%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  :

% Alignment overhaul timestamp: around watching GhostNote Live in Utrecht 2022
% (energizing funky professionalism).

%D The following macros are moved to this module because here we deal mostly with
%D alignment issues. In principle one should see strc-mat, math-ini and math-ali as
%D a close operation. The \type {\displaywidth} is only known inside a display
%D formula, so we need to catch it when still zero.

\permanent\def\checkeddisplaywidth % hsize if zero
  {\dimexpr
     \ifzeropt\displaywidth
       \hsize
     \else
       \displaywidth
     \fi
   \relax}

\permanent\def\maximizeddisplaywidth % larger than zero but within hsize
  {\dimexpr
     \ifzeropt\displaywidth
       \hsize
     \orelse\ifdim\displaywidth>\hsize
       \hsize
     \else
       \displaywidth
     \fi
   \relax}

%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.

% \startformula
%     \startalign[m=3, n=2, align={1:right,2:left},distance=2em]
%         \NC 1.1 \NC = 1.2 \NC 2.1 \NC = 2.2 \NC 3.1 \NC = 3.2 \NR
%         \NC 1   \NC = 1   \NC 2   \NC = 2   \NC 3   \NC = 3   \NR
%         \NC 1.1 \NC = 1.2 \NC 2.1 \NC = 2.2 \NC 3.1 \NC = 3.2 \NR
%     \stopalign
% \stopformula

\newtoks     \mathdisplayaligntweaks

\newtoks     \t_math_align_a
\newtoks     \t_math_align_b
\newtoks     \t_math_align_c
\newgluespec \d_math_eqalign_distance
\newgluespec \d_math_eqalign_rulethickness
\newdimension\d_math_eqalign_number_distance
\newinteger  \c_math_eqalign_repeat

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

\protected\def\math_eqalign_distance
  {%global\expandafter\integerdef\csname\??mathbeginclass\the\c_math_eqalign_column\endcsname\mathbegincode
   \global\expandafter\integerdef\csname\??mathendclass  \the\c_math_eqalign_column\endcsname\mathendcode
   \mathalignmentparameter\c!separator
   \relax}

\def\math_build_eqalign
  {\scratchtoks\emptytoks
   \d_math_eqalign_distance\mathalignmentparameter\c!distance\relax
   \ifcstok{\mathalignmentparameter\c!align}\v!auto
     \d_math_eqalign_number_distance\mathalignmentparameter\c!numberdistance\relax
     \letmathalignmentparameter\c!align\v!middle
   \else
     \d_math_eqalign_number_distance\zeropoint
   \fi
   \scratchcounterone\mathalignmentparameter\c!m
   \scratchcountertwo\mathalignmentparameter\c!n
   \toksapp\scratchtoks\t_math_align_a
   \toksapp\scratchtoks{\global\c_math_eqalign_repeat\zerocount}%
   \scratchcounter\plusone
   \dorecurse{\numexpr\scratchcounterone*\scratchcountertwo-\plusone\relax}
     {\ifnum\scratchcounter=\scratchcountertwo
        \scratchcounter\plusone
        % preamble expansion hell ...
        \toksapp\scratchtoks {\tabskip\d_math_eqalign_distance}%
        % so ...
        \toksapp\scratchtoks {\relax\math_eqalign_distance}%
        \etoksapp\scratchtoks{\global\advanceby\c_math_eqalign_repeat\the\scratchcountertwo\relax}%
      \else
        \advanceby\scratchcounter\plusone
      \fi
      \toksapp\scratchtoks\t_math_align_b}%
   \toksapp\scratchtoks\t_math_align_c
   \toksapp\scratchtoks{\global\c_math_eqalign_repeat\zerocount}}

\def\math_eqalign_set_defaults
  {\normalbaselines % hm, spacing ?
   \mathsurround\zeropoint
   \tabskip\zeropoint
   \everycr\emptytoks}

%installcorenamespace{mathbeginclass} % not needed currently
\installcorenamespace{mathendclass}

%global\expandafter\integerdef\csname\??mathbeginclass\the\zerocount\endcsname\mathbegincode
\global\expandafter\integerdef\csname\??mathendclass  \the\zerocount\endcsname\mathendcode

\protected\def\math_math_in_eqalign#1%
  {\mathbeginclass\ifcsname\??mathendclass\the\numexpr\c_math_eqalign_column-\plusone\relax\endcsname\lastnamedcs\else\mathunsetcode\fi
   \startforceddisplaymath
   \tabskip\zeropoint
   \everycr\emptytoks
   #1%
   \stopforceddisplaymath
   \ifnum\lastrightclass<\mathunsetcode
     %global\expandafter\integerdef\csname\??mathbeginclass\the\c_math_eqalign_column\endcsname\lastleftclass
     \global\expandafter\integerdef\csname\??mathendclass  \the\c_math_eqalign_column\endcsname\lastrightclass
   \fi
   }

\noaligned\protected\def\math_text_in_eqalign#1%
  {\mathbeginclass\mathordcode
   \mathendclass  \mathordcode
   \startimath
   \tabskip\zeropoint
   \everycr\emptytoks
   #1%
   \stopimath}

% the preamble is scanned for tabskips so we need the span to prevent an error
% message but we can probably do without that hack now .. best not change this
% now .. what works now keeps working

\setnewconstant\c_strc_formulas_check_width\plusone

\newboundary\c_math_align_l_marker
\newboundary\c_math_align_r_marker

% formula   : numbermethod        down : default
% formula   : numberlocation   overlay : option
% mathalign : align           ..| auto :
% mathalign : adaptive             yes : synchronize glue

% \startplaceformula
% \startformula[numbermethod=down,numberlocation=normal]
% \medmuskip 4mu plus 2mu minus 2mu \showmakeup[mathglue]\showglyphs\showboxes
% \startalign[adaptive=yes,align=auto]
% \NC aaa+x+xxxxxxxx+x+xxxx \EQ x+xxx                   \NR[eq:two:zz]
% \NC x+x                   \EQ x+x+x+xxx+x+x+xxx+xx+xx \NR[eq:two:xx]
% \stopalign
% \stopformula
% \stopplaceformula
%
% \startplaceformula
% \startformula[numbermethod=normal,numberlocation=normal]
% \medmuskip 4mu plus 2mu minus 2mu \showmakeup[mathglue]\showglyphs\showboxes
% \startalign[adaptive=no,align=middle]
% \NC aaa+x+xxxxxxxx+x+xxxx \EQ x+xxx                   \NR[eq:two:zz]
% \NC x+x                   \EQ x+x+x+xxx+x+x+xxx+xx+xx \NR[eq:two:xx]
% \stopalign
% \stopformula
% \stopplaceformula

\newconditional\c_math_align_overflow_mode     \settrue\c_math_align_overflow_mode
\newconditional\c_math_align_reformat_mode     \settrue\c_math_align_reformat_mode
\newconditional\c_strc_formulas_overlay_number \settrue\c_strc_formulas_overlay_number

\protected\def\math_text_in_align
  {\scratchcounter\numexpr\c_math_eqalign_row+\plusone\relax
   \usemathalignmentstyleandcolor\c!textstyle\c!textcolor
   \usemathalignmentstyleandcolor{\c!textstyle:\the\scratchcounter}{\c!textcolor:\the\scratchcounter}%
   \mathalignmentparameter\c!text
   \mathalignmentparameter{\c!text:\the\scratchcounter}}

\def\math_align_initialize_class_states
  {}

\def\math_align_reset_class_states
  {\lastleftclass \mathbegincode
   \lastrightclass\mathendcode}

