07_math.tex.lua

---% language=uk engine=luatex runpath=texruns:manuals/luatex
---
---\environment luatex-style
---
---\startcomponent luatex-math
---
---# Math
---
---# Traditional alongside *OpenType*
---
---The handling of mathematics in *LuaTeX* differs quite a bit from how *TeX*82 (and
---therefore *PDF*TEX) handles math. First, *LuaTeX* adds primitives and extends some
---others so that *Unicode* input can be used easily. Second, all of *TeX*82'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.
---
----------------------------------------------------------------


---
---# Unicode math characters
---
---Character handling is now extended up to the full *Unicode* range (the `\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: `mathcode`, and `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:
---
---```
---\def\overbrace{\Umathaccent 0 1 "23DE }
---```
---
---The altered *TeX*82 primitives are:
---
--- primitive        min  max     \kern 2em  min  max    
---
--- `mathcode`  0    10FFFF  =          0    8000   
--- `delcode`   0    10FFFF  =          0    FFFFFF 
---
---The unaltered ones are:
---
--- primitive           min  max     
---
--- `mathchardef`  0       8000 
--- `mathchar`     0       7FFF 
--- `mathaccent`   0       7FFF 
--- `delimiter`    0    7FFFFFF 
--- `radical`      0    7FFFFFF 
---
---For practical reasons `mathchardef` will silently accept values larger
---that `0x8000` and interpret it as `Umathcharnumdef`. This is needed
---to satisfy older macro packages.
---
---The following new primitives are compatible with \XETEX:
---
---% somewhat fuzzy:
---
--- primitive                              min        max          \kern 2em  min        max         
---
--- `Umathchardef`                    0+0+0      7+FF+10FFFF                                    
--- `Umathcharnumdef`\rlap{\high{5}}  -80000000     7FFFFFFF                                    
--- `Umathcode`                       0               10FFFF  =          0+0+0      7+FF+10FFFF 
--- `Udelcode`                        0               10FFFF  =          0+0          FF+10FFFF 
--- `Umathchar`                       0+0+0      7+FF+10FFFF                                    
--- `Umathaccent`                     0+0+0      7+FF+10FFFF                                    
--- `Udelimiter`                      0+0+0      7+FF+10FFFF                                    
--- `Uradical`                        0+0          FF+10FFFF                                    
--- `Umathcharnum`                    -80000000     7FFFFFFF                                    
--- `Umathcodenum`                    0               10FFFF  =          -80000000     7FFFFFFF 
--- `Udelcodenum`                     0               10FFFF  =          -80000000     7FFFFFFF 
---
---Specifications typically look like:
---
---```
---\Umathchardef\xx="1"0"456
---\Umathcode   123="1"0"789
---```
---
---The new primitives that deal with delimiter-style objects do not set up a
---“large family”. Selecting a suitable size for display purposes is expected
---to be dealt with by the font via the `Umathoperatorsize` parameter.
---
---For some of these primitives, all information is packed into a single signed
---integer. For the first two (`Umathcharnum` and `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 `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 `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:
---
--- primitive                 value range (in hex) 
---
--- `Uroot`            0 + 0--FF + 10FFFF   
--- `Uoverdelimiter`   0 + 0--FF + 10FFFF   
--- `Uunderdelimiter`  0 + 0--FF + 10FFFF   
--- `Udelimiterover`   0 + 0--FF + 10FFFF   
--- `Udelimiterunder`  0 + 0--FF + 10FFFF   
---
----------------------------------------------------------------


---
---# Math styles
---
---# `mathstyle`
---
---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: `mathstyle`. This is a “convert command” like e.g. `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:
---
---```
---\ifnum\mathstyle=\textstyle
---    \message{normal text style}
---\else \ifnum\mathstyle=\crampedtextstyle
---    \message{cramped text style}
---\fi \fi
---```
---
---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 `\fam 12` mid-formula spoils over to
---preceding use of that family).
---
---The style switching primitives like `textstyle` are turned into nodes so the
---styles set there are frozen. The `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 `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 `begingroup` \unknown\ `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 `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.
