From f210bce174e1f2f05305ab03e88e120a1cbfc4da Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Thu, 5 Mar 2020 00:48:46 +0000
Subject: context (from cont-tmf.zip of Feb 17 16:00, size 116339406)

git-svn-id: svn://tug.org/texlive/trunk@54086 c570f23f-e606-0410-a88d-b1316a301751
---
 .../general/manuals/luametatex/luametatex-math.tex | 1587 ++++++++++++++++++++
 1 file changed, 1587 insertions(+)
 create mode 100644 Master/texmf-dist/doc/context/sources/general/manuals/luametatex/luametatex-math.tex

(limited to 'Master/texmf-dist/doc/context/sources/general/manuals/luametatex/luametatex-math.tex')

diff --git a/Master/texmf-dist/doc/context/sources/general/manuals/luametatex/luametatex-math.tex b/Master/texmf-dist/doc/context/sources/general/manuals/luametatex/luametatex-math.tex
new file mode 100644
index 00000000000..ce4fe154482
--- /dev/null
+++ b/Master/texmf-dist/doc/context/sources/general/manuals/luametatex/luametatex-math.tex
@@ -0,0 +1,1587 @@
+% language=uk
+
+\environment luametatex-style
+
+\startcomponent luametatex-math
+
+\startchapter[reference=math,title={Math}]
+
+\startsection[title={Traditional alongside \OPENTYPE}]
+
+\topicindex {math}
+
+At this point there is no difference between \LUAMETATEX\ and \LUATEX\ with
+respect to math. The handling of mathematics in \LUATEX\ differs quite a bit from
+how \TEX82 (and therefore \PDFTEX) handles math. First, \LUATEX\ adds primitives
+and extends some others so that \UNICODE\ input can be used easily. Second, all
+of \TEX82's internal special values (for example for operator spacing) have been
+made accessible and changeable via control sequences. Third, there are extensions
+that make it easier to use \OPENTYPE\ math fonts. And finally, there are some
+extensions that have been proposed or considered in the past that are now added
+to the engine.
+
+\stopsection
+
+\startsection[title={Unicode math characters}]
+
+\topicindex {math+\UNICODE}
+\topicindex {\UNICODE+math}
+
+Character handling is now extended up to the full \UNICODE\ range (the \type {\U}
+prefix), which is compatible with \XETEX.
+
+The math primitives from \TEX\ are kept as they are, except for the ones that
+convert from input to math commands: \type {mathcode}, and \type {delcode}. These
+two now allow for a 21-bit character argument on the left hand side of the equals
+sign.
+
+Some of the new \LUATEX\ primitives read more than one separate value. This is
+shown in the tables below by a plus sign.
+
+The input for such primitives would look like this:
+
+\starttyping
+\def\overbrace{\Umathaccent 0 1 "23DE }
+\stoptyping
+
+The altered \TEX82 primitives are:
+
+\starttabulate[|l|l|r|c|l|r|]
+\DB primitive       \BC min \BC max    \BC \kern 2em \BC min \BC max    \NC \NR
+\TB
+\NC \prm {mathcode} \NC 0   \NC 10FFFF \NC =         \NC 0   \NC 8000   \NC \NR
+\NC \prm {delcode}  \NC 0   \NC 10FFFF \NC =         \NC 0   \NC FFFFFF \NC \NR
+\LL
+\stoptabulate
+
+The unaltered ones are:
+
+\starttabulate[|l|l|r|]
+\DB primitive          \BC min \BC max     \NC \NR
+\TB
+\NC \prm {mathchardef} \NC 0   \NC    8000 \NC \NR
+\NC \prm {mathchar}    \NC 0   \NC    7FFF \NC \NR
+\NC \prm {mathaccent}  \NC 0   \NC    7FFF \NC \NR
+\NC \prm {delimiter}   \NC 0   \NC 7FFFFFF \NC \NR
+\NC \prm {radical}     \NC 0   \NC 7FFFFFF \NC \NR
+\LL
+\stoptabulate
+
+For practical reasons \prm {mathchardef} will silently accept values larger
+that \type {0x8000} and interpret it as \lpr {Umathcharnumdef}. This is needed
+to satisfy older macro packages.
+
+The following new primitives are compatible with \XETEX:
+
+% somewhat fuzzy:
+
+\starttabulate[|l|l|r|c|l|r|]
+\DB primitive                             \BC min       \BC max         \BC \kern 2em \BC min       \BC max         \NC \NR
+\TB
+\NC \lpr {Umathchardef}                   \NC 0+0+0     \NC 7+FF+10FFFF \NC           \NC           \NC             \NC \NR
+\NC \lpr {Umathcharnumdef}\rlap{\high{5}} \NC -80000000 \NC    7FFFFFFF \NC           \NC           \NC             \NC \NR
+\NC \lpr {Umathcode}                      \NC 0         \NC      10FFFF \NC =         \NC 0+0+0     \NC 7+FF+10FFFF \NC \NR
+\NC \lpr {Udelcode}                       \NC 0         \NC      10FFFF \NC =         \NC 0+0       \NC   FF+10FFFF \NC \NR
+\NC \lpr {Umathchar}                      \NC 0+0+0     \NC 7+FF+10FFFF \NC           \NC           \NC             \NC \NR
+\NC \lpr {Umathaccent}                    \NC 0+0+0     \NC 7+FF+10FFFF \NC           \NC           \NC             \NC \NR
+\NC \lpr {Udelimiter}                     \NC 0+0+0     \NC 7+FF+10FFFF \NC           \NC           \NC             \NC \NR
+\NC \lpr {Uradical}                       \NC 0+0       \NC   FF+10FFFF \NC           \NC           \NC             \NC \NR
+\NC \lpr {Umathcharnum}                   \NC -80000000 \NC    7FFFFFFF \NC           \NC           \NC             \NC \NR
+\NC \lpr {Umathcodenum}                   \NC 0         \NC      10FFFF \NC =         \NC -80000000 \NC    7FFFFFFF \NC \NR
+\NC \lpr {Udelcodenum}                    \NC 0         \NC      10FFFF \NC =         \NC -80000000 \NC    7FFFFFFF \NC \NR
+\LL
+\stoptabulate
+
+Specifications typically look like:
+
+\starttyping
+\Umathchardef\xx="1"0"456
+\Umathcode   123="1"0"789
+\stoptyping
+
+The new primitives that deal with delimiter|-|style objects do not set up a
+\quote {large family}. Selecting a suitable size for display purposes is expected
+to be dealt with by the font via the \lpr {Umathoperatorsize} parameter.
+
+For some of these primitives, all information is packed into a single signed
+integer. For the first two (\lpr {Umathcharnum} and \lpr {Umathcodenum}), the
+lowest 21 bits are the character code, the 3 bits above that represent the math
+class, and the family data is kept in the topmost bits. This means that the values
+for math families 128--255 are actually negative. For \lpr {Udelcodenum} there
+is no math class. The math family information is stored in the bits directly on
+top of the character code. Using these three commands is not as natural as using
+the two- and three|-|value commands, so unless you know exactly what you are
+doing and absolutely require the speedup resulting from the faster input
+scanning, it is better to use the verbose commands instead.
+
+The \lpr {Umathaccent} command accepts optional keywords to control various
+details regarding math accents. See \in {section} [mathacc] below for details.
+
+There are more new primitives and all of these will be explained in following
+sections:
+
+\starttabulate[|l|l|]
+\DB primitive                \BC value range (in hex) \NC \NR
+\TB
+\NC \lpr {Uroot}           \NC 0 + 0--FF + 10FFFF   \NC \NR
+\NC \lpr {Uoverdelimiter}  \NC 0 + 0--FF + 10FFFF   \NC \NR
+\NC \lpr {Uunderdelimiter} \NC 0 + 0--FF + 10FFFF   \NC \NR
+\NC \lpr {Udelimiterover}  \NC 0 + 0--FF + 10FFFF   \NC \NR
+\NC \lpr {Udelimiterunder} \NC 0 + 0--FF + 10FFFF   \NC \NR
+\LL
+\stoptabulate
+
+\stopsection
+
+\startsection[title={Math styles}]
+
+\subsection{\lpr {mathstyle}}
+
+\topicindex {math+styles}
+
+It is possible to discover the math style that will be used for a formula in an
+expandable fashion (while the math list is still being read). To make this
+possible, \LUATEX\ adds the new primitive: \lpr {mathstyle}. This is a \quote
+{convert command} like e.g. \prm {romannumeral}: its value can only be read,
+not set.
+
+The returned value is between 0 and 7 (in math mode), or $-1$ (all other modes).
+For easy testing, the eight math style commands have been altered so that they can
+be used as numeric values, so you can write code like this:
+
+\starttyping
+\ifnum\mathstyle=\textstyle
+    \message{normal text style}
+\else \ifnum\mathstyle=\crampedtextstyle
+    \message{cramped text style}
+\fi \fi
+\stoptyping
+
+Sometimes you won't get what you expect so a bit of explanation might help to
+understand what happens. When math is parsed and expanded it gets turned into a
+linked list. In a second pass the formula will be build. This has to do with the
+fact that in order to determine the automatically chosen sizes (in for instance
+fractions) following content can influence preceding sizes. A side effect of this
+is for instance that one cannot change the definition of a font family (and
+thereby reusing numbers) because the number that got used is stored and used in
+the second pass (so changing \type {\fam 12} mid|-|formula spoils over to
+preceding use of that family).
