%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} and \type {\displayindent} variables
%D are only known and used inside a display formula, In \MKXL\ we no longer use
%D display mode at all.

% \checkeddisplaywidth   % obsolete
% \maximizeddisplaywidth % obsolete

%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     \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
\newtoks     \t_math_matrix_NL_NR

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

\installcorenamespace{mathalignendclass}   % maybe {complexmathendclass}

\global\expandafter\integerdef\csname\??mathalignendclass\the\zerocount\endcsname\mathendcode

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

%D Really needed when we grid snap (and package):

\appendtoks
    \parindent\zeropoint
\to \everybeforedisplayformula

%D For compatibility we have this location stuff. It is kind of messy and uses
%D tabskip magick plus signal 0x08 for an exception. Contrary to normal left
%D aligned formulas we keep the number inline.

% \startbuffer
%     \startformula
%       A = B
%     \stopformula
%
%     \startplaceformula \startformula
%       A = B
%     \stopformula \stopplaceformula
%
%     \startformula \startalign
%       \NC A \EQ B \NR
%       \NC A \EQ B \NR
%     \stopalign \stopformula
%
%     \startplaceformula \startformula \startalign
%       \NC A \EQ B \NR[+]
%       \NC A \EQ B \NR[+]
%     \stopalign \stopformula \stopplaceformula
% \stopbuffer
%
% \startbuffer[all]
%     \section[title=middle] \setupmathalignment[location={center,middle}] \getbuffer
%     \section[title=left]   \setupmathalignment[location={center,left}]   \getbuffer
%     \section[title=right]  \setupmathalignment[location={center,right}]  \getbuffer
% \stopbuffer
%
% {\setupformula[location=right] \getbuffer[all] \page}
% {\setupformula[location=left]  \getbuffer[all] \page}

\newcount\c_math_eqalign_slots

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

\def\math_eqalign_set_defaults
  {%\normalbaselines % per januari 2024 commented
   \mathsurround\zeropoint
   \mathsurroundskip\zeroskip
   \tabskip\zeroskip
   \everycr\emptytoks}

\protected\def\math_math_in_eqalign_start
  {\mathbeginclass
     \ifconditional\c_math_eqalign_force_text
       % really? check mtext
       \mathordcode
     \orelse\ifcase\c_math_eqalign_column\or
       \mathunsetcode
     \orelse\ifcsname\??mathalignendclass\tointeger{\c_math_eqalign_column-\plusone}\endcsname
       \lastnamedcs
     \else
       \mathunsetcode
     \fi
   \mathendclass\mathordinarycode % added
   \ifconditional\c_math_eqalign_force_text
     \usemathstyleparameter\mathalignmentparameter\c!textstyle
   \else
     \startforceddisplaymath
     \usemathstyleparameter\mathalignmentparameter\c!mathstyle
   \fi}

\protected\def\math_math_in_eqalign_stop
  {\ifconditional\c_math_eqalign_force_text
     % really? check mtext
     \global\expandafter\integerdef\csname\??mathalignendclass\the\c_math_eqalign_column\endcsname\mathordcode
   \else
      \stopforceddisplaymath
      \ifnum\lastrightclass<\mathunsetcode
        \global\expandafter\integerdef\csname\??mathalignendclass\the\c_math_eqalign_column\endcsname\lastrightclass
      \fi
   \fi
   \global\c_math_eqalign_force_text\conditionalfalse}

\protected\def\math_math_in_eqalign#1% protected is not obeyed with \span
  {% preamble \span ... i really need some extension
   \tabskip\zeroskip
   \everycr\emptytoks
   \math_math_in_eqalign_start % protected
   #1%
   \math_math_in_eqalign_stop} % protected

\noaligned\protected\def\math_text_in_eqalign#1%
  {\mathbeginclass\mathordcode
   \mathendclass  \mathordcode
   \startimath
   \tabskip\zeroskip
   \everycr\emptytoks
   #1% huh, imath?
   \stopimath}

\def\math_place_number_in_alignment#1#2%
  {\c_strc_formulas_number_in_alignment\conditionaltrue
   \dostarttaggednodetail\t!mtext
     \strc_formulas_place_number_nested{#1}{#2}%
   \dostoptagged}

%D There was a request for rules on the list when we had the 2024 meeting:
%D
%D \starttyping
%D \startformula
%D \startalign[n=7,align=*:middle,rulecolor=red,rulethickness=.25ex]
%D \NC 1   \NC + \NC 222 \NC + \NC  33  \NC + \NC  44  \NR
%D \HL
%D \NC 11  \NC + \NC 22  \NC + \NC  3   \NC + \NC  4   \NR
%D \HL[1,green,3mm,3,reset,5,blue,7]
%D \NC 111 \NC + \NC 2   \NC + \NC  333 \NC + \NC  444 \NR
%D \stopalign
%D \stopformula
%D \stoptyping

% musical timestamp, listening to Anna Von Hausswolff on pipe organ (ctx 2024 after
% party with Mikael S)

\newdimension\d_math_alignment_HL_width

\lettonothing\p_math_alignment_HL_color

\lettonothing\p_math_alignment_number

\protected\def\math_alignment_HL_rule
  {\leaders
     \hrule
       \s!height \d_math_alignment_HL_width
       \s!depth  \d_math_alignment_HL_width
     \relax
     \hfill}

\def\math_alignment_HL_reset
  {\d_math_alignment_HL_width{\mathalignmentparameter\c!rulethickness/2}%
   \edef\p_math_alignment_HL_color{\mathalignmentparameter\c!rulecolor}}

\def\math_alignment_HL_step_add#1%
  {\ifcase\scratchcounter\else
     \expandedrepeat{#1-\scratchcounter}{\toksapp\scratchtoks{\aligntab\omit}}%
   \fi
   \scratchcounter#1\relax
   \etoksapp\scratchtoks{%
   % \noexpand\def\noexpand\p_math_alignment_HL_color{\p_math_alignment_HL_color}%
     \colo_helpers_activate{\p_math_alignment_HL_color}%
     \d_math_alignment_HL_width\the\d_math_alignment_HL_width\relax
     \math_alignment_HL_rule}}

\def\math_alignment_HL_step#1%
  {\ifcstok{#1}\v!reset
     \math_alignment_HL_reset
   \orelse\ifchkdim#1\or
     \d_math_alignment_HL_width#1\relax
   \orelse\ifchknum#1\or
     \math_alignment_HL_step_add{#1}%
   \else
     \def\p_math_alignment_HL_color{#1}%
   \fi}

\tolerant\def\math_alignment_HL[#1]%
  {\noalign{\nointerlineskip}%
   \omit\aligntab\omit
   \math_alignment_HL_reset
   \novrule
     \s!height {\mathalignmentparameter\c!toffset}%
     \s!depth  {\mathalignmentparameter\c!boffset}%
   \relax
   \ifparameter#1\or
     \global\scratchcounter\zerocount
     \scratchtoks{\aligntab\omit}%
     \processcommalist[#1]\math_alignment_HL_step
     \expand\scratchtoks
   \else
     \colo_helpers_activate\p_math_alignment_HL_color
     \math_alignment_HL_rule
     \expandedrepeat{\c_math_eqalign_slots+\minusone}{\span\omit}%
   \fi
   \crcr
   \noalign{\nointerlineskip}}

% 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

\permanent\def\strc_math_effective_width
  {\dimexpr
     \ifzeropt\d_strc_formulas_display_width
       \hsize
     \else
       \d_strc_formulas_display_width
     \fi
      -\leftskip
      -\rightskip
   \relax}

% 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     \c_math_align_overflow_mode\conditionaltrue
\newconditional\c_math_align_reformat_mode     \c_math_align_reformat_mode\conditionaltrue
\newconditional\c_strc_formulas_overlay_number \c_strc_formulas_overlay_number\conditionaltrue

\protected\def\math_text_in_align
  {\scratchcounter{\c_math_eqalign_row+\plusone}%
   \usemathalignmentstyleandcolor\c!textstyle\c!textcolor
   \usemathalignmentstyleandcolor{\c!textstyle:\the\scratchcounter}{\c!textcolor:\the\scratchcounter}%
   \mathalignmentparameter\c!text
   \dostarttaggednodetail\t!mtext
   \mathalignmentparameter{\c!text:\the\scratchcounter}%
   \dostoptagged}

\def\math_align_initialize_class_states
  {}

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

% the fill skips are somewhat hackery here ...

% left

\def\math_prepare_l_eqalign_no_a
  {\relax
   \strut
   \math_text_in_align
   \aligncontent % for picking up the number
   \ifcase\c_strc_formulas_align_alignment
     \ifnum\c_strc_math_ragged_status=\plusthree
       \tabskip\zeroskip
     \else
       \tabskip\centeringskip
     \fi
   \or
     \ifnum\c_strc_math_ragged_status=\plusthree
       \tabskip\zeroskip
     \else
       \tabskip\centeringskip
     \fi
   \or
     \tabskip\stretchingfillskip
   \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\zeroskip}

\def\math_prepare_l_eqalign_no_b
  {\aligntab
   \math_next_in_eqalign
   \math_left_of_eqalign
   \span
   \math_math_in_eqalign{\aligncontent}%
   \math_right_of_eqalign
   \tabskip\zeroskip
   }

\def\math_prepare_l_eqalign_no_c_three
  {\hfil
   \tabskip\zeroskip
   \aligntab
   \span
   \boundary\c_math_align_r_marker
   \math_alignment_rbox{\aligncontent}%
   \tabskip\zeroskip}

\def\math_prepare_l_eqalign_no_c_one
  {\hfil
   \tabskip\stretchingfillskip
   \aligntab
   \span
   \boundary\c_math_align_r_marker
   \math_alignment_rbox{\aligncontent}%
   \tabskip\zeroskip}

\def\math_prepare_l_eqalign_no_c_other
  {\hfil
   \tabskip\centeringskip
   \aligntab
   \span
   \boundary\c_math_align_r_marker
   \math_alignment_rbox{\aligncontent}%
   \ifcase\c_strc_formulas_align_alignment
     \tabskip\zeroskip
   \or
     \ifconditional\c_strc_formulas_handle_number
      %\tabskip\zeroskip
       \tabskip\stretchingfillskip
     \else
       \tabskip\stretchingfillskip
     \fi
   \or
     \tabskip\zeroskip
   \fi
  }

\def\math_prepare_l_eqalign_no  % \checkeddisplaymath
  {\math_align_initialize_class_states
   \t_math_align_a{\math_prepare_l_eqalign_no_a}%
   \t_math_align_b{\math_prepare_l_eqalign_no_b}%
   \ifnum\c_strc_math_ragged_status=\plusthree
     \t_math_align_c{\math_prepare_l_eqalign_no_c_three}%
   \orelse\ifnum\c_strc_math_ragged_status=\plusone
     \t_math_align_c{\math_prepare_l_eqalign_no_c_one}%
   \else
     \t_math_align_c{\math_prepare_l_eqalign_no_c_other}%
   \fi
   \math_build_eqalign
   \ifnum\c_strc_math_ragged_status=\plusthree
     \tabskip\stretchingfillskip
   \else
     \tabskip\zeroskip
   \fi}

