let\math_cases_strut\strut
   \else
     \enforced\let\math_cases_strut\relax
   \fi
   \push_macro_c_math_cases_nc
   \mathcasesparameter\c!left
   \vcenter\bgroup
   \enforced\let\MC\math_cases_NC
   \enforced\let\NC\math_cases_NC
   \enforced\let\NR\math_cases_NR
   \enforced\let\TC\math_cases_TC
   \enforced\let\TB\math_common_TB
   \normalbaselines
   \mathsurround\zeropoint
   \everycr\emptytoks
   \tabskip\zeropoint
   \global\c_math_eqalign_column\plusone
   \global\c_math_eqalign_row\plusone
   \global\c_math_cases_nc\zerocount
   \halign\bgroup
     \ifmmode\else\startimath\fi
     \mathcasesparameter\c!style
     \aligncontent
     \ifmmode\stopimath\fi
     \hfil
     \aligntab
     \hskip\mathcasesparameter\c!distance\relax
     \math_cases_strut % looks better
     \aligncontent
     \hfil
     \aligntab
     \hskip\mathcasesparameter\c!numberdistance\relax
     \span\math_text_in_eqalign{\aligncontent}%
     \crcr} % todo: number

\noaligned\permanent\protected\def\math_cases_stop
  {\crcr
   \egroup
   \egroup
   \mathcasesparameter\c!right
   \pop_macro_c_math_cases_nc
   \endgroup}

\definemathcases[cases]
\definemathcases[\v!mathcases]

%D \startbuffer
%D \placeformula \startformula \startcases
%D \NC 2 \NC $ y > 0 $ \NR
%D \NC 7 \NC $ x = 7 $ \NR[+]
%D \NC 4 \NC otherwise \NR
%D \stopcases \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula x \startcases
%D \NC 2 \NC $ y > 0 $ \NR[+]
%D \NC 7 \NC $ x = 7 $ \NR
%D \NC 4 \NC otherwise \NR
%D \stopcases \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula \startcases
%D \NC 2 \NC $ y > 0 $ \NR
%D \NC 7 \NC $ x = 7 $ \NR
%D \NC 4 \NC otherwise \NR
%D \stopcases \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \placeformula \startformula x \startcases
%D \NC 2 \NC $ y > 0 $ \NR
%D \NC 7 \NC $ x = 7 $ \NR
%D \NC 4 \NC otherwise \NR
%D \stopcases \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer

%D \macros
%D   {definemathmatrix, setupmathmatrix, startmathmatrix}
%D
%D Yet another one \unknown. This time we implement the lot a bit
%D different which is a side effect of getting the tagging right. In
%D retrospect the main alignment could be done this way but \unknown

\installcorenamespace{mathmatrix}

\installcommandhandler \??mathmatrix {mathmatrix} \??mathmatrix

\setupmathmatrix
  [\c!distance=\emwidth,
   \c!left=,
   \c!right=,
   \c!align=\v!middle,
   \c!rulecolor=,
   \c!rulethickness=\linewidth]

\appendtoks
    \frozen\instance\protected\edefcsname\e!start\currentmathmatrix\endcsname{\math_matrix_start[\currentmathmatrix]}%
    % \noaligned\protected should work here:
    \frozen\instance          \defcsname \e!stop \currentmathmatrix\endcsname{\math_matrix_stop}% no u else lookahead problem
\to \everydefinemathmatrix

\def\math_matrix_start_table
  {\global\c_math_eqalign_column\zerocount
   \global\c_math_eqalign_row\zerocount
   \dostarttagged\t!math\empty
   \dostarttagged\t!mtable\empty}

\def\math_matrix_stop_table
  {\dostoptagged
   \dostoptagged}

% \def\math_matrix_start_row
%   {\noalign{\global\c_math_eqalign_column\zerocount}%
%    \dostarttagged\t!mtablerow\empty}
%
% \def\math_matrix_stop_row
%   {\dostoptagged}

\def\math_matrix_start_row
  {\beginlocalcontrol
   \global\c_math_eqalign_column\zerocount
   \global\advance\c_math_eqalign_row\plusone
   \dostarttagged\t!mtablerow\empty
   \endlocalcontrol}

\def\math_matrix_stop_row
  {\beginlocalcontrol
   \dostoptagged
   \endlocalcontrol}

\protected\def\math_matrix_start_cell
  {\dostarttagged\t!mtablecell\empty
   \hss
   \math_left_of_eqalign
   \startimath
   \math_matrix_set_style
   \tabskip\zeropoint
   \everycr\emptytoks}

\protected\def\math_matrix_stop_cell
  {\stopimath
   \math_right_of_eqalign
   \hss
   \dostoptagged}

% We could construct a preamble with alignment and such embedded but the number
% of matrices with many rows is normally so low that it doesn't pay of at all.

\newconditional\c_math_matrix_first
\newconstant   \c_math_matrix_anchor_mode

% enabled    : 1
% left/both  : 2
% right/both : 4

% \c_math_matrix_anchor_mode3

\permanent\protected\def\setmathmatrixanchoring[#1]%
  {\c_math_matrix_anchor_mode\zerocount
   \processaction
     [#1]
     [    \v!left=>\bitwiseflip\c_math_matrix_anchor_mode\numexpr\plusone+\plustwo\relax,
         \v!right=>\bitwiseflip\c_math_matrix_anchor_mode\numexpr\plusone+\plusfour\relax,
          \v!both=>\bitwiseflip\c_math_matrix_anchor_mode\numexpr\plusone+\plustwo+\plusfour\relax,
           \v!yes=>\bitwiseflip\c_math_matrix_anchor_mode\numexpr\plusone]}

\def\math_matrix_anchor
  {\ifbitwiseand\c_math_matrix_anchor_mode\plusone
     \markanchor{matrix}{\numexpr\c_math_eqalign_column+1\relax}\c_math_eqalign_row
   \fi}