+
+The style switching primitives like \prm {textstyle} are turned into nodes so the
+styles set there are frozen. The \prm {mathchoice} primitive results in four
+lists being constructed of which one is used in the second pass. The fact that
+some automatic styles are not yet known also means that the \lpr {mathstyle}
+primitive expands to the current style which can of course be different from the
+one really used. It's a snapshot of the first pass state. As a consequence in the
+following example you get a style number (first pass) typeset that can actually
+differ from the used style (second pass). In the case of a math choice used
+ungrouped, the chosen style is used after the choice too, unless you group.
+
+\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
+
+\typebuffer[1]
+
+% \typebuffer[2]
+
+This gives:
+
+\blank $\displaystyle \getbuffer[1]$ \blank
+\blank $\textstyle    \getbuffer[1]$ \blank
+
+Using \prm {begingroup} \unknown\ \prm {endgroup} instead gives:
+
+\blank $\displaystyle \getbuffer[2]$ \blank
+\blank $\textstyle    \getbuffer[2]$ \blank
+
+This might look wrong but it's just a side effect of \lpr {mathstyle} expanding
+to the current (first pass) style and the number being injected in the list that
+gets converted in the second pass. It all makes sense and it illustrates the
+importance of grouping. In fact, the math choice style being effective afterwards
+has advantages. It would be hard to get it otherwise.
+
+\subsection{\lpr {Ustack}}
+
+\topicindex {math+stacks}
+
+There are a few math commands in \TEX\ where the style that will be used is not
+known straight from the start. These commands (\prm {over}, \prm {atop},
+\prm {overwithdelims}, \prm {atopwithdelims}) would therefore normally return
+wrong values for \lpr {mathstyle}. To fix this, \LUATEX\ introduces a special
+prefix command: \lpr {Ustack}:
+
+\starttyping
+$\Ustack {a \over b}$
+\stoptyping
+
+The \lpr {Ustack} command will scan the next brace and start a new math group
+with the correct (numerator) math style.
+
+\subsection{The new \type {\cramped...style} commands}
+
+\topicindex {math+styles}
+\topicindex {math+spacing}
+\topicindex {math+cramped}
+
+\LUATEX\ has four new primitives to set the cramped math styles directly:
+
+\starttyping
+\crampeddisplaystyle
+\crampedtextstyle
+\crampedscriptstyle
+\crampedscriptscriptstyle
+\stoptyping
+
+These additional commands are not all that valuable on their own, but they come
+in handy as arguments to the math parameter settings that will be added shortly.
+
+In Eijkhouts \quotation {\TEX\ by Topic} the rules for handling styles in scripts
+are described as follows:
+
+\startitemize
+\startitem
+    In any style superscripts and subscripts are taken from the next smaller style.
+    Exception: in display style they are in script style.
+\stopitem
+\startitem
+    Subscripts are always in the cramped variant of the style; superscripts are only
+    cramped if the original style was cramped.
+\stopitem
+\startitem
+    In an \type {..\over..} formula in any style the numerator and denominator are
+    taken from the next smaller style.
+\stopitem
+\startitem
+    The denominator is always in cramped style; the numerator is only in cramped
+    style if the original style was cramped.
+\stopitem
+\startitem
+    Formulas under a \type {\sqrt} or \prm {overline} are in cramped style.
+\stopitem
+\stopitemize
+
+In \LUATEX\ one can set the styles in more detail which means that you sometimes
+have to set both normal and cramped styles to get the effect you want. (Even) if
+we force styles in the script using \prm {scriptstyle} and \lpr
+{crampedscriptstyle} we get this:
+
+\startbuffer[demo]
+\starttabulate
+\DB style         \BC example \NC \NR
+\TB
+\NC default       \NC $b_{x=xx}^{x=xx}$ \NC \NR
+\NC script        \NC $b_{\scriptstyle x=xx}^{\scriptstyle x=xx}$ \NC \NR
+\NC crampedscript \NC $b_{\crampedscriptstyle x=xx}^{\crampedscriptstyle x=xx}$ \NC \NR
+\LL
+\stoptabulate
+\stopbuffer
+
+\getbuffer[demo]
+
+Now we set the following parameters
+
+\startbuffer[setup]
+\Umathordrelspacing\scriptstyle=30mu
+\Umathordordspacing\scriptstyle=30mu
+\stopbuffer
+
+\typebuffer[setup]
+
+This gives a different result:
+
+\start\getbuffer[setup,demo]\stop
+
+But, as this is not what is expected (visually) we should say:
+
+\startbuffer[setup]
+\Umathordrelspacing\scriptstyle=30mu
+\Umathordordspacing\scriptstyle=30mu
+\Umathordrelspacing\crampedscriptstyle=30mu
+\Umathordordspacing\crampedscriptstyle=30mu
+\stopbuffer
+
+\typebuffer[setup]
+
+Now we get:
+
+\start\getbuffer[setup,demo]\stop
+
+\stopsection
+
+\startsection[title={Math parameter settings}]
+
+\subsection {Many new \lpr {Umath*} primitives}
+
+\topicindex {math+parameters}
+
+In \LUATEX, the font dimension parameters that \TEX\ used in math typesetting are
+now accessible via primitive commands. In fact, refactoring of the math engine
+has resulted in many more parameters than were not accessible before.
+
+\starttabulate
+\DB primitive name                   \BC description \NC \NR
+\TB
+\NC \lpr {Umathquad}               \NC the width of 18 mu's \NC \NR
+\NC \lpr {Umathaxis}               \NC height of the vertical center axis of
+                                         the math formula above the baseline \NC \NR
+\NC \lpr {Umathoperatorsize}       \NC minimum size of large operators in display mode \NC \NR
+\NC \lpr {Umathoverbarkern}        \NC vertical clearance above the rule \NC \NR
+\NC \lpr {Umathoverbarrule}        \NC the width of the rule \NC \NR
+\NC \lpr {Umathoverbarvgap}        \NC vertical clearance below the rule \NC \NR
+\NC \lpr {Umathunderbarkern}       \NC vertical clearance below the rule \NC \NR
+\NC \lpr {Umathunderbarrule}       \NC the width of the rule \NC \NR
+\NC \lpr {Umathunderbarvgap}       \NC vertical clearance above the rule \NC \NR
+\NC \lpr {Umathradicalkern}        \NC vertical clearance above the rule \NC \NR
+\NC \lpr {Umathradicalrule}        \NC the width of the rule \NC \NR
+\NC \lpr {Umathradicalvgap}        \NC vertical clearance below the rule \NC \NR
+\NC \lpr {Umathradicaldegreebefore}\NC the forward kern that takes place before placement of
+                                       the radical degree \NC \NR
+\NC \lpr {Umathradicaldegreeafter} \NC the backward kern that takes place after placement of
+                                       the radical degree \NC \NR
+\NC \lpr {Umathradicaldegreeraise} \NC this is the percentage of the total height and depth of
+                                       the radical sign that the degree is raised by; it is
+                                       expressed in \type {percents}, so 60\% is expressed as the
+                                       integer $60$ \NC \NR
+\NC \lpr {Umathstackvgap}          \NC vertical clearance between the two
+                                       elements in a \prm {atop} stack \NC \NR
+\NC \lpr {Umathstacknumup}         \NC numerator shift upward in \prm {atop} stack \NC \NR
+\NC \lpr {Umathstackdenomdown}     \NC denominator shift downward in \prm {atop} stack \NC \NR
+\NC \lpr {Umathfractionrule}       \NC the width of the rule in a \prm {over} \NC \NR
+\NC \lpr {Umathfractionnumvgap}    \NC vertical clearance between the numerator and the rule \NC \NR
+\NC \lpr {Umathfractionnumup}      \NC numerator shift upward in \prm {over} \NC \NR
+\NC \lpr {Umathfractiondenomvgap}  \NC vertical clearance between the denominator and the rule \NC \NR
+\NC \lpr {Umathfractiondenomdown}  \NC denominator shift downward in \prm {over} \NC \NR
+\NC \lpr {Umathfractiondelsize}    \NC minimum delimiter size for \type {\...withdelims} \NC \NR
+\NC \lpr {Umathlimitabovevgap}     \NC vertical clearance for limits above operators \NC \NR
+\NC \lpr {Umathlimitabovebgap}     \NC vertical baseline clearance for limits above operators \NC \NR
+\NC \lpr {Umathlimitabovekern}     \NC space reserved at the top of the limit \NC \NR
+\NC \lpr {Umathlimitbelowvgap}     \NC vertical clearance for limits below operators \NC \NR
+\NC \lpr {Umathlimitbelowbgap}     \NC vertical baseline clearance for limits below operators \NC \NR
+\NC \lpr {Umathlimitbelowkern}     \NC space reserved at the bottom of the limit \NC \NR
+\NC \lpr {Umathoverdelimitervgap}  \NC vertical clearance for limits above delimiters \NC \NR
+\NC \lpr {Umathoverdelimiterbgap}  \NC vertical baseline clearance for limits above delimiters \NC \NR
+\NC \lpr {Umathunderdelimitervgap} \NC vertical clearance for limits below delimiters \NC \NR
+\NC \lpr {Umathunderdelimiterbgap} \NC vertical baseline clearance for limits below delimiters \NC \NR
+\NC \lpr {Umathsubshiftdrop}       \NC subscript drop for boxes and subformulas \NC \NR
+\NC \lpr {Umathsubshiftdown}       \NC subscript drop for characters \NC \NR
+\NC \lpr {Umathsupshiftdrop}       \NC superscript drop (raise, actually) for boxes and subformulas \NC \NR
+\NC \lpr {Umathsupshiftup}         \NC superscript raise for characters \NC \NR
+\NC \lpr {Umathsubsupshiftdown}    \NC subscript drop in the presence of a superscript \NC \NR
+\NC \lpr {Umathsubtopmax}          \NC the top of standalone subscripts cannot be higher than this
+                                       above the baseline \NC \NR
+\NC \lpr {Umathsupbottommin}       \NC the bottom of standalone superscripts cannot be less than
+                                       this above the baseline \NC \NR
+\NC \lpr {Umathsupsubbottommax}    \NC the bottom of the superscript of a combined super- and subscript
+                                       be at least as high as this above the baseline \NC \NR
+\NC \lpr {Umathsubsupvgap}         \NC vertical clearance between super- and subscript \NC \NR
+\NC \lpr {Umathspaceafterscript}   \NC additional space added after a super- or subscript \NC \NR
+\NC \lpr {Umathconnectoroverlapmin}\NC minimum overlap between parts in an extensible recipe \NC \NR
+\LL
+\stoptabulate
+
+Each of the parameters in this section can be set by a command like this:
+
+\starttyping
+\Umathquad\displaystyle=1em
+\stoptyping
+
+they obey grouping, and you can use \type {\the\Umathquad\displaystyle} if
+needed.