\def\math_prepare_l_eqalign_no  % \checkeddisplaymath
  {\math_align_initialize_class_states
   \t_math_align_a
     {\relax
      \strut
      \math_text_in_align
      \aligncontent % for picking up the number
      \ifnum\c_strc_math_ragged_status=\plusthree
        \tabskip\zeropoint\relax
      \else
        \tabskip\centeringskip
      \fi
      \boundary\c_math_align_l_marker
      \math_align_reset_class_states
      \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\c_strc_math_ragged_status=\plusthree
     \t_math_align_c
       {\hfil
        \tabskip\zeropoint
        \aligntab
        \span
        \boundary\c_math_align_r_marker
        \math_alignment_rbox{\aligncontent}%
        \tabskip\zeropoint}%
   \orelse\ifnum\c_strc_math_ragged_status=\plusone
     \t_math_align_c
       {\hfil
        \tabskip\stretchingfillskip
        \aligntab
        \span
        \boundary\c_math_align_r_marker
        \math_alignment_rbox{\aligncontent}%
        \tabskip\zeropoint}%
   \else
     \t_math_align_c
       {\hfil
        \tabskip\centeringskip
        \aligntab
        \span
        \boundary\c_math_align_r_marker
        \math_alignment_rbox{\aligncontent}%
        \tabskip\zeropoint}%
   \fi
   \math_build_eqalign
   \the\mathdisplayaligntweaks
   \tabskip\zeropoint
   \ifnum\c_strc_math_ragged_status=\plusthree
     \tabskip\stretchingfillskip
   \fi}

\def\math_prepare_r_eqalign_no
  {\math_align_initialize_class_states
   \t_math_align_a
     {\relax
      \strut
      \math_text_in_align
      \tabskip\centeringskip
      \aligncontent % for picking up the number
      \boundary\c_math_align_l_marker
      \math_align_reset_class_states
      \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\c_strc_math_ragged_status=\plusthree
     \t_math_align_c
       {\hfil
        \aligntab
        \hfill % the only one !
        \span
        \boundary\c_math_align_r_marker
        \math_alignment_lbox{\aligncontent}%
        \tabskip\zeropoint}%
   \orelse\ifnum\c_strc_math_ragged_status=\plusone
     \ifnum\c_strc_math_number_variant=\plusone
       \t_math_align_c
         {\hfil
          \tabskip\stretchingfillskip
          \aligntab
          \span
          \boundary\c_math_align_r_marker
          \math_alignment_lbox{\aligncontent}%
          \tabskip\zeropoint}%
     \else
       \t_math_align_c
         {\hfil
          \tabskip\zeropoint
          \aligntab
          \span
          \boundary\c_math_align_r_marker
          \math_alignment_lbox{\aligncontent}%
          \tabskip\stretchingfillskip}%
     \fi
   \else
     \t_math_align_c
       {\hfil
        \tabskip\centeringskip % fails in some cases
        \aligntab
        \span
        \boundary\c_math_align_r_marker
        \math_alignment_lbox{\aligncontent}%
        \tabskip\zeropoint}%
   \fi
   \math_build_eqalign
   \the\mathdisplayaligntweaks
   \tabskip\zeropoint}

% \def\math_halign_checked_nop
%   {\halign
%      \ifconditional\c_math_align_overflow_mode
%        callback
%        attr
%          \mathnumberlocationattribute
%          \numexpr\ifconditional\c_math_align_reformat_mode\plusfour\else\plustwo\fi * \plussixteen\relax % just a signal
%      \fi}
%
% \def\math_halign_checked_yes
%   {\math_halign_checked_nop
%      \ifcase\c_strc_formulas_check_width\else
%         to \checkeddisplaywidth
%      \fi}
%
% \def\math_halign_checked
%   {\ifnum\c_strc_formulas_place_number_mode =\plusthree \math_halign_checked_yes \orelse
%    \ifnum\c_strc_formulas_number_mode       =\plusthree \math_halign_checked_yes \orelse
%    \ifnum\c_strc_formulas_sub_number_mode   =\plusthree \math_halign_checked_yes \orelse
%    \ifnum\c_strc_formulas_nested_number_mode=\plusthree \math_halign_checked_yes \else
%                                                         \math_halign_checked_nop \fi}

\def\math_halign_checked
  {\enablematrixalign
   \halign
     \ifconditional\c_math_align_overflow_mode
       callback
       \s!attr
         \mathnumberlocationattribute
         \numexpr\ifconditional\c_math_align_reformat_mode\plusfour\else\plustwo\fi * \plussixteen\relax % just a signal
     \fi
     \ifcase\c_strc_formulas_check_width\else
        to \checkeddisplaywidth
     \fi}

\installcorenamespace {mathalignlocation}

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

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

\newinteger    \c_math_eqalign_column
\newinteger    \c_math_eqalign_row
\newconditional\c_math_eqalign_first

\newtoks       \everymathalignment
\newtoks       \everymathalignmentdone

\newdimension  \d_math_eqalign_number_threshold

\definesystemattribute[mathnumberlocation] [public]
\definesystemattribute[mathnumberthreshold][public]

\protected\def\math_alignment_lbox#1%
  {\begingroup
   \setbox\scratchbox\hbox{\resetformulaparameter\c!location#1}%
   \ifzeropt\wd\scratchbox\else
    %\enablematrixalign
     \hpack
       \s!attr \mathnumberlocationattribute \numexpr\c_strc_math_ragged_status * \plussixteen + \plusone\relax
       \s!attr \mathnumberthresholdattribute \numexpr\d_math_eqalign_number_threshold\relax
       {\strc_formulas_add_distance \plustwo\v!left\mathalignmentparameter
        \box\scratchbox}%
   \fi
   \global\d_math_eqalign_number_threshold\zeropoint % move to begin of row
   \endgroup}

\protected\def\math_alignment_rbox#1%
  {\begingroup
   \setbox\scratchbox\hbox{\resetformulaparameter\c!location#1}%
   \ifzeropt\wd\scratchbox\else
    %\enablematrixalign
     \hpack
       \s!attr \mathnumberlocationattribute  \numexpr\c_strc_math_ragged_status * \plussixteen + \plustwo\relax
       \s!attr \mathnumberthresholdattribute \numexpr\d_math_eqalign_number_threshold\relax
       {\box\scratchbox
        \strc_formulas_add_distance \plustwo\v!right\mathalignmentparameter}%
   \fi
   \global\d_math_eqalign_number_threshold\zeropoint % move to begin of row
   \endgroup}

\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
    \global\s_strc_math_alignment_inbetween\zeroskip
\to \everymathalignment

\appendtoks
    \pop_macro_TB
    \pop_macro_NR
    \pop_macro_EQ
    \pop_macro_NN
    \pop_macro_NC
    \global\s_strc_math_alignment_inbetween\zeroskip
\to \everymathalignmentdone

% % 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}]

\newgluespec\s_strc_math_alignment_inbetween

\def\strc_math_setup_spacing_aligned#1%
  {\begingroup
   % here we abuse the whitespace setter
   \edef\v_spac_whitespace_current{#1\c!spaceinbetween}%
   \ifempty\v_spac_whitespace_current
     \global\s_strc_math_alignment_inbetween\zeroskip
   \else
     \spac_whitespace_setup
     \global\s_strc_math_alignment_inbetween\parskip
   \fi
   \endgroup}

\permanent\tolerant\protected\def\math_alignment_start[#1]#*[#2]%
  {\begingroup
   \edef\currentmathalignment{#1}%
   \ifarguments\or\or
     \setupmathalignment[#1][#2]%
   \fi
   \ifcstok{\mathalignmentparameter\c!adaptive}\v!yes
     \settrue\c_math_align_reformat_mode
   \else
     \setfalse\c_math_align_reformat_mode
   \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]%
     {\advanceby\c_math_eqalign_column\plusone\math_eqalign_set_column}% takes argument
   \global\c_math_eqalign_column\plusone
   \strc_math_setup_spacing_aligned\mathalignmentparameter
   \dostarttagged\t!math\empty
   \dostarttagged\t!mtable\currentmathalignment
   % is this check still valid?
   \ifmmode
     % we're always in mathmode
     \the\mathdisplayaligntweaks
     \ifcsname\??mathalignlocation\mathalignmentparameter\c!location\endcsname
       \lastnamedcs % top|bottom|center as suggested by HM
     \else
       \vcenter
     \fi
   \fi
   \bgroup
   \ifcstok{\formulaparameter\c!location}\v!left
     \math_prepare_l_eqalign_no
   \else
     \math_prepare_r_eqalign_no
   \fi
   \math_halign_checked\expandafter\bgroup\the\scratchtoks\crcr}