\protected\def\math_matrix_distance
  {\relax
   \ifdim\d_math_eqalign_distance>\zeropoint
     \hskip.5\d_math_eqalign_distance
   \fi
   \math_matrix_anchor
   \ifdim\d_math_eqalign_distance>\zeropoint
     \hskip.5\d_math_eqalign_distance
   \fi
   \relax}

\protected\def\math_matrix_distance_first
  {\relax
   \ifbitwiseand\c_math_matrix_anchor_mode\plusone
     \math_matrix_anchor
   \fi
   \ifdim\d_math_eqalign_distance>\zeropoint
     \ifbitwiseand\c_math_matrix_anchor_mode\plustwo
       \hskip.5\d_math_eqalign_distance
     \fi
   \fi
   \relax}

\protected\def\math_matrix_distance_last
  {\relax
   \ifdim\d_math_eqalign_distance>\zeropoint
     \ifbitwiseand\c_math_matrix_anchor_mode\plusfour
       \hskip.5\d_math_eqalign_distance
     \fi
   \fi
   \ifbitwiseand\c_math_matrix_anchor_mode\plusone
     \math_matrix_anchor
   \fi
   \relax}

\def\math_matrix_preamble
  {\math_matrix_strut
   \math_matrix_distance_first
   \global\advance\c_math_eqalign_column\plusone
   \math_matrix_start_cell
     \aligncontent
   \math_matrix_stop_cell
   \aligntab
   \aligntab
   \math_matrix_distance
   \global\advance\c_math_eqalign_column\plusone
   \math_matrix_start_cell
     \aligncontent
   \math_matrix_stop_cell}

\permanent\protected\def\math_matrix_NR
  {\aligntab\omit
   \math_matrix_distance_last
   \math_matrix_stop_row
   \math_matrix_pickup
   \crcr
   \math_matrix_start_row}

\permanent\protected\def\math_matrix_NC
  {\ifconditional\c_math_matrix_first
     \expandafter\math_matrix_NC_yes
   \else
     \expandafter\math_matrix_NC_nop
   \fi}

\permanent\protected\def\math_matrix_pickup{\global\settrue \c_math_matrix_first}
\permanent\protected\def\math_matrix_NC_yes{\global\setfalse\c_math_matrix_first}
\permanent\protected\def\math_matrix_NC_nop{\aligntab} % avoids lookahead

% \def\math_matrix_stop_wrapup
%   {\crcr
%    \strut
%    \crcr
%    \noalign{\vskip-\struthtdp}}

\def\math_matrix_check_rule_step#1%
  {\doifelsenumber{#1}
     {\scratchdimen#1\d_math_eqalign_rulethickness}
     {\edef\p_rulecolor{#1}}}

\def\math_matrix_check_rule[#1]%
  {\d_math_eqalign_rulethickness\mathmatrixparameter\c!rulethickness\relax
   \scratchdimen\d_math_eqalign_rulethickness
   \edef\p_rulecolor{\mathmatrixparameter\c!rulecolor}%
   \iftok{#1}\emptytoks\else
     \rawprocesscommalist[#1]\math_matrix_check_rule_step
   \fi
   \ifempty\p_rulecolor\else
     \dousecolorparameter\p_rulecolor
   \fi}

\noaligned\permanent\tolerant\protected\def\math_matrix_HL[#1]#*%
  {\noalign\bgroup
     \math_matrix_check_rule[#1]%
     \divide\scratchdimen\plustwo
     \autorule\s!height\scratchdimen\s!depth\scratchdimen\relax
   \egroup}

\permanent\tolerant\protected\def\math_matrix_VL[#1]#*%
  {\NC
     \math_matrix_check_rule[#1]%
     \divide\d_math_eqalign_distance\plustwo
     \hskip-\d_math_eqalign_distance
     \autorule\s!width\scratchdimen\relax
     \hskip-\d_math_eqalign_distance
   \NC}

\newtoks\everymathmatrix

\appendtoks
   \enforced\let\NR\math_matrix_NR
   \enforced\let\NC\math_matrix_NC
   \enforced\let\MC\math_matrix_NC
   \enforced\let\HL\math_matrix_HL
   \enforced\let\VL\math_matrix_VL
   \enforced\let\TB\math_common_TB
\to \everymathmatrix

\def\math_matrix_start_processing
  {\dontleavehmode
   \bgroup
   \tabskip\zeropoint
   \math_matrix_pickup
   \the\everymathmatrix
   %
 % \enforced\let\endmath\relax
   %
   \setbox\nextbox\vbox\bgroup
   \math_matrix_start_table
   \halign \bgroup
     % preamble
     \span\math_matrix_preamble
     % done
     \crcr
     \math_matrix_start_row}

\def\math_matrix_stop_processing
  {%\math_matrix_stop_wrapup % optional
   \math_matrix_stop_row
   \egroup
   \math_matrix_stop_table
   \egroup
   \mathmatrixleft
   \math_matrix_finish_nextbox
   \mathmatrixright
   \egroup}

\let\math_matrix_strut    \strut
\let\math_matrix_set_style\relax

\def\math_matrix_check_settings
  {\edef\p_strut{\mathmatrixparameter\c!strut}%
   \ifx\p_strut\v!no
     \enforced\let\math_matrix_strut\relax
   \else
     \enforced\let\math_matrix_strut\strut
     \ifx\p_strut\v!yes\else
       \spacing\p_strut
     \fi
   \fi
   \d_math_eqalign_distance\mathmatrixparameter\c!distance\relax
 % \d_math_eqalign_rulethickness\mathmatrixparameter\c!rulethickness\relax
 % \edef\p_rulecolor{\mathmatrixparameter\c!rulecolor}
   \edef\math_matrix_set_style{\mathmatrixparameter\c!style}}

\def\math_matrix_set_defaults
  {\normalbaselines % hm, spacing ?
   \mathsurround\zeropoint
   \tabskip\zeropoint}