+
+\subsection{Font|-|based math parameters}
+
+\topicindex {math+parameters}
+
+While it is nice to have these math parameters available for tweaking, it would
+be tedious to have to set each of them by hand. For this reason, \LUATEX\
+initializes a bunch of these parameters whenever you assign a font identifier to
+a math family based on either the traditional math font dimensions in the font
+(for assignments to math family~2 and~3 using \TFM|-|based fonts like \type
+{cmsy} and \type {cmex}), or based on the named values in a potential \type
+{MathConstants} table when the font is loaded via Lua. If there is a \type
+{MathConstants} table, this takes precedence over font dimensions, and in that
+case no attention is paid to which family is being assigned to: the \type
+{MathConstants} tables in the last assigned family sets all parameters.
+
+In the table below, the one|-|letter style abbreviations and symbolic tfm font
+dimension names match those used in the \TeX book. Assignments to \prm
+{textfont} set the values for the cramped and uncramped display and text styles,
+\prm {scriptfont} sets the script styles, and \prm {scriptscriptfont} sets the
+scriptscript styles, so we have eight parameters for three font sizes. In the
+\TFM\ case, assignments only happen in family~2 and family~3 (and of course only
+for the parameters for which there are font dimensions).
+
+Besides the parameters below, \LUATEX\ also looks at the \quote {space} font
+dimension parameter. For math fonts, this should be set to zero.
+
+\def\MathLine#1#2#3#4#5%
+  {\TB
+   \NC \llap{\high{\tx #2\enspace}}\ttbf \string #1 \NC \tt #5 \NC \NR
+   \NC \tx #3 \NC \tt #4 \NC \NR}
+
+\starttabulate[|l|l|]
+\DB variable / style \BC tfm / opentype \NC \NR
+\MathLine{\Umathaxis}               {}   {}                     {AxisHeight}                              {axis_height}
+\MathLine{\Umathoperatorsize}       {6}  {D, D'}                {DisplayOperatorMinHeight}                {\emdash}
+\MathLine{\Umathfractiondelsize}    {9}  {D, D'}                {FractionDelimiterDisplayStyleSize}       {delim1}
+\MathLine{\Umathfractiondelsize}    {9}  {T, T', S, S', SS, SS'}{FractionDelimiterSize}                   {delim2}
+\MathLine{\Umathfractiondenomdown}  {}   {D, D'}                {FractionDenominatorDisplayStyleShiftDown}{denom1}
+\MathLine{\Umathfractiondenomdown}  {}   {T, T', S, S', SS, SS'}{FractionDenominatorShiftDown}            {denom2}
+\MathLine{\Umathfractiondenomvgap}  {}   {D, D'}                {FractionDenominatorDisplayStyleGapMin}   {3*default_rule_thickness}
+\MathLine{\Umathfractiondenomvgap}  {}   {T, T', S, S', SS, SS'}{FractionDenominatorGapMin}               {default_rule_thickness}
+\MathLine{\Umathfractionnumup}      {}   {D, D'}                {FractionNumeratorDisplayStyleShiftUp}    {num1}
+\MathLine{\Umathfractionnumup}      {}   {T, T', S, S', SS, SS'}{FractionNumeratorShiftUp}                {num2}
+\MathLine{\Umathfractionnumvgap}    {}   {D, D'}                {FractionNumeratorDisplayStyleGapMin}     {3*default_rule_thickness}
+\MathLine{\Umathfractionnumvgap}    {}   {T, T', S, S', SS, SS'}{FractionNumeratorGapMin}                 {default_rule_thickness}
+\MathLine{\Umathfractionrule}       {}   {}                     {FractionRuleThickness}                   {default_rule_thickness}
+\MathLine{\Umathskewedfractionhgap} {}   {}                     {SkewedFractionHorizontalGap}             {math_quad/2}
+\MathLine{\Umathskewedfractionvgap} {}   {}                     {SkewedFractionVerticalGap}               {math_x_height}
+\MathLine{\Umathlimitabovebgap}     {}   {}                     {UpperLimitBaselineRiseMin}               {big_op_spacing3}
+\MathLine{\Umathlimitabovekern}     {1}  {}                     {0}                                       {big_op_spacing5}
+\MathLine{\Umathlimitabovevgap}     {}   {}                     {UpperLimitGapMin}                        {big_op_spacing1}
+\MathLine{\Umathlimitbelowbgap}     {}   {}                     {LowerLimitBaselineDropMin}               {big_op_spacing4}
+\MathLine{\Umathlimitbelowkern}     {1}  {}                     {0}                                       {big_op_spacing5}
+\MathLine{\Umathlimitbelowvgap}     {}   {}                     {LowerLimitGapMin}                        {big_op_spacing2}
+\MathLine{\Umathoverdelimitervgap}  {}   {}                     {StretchStackGapBelowMin}                 {big_op_spacing1}
+\MathLine{\Umathoverdelimiterbgap}  {}   {}                     {StretchStackTopShiftUp}                  {big_op_spacing3}
+\MathLine{\Umathunderdelimitervgap} {}   {}                     {StretchStackGapAboveMin}                 {big_op_spacing2}
+\MathLine{\Umathunderdelimiterbgap} {}   {}                     {StretchStackBottomShiftDown}             {big_op_spacing4}
+\MathLine{\Umathoverbarkern}        {}   {}                     {OverbarExtraAscender}                    {default_rule_thickness}
+\MathLine{\Umathoverbarrule}        {}   {}                     {OverbarRuleThickness}                    {default_rule_thickness}
+\MathLine{\Umathoverbarvgap}        {}   {}                     {OverbarVerticalGap}                      {3*default_rule_thickness}
+\MathLine{\Umathquad}               {1}  {}                     {<font_size(f)>}                          {math_quad}
+\MathLine{\Umathradicalkern}        {}   {}                     {RadicalExtraAscender}                    {default_rule_thickness}
+\MathLine{\Umathradicalrule}        {2}  {}                     {RadicalRuleThickness}                    {<not set>}
+\MathLine{\Umathradicalvgap}        {3}  {D, D'}                {RadicalDisplayStyleVerticalGap}          {default_rule_thickness+abs(math_x_height)/4}
+\MathLine{\Umathradicalvgap}        {3}  {T, T', S, S', SS, SS'}{RadicalVerticalGap}                      {default_rule_thickness+abs(default_rule_thickness)/4}
+\MathLine{\Umathradicaldegreebefore}{2}  {}                     {RadicalKernBeforeDegree}                 {<not set>}
+\MathLine{\Umathradicaldegreeafter} {2}  {}                     {RadicalKernAfterDegree}                  {<not set>}
+\MathLine{\Umathradicaldegreeraise} {2,7}{}                     {RadicalDegreeBottomRaisePercent}         {<not set>}
+\MathLine{\Umathspaceafterscript}   {4}  {}                     {SpaceAfterScript}                        {script_space}
+\MathLine{\Umathstackdenomdown}     {}   {D, D'}                {StackBottomDisplayStyleShiftDown}        {denom1}
+\MathLine{\Umathstackdenomdown}     {}   {T, T', S, S', SS, SS'}{StackBottomShiftDown}                    {denom2}
+\MathLine{\Umathstacknumup}         {}   {D, D'}                {StackTopDisplayStyleShiftUp}             {num1}
+\MathLine{\Umathstacknumup}         {}   {T, T', S, S', SS, SS'}{StackTopShiftUp}                         {num3}
+\MathLine{\Umathstackvgap}          {}   {D, D'}                {StackDisplayStyleGapMin}                 {7*default_rule_thickness}
+\MathLine{\Umathstackvgap}          {}   {T, T', S, S', SS, SS'}{StackGapMin}                             {3*default_rule_thickness}
+\MathLine{\Umathsubshiftdown}       {}   {}                     {SubscriptShiftDown}                      {sub1}
+\MathLine{\Umathsubshiftdrop}       {}   {}                     {SubscriptBaselineDropMin}                {sub_drop}
+\MathLine{\Umathsubsupshiftdown}    {8}  {}                     {SubscriptShiftDownWithSuperscript}       {\emdash}
+\MathLine{\Umathsubtopmax}          {}   {}                     {SubscriptTopMax}                         {abs(math_x_height*4)/5}
+\MathLine{\Umathsubsupvgap}         {}   {}                     {SubSuperscriptGapMin}                    {4*default_rule_thickness}
+\MathLine{\Umathsupbottommin}       {}   {}                     {SuperscriptBottomMin}                    {abs(math_x_height/4)}
+\MathLine{\Umathsupshiftdrop}       {}   {}                     {SuperscriptBaselineDropMax}              {sup_drop}
+\MathLine{\Umathsupshiftup}         {}   {D}                    {SuperscriptShiftUp}                      {sup1}
+\MathLine{\Umathsupshiftup}         {}   {T, S, SS,}            {SuperscriptShiftUp}                      {sup2}
+\MathLine{\Umathsupshiftup}         {}   {D', T', S', SS'}      {SuperscriptShiftUpCramped}               {sup3}
+\MathLine{\Umathsupsubbottommax}    {}   {}                     {SuperscriptBottomMaxWithSubscript}       {abs(math_x_height*4)/5}
+\MathLine{\Umathunderbarkern}       {}   {}                     {UnderbarExtraDescender}                  {default_rule_thickness}
+\MathLine{\Umathunderbarrule}       {}   {}                     {UnderbarRuleThickness}                   {default_rule_thickness}
+\MathLine{\Umathunderbarvgap}       {}   {}                     {UnderbarVerticalGap}                     {3*default_rule_thickness}
+\MathLine{\Umathconnectoroverlapmin}{5}  {}                     {MinConnectorOverlap}                     {0}
+\LL
+\stoptabulate
+
+Note 1: \OPENTYPE\ fonts set \lpr {Umathlimitabovekern} and \lpr
+{Umathlimitbelowkern} to zero and set \lpr {Umathquad} to the font size of the
+used font, because these are not supported in the \type {MATH} table,
+
+Note 2: Traditional \TFM\ fonts do not set \lpr {Umathradicalrule} because
+\TEX82\ uses the height of the radical instead. When this parameter is indeed not
+set when \LUATEX\ has to typeset a radical, a backward compatibility mode will
+kick in that assumes that an oldstyle \TEX\ font is used. Also, they do not set
+\lpr {Umathradicaldegreebefore}, \lpr {Umathradicaldegreeafter}, and \lpr
+{Umathradicaldegreeraise}. These are then automatically initialized to
+$5/18$quad, $-10/18$quad, and 60.
