path: root/doc/context/sources/general/manuals/math/math-tricks.tex

\environment math-layout

\startcomponent math-tricks

\startchapter[title=Tricks]

\startsection[title=Introduction]

Math support in \CONTEXT\ is wrapped around basic \TEX\ primitives and
unfortunately not all we want is easy to configure. This is not surprising
because the original ideas behind \TEX\ are that one makes a style per book and a
one macro package \quote {we-can-do-it-all} approach is not what Don Knuth had in
mind at that time.

So, for instance support for configurable spacing per math element, coloring of
specific (sub) elements, simple switching of whatever combination of alignments
and number placement, these all take quite a bit of code and hackery.

Even configuring something seemingly trivial as fractions or top, bottom, left,
middle and right fences take some effort. This is because the engine uses
information from fonts to combine shapes and paste the content and ornaments to
together.

For that reason already in \MKII\ but more extensively in \MKIV\ we did a lot of
these things in wrapper macros. When the math renderer was finalized for
\OPENTYPE\ math some extra control was added that can make these things easier.
However, because we go a bit beyond what is possible using this new functionality
these new mechanisms are not yet used in \MKIV, but they might be eventually.
Here we just show some of the (newer) low level trickery. For details about what
was already possible in pure \TEX, we refer to the ultimate references: the \TeX
book (by Donald Knuth) and \TeX\ by Topic (by Victor Eijkhout).

\stopsection

\startsection[title=Kerning]

Kerning in \OPENTYPE\ math is not the same as in traditional \TEX: instead of a
single value, we have staircase kerns, that is, depending on the location (left
or right) and the vertical position, at discrete distances between depth and
height. In addition there is italic correction but that is only applied in
certain cases, one of which is the script location.

Unfortunately not all fonts follow the same route. Some fonts have a true width
and a moderate italic correction is added to it (of at all), while other fonts
lie about the width and depend on an excessive italic correction to compensate
for that.

\definemeasure[quarter][\dimexpr(\textwidth-3em)/4\relax]

\def\TestKern#1%
  {\scale
     [width=\measure{quarter}]
     {\hbox to 50pt{\hss\showboxes\switchtobodyfont[#1]$V_i^i = W_i^i$\hss}}}

\startlinecorrection
\startcombination[nx=4,ny=2,distance=1em]
    {\TestKern  {modern}} {\infofont  modern}
    {\TestKern {cambria}} {\infofont cambria}
    {\TestKern{lucidaot}} {\infofont  lucida}
    {\TestKern  {dejavu}} {\infofont  dejavu}
    {\TestKern {pagella}} {\infofont pagella}
    {\TestKern  {termes}} {\infofont  termes}
    {\TestKern   {bonum}} {\infofont   bonum}
    {\TestKern  {schola}} {\infofont  schola}
\stopcombination
\stoplinecorrection

I will not discuss the details because when a font gets updated, it might look
better or worse. These fonts were loaded with the following directive set:

\starttyping
\enabledirectives[fontgoodies.mathkerning]
\stoptyping

An example of a fontgoodie that fixed the kerning is \type {pagella-math.lfg}. Here
is the relevant bit:

\starttyping
local kern_200 = { bottomright = { { kern = -200 } } }
local kern_100 = { bottomright = { { kern = -100 } } }

return {
  .....
  mathematics = {
    .....
    kerns = {
      [0x1D449] = kern_200, -- 𝑉
      [0x1D44A] = kern_100, -- 𝑊
    },
    .....
  }
}
\stoptyping

This fixes the real bad kerning of Pagella Math which at least in 2017 was not
(yet) fixed. When the fonts are frozen we can start makling permanent runtime
fixes like this.

\stopsection

\startsection[title=Primes]

Primes are a pain in the butt. The reason for this is that they are independent
characters on the one hand but can be seen as a superscript on the other. Let's
first look at the symbols at the three sizes that are used in math.