% right

\def\math_prepare_r_eqalign_no_a
  {\relax
   \strut
   \math_text_in_align
   \tabskip\centeringskip
   \aligncontent % for picking up the number
   \ifcase\c_strc_formulas_align_alignment
     % middle
     \boundary\c_math_align_l_marker% This is flush left when number
     \tabskip\centeringskip
   \or
     % left
     \tabskip\zeroskip
   \or
     % right
     \tabskip\stretchingfilllskip
   \fi
   \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\zeroskip}

\def\math_prepare_r_eqalign_no_b
  {\aligntab
   \math_next_in_eqalign
   \math_left_of_eqalign
   \span
   \math_math_in_eqalign{\aligncontent}%
   \math_right_of_eqalign
   \tabskip\zeroskip}

\def\math_prepare_r_eqalign_no_c_three
  {\hfil
   \aligntab
   \hfill % the only one !
   \span
   \boundary\c_math_align_r_marker
   \math_alignment_lbox{\aligncontent}%
   \tabskip\zeroskip}

\def\math_prepare_r_eqalign_no_c_one_one
  {\hfil
   \tabskip\stretchingfillskip
   \aligntab
   \span
   \boundary\c_math_align_r_marker
   \math_alignment_lbox{\aligncontent}%
   \tabskip\zeroskip}

\def\math_prepare_r_eqalign_no_c_one_other
  {\hfil
   \tabskip\zeroskip
   \aligntab
   \span
   \boundary\c_math_align_r_marker
   \math_alignment_lbox{\aligncontent}%
   \tabskip\stretchingfillskip}

\def\math_prepare_r_eqalign_no_c_other
  {\hfil
   \ifcase\c_strc_formulas_align_alignment
     % middle
     \tabskip\centeringskip % fails in some cases
   \or
     % left
     \ifconditional\c_strc_formulas_handle_number
       \tabskip\stretchingfillskip
     \else
       \tabskip\zeroskip
     \fi
   \or
     % right
     \ifconditional\c_strc_formulas_handle_number
       \tabskip\stretchingfillskip
     \else
       \tabskip\zeroskip
     \fi
   \fi
   \aligntab
   \span
   \hss % for MS to test this
   \boundary\c_math_align_r_marker
   \math_alignment_lbox{\aligncontent}%
   \ifcase\c_strc_formulas_align_alignment
     % middle
     \tabskip\zeroskip
   \or
     % left
     \ifconditional\c_strc_formulas_handle_number
       \tabskip\zeroskip
     \else
       \tabskip\stretchingfillskip
     \fi
   \or
     % right
     \ifconditional\c_strc_formulas_handle_number
       \tabskip\stretchingfillskip
     \else
       \tabskip\zeroskip
     \fi
   \fi}

\def\math_prepare_r_eqalign_no
  {\math_align_initialize_class_states
   \t_math_align_a{\math_prepare_r_eqalign_no_a}%
   \t_math_align_b{\math_prepare_r_eqalign_no_b}%
   \ifnum\c_strc_math_ragged_status=\plusthree
     \t_math_align_c{\math_prepare_r_eqalign_no_c_three}%
   \orelse\ifnum\c_strc_math_ragged_status=\plusone
     \ifnum\c_strc_math_number_variant=\plusone
       \t_math_align_c{\math_prepare_r_eqalign_no_c_one_one}%
     \else
       \t_math_align_c{\math_prepare_r_eqalign_no_c_one_other}%
     \fi
   \else
     \t_math_align_c{\math_prepare_r_eqalign_no_c_other}%
   \fi
   \math_build_eqalign
   \tabskip\zeroskip}

% done
%
% if we have an issue then we need to check the unless case below

\def\math_halign_checked
  {\enablemathalignrelocate
   \ifgridlinesnapping
     \ifcsname\??snapping\mathalignmentparameter\c!snapping\endcsname
       \alignsnapping\lastnamedcs
     \fi
   \fi
   \halign
     \ifconditional\c_math_align_overflow_mode
       \s!callback
         \align_callback_mathalign
       \s!attr
         \mathnumberlocationattribute{% on whole, different on l/rbox
            %\unless
            \ifcase\c_strc_formulas_align_alignment
              \plustwo
            \orelse\ifconditional\c_math_align_reformat_mode
              \plusfour
            \orelse\ifnum\c_strc_formulas_align_alignment=\plusone
              \ifcstok{\formulaparameter\c!location}\v!left
                \pluseight
              \else
                \plustwo
              \fi
            \else
              \plustwo
            \fi
          * \plussixteen % just a signal
       }%
     \fi
     \ifcase\c_strc_formulas_check_width\else
        to \strc_math_effective_width
     \fi}

\installcorenamespace {mathalignlocation}

\setnewconstant\c_strc_formulas_align_alignment\zerocount % 1=left 2=right
\setnewconstant\c_strc_formulas_align_packed   \zerocount

\let\math_alignment_location_box\hpack

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

\defcsname\??mathalignlocation\v!middle\endcsname{\c_strc_formulas_align_alignment\zerocount}
\defcsname\??mathalignlocation\v!left  \endcsname{\c_strc_formulas_align_alignment\plusone}
\defcsname\??mathalignlocation\v!right \endcsname{\c_strc_formulas_align_alignment\plustwo}

\defcsname\??mathalignlocation\v!packed\endcsname
  {\c_strc_formulas_align_packed\plusone}

\defcsname\??mathalignlocation\v!unpacked\endcsname
  {\c_strc_formulas_align_packed\plustwo}

\defcsname\??mathalignlocation\v!formula\endcsname
  {\c_strc_formulas_align_alignment
     \ifcstok{\formulaparameter\c!align}\v!flushleft
       \plusone
   % \orelse\expandafter\ifx\lastnamedcs\v!flushright
     \orelse\ifcstok{\lastnamedcs}\v!flushright
       \plustwo
     \else
       \zerocount
     \fi}

\def\math_alignment_location_box_set#1{\begincsname\??mathalignlocation#1\endcsname}

\def\math_alignment_location_check#1%
  {\c_strc_formulas_align_alignment\zerocount
   \c_strc_formulas_align_packed\zerocount
   \let\math_alignment_location_box\vcenter
   \processcommacommand[#1]\math_alignment_location_box_set}

%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
     \hpack
       \s!attr \mathnumberlocationattribute{%
        % \c_strc_formulas_align_packed*\pluscclvi % 0x0.00
          \c_math_alignment_packed_signal          % 0x0.00
        + \c_strc_math_ragged_status*\plussixteen  % 0x00.0
        + \plusone                                 % 0x000.
       }%
       \s!attr \mathnumberthresholdattribute{%
         \d_math_eqalign_number_threshold
       }%
       {\strc_formulas_add_distance \plustwo\v!left\mathalignmentparameter
        \box\scratchbox
        \hskip\d_math_alignment_packed_margin
        }%
   \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
     \hpack
       \s!attr \mathnumberlocationattribute{%
        % \c_strc_formulas_align_packed*\pluscclvi % 0x0.00
          \c_math_alignment_packed_signal          % 0x0.00
        + \c_strc_math_ragged_status*\plussixteen  % 0x00.0
        + \plustwo                                 % 0x000.
       }%
       \s!attr \mathnumberthresholdattribute{%
         \d_math_eqalign_number_threshold
       }%
       {\hskip\d_math_alignment_packed_margin
        \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
%    \dostarttaggednodetail\t!mtext
% \c_strc_formulas_number_in_alignment\conditionaltrue
%    \strc_formulas_place_number_nested{#1}{#2}%
% \dostoptagged % mtext
\math_place_number_in_alignment{#1}{#2}%
\dostoptagged % math
\dostoptagged % subformla
   \math_number_right_of_eqalign
   \global\c_math_eqalign_first\conditionaltrue
   \crcr}

\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\c_math_eqalign_first\conditionalfalse
   \fi
   \math_number_left_of_eqalign
   \aligntab}

\newconditional\c_math_eqalign_force_text

\permanent\protected\def\math_alignment_TC
  {\relax
   \ifconditional\c_math_eqalign_first
     \ifx\p_math_alignment_number\v!auto
       \strc_formulas_place_number_nested{+}{}%
     \fi
     \global\c_math_eqalign_first\conditionalfalse
   \fi
   \math_number_left_of_eqalign
   \global\c_math_eqalign_force_text\conditionaltrue
   \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\TC % idem
\installmacrostack\NN % idem
\installmacrostack\EQ % idem
\installmacrostack\NR % idem
\installmacrostack\BC % idem
\installmacrostack\EC % idem
\installmacrostack\HL % idem
\installmacrostack\TB % idem

\appendtoks
    \push_macro_NC
    \push_macro_TC
    \push_macro_NN
    \push_macro_EQ
    \push_macro_NR
    \push_macro_HL
    \push_macro_TB
    \enforced\let\NC\math_alignment_NC
    \enforced\let\TC\math_alignment_TC
    \enforced\let\NN\math_alignment_NN
    \enforced\let\EQ\math_alignment_EQ
    \enforced\let\NR\math_alignment_NR
    \enforced\let\HL\math_alignment_HL
    \enforced\let\TB\math_common_TB
    \global\c_math_eqalign_first\conditionaltrue
    \global\s_strc_math_alignment_inbetween\zeroskip
\to \everymathalignment

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

\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
   \orelse\ifgridlinesnapping
     \global\s_strc_math_alignment_inbetween\zeroskip
   \orelse\ifgridsnapping
     \global\s_strc_math_alignment_inbetween\zeroskip
   \else
     \spac_whitespace_setup
     \global\s_strc_math_alignment_inbetween\parskip
   \fi
   \endgroup}

\newinteger  \c_math_alignment_packed_signal
\newdimension\d_math_alignment_packed_margin

\def\math_alignment_packed_start
  {%\math_eqalign_set_defaults
   \c_strc_formulas_check_width\zerocount
   \c_math_alignment_packed_signal{\c_strc_formulas_align_packed*\pluscclvi}%
   \d_math_alignment_packed_margin\rightskip
   \mathatom
     \s!class \mathwrappedcode
     \s!attr  \mathnumberlocationattribute \c_math_alignment_packed_signal
   \relax
   \bgroup
 % \scratchdimen\mathalignmentparameter\c!leftmargin\relax
 % \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
 % \mathalignmentparameter\c!left\relax
   \math_fenced_start_wrap{\mathalignmentparameter\c!fences}%
   \mathatom
     \s!class \mathconstructcode
   \bgroup}

\def\math_alignment_packed_stop
  {\egroup
   \math_fenced_stop_wrap
 % \mathalignmentparameter\c!right\relax
 % \scratchdimen\mathalignmentparameter\c!rightmargin\relax
 % \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
 % \setbox\scratchbox\hbox{\mathalignmentparameter\c!text}%
 % \ifvoid\scratchbox\else
 %   \kern\mathalignmentparameter\c!textdistance
 %   \vcenter{\box\scratchbox}%
 % \fi
   \egroup
   \d_math_alignment_packed_margin\zeropoint
   \c_math_alignment_packed_signal\zerocount}