+
+Note 3: If \TFM\ fonts are used, then the \lpr {Umathradicalvgap} is not set
+until the first time \LUATEX\ has to typeset a formula because this needs
+parameters from both family~2 and family~3. This provides a partial backward
+compatibility with \TEX82, but that compatibility is only partial: once the \lpr
+{Umathradicalvgap} is set, it will not be recalculated any more.
+
+Note 4: When \TFM\ fonts are used a similar situation arises with respect to \lpr
+{Umathspaceafterscript}: it is not set until the first time \LUATEX\ has to
+typeset a formula. This provides some backward compatibility with \TEX82. But
+once the \lpr {Umathspaceafterscript} is set, \prm {scriptspace} will never be
+looked at again.
+
+Note 5: Traditional \TFM\ fonts set \lpr {Umathconnectoroverlapmin} to zero
+because \TEX82\ always stacks extensibles without any overlap.
+
+Note 6: The \lpr {Umathoperatorsize} is only used in \prm {displaystyle}, and is
+only set in \OPENTYPE\ fonts. In \TFM\ font mode, it is artificially set to one
+scaled point more than the initial attempt's size, so that always the \quote
+{first next} will be tried, just like in \TEX82.
+
+Note 7: The \lpr {Umathradicaldegreeraise} is a special case because it is the
+only parameter that is expressed in a percentage instead of a number of scaled
+points.
+
+Note 8: \type {SubscriptShiftDownWithSuperscript} does not actually exist in the
+\quote {standard} \OPENTYPE\ math font Cambria, but it is useful enough to be
+added.
+
+Note 9: \type {FractionDelimiterDisplayStyleSize} and \type
+{FractionDelimiterSize} do not actually exist in the \quote {standard} \OPENTYPE\
+math font Cambria, but were useful enough to be added.
+
+\stopsection
+
+\startsection[title={Math spacing}]
+
+\subsection{Setting inline surrounding space with \lpr {mathsurround[skip]}}
+
+\topicindex {math+spacing}
+
+Inline math is surrounded by (optional) \prm {mathsurround} spacing but that is a fixed
+dimension. There is now an additional parameter \lpr {mathsurroundskip}. When set to a
+non|-|zero value (or zero with some stretch or shrink) this parameter will replace
+\prm {mathsurround}. By using an additional parameter instead of changing the nature
+of \prm {mathsurround}, we can remain compatible. In the meantime a bit more
+control has been added via \lpr {mathsurroundmode}. This directive can take 6 values
+with zero being the default behaviour.
+
+\start
+
+\def\MathHack#1{\mathsurroundmode#1\relax\inlinebuffer}
+
+\def\OneLiner#1#2%
+  {\NC \type{#1}
+   \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\hsize 100pt  x$\MathHack{#1}x$x}
+   \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\hsize 100pt x $\MathHack{#1}x$ x}
+   \NC #2
+   \NC \NR}
+
+\startbuffer
+\mathsurround    10pt
+\mathsurroundskip20pt
+\stopbuffer
+
+\typebuffer
+
+\starttabulate[|c|c|c|pl|]
+\DB mode \BC x\$x\$x \BC x \$x\$ x \BC effect \NC \NR
+\TB
+\OneLiner{0}{obey \prm {mathsurround} when \lpr {mathsurroundskip} is 0pt}
+\OneLiner{1}{only add skip to the left}
+\OneLiner{2}{only add skip to the right}
+\OneLiner{3}{add skip to the left and right}
+\OneLiner{4}{ignore the skip setting, obey \prm {mathsurround}}
+\OneLiner{5}{disable all spacing around math}
+\OneLiner{6}{only apply \lpr {mathsurroundskip} when also spacing}
+\OneLiner{7}{only apply \lpr {mathsurroundskip} when no spacing}
+\LL
+\stoptabulate
+
+\stop
+
+Method six omits the surround glue when there is (x)spacing glue present while
+method seven does the opposite, the glue is only applied when there is (x)space
+glue present too. Anything more fancy, like checking the begining or end of a
+paragraph (or edges of a box) would not be robust anyway. If you want that you
+can write a callback that runs over a list and analyzes a paragraph. Actually, in
+that case you could also inject glue (or set the properties of a math node)
+explicitly. So, these modes are in practice mostly useful for special purposes
+and experiments (they originate in a tracker item). Keep in mind that this glue
+is part of the math node and not always treated as normal glue: it travels with
+the begin and end math nodes. Also, method 6 and 7 will zero the skip related
+fields in a node when applicable in the first occasion that checks them
+(linebreaking or packaging).
+
+\subsection{Pairwise spacing and \lpr {Umath...spacing} commands}
+
+\topicindex {math+spacing}
+
+Besides the parameters mentioned in the previous sections, there are also 64 new
+primitives to control the math spacing table (as explained in Chapter~18 of the
+\TEX book). The primitive names are a simple matter of combining two math atom
+types, but for completeness' sake, here is the whole list:
+
+\starttwocolumns
+\startlines
+\lpr {Umathordordspacing}
+\lpr {Umathordopspacing}
+\lpr {Umathordbinspacing}
+\lpr {Umathordrelspacing}
+\lpr {Umathordopenspacing}
+\lpr {Umathordclosespacing}
+\lpr {Umathordpunctspacing}
+\lpr {Umathordinnerspacing}
+\lpr {Umathopordspacing}
+\lpr {Umathopopspacing}
+\lpr {Umathopbinspacing}
+\lpr {Umathoprelspacing}
+\lpr {Umathopopenspacing}
+\lpr {Umathopclosespacing}
+\lpr {Umathoppunctspacing}
+\lpr {Umathopinnerspacing}
+\lpr {Umathbinordspacing}
+\lpr {Umathbinopspacing}
+\lpr {Umathbinbinspacing}
+\lpr {Umathbinrelspacing}
+\lpr {Umathbinopenspacing}
+\lpr {Umathbinclosespacing}
+\lpr {Umathbinpunctspacing}
+\lpr {Umathbininnerspacing}
+\lpr {Umathrelordspacing}
+\lpr {Umathrelopspacing}
+\lpr {Umathrelbinspacing}
+\lpr {Umathrelrelspacing}
+\lpr {Umathrelopenspacing}
+\lpr {Umathrelclosespacing}
+\lpr {Umathrelpunctspacing}
+\lpr {Umathrelinnerspacing}
+\lpr {Umathopenordspacing}
+\lpr {Umathopenopspacing}
+\lpr {Umathopenbinspacing}
+\lpr {Umathopenrelspacing}
+\lpr {Umathopenopenspacing}
+\lpr {Umathopenclosespacing}
+\lpr {Umathopenpunctspacing}
+\lpr {Umathopeninnerspacing}
+\lpr {Umathcloseordspacing}
+\lpr {Umathcloseopspacing}
+\lpr {Umathclosebinspacing}
+\lpr {Umathcloserelspacing}
+\lpr {Umathcloseopenspacing}
+\lpr {Umathcloseclosespacing}
+\lpr {Umathclosepunctspacing}
+\lpr {Umathcloseinnerspacing}
+\lpr {Umathpunctordspacing}
+\lpr {Umathpunctopspacing}
+\lpr {Umathpunctbinspacing}
+\lpr {Umathpunctrelspacing}
+\lpr {Umathpunctopenspacing}
+\lpr {Umathpunctclosespacing}
+\lpr {Umathpunctpunctspacing}
+\lpr {Umathpunctinnerspacing}
+\lpr {Umathinnerordspacing}
+\lpr {Umathinneropspacing}
+\lpr {Umathinnerbinspacing}
+\lpr {Umathinnerrelspacing}
+\lpr {Umathinneropenspacing}
+\lpr {Umathinnerclosespacing}
+\lpr {Umathinnerpunctspacing}
+\lpr {Umathinnerinnerspacing}
+\stoplines
+\stoptwocolumns
+
+These parameters are of type \prm {muskip}, so setting a parameter can be done
+like this:
+
+\starttyping
+\Umathopordspacing\displaystyle=4mu plus 2mu
+\stoptyping
+
+They are all initialized by \type {initex} to the values mentioned in the table
+in Chapter~18 of the \TEX book.