\startbuffer[prime]
$
    {\textstyle        \char"2032}
    {\scriptstyle      \char"2032}
    {\scriptscriptstyle\char"2032}
\quad
    {\textstyle        \char"FE931}
    {\scriptstyle      \char"FE931}
    {\scriptscriptstyle\char"FE931}
\quad
    {\textstyle        \char"FE932}
    {\scriptstyle      \char"FE932}
    {\scriptscriptstyle\char"FE932}
$
\stopbuffer

\typebuffer[prime]

We blow up the characters a bit and get this:

\startlinecorrection
\scale[scale=5000]{\showglyphs\inlinebuffer[prime]}
\stoplinecorrection

\def\TestPrime#1%
  {\scale
     [width=\measure{quarter}]
     {\ruledhbox to 65pt{%
       \hss
       \showglyphs
       \switchtobodyfont[#1]%
       \inlinebuffer[prime]%
       \hss}}}

The first set is the normal prime character scaled to the text, script and
scriptscriptsize. The second set shows the characters (at three sizes) as they
are in the font. The largest character is raised while the other two are closer
to the baseline. In some fonts the smaller sizes arenot smaller at all. The last
set is a variant of the the first set but we made them into virtual characters
with a displacement and different dimensions. Those are the ones we use as
primes.

\startlinecorrection
\startcombination[nx=4,ny=2,distance=1em]
    {\TestPrime  {modern}} {\infofont  modern}
    {\TestPrime {cambria}} {\infofont cambria}
    {\TestPrime{lucidaot}} {\infofont  lucida}
    {\TestPrime  {dejavu}} {\infofont  dejavu}
    {\TestPrime {pagella}} {\infofont pagella}
    {\TestPrime  {termes}} {\infofont  termes}
    {\TestPrime   {bonum}} {\infofont   bonum}
    {\TestPrime  {schola}} {\infofont  schola}
\stopcombination
\stoplinecorrection

Next we show how primes show up in real math. The examples
explain themselves.

\startbuffer
{\textstyle         f = g} \quad
{\scriptstyle       f = g} \quad
{\scriptscriptstyle f = g}
\stopbuffer

\typebuffer

\startlinecorrection
\scale[scale=2000]{\showglyphs$\inlinebuffer$}
\stoplinecorrection

\startbuffer
{\textstyle         f_i' = g_i'} \quad
{\scriptstyle       f_i' = g_i'} \quad
{\scriptscriptstyle f_i' = g_i'}
\stopbuffer

\typebuffer

\startlinecorrection
\scale[scale=2000]{\showglyphs$\inlinebuffer$}
\stoplinecorrection

\startbuffer
{\textstyle         f^{\char"2032}(0) = g^{\char"2032}(0)} \quad
{\scriptstyle       f^{\char"2032}(0) = g^{\char"2032}(0)} \quad
{\scriptscriptstyle f^{\char"2032}(0) = g^{\char"2032}(0)}
\stopbuffer

\typebuffer

\startlinecorrection
\scale[scale=2000]{\showglyphs$\inlinebuffer$}
\stoplinecorrection

\startbuffer
{\textstyle         f'(0) = g'(0)} \quad
{\scriptstyle       f'(0) = g'(0)} \quad
{\scriptscriptstyle f'(0) = g'(0)}
\stopbuffer

\typebuffer

\startlinecorrection
\scale[scale=2000]{\showglyphs$\inlinebuffer$}
\stoplinecorrection

\startbuffer
{\textstyle         f^{\char"2032}(0) = g^{\char"2032}(0)} \quad
{\scriptstyle       f^{\char"2032}(0) = g^{\char"2032}(0)} \quad
{\scriptscriptstyle f^{\char"2032}(0) = g^{\char"2032}(0)}
\stopbuffer

\typebuffer

\startlinecorrection
\scale[scale=2000]{\showglyphs$\inlinebuffer$}
\stoplinecorrection

\startbuffer
{\textstyle         f^{\char"2032}(0) = g^{\char"2032}(0)} \quad
{\scriptstyle       f^{\char"2032}(0) = g^{\char"2032}(0)} \quad
{\scriptscriptstyle f^{\char"2032}(0) = g^{\char"2032}(0)}
\stopbuffer

\typebuffer

\startlinecorrection
\scale[scale=2000]{\showglyphs$\inlinebuffer$}
\stoplinecorrection

The prime analyzer can deal with sizes, subscripts but also converts a sequence
of upright quotes into one unicode symbol. So,

\startbuffer
f'_i \neq f''_i \neq f'''_i \neq f''''_i
\stopbuffer

\typebuffer

becomes:

\startlinecorrection
\scale[scale=4000]{\showglyphs$\inlinebuffer$}
\stoplinecorrection

\stopsection

\startsection[title=Radicals]