\permanent\tolerant\protected\def\math_alignment_start[#1]#*[#S#2]%
  {\begingroup
   \currentmathblobnesting\minusone
   \cdef\currentmathalignment{#1}%
   \ifarguments\or\or
     \setupmathalignment[#1][#2]%
   \fi
   \ifcstok{\mathalignmentparameter\c!adaptive}\v!yes
     \c_math_align_reformat_mode\conditionaltrue
   \else
     \c_math_align_reformat_mode\conditionalfalse
   \fi
   \math_alignment_location_check{\mathalignmentparameter\c!location}% vcenter etc
   %
   \expand\everymathalignment
   \c_math_eqalign_row   \zerocount
   \c_math_eqalign_column\zerocount
   \processcommacommand
     [\mathalignmentparameter\c!align]%
     {\advanceby\c_math_eqalign_column\plusone\math_eqalign_set_column}% takes argument
   \global\c_math_eqalign_column\plusone
   %
   \edef\p_math_alignment_number{\mathalignmentparameter\c!number}%
   \strc_math_setup_spacing_aligned\mathalignmentparameter
   % make preamble
   \ifcstok{\formulaparameter\c!location}\v!left
     \math_prepare_l_eqalign_no
   \else
     \math_prepare_r_eqalign_no
   \fi
   %
   \ifcase\c_strc_formulas_align_packed\else
     \math_alignment_packed_start
   \fi
 % \everycr{\ifcase\c_math_eqalign_row\else\noalign{\penalty\interdisplaylinepenalty}\fi}%
   \math_alignment_location_box
   \ifgridlinesnapping \s!linesnapping \linesnapping \fi
   \bgroup
   \math_halign_checked\expandafter\bgroup\the\scratchtoks\crcr}


\def\math_alignment_stop % can be protected
  {\crcr
   \egroup
   \egroup
   \ifcase\c_strc_formulas_align_packed\else
     \math_alignment_packed_stop
   \fi
   \expand\everymathalignmentdone
   \endgroup}

\installcorenamespace{mathalignment}
\installcorenamespace{mathalignmentvariant}

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

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

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

\setupmathalignment
  [\c!n=2,
   \c!m=1,
   \c!leftmargin=\zeropoint,
   \c!rightmargin=\zeropoint,
   \c!fences=,
   \c!left=,
   \c!right=,
   \c!distance=\emwidth,
   \c!location=\v!formula,
   \c!spaceinbetween=\formulaparameter\c!spaceinbetween,
   \c!numberthreshold=\zeropoint,
   \c!grid=\v!math,
  %\c!rulecolor=red,
   \c!moffset=.25\exheight,
   \c!toffset=\mathalignmentparameter\c!moffset,
   \c!boffset=\mathalignmentparameter\c!moffset,
   \c!rulethickness=\linewidth]

\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

%

\protected\def\math_first_in_eqalign % protection prevents tagging expansion
  {\global\c_math_eqalign_column\plusone
   \global\advanceby\c_math_eqalign_row\plusone
   \currentmathblobnesting\minusone
   \dostarttaggednodetail\t!subformula
   \dostarttaggednodetail\t!math
   }

\protected\def\math_next_in_eqalign % protection prevents tagging expansion
  {\global\advanceby\c_math_eqalign_column\plusone
   \currentmathblobnesting\minusone}

\protected\def\math_left_of_eqalign
  {\ifcsname\??mathalignmentvariant\the\c_math_eqalign_column\endcsname
     \ifcase\lastnamedcs \or \relax \or \hfill \or \hfill \fi
   \orelse\ifcsname\??mathalignmentvariant\the\zerocount\endcsname
     \ifcase\lastnamedcs \or \relax \or \hfill \or \hfill \fi
   \orelse\ifcsname\??mathalignmentvariant\tointeger{\c_math_eqalign_column-\c_math_eqalign_repeat}\endcsname
     \ifcase\lastnamedcs \or \relax \or \hfill \or \hfill \fi
   \fi}

\protected\def\math_right_of_eqalign
  {\ifcsname\??mathalignmentvariant\the\c_math_eqalign_column\endcsname
     \ifcase\lastnamedcs \or \hfill \or \relax \or \hfill \fi
   \orelse\ifcsname\??mathalignmentvariant\the\zerocount\endcsname
     \ifcase\lastnamedcs \or \hfill \or \relax \or \hfill \fi
   \orelse\ifcsname\??mathalignmentvariant\tointeger{\c_math_eqalign_column-\c_math_eqalign_repeat}\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\d_strc_formulas_number\else
     \ifconditional\c_math_alignment_local_number
       \ifcase\c_strc_math_number_location\or\or
         \strc_math_flush_number_box
       \fi
     \else
       \strc_math_flush_number_box
     \fi
   \fi}

\def\math_number_left_of_eqalign
  {\ifcase\d_strc_formulas_number\else
     \ifconditional\c_math_alignment_local_number
       \ifcase\c_strc_math_number_location\or
         \strc_math_flush_number_box
       \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
  {\ifempty{#2}%
     % current counter
   \orelse\ifchknumber#1\or
     \c_math_eqalign_column\lastchknumber
   \else
     \c_math_eqalign_column\zerocount
   \fi
   \expandafter\integerdef\csname\??mathalignmentvariant\the\c_math_eqalign_column\endcsname
     \ifcsname\??mathalignmentvariant#2\endcsname\lastnamedcs\else\zerocount\fi\relax}

\def\math_eqalign_set_column#1%
  {\expanded{\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}

% can't we reuse these numbers ?

\letcsname\??mathalignmentvariant\v!normal    \endcsname\zerocount
\letcsname\??mathalignmentvariant\v!flushright\endcsname\plusone
\letcsname\??mathalignmentvariant\v!left      \endcsname\plusone
\letcsname\??mathalignmentvariant\v!right     \endcsname\plustwo
\letcsname\??mathalignmentvariant\v!flushleft \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
    \protected\frozen\instance\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
   \cdef\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
        \protected\frozen\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
     \usemathstyleparameter\mathcasesparameter\c!mathstyle
   \fi}

\def\math_cases_NC_one
  {\mathcasesparameter\c!lefttext\relax
   \ifmmode\stopimath\fi
   \aligntab
   \ifmmode\else
     \startimath
     \usemathstyleparameter\mathcasesparameter\c!mathstyle
   \fi
   \mathcasesparameter\c!righttext\relax}

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

\def\math_cases_TC_zero % needs checking
 %{\ifmmode\else\startimath\fi}
  {}

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

\def\math_cases_TC_two
 %{\ifmmode\stopimath\fi} % needs checking
  {}

\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}

%D The \type {#.} catches this case:
%D
%D \starttyping
%D \dm {
%D     \startcases[righttext=\mtext{if }]
%D         \NC -x \NC x < 0 \NR % see (**)
%D         \NC  x \NC x > 0 \NR
%D
%D     \stopcases
%D }
%D \stoptyping

\noaligned\tolerant\permanent\protected\def\math_cases_NR#.[#1]#*[#2]%
  {\unskip
   \ifmmode\stopimath\fi
   \aligntab
   \global\c_math_cases_nc\zerocount
% \c_strc_formulas_number_in_alignment\conditionaltrue
% \dostarttaggednodetail\t!mtext
%    \strc_formulas_place_number_nested{#1}{#2}%
% \dostoptagged
\math_place_number_in_alignment{#1}{#2}%
   \math_number_right_of_eqalign
   \dostarttaggednodetail\t!mtablerow
   \dostarttaggednodetail\t!mtablecell
   \hpack{\box\b_strc_formulas_number}%
   \dostoptagged % cell
   \dostoptagged % row
   \crcr}

\installglobalmacrostack\c_math_cases_nc

\permanent\tolerant\protected\def\math_cases_start[#1]#*[#S#2]%
  {\begingroup
   \currentmathblobnesting\minusone
   \cdef\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}%
   \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
   \mathcasesparameter\c!left
   \math_fenced_start_wrap{\mathcasesparameter\c!fences}%
   \mathatom \s!class \mathconstructcode \bgroup
   \vcenter\bgroup
   \mathbeginclass\mathbegincode % not really needed, see (**)
   \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
   \enablemathalignrelocate
   \dostarttagged\t!math{cases}% \empty
   \dostarttagged\t!mtable\currentmathcases
   \halign
     \s!callback
       \align_callback_mathalign
     \s!attr
       \mathnumberlocationattribute \zerocount
     \bgroup % use \indexofregister here
     \dostarttaggednodetail\t!mtablerow
     \ifmmode\else\startimath\fi
     \usemathstyleparameter\mathcasesparameter\c!mathstyle
     \dostarttaggednodetail\t!mtablecell
     \aligncontent
     \dostoptagged % cell
     \ifmmode\stopimath\fi
     \hfil
     \aligntab
     \kern{\mathcasesparameter\c!distance}%
     \math_cases_strut % looks better
     \dostarttaggednodetail\t!mtablecell
     \aligncontent
     \dostoptagged % cell
     \hfil
     \aligntab
     \kern{\mathcasesparameter\c!numberdistance}%
     \span
     \math_text_in_eqalign
       {\dostarttaggednodetail\t!mtablecell
        \aligncontent
        \dostoptagged % cell
        \dostoptagged}% row
     \crcr} % todo: number

\noaligned\permanent\protected\def\math_cases_stop
  {\crcr
   \egroup
   \dostoptagged % table
   \dostoptagged % math
   \egroup
   \egroup
   \math_fenced_stop_wrap
   \mathcasesparameter\c!right\relax
   \scratchdimen{\mathcasesparameter\c!rightmargin}%
   \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
%D together 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
    \protected\frozen\instance\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
   \dostarttaggednodetail\t!math
   \dostarttaggednodetail\t!mtable}

\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
   \dostarttaggednodetail\t!mtablerow
   \endlocalcontrol}

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

\protected\def\math_matrix_start_cell
  {\currentmathblobnesting\minusone
   \dostarttaggednodetail\t!mtablecell
   \hss
   \math_left_of_eqalign
   \everycr\emptytoks
   \startimath
   \usemathstyleparameter\mathmatrixparameter\c!mathstyle}

\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
     {\ifchknumber#1\or\lastchknumber\else(\c_math_matrix_columns+\minusone)\fi}%
     \plusone
   {\omit\span}%
   \kern-.25\d_math_eqalign_distance % bah but needed
   \expanded{\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
\newconditional\c_math_matrix_sl_seen

% 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}

\def\math_matrix_preamble
  {\math_matrix_strut
   \kern-.25\d_math_eqalign_distance
   \math_matrix_anchor
   \kern.25\d_math_eqalign_distance
   \global\advanceby\c_math_eqalign_column\plusone
   \math_matrix_start_cell
   \aligncontent
   \math_matrix_stop_cell
   % from here we repeat
   \aligntab
   \aligntab
   \kern.25\d_math_eqalign_distance
   \math_matrix_anchor
   \kern.25\d_math_eqalign_distance
   \global\advanceby\c_math_eqalign_column\plusone
   \math_matrix_start_cell
   \aligncontent
   \math_matrix_stop_cell}