+
+Note 1: for ease of use as well as for backward compatibility, \prm {thinmuskip},
+\prm {medmuskip} and \prm {thickmuskip} are treated specially. In their case a
+pointer to the corresponding internal parameter is saved, not the actual \prm
+{muskip} value. This means that any later changes to one of these three
+parameters will be taken into account.
+
+Note 2: Careful readers will realise that there are also primitives for the items
+marked \type {*} in the \TEX book. These will not actually be used as those
+combinations of atoms cannot actually happen, but it seemed better not to break
+orthogonality. They are initialized to zero.
+
+\subsection{Local settings}
+
+Math is processed in two passes. The first pass is needed to intercept for
+instance \type {\over}, one of the few \TEX\ commands that actually has a
+preceding argument. There are often lots of curly braces used in math and these
+can result in a nested run of the math sub engine. However, you need to be aware
+of the fact that some properties are kind of global to a formula and the last
+setting (for instance a family switch) wins. This also means that a change (or
+again, the last one) in math parameters affects the whole formula. In
+\LUAMETATEX\ we have changed this model a bit. One can argue that this introduces
+an incompatibility but it's hard to imagine a reason for setting the parameters
+at the end of a formula run and assume that they also influence what goes in
+front.
+
+\startbuffer
+$
+                                            x \Usubscript  {-}
+     \frozen\Umathsubshiftdown\textstyle  0pt  x \Usubscript  {0}
+    {\frozen\Umathsubshiftdown\textstyle  5pt  x \Usubscript  {5}}
+                                               x \Usubscript  {0}
+    {\frozen\Umathsubshiftdown\textstyle 15pt  x \Usubscript {15}}
+                                               x \Usubscript  {0}
+    {\frozen\Umathsubshiftdown\textstyle 20pt  x \Usubscript {20}}
+                                               x \Usubscript  {0}
+     \frozen\Umathsubshiftdown\textstyle 10pt  x \Usubscript {10}
+                                               x \Usubscript  {0}
+$
+\stopbuffer
+
+\typebuffer
+
+The \type {\frozen} prefix does the magic: it injects information in the
+math list about the set parameter.
+
+In \LUATEX\ 1.10 the last setting, the \type {10pt} drop wins, but in
+\LUAMETATEX\ you will see each local setting taking effect. The implementation
+uses a new node type, parameters nodes, so you you might encounter these in an
+unprocessed math list. The result looks as follows:
+
+\blank \getbuffer \blank
+
+
+
+\subsection{Skips around display math and \lpr {mathdisplayskipmode}}
+
+\topicindex {math+spacing}
+
+The injection of \prm {abovedisplayskip} and \prm {belowdisplayskip} is not
+symmetrical. An above one is always inserted, also when zero, but the below is
+only inserted when larger than zero. Especially the latter makes it sometimes hard
+to fully control spacing. Therefore \LUATEX\ comes with a new directive: \lpr
+{mathdisplayskipmode}. The following values apply:
+
+\starttabulate[|c|l|]
+\DB value  \BC meaning \NC \NR
+\TB
+\NC 0 \NC normal \TEX\ behaviour \NC \NR
+\NC 1 \NC always (same as 0) \NC \NR
+\NC 2 \NC only when not zero \NC \NR
+\NC 3 \NC never, not even when not zero \NC \NR
+\LL
+\stoptabulate
+
+\subsection {Nolimit correction with \lpr {mathnolimitsmode}}
+
+\topicindex {math+limits}
+
+There are two extra math parameters \lpr {Umathnolimitsupfactor} and \lpr
+{Umathnolimitsubfactor} that were added to provide some control over how limits
+are spaced (for example the position of super and subscripts after integral
+operators). They relate to an extra parameter \lpr {mathnolimitsmode}. The half
+corrections are what happens when scripts are placed above and below. The
+problem with italic corrections is that officially that correction italic is used
+for above|/|below placement while advanced kerns are used for placement at the
+right end. The question is: how often is this implemented, and if so, do the
+kerns assume correction too. Anyway, with this parameter one can control it.
+
+\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
+    \BC mode
+        \NC \tttf 0
+        \NC \tttf 1
+        \NC \tttf 2
+        \NC \tttf 3
+        \NC \tttf 4
+        \NC \tttf 8000
+    \NC \NR
+    \BC superscript
+        \NC 0
+        \NC font
+        \NC 0
+        \NC 0
+        \NC +ic/2
+        \NC 0
+    \NC \NR
+    \BC subscript
+        \NC -ic
+        \NC font
+        \NC 0
+        \NC -ic/2
+        \NC -ic/2
+        \NC 8000ic/1000
+    \NC \NR
+\stoptabulate
+
+When the mode is set to one, the math parameters are used. This way a macro
+package writer can decide what looks best. Given the current state of fonts in
+\CONTEXT\ we currently use mode 1 with factor 0 for the superscript and 750 for
+the subscripts. Positive values are used for both parameters but the subscript
+shifts to the left. A \lpr {mathnolimitsmode} larger that 15 is considered to
+be a factor for the subscript correction. This feature can be handy when
+experimenting.
+
+\subsection {Controlling math italic mess with \lpr {mathitalicsmode}}
+
+\topicindex {math+italics}
+
+The \lpr {mathitalicsmode} parameter can be set to~1 to force italic correction
+before noads that represent some more complex structure (read: everything
+that is not an ord, bin, rel, open, close, punct or inner). We show a Cambria
+example.
+
+\starttexdefinition Whatever #1
+    \NC \type{\mathitalicsmode = #1}
+    \NC \mathitalicsmode#1\ruledhbox{$\left|T^1\right|$}
+    \NC \mathitalicsmode#1\ruledhbox{$\left|T\right|$}
+    \NC \mathitalicsmode#1\ruledhbox{$T+1$}
+    \NC \mathitalicsmode#1\ruledhbox{$T{1\over2}$}
+    \NC \mathitalicsmode#1\ruledhbox{$T\sqrt{1}$}
+    \NC \NR
+\stoptexdefinition
+
+\start
+    \switchtobodyfont[cambria]
+    \starttabulate[|c|c|c|c|c|c|]
+        \Whatever{0}%
+        \Whatever{1}%
+    \stoptabulate
+\stop
+
+This kind of parameters relate to the fact that italic correction in \OPENTYPE\
+math is bound to fuzzy rules. So, control is the solution.
+
+\subsection {Influencing script kerning with \lpr {mathscriptboxmode}}
+
+\topicindex {math+kerning}
+\topicindex {math+scripts}
+
+If you want to typeset text in math macro packages often provide something \type
+{\text} which obeys the script sizes. As the definition can be anything there is
+a good chance that the kerning doesn't come out well when used in a script. Given
+that the first glyph ends up in a \prm {hbox} we have some control over this.
+And, as a bonus we also added control over the normal sublist kerning. The \lpr
+{mathscriptboxmode} parameter defaults to~1.
+
+\starttabulate[|c|l|]
+\DB value     \BC meaning \NC \NR
+\TB
+\NC \type {0} \NC forget about kerning \NC \NR
+\NC \type {1} \NC kern math sub lists with a valid glyph \NC \NR
+\NC \type {2} \NC also kern math sub boxes that have a valid glyph \NC \NR
+\NC \type {2} \NC only kern math sub boxes with a boundary node present\NC \NR
+\LL
+\stoptabulate
+
+Here we show some examples. Of course this doesn't solve all our problems, if
+only because some fonts have characters with bounding boxes that compensate for
+italics, while other fonts can lack kerns.