\def\math_matrix_set_columns_step
  {\advance\c_math_eqalign_column\plusone
  %\c_math_matrix_columns\c_math_eqalign_column
   \math_eqalign_set_column}

\def\math_matrix_set_columns
  {\c_math_eqalign_column\zerocount
   \rawprocesscommacommand[\mathmatrixparameter\c!align]\math_matrix_set_columns_step}

\newcount\c_math_eqalign_column_saved
\newcount\c_math_eqalign_row_saved

% \installglobalmacrostack\c_math_matrix_first

\tolerant\protected\def\math_matrix_start[#1]#*[#2]%
  {\begingroup
   \globalpushmacro\c_math_matrix_first % hm, does that work?
   \c_math_eqalign_column_saved\c_math_eqalign_column
   \c_math_eqalign_row_saved\c_math_eqalign_row
   \globalpushmacro\c_math_eqalign_first
   \edef\currentmathmatrix{#1}%
   \setupcurrentmathmatrix[#2]%
   \math_matrix_check_settings
   \math_matrix_set_defaults
   \math_matrix_set_columns
   \math_matrix_start_processing}

\def\math_matrix_stop
  {\math_matrix_stop_processing
   \globalpushmacro\c_math_eqalign_first
   \global\c_math_eqalign_column\c_math_eqalign_column_saved
   \global\c_math_eqalign_row\c_math_eqalign_row_saved
   \globalpopmacro\c_math_matrix_first
   \endgroup}

% vcenter:
%
% delta     = (height(v) + depth(v))/2
% axis      = math_axis_size(cur_size)
% height(v) = delta + axis
% depth(v)  = delta - axis

\installcorenamespace{mathmatrixalignlocation}

\mutable\let\mathmatrixleft \empty % experimental hook
\mutable\let\mathmatrixright\empty % experimental hook

\defcsname\??mathmatrixalignlocation\v!top   \endcsname{\raise\dimexpr(\nextboxdp-\nextboxht)/2 +\mathaxisheight\mathstyle\relax}
\defcsname\??mathmatrixalignlocation\v!high  \endcsname{\raise\dimexpr(\nextboxdp-\nextboxht)/2\relax}
\defcsname\??mathmatrixalignlocation\v!center\endcsname{\relax}
\defcsname\??mathmatrixalignlocation\v!lohi  \endcsname{\relax}
\defcsname\??mathmatrixalignlocation\v!normal\endcsname{\relax}
\defcsname\??mathmatrixalignlocation\v!bottom\endcsname{\lower\dimexpr(\nextboxdp-\nextboxht)/2 +\mathaxisheight\mathstyle\relax}
\defcsname\??mathmatrixalignlocation\v!low   \endcsname{\lower\dimexpr(\nextboxdp-\nextboxht)/2\relax}

\def\math_matrix_finish_nextbox
  {\begincsname\??mathmatrixalignlocation\mathmatrixparameter\c!location\endcsname\hbox\bgroup
     \normalstartimath
     \mathmatrixparameter\c!left
     \vcenter{\box\nextbox}%
     \mathmatrixparameter\c!right
     \normalstopimath
   \egroup}

\definemathmatrix[matrix]
\definemathmatrix[\v!mathmatrix]

%D \startbuffer
%D \placeformula \startformula[-] \startmatrix
%D \NC 1 \NC x \NC a \NR
%D \NC 2 \NC y \NC b \NR
%D \NC 3 \NC z \NC c \NR
%D \stopmatrix \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \definemathmatrix[bmatrix][left={\left[\mskip\thinmuskip},right={\mskip\thinmuskip\right]},strut=1.25]
%D
%D \startbuffer
%D \placeformula \startformula[-] \startbmatrix
%D \NC 1 \NC x \NC a \NR
%D \NC 2 \NC y \NC b \NR
%D \NC 3 \NC z \NC c \NR
%D \stopbmatrix \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D Taco added some code (dedicated to Aditya Mahajan) that gives more
%D control over aligments:

%D \startbuffer
%D \startformula
%D   \startmatrix
%D    \NC a + x \NC = \NC a + d \NR
%D    \NC y     \NC = \NC d     \NR
%D   \stopmatrix
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer

%D \startbuffer
%D \startformula
%D   \startmatrix [distance=3pt,align={right,left}]
%D    \NC a + x \NC = a + d \NR
%D    \NC y     \NC = d     \NR
%D   \stopmatrix
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer

%D \startbuffer
%D \startformula
%D   \startmatrix [left=\left(,right=\right)]
%D    \NC a + x \NR
%D    \NC y    \NR
%D   \stopmatrix
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D A bit more complex code:
%D
%D \startbuffer
%D \startformula
%D    \text{Let }{\cal R} = \bigcup_{P_{X_1},P_{X_2}}
%D    \left\{ (R_1, R_2) :
%D    \startmatrix[distance=1em,align={left,left,right}]
%D      \NC R_1        \NC < I(X_1 ; Y \mid X_2)      \NC R_1       \NR
%D      \NC \hfill Q_2 \NC < I(X_2 ; Y \mid X_1)      \NC R_2       \NR
%D      \NC R_1 + R_2  \NC < I(X_1 ; Y)               \NC R_1 + R_2 \NR
%D    \stopmatrix
%D    \right\}
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer

%D \macros
%D   {startmatrices}
%D
%D Just a handy keystroke safer:

\permanent\protected\def\startmatrices
  {\begingroup
   \setupmathmatrix}

\permanent\protected\def\stopmatrices
  {\endgroup}

%D \startbuffer
%D \startformula
%D   \startmatrix[left={\left(},right={\right)}]
%D     \NC A \NC B \NR \NC C \NC D \NR
%D   \stopmatrix
%D   =
%D   \startmatrix[left={\left(},right={\right)},location=low]
%D     \NC A \NC B \NR \NC C \NC D \NR
%D   \stopmatrix
%D   =
%D   \startmatrix[left={\left(},right={\right)},location=high]
%D     \NC A \NC B \NR \NC C \NC D \NR
%D   \stopmatrix
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \startformula
%D   \startmatrices[left={\left(},right={\right)}]
%D     \startmatrix
%D       \NC A \NC B \NR \NC C \NC D \NR
%D     \stopmatrix
%D     =
%D     \startmatrix[location=bottom]
%D       \NC A \NC B \NR \NC C \NC D \NR
%D     \stopmatrix
%D     =
%D     \startmatrix[location=top]
%D       \NC A \NC B \NR \NC C \NC D \NR
%D     \stopmatrix
%D   \stopmatrices
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer  % does not run well: \getbuffer

%D Handy for the \type {m-matrix} module:

\permanent\tolerant\protected\def\startnamedmatrix[#1]#*[#2]%
  {\begingroup
   \edef\currentmathmatrix{#1}%
   \setupcurrentmathmatrix[#2]%
   \math_matrix_start[\currentmathmatrix]}

\noaligned\permanent\protected\def\stopnamedmatrix
  {\math_matrix_stop
   \endgroup}

%D The following code is derived from Aditya's simplematrix prototype but adapted to
%D regular mathmatrices:

% We keep this as reference:
%
% \def\math_matrix_simple_row#1%
%   {\rawprocesscommalist[#1]\math_matrix_simple_col
%    \toksapp\scratchtoks{\NR}}
%
% \def\math_matrix_simple_col#1%
%   {\toksapp\scratchtoks{\NC#1}}
%
% \permanent\tolerant\protected\def\math_matrix_simple[#1]#*[#2]#:#3%
%   {\begingroup
%    \edef\currentmathmatrix{#1}%
%    \setupcurrentmathmatrix[#2]%
%    \scratchtoks\emptytoks
%    \processlist[];\math_matrix_simple_row[#3]%
%    \math_matrix_start[\currentmathmatrix]%
%    \the\scratchtoks
%    \math_matrix_stop
%    \endgroup}

%D With a little help from \LUA\ we now have this:
%D
%D \startbuffer
%D \definemathmatrix [Pmatrix] [matrix:parentheses]
%D   [align={all:right},
%D    simplecommand=Pmatrix]
%D
%D \definemathmatrix [Tmatrix] [Pmatrix]
%D   [action=transpose,
%D    simplecommand=Tmatrix]
%D
%D \definemathmatrix [Nmatrix] [Pmatrix]
%D   [action=negate,
%D    simplecommand=Nmatrix]
%D
%D \startformula
%D     \Pmatrix{ -1, 2, 3; 4,-5, 6; 7, 8,-9 } \neq
%D     \Tmatrix{ -1, 2, 3; 4,-5, 6; 7, 8,-9 } \neq
%D     \Nmatrix{ -1, 2, 3; 4,-5, 6; 7, 8,-9 }
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer

\permanent\tolerant\protected\def\math_matrix_simple[#1]#*[#2]#:#3%
  {\begingroup
   \edef\currentmathmatrix{#1}%
   \setupcurrentmathmatrix[#2]%
   \math_matrix_start[\currentmathmatrix]%
   \clf_simplematrix{\mathmatrixparameter\c!action}{#3}%
   \math_matrix_stop
   \endgroup}

%D We hook it into the normal mathmatrix code:

\appendtoks
    \edef\p_simplecommand{\mathmatrixparameter\c!simplecommand}%
    \ifempty\p_simplecommand\else
        \frozen\protected\instance\edefcsname\p_simplecommand\endcsname{\math_matrix_simple[\currentmathmatrix]}%
    \fi
\to \everydefinemathmatrix

%D And predefine some matrices:

\definemathmatrix[matrix:parentheses][\c!left={\left(\mskip\thinmuskip},\c!right={\mskip\thinmuskip\right)},\c!align=\v!middle]
\definemathmatrix[matrix:brackets]   [\c!left={\left[\mskip\thinmuskip},\c!right={\mskip\thinmuskip\right]},\c!align=\v!middle]
\definemathmatrix[matrix:bars]       [\c!left={\left|\mskip\thinmuskip},\c!right={\mskip\thinmuskip\right|},\c!align=\v!middle]

\definemathmatrix[thematrix][matrix:parentheses][\c!simplecommand=thematrix]

%D \startbuffer
%D \startformula
%D \thematrix{1,2,3,4;5,6,7,8;9,10,11,12}
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer
%D
%D \startbuffer
%D \startformula
%D \startthematrix
%D     \NC 1\NC 2\NC 3\NC 4\NR
%D     \NC 5\NC 6\NC 7\NC 8\NR
%D     \NC 9\NC10\NC11\NC12\NR
%D \stopthematrix
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer

%D \macros
%D   {startintertext}
%D
%D Preliminary feature:
%D
%D {\em example code}
%D
%D The intertext commands have to be expandable (in aligment lookahead) so
%D we cannot use \type {\protected}.

\permanent\def\startintertext#1\stopintertext
  {\noalign{\math_intertext{#1}}}

\permanent\let\stopintertext\relax

\permanent\def\intertext#1%
  {\noalign{\math_intertext{#1}}}

\protected\def\math_intertext#1%
  {\penalty\postdisplaypenalty
   \afterdisplayspace
   \vbox{\forgetall\noindent#1\par}%
   \penalty\predisplaypenalty
   \beforedisplayspace}

%D \macros
%D   {substack}
%D
%D Preliminary code:
%D
%D \startbuffer
%D \startformula
%D    \sum_{%
%D      \startsubstack
%D       i = 1 \NR
%D       i \neq n \NR
%D       i \neq m
%D       \stopsubstack
%D     }a_i
%D \stopformula
%D \stopbuffer
%D
%D \getbuffer which was typed as \typebuffer
%D
%D Notice that these macros give the correct spacing for
%D subscripts. Compare for example
%D
%D \startbuffer
%D \startformula
%D \sum_{\startsubstack a \NR b \NR \stopsubstack}
%D \text{ and }
%D \sum_{\scriptstyle a \atop \scriptstyle}
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer which gives \getbuffer

% no tagging yet : how is it supposed to be coded?