\def\math_alignment_stop % can be protected
  {\crcr\egroup\egroup
   \dostoptagged
   \dostoptagged
   \the\everymathalignmentdone
   \math_alignment_snap_stop
   \endgroup}

\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}%
\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!spaceinbetween=\formulaparameter\c!spaceinbetween,
   \c!numberthreshold=\zeropoint,
   \c!grid=\v!math]

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

% this needs some consideration, it might be obsolete now:

\protected\def\math_display_align_hack
  {\everycr{\noalign{\penalty\interdisplaylinepenalty}}}

\appendtoks
    \math_display_align_hack
\to \mathdisplayaligntweaks

% 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

%

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

\def\math_next_in_eqalign
  {\global\advanceby\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
   \orelse\ifcsname\??mathalignmentvariant\number\zerocount\endcsname
     \ifcase\lastnamedcs \or \relax \or \hfill \or \hfill \fi
   \orelse\ifcsname\??mathalignmentvariant\number\numexpr\c_math_eqalign_column-\c_math_eqalign_repeat\relax\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
   \orelse\ifcsname\??mathalignmentvariant\number\numexpr\c_math_eqalign_column-\c_math_eqalign_repeat\relax\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}

\protected\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
   \expandafter\integerdef\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::]}}

\def\math_eqalign_set_columns_step
  {\advanceby\c_math_eqalign_column\plusone
  %\c_math_matrix_columns\c_math_eqalign_column
   \math_eqalign_set_column}

\def\math_eqalign_set_columns#1%
  {\c_math_eqalign_column\zerocount
   \rawprocesscommacommand[#1]\math_eqalign_set_columns_step}

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

%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 \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!spaceinbetween=\mathalignmentparameter\c!spaceinbetween,
  %\c!numberdistance=2.5\emwidth,
   \c!numberdistance=\zeropoint]

\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

%D Why not \unknown:
%D
%D \starttyping
%D \definemathcases[mycases][simplecommand=mycases]
%D
%D \startformula
%D \startmycases
%D \NC 1  \NC x>0 \NR
%D \NC -1 \NC x<0 \NR
%D \stopmycases
%D \stopformula
%D
%D \startformula
%D     \mycases{1,x>0;-1,x<0}
%D \stopformula
%D \stoptyping

\permanent\tolerant\protected\def\math_cases_simple[#1]#*[#2]#:#3%
  {\begingroup
   \edef\currentmathcases{#1}%
   \setupcurrentmathcases[#2]%
   \math_cases_start[\currentmathcases]%
   \clf_simplecases{\mathcasesparameter\c!action}{#3}%
   \math_cases_stop
   \endgroup}

\appendtoks
    \edef\p_simplecommand{\mathcasesparameter\c!simplecommand}%
    \ifempty\p_simplecommand\else
        \frozen\protected\instance\edefcsname\p_simplecommand\endcsname{\math_cases_simple[\currentmathcases]}%
    \fi
\to \everydefinemathcases

\let\math_cases_strut\relax

\newinteger\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\advanceby\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\advanceby\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
   \strc_formulas_place_number_nested{#1}{#2}\crcr}

\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
   \mathatom \s!class \mathwrappedcode \bgroup
   \scratchdimen\mathcasesparameter\c!leftmargin\relax
   \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
   \mathcasesparameter\c!left
   \math_fenced_start_wrap{\mathcasesparameter\c!fences}%
   \mathatom \s!class \mathconstructcode \bgroup
   \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
   \math_eqalign_set_defaults
   \global\c_math_eqalign_column\plusone
   \global\c_math_eqalign_row\plusone
   \global\c_math_cases_nc\zerocount
   \strc_math_setup_spacing_aligned\mathcasesparameter
   \enablematrixalign
   \halign callback \s!attr \mathnumberlocationattribute \zerocount \bgroup % use \indexofregister here
     \ifmmode\else\startimath\fi
     \mathcasesparameter\c!style
     \aligncontent
     \ifmmode\stopimath\fi
     \hfil
     \aligntab
     \kern\mathcasesparameter\c!distance\relax % hskip
     \math_cases_strut % looks better
     \aligncontent
     \hfil
     \aligntab
     \kern\mathcasesparameter\c!numberdistance\relax % hskip
     \span\math_text_in_eqalign{\aligncontent}%
     \crcr} % todo: number

\noaligned\permanent\protected\def\math_cases_stop
  {\crcr
   \egroup
   \egroup
   \egroup
   \math_fenced_stop_wrap
   \mathcasesparameter\c!right\relax
   \scratchdimen\mathcasesparameter\c!rightmargin\relax
   \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
   \egroup
   \pop_macro_c_math_cases_nc
   \endgroup}

% \definemathfence [cases] [\c!left="007B,\c!right=\v!none]
% \definemathfence [sesac] [\c!left=\v!none,\c!right="007D]

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

% This might become key=cases in the end:

\setupmathcases
% [cases]
  [\c!leftmargin=\zeropoint,
   \c!rightmargin=\zeropoint,
   \c!left=,
   \c!right=,
   \c!fences=cases]

\definemathcases
  [sesac]
  [\c!fences=sesac]

%D \startbuffer
%D \placeformula \startformula \startcases
%D \NC 2 \NC y > 0     \NR
%D \NC 7 \NC x = 7     \NR[+]
%D \NC 4 \TC 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 \TC 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 \TC 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 \TC 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

%D In the end is is way easier to not use alignments and just paste boxes together
%D but let's be a bit texie.

\installcorenamespace{mathmatrix}

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

\setupmathmatrix
  [\c!distance=\emwidth,
   \c!fences=,
   \c!left=,
   \c!right=,
   \c!align=\v!middle,
   \c!leftmargin=\zeropoint,
   \c!rightmargin=\zeropoint,
   \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

\newinteger\c_math_matrix_columns

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

\def\math_matrix_stop_table
  {\dostoptagged
   \dostoptagged}

\def\math_matrix_start_row
  {\beginlocalcontrol
   \global\c_math_matrix_columns\c_math_eqalign_column
   \global\c_math_eqalign_column\zerocount
   \global\advanceby\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
   \everycr\emptytoks}

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

% \dorecurse{10}{test }
%
% \startformula
%     \startmatrix[left=\left(,right=\right)]
%       \NC x \NC       \NC yy \NC       \NC zzz \NR
%       \NC x \NC \dots \NC yy \NC \dots \NC zzz \NR
%       \HF[2]                                   \NR
%       \NC x \NC \dots \NC yy \NC \dots \NC zzz \NR
%       \HF                                      \NR
%       \NC x \NC \dots \NC yy \NC \dots \NC zzz \NR
%       \NC \HF[2]                               \NR
%       \NC x \NC \dots \NC yy \NC \dots \NC zzz \NR
%       \NC \NC \HF[2][rule]                     \NR
%       \NC x \NC \dots \NC yy \NC \dots \NC zzz \NR
%       \HL
%       \NC x \VL \dots \VL yy \NC \dots \VL zzz \NR
%       \NC x \VL \dots \VL yy \NC \dots \VL zzz \NR
%       \HL
%     \stopmatrix
% \stopformula
%
% \dorecurse{10}{test }
%
% \startformula
%     \startmatrix[left=\left(,right=\right)]
%       \NC        \TT \ttx 1 \NC       \TT \ttx 2 \NC       \TT \ttx 3 \NC        \NR
%       \LT \ttx 1 \NC a      \NC \dots \NC aa     \NC \dots \NC aaa    \RT \ttx 1 \NR
%       \LT \ttx 2 \NC b      \NC \dots \NC bb     \NC \dots \NC bbb    \RT \ttx 2 \NR
%       \LT \ttx 3 \NC c      \NC \dots \NC cc     \NC \dots \NC ccc    \RT \ttx 3 \NR
%       \NC        \BT \ttx 1 \NC       \BT \ttx 2 \NC       \BT \ttx 3 \NC        \NR
%     \stopmatrix
% \stopformula
%
% \dorecurse{10}{test }
%
% \startformula
%     \startmatrix[left=\left(,right=\right)]
%       \NC        \TT \ttx 1 \NC       \TT \ttx 2 \NC       \TT \ttx 3 \NR
%       \LT \ttx 1 \NC a      \NC \dots \NC aa     \NC \dots \NC aaa    \NR
%       \LT \ttx 2 \NC b      \NC \dots \NC bb     \NC \dots \NC bbb    \NR
%       \LT \ttx 3 \NC c      \NC \dots \NC cc     \NC \dots \NC ccc    \NR
%       \NC        \BT \ttx 1 \NC       \BT \ttx 2 \NC       \BT \ttx 3 \NR
%     \stopmatrix
% \stopformula
%
% \dorecurse{10}{test }