Sometimes users complain about the look of a radical symbol. This is however a matter
of design. Some fonts let the shape start more below the baseline than others. Soem go
more straight up than relatives in another font. When largers sizes are needed, some
fonts offer smaller than others. Just look at the different desings:

\def\TestRadical#1%
  {\NC
     \type{#1}\blackrule[width=0pt,height=2.5ex,depth=2ex]\NC
     \switchtobodyfont[#1]\scale[scale=2000]{\showglyphs$\surd   $}\NC
     \switchtobodyfont[#1]\scale[scale=2000]{\showglyphs$\sqrt{} $}\NC
     \switchtobodyfont[#1]\scale[scale=2000]{\showglyphs$\sqrt{.}$}\NC
     \switchtobodyfont[#1]\scale[scale=2000]{\showglyphs$\sqrt{x}$}\NC
     \switchtobodyfont[#1]\scale[scale=2000]{\showglyphs$\surd \sqrt{} \sqrt{.} \sqrt{x}$}\NC
   \NR}

\starttabulate[|l|c|c|c|c|c|]
    \NC \NC \type{\surd} \NC \type{\sqrt{}} \NC \type{\sqrt{.}} \NC \type{\sqrt{x}} \NC \NR
    \TestRadical{modern}
    \TestRadical{cambria}
    \TestRadical{lucidaot}
    \TestRadical{dejavu}
    \TestRadical{pagella}
    \TestRadical{termes}
    \TestRadical{bonum}
    \TestRadical{schola}
\stoptabulate

The automatic scaling doesn't always work out as expected but on the average is
okay. Keep in mind that often the content is not that extreme.

\def\TestRadical#1%
  {\NC
     \type{#1}\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=1.0ex,color=darkgray]}$\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=1.5ex,color=darkgray]}$\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=2.0ex,color=darkgray]}$\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=2.5ex,color=darkgray]}$\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=3.0ex,color=darkgray]}$\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=3.5ex,color=darkgray]}$\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=4.0ex,color=darkgray]}$\NC
     \switchtobodyfont[#1]\showglyphs$\sqrt{\blackrule[width=1em,height=4.5ex,color=darkgray]}$\NC
   \NR}

\starttabulate[|l|c|c|c|c|c|c|c|c|]
    \NC \NC 1.0ex \NC 1.5ex \NC 2.0ex \NC 2.5ex \NC 3.0ex \NC 3.5ex \NC 4.0ex \NC 4.5ex \NC \NR
    \TestRadical{modern}
    \TestRadical{cambria}
    \TestRadical{lucidaot}
    \TestRadical{dejavu}
    \TestRadical{pagella}
    \TestRadical{termes}
    \TestRadical{bonum}
    \TestRadical{schola}
\stoptabulate

In Lucida (the version at the time of writing this) we have to correct the threshold
a bit in the goodie file:

\starttyping
local function FixRadicalDisplayStyleVerticalGap(value,target,original)
  local o = original.mathparameters.RadicalVerticalGap -- 50
  return 2 * o * target.parameters.factor
end

return {
  .....
  mathematics = {
    .....
    parameters = {
      RadicalDisplayStyleVerticalGap =
        FixRadicalDisplayStyleVerticalGap,
    },
    .....
  },
}
\stoptyping

\stopsection

\startsection[title=Integrals]

A curious exception in the math system is the integral sign. Its companions are
the summation and product signs, but integral has as extra property that it has a
slant. In \LUATEX\ there is rather advanced control over how the (optional)
scripts are positioned (which relates to italic correction) but in \CONTEXT\ we
only make limited use of that. The main reason is that we also need to support
additional features like color. Therefore integrals are handled by the extensible
mechanism.

The size of an integral is more of less fixed but you can enlarge to your
liking. One reason for this is that you might want a consistent size across
formulas. Let's use the following setup:

\startbuffer[setup]
\setupmathextensible
  [integral]
  [rightoffset=-1mu,
   exact=yes,
   factor=2]

\let\int\integral
\stopbuffer

\typebuffer[setup]

We use the following exmaple:

\startbuffer[demo]
\ruledhbox{$\integral                  f\frac{1}{2}           $}\quad
\ruledhbox{$\integral[rightoffset=3mu] f\frac{1}{2}           $}\quad
\ruledhbox{$\integral[exact=no]        f\frac{1}{2}           $}\quad
\ruledhbox{$\integral                  f\frac{\frac{1}{2}}{x} $}\quad
\ruledhbox{$\integral[exact=no]        f\frac{\frac{1}{2}}{x} $}\quad
\ruledhbox{$\integral[factor=1]        f\frac{1}{2}           $}\quad
\ruledhbox{$\integral[factor=3]        f\frac{\frac{1}{2}}{x} $}\quad
\ruledhbox{$\integral[factor=3]        f\frac{1}{2}           $}\quad
\ruledhbox{$\int                       f\frac{1}{2}           $}% bonus
\stopbuffer