\permanent\protected\def\startsubstack
  {\begingroup
   \vcenter\bgroup
   \baselineskip\mathstacktotal
   \lineskip\mathstackvgap
   \lineskiplimit\lineskip
   \mathsurround\zeropoint
   \everycr\emptytoks
   \enforced\let\NC\relax
   \enforced\let\MC\relax
   \enforced\let\NR\crcr
   \halign\bgroup\hfil\normalstartimath\scriptstyle\aligncontent\normalstopimath\hfil\crcr}

\noaligned\permanent\protected\def\stopsubstack
  {\crcr
   \egroup
   \egroup
   \endgroup}

% %D \macros
% %D   {bordermatrix}
% %D
% %D In \PLAIN\ \TEX\ the width of a parenthesis is stored in
% %D the \DIMENSION\ \type{\mathparentwd}. This value is derived from
% %D the width of \type{\tenrm B}, so let's take care of it now:
%
% \ifdefined\mathparentwd \else \newdimen\mathparentwd \fi
%
% \let\normalbordermatrix\bordermatrix % move that code to here instead
%
% \protected\def\bordermatrix
%   {\begingroup
%    \setbox\scratchbox\hbox{\mr\char"239C}%
%    \global\mathparentwd\wd\scratchbox
%    \endgroup
%    \normalbordermatrix}
%
% \def\bordermatrix
%   {\begingroup
%    \mr
%    \global\mathparentwd\fontcharwd\font"239C\relax
%    \endgroup
%    \normalbordermatrix}

%D \macros{overset, underset}
%D
%D The macros \type{\overset} and \type{\underset} are provided by
%D \AMS\ packages in \LATEX. These macro allows you to place a symbol
%D above or below another symbol, irrespective of whether the other
%D symbol is a relation or something else, and without influencing the
%D spacing.  For most cases there is a better way to do such things
%D (declaring a math command with limop option, or using accents), but
%D occasionally these macros can be useful, for example:
%D
%D \startbuffer
%D \startformula
%D \overset{*}{X} \underset{*}{X}
%D \stopformula
%D \stopbuffer
%D \typebuffer \getbuffer
%D
%D Use these macros sparingly. Remember, \TEX\ was designed for
%D mathematics, so there is usually a proper method for typesetting
%D common math notation.
%D
%D These macros are a cleaner version of \type {\binrel@} and
%D \type {\binrel@@} macros in \AMSTEX\ packages.

\def\math_binrel_apply#1%
  {\begingroup
   \setbox\scratchbox\hbox
     {\thinmuskip   0mu
      \medmuskip   -1mu
      \thickmuskip -1mu
      \setbox\scratchbox\hbox{\normalstartimath#1\mathsurround\zeropoint\normalstopimath}%
      \kern-\wd\scratchbox
      \normalstartimath{}#1{}\mathsurround\zeropoint\normalstopimath}%
   \ifdim\wd\scratchbox<\zeropoint
     \endgroup
     \expandafter\mathbin
   \orelse\ifdim\wd\scratchbox>\zeropoint
     \endgroup
     \doubleexpandafter\mathrel
   \else
     \endgroup
     \doubleexpandafter\firstofoneargument
   \fi}

\permanent\protected\def\overset#1#2%
  {\math_binrel_apply{#2}{\mathop{\kern\zeropoint#2}\limits\normalsuperscript{#1}}}

\permanent\protected\def\underset#1#2%
  {\math_binrel_apply{#2}{\mathop{\kern\zeropoint#2}\limits\normalsubscript  {#1}}}

%D The following code comes from \type {math-str.mkiv}.
%D
%D Here we implement a basic math alignment mechanism. Numbers are also handled. The macros
%D \type {\startinnermath} and \type {\stopinnermath} can be overloaded in specialized
%D modules.

\installcorenamespace{mathinnerstart}
\installcorenamespace{mathinnerstop}

% \protected\def\startinnermath{\csname\??mathinnerstart\formulaparameter\c!align\endcsname}
% \protected\def\stopinnermath {\csname\??mathinnerstop \formulaparameter\c!align\endcsname}

\permanent\protected\def\startinnermath{\expandnamespaceparameter\??mathinnerstart\formulaparameter\c!align\v!normal}
\permanent\protected\def\stopinnermath {\expandnamespaceparameter\??mathinnerstop \formulaparameter\c!align\v!normal}

\permanent\protected\def\mathinnerstrut
  {\doif{\formulaparameter\c!strut}\v!yes\strut}

\permanent\protected\def\defineinnermathhandler#1#2#3%
  {\defcsname\??mathinnerstart#1\endcsname{#2}%
   \defcsname\??mathinnerstop #1\endcsname{#3}}

\installtextracker
  {formulas.boxes}
  {\enforced\let\math_hbox\ruledhbox}
  {\enforced\let\math_hbox\hbox}

\let\math_hbox\hbox

\newconstant\mathraggedstatus % normal left center  right
\newconstant\mathnumberstatus % nothing normal shift_right

\newdimen\d_math_number_correction

\def\math_box_llapped_math_no
  {\ifcase\mathraggedstatus\or
     \box\b_strc_formulas_number
   \or
     \llap{\box\b_strc_formulas_number}%
   \or
     \llap{\box\b_strc_formulas_number}%
   \fi}

\def\math_box_rlapped_math_no
  {\ifcase\mathraggedstatus\or
     \rlap{\box\b_strc_formulas_number}%
   \or
     \rlap{\box\b_strc_formulas_number}%
   \or
     \box\b_strc_formulas_number
   \fi}