\permanent\protected\def\math_matrix_NR
  {% we need to make sure we end the cell first (otherwise export looses mtd)
   \math_matrix_stop_cell
   \let\math_matrix_stop_cell\relax
   %
   \kern.25\d_math_eqalign_distance
   \math_matrix_anchor
   \kern-.25\d_math_eqalign_distance
   \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
   \grph_line_inject_VL_space} % see later

\permanent\protected\def\math_matrix_pickup{\global\c_math_matrix_first\conditionaltrue}
\permanent\protected\def\math_matrix_NC_yes{\global\c_math_matrix_first\conditionalfalse}
\permanent\protected\def\math_matrix_NC_nop{\aligntab} % avoids lookahead

\def\math_matrix_check_rule_step#1%
  {\ifchkdim#1\or
     \scratchdimen#1\relax
 % \orelse\ifchknum#1\or
   \orelse\ifchkdim#1pt\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}%
   \scratchdimen\d_math_eqalign_rulethickness
   \edef\p_rulecolor{\mathmatrixparameter\c!rulecolor}%
   \ifempty{#1}\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]
\definesystemattribute[mathalignmenttop]  [public]
\definesystemattribute[mathalignmentmid]  [public]
\definesystemattribute[mathalignmentbot]  [public]

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

\newconditional\c_math_matrix_trace_hl

\installtextracker
  {math.matrices.hl}
  {\c_math_matrix_trace_hl\conditionaltrue}
  {\c_math_matrix_trace_hl\conditionalfalse}

\def\math_matrix_HL_indeed#1#2%
  {\noalign\bgroup
     \math_matrix_check_rule[#2]%
     \divideby\scratchdimen\plustwo
     \ifdim\scratchdimen>\zeropoint
       \attribute\mathalignmenttopattribute\dimexpr\mathmatrixparameter\c!toffset\relax
       \attribute\mathalignmentbotattribute\dimexpr\mathmatrixparameter\c!boffset\relax
       \scratchdistance{\mathmatrixparameter\c!moffset}%
       \ifdim\scratchdistance>\zeropoint
         \begingroup
         \ifconditional\c_math_matrix_trace_hl
           \darkred \hrule \s!width \onepoint
         \else
           \nohrule
         \fi
           \s!attr  \mathalignmentvruleattribute\plustwo
           \s!height\scratchdistance
           \s!depth \zeropoint
         \relax
         \endgroup
       \fi
       \hrule
         \s!attr  \mathalignmentvruleattribute\plusthree
         \s!height\scratchdimen
         \s!depth \scratchdimen
       \relax
       \scratchdimentwo\zeropoint
       \ifnum#1>\plusone
         \scratchdimenone.125\d_math_eqalign_distance
         \localcontrolledloop\plustwo#1\plusone
            {\kern\scratchdimenone
             \advanceby\scratchdimentwo\scratchdimenone
             \hrule
               \s!attr  \mathalignmentvruleattribute\plusthree
               \s!height\scratchdimen
               \s!depth \scratchdimen
             \relax
             \advanceby\scratchdimentwo\scratchdimen
             \advanceby\scratchdimentwo\scratchdimen
            }%
       \fi
       \ifdim\scratchdistance>\zeropoint
         \begingroup
         \ifconditional\c_math_matrix_trace_hl
           \darkgreen \hrule \s!width \onepoint
         \else
           \nohrule
         \fi
           \s!attr  \mathalignmentvruleattribute\plusfour
           \s!attr  \mathalignmentmidattribute\scratchdimentwo
           \s!height\zeropoint
           \s!depth \scratchdistance
         \relax
         \endgroup
       \fi
     \else
        % zero dimensions disable the rule
     \fi
   \egroup}

\permanent\tolerant\noaligned\protected\def\math_matrix_HL  [#1]#*{\math_matrix_HL_indeed\plusone{#1}}
\permanent\tolerant\noaligned\protected\def\math_matrix_HLHL[#1]#*{\math_matrix_HL_indeed\plustwo{#1}}

\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\c_math_matrix_first\conditionalfalse
   \global\c_math_matrix_sl_seen\conditionaltrue
   \enablematrixrules
 % \begingroup
 % \attribute\mathalignmenthruleattribute\plusone % we check the glue
   \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
 % \endgroup
   \kern.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
     {(\ifchknumber#1\or\lastchknumber\else\c_math_matrix_columns\fi)*\plustwo+\minusone}%
     \plusone
   {\span\omit}}%

\def\math_matrix_hrule_progress_first#1%
  {\expandedloop
     \plusone
     {(\ifchknumber#1\or\lastchknumber\else\c_math_matrix_columns\fi+\minusone)*\plustwo+\plusone}%
     \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\math_matrix_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\SL\math_matrix_SL
   \enforced\let\NR\math_matrix_NL_NR}

\def\math_matrix_VL_indeed#1#2%
  {\aligntab
   \math_matrix_vertical_rule_yes{#2}%
   \localcontrolledloop\plustwo#1\plusone
     {\kern.125\d_math_eqalign_distance
      \math_matrix_vertical_rule_yes{#2}}%
%    \kern.5\d_math_eqalign_distance
   \global\c_math_matrix_first\conditionalfalse
   \aligntab
   \boundary\c_math_matrix_vl_boundary
   \enforced\let\NR\math_matrix_NL_NR}

\appendtoks
    % vl delegated to lua tex rules
    \ifnum\lastboundary=\c_math_matrix_vl_boundary
        \kern\ifconditional \c_math_matrix_sl_seen-1.5\else-.5\fi\d_math_eqalign_distance
    \fi
\to \t_math_matrix_NL_NR

\permanent\tolerant\protected\def\math_matrix_VL  [#1]#*{\math_matrix_VL_indeed\plusone{#1}}
\permanent\tolerant\protected\def\math_matrix_VLVL[#1]#*{\math_matrix_VL_indeed\plustwo{#1}}

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

\permanent\protected\def\math_matrix_NL_NR
  {\expand\t_math_matrix_NL_NR
   \math_matrix_anchor
   \math_matrix_stop_row
   \math_matrix_pickup
   \crcr
   \math_matrix_start_row}

\appendtoks
   \enforced\let\NL\math_matrix_NL
   \global\c_math_matrix_sl_seen\conditionalfalse
\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
   \dostarttaggednodetail\t!mtablerow
   \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
   % just because it's easy:
   \enforced\let\VLVL\math_matrix_VLVL
   \enforced\let\HLHL\math_matrix_HLHL
\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

\newdimension\d_math_matrix_max_left
\newdimension\d_math_matrix_max_right

\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\c_math_matrix_text\conditionaltrue
   \global#1\conditionaltrue
   \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\c_math_matrix_text\conditionalfalse
   \global\c_math_matrix_text_l\conditionalfalse
   \global\c_math_matrix_text_r\conditionalfalse
   \global\c_math_matrix_text_t\conditionalfalse
   \global\c_math_matrix_text_b\conditionalfalse
   \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

\newconditional\c_math_matrix_text_mode

% \def\math_matrix_start_processing
%   {%
%    \ifmmode
%      \c_math_matrix_text_mode\conditionalfalse
%    \else
%      \c_math_matrix_text_mode\conditionaltrue
%    \fi
%    \ifconditional\c_math_matrix_text_mode
%      \dontleavehmode
%    \else
%      \mathmatrixparameter\c!left\relax
%      \math_fenced_start_wrap{\mathmatrixparameter\c!fences}%
%      \mathatom \s!class \mathconstructcode
%    \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
%    \global\d_math_matrix_max_left \zeropoint
%    \global\d_math_matrix_max_right\zeropoint
%   %\tabskip.5\d_math_eqalign_distance
%    \tabskip\zeroskip
%    \math_matrix_pickup
%    \expand\everymathmatrix
%    %
%    \setbox\nextbox\vbox\bgroup
%    \math_matrix_start_table
%    \halign
%       \s!callback
%         \align_callback_mathmatrix
%    \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
%    \ifconditional\c_math_matrix_text_mode\else
%      \math_fenced_stop_wrap
%      \mathmatrixparameter\c!right\relax
%    \fi}

\def\math_matrix_start_processing
  {\bgroup % outer
   \ifmmode
     \c_math_matrix_text_mode\conditionalfalse
   \else
     \c_math_matrix_text_mode\conditionaltrue
     \dontleavehmode
     \startimath
   \fi
   \d_math_matrix_margin_l{\mathmatrixparameter\c!leftmargin }%
   \d_math_matrix_margin_r{\mathmatrixparameter\c!rightmargin}%
   \d_math_matrix_margin_t\strutdp
   \d_math_matrix_margin_b\strutht
   \global\d_math_matrix_max_left \zeropoint
   \global\d_math_matrix_max_right\zeropoint
   \tabskip\zeroskip
   \math_matrix_pickup
   \expand\everymathmatrix
   %
   \setbox\nextbox\vbox
   \bgroup % vbox
   \math_matrix_start_table
   \halign \s!callback \align_callback_mathmatrix
   \bgroup % halign
     % 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 % halign
   \math_matrix_stop_table
   \egroup % vbox
   \mathmatrixleft  % experimental hook
   \math_matrix_finish_nextbox
   \mathmatrixright % experimental hook
   \ifconditional\c_math_matrix_text_mode
     \stopimath
   \fi
   \egroup} % outer

\permanent\protected\def\mathmatrixmaxleftwidth {\d_math_matrix_max_left }
\permanent\protected\def\mathmatrixmaxrightwidth{\d_math_matrix_max_right}

\let\math_matrix_strut\strut

\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}

\newinteger\c_math_eqalign_column_saved
\newinteger\c_math_eqalign_row_saved

% \installglobalmacrostack\c_math_matrix_first

\tolerant\protected\def\math_matrix_start[#1]#*[#S#2]%
  {\begingroup
   \currentmathblobnesting\minusone
   \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
   \cdef\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

% This alignment option will either go away or become a atom property (key).