\newtoks\everymathmatrix

\tolerant\permanent\def\math_matrix_HF[#1]#*[#2]% [n] [name] | [name] | [n]
  {\expandedloop
     \plusone
     \numexpr\ifchknum#1\or#1\else(\c_math_matrix_columns+\minusone)\fi*\plustwo\relax
     \plusone
   {\omit\span}%
   \normalexpanded{\filler[%
     \ifcsname\??filleralternative matrix:#1\endcsname matrix:#1\orelse
     \ifcsname\??filleralternative matrix:#2\endcsname matrix:#2\orelse
     \ifcsname\??filleralternative        #1\endcsname        #1\orelse
     \ifcsname\??filleralternative        #2\endcsname        #2\else
                                                matrix:\v!normal\fi
   ]}}

\appendtoks
   \enforced\let\HF\math_matrix_HF
\to \everymathmatrix

\definefiller
  [matrix:\v!normal]
  [\c!symbol=\textperiod,
   \c!style=\v!normal,
   \c!method=\v!broad,
   \c!width=\emwidth,
   \c!leftmargin=-.1\emwidth,
   \c!rightmargin=-.1\emwidth]

\definefiller
  [matrix:\v!middle]
  [\c!symbol=\textperiod,
   \c!style=\v!normal,
   \c!method=\v!middle,
   \c!width=\emwidth,
   \c!leftmargin=.5\emwidth,
   \c!rightmargin=.5\emwidth]

\definefiller
  [matrix:ldots]
  [matrix:\v!normal]

\definefiller
  [matrix:cdots]
  [matrix:\v!normal]
  [\c!symbol=\cdot]

% 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

\permanent\protected\def\setmathmatrixanchoring[#1]%
  {\c_math_matrix_anchor_mode\zerocount
   \processaction
     [#1]%
     [\v!both=>\c_math_matrix_anchor_mode\plusone,%
       \v!yes=>\c_math_matrix_anchor_mode\plusone]}

\def\math_matrix_anchor
  {\ifcase\c_math_matrix_anchor_mode\else
     \markanchor{matrix}{\numexpr\c_math_eqalign_column+\plusone\relax}\c_math_eqalign_row
   \fi}

\protected\def\math_matrix_anchor_first
  {\relax
   \ifcase\c_math_matrix_anchor_mode\else
     \math_matrix_anchor
   % \ifdim\d_math_eqalign_distance>\zeropoint
   %   \ifbitwiseand\c_math_matrix_anchor_mode\plustwo
   %      \kern.5\d_math_eqalign_distance
   %   \fi
   % \fi
   \fi}

\protected\def\math_matrix_anchor_last
  {\relax
   \ifcase\c_math_matrix_anchor_mode\else
   % \ifdim\d_math_eqalign_distance>\zeropoint
   %   \ifbitwiseand\c_math_matrix_anchor_mode\plusfour
   %     \kern.5\d_math_eqalign_distance
   %   \fi
   % \fi
     \math_matrix_anchor
   \fi}

\def\math_matrix_preamble
  {\math_matrix_strut
   \math_matrix_anchor_first
   \global\advanceby\c_math_eqalign_column\plusone
   \math_matrix_start_cell
     \aligncontent
   \math_matrix_stop_cell
   \aligntab
   \aligntab
   \math_matrix_anchor
   \kern.5\d_math_eqalign_distance % hskip
   \aligncontent
   \aligntab
   \global\advanceby\c_math_eqalign_column\plusone
   \math_matrix_start_cell
     \aligncontent
   \math_matrix_stop_cell}

\permanent\protected\def\math_matrix_NR
  {\math_matrix_anchor_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\aligntab} % avoids lookahead

\def\math_matrix_check_rule_step#1%
  {\ifchkdim#1\or
     \scratchdimen#1\relax
   \orelse\ifchknum#1\or
     \scratchdimen#1\d_math_eqalign_rulethickness
   \else
     \edef\p_rulecolor{#1}
   \fi}

\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}

% These offset are an experiment so we abuse some existing keys or we have to
% cook up new ones. Maybe we then should provide small medium big halfline etc.
% but all depends on actual demand for this feature.

% Musical timestamp VL, NL, SL: Bad Hombre II by Antonio Sanches
%
% \startformula
% \startmatrix[left=\left(,right=\right)]
% \NC 0  \NL 0  \NC 0  \NC 2x \NC 1  \NC 0  \NC 0  \NL \NR
% \NC 0  \VL 0  \NC 0  \NC 0  \NC 2x \NC 0  \NC 0  \NL \NR
% \NC 0  \VL 0  \NC 0  \NC 0  \NC 0  \NC 3x \NC 0  \NL \NR
% \NC 0  \NL 0  \NC 0  \NC 0  \NC 0  \NC 0  \NC 4x \VL \NR
% \stopmatrix
% \stopformula
%
% \startformula
% \startmatrix[left=\left(,right=\right)]
% \SL[3]               \NL    \NL    \NL    \NL    \NL \NR
% \VL 2x \NL 1  \NL 0  \VL 0  \NL 0  \NL 0  \NL 0  \NL \NR
% \VL 0  \NL 2x \NL 1  \VL 0  \NL 0  \NL 0  \NL 0  \NL \NR
% \VL 0  \NL 0  \NL 2x \VL 0  \NL 0  \NL 0  \NL 0  \NL \NR
% \SL[5]                             \NL    \NL    \NL \NR
% \NL 0  \NL 0  \NL 0  \VL 2x \NL 1  \VL 0  \NL 0  \NL \NR
% \NL 0  \NL 0  \NL 0  \VL 0  \NL 2x \VL 0  \NL 0  \NL \NR
% \NL    \NL    \NL    \SL[3]               \NL    \NL \NR
% \NL 0  \NL 0  \NL 0  \NL 0  \NL 0  \VL 3x \VL 0  \NL \NR
% \NL    \NL    \NL    \NL    \NL    \SL[2]        \NL \NR
% \NL 0  \NL 0  \NL 0  \NL 0  \NL 0  \NL 0  \VL 3x \VL \NR
% \NL    \NL    \NL    \NL    \NL    \NL    \SL[1] \NL \NR
% \stopmatrix
% \stopformula

\definesystemattribute[mathalignmentvrule][public]
\definesystemattribute[mathalignmenthrule][public]

\setupmathmatrix
  [%c!toffset=\zeropoint,
   \c!toffset=.25\exheight,
   \c!boffset=\mathmatrixparameter\c!toffset]