\newconditional\c_strc_math_has_number
\newconditional\c_strc_math_display_overflow
\newconstant   \c_strc_math_number_location
\newdimen      \d_strc_math_number_width
\newdimen      \d_strc_math_display_width
\newbox        \b_strc_math_display
\newconstant   \c_strc_formulas_frame_mode
\newdimen      \d_strc_math_indent
\newconditional\c_strc_math_indent

\newdimen\d_strc_math_framed_width

\defcsname\??formulaoption\v!frame\endcsname
  {\edef\p_frame{\formulaparameter\c!frame}%
   \ifx\p_frame\v!number
     \c_strc_formulas_frame_mode\plustwo % inside frame
   \else
     \c_strc_formulas_frame_mode\plusone % outside frame
   \fi}

% mode: 0=no frame | 1=number inside frame | 2=number outside frame

\def\strc_math_flush_aligned
  {\ifcase\c_strc_math_vertical
     \ifcase\mathraggedstatus\or\hfill\or\hfill\fi
     \box\b_strc_math_display
     \ifcase\mathraggedstatus\or\or\hfill\or\hfill\fi
   \else
     \ifconditional\c_strc_math_indent
       \ifzeropt\d_strc_math_indent\else
         \hangafter\plusone
         \hangindent\d_strc_math_indent
       \fi
     \fi
     \edef\p_interlinespace{\formulaparameter\c!interlinespace}%
     \ifempty\p_interlinespace\else\baselineskip\p_interlinespace\fi
     \global\d_strc_math_indent\zeropoint
     \ifcase\mathraggedstatus\or\raggedleft\or\raggedcenter\or\raggedright\fi
     \unhbox\b_strc_math_display
   \fi}

\def\strc_math_flush_box_normal
  {\ifcase\c_strc_math_vertical
     \hbox to \displaywidth\bgroup
        \strc_math_flush_aligned
     \egroup
   \else
     \strc_math_flush_aligned
   \fi}

\def\strc_math_flush_box_framed_common
  {\d_strc_math_framed_width\displaywidth
   \setformulaframedparameter\c!align{\formulaparameter\c!align}%
   \letformulaframedparameter\c!strut\v!no
   \d_framed_formula\ht\b_strc_math_display
   \ifcase\mathraggedstatus\or\hfill\or\hfill         \fi
   \inheritedformulaframedframed{\box\b_strc_math_display}%
   \ifcase\mathraggedstatus\or      \or\hfill\or\hfill\fi}

\def\strc_math_flush_box_framed_display
  {\let\currentformulaframed\currentformula
   \letformulaframedparameter\c!location\v!formula
   \setformulaframedparameter\c!width{\d_strc_math_framed_width}%
   \strc_math_flush_box_framed_common}

\def\strc_math_flush_box_framed_fit_inline
  {\let\currentformulaframed\currentformula
   \letformulaframedparameter\c!location\empty
   \letformulaframedparameter\c!width\v!fit
   \strc_math_flush_box_framed_common}

\def\strc_math_flush_box_framed_fit_display
  {\let\currentformulaframed\currentformula
   \letformulaframedparameter\c!location\v!formula
   \letformulaframedparameter\c!width\v!fit
   \strc_math_flush_box_framed_common}

% combiners

\def\strc_math_flush_box
  {\ifcase\c_strc_formulas_frame_mode
     \strc_math_flush_box_normal
   \else
     \strc_math_flush_box_framed_display
   \fi}

\def\strc_math_number_right_normal
  {\strc_math_flush_aligned
   \hss % hss makes room for number
   \math_box_llapped_math_no}

\def\strc_math_number_left_normal
  {\math_box_rlapped_math_no
   \strc_math_flush_aligned
   \hss} % hss makes room for number

\def\strc_math_number_right_normal_outside
  {\ifconditional\c_strc_formulas_tight
     \strc_math_flush_box_framed_fit_display
   \else
     \strc_math_flush_box_framed_display
   \fi
   \hss % hss makes room for number
   \math_box_llapped_math_no}

\def\strc_math_number_left_normal_outside
  {\math_box_rlapped_math_no
   \hss % hss makes room for number
   \ifconditional\c_strc_formulas_tight
     \strc_math_flush_box_framed_fit_display
   \else
     \strc_math_flush_box_framed_display
   \fi}

\def\strc_math_number_right_normal_inside
  {\setbox\b_strc_math_display\hpack to \dimexpr\displaywidth-\d_framed_locator_lo-\d_framed_locator_ro\relax\bgroup
     \strc_math_flush_aligned
     \hss
     \math_box_llapped_math_no
   \egroup
   \strc_math_flush_box_framed_fit_inline}

\def\strc_math_number_left_normal_inside
  {\setbox\b_strc_math_display\hpack to \dimexpr\displaywidth-\d_framed_locator_lo-\d_framed_locator_ro\relax\bgroup
     \math_box_rlapped_math_no
     \hss
     \strc_math_flush_aligned
   \egroup
   \strc_math_flush_box_framed_fit_inline}

\def\strc_math_number_right_overflow
  {\vpack\bgroup
     \strc_math_flush_box
     \par
     \hpack to \displaywidth\bgroup
       \hss
       \math_box_llapped_math_no
     \egroup
   \egroup}

\def\strc_math_number_left_overflow
  {\vpack\bgroup
     \hpack to \displaywidth\bgroup
       \math_box_rlapped_math_no
       \hss
     \egroup
     \strc_math_flush_box
   \egroup}

\def\strc_math_number_right_overflow_outside
  {\vpack\bgroup
     \strc_math_flush_box_framed_fit_inline
    %\hskip\zeropoint % nicely breaks the line without introducing funny vertical spacing ... why o why
     \hpack to \displaywidth\bgroup
       \hss
       \math_box_llapped_math_no
     \egroup
   \egroup}