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

% \def\math_matrix_finish_nextbox
%   {\scratchcounter\mathstyle\relax
%    \scratchwidth\wd\nextbox
% \setbox\scratchbox\hbox\bgroup
%    \begincsname\??mathmatrixalignlocation\mathmatrixparameter\c!location\endcsname\hbox\bgroup
%      \normalstartimath
%      \givenmathstyle\scratchcounter
%      \ifzeropt\d_math_matrix_margin_l\else\kern\d_math_matrix_margin_l\fi
%      \ifconditional\c_math_matrix_text_mode
%        \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
%      \else
%         \vcenter{\box\nextbox}% \was \vcenter
%      \fi
%      \ifzeropt\d_math_matrix_margin_r\else\kern\d_math_matrix_margin_r\fi
%      \normalstopimath
%    \egroup
% \egroup
%    \ifconditional\c_math_matrix_text
%      \ifempty{\mathmatrixparameter\c!left\mathmatrixparameter\c!right\mathmatrixparameter\c!fences}\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
%    \edef\p_leftedge {\mathmatrixparameter\c!leftedge }%
%    \edef\p_rightedge{\mathmatrixparameter\c!rightedge}%
%    \ifempty\p_leftedge\else
%      \hskip\dimexpr\d_math_matrix_max_left+\p_leftedge\relax
%    \fi
% %    \ifconditional\c_math_matrix_text_mode
%      \box\scratchbox
% %    \else
% %      \mathatom \s!class \mathconstructcode {\box\scratchbox}%
% %    \fi
%    \ifempty\p_rightedge\else
%      \hskip\dimexpr\d_math_matrix_max_right+\p_rightedge\relax
%    \fi
%    }

%D \starttyping
%D \ruledhbox{\im{
%D     \startmatrix[left=\left(,right=\right)]
%D       \NC        \TT \ttx 1 \NC       \TT \ttx 2 \NC       \TT \ttx 3 \NC        \NR
%D       \LT \ttx 1 \NC a      \NC \dots \NC aa     \NC \dots \NC aaa    \RT \ttx 1 \NR
%D       \LT \ttx 2 \NC b      \NC \dots \NC bb     \NC \dots \NC bbb    \RT \ttx 2 \NR
%D       \LT \ttx 3 \NC c      \NC \dots \NC cc     \NC \dots \NC ccc    \RT \ttx 3 \NR
%D       \NC        \BT \ttx 1 \NC       \BT \ttx 2 \NC       \BT \ttx 3 \NC        \NR
%D     \stopmatrix
%D }}
%D \ruledhbox{\im{
%D     \startmatrix[left=\left(,right=\right),rightedge=none,leftedge=none]
%D       \NC        \TT \ttx 1 \NC       \TT \ttx 2 \NC       \TT \ttx 3 \NC        \NR
%D       \LT \ttx 1 \NC a      \NC \dots \NC aa     \NC \dots \NC aaa    \RT \ttx 1 \NR
%D       \LT \ttx 2 \NC b      \NC \dots \NC bb     \NC \dots \NC bbb    \RT \ttx 2 \NR
%D       \LT \ttx 3 \NC c      \NC \dots \NC cc     \NC \dots \NC ccc    \RT \ttx 3 \NR
%D       \NC        \BT \ttx 1 \NC       \BT \ttx 2 \NC       \BT \ttx 3 \NC        \NR
%D     \stopmatrix
%D }}
%D \stoptyping

\newconstant\c_math_last_l_class
\newconstant\c_math_last_r_class

\setupmathmatrix
  [\c!rightedge=\zeropoint,
   \c!leftedge=\zeropoint]

\def\math_matrix_finish_nextbox
  {\scratchcounter\mathstyle\relax
   \scratchwidth\wd\nextbox
   \dostarttagged\t!math\empty % needed !
   \setbox\scratchbox\hbox\bgroup
     \begincsname\??mathmatrixalignlocation\mathmatrixparameter\c!location\endcsname\hbox\bgroup
       \normalstartimath
       \givenmathstyle\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
            }%
       }%
       \math_fenced_stop_wrap
       \mathmatrixparameter\c!right\relax
       \ifzeropt\d_math_matrix_margin_r\else\kern\d_math_matrix_margin_r\fi
       \normalstopimath
       % or carry over one group
       \global\c_math_last_l_class\lastleftclass
       \global\c_math_last_r_class\lastrightclass
     \egroup
   \egroup
   \ifconditional\c_math_matrix_text % not _mode
     \ifempty{\mathmatrixparameter\c!left\mathmatrixparameter\c!right\mathmatrixparameter\c!fences}\else
       \scratchdistance{(\wd\scratchbox-\scratchwidth)/\plustwo}%
       \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{\dp\scratchbox+\lineheight}%
   \fi
   \ifconditional\c_math_matrix_text_t
     \ht\scratchbox{\ht\scratchbox+\lineheight}%
   \fi
   \mathatom
     \s!leftclass  \c_math_last_l_class
     \s!rightclass \c_math_last_r_class
     \bgroup
       \edef\p_leftedge {\mathmatrixparameter\c!leftedge }%
       \edef\p_rightedge{\mathmatrixparameter\c!rightedge}%
       \ifempty\p_leftedge\orelse\ifx\p_leftedge\v!none\else
         \hkern{\d_math_matrix_max_left+\p_leftedge}%
       \fi
       \box\scratchbox
       \ifempty\p_rightedge\orelse\ifx\p_rightedge\v!none\else
         \hkern{\d_math_matrix_max_right+\p_rightedge}%
       \fi
     \egroup
   \dostoptagged}

%D Begin of plugin.
%D
%D Fancy:
%D
%D \starttyping
%D \startformula \showstruts
%D     \startmatrix
%D         \NC 1         \NC   \NC \GL[2][m,s,h]  \NC 3 \NC \NR
%D         \NC 1         \NC   \NC               \NC 3 \NC \NR
%D         \NC 1         \NC   \NC               \NC 3 \NC \NR
%D         \NC \GL[2][d] \NC 2 \NC \GL[2][s,d,c] \NC 3 \NC \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula \showstruts
%D     \startmatrix[fences=bracket,rulecolor=red]
%D         \NC 1 \NC \GL[2][a]      \NC \GL[2][a,e] \NC \NR
%D         \NC 1 \NC \GL[2][x,blue] \NC \GL[2][x,e] \NC \NR
%D         \NC 1 \NC 2              \NC 3           \NC \NR
%D         \NC 1 \NC 2              \NC 3           \NC \NR
%D         \NC 1 \NC \GL[2][a]      \NC \GL[2][a,e] \NC \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula \showstruts
%D     \startmatrix[fences=bracket]
%D         \NC 1 \NC   \NC \GL[2][t] \NC 3 \NC \NR
%D         \NC 1 \NC   \NC           \NC 3 \NC \NR
%D         \NC 1 \NC   \NC           \NC 3 \NC \NR
%D         \NC 1 \NC 2 \NC \GL[2][b] \NC 3 \NC \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula \showstruts
%D     \startmatrix[fences=bracket,rulecolor=red]
%D         \NC 1 \NC   \NC \GL[2][T] \NC 3 \NC \NR
%D         \NC 1 \NC   \NC           \NC 3 \NC \NR
%D         \NC 1 \NC   \NC           \NC 3 \NC \NR
%D         \NC 1 \NC 2 \NC \GL[2][B] \NC 3 \NC \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix[fences=bracket]
%D         \NC \GL[2][h] \NC 2 \NC \GL[2][h]   \NC 3 \NC \NR
%D         \NC           \NC 2 \NC             \NC 3 \NC \NR
%D         \NC           \NC 2 \NC             \NC 3 \NC \NR
%D         \NC \GL[2][d] \NC 2 \NC \GL[2][d,c] \NC 3 \NC \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix
%D         \NC \GL[2][h] \NC 2 \NC       \NC \GL[2][h]     \NC             \NC \NR
%D         \NC \GL[3][d] \NC \GL[3][d,e] \NC \NC \GL[2][d] \NC \GL[2][d]   \NC \NR
%D         \NC           \NC 2 \NC       \NC 3             \NC \GL[3][d] \hskip1cm \GL[3][d,e] \NC \NR
%D         \NC \GL[2][d] \NC 2 \NC       \NC 3             \NC \GL[2][d,c] \NC \NR
%D     \stopmatrix
%D \stopformula
%D \stoptyping
%D
%D % \graphicline[1][o]\input tufte \removeunwantedspaces\graphicline[1][o,e]
%D
%D Easier:
%D
%D \starttyping
%D \startformula
%D     \startmatrix[fences=bracket,rulecolor=red]
%D         \NC 1 \NC 2 \VL 3 \NR
%D         \NC 1 \NC 2 \VL 3 \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix[fences=bracket,rulecolor=red]
%D         \NC 1 \NC 2 \VL 3 \VL \NR
%D         \NC 1 \NC 2 \VL 3 \VL \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix[fences=bracket,rulecolor=red]
%D         \NC 1 \NC 2 \VLT 3 \VLT[2,blue] 4 \NR
%D         \NC 1 \NC 2 \NC  3 \NC  4 \NR
%D         \NC 1 \NC 2 \VLB 3 \VLB 4 \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix[fences=bracket,rulecolor=red]
%D         \NC 1 \NC 2 \VLT 3 \VLT[2pt,blue] 4 \NR
%D         \NC 1 \NC 2 \NC  3 \NC  4 \NR
%D         \NC 1 \NC 2 \VLB 3 \VLB 4 \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix[fences=bracket,rulecolor=red]
%D         \NC 1 \NC 2 \VLT 3 \VLT[2pt,blue] 4 \NR
%D         \NC 1 \NC 2 \NC  3 \NC            4 \NR
%D         \NC 1 \NC 2 \VLB 3 \VLB           4 \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix[fences=bracket]
%D         \NC 11 \NC 12 \NC 13 \VL 14 \NR
%D         \NC 21 \NC 22 \NC 23 \NL 24 \NR
%D         \NC 31 \NC 32 \NC 33 \VL 34 \NR
%D     \stopmatrix
%D \stopformula
%D
%D
%D \startformula
%D     \startmatrix[fences=bracket]
%D         \NC 11 \NC 12 \NC 13 \VL 14 \NR
%D         \NC 21 \NC 22 \NC 23 \VL 24 \NR
%D         \NC 31 \NC 32 \NC 33 \VL 34 \NR
%D     \stopmatrix
%D \stopformula
%D
%D \startformula
%D     \startmatrix[fences=bracket]
%D         \NC A \VL  B \NR
%D         \HL
%D         \NC C \VL  D \NR
%D     \stopmatrix
%D \stopformula

%D \stoptyping

\installcorenamespace{matrixvl}

\appendtoks
    \enforced\let\GL\grph_line_inject
\to \everymathmatrix

\newboundary\c_math_matrix_vlx_boundary

\tolerant\permanent\protected\def\grph_line_inject_VLT[#1]%
  {\aligntab
   \grph_line_inject[\??matrixvl:\number\c_math_eqalign_column][T,#1]%
   \global\expandafter\integerdef\csname\??matrixvl::\number\c_math_eqalign_column\endcsname\plusone
%    \kern.5\d_math_eqalign_distance
   \global\c_math_matrix_first\conditionalfalse
   \aligntab
   \enforced\let\NR\math_matrix_NL_NR
   \boundary\c_math_matrix_vlx_boundary
   }

\tolerant\permanent\protected\def\grph_line_inject_VLB[#1]%
  {\aligntab
   \grph_line_inject[\??matrixvl:\number\c_math_eqalign_column][B,#1]%
   \global\expandafter\integerdef\csname\??matrixvl::\number\c_math_eqalign_column\endcsname\zerocount
%    \kern.5\d_math_eqalign_distance
   \global\c_math_matrix_first\conditionalfalse
   \aligntab
   \enforced\let\NR\math_matrix_NL_NR
   \boundary\c_math_matrix_vlx_boundary
   }

\def\grph_line_inject_VL_tab{\aligntab}

\permanent\protected\def\grph_line_inject_VL_space
  {\ifcsname\??matrixvl::\number\c_math_eqalign_column\endcsname
     \ifcase\lastnamedcs\else
%       \kern.5\d_math_eqalign_distance
        \expandafter\expandafter\expandafter\grph_line_inject_VL_tab
     \fi
   \fi}

\appendtoks
    \enforced\let\VLT\grph_line_inject_VLT
    \enforced\let\VLB\grph_line_inject_VLB
\to \everymathmatrix

\appendtoks
    % vl delegated to lua graphiclines
    \ifnum\lastboundary=\c_math_matrix_vlx_boundary
        \kern\ifconditional \c_math_matrix_sl_seen-1.5\else-.5\fi\d_math_eqalign_distance
    \fi
\to \t_math_matrix_NL_NR

%D End of plugin.