---
---# `Ustack`
---
---There are a few math commands in *TeX* where the style that will be used is not
---known straight from the start. These commands (`over`, `atop`,
---`overwithdelims`, `atopwithdelims`) would therefore normally return
---wrong values for `mathstyle`. To fix this, *LuaTeX* introduces a special
---prefix command: `Ustack`:
---
---```
---`\Ustack {a \over b}`
---```
---
---The `Ustack` command will scan the next brace and start a new math group
---with the correct (numerator) math style.
---
---# Cramped math styles
---
---*LuaTeX* has four new primitives to set the cramped math styles directly:
---
---```
---\crampeddisplaystyle
---\crampedtextstyle
---\crampedscriptstyle
---\crampedscriptscriptstyle
---```
---
---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:
---
---* In any style superscripts and subscripts are taken from the next smaller style.
---    Exception: in display style they are in script style.
---
---* Subscripts are always in the cramped variant of the style; superscripts are only
---    cramped if the original style was cramped.
---
---* In an `..\over..` formula in any style the numerator and denominator are
---    taken from the next smaller style.
---
---* The denominator is always in cramped style; the numerator is only in cramped
---    style if the original style was cramped.
---
---* Formulas under a `\sqrt` or `overline` are in cramped style.
---
---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 `scriptstyle` and `crampedscriptstyle` we get this:
---
---\startbuffer[demo]
---\starttabulate
--- style          example 
---
--- default        `b_{x=xx}^{x=xx}` 
--- script         `b_{\scriptstyle x=xx}^{\scriptstyle x=xx}` 
--- crampedscript  `b_{\crampedscriptstyle x=xx}^{\crampedscriptstyle x=xx}` 
---
---\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
---
----------------------------------------------------------------


---
---# Math parameter settings
---
---\subsection {Many new `Umath*` primitives}
---
---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
--- primitive name                    description 
---
--- `Umathquad`                the width of 18 mu's 
--- `Umathaxis`                height of the vertical center axis of the math formula above the baseline 
--- `Umathoperatorsize`        minimum size of large operators in display mode 
--- `Umathoverbarkern`         vertical clearance above the rule 
--- `Umathoverbarrule`         the width of the rule 
--- `Umathoverbarvgap`         vertical clearance below the rule 
--- `Umathunderbarkern`        vertical clearance below the rule 
--- `Umathunderbarrule`        the width of the rule 
--- `Umathunderbarvgap`        vertical clearance above the rule 
--- `Umathradicalkern`         vertical clearance above the rule 
--- `Umathradicalrule`         the width of the rule 
--- `Umathradicalvgap`         vertical clearance below the rule 
--- `Umathradicaldegreebefore` the forward kern that takes place before placement of the radical degree 
--- `Umathradicaldegreeafter`  the backward kern that takes place after placement of the radical degree 
--- `Umathradicaldegreeraise`  this is the percentage of the total height and depth of the radical sign that the degree is raised by; it is expressed in `percents`, so 60\% is expressed as the integer `60` 
--- `Umathstackvgap`           vertical clearance between the two elements in a `atop` stack 
--- `Umathstacknumup`          numerator shift upward in `atop` stack 
--- `Umathstackdenomdown`      denominator shift downward in `atop` stack 
--- `Umathfractionrule`        the width of the rule in a `over` 
--- `Umathfractionnumvgap`     vertical clearance between the numerator and the rule 
--- `Umathfractionnumup`       numerator shift upward in `over` 
--- `Umathfractiondenomvgap`   vertical clearance between the denominator and the rule 
--- `Umathfractiondenomdown`   denominator shift downward in `over` 
--- `Umathfractiondelsize`     minimum delimiter size for `\...withdelims` 
--- `Umathlimitabovevgap`      vertical clearance for limits above operators 
--- `Umathlimitabovebgap`      vertical baseline clearance for limits above operators 
--- `Umathlimitabovekern`      space reserved at the top of the limit 
--- `Umathlimitbelowvgap`      vertical clearance for limits below operators 