\def\strc_math_number_left_overflow_outside
  {\vpack\bgroup
     \hpack to \dimexpr\displaywidth-\d_framed_locator_lo\relax\bgroup
       \math_box_rlapped_math_no
       \hss
     \egroup
     \hskip\zeropoint % nicely breaks the line without introducing funny vertical spacing ... why o why
     \strc_math_flush_box_framed_fit_inline
   \egroup}

\def\strc_math_number_right_overflow_inside
  {\setbox\b_strc_math_display\vpack\bgroup
     \box\b_strc_math_display
     \hpack to \displaywidth\bgroup
       \hss
       \math_box_llapped_math_no
       \hskip\d_framed_locator_ro
     \egroup
   \egroup
   \strc_math_flush_box_framed_fit_inline}

\def\strc_math_number_left_overflow_inside
  {\setbox\b_strc_math_display\vpack\bgroup
     \hpack to \displaywidth\bgroup
     % \hskip\d_framed_locator_lo
       \math_box_rlapped_math_no
       \hss
     \egroup
     \box\b_strc_math_display
   \egroup
   \strc_math_flush_box_framed_fit_inline}

% checkers

\def\strc_math_number_check
  {\d_strc_math_display_width\wd\b_strc_math_display
   \ifconditional\c_strc_formulas_tight
     \ifdim\d_strc_math_display_width>\displaywidth
       \settrue\c_strc_math_display_overflow
     \else
       \displaywidth\d_strc_math_display_width
       \setfalse\c_strc_math_display_overflow
     \fi
   \else
     \ifdim\d_strc_math_display_width>\displaywidth
       \settrue\c_strc_math_display_overflow
     \else
       \setfalse\c_strc_math_display_overflow
     \fi
   \fi}

\def\strc_math_number_check_outside
  {\d_strc_math_display_width\naturalwd\b_strc_math_display
   \ifdim\dimexpr\d_strc_math_display_width+\d_framed_locator_lo+\d_framed_locator_ro\relax>\displaywidth
     \settrue\c_strc_math_display_overflow
   \else
     \setfalse\c_strc_math_display_overflow
   \fi
   % still ok?
   \ifnum\mathraggedstatus=\plustwo
     \d_strc_math_framed_width\dimexpr\displaywidth-2\wd\b_strc_formulas_number\relax
   \else
     \d_strc_math_framed_width\dimexpr\displaywidth- \wd\b_strc_formulas_number\relax
   \fi}

\let\strc_math_number_check_inside\strc_math_number_check_outside

% offsets

\def\strc_math_number_check_offsets
  {\begingroup
     \setbox\scratchbox\hbox
       {\inheritedformulaframedframed
          {\pack_framed_locator_set_lo\pack_framed_locator_set_ro}}%
   \endgroup}

% tracing

\def\strc_math_traced_state_yes
  {\llap{\setbox\scratchbox\hbox{\infofont
   \ifcase\mathraggedstatus unset\or right\or middle\or left\fi
   \space
   \ifcase\c_strc_formulas_frame_mode no\or out\or in\fi
   \space
   \ifconditional\c_strc_math_display_overflow overflow\else fit\fi
   \quad}\ht\scratchbox\zeropoint\dp\scratchbox\zeropoint\box\scratchbox}}

\let\strc_math_traced_state\relax

\installtextracker
  {formulas.framed}
  {\let\strc_math_traced_state\strc_math_traced_state_yes}
  {\let\strc_math_traced_state\relax}

% packaging

\protected\def\strc_math_box_start#1%
  {\hsize\displaywidth % \checkeddisplaymath
   \global\mathnumberstatus\plusone
   \mathraggedstatus#1\relax
   %
   \global\d_math_number_correction\zeropoint
   %
   \edef\p_location{\formulaparameter\c!location}%
   \useformulacolorparameter\c!color
   \c_strc_math_number_location\ifx\p_location\v!left\plusone\orelse\ifx\p_location\v!right\plustwo\else\zerocount\fi
   %
  %\strc_formulas_place_number % not here as we can have inner alignment numbers
   \dontcomplain
   \setbox\b_strc_math_display\math_hbox\bgroup % \checkeddisplaymath
     \mathinnerstrut
     \startforceddisplaymath}

\def\strc_math_flush_number_no
  {\ifcase\c_strc_math_vertical
     \ifconditional\c_strc_math_display_overflow
       \ifcase\c_strc_formulas_frame_mode
         \strc_math_flush_box_normal
       \else
         \strc_math_flush_box_framed_fit_inline
       \fi
     \else
       \ifcase\c_strc_formulas_frame_mode
        %\ifconditional\c_strc_formulas_tight
        %  \strc_math_flush_box_normal
        %\else
           \strc_math_flush_box_normal
        %\fi
       \else
         \ifconditional\c_strc_formulas_tight
           \strc_math_flush_box_framed_fit_inline
         \else
           \strc_math_flush_box_framed_display
         \fi
       \fi
     \fi
   \else
     \strc_math_flush_box
   \fi}

\def\strc_math_flush_number_left
  {\ifcase\c_strc_math_vertical
     \ifconditional\c_strc_math_display_overflow
       \ifcase\c_strc_formulas_frame_mode
         \strc_math_number_left_overflow
       \or
         \strc_math_number_left_overflow_outside
       \or
         \strc_math_number_left_overflow_inside
       \fi
     \else
       \ifcase\c_strc_formulas_frame_mode
         \strc_math_number_left_normal
       \or
         \strc_math_number_left_normal_outside
       \or
         \strc_math_number_left_normal_inside
       \fi
     \fi
   \else
     \box\b_strc_formulas_number
     \hfill
     \strc_math_flush_aligned
   \fi}

\def\strc_math_flush_number_right
  {\ifcase\c_strc_math_vertical
     \ifconditional\c_strc_math_display_overflow
       \ifcase\c_strc_formulas_frame_mode
         \strc_math_number_right_overflow
       \or
         \strc_math_number_right_overflow_outside
       \or
         \strc_math_number_right_overflow_inside
       \fi
     \else
       \ifcase\c_strc_formulas_frame_mode
         \strc_math_number_right_normal
       \or
         \strc_math_number_right_normal_outside
       \or
         \strc_math_number_right_normal_inside
       \fi
     \fi
   \else
     \strc_math_flush_aligned
     \hfill
     \box\b_strc_formulas_number
   \fi}