+
+\startbuffer[1]
+    $T_{\tf fluff}$
+\stopbuffer
+
+\startbuffer[2]
+    $T_{\text{fluff}}$
+\stopbuffer
+
+\startbuffer[3]
+    $T_{\text{\boundary1 fluff}}$
+\stopbuffer
+
+\unexpanded\def\Show#1#2#3%
+  {\doifelsenothing{#3}
+     {\small\tx\typeinlinebuffer[#1]}
+     {\doifelse{#3}{-}
+        {\small\bf\tt mode #2}
+        {\switchtobodyfont[#3]\showfontkerns\showglyphs\mathscriptboxmode#2\relax\inlinebuffer[#1]}}}
+
+\starttabulate[|lBT|c|c|c|c|c|]
+    \NC          \NC \Show{1}{0}{}         \NC\Show{1}{1}{}         \NC \Show{2}{1}{}         \NC \Show{2}{2}{}         \NC \Show{3}{3}{}         \NC \NR
+    \NC          \NC \Show{1}{0}{-}        \NC\Show{1}{1}{-}        \NC \Show{2}{1}{-}        \NC \Show{2}{2}{-}        \NC \Show{3}{3}{-}        \NC \NR
+    \NC modern   \NC \Show{1}{0}{modern}   \NC\Show{1}{1}{modern}   \NC \Show{2}{1}{modern}   \NC \Show{2}{2}{modern}   \NC \Show{3}{3}{modern}   \NC \NR
+    \NC lucidaot \NC \Show{1}{0}{lucidaot} \NC\Show{1}{1}{lucidaot} \NC \Show{2}{1}{lucidaot} \NC \Show{2}{2}{lucidaot} \NC \Show{3}{3}{lucidaot} \NC \NR
+    \NC pagella  \NC \Show{1}{0}{pagella}  \NC\Show{1}{1}{pagella}  \NC \Show{2}{1}{pagella}  \NC \Show{2}{2}{pagella}  \NC \Show{3}{3}{pagella}  \NC \NR
+    \NC cambria  \NC \Show{1}{0}{cambria}  \NC\Show{1}{1}{cambria}  \NC \Show{2}{1}{cambria}  \NC \Show{2}{2}{cambria}  \NC \Show{3}{3}{cambria}  \NC \NR
+    \NC dejavu   \NC \Show{1}{0}{dejavu}   \NC\Show{1}{1}{dejavu}   \NC \Show{2}{1}{dejavu}   \NC \Show{2}{2}{dejavu}   \NC \Show{3}{3}{dejavu}   \NC \NR
+\stoptabulate
+
+Kerning between a character subscript is controlled by \lpr {mathscriptcharmode}
+which also defaults to~1.
+
+Here is another example. Internally we tag kerns as italic kerns or font kerns
+where font kerns result from the staircase kern tables. In 2018 fonts like Latin
+Modern and Pagella rely on cheats with the boundingbox, Cambria uses staircase
+kerns and Lucida a mixture. Depending on how fonts evolve we might add some more
+control over what one can turn on and off.
+
+\def\MathSample#1#2#3%
+  {\NC
+   #1 \NC
+   #2 \NC
+   \showglyphdata \switchtobodyfont[#2,17.3pt]$#3T_{f}$         \NC
+   \showglyphdata \switchtobodyfont[#2,17.3pt]$#3\gamma_{e}$    \NC
+   \showglyphdata \switchtobodyfont[#2,17.3pt]$#3\gamma_{ee}$   \NC
+   \showglyphdata \switchtobodyfont[#2,17.3pt]$#3T_{\tf fluff}$ \NC
+   \NR}
+
+\starttabulate[|Tl|Tl|l|l|l|l|]
+    \FL
+    \MathSample{normal}{modern}  {\mr}
+    \MathSample{}      {pagella} {\mr}
+    \MathSample{}      {cambria} {\mr}
+    \MathSample{}      {lucidaot}{\mr}
+    \ML
+    \MathSample{bold}  {modern}  {\mb}
+    \MathSample{}      {pagella} {\mb}
+    \MathSample{}      {cambria} {\mb}
+    \MathSample{}      {lucidaot}{\mb}
+    \LL
+\stoptabulate
+
+\subsection{Forcing fixed scripts with \lpr {mathscriptsmode}}
+
+We have three parameters that are used for this fixed anchoring:
+
+\starttabulate[|c|l|]
+\DB parameter \BC register \NC \NR
+\NC $d$ \NC \lpr {Umathsubshiftdown}    \NC \NR
+\NC $u$ \NC \lpr {Umathsupshiftup}      \NC \NR
+\NC $s$ \NC \lpr {Umathsubsupshiftdown} \NC \NR
+\LL
+\stoptabulate
+
+When we set \lpr {mathscriptsmode} to a value other than zero these are used
+for calculating fixed positions. This is something that is needed for instance
+for chemistry. You can manipulate the mentioned variables to achieve different
+effects.
+
+\def\SampleMath#1%
+  {$\mathscriptsmode#1\mathupright CH_2 + CH^+_2 + CH^2_2$}
+
+\starttabulate[|c|c|c|p|]
+\DB mode \BC down          \BC up            \BC example        \NC \NR
+\TB
+\NC 0    \NC dynamic       \NC dynamic       \NC \SampleMath{0} \NC \NR
+\NC 1    \NC $d$           \NC $u$           \NC \SampleMath{1} \NC \NR
+\NC 2    \NC $s$           \NC $u$           \NC \SampleMath{2} \NC \NR
+\NC 3    \NC $s$           \NC $u + s - d$   \NC \SampleMath{3} \NC \NR
+\NC 4    \NC $d + (s-d)/2$ \NC $u + (s-d)/2$ \NC \SampleMath{4} \NC \NR
+\NC 5    \NC $d$           \NC $u + s - d$   \NC \SampleMath{5} \NC \NR
+\LL
+\stoptabulate
+
+The value of this parameter obeys grouping but applies to the whole current
+formula.
+
+% if needed we can put the value in stylenodes but maybe more should go there
+
+\subsection{Penalties: \lpr {mathpenaltiesmode}}
+
+\topicindex {math+penalties}
+
+Only in inline math penalties will be added in a math list. You can force
+penalties (also in display math) by setting:
+
+\starttyping
+\mathpenaltiesmode = 1
+\stoptyping
+
+This primnitive is not really needed in \LUATEX\ because you can use the callback
+\cbk {mlist_to_hlist} to force penalties by just calling the regular routine
+with forced penalties. However, as part of opening up and control this primitive
+makes sense. As a bonus we also provide two extra penalties:
+
+\starttyping
+\prebinoppenalty = -100 % example value
+\prerelpenalty   =  900 % example value
+\stoptyping
+
+They default to inifinite which signals that they don't need to be inserted. When
+set they are injected before a binop or rel noad. This is an experimental feature.
+
+\subsection{Equation spacing: \lpr {matheqnogapstep}}
+
+By default \TEX\ will add one quad between the equation and the number. This is
+hard coded. A new primitive can control this:
+
+\startsyntax
+\matheqnogapstep = 1000
+\stopsyntax
+
+Because a math quad from the math text font is used instead of a dimension, we
+use a step to control the size. A value of zero will suppress the gap. The step
+is divided by 1000 which is the usual way to mimmick floating point factors in
+\TEX.
+
+\stopsection
+
+\startsection[title={Math constructs}]
+
+\subsection {Unscaled fences and \lpr{mathdelimitersmode}}
+
+\topicindex {math+fences}
+
+The \lpr {mathdelimitersmode} primitive is experimental and deals with the
+following (potential) problems. Three bits can be set. The first bit prevents an
+unwanted shift when the fence symbol is not scaled (a cambria side effect). The
+second bit forces italic correction between a preceding character ordinal and the
+fenced subformula, while the third bit turns that subformula into an ordinary so
+that the same spacing applies as with unfenced variants. Here we show Cambria
+(with \lpr {mathitalicsmode} enabled).
+
+\starttexdefinition Whatever #1
+    \NC \type{\mathdelimitersmode = #1}
+    \NC \mathitalicsmode1\mathdelimitersmode#1\ruledhbox{\showglyphs\showfontkerns\showfontitalics$f(x)$}
+    \NC \mathitalicsmode1\mathdelimitersmode#1\ruledhbox{\showglyphs\showfontkerns\showfontitalics$f\left(x\right)$}
+    \NC \NR
+\stoptexdefinition
+
+\start
+    \switchtobodyfont[cambria]
+    \starttabulate[|l|l|l|]
+        \Whatever{0}\Whatever{1}\Whatever{2}\Whatever{3}%
+        \Whatever{4}\Whatever{5}\Whatever{6}\Whatever{7}%
+    \stoptabulate
+\stop
+
+So, when set to 7 fenced subformulas with unscaled delimiters come out the same
+as unfenced ones. This can be handy for cases where one is forced to use \prm
+{left} and \prm {right} always because of unpredictable content. As said, it's an
+experimental feature (which somehow fits in the exceptional way fences are dealt
+with in the engine). The full list of flags is given in the next table:
+
+\starttabulate[|c|l|]
+\DB value  \BC meaning \NC \NR
+\TB
+\NC \type{"01} \NC don't apply the usual shift \NC \NR
+\NC \type{"02} \NC apply italic correction when possible \NC \NR
+\NC \type{"04} \NC force an ordinary subformula \NC \NR
+\NC \type{"08} \NC no shift when a base character \NC \NR
+\NC \type{"10} \NC only shift when an extensible \NC \NR
+\LL
+\stoptabulate
+
+The effect can depend on the font (and for Cambria one can use for instance \type {"16}).
+
+\subsection[mathacc]{Accent handling with \lpr {Umathaccent}}
+
+\topicindex {math+accents}
+
+\LUATEX\ supports both top accents and bottom accents in math mode, and math
+accents stretch automatically (if this is supported by the font the accent comes
+from, of course). Bottom and combined accents as well as fixed-width math accents
+are controlled by optional keywords following \lpr {Umathaccent}.