\typebuffer[demo]

This renders as:

\dontleavehmode\hbox{\getbuffer[setup,demo]}

\stopsection

\startsection[title=Fancy fences]

Here I only show an example of fences drawn by \METAPOST. For the implementation
you can consult the library file \type {meta-imp-mat.mkiv} in the \CONTEXT\
distribution.

\startbuffer[setup]
\useMPlibrary[mat]

\setupmathstackers
  [both] % vfenced]
  [color=darkred,
   alternative=mp]

\setupmathstackers
  [top]
  [color=darkred,
   alternative=mp]

\setupmathstackers
  [bottom]
  [color=darkred,
   alternative=mp]
\stopbuffer

\typebuffer[setup]

We keep the demo simple:

\startbuffer[demo]
$ \overbracket     {a+b+c+d} \quad
  \underbracket    {a+b+c+d} \quad
  \doublebracket   {a+b+c+d} \quad
  \overparent      {a+b+c+d} \quad
  \underparent     {a+b+c+d} \quad
  \doubleparent    {a+b+c+d} $ \blank
$ \overbrace       {a+b+c+d} \quad
  \underbrace      {a+b+c+d} \quad
  \doublebrace     {a+b+c+d} \quad
  \overbar         {a+b+c+d} \quad
  \underbar        {a+b+c+d} \quad
  \doublebar       {a+b+c+d} $ \blank
$ \overleftarrow   {a+b+c+d} \quad
  \overrightarrow  {a+b+c+d} \quad
  \underleftarrow  {a+b+c+d} \quad
  \underrightarrow {a+b+c+d} $ \blank
\stopbuffer

\typebuffer[demo]

Or visualized:

\start
\getbuffer[setup,demo]
\stop

\stopsection

\startsection[title=Combined characters]

We have some magic built with respect to sequences of characters. They are derived
from information in the character database that ships with \CONTEXT\ and are
implemented as a sort of ligatures. Some are defined in \UNICODE, others are
defined explicitly.

\usemodule[math-ligatures]

\start
    \switchtobodyfont[small]
    \showmathligatures
\stop

\stopsection

\startsection[title=Middle class fences]

The next examples are somewhat obscure. They are a side effect of some extensions
to the engine that were introduced to control spacing around the \type {\middle}
class fences. Actually there is no real middle class and spacing was somewhat
hard codes when \type {\middle} was added to \ETEX. In \LUATEX\ we have
introduced keywords to some primitives that control spacing and other properties.
This permits better control over spacing than messing around with (for instance)
injected \type {\mathrel} commands that can have their own side effects.

\startbuffer
\def\Middle{\middle|}
\def\Riddle{\Umiddle class 5 |}
\def\Left  {\left  (}
\def\Right {\right )}
\def\Rel   {\mathrel{}}
\def\Per   {\mathrel{.}}
\stopbuffer

\startbuffer[1a]
$          a                b          $
\stopbuffer
\startbuffer[1b]
$     \Rel a\Rel            b\Rel      $
\stopbuffer

\startbuffer[2a]
$          a                b          $
\stopbuffer
\startbuffer[2b]
$     \Per a\Per            b\Per      $
\stopbuffer

\startbuffer[3a]
$\Left     a    \Middle     b    \Right$
\stopbuffer
\startbuffer[3b]
$\Left\Rel a    \Middle\Rel b\Rel\Right$
\stopbuffer

\startbuffer[4a]
$\Left     a    \Middle     b    \Right$
\stopbuffer
\startbuffer[4b]
$\Left\Rel a    \Middle\Per b\Per\Right$
\stopbuffer

\startbuffer[5a]
$\Left     a    \Middle     b    \Right$
\stopbuffer
\startbuffer[5b]
$\Left\Rel a\Rel\Middle\Rel b\Rel\Right$
\stopbuffer

\startbuffer[6a]
$\Left     a    \Middle     b    \Right$
\stopbuffer
\startbuffer[6b]
$\Left\Per a\Per\Middle\Per b\Per\Right$
\stopbuffer