--- `Umathlimitbelowbgap`      vertical baseline clearance for limits below operators 
--- `Umathlimitbelowkern`      space reserved at the bottom of the limit 
--- `Umathoverdelimitervgap`   vertical clearance for limits above delimiters 
--- `Umathoverdelimiterbgap`   vertical baseline clearance for limits above delimiters 
--- `Umathunderdelimitervgap`  vertical clearance for limits below delimiters 
--- `Umathunderdelimiterbgap`  vertical baseline clearance for limits below delimiters 
--- `Umathsubshiftdrop`        subscript drop for boxes and subformulas 
--- `Umathsubshiftdown`        subscript drop for characters 
--- `Umathsupshiftdrop`        superscript drop (raise, actually) for boxes and subformulas 
--- `Umathsupshiftup`          superscript raise for characters 
--- `Umathsubsupshiftdown`     subscript drop in the presence of a superscript 
--- `Umathsubtopmax`           the top of standalone subscripts cannot be higher than this above the baseline 
--- `Umathsupbottommin`        the bottom of standalone superscripts cannot be less than this above the baseline 
--- `Umathsupsubbottommax`     the bottom of the superscript of a combined super- and subscript be at least as high as this above the baseline 
--- `Umathsubsupvgap`          vertical clearance between super- and subscript 
--- `Umathspaceafterscript`    additional space added after a super- or subscript 
--- `Umathconnectoroverlapmin` minimum overlap between parts in an extensible recipe 
---
---Each of the parameters in this section can be set by a command like this:
---
---```
---\Umathquad\displaystyle=1em
---```
---
---they obey grouping, and you can use `\the\Umathquad\displaystyle` if
---needed.
---
---# Font-based 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 `cmsy` and `cmex`), or based on the named values in a potential `MathConstants` table when the font is loaded via Lua. If there is a `MathConstants` table, this takes precedence over font dimensions, and in that
---case no attention is paid to which family is being assigned to: the `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 `textfont` set the values for the cramped and uncramped display and text styles,
---`scriptfont` sets the script styles, and `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 “space” font
---dimension parameter. For math fonts, this should be set to zero.
---
---\def\MathLine#1#2#3#4#5%
---  {
---    \llap{\high{\tx #2\enspace}}\ttbf \string #1  \tt #5 
---    \tx #3  \tt #4 }
---
--- variable / style  tfm / opentype 
---\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}
---
---Note 1: *OpenType* fonts set `Umathlimitabovekern` and `Umathlimitbelowkern` to zero and set `Umathquad` to the font size of the
---used font, because these are not supported in the `MATH` table,
---
---Note 2: Traditional *tfm* fonts do not set `Umathradicalrule` because
---*TeX*82\ 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
---`Umathradicaldegreebefore`, `Umathradicaldegreeafter`, and `Umathradicaldegreeraise`. These are then automatically initialized to
---`5/18`quad, `-10/18`quad, and 60.
---
---Note 3: If *tfm* fonts are used, then the `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 *TeX*82, but that compatibility is only partial: once the `Umathradicalvgap` is set, it will not be recalculated any more.
---
---Note 4: When *tfm* fonts are used a similar situation arises with respect to `Umathspaceafterscript`: it is not set until the first time *LuaTeX* has to
---typeset a formula. This provides some backward compatibility with *TeX*82. But
---once the `Umathspaceafterscript` is set, `scriptspace` will never be
---looked at again.
---
---Note 5: Traditional *tfm* fonts set `Umathconnectoroverlapmin` to zero
---because *TeX*82\ always stacks extensibles without any overlap.
---
---Note 6: The `Umathoperatorsize` is only used in `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 “first next” will be tried, just like in *TeX*82.
---
---Note 7: The `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: `SubscriptShiftDownWithSuperscript` does not actually exist in the
---“standard” *OpenType* math font Cambria, but it is useful enough to be
---added.
---
---Note 9: `FractionDelimiterDisplayStyleSize` and `FractionDelimiterSize` do not actually exist in the “standard” *OpenType*
---math font Cambria, but were useful enough to be added.