\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]#*[#S#2]%
  {\begingroup
   \cdef\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
%D \startformula
%D     \bmatrix { {A__1(x,y)} ; {A__2(x,y)} } =
%D     \bmatrix { {A__1(x,y)}; {A__2(x,y)} } =
%D     \bmatrix {{A__1(x,y)};{A__2(x,y)}}
%D \stopformula
%D \stopbuffer
%D
%D \typebuffer \getbuffer

\permanent\tolerant\protected\def\math_matrix_simple[#1]#*[#S#2]#:#3%
  {\begingroup
   \cdef\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
        \protected\frozen\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:none]
  [\c!align=\v!middle,
   \c!simplecommand=matrix]

\definemathmatrix
  [matrix:brackets]
  [\c!fences=bracket,
   \c!align=\v!middle,
   \c!simplecommand=bmatrix]

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

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

\definemathmatrix
  [matrix:doublebars]
  [\c!fences=doublebar,
   \c!align=\v!middle,
   \c!simplecommand=vvmatrix]

\definemathmatrix
  [matrix:triplebars]
  [\c!fences=triplebar,
   \c!align=\v!middle,
   \c!simplecommand=vvvmatrix]

\definemathmatrix
  [matrix:groups]
  [\c!fences=group,
   \c!align=\v!middle,
   \c!simplecommand=gmatrix]

\definemathmatrix
  [matrix:braces]
  [\c!fences=brace,
   \c!align=\v!middle,
   \c!simplecommand=bracematrix] % Seldom used, bmatrix occupied by brackets

% MPS: Is this one really used? Yes, in the test suite ...

\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 % this will go .. replaced
   \afterdisplayspace
   \vbox{\forgetall\noindent#1\par}%
   \penalty\predisplaypenalty  % this will do .. replaced
   \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

% \permanent\protected\def\startsubstack
%   {\begingroup
%    \vcenter\bgroup
%    \currentmathblobnesting\minusone
%    \baselineskip\mathstacktotal
%    \lineskip\mathstackvgap
%    \lineskiplimit\lineskip
%    \mathsurround\zeropoint
%    \mathsurroundskip\zeroskip
%    \everycr\emptytoks
%    \enforced\let\NC\relax
%    \enforced\let\MC\relax
%    \enforced\let\NR\crcr
%  % \enablemathalignrelocate
%    \dostarttagged\t!math{substack}% needed, otherwise no mtr
%    \dostarttaggednodetail\t!mtable
%    \halign\bgroup
%     \dostarttaggednodetail\t!mtablerow
%     \hfil
%     \dostarttaggednodetail\t!mtablecell
%     \normalstartimath
%     \scriptstyle
%     \aligncontent
%     \normalstopimath
%     \dostoptagged
%     \hfil
%     \dostoptagged
%     \crcr}
%
% \noaligned\permanent\protected\def\stopsubstack
%   {\crcr
%    \egroup
%    \dostoptagged
%    \dostoptagged
%    \egroup
%    \endgroup}

\newinteger\c_align_substack

\permanent\protected\def\startsubstack
  {\begingroup
   \vcenter\bgroup
   \currentmathblobnesting\minusone
   \baselineskip\mathstacktotal
   \lineskip\mathstackvgap
   \lineskiplimit\lineskip
   \mathsurround\zeropoint
   \mathsurroundskip\zeroskip
%    \tabskip\zeropoint
   \everycr\emptytoks
   \enforced\let\NC\relax
   \enforced\let\MC\relax
   \enforced\let\NR\crcr
   \dostarttagged\t!math{substack}% \empty
   \pushmacro\c_align_substack
   \global\c_align_substack\plusone
   \halign\bgroup
    \dostarttaggednodetail\t!mstack
    \global\advanceby\c_align_substack\plusone
    \hfil
    \normalstartimath
    \scriptstyle
    \aligncontent
    \normalstopimath
    \hfil
    \crcr}

\noaligned\permanent\protected\def\stopsubstack
  {\crcr
   \egroup
   \dorecurse\c_align_substack\dostoptagged
   \egroup
   \popmacro\c_align_substack
   \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_normal{\box\b_strc_formulas_number}
\def\strc_math_flush_number_box_visual{\ruledhbox{\box\b_strc_formulas_number}}

\let\strc_math_flush_number_box\strc_math_flush_number_box_normal

% \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}

% The next section is experimental ...

\permanent\protected\def\grph_handle_formula_image_tagged#1#2%
  {\begingroup
   \global\advanceby\nofexportedboxes\plusone
   \edef\figureexported{\the\nofexportedboxes}%
   \def\figurecategory{formula}%
   \dostarttagged\t!image
   \setbox\b_grph_image\vpack\bgroup
     \vkern\zeropoint
     \hpack\bgroup
       \hkern-\d_strc_math_left_shift
       \copy#2%
       \hkern-\d_strc_math_right_shift
     \egroup
     \vkern\zeropoint
   \egroup
 % \copy\b_grph_image
   \dotagexported
   \dostoptagged
   \dotagregisterformula{\number\c_strc_formulas_n}{\number\nofexportedboxes}%
   \ifconditional\c_grph_exported % move up
     \putboxincache\s!exported{\the\nofexportedboxes}\b_grph_image
   \fi
   #1#2%
   \endgroup}

\permanent\protected\def\grph_handle_formula_image_normal#1#2%
  {#1#2}

\enforced\let\handle_formula_image\grph_handle_formula_image_normal

\appendtoks % this might move
    \enforced\let\handle_formula_image\grph_handle_formula_image_tagged
\to \everyenableelements

\appendtoks % this might move
    \enforced\let\handle_formula_image\grph_handle_formula_image_normal
\to \everydisableelements

% ... till here.

% 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
   \handle_formula_image\box\b_strc_math_display
   \llap{\strc_math_flush_number_box}}

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

\def\strc_math_flush_aligned_left_number_indeed#1%
  {\ifvoid\b_strc_formulas_number\else
     \setbox\b_strc_formulas_number\hbox to \d_strc_formulas_display_width\bgroup
       \hss
     % \ifcase#1\orelse\ifdim\dimexpr\d_strc_math_max_left-\d_strc_math_first_left\relax>\zeropoint
     %    \raise\htdp\b_strc_formulas_number % horrible hack
     % \fi
       \hbox{\strc_math_flush_number_box}%
     \egroup
     \ifcase\c_strc_math_number_location\or
       \boxxoffset\b_strc_formulas_number{-\d_strc_formulas_display_width+\d_strc_formulas_number+\s_strc_formulas_margin_left}% brrrrr
       \boxyoffset\b_strc_formulas_number-\d_strc_math_first_height
       \htdp\b_strc_formulas_number\zeropoint
       \strc_math_flush_number_box % left
     \fi
   \fi}

\def\strc_math_flush_aligned_right_number_indeed#1%
  {\ifvoid\b_strc_formulas_number\else
     \setbox\b_strc_formulas_number\hbox to \d_strc_formulas_display_width\bgroup
       \hss
       \ifcase#1\orelse\ifdim{\d_strc_math_max_right-\d_strc_math_last_right}>\zeropoint
          \lower\htdp\b_strc_formulas_number % horrible hack
       \fi
       \hbox{\strc_math_flush_number_box}%
     \egroup
     \ifcase\c_strc_math_number_location\or\else
       \boxxoffset\b_strc_formulas_number-\s_strc_formulas_margin_right
       \boxyoffset\b_strc_formulas_number\d_strc_math_last_depth
       \htdp\b_strc_formulas_number\zeropoint
     \strc_math_flush_number_box % right
     \fi
   \fi}

% \c_strc_math_ignore_number\conditionaltrue

% cleanup timestamp: tales of time, joe bonamassa (live blu-ray in loop mode, 2023)

\dimensiondef\d_strc_math_number_eps 5\scaledpoint

% line mode

\def\strc_math_flush_line_mode
  {\ifcase\c_strc_math_ragged_status\or\or\hfill\or\hfill\fi
   \handle_formula_image\box\b_strc_math_display
   \ifcase\c_strc_math_ragged_status\or\hfill\or\hfill\or\fi}

% wrap/flow mode

\def\strc_math_grid_snapped_box#1%
  {\scratchtotal\htdp\scratchbox
   \getnoflines\scratchtotal
   \ifnum\noflines>\plusone
     \scratchwidth \wd\scratchbox
    %\scratchheight\ht\scratchbox
     \scratchdepth \dp\scratchbox
     \scratchdimen\noflines\lineheight
     \scratchdistance{\scratchdimen-\scratchtotal}%
     \advanceby\scratchdimen-\strutdp
     \setbox\scratchbox\tpack\bgroup
       \novrule
         \s!pair  \scratchdimen \strutdp
         \s!width \zeropoint
       \relax
       \ifcase#1\or
         \begingroup
           \gray
           \virtualvrule
             \s!pair  \scratchdimen \strutdp
             \s!width \scratchwidth
         \endgroup
       \fi
       \boxyoffset\scratchbox{%
           \scratchdepth
          -\strutdp
          +\scratchdistance/\plustwo
         %+2pt % can be an optional parameter
        }%
       \box\scratchbox
     \egroup
     \ht\scratchbox\scratchdimen
   \else
     \ht\scratchbox\strutht
   \fi
   \dp\scratchbox\strutdp
   \box\scratchbox}

\def\strc_math_flush_result_normal_begin
  {\ifconditional\c_strc_math_pack_mode
     \ifgridlinesnapping
       \setbox\scratchbox
     \orelse\ifgridsnapping
       \setbox\scratchbox
     \fi
     \vpack\bgroup
   \fi}

\def\strc_math_flush_result_normal_end
  {\ifconditional\c_strc_math_pack_mode
     \egroup
     % We just use the math snapper for both cases.
     \ifgridlinesnapping
       \strc_math_grid_snapped_box\zerocount
     \orelse\ifgridsnapping
       \strc_math_grid_snapped_box\zerocount
     \fi
   \fi}

\def\strc_math_flush_result_traced_begin
  {\ifconditional\c_strc_math_pack_mode
     \ifgridlinesnapping
       \setbox\scratchbox
     \orelse\ifgridsnapping
       \setbox\scratchbox
     \fi
     \ruledvpack\bgroup
    %\ruledvpack\bgroup
    %\ruleddpack\bgroup
     \hpack\bgroup
        \begingroup
        \darkgray
        \virtualvrule
           \s!pair  \ht\b_strc_math_display \dp\b_strc_math_display
           \c!width 2\onepoint
        \virtualvrule
           \s!pair  \onepoint \onepoint
           \c!width 10\onepoint
        \endgroup
        \ruleddpack\bgroup
   \fi}