+
+The keyword \type {bottom} after \lpr {Umathaccent} signals that a bottom accent
+is needed, and the keyword \type {both} signals that both a top and a bottom
+accent are needed (in this case two accents need to be specified, of course).
+
+Then the set of three integers defining the accent is read. This set of integers
+can be prefixed by the \type {fixed} keyword to indicate that a non-stretching
+variant is requested (in case of both accents, this step is repeated).
+
+A simple example:
+
+\starttyping
+\Umathaccent both fixed 0 0 "20D7 fixed 0 0 "20D7 {example}
+\stoptyping
+
+If a math top accent has to be placed and the accentee is a character and has a
+non-zero \type {top_accent} value, then this value will be used to place the
+accent instead of the \prm {skewchar} kern used by \TEX82.
+
+The \type {top_accent} value represents a vertical line somewhere in the
+accentee. The accent will be shifted horizontally such that its own \type
+{top_accent} line coincides with the one from the accentee. If the \type
+{top_accent} value of the accent is zero, then half the width of the accent
+followed by its italic correction is used instead.
+
+The vertical placement of a top accent depends on the \type {x_height} of the
+font of the accentee (as explained in the \TEX book), but if a value turns out
+to be zero and the font had a \type {MathConstants} table, then \type
+{AccentBaseHeight} is used instead.
+
+The vertical placement of a bottom accent is straight below the accentee, no
+correction takes place.
+
+Possible locations are \type {top}, \type {bottom}, \type {both} and \type
+{center}. When no location is given \type {top} is assumed. An additional
+parameter \nod {fraction} can be specified followed by a number; a value of for
+instance 1200 means that the criterium is 1.2 times the width of the nucleus. The
+fraction only applies to the stepwise selected shapes and is mostly meant for the
+\type {overlay} location. It also works for the other locations but then it
+concerns the width.
+
+\subsection{Building radicals with \lpr {Uradical} and \lpr {Uroot}}
+
+\topicindex {math+radicals}
+
+The new primitive \lpr {Uroot} allows the construction of a radical noad
+including a degree field. Its syntax is an extension of \lpr {Uradical}:
+
+\starttyping
+\Uradical <fam integer> <char integer> <radicand>
+\Uroot    <fam integer> <char integer> <degree> <radicand>
+\stoptyping
+
+The placement of the degree is controlled by the math parameters \lpr
+{Umathradicaldegreebefore}, \lpr {Umathradicaldegreeafter}, and \lpr
+{Umathradicaldegreeraise}. The degree will be typeset in \prm
+{scriptscriptstyle}.
+
+\subsection{Super- and subscripts}
+
+The character fields in a \LUA|-|loaded \OPENTYPE\ math font can have a \quote
+{mathkern} table. The format of this table is the same as the \quote {mathkern}
+table that is returned by the \type {fontloader} library, except that all height
+and kern values have to be specified in actual scaled points.
+
+When a super- or subscript has to be placed next to a math item, \LUATEX\ checks
+whether the super- or subscript and the nucleus are both simple character items.
+If they are, and if the fonts of both character items are \OPENTYPE\ fonts (as
+opposed to legacy \TEX\ fonts), then \LUATEX\ will use the \OPENTYPE\ math
+algorithm for deciding on the horizontal placement of the super- or subscript.
+
+This works as follows:
+
+\startitemize
+    \startitem
+        The vertical position of the script is calculated.
+    \stopitem
+    \startitem
+        The default horizontal position is flat next to the base character.
+    \stopitem
+    \startitem
+        For superscripts, the italic correction of the base character is added.
+    \stopitem
+    \startitem
+        For a superscript, two vertical values are calculated: the bottom of the
+        script (after shifting up), and the top of the base. For a subscript, the two
+        values are the top of the (shifted down) script, and the bottom of the base.
+    \stopitem
+    \startitem
+        For each of these two locations:
+        \startitemize
+            \startitem
+                find the math kern value at this height for the base (for a subscript
+                placement, this is the bottom_right corner, for a superscript
+                placement the top_right corner)
+            \stopitem
+            \startitem
+                find the math kern value at this height for the script (for a
+                subscript placement, this is the top_left corner, for a superscript
+                placement the bottom_left corner)
+            \stopitem
+            \startitem
+                add the found values together to get a preliminary result.
+            \stopitem
+        \stopitemize
+    \stopitem
+    \startitem
+        The horizontal kern to be applied is the smallest of the two results from
+        previous step.
+    \stopitem
+\stopitemize
+
+The math kern value at a specific height is the kern value that is specified by the
+next higher height and kern pair, or the highest one in the character (if there is no
+value high enough in the character), or simply zero (if the character has no math kern
+pairs at all).
+
+\subsection{Scripts on extensibles: \lpr {Uunderdelimiter}, \lpr {Uoverdelimiter},
+\lpr {Udelimiterover}, \lpr {Udelimiterunder} and \lpr {Uhextensible}}
+
+\topicindex {math+scripts}
+\topicindex {math+delimiters}
+\topicindex {math+extensibles}
+
+The primitives \lpr {Uunderdelimiter} and \lpr {Uoverdelimiter} allow the
+placement of a subscript or superscript on an automatically extensible item and
+\lpr {Udelimiterunder} and \lpr {Udelimiterover} allow the placement of an
+automatically extensible item as a subscript or superscript on a nucleus. The
+input:
+
+% these produce radical noads .. in fact the code base has the numbers wrong for
+% quite a while, so no one seems to use this
+
+\startbuffer
+$\Uoverdelimiter  0 "2194 {\hbox{\strut  overdelimiter}}$
+$\Uunderdelimiter 0 "2194 {\hbox{\strut underdelimiter}}$
+$\Udelimiterover  0 "2194 {\hbox{\strut  delimiterover}}$
+$\Udelimiterunder 0 "2194 {\hbox{\strut delimiterunder}}$
+\stopbuffer
+
+\typebuffer will render this:
+
+\blank \startnarrower \getbuffer \stopnarrower \blank
+
+The vertical placements are controlled by \lpr {Umathunderdelimiterbgap}, \lpr
+{Umathunderdelimitervgap}, \lpr {Umathoverdelimiterbgap}, and \lpr
+{Umathoverdelimitervgap} in a similar way as limit placements on large operators.
+The superscript in \lpr {Uoverdelimiter} is typeset in a suitable scripted style,
+the subscript in \lpr {Uunderdelimiter} is cramped as well.
+
+These primitives accepts an option \type {width} specification. When used the
+also optional keywords \type {left}, \type {middle} and \type {right} will
+determine what happens when a requested size can't be met (which can happen when
+we step to successive larger variants).
+
+An extra primitive \lpr {Uhextensible} is available that can be used like this:
+
+\startbuffer
+$\Uhextensible width 10cm 0 "2194$
+\stopbuffer
+
+\typebuffer This will render this:
+
+\blank \startnarrower \getbuffer \stopnarrower \blank
+
+Here you can also pass options, like:
+
+\startbuffer
+$\Uhextensible width 1pt middle 0 "2194$
+\stopbuffer
+
+\typebuffer This gives:
+
+\blank \startnarrower \getbuffer \stopnarrower \blank
+
+\LUATEX\ internally uses a structure that supports \OPENTYPE\ \quote
+{MathVariants} as well as \TFM\ \quote {extensible recipes}. In most cases where
+font metrics are involved we have a different code path for traditional fonts end
+\OPENTYPE\ fonts.
+
+\subsection{Fractions and the new \lpr {Uskewed} and \lpr {Uskewedwithdelims}}
+
+\topicindex {math+fractions}
+
+The \prm {abovewithdelims} command accepts a keyword \type {exact}. When issued
+the extra space relative to the rule thickness is not added. One can of course
+use the \type {\Umathfraction..gap} commands to influence the spacing. Also the
+rule is still positioned around the math axis.
+
+\starttyping
+$$ { {a} \abovewithdelims() exact 4pt {b} }$$
+\stoptyping
+
+The math parameter table contains some parameters that specify a horizontal and
+vertical gap for skewed fractions. Of course some guessing is needed in order to
+implement something that uses them. And so we now provide a primitive similar to the
+other fraction related ones but with a few options so that one can influence the
+rendering. Of course a user can also mess around a bit with the parameters
+\lpr {Umathskewedfractionhgap} and \lpr {Umathskewedfractionvgap}.
+
+The syntax used here is:
+
+\starttyping
+{ {1} \Uskewed / <options> {2} }
+{ {1} \Uskewedwithdelims / () <options> {2} }
+\stoptyping
+
+where the options can be \type {noaxis} and \type {exact}. By default we add half
+the axis to the shifts and by default we zero the width of the middle character.