\noaligned\permanent\tolerant\protected\def\math_matrix_HL[#1]#*%
  {\noalign\bgroup
     \math_matrix_check_rule[#1]%
     \divideby\scratchdimen\plustwo
     \ifdim\scratchdimen>\zeropoint
     % \autorule\s!height\scratchdimen\s!depth\scratchdimen\relax
       \scratchdistance\mathmatrixparameter\c!toffset\relax
       \ifdim\scratchdistance>\zeropoint
         \nohrule
             \s!attr  \mathalignmentvruleattribute\plustwo
             \s!height\scratchdistance
             \s!depth \zeropoint
         \relax
       \fi
       \hrule
           \s!attr  \mathalignmentvruleattribute\plusthree
           \s!height\scratchdimen
           \s!depth \scratchdimen
       \relax
       \scratchdistance\mathmatrixparameter\c!boffset\relax
       \ifdim\scratchdistance>\zeropoint
         \nohrule
             \s!attr  \mathalignmentvruleattribute\plusfour
             \s!height\zeropoint
             \s!depth \scratchdistance
         \relax
       \fi
     \else
        % zero dimensions disable the rule
     \fi
   \egroup}

\protected\def\math_matrix_vertical_rule_indeed#1#2%
  {\math_matrix_check_rule[#2]%
   \enablematrixrules
   #1
      \s!attr   \mathalignmentvruleattribute\plusone
      \s!width  \scratchdimen
      \s!top   -\dimexpr\mathmatrixparameter\c!toffset\relax
      \s!bottom-\dimexpr\mathmatrixparameter\c!boffset\relax
   \relax}

\protected\def\math_matrix_vertical_rule_yes{\math_matrix_vertical_rule_indeed\vrule  }
\protected\def\math_matrix_vertical_rule_nop{\math_matrix_vertical_rule_indeed\novrule}

\installcorenamespace{mathmatrixrulealternative}

\newboundary\c_math_matrix_vl_boundary
%newboundary\c_math_matrix_sl_boundary

\protected\def\math_matrix_horizontal_rule_indeed#1#2%
  {\math_matrix_check_rule[#2]%
   \global\setfalse\c_math_matrix_first
   \global\settrue\c_math_matrix_sl_seen
   \enablematrixrules
   \leaders#1%
      \s!attr   \mathalignmenthruleattribute\plusone
      \s!height .5\scratchdimen
      \s!depth  .5\scratchdimen
    % \s!top   -\dimexpr\mathmatrixparameter\c!toffset\relax
    % \s!bottom-\dimexpr\mathmatrixparameter\c!boffset\relax
   \hfilll
   \kern\dimexpr.5\d_math_eqalign_distance\relax
   \aligntab}

\protected\def\math_matrix_horizontal_rule_yes{\math_matrix_horizontal_rule_indeed\hrule  }
\protected\def\math_matrix_horizontal_rule_nop{\math_matrix_horizontal_rule_indeed\nohrule}

\def\math_matrix_hrule_progress_rest#1%
  {\expandedloop
     \plusone
     \numexpr(\ifchknum#1\or#1\else\c_math_matrix_columns\fi)*\plustwo+\minusone\relax
     \plusone
   {\span\omit}}%

\def\math_matrix_hrule_progress_first#1%
  {\expandedloop
     \plusone
     \numexpr(\ifchknum#1\or#1\else\c_math_matrix_columns\fi+\minusone)*\plustwo+\plusone\relax
     \plusone
   {\span\omit}}%

\def\math_matrix_hrule_progress
  {\NL
   \ifconditional\c_math_matrix_first
     \expandafter\math_matrix_hrule_progress_first
   \else
     \expandafter\math_matrix_hrule_progress_rest
   \fi}

\tolerant\permanent\protected\def\SL[#1]#*[#2]#*% [n] [name] | [name] | [n]
  {\ifcsname\??mathmatrixrulealternative#2\endcsname
     \lastnamedcs{#1}{#2}%
   \orelse\ifcsname\??mathmatrixrulealternative#1\endcsname
     \lastnamedcs{#2}{#1}%
   \else
     \csname\??mathmatrixrulealternative\v!auto\endcsname{#1}{#2}%
   \fi}

\defcsname\??mathmatrixrulealternative\v!auto\endcsname#1#2%
  {\math_matrix_hrule_progress{#1}%
 % \ifzero\c_math_matrix_first
 %   \kern-\dimexpr\linewidth\relax
 % \else
 %   \kern-\dimexpr.5\d_math_eqalign_distance+\linewidth\relax
 % \fi
   \kern-\dimexpr\ifzero\c_math_matrix_first\else.5\d_math_eqalign_distance+\fi\linewidth\relax
   \math_matrix_horizontal_rule_yes{#2}%
   %boundary\c_math_matrix_sl_boundary
   \enforced\let\NR\math_matrix_NL_NR}

\permanent\tolerant\protected\def\math_matrix_VL[#1]#*%
  {\span\omit
   \ifconditional\c_math_matrix_first\else
     \kern.5\d_math_eqalign_distance % hskip
   \fi
   \math_matrix_vertical_rule_yes{#1}%
   \kern.5\d_math_eqalign_distance % hskip
   \global\setfalse\c_math_matrix_first
   \aligntab
   \boundary\c_math_matrix_vl_boundary
   \enforced\let\NR\math_matrix_NL_NR
   }

\permanent\tolerant\protected\def\math_matrix_NL[#1]#*%
  {\span\omit
   \ifconditional\c_math_matrix_first\else
     \kern.5\d_math_eqalign_distance % hskip
   \fi
   \math_matrix_vertical_rule_nop{#1}%
   \kern.5\d_math_eqalign_distance % hskip
   \global\setfalse\c_math_matrix_first
   \aligntab
   \boundary\c_math_matrix_vl_boundary
   \enforced\let\NR\math_matrix_NL_NR}

\permanent\protected\def\math_matrix_NL_NR
  {\ifnum\lastboundary=\c_math_matrix_vl_boundary
     \ifconditional \c_math_matrix_sl_seen
       \kern-1.5\d_math_eqalign_distance % hskip
     \else
       \kern-.5\d_math_eqalign_distance % hskip
     \fi
   \fi
   \math_matrix_anchor_last
   \math_matrix_stop_row
   \math_matrix_pickup
   \crcr
   \math_matrix_start_row}

\appendtoks
   \enforced\let\NL\math_matrix_NL
   \global\setfalse\c_math_matrix_sl_seen
\to \everymathmatrix

\permanent\tolerant\protected\def\math_matrix_VC[#1]#*%
  {\NC
   \math_matrix_vertical_rule_yes{#1}%
   \NC}

\permanent\tolerant\protected\def\math_matrix_VT[#1]#*%
  {\span\omit
   \math_matrix_vertical_rule_yes{#1}%
   \aligntab}

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

\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 % like the old ones
   \enforced\let\VL\math_matrix_VL % like the old ones
   \enforced\let\VC\math_matrix_VC % bonus, extra column
   \enforced\let\VT\math_matrix_VT % bonus, idem but tight
   \enforced\let\TB\math_common_TB
\to \everymathmatrix

\definesystemattribute[mathmatrixornament][public]

\newdimension\d_math_matrix_margin_l
\newdimension\d_math_matrix_margin_r
\newdimension\d_math_matrix_margin_t
\newdimension\d_math_matrix_margin_b

\newboundary \c_math_matrix_ornament_l
\newboundary \c_math_matrix_ornament_r
\newboundary \c_math_matrix_ornament_t
\newboundary \c_math_matrix_ornament_b

% anchors are wrong now

\newconditional\c_math_matrix_text
\newconditional\c_math_matrix_text_l
\newconditional\c_math_matrix_text_r
\newconditional\c_math_matrix_text_t
\newconditional\c_math_matrix_text_b

\def\math_matrix_ornaments#1#2%
  {\NC
   \enablematrixornaments
   \global\settrue\c_math_matrix_text
   \global\settrue#1
   \boundary#2%
   \ignorespaces}

\permanent\protected\def\math_matrix_LT{\math_matrix_ornaments\c_math_matrix_text_l\c_math_matrix_ornament_l}
\permanent\protected\def\math_matrix_RT{\math_matrix_ornaments\c_math_matrix_text_r\c_math_matrix_ornament_r}
\permanent\protected\def\math_matrix_TT{\math_matrix_ornaments\c_math_matrix_text_t\c_math_matrix_ornament_t}
\permanent\protected\def\math_matrix_BT{\math_matrix_ornaments\c_math_matrix_text_b\c_math_matrix_ornament_b}