\def\strc_math_flush_result_traced_end
  {\ifconditional\c_strc_math_pack_mode
     \egroup
     \egroup
     \egroup
     \ifgridlinesnapping
       \strc_math_grid_snapped_box\plusone
     \orelse\ifgridsnapping
       \strc_math_grid_snapped_box\plusone
     \fi
   \fi}

\let\strc_math_flush_result_begin\strc_math_flush_result_normal_begin
\let\strc_math_flush_result_end  \strc_math_flush_result_normal_end

\installtextracker{math.nosplit}
  {\let\strc_math_flush_result_begin\strc_math_flush_result_traced_begin
   \let\strc_math_flush_result_end  \strc_math_flush_result_traced_end}
  {\let\strc_math_flush_result_begin\strc_math_flush_result_normal_begin
   \let\strc_math_flush_result_end  \strc_math_flush_result_normal_end}


\def\strc_math_flush_v_box_bottom
  {\ifdone
     \global\c_strc_math_positioning42\relax
\strc_math_flush_result_begin
     \handle_formula_image\unvbox\b_strc_math_display
     \strc_math_flush_number_box
\strc_math_flush_result_end
   \else
     \global\c_strc_math_positioning43\relax
\strc_math_flush_result_begin
     \handle_formula_image\unvbox\b_strc_math_display
     \nointerlineskip
     \ht\b_strc_formulas_number\zeropoint
     \dp\b_strc_formulas_number\zeropoint
     \boxyoffset\b_strc_formulas_number\d_strc_math_last_depth
     \strc_math_flush_number_box % right
\strc_math_flush_result_end
     \prevdepth\d_strc_math_last_depth
   \fi}

\def\strc_math_flush_v_box_top
  {\ifdone
     \global\c_strc_math_positioning45\relax
     \dontleavehmode
\strc_math_flush_result_begin
     \strc_math_flush_number_box
     \handle_formula_image\unvbox\b_strc_math_display
\strc_math_flush_result_end
   \else
     \scratchdepth\dp\b_strc_formulas_number
     \global\c_strc_math_positioning46\relax
     \ht\b_strc_formulas_number\strutht
     \dp\b_strc_formulas_number\strutdp
     \dontleavehmode
\strc_math_flush_result_begin
     \vkern{\d_strc_math_first_height+\scratchdepth-\lineheight}%
% or \ht\b_strc_formulas_number{\d_strc_math_first_height+\scratchdepth-\strutdp}%
     \nointerlineskip
     \strc_math_flush_number_box % left
     \vkern{-\d_strc_math_first_height-\scratchdepth}%
     \handle_formula_image\unvbox\b_strc_math_display
\strc_math_flush_result_end   \fi}

\def\strc_math_flush_v_box_right
  {\ifconditional\c_strc_math_ignore_number
     \d_strc_formulas_number\zeropoint
   \fi
   \strc_formulas_start_side_box
   \ifzeropt\d_strc_formulas_number
     \global\c_strc_math_positioning41\relax
\strc_math_flush_result_begin
     \handle_formula_image\unvbox\b_strc_math_display
\strc_math_flush_result_end
   \else
     % better verbose than compact so some overlap in code here
     \ifcase\c_strc_math_number_variant\or
       \s_strc_formulas_margin_right\zeroskip
     \fi
     \setbox\b_strc_formulas_number\hbox to \d_strc_formulas_display_width\bgroup
       \hss
       \strc_math_flush_number_box
       \kern\s_strc_formulas_margin_right
     \egroup
     \ifcstok{\formulaparameter\c!order}\v!reverse
       \ifdim{\d_strc_math_first_right-\s_strc_formulas_margin_right}<{\d_strc_formulas_number-\d_strc_math_number_eps}%
         \donetrue
       \else
         \donefalse
       \fi
       \strc_math_flush_v_box_top
     \else
       \ifdim{\d_strc_math_last_right-\s_strc_formulas_margin_right}<{\d_strc_formulas_number-\d_strc_math_number_eps}%
         \donetrue
       \else
         \donefalse
       \fi
       \strc_math_flush_v_box_bottom
     \fi
   \fi
   \strc_formulas_stop_side_box}

\def\strc_math_flush_v_box_left
  {\ifconditional\c_strc_math_ignore_number
     \d_strc_formulas_number\zeropoint
   \fi
   \strc_formulas_start_side_box
   \ifzeropt\d_strc_formulas_number
     \global\c_strc_math_positioning44\relax
\strc_math_flush_result_begin
     \handle_formula_image\unvbox\b_strc_math_display
\strc_math_flush_result_end
   \else
     % better verbose than compact so some overlap in code here
     \ifcase\c_strc_math_number_variant\or
       \s_strc_formulas_margin_left\zeroskip
     \fi
     \setbox\b_strc_formulas_number\hbox to \d_strc_formulas_display_width\bgroup
       \kern\s_strc_formulas_margin_left
       \strc_math_flush_number_box
       \hss
     \egroup
     \ifcstok{\formulaparameter\c!order}\v!reverse
       \ifdim{\d_strc_math_last_left-\s_strc_formulas_margin_left}<{\d_strc_formulas_number-\d_strc_math_number_eps}%
         \donetrue
       \else
         \donefalse
       \fi
       \strc_math_flush_v_box_bottom
     \else
       \ifdim{\d_strc_math_first_left-\s_strc_formulas_margin_left}<{\d_strc_formulas_number-\d_strc_math_number_eps}%
         \donetrue
       \else
         \donefalse
       \fi
       \strc_math_flush_v_box_top
     \fi
   \fi
   \strc_formulas_stop_side_box}

\def\strc_math_flush_h_mode
  {\global\c_strc_math_positioning\plusthree
   \dontleavehmode
   \strc_math_flush_aligned_left_number_indeed\zerocount
   \handle_formula_image\box\b_strc_math_display
   \strc_math_flush_aligned_right_number_indeed\zerocount}

\def\strc_math_flush_h_box
  {\global\c_strc_math_positioning\plusfive
   \dontleavehmode
   \strc_math_flush_aligned_left_number_indeed\zerocount
   \handle_formula_image\box\b_strc_math_display
   \strc_math_flush_aligned_right_number_indeed\zerocount}

\def\strc_math_flush_text_mode
  {\strc_math_setup_align_auto
   \bgroup
     \leftskip \zeroskip
     \rightskip\zeroskip
     \ifhmode
       % nil the tracing
       \strc_math_flush_h_mode
     \orelse\ifvbox\b_strc_math_display
       \ifnum\c_strc_math_number_location=\plusone
         \strc_math_flush_v_box_left
       \else
         \strc_math_flush_v_box_right
       \fi
     \else
       % nil the tracing, might never happen
       \strc_math_flush_h_box
     \fi
   \egroup
   \ifvmode
     \nointerlineskip
   \fi}

% all modes:

\protected\def\strc_math_flush_aligned
  {\ifconditional\c_strc_math_split_mode
     \strc_math_flush_text_mode
   \else
     \strc_math_flush_line_mode
   \fi}

\def\strc_math_flush_box_normal
  {\ifconditional\c_strc_math_split_mode
     \strc_math_flush_aligned
   \else
     \hbox to \d_strc_formulas_display_width\bgroup
        \strc_math_flush_aligned
     \egroup
   \fi}

\def\strc_math_flush_box_framed_common
  {\d_strc_math_framed_width\d_strc_formulas_display_width
   \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{\handle_formula_image\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
   \rlap{\strc_math_flush_number_box}} % needs checking

\def\strc_math_number_left_normal_outside
  {\llap{\strc_math_flush_number_box}% needs checking
   \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 {\d_strc_formulas_display_width-\d_framed_locator_lo-\d_framed_locator_ro}\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 {\d_strc_formulas_display_width-\d_framed_locator_lo-\d_framed_locator_ro}\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 \d_strc_formulas_display_width\bgroup
       \hss
       \strc_math_flush_number_box_right
     \egroup
   \egroup}

\def\strc_math_number_left_overflow
  {\vpack\bgroup
     \hpack to \d_strc_formulas_display_width\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\zeroskip % nicely breaks the line without introducing funny vertical spacing ... why o why
     \hpack to \d_strc_formulas_display_width\bgroup
       \hss
       \strc_math_flush_number_box
     \egroup
   \egroup}

\def\strc_math_number_left_overflow_outside
  {\vpack\bgroup
     \hpack to {\d_strc_formulas_display_width-\d_framed_locator_lo}\bgroup
       \strc_math_flush_number_box
       \hss
     \egroup
     \hskip\zeroskip % 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
     \handle_formula_image\box\b_strc_math_display
     \hpack to \d_strc_formulas_display_width\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 \d_strc_formulas_display_width\bgroup
     % \kern\d_framed_locator_lo
       \strc_math_flush_number_box
       \hss
     \egroup
     \handle_formula_image\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+\d_strc_formulas_number
     \ifconditional\c_strc_formulas_overlay_number
        \ifcase\c_strc_math_ragged_status\or\or+\d_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>\d_strc_formulas_display_width
       \c_strc_math_display_overflow\conditionaltrue
     \else
       \d_strc_formulas_display_width\d_strc_math_total_display_width
       \c_strc_math_display_overflow\conditionalfalse
     \fi
   \else
     \ifdim{\d_strc_math_total_display_width+(\formulaparameter\c!numberthreshold)}>\d_strc_formulas_display_width
       \c_strc_math_display_overflow\conditionaltrue
     \else
       \c_strc_math_display_overflow\conditionalfalse
     \fi
   \fi}

\def\strc_math_number_check_outside
  {\d_strc_math_display_width\naturalwd\b_strc_math_display
   \ifdim{\d_strc_math_total_display_width+\d_framed_locator_lo+\d_framed_locator_ro}>\d_strc_formulas_display_width
     \c_strc_math_display_overflow\conditionaltrue
   \else
     \c_strc_math_display_overflow\conditionalfalse
   \fi
   % still ok?
   \ifnum\c_strc_math_ragged_status=\plustwo
     \d_strc_math_framed_width{\d_strc_formulas_display_width-2\d_strc_formulas_number}%
   \else
     \d_strc_math_framed_width{\d_strc_formulas_display_width- \d_strc_formulas_number}%
   \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!atleftmargin\endcsname
  {\c_strc_math_number_location\plusone
   \ifzeropt\s_strc_formulas_margin_left
     % this can be a helper as now mixed in math-ali
     \parinitleftskip\zeroskip
   \else
     \c_strc_math_number_variant \plusone
   \fi}

\defcsname\??mathboxlocation\v!atrightmargin\endcsname
  {\c_strc_math_number_location\plustwo
   \ifzeropt\s_strc_formulas_margin_right
     % this can be a helper as now mixed in math-ali
     \parfillrightskip\zeroskip
   \else
     \c_strc_math_number_variant \plusone
   \fi}

\newconditional\c_strc_math_signal

\protected\def\strc_math_check_location
  {\c_strc_math_signal\conditionalfalse}

\protected\def\strc_math_signal_location
  {\ifconditional\c_strc_math_signal
     \signalrightpage
   \fi}