\startbuffer[7a]
$\Left     a    \Riddle     b    \Right$
\stopbuffer
\startbuffer[7b]
$\Left\Rel a    \Riddle\Rel b\Rel\Right$
\stopbuffer

\startbuffer[8a]
$\Left     a    \Riddle     b    \Right$
\stopbuffer
\startbuffer[8b]
$\Left\Rel a    \Riddle\Per b\Per\Right$
\stopbuffer

\startbuffer[9a]
$\Left     a    \Riddle     b    \Right$
\stopbuffer
\startbuffer[9b]
$\Left\Rel a\Rel\Riddle\Rel b\Rel\Right$
\stopbuffer

\startbuffer[10a]
$\Left     a    \Riddle     b    \Right$
\stopbuffer
\startbuffer[10b]
$\Left\Per a\Per\Riddle\Per b\Per\Right$
\stopbuffer

We use the following definitions:

\typebuffer

Applied to samples these give the following outcome and spacing:

\start
    \getbuffer

    \starttabulate
        \NC \ruledhbox{\typeinlinebuffer[1a]}  \NC \showglyphs \inlinebuffer[1a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[1b]}  \NC \showglyphs \inlinebuffer[1b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[2a]}  \NC \showglyphs \inlinebuffer[2a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[2b]}  \NC \showglyphs \inlinebuffer[2b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[3a]}  \NC \showglyphs \inlinebuffer[3a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[3b]}  \NC \showglyphs \inlinebuffer[3b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[4a]}  \NC \showglyphs \inlinebuffer[4a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[4b]}  \NC \showglyphs \inlinebuffer[4b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[5a]}  \NC \showglyphs \inlinebuffer[5a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[5b]}  \NC \showglyphs \inlinebuffer[5b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[6a]}  \NC \showglyphs \inlinebuffer[6a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[6b]}  \NC \showglyphs \inlinebuffer[6b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[7a]}  \NC \showglyphs \inlinebuffer[7a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[7b]}  \NC \showglyphs \inlinebuffer[7b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[8a]}  \NC \showglyphs \inlinebuffer[8a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[8b]}  \NC \showglyphs \inlinebuffer[8b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[9a]}  \NC \showglyphs \inlinebuffer[9a]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[9b]}  \NC \showglyphs \inlinebuffer[9b]  \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[10a]} \NC \showglyphs \inlinebuffer[10a] \NC \NR
        \NC \ruledhbox{\typeinlinebuffer[10b]} \NC \showglyphs \inlinebuffer[10b] \NC \NR
    \stoptabulate
\stop

\stopsection

\startsection[title=Auto|-|punctuation]

\def\TestA#1#2#3%
  {\ifnum#1=0 \type{#2}\else\setupmathematics[autopunctuation={#2}]$#3$\fi}

\def\TestB#1#2%
  {\NC \TestA{#1}{no}           {#2}
   \NC \TestA{#1}{yes}          {#2}
   \NC \TestA{#1}{yes,semicolon}{#2}
   \NC \TestA{#1}{all}          {#2}
   \NC \TestA{#1}{all,semicolon}{#2}
   \NC \NR}

The \type {\setupmathematics} command has an option \type {autopunctuation} that
influences the way spacing after punctuatuon is handled, especially in cases like
the following (coordinates and such):

\starttabulate[|c|c|c|c|c|]
   \TestB{0}{}
   \TestB{1}{(1,2)=(1, 2)}
   \TestB{1}{(1.2)=(1. 2)}
   \TestB{1}{(1;2)=(1; 2)}
\stoptabulate

\stopsection

\stopcomponent

% \enabletrackers[math.makeup=boxes]

% \startTEXpage[offset=10pt]
%     $\displaystyle      {{1}\normalover{2}}+x$\quad $\crampeddisplaystyle     {{1}\normalover{2}}+x$\blank
%     $\textstyle         {{1}\normalover{2}}+x$\quad $\crampedtextstyle        {{1}\normalover{2}}+x$\blank
%     $\scriptstyle       {{1}\normalover{2}}+x$\quad $\crampedscriptstyle      {{1}\normalover{2}}+x$\blank
%     $\scriptscriptstyle {{1}\normalover{2}}+x$\quad $\crampedscriptscriptstyle{{1}\normalover{2}}+x$\blank
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     $e=mc^2$
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     $\sqrt{\frac{1}{2}+x}$
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     $\int^0_1{\frac{1}{2}+x}$
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     $\displaystyle\the\everydisplay\int^0_1{\frac{1}{2}+x}$
% \stopTEXpage