+For Latin Modern the result looks as follows:
+
+\def\ShowA#1#2#3{$x + { {#1} \Uskewed           /    #3 {#2} } + x$}
+\def\ShowB#1#2#3{$x + { {#1} \Uskewedwithdelims / () #3 {#2} } + x$}
+
+\start
+    \switchtobodyfont[modern]
+    \starttabulate[||||||]
+        \NC \NC
+            \ShowA{a}{b}{} \NC
+            \ShowA{1}{2}{} \NC
+            \ShowB{a}{b}{} \NC
+            \ShowB{1}{2}{} \NC
+        \NR
+        \NC \type{exact} \NC
+            \ShowA{a}{b}{exact} \NC
+            \ShowA{1}{2}{exact} \NC
+            \ShowB{a}{b}{exact} \NC
+            \ShowB{1}{2}{exact} \NC
+        \NR
+        \NC \type{noaxis} \NC
+            \ShowA{a}{b}{noaxis} \NC
+            \ShowA{1}{2}{noaxis} \NC
+            \ShowB{a}{b}{noaxis} \NC
+            \ShowB{1}{2}{noaxis} \NC
+        \NR
+        \NC \type{exact noaxis} \NC
+            \ShowA{a}{b}{exact noaxis} \NC
+            \ShowA{1}{2}{exact noaxis} \NC
+            \ShowB{a}{b}{exact noaxis} \NC
+            \ShowB{1}{2}{exact noaxis} \NC
+        \NR
+    \stoptabulate
+\stop
+
+\subsection {Delimiters: \type{\Uleft}, \prm {Umiddle} and \prm {Uright}}
+
+\topicindex {math+delimiters}
+
+Normally you will force delimiters to certain sizes by putting an empty box or
+rule next to it. The resulting delimiter will either be a character from the
+stepwise size range or an extensible. The latter can be quite differently
+positioned than the characters as it depends on the fit as well as the fact if
+the used characters in the font have depth or height. Commands like (plain \TEX
+s) \type {\big} need use this feature. In \LUATEX\ we provide a bit more control
+by three variants that support optional parameters \type {height}, \type {depth}
+and \type {axis}. The following example uses this:
+
+\startbuffer
+\Uleft   height 30pt depth 10pt      \Udelimiter "0 "0 "000028
+\quad x\quad
+\Umiddle height 40pt depth 15pt      \Udelimiter "0 "0 "002016
+\quad x\quad
+\Uright  height 30pt depth 10pt      \Udelimiter "0 "0 "000029
+\quad \quad \quad
+\Uleft   height 30pt depth 10pt axis \Udelimiter "0 "0 "000028
+\quad x\quad
+\Umiddle height 40pt depth 15pt axis \Udelimiter "0 "0 "002016
+\quad x\quad
+\Uright  height 30pt depth 10pt axis \Udelimiter "0 "0 "000029
+\stopbuffer
+
+\typebuffer
+
+\startlinecorrection
+\ruledhbox{\mathematics{\getbuffer}}
+\stoplinecorrection
+
+The keyword \type {exact} can be used as directive that the real dimensions
+should be applied when the criteria can't be met which can happen when we're
+still stepping through the successively larger variants. When no dimensions are
+given the \type {noaxis} command can be used to prevent shifting over the axis.
+
+You can influence the final class with the keyword \type {class} which will
+influence the spacing. The numbers are the same as for character classes.
+
+\subsection {Accents: \type{\mathlimitsmode}}
+
+\topicindex {math+accents}
+
+When you use \type {\limits} or \type {\nolimits} without scripts spacing might
+get messed up. This can be prevented by setting \type {\mathlimitsmode} to a
+non|-|zero value.
+
+\stopsection
+
+\startsection[title={Extracting values}]
+
+\subsection{Codes and using \lpr {Umathcode}, \lpr {Umathcharclass}, \lpr
+{Umathcharfam} and \lpr {Umathcharslot}}
+
+\topicindex {math+codes}
+
+You can extract the components of a math character. Say that we have defined:
+
+\starttyping
+\Umathcode 1 2 3 4
+\stoptyping
+
+then
+
+\starttyping
+[\Umathcharclass1] [\Umathcharfam1] [\Umathcharslot1]
+\stoptyping
+
+will return:
+
+\starttyping
+[2] [3] [4]
+\stoptyping
+
+These commands are provides as convenience. Before they come available you could
+do the following:
+
+\starttyping
+\def\Umathcharclass{\directlua{tex.print(tex.getmathcode(token.scan_int())[1])}}
+\def\Umathcharfam  {\directlua{tex.print(tex.getmathcode(token.scan_int())[2])}}
+\def\Umathcharslot {\directlua{tex.print(tex.getmathcode(token.scan_int())[3])}}
+\stoptyping
+
+\subsection {Last lines and \lpr{predisplaygapfactor}}
+
+\topicindex {math+last line}
+
+There is a new primitive to control the overshoot in the calculation of the
+previous line in mid|-|paragraph display math. The default value is 2 times
+the em width of the current font:
+
+\starttyping
+\predisplaygapfactor=2000
+\stoptyping
+
+If you want to have the length of the last line independent of math i.e.\ you don't
+want to revert to a hack where you insert a fake display math formula in order to
+get the length of the last line, the following will often work too:
+
+\starttyping
+\def\lastlinelength{\dimexpr
+    \directlua {tex.sprint (
+        (nodes.dimensions(node.tail(tex.lists.page_head).list))
+    )}sp
+\relax}
+\stoptyping
+
+\stopsection
+
+\startsection[title={Math mode}]
+
+\subsection {Verbose versions of single|-|character math commands like \lpr {Usuperscript}
+and \lpr {Usubscript}}
+
+\topicindex {math+styles}
+
+\LUATEX\ defines six new primitives that have the same function as
+\type {^}, \type {_}, \type {$}, and \type {$$}:
+
+\starttabulate[|l|l|]
+\DB primitive                  \BC explanation \NC \NR
+\TB
+\NC \lpr {Usuperscript}      \NC duplicates the functionality of \type {^} \NC \NR
+\NC \lpr {Usubscript}        \NC duplicates the functionality of \type {_} \NC \NR
+\NC \lpr {Ustartmath}        \NC duplicates the functionality of \type {$}, % $
+                                   when used in non-math mode. \NC \NR
+\NC \lpr {Ustopmath}         \NC duplicates the functionality of \type {$}, % $
+                                   when used in inline math mode. \NC \NR
+\NC \lpr {Ustartdisplaymath} \NC duplicates the functionality of \type {$$}, % $$
+                                   when used in non-math mode. \NC \NR
+\NC \lpr {Ustopdisplaymath}  \NC duplicates the functionality of \type {$$}, % $$
+                                   when used in display math mode. \NC \NR
+\LL
+\stoptabulate
+
+The \lpr {Ustopmath} and \lpr {Ustopdisplaymath} primitives check if the current
+math mode is the correct one (inline vs.\ displayed), but you can freely intermix
+the four mathon|/|mathoff commands with explicit dollar sign(s).
+
+\subsection{Script commands \lpr {Unosuperscript} and \lpr {Unosubscript}}
+
+\topicindex {math+styles}
+\topicindex {math+scripts}
+
+These two commands result in super- and subscripts but with the current style (at the
+time of rendering). So,
+
+\startbuffer[script]
+$
+    x\Usuperscript  {1}\Usubscript  {2} =
+    x\Unosuperscript{1}\Unosubscript{2} =
+    x\Usuperscript  {1}\Unosubscript{2} =
+    x\Unosuperscript{1}\Usubscript  {2}
+$
+\stopbuffer
+
+\typebuffer
+
+results in \inlinebuffer[script].
+
+\subsection{Allowed math commands in non|-|math modes}
+
+\topicindex {math+text}
+\topicindex {text+math}
+
+The commands \prm {mathchar}, and \lpr {Umathchar} and control sequences that are
+the result of \prm {mathchardef} or \lpr {Umathchardef} are also acceptable in
+the horizontal and vertical modes. In those cases, the \prm {textfont} from the
+requested math family is used.
+
+\stopsection
+
+\startsection[title={Goodies}]
+
+\subsection {Flattening: \lpr {mathflattenmode}}
+
+\topicindex {math+flattening}
+
+The \TEX\ math engine collapses \type {ord} noads without sub- and superscripts
+and a character as nucleus. and which has the side effect that in \OPENTYPE\ mode
+italic corrections are applied (given that they are enabled).
+
+\startbuffer[sample]
+\switchtobodyfont[modern]
+$V \mathbin{\mathbin{v}} V$\par
+$V \mathord{\mathord{v}} V$\par
+\stopbuffer
+
+\typebuffer[sample]
+
+This renders as:
+
+\blank \start \mathflattenmode\plusone \getbuffer[sample] \stop \blank
+
+When we set \lpr {mathflattenmode} to 31 we get:
+
+\blank \start \mathflattenmode\numexpr1+2+4+8+16\relax \getbuffer[sample] \stop \blank
+
+When you see no difference, then the font probably has the proper character
+dimensions and no italic correction is needed. For Latin Modern (at least till
+2018) there was a visual difference. In that respect this parameter is not always
+needed unless of course you want efficient math lists anyway.
+
+You can influence flattening by adding the appropriate number to the value of the
+mode parameter. The default value is~1.
+
+\starttabulate[|Tc|c|]
+\DB mode \BC class \NC \NR
+\TB
+\NC  1   \NC ord   \NC \NR
+\NC  2   \NC bin   \NC \NR
+\NC  4   \NC rel   \NC \NR
+\NC  8   \NC punct \NC \NR
+\NC 16   \NC inner \NC \NR
+\LL
+\stoptabulate
+
+\subsection {Less Tracing}
+
+\topicindex {math+tracing}
+
+Because there are quite some math related parameters and values, it is possible
+to limit tracing. Only when \type {tracingassigns} and|/|or \type
+{tracingrestores} are set to~2 or more they will be traced.
+
+\stopsection
+
+\stopchapter
+
+\stopcomponent
-- 
cgit v1.2.3