\appendtoks
   \global\setfalse\c_math_matrix_text
   \global\setfalse\c_math_matrix_text_l
   \global\setfalse\c_math_matrix_text_r
   \global\setfalse\c_math_matrix_text_t
   \global\setfalse\c_math_matrix_text_b
   \enforced\let\LT\math_matrix_LT
   \enforced\let\RT\math_matrix_RT
   \enforced\let\TT\math_matrix_TT
   \enforced\let\BT\math_matrix_BT
\to \everymathmatrix

\def\math_matrix_start_processing
  {\ifmmode
     \mathatom \s!class \mathwrappedcode
   \else
     \dontleavehmode
   \fi
   \bgroup
   \d_math_matrix_margin_l\mathmatrixparameter\c!leftmargin \relax
   \d_math_matrix_margin_r\mathmatrixparameter\c!rightmargin\relax
   \d_math_matrix_margin_t\strutdp
   \d_math_matrix_margin_b\strutht
  %\tabskip.5\d_math_eqalign_distance
   \tabskip\zeropoint
   \math_matrix_pickup
   \the\everymathmatrix
   %
   \setbox\nextbox\vbox\bgroup
   \math_matrix_start_table
   \halign
      callback
      \s!attr \mathmatrixornamentattribute "10
      \s!attr \mathalignmentvruleattribute \plusone
      \s!attr \mathalignmenthruleattribute \plusone
   \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  % experimental hook
   \math_matrix_finish_nextbox
   \mathmatrixright % experimental hook
   \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}}

\newinteger\c_math_eqalign_column_saved
\newinteger\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_eqalign_set_defaults
   \math_eqalign_set_columns{\mathmatrixparameter\c!align}%
   \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\lettonothing\mathmatrixleft  % experimental hook
\mutable\lettonothing\mathmatrixright % 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
  {\scratchcounter\mathstyle\relax
   \scratchwidth\wd\nextbox
   \setbox\scratchbox\begincsname\??mathmatrixalignlocation\mathmatrixparameter\c!location\endcsname\hbox\bgroup
     \normalstartimath
     \Ustyle\scratchcounter
     \ifzeropt\d_math_matrix_margin_l\else\kern\d_math_matrix_margin_l\fi
     \mathmatrixparameter\c!left\relax
     \math_fenced_start_wrap{\mathmatrixparameter\c!fences}%
     \mathatom \s!class \mathconstructcode {\vcenter{\box\nextbox}}% \was \vcenter
     \math_fenced_stop_wrap
     \mathmatrixparameter\c!right\relax
     \ifzeropt\d_math_matrix_margin_r\else\kern\d_math_matrix_margin_r\fi
     \normalstopimath
   \egroup
   \ifconditional\c_math_matrix_text
     \ifcstok{\mathmatrixparameter\c!left\mathmatrixparameter\c!right}\emptytoks\else
       \scratchdistance\dimexpr(\wd\scratchbox-\scratchwidth)/\plustwo\relax
       \advanceby\d_math_matrix_margin_l\scratchdistance
       \advanceby\d_math_matrix_margin_r\scratchdistance
       \clf_shiftmatrixornaments\scratchbox
     \fi
   \fi
   \ifconditional\c_math_matrix_text_b
     \dp\scratchbox\dimexpr\dp\scratchbox+\lineheight\relax
   \fi
   \ifconditional\c_math_matrix_text_t
     \ht\scratchbox\dimexpr\ht\scratchbox+\lineheight\relax
   \fi
   \box\scratchbox}

\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. 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
  [matrix:brackets]
  [\c!fences=bracket,
   \c!align=\v!middle]

\definemathmatrix
  [matrix:parentheses]
  [\c!fences=parenthesis,
   \c!align=\v!middle]

\definemathmatrix
  [matrix:bars]
  [\c!fences=bar,
   \c!align=\v!middle]

\definemathmatrix
  [matrix:braces]
  [\c!fences=brace,
   \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 Mikael needed this matrix in one of his advanced math courses that ran begin april 2022
%D where new concepts were introduced:

% \definemathfence
%   [tekcarb]
%   [\c!left="005D,\c!right="005B]

\definemathmatrix
  [xıɹʇɐɯ]
  [\c!fences=tekcarb]

%D Fortunately we were read for it:
%D
%D \startbuffer
%D \startformula
%D \startxıɹʇɐɯ
%D   \NC a_1 \NC b_1 \NC c_1 \NR
%D   \NC a_2 \NC b_2 \NC c_2 \NR
%D \stopxıɹʇɐɯ
%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{overset, underset}
%D
%D The macros \type {\overset} and \type {\underset} are provided by \AMS\ packages
%D in \LATEX. These macro allows you to place a symbol above or below another
%D symbol, irrespective of whether the other symbol is a relation or something else,
%D and without influencing the spacing. Because in \LUAMETATEX\ we're less limited,
%D we have rather simple definitions compared to \MKIV. One cna also do:
%D
%D \starttyping
%D $b\limits^a$
%D $<\limits^a$
%D \stoptyping

\permanent\protected\def\overset #1#2{\mathrel{#2}\limits\normalsuperscript{#1}}
\permanent\protected\def\underset#1#2{\mathrel{#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
%D macros \type {\startinnermath} and \type {\stopinnermath} can be overloaded in
%D specialized modules.

\installcorenamespace{mathinnerstart}
\installcorenamespace{mathinnerstop}

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

\def\strc_math_flush_number_box{\box\b_strc_formulas_number}

% \newdimension  \d_strc_math_display_width
% \newdimension  \d_strc_math_indent
% \newconditional\c_strc_math_indent

\newconditional\c_strc_math_display_overflow
\newconstant   \c_strc_math_number_location
\newconstant   \c_strc_math_number_variant
\newconstant   \c_strc_formulas_frame_mode
\newdimension  \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

% it is a bit of a mess because we solve all kind of bordercases but at some
% point it will become clean

\def\strc_math_flush_aligned_boxed_direct_yes
  {\dontleavehmode
   \box\b_strc_math_display
   \llap{\box\b_strc_formulas_number}}

\def\strc_math_flush_aligned_boxed_direct_nop
  {\dontleavehmode
   \box\b_strc_math_display}

\def\strc_math_flush_aligned_left_number_indeed
  {\ifvoid\b_strc_formulas_number\else
     \scratchwidth\wd\b_strc_formulas_number
     \setbox\b_strc_formulas_number\hbox to \displaywidth{\hss\hbox{\box\b_strc_formulas_number}}%
     \ifcase\c_strc_math_number_location\or
       \boxxoffset\b_strc_formulas_number\dimexpr-\displaywidth+\scratchwidth\relax
       \boxyoffset\b_strc_formulas_number-\d_strc_math_first_height
       \htdp\b_strc_formulas_number\zeropoint
       \box\b_strc_formulas_number % left
     \fi
   \fi}

\def\strc_math_flush_aligned_right_number_indeed
  {\ifvoid\b_strc_formulas_number\else
     \scratchwidth\wd\b_strc_formulas_number
     \setbox\b_strc_formulas_number\hbox to \displaywidth{\hss\hbox{\box\b_strc_formulas_number}}%
     \ifcase\c_strc_math_number_location\or\else
       \boxyoffset\b_strc_formulas_number\d_strc_math_last_depth
       \htdp\b_strc_formulas_number\zeropoint
       \box\b_strc_formulas_number % right
     \fi
   \fi}