% \startbuffer
% ${}^2_2x^3_4 {}^2x_4$
% \stopbuffer

% % d : \Umathsubshiftdown
% % u : \Umathsupshiftup
% % s : \Umathsubsupshiftdown

% \startTEXpage[offset=10pt]
%     \starttabulate[|T||cT|cT|]
%         \NC 0 \NC \mathscriptsmode 0 \inlinebuffer \NC dynamic       \NC dynamic       \NC \NR \TB
%         \NC 1 \NC \mathscriptsmode 1 \inlinebuffer \NC d             \NC u             \NC \NR \TB
%         \NC 2 \NC \mathscriptsmode 2 \inlinebuffer \NC s             \NC u             \NC \NR \TB
%         \NC 3 \NC \mathscriptsmode 3 \inlinebuffer \NC s             \NC u + s − d     \NC \NR \TB
%         \NC 4 \NC \mathscriptsmode 4 \inlinebuffer \NC d + (s − d)/2 \NC u + (s − d)/2 \NC \NR \TB
%         \NC 5 \NC \mathscriptsmode 5 \inlinebuffer \NC d             \NC u + s − d     \NC \NR
%     \stoptabulate
% \stopTEXpage

% \startTEXpage[offset=10pt] \tt
%     \starttabulate[|l|ck1|ck1|ck1|ck1|ck1|ck1|]
%         \NC
%             \NC \mathnolimitsmode0    $\displaystyle\int\nolimits^0_1$
%             \NC \mathnolimitsmode1    $\displaystyle\int\nolimits^0_1$
%             \NC \mathnolimitsmode2    $\displaystyle\int\nolimits^0_1$
%             \NC \mathnolimitsmode3    $\displaystyle\int\nolimits^0_1$
%             \NC \mathnolimitsmode4    $\displaystyle\int\nolimits^0_1$
%             \NC \mathnolimitsmode8000 $\displaystyle\int\nolimits^0_1$
%         \NC \NR
%         \TB
%         \NC \bf mode
%             \NC 0
%             \NC 1
%             \NC 2
%             \NC 3
%             \NC 4
%             \NC 8000
%         \NC \NR
%         \NC \bf superscript
%             \NC 0
%             \NC font
%             \NC 0
%             \NC 0
%             \NC +ic/2
%             \NC 0
%         \NC \NR
%         \NC \bf subscript
%             \NC -ic
%             \NC font
%             \NC 0
%             \NC -ic/2
%             \NC -ic/2
%             \NC 8000ic/1000
%         \NC \NR
%     \stoptabulate
% \stopTEXpage

{ } \bgroup \egroup \begingroup \endgroup

\startbuffer[1]
    [a:\mathstyle]\quad
    \bgroup
    \mathchoice
        {\bf \scriptstyle       (x:d :\mathstyle)}
        {\bf \scriptscriptstyle (x:t :\mathstyle)}
        {\bf \scriptscriptstyle (x:s :\mathstyle)}
        {\bf \scriptscriptstyle (x:ss:\mathstyle)}
    \egroup
    \quad[b:\mathstyle]\quad
    \mathchoice
        {\bf \scriptstyle       (y:d :\mathstyle)}
        {\bf \scriptscriptstyle (y:t :\mathstyle)}
        {\bf \scriptscriptstyle (y:s :\mathstyle)}
        {\bf \scriptscriptstyle (y:ss:\mathstyle)}
    \quad[c:\mathstyle]\quad
    \bgroup
    \mathchoice
        {\bf \scriptstyle       (z:d :\mathstyle)}
        {\bf \scriptscriptstyle (z:t :\mathstyle)}
        {\bf \scriptscriptstyle (z:s :\mathstyle)}
        {\bf \scriptscriptstyle (z:ss:\mathstyle)}
    \egroup
    \quad[d:\mathstyle]
\stopbuffer