\defcsname\??mathboxlocation\v!outer\endcsname
  {\c_strc_math_signal\conditionaltrue
   \doifelseupcomingrightpage
     {\letformulaparameter\c!location\v!right}%
     {\letformulaparameter\c!location\v!left}%
   \begincsname\??mathboxlocation\formulaparameter\c!location\endcsname}

\defcsname\??mathboxlocation\v!inner\endcsname
  {\c_strc_math_signal\conditionaltrue
   \doifelseupcomingrightpage
     {\letformulaparameter\c!location\v!left}%
     {\letformulaparameter\c!location\v!right}%
   \begincsname\??mathboxlocation\formulaparameter\c!location\endcsname}

\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
   \strc_math_check_location
   \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
     \strc_math_signal_location
     \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
   \ifconditional\c_strc_math_split_mode
     \bgroup
   \else
     \noindent % \noindentation % not \dontleavehmode
     \hbox to \strc_math_effective_width \bgroup
   \fi
   \ifcase\c_strc_math_number_location
     \strc_math_flush_box
   \or % number left
     \ifzeropt\d_strc_formulas_number
       \strc_math_flush_number_no
     \else
       \strc_math_flush_number_left
     \fi
   \else % number right
     \ifzeropt\d_strc_formulas_number
       \strc_math_flush_number_no
     \else
       \strc_math_flush_number_right
     \fi
   \fi
   \egroup
   \ifconditional\c_strc_math_split_mode
     \ifhmode \else
       \strc_math_show_margins
     \fi
   \fi}

\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
  {\ifconditional\c_strc_math_split_mode
     \strc_math_flush_box
   \orelse\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
   \orelse\ifcase\c_strc_formulas_frame_mode
     \strc_math_flush_box_normal
   \orelse\ifconditional\c_strc_formulas_tight
      \strc_math_flush_box_framed_fit_inline
   \else
      \strc_math_flush_box_framed_display
   \fi}

\def\strc_math_flush_number_left
  {\ifconditional\c_strc_math_split_mode
     \strc_math_flush_aligned % we flush in here, otherwise wrong positioning of number (we need to unvbox)
   \orelse\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}

\def\strc_math_flush_number_right
  {\ifconditional\c_strc_math_split_mode
     \strc_math_flush_aligned
   \orelse\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}

%D Some inline math tweak.

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

\setupmathematics
  [\c!textdistance=\zeropoint]

%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
    \protected\frozen\instance\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}

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

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

\aliased\let\math_align_strut\relax

\newconditional\c_math_align_text

\permanent\protected\def\math_simplealign_NC{\relax\global\c_math_align_text\conditionalfalse\aligntab}
\permanent\protected\def\math_simplealign_EQ{\relax\global\c_math_align_text\conditionalfalse\aligntab=}
\permanent\protected\def\math_simplealign_TC{\relax\global\c_math_align_text\conditionaltrue \aligntab}

\installcorenamespace{mathsimpleendclass}

\global\expandafter\integerdef\csname\??mathsimpleendclass\the\zerocount\endcsname\mathendcode

% \permanent\tolerant\protected\def\math_simplealign_start[#1]#*[#S#2]%
%   {\begingroup
%    \cdef\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
%    \math_alignment_location_check{\mathsimplealignparameter\c!location}% vcenter etc
%    \math_alignment_location_box
%    \bgroup
%    \enforced\let\MC\math_simplealign_NC
%    \enforced\let\NC\math_simplealign_NC
%    \enforced\let\TC\math_simplealign_TC
%    \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\mathsimplealignparameter
%    \enablemathalignrelocate
%    \halign
%      \s!callback
%        \align_callback_mathalign
%      \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
%    % \mathbeginclass\ifcsname\??mathsimpleendclass\the\numexpr\c_math_eqalign_column-\plusone\relax\endcsname\lastnamedcs\else\mathunsetcode\fi
%      \mathbeginclass\mathbegincode
%      \startforceddisplaymath
%      \aligncontent
%      \stopforceddisplaymath
%      \ifnum\lastrightclass<\mathunsetcode
%        \global\expandafter\integerdef\csname\??mathsimpleendclass\the\c_math_eqalign_column\endcsname\lastrightclass
%      \fi
%      \removeunwantedspaces
%      \math_right_of_eqalign % \hfil
%      \aligntab
%      \aligntab
%      % repeater
%      \global\advanceby\c_math_eqalign_column\plusone
%      \math_left_of_eqalign  % \hfil
%      \ifx\m_simplealign_distance\v!math
%        \mathbeginclass\ifcsname\??mathsimpleendclass\the\numexpr\c_math_eqalign_column-\plusone\relax\endcsname\lastnamedcs\else\mathunsetcode\fi
%      \else
%        \kern\m_simplealign_distance
%      \fi
%      \ignorespaces
%      \math_align_strut
%      \ifconditional\c_math_align_text
%        % somehow we can't use content as an argument
%      \else
%        \startforceddisplaymath
%      \fi
%      \aligncontent
%      \ifmmode
%        \stopforceddisplaymath
%      \fi
%      \ifnum\lastrightclass<\mathunsetcode
%        \global\expandafter\integerdef\csname\??mathsimpleendclass\the\c_math_eqalign_column\endcsname\lastrightclass
%      \fi
%      \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
%      \vcenter{\box\scratchbox}%
%    \fi
%    \egroup
%    \endgroup}

% Split up so we can better compare to the normal align:

\newtoks\everymathsimplealign
\newtoks\everymathsimplealigndone

\lettonothing\m_simplealign_distance

\def\math_simplealign_preamble
  {\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
  %\mathbeginclass\ifcsname\??mathsimpleendclass\tointeger{\c_math_eqalign_column-\plusone}\endcsname\lastnamedcs\else\mathunsetcode\fi
   \mathbeginclass\mathbegincode
   \startforceddisplaymath
   \aligncontent
   \stopforceddisplaymath
   \ifnum\lastrightclass<\mathunsetcode
     \global\expandafter\integerdef\csname\??mathsimpleendclass\the\c_math_eqalign_column\endcsname\lastrightclass
   \fi
   \removeunwantedspaces
   \math_right_of_eqalign % \hfil
   \aligntab
   \aligntab
   % repeater
   \global\advanceby\c_math_eqalign_column\plusone
   \math_left_of_eqalign  % \hfil
   \ifx\m_simplealign_distance\v!math
     \mathbeginclass\ifcsname\??mathsimpleendclass\tointeger{\c_math_eqalign_column-\plusone}\endcsname\lastnamedcs\else\mathunsetcode\fi
   \else
     \kern\m_simplealign_distance
   \fi
   \startforceddisplaymath
   \aligncontent
   \stopforceddisplaymath
   \ifnum\lastrightclass<\mathunsetcode
     \global\expandafter\integerdef\csname\??mathsimpleendclass\the\c_math_eqalign_column\endcsname\lastrightclass
   \fi
   \math_right_of_eqalign} % \hfil

\appendtoks
   \enforced\let\MC\math_simplealign_NC
   \enforced\let\NC\math_simplealign_NC
   \enforced\let\TC\math_simplealign_TC
   \enforced\let\NR\math_simplealign_NR
   \enforced\let\EQ\math_simplealign_EQ
   \enforced\let\TB\math_common_TB
\to \everymathsimplealign

\appendtoks
\to \everymathsimplealigndone

\def\math_simple_halign_checked
  {\enablemathalignrelocate
   \halign
     \s!callback
       \align_callback_mathalign
     \s!attr
       \mathnumberlocationattribute \zerocount}

\permanent\tolerant\protected\def\math_simplealign_start[#1]#*[#S#2]%
  {\begingroup
   \currentmathblobnesting\minusone
   \cdef\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
   \expand\everymathsimplealign
   \global\c_math_eqalign_column\zerocount
   \global\c_math_eqalign_row\plusone
   \math_eqalign_set_defaults
   \math_eqalign_set_columns{\mathsimplealignparameter\c!align}%
   \math_alignment_location_check{\mathsimplealignparameter\c!location}% vcenter etc
   \edef\m_simplealign_distance{\mathsimplealignparameter\c!distance}%
   \strc_math_setup_spacing_aligned\mathsimplealignparameter
   %
   \mathatom \s!class \mathwrappedcode \bgroup
   \scratchdimen{\mathsimplealignparameter\c!leftmargin}%
   \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
   \mathsimplealignparameter\c!left\relax
   \math_fenced_start_wrap{\mathsimplealignparameter\c!fences}%
   \mathatom \s!class \mathconstructcode \bgroup
   \math_alignment_location_box
   \ifgridlinesnapping \s!linesnapping \linesnapping \fi
   \bgroup
   \math_simple_halign_checked\expandafter\bgroup\math_simplealign_preamble\crcr}

\noaligned\permanent\protected\def\math_simplealign_stop
  {\crcr
   \egroup % halign
   \egroup % box
   \egroup % construct
   \math_fenced_stop_wrap
   \mathsimplealignparameter\c!right\relax
   \scratchdimen{\mathsimplealignparameter\c!rightmargin}%
   \ifzeropt\scratchdimen\else\kern\scratchdimen\fi
   \setbox\scratchbox\hbox{\mathsimplealignparameter\c!text}%
   \ifvoid\scratchbox\else
     \kern{\mathsimplealignparameter\c!textdistance}%
     \vcenter{\box\scratchbox}%
   \fi
   \egroup % wrapped
   \expand\everymathsimplealigndone
   \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 = r           \cos\theta \NR
%D       \NC y \NC = \frac{1}{2} \sin\theta \NR
%D       \NC 9 \NC = 123         \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]{\ifempty\scratchtoks\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]#*[#S#2]#:#3%
  {\begingroup
   \cdef\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
        \protected\frozen\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]

%D There are users who use this so let's for now keep it (I also need to adapt
%D x-mathml.mkxl):

\newskip \math_old_hideskip   \math_old_hideskip  = -1000pt plus 1fill
\newskip \math_old_centering  \math_old_centering =     0pt plus 1000pt minus 1000pt

\ifdefined\hidewidth \else \aliased\let\hidewidth\relax \fi

\permanent\protected\def\eqalign#1% rather plain, is this used at all ...
  {\dontleavehmode
   \mskip\thinmuskip\vcenter\bgroup % \vcenter \s!class \mathwrappercode \bgroup
     \currentmathblobnesting\minusone
     \mathsurround\zeropoint        % \math_eqalign_set_defaults
     \everycr\emptytoks
     \tabskip\zeroskip
     \enforced\let\hideskip\math_old_hideskip
     \enforced\let\centering\math_old_centering
     \enforced\def\hidewidth{\hskip\hideskip} % for alignment entries that can stick out
     \amcode\ampersandasciicode\alignmentcatcode
     \halign
       {\strut
        \hfil
        \mathbeginclass\mathordcode
        \mathendclass  \mathordcode
        \startforceddisplaymath\aligncontent\stopforceddisplaymath
        \aligntab
        \mathbeginclass\mathordcode
        \mathendclass  \mathordcode
        \startforceddisplaymath\aligncontent\stopforceddisplaymath
        \hfil
        \crcr
        #1%
        \crcr}%
   \egroup\mskip\thinmuskip}        % \egroup

\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