\protected\def\strc_math_flush_aligned_indeed
  {\ifcase\c_strc_math_ragged_status
     % align: error
     \strc_math_flush_aligned_boxed_direct_yes
   \or
     % align: flushleft, number right
     \strc_math_flush_aligned_boxed_direct_yes
   \or
     % align: middle
     \ifnum\c_strc_math_split_mode=\c_strc_math_line_mode
       \leftskip \zeropoint
       \rightskip\zeropoint
       \strc_math_flush_aligned_boxed_direct_yes
     \orelse\ifnum\c_strc_math_split_mode=\c_strc_math_wrap_mode
       \dontleavehmode
       \vbox\bgroup
       \strc_math_flush_aligned_left_number_indeed
       \unvbox\b_strc_math_display
       \strc_math_flush_aligned_right_number_indeed
       \egroup
     \orelse\ifhmode
       % untested
       \dontleavehmode
       \strc_math_flush_aligned_left_number_indeed
       \box\b_strc_math_display
       \strc_math_flush_aligned_right_number_indeed
     \orelse\ifvbox\b_strc_math_display
       \strc_math_flush_aligned_left_number_indeed
       \unvbox\b_strc_math_display
       \strc_math_flush_aligned_right_number_indeed
     \else
       % untested
       \dontleavehmode
       \strc_math_flush_aligned_left_number_indeed
       \box\b_strc_math_display
       \strc_math_flush_aligned_right_number_indeed
     \fi
   \or
     % align: flushright
     % packaged, number (kind of ugly as we now stick in the margin)
     \ifcase\c_strc_math_n_of_lines\or
       \dontleavehmode
       \kern-\wd\b_strc_formulas_number
       \box\b_strc_math_display
       \ifcase\c_strc_math_n_of_lines\or
         \box\b_strc_formulas_number
       \else
         \llap{\box\b_strc_formulas_number}%
       \fi
     \orelse\iftrue % can become option
       \ifdim\d_strc_math_last_width>\wd\b_strc_formulas_number
         \ifdim\d_strc_math_max_width<\d_strc_math_last_width
           \strc_math_flush_aligned_boxed_direct_yes
         \else
           \dontleavehmode
           \kern-\wd\b_strc_formulas_number
           \box\b_strc_math_display
           \box\b_strc_formulas_number
         \fi
       \else
         % delay number till later
         \strc_math_flush_aligned_boxed_direct_nop
       \fi
     \else
       % delay number till later
       \strc_math_flush_aligned_boxed_direct_nop
     \fi
   \fi
   \ifvmode
      \nointerlineskip
   \fi}

\protected\def\strc_math_flush_aligned_simple
  {\ifcase\c_strc_math_ragged_status\or\or\hfill\or\hfill\fi
   \box\b_strc_math_display
   \ifcase\c_strc_math_ragged_status\or\hfill\or\hfill\or\fi}

\protected\def\strc_math_flush_aligned
  {\ifnum\c_strc_math_split_mode=\c_strc_math_line_mode
     \strc_math_flush_aligned_simple
   \orelse\ifconditional\c_strc_math_indent
     % in this case the already set text align is overloaded
     \strc_math_setup_align_auto
     \strc_math_flush_aligned_indeed
   \else
     % normally we don't end up here
     \strc_math_setup_spacing_aligned\mathalignmentparameter
     \begingroup
       \forgetall
       \unhbox\b_strc_math_display
       \par
     \endgroup
   \fi}

\def\strc_math_flush_box_normal
  {\ifnum\c_strc_math_split_mode=\c_strc_math_line_mode
     \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\c_strc_math_ragged_status\or      \or\hfill\or\hfill\fi
   \inheritedformulaframedframed{\box\b_strc_math_display}%
   \ifcase\c_strc_math_ragged_status\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
   \resetformulaframedparameter\c!location
   \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_number_box_left {\ifconditional\c_strc_formulas_overlay_number\rlap\fi{\strc_math_flush_number_box}}
\def\strc_math_flush_number_box_right{\ifconditional\c_strc_formulas_overlay_number\llap\fi{\strc_math_flush_number_box}}

\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
   \strc_math_flush_number_box_right}

\def\strc_math_number_left_normal
  {\strc_math_flush_number_box_left
   \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
   \strc_math_flush_number_box}

\def\strc_math_number_left_normal_outside
  {\strc_math_flush_number_box
   \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
     \strc_math_flush_number_box
   \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
     \strc_math_flush_number_box
     \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
       \strc_math_flush_number_box_right
     \egroup
   \egroup}

\def\strc_math_number_left_overflow
  {\vpack\bgroup
     \hpack to \displaywidth\bgroup
       \strc_math_flush_number_box_left
       \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
       \strc_math_flush_number_box
     \egroup
   \egroup}

\def\strc_math_number_left_overflow_outside
  {\vpack\bgroup
     \hpack to \dimexpr\displaywidth-\d_framed_locator_lo\relax\bgroup
       \strc_math_flush_number_box
       \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
       \strc_math_flush_number_box
       \kern\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
     % \kern\d_framed_locator_lo
       \strc_math_flush_number_box
       \hss
     \egroup
     \box\b_strc_math_display
   \egroup
   \strc_math_flush_box_framed_fit_inline}

% checkers

\setupmathalignment
  [\c!numberdistance=\formulaparameter\c!numberdistance]

\protected\def\d_strc_math_total_display_width
  {\dimexpr
     \d_strc_math_display_width+\wd\b_strc_formulas_number
     \ifconditional\c_strc_formulas_overlay_number
        \ifcase\c_strc_math_ragged_status\or\or+\wd\b_strc_formulas_number\or\fi
     \fi
   \relax}

\def\strc_math_number_check
  {\d_strc_math_display_width\wd\b_strc_math_display
   \ifconditional\c_strc_formulas_tight
     \ifdim\d_strc_math_total_display_width>\displaywidth
       \settrue\c_strc_math_display_overflow
     \else
       \displaywidth\d_strc_math_total_display_width
       \setfalse\c_strc_math_display_overflow
     \fi
   \else
     \ifdim\dimexpr\d_strc_math_total_display_width+\formulaparameter\c!numberthreshold\relax>\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_total_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\c_strc_math_ragged_status=\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\c_strc_math_ragged_status unset\or flushleft\or middle\or flushright\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

\installcorenamespace{mathboxlocation}

\defcsname\??mathboxlocation\v!left \endcsname
  {\c_strc_math_number_location\plusone}

\defcsname\??mathboxlocation\v!right\endcsname
  {\c_strc_math_number_location\plustwo}

\defcsname\??mathboxlocation\v!atrightmargin\endcsname
  {\c_strc_math_number_location\plustwo
   \c_strc_math_number_variant \plusone}

\protected\def\strc_math_box_start#1%
  {\c_strc_math_ragged_status#1\relax % already set
   \useformulacolorparameter\c!color
   \c_strc_math_number_location\zerocount
   \c_strc_math_number_variant \zerocount
   \begincsname\??mathboxlocation\formulaparameter\c!location\endcsname
   %
   % We collect the math formula in an hbox. Dimensions don't really play
   % a role yet but beware of nesting!
   %
   \dontcomplain
  %\holdingmigrations\plusfour
   \setbox\b_strc_math_display\hbox retain \plusfour\bgroup
     \startforceddisplaymath}

\protected\def\strc_math_box_stop
  {\stopforceddisplaymath
   \egroup
   % 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
   \strc_math_traced_state
   \ifnum\c_strc_math_split_mode=\c_strc_math_line_mode
     \noindent % \noindentation % not \dontleavehmode
     \hbox to \displaywidth \bgroup
   \else
     \bgroup
     \strc_math_show_margins
   \fi
   \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
   \egroup}

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

\def\strc_math_flush_number_no
  {\ifnum\c_strc_math_split_mode=\c_strc_math_line_mode
     \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
  {\ifnum\c_strc_math_split_mode=\c_strc_math_line_mode
     \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 % we flush in here, otherwise wrong positioning of number (we need to unvbox)
   \fi}

\def\strc_math_flush_number_right
  {\ifnum\c_strc_math_split_mode=\c_strc_math_line_mode
     \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 % we flush in here
   \fi}

%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 % \everymathematics
\to \everymathematics

%D Here is simple alignment mechanism:

\installcorenamespace{mathsimplealign}

\installcommandhandler \??mathsimplealign {mathsimplealign} \??mathsimplealign

\setupmathsimplealign
  [\c!distance=\v!math,
   \c!leftmargin=\zeropoint,
   \c!rightmargin=\zeropoint,
   \c!left=,
   \c!right=,
   \c!strut=\v!yes,
   \c!spaceinbetween=\mathalignmentparameter\c!spaceinbetween,
   \c!align=\v!all:\v!middle,
   \c!textdistance=.25\emwidth]

\appendtoks
    \frozen\instance\protected\edefcsname\e!start\currentmathsimplealign\endcsname{\math_simplealign_start[\currentmathsimplealign]}%
    \frozen\instance          \defcsname \e!stop \currentmathsimplealign\endcsname{\math_simplealign_stop}%
\to \everydefinemathsimplealign

\permanent\protected\def\math_simplealign_NC
  {\aligntab}

\permanent\protected\def\math_simplealign_EQ
  {\aligntab=\aligntab}

\noaligned\tolerant\permanent\protected\def\math_simplealign_NR[#1]#*[#2]%
  {\unskip
   \strc_formulas_place_number_nested{#1}{#2}\crcr}

\permanent\tolerant\protected\def\math_simplealign_start[#1]#*[#2]%
  {\begingroup
   \edef\currentmathsimplealign{#1}%
   \ifarguments\or\or
     \setupcurrentmathsimplealign[#2]%
   \fi
   \edef\p_strut{\mathsimplealignparameter\c!strut}%
   \ifx\p_strut\v!yes
     \enforced\let\math_align_strut\strut
   \else
     \enforced\let\math_align_strut\relax
   \fi
   \mathatom \s!class \mathwrappedcode \bgroup
   \scratchdimen\mathsimplealignparameter\c!leftmargin\relax
   \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
   \mathsimplealignparameter\c!left\relax
   \math_fenced_start_wrap{\mathsimplealignparameter\c!fences}%
   \mathatom \s!class \mathconstructcode \bgroup
   \vcenter\bgroup
   \enforced\let\MC\math_simplealign_NC
   \enforced\let\NC\math_simplealign_NC
   \enforced\let\NR\math_simplealign_NR
   \enforced\let\EQ\math_simplealign_EQ
   \enforced\let\TB\math_common_TB
   \math_eqalign_set_defaults
   \math_eqalign_set_columns{\mathsimplealignparameter\c!align}%
   \global\c_math_eqalign_column\zerocount
   \global\c_math_eqalign_row\plusone
   \edef\m_simplealign_distance{\mathsimplealignparameter\c!distance}%
   \strc_math_setup_spacing_aligned\mathcasesparameter
   \enablematrixalign
   \halign callback \s!attr \mathnumberlocationattribute \zerocount \bgroup
     \global\c_math_eqalign_column\zerocount
     \global\advanceby\c_math_eqalign_row\zerocount
     \ignorespaces
     \aligncontent % dummy
     \removeunwantedspaces
     \lastleftclass \mathbegincode
     \lastrightclass\mathendcode
     \aligntab
     \global\advanceby\c_math_eqalign_column\plusone
     \math_left_of_eqalign  % \hfil
     \ignorespaces
     \math_align_strut
     \startforceddisplaymath
     \aligncontent
     \stopforceddisplaymath
     \removeunwantedspaces
     \math_right_of_eqalign % \hfil
     \aligntab
     \aligntab
     \global\advanceby\c_math_eqalign_column\plusone
     \math_left_of_eqalign  % \hfil
     \ifx\m_simplealign_distance\v!math
       \mathbeginclass\lastrightclass
     \else
       \kern\m_simplealign_distance
     \fi
     \ignorespaces
     \math_align_strut
     \startforceddisplaymath
     \aligncontent
     \stopforceddisplaymath
     \removeunwantedspaces
     \math_right_of_eqalign % \hfil
     \crcr}

\noaligned\permanent\protected\def\math_simplealign_stop
  {\crcr
   \egroup
   \egroup
   \egroup
   \math_fenced_stop_wrap
   \mathsimplealignparameter\c!right\relax
   \scratchdimen\mathsimplealignparameter\c!rightmargin\relax
   \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
   \setbox\scratchbox\hbox{\mathsimplealignparameter\c!text}%
   \ifvoid\scratchbox\else
     \kern\mathsimplealignparameter\c!textdistance % hskip
     \vcenter{\box\scratchbox}%
   \fi
   \egroup
   \endgroup}

%D It's not that spectacular apart from spacing being proper inter atom spacing
%D using one of the new \LUAMETATEX\ mechanisms.
%D
%D \starttyping
%D \definemathsimplealign
%D   [whatever]
%D   [left={\startmathfenced[sesac]},
%D    right=\stopmathfenced]
%D
%D  % distance=math,
%D  % distance=\zeropoint,
%D  % distance=1cm,
%D  % align={all:left}]
%D
%D \startformula
%D     \startwhatever[text=simple]
%D       \NC x \NC = \NC r   \NC \cos\theta \NR
%D       \NC y \NC = \NC \frac{1}{2}   \NC \sin\theta \NR
%D       \NC 9 \NC = \NC 123 \NC \sin\theta \NR
%D     \stopwhatever
%D \stopformula
%D \stoptyping

%D Usage \type {\sum _ {\mstack {i \in V_{0}, i \neq j}}}, documented by Mikael:

\permanent\protected\def\mstack#1% todo: make it configurable
   {\begingroup
    \scratchtoks\emptytoks \setcharstrut(\relax
    \processcommalist[#1]{\iftok\scratchtoks\emptytoks\else\toksapp\scratchtoks{\mathstrut\NR}\fi\toksapp\scratchtoks}%
    \expandafter\startsubstack\the\scratchtoks\mathstrut\stopsubstack
    \endgroup}

%D Similar to simplecases:
%D
%D \starttyping
%D \startformula
%D     \equationsystem {
%D        {(1-a)}x^{2x} - 3y_2 + 14z  = 2 + x,
%D        {(1-a)}x^2    - 3y_2 +  4z <= 62,
%D        {(1-a)}x^a    - 3y_2 +  4z >= 12,
%D        {(1-a)}x^{2a} - 3y_2 + 24z != 4,
%D               x^^2   - 3y_2 +  4z ~  1,
%D               x^^2   - 3y_2 +  4z ≠  1,
%D             -2x      -         4z <> 10,
%D     }
%D \stopformula
%D \stoptyping

\permanent\tolerant\protected\def\math_align_simple[#1]#*[#2]#:#3%
  {\begingroup
   \edef\currentmathsimplealign{#1}%
   \setupcurrentmathsimplealign[#2]%
   \math_simplealign_start[\currentmathsimplealign]%
   \clf_simplealign{\mathsimplealignparameter\c!alternative}{\mathsimplealignparameter\c!action}{#3}%
   \math_simplealign_stop
   \endgroup}

\appendtoks
    \edef\p_simplecommand{\mathsimplealignparameter\c!simplecommand}%
    \ifempty\p_simplecommand\else
        \frozen\protected\instance\edefcsname\p_simplecommand\endcsname{\math_align_simple[\currentmathsimplealign]}%
    \fi
\to \everydefinemathsimplealign

\definemathsimplealign % new !
  [equationsystem]
  [\c!simplecommand=equationsystem,
   \c!alternative=equationsystem, % for the moment we use this key
   \c!align={all:right},
   \c!distance=\v!math,
   \c!left=,
   \c!right=]

\definemathsimplealign
  [lequationsystem]
  [equationsystem]
  [\c!simplecommand=lequationsystem,
   \c!left={\startmathfenced[cases]},
   \c!right=\stopmathfenced]

\definemathsimplealign
  [requationsystem]
  [equationsystem]
  [\c!simplecommand=requationsystem,
   \c!left={\startmathfenced[sesac]},
   \c!right=\stopmathfenced]

\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