---
----------------------------------------------------------------


---
---# Math spacing
---
---# Inline surrounding space
---
---Inline math is surrounded by (optional) `mathsurround` spacing but that is a fixed
---dimension. There is now an additional parameter `mathsurroundskip`. When set to a
---non-zero value (or zero with some stretch or shrink) this parameter will replace
---`mathsurround`. By using an additional parameter instead of changing the nature
---of `mathsurround`, we can remain compatible. In the meantime a bit more
---control has been added via `mathsurroundmode`. This directive can take 6 values
---with zero being the default behaviour.
---
---\start
---
---\def\OneLiner#1#2%
---  { `#1`
---    \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\mathsurroundmode#1\relax\hsize 100pt   x`x`x}
---    \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\mathsurroundmode#1\relax\hsize 100pt x `x` x}
---    #2
---   }
---
---\startbuffer
---\mathsurround    10pt
---\mathsurroundskip20pt
---\stopbuffer
---
---\typebuffer \getbuffer
---
--- mode  x\`x\`x  x \`x\` x  effect 
---
---\OneLiner{0}{obey `mathsurround` when `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 `mathsurround`}
---\OneLiner{5}{disable all spacing around math}
---\OneLiner{6}{only apply `mathsurroundskip` when also spacing}
---\OneLiner{7}{only apply `mathsurroundskip` when no spacing}
---
---\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).
---
---# Pairwise 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
---`Umathordordspacing`
---`Umathordopspacing`
---`Umathordbinspacing`
---`Umathordrelspacing`
---`Umathordopenspacing`
---`Umathordclosespacing`
---`Umathordpunctspacing`
---`Umathordinnerspacing`
---`Umathopordspacing`
---`Umathopopspacing`
---`Umathopbinspacing`
---`Umathoprelspacing`
---`Umathopopenspacing`
---`Umathopclosespacing`
---`Umathoppunctspacing`
---`Umathopinnerspacing`
---`Umathbinordspacing`
---`Umathbinopspacing`
---`Umathbinbinspacing`
---`Umathbinrelspacing`
---`Umathbinopenspacing`
---`Umathbinclosespacing`
---`Umathbinpunctspacing`
---`Umathbininnerspacing`
---`Umathrelordspacing`
---`Umathrelopspacing`
---`Umathrelbinspacing`
---`Umathrelrelspacing`
---`Umathrelopenspacing`
---`Umathrelclosespacing`
---`Umathrelpunctspacing`
---`Umathrelinnerspacing`
---`Umathopenordspacing`
---`Umathopenopspacing`
---`Umathopenbinspacing`
---`Umathopenrelspacing`
---`Umathopenopenspacing`
---`Umathopenclosespacing`
---`Umathopenpunctspacing`
---`Umathopeninnerspacing`
---`Umathcloseordspacing`
---`Umathcloseopspacing`
---`Umathclosebinspacing`
---`Umathcloserelspacing`
---`Umathcloseopenspacing`
---`Umathcloseclosespacing`
---`Umathclosepunctspacing`
---`Umathcloseinnerspacing`
---`Umathpunctordspacing`
---`Umathpunctopspacing`
---`Umathpunctbinspacing`
---`Umathpunctrelspacing`
---`Umathpunctopenspacing`
---`Umathpunctclosespacing`
---`Umathpunctpunctspacing`
---`Umathpunctinnerspacing`
---`Umathinnerordspacing`
---`Umathinneropspacing`
---`Umathinnerbinspacing`
---`Umathinnerrelspacing`
---`Umathinneropenspacing`
---`Umathinnerclosespacing`
---`Umathinnerpunctspacing`
---`Umathinnerinnerspacing`
---\stoplines
---\stoptwocolumns
---
---These parameters are of type `muskip`, so setting a parameter can be done
---like this:
---
---```
---\Umathopordspacing\displaystyle=4mu plus 2mu
---```
---
---They are all initialized by `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, `thinmuskip`,
---`medmuskip` and `thickmuskip` are treated specially. In their case a
---pointer to the corresponding internal parameter is saved, not the actual `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 `*` 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.
---
---# Skips around display math
---
---The injection of `abovedisplayskip` and `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: `mathdisplayskipmode`. The following values apply:
---
--- value   meaning 
---
--- 0  normal *TeX* behaviour 
--- 1  always (same as 0) 
--- 2  only when not zero 
--- 3  never, not even when not zero 
---
---By default the short skip detection is not adapted to r2l typesetting and that
---hasn't been the case since the start of the project. Changing it could break
---hacks that users came up with but when you set `matheqdirmode` to a positive
---value direction will be taken into account.