\startbuffer[2]
    [a:\mathstyle]\quad
    \begingroup
    \mathchoice
        {\bf \scriptstyle       (x:d :\mathstyle)}
        {\bf \scriptscriptstyle (x:t :\mathstyle)}
        {\bf \scriptscriptstyle (x:s :\mathstyle)}
        {\bf \scriptscriptstyle (x:ss:\mathstyle)}
    \endgroup
    \quad[b:\mathstyle]\quad
    \mathchoice
        {\bf \scriptstyle       (y:d :\mathstyle)}
        {\bf \scriptscriptstyle (y:t :\mathstyle)}
        {\bf \scriptscriptstyle (y:s :\mathstyle)}
        {\bf \scriptscriptstyle (y:ss:\mathstyle)}
    \quad[c:\mathstyle]\quad
    \begingroup
    \mathchoice
        {\bf \scriptstyle       (z:d :\mathstyle)}
        {\bf \scriptscriptstyle (z:t :\mathstyle)}
        {\bf \scriptscriptstyle (z:s :\mathstyle)}
        {\bf \scriptscriptstyle (z:ss:\mathstyle)}
    \endgroup
    \quad[d:\mathstyle]
\stopbuffer

% % \bgroup .. \egroup

% \startTEXpage[offset=10pt]
%     $\displaystyle \getbuffer[1]$ \blank
%     $\textstyle    \getbuffer[1]$
% \stopTEXpage

% % \begingroup .. \endgroup

% \startTEXpage[offset=10pt]
%     $\displaystyle \getbuffer[2]$ \blank
%     $\textstyle    \getbuffer[2]$
% \stopTEXpage


% \startTEXpage[offset=10pt]
%     $\Uleft                           ( x \Umiddle\| \Uright                           )$
%     $\Uleft height 3ex                ( x \Umiddle\| \Uright height 3ex                )$
%     $\Uleft axis height 3ex           ( x \Umiddle\| \Uright axis height 3ex           )$
%     $\Uleft axis height 3ex depth 1ex ( x \Umiddle\| \Uright axis height 3ex depth 1ex )$
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     $\Uvextensible                                 ( \frac{1}{x}$
%     $\Uvextensible height 3ex                      ( \frac{1}{x}$
%     $\Uvextensible axis height 3ex                 ( \frac{1}{x}$
%     $\Uvextensible axis height 3ex depth 1ex       ( \frac{1}{x}$
%     $\Uvextensible exact axis height 3ex depth 1ex ( \frac{1}{x}$
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     \ruledhbox{$\Uhextensible                  "0 "23DE$}
%     \ruledhbox{$\Uhextensible        width 3ex "0 "23DE$}
%     \ruledhbox{$\Uhextensible middle width 3ex "0 "23DE$}
%     \ruledhbox{$\Uhextensible left   width 3ex "0 "23DE$}
%     \ruledhbox{$\Uhextensible right  width 3ex "0 "23DE$}
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     \ruledhbox{$\Umathaccent         "0 "0 "23DE                          {1+x}$}
%     \ruledhbox{$\Umathaccent fixed   "0 "0 "23DE                          {1+x}$}
%     \ruledhbox{$\Umathaccent top     "0 "0 "23DE                          {1+x}$}
%     \ruledhbox{$\Umathaccent bottom              "0 "0 "23DF              {1+x}$}
%     \ruledhbox{$\Umathaccent both    "0 "0 "23DE "0 "0 "23DF              {1+x}$}
%     \ruledhbox{$\Umathaccent overlay "0 "0 "23DE                          {1+x}$}
%     \ruledhbox{$\Umathaccent top     "0 "0 "23DE             fraction 800 {1+x}$}
% \stopTEXpage

% \startTEXpage[offset=10pt]
%     ${ {1} \Uskewed           /                   {2} }$
%     ${ {1} \Uskewed           /     exact         {2} }$
%     ${ {1} \Uskewed           /     noaxis        {2} }$
%     ${ {1} \Uskewed           /     exact noaxis  {2} }$
%     ${ {1} \Uskewedwithdelims / ()                {2} }$
%     ${ {1} \Uskewedwithdelims / ()  exact         {2} }$
%     ${ {1} \Uskewedwithdelims / ()  noaxis        {2} }$
%     ${ {1} \Uskewedwithdelims / ()  exact noaxis  {2} }$
% \stopTEXpage

% \disabletrackers[math.makeup]

% \stopchapter
%
% \stopcomponent

% A \type {\matheqnogapstep} factor that determines the gap between formula and
% equation number.
%
% A \type {\mathdisplayskipmode} directive that controls display skips: 1 = always,
% 2 = only when not zero, 3 = never.
%
% \mathstyle
%
% \suppressmathparerror