\protected\def\strc_math_box_stop
  {\stopforceddisplaymath
   \egroup
   % check number
   \d_strc_math_number_width\wd\b_strc_formulas_number
   %
   \ifcase\mathnumberstatus
     \setfalse\c_strc_math_has_number
   \or\ifzeropt\d_strc_math_number_width
     \setfalse\c_strc_math_has_number
   \else
     \settrue\c_strc_math_has_number
   \fi\fi
   % preroll left and right offsets
   \ifcase\c_strc_formulas_frame_mode
     % no frame
   \else
     \strc_math_number_check_offsets
   \fi
   \ifcase\c_strc_formulas_frame_mode
     \strc_math_number_check
   \or
     \strc_math_number_check_outside
   \else
     \strc_math_number_check_inside
   \fi
   \noindent % \noindentation % not \dontleavehmode
   \hskip\d_strc_formulas_display_margin_left % was kern but that doesn't indent
   \strc_math_traced_state
   \ifcase\c_strc_math_vertical
     \hbox to \displaywidth \bgroup
   \or
     \vbox \bgroup \hsize\displaywidth
   \or
     \bgroup \hsize\displaywidth
   \fi
   \ifcase\mathnumberstatus
     \strc_math_flush_box
   \or % status 1
     \ifcase\c_strc_math_number_location
       \strc_math_flush_box
     \or % number left
       \ifzeropt\wd\b_strc_formulas_number
         \strc_math_flush_number_no
       \else
         \strc_math_flush_number_left
       \fi
     \else % number right
       \ifzeropt\wd\b_strc_formulas_number
         \strc_math_flush_number_no
       \else
         \strc_math_flush_number_right
       \fi
     \fi
   \or % status 2
      \hskip\d_math_number_correction % probably no longer used
      \strc_math_flush_box
      \hss
   \else
     \strc_math_flush_box
   \fi
   \ifcase\c_strc_math_vertical
   \or
   \or
     \par
   \fi
   \egroup}

\defineinnermathhandler\v!left      {\strc_math_box_start\plusone  }{\strc_math_box_stop}
\defineinnermathhandler\v!middle    {\strc_math_box_start\plustwo  }{\strc_math_box_stop}
\defineinnermathhandler\v!right     {\strc_math_box_start\plusthree}{\strc_math_box_stop}
\defineinnermathhandler\v!flushleft {\strc_math_box_start\plusthree}{\strc_math_box_stop}
\defineinnermathhandler\v!center    {\strc_math_box_start\plustwo  }{\strc_math_box_stop}
\defineinnermathhandler\v!flushright{\strc_math_box_start\plusone  }{\strc_math_box_stop}
\defineinnermathhandler\v!normal    {\strc_math_box_start\plustwo  }{\strc_math_box_stop}

%D Some inline math tweak.

\appendtoks
    \ifcase\mathnestinglevel\or
        % 4=disable 6=only when no spaces
        \mathsurroundskip\mathematicsparameter\c!textdistance\relax
        \ifzeropt\mathsurroundskip
          \ifzeropt\gluestretch\mathsurroundskip
            \ifzeropt\glueshrink\mathsurroundskip
              \mathsurroundmode\plussix
            \else
              \mathsurroundskip\zeropoint
              \mathsurroundmode\plusfour
            \fi
          \else
            \mathsurroundmode\plussix
          \fi
        \else
          \mathsurroundmode\plussix
        \fi
    \else
      \mathsurroundmode\plusfour
      \mathsurroundskip\zeropoint
    \fi
\to \everymathematics

\setupmathematics
  [\c!textdistance=\zeropoint]

%D This is an experiment. No fancy spacing and alignments here. If we ever
%D go that route it might result in incompatible rendering.

\permanent\protected\def\startsplitformula
  {\ifhmode
     \par
   \fi
   \begingroup
   \beforedisplayspace
   % subset of \everydisplay:
   \c_attr_mathmode\plusone
   \settrue \indisplaymath
   % end of subset
   \informulatrue}

\permanent\protected\def\stopsplitformula
  {\afterdisplayspace
   \endgroup}

%D Kind of new (February 2022):

\installcorenamespace {maththreshold}

\setupmathematics[\c!threshold=\zeropoint]

\permanent\protected\def\installmaththreshold#1#2%
  {\expandafter\gluespecdef\csname\??maththreshold#1\endcsname#2\relax}

\installmaththreshold\v!none  {\zeropoint}
\installmaththreshold\v!small {3\emwidth plus 0.50\emwidth minus 0.25\emwidth}
\installmaththreshold\v!medium{4\emwidth plus 0.75\emwidth minus 0.50\emwidth}
\installmaththreshold\v!big   {5\emwidth plus 1.00\emwidth minus 0.75\emwidth}

\appendtoks
    \edef\p_threshold{\mathematicsparameter\c!threshold}%
    \maththreshold\ifcsname\??maththreshold\p_threshold\endcsname\lastnamedcs\else\p_threshold\fi\relax
\to \everymath % \everyemathematics

\protect \endinput

% \placeformula \startformula[-] \startmatrix
% \NC 1 \NC x \NC a \NR
% \NC 2 \NC y \NC b \NR
% \NC 3 \NC z \NC c \NR
% \stopmatrix \stopformula

% \definemathmatrix[bordermatrix][left={\left[\mskip\thinmuskip},right={\mskip\thinmuskip\right]}]

% \placeformula \startformula[-] \startbordermatrix
% \NC 1 \NC x \NC a \NR
% \NC 2 \NC y \NC b \NR
% \NC 3 \NC z \NC c \NR
% \stopbordermatrix \stopformula