---
---\subsection {Nolimit correction}
---
---There are two extra math parameters `Umathnolimitsupfactor` and `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 `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.
---
---    
---         \mathnolimitsmode0    `\displaystyle\int\nolimits^0_1`
---         \mathnolimitsmode1    `\displaystyle\int\nolimits^0_1`
---         \mathnolimitsmode2    `\displaystyle\int\nolimits^0_1`
---         \mathnolimitsmode3    `\displaystyle\int\nolimits^0_1`
---         \mathnolimitsmode4    `\displaystyle\int\nolimits^0_1`
---         \mathnolimitsmode8000 `\displaystyle\int\nolimits^0_1`
---    
---    
---     mode
---         \tttf 0
---         \tttf 1
---         \tttf 2
---         \tttf 3
---         \tttf 4
---         \tttf 8000
---    
---     superscript
---         0
---         font
---         0
---         0
---         +ic/2
---         0
---    
---     subscript
---         -ic
---         font
---         0
---         -ic/2
---         -ic/2
---         8000ic/1000
---    
---
---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 `mathnolimitsmode` larger that 15 is considered to
---be a factor for the subscript correction. This feature can be handy when
---experimenting.
---
---\subsection {Math italic mess}
---
---The `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). A value of 2 will enforce the
---old school font code path for all italics. We show a Cambria example.
---
---\starttexdefinition Whatever #1
---     `\mathitalicsmode = #1`
---     \mathitalicsmode#1\ruledhbox{`\left|T^1\right|`}
---     \mathitalicsmode#1\ruledhbox{`\left|T\right|`}
---     \mathitalicsmode#1\ruledhbox{`T+1`}
---     \mathitalicsmode#1\ruledhbox{`T{1\over2}`}
---     \mathitalicsmode#1\ruledhbox{`T\sqrt{1}`}
---    
---\stoptexdefinition
---
---\start
---    \switchtobodyfont[cambria]
---    
---        \Whatever{0}%
---        \Whatever{1}%
---    
---\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 {Script and kerning}
---
---If you want to typeset text in math macro packages often provide something `\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 `hbox` we have some control over this.
---And, as a bonus we also added control over the normal sublist kerning. The `mathscriptboxmode` parameter defaults to 1.
---
--- value      meaning 
---
--- `0`  forget about kerning 
--- `1`  kern math sub lists with a valid glyph 
--- `2`  also kern math sub boxes that have a valid glyph 
---@field 2 only kern math sub boxes with a boundary node # present
---
---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]}}}
--- \Show{1}{0}{}         \Show{1}{1}{}          \Show{2}{1}{}          \Show{2}{2}{}          \Show{3}{3}{}          \Show{1}{0}{-}        \Show{1}{1}{-}         \Show{2}{1}{-}         \Show{2}{2}{-}         \Show{3}{3}{-}        
---     modern    \Show{1}{0}{modern}   \Show{1}{1}{modern}    \Show{2}{1}{modern}    \Show{2}{2}{modern}    \Show{3}{3}{modern}   
---     lucidaot  \Show{1}{0}{lucidaot} \Show{1}{1}{lucidaot}  \Show{2}{1}{lucidaot}  \Show{2}{2}{lucidaot}  \Show{3}{3}{lucidaot} 
---     pagella   \Show{1}{0}{pagella}  \Show{1}{1}{pagella}   \Show{2}{1}{pagella}   \Show{2}{2}{pagella}   \Show{3}{3}{pagella}  
---     cambria   \Show{1}{0}{cambria}  \Show{1}{1}{cambria}   \Show{2}{1}{cambria}   \Show{2}{2}{cambria}   \Show{3}{3}{cambria}  
---     dejavu    \Show{1}{0}{dejavu}   \Show{1}{1}{dejavu}    \Show{2}{1}{dejavu}    \Show{2}{2}{dejavu}    \Show{3}{3}{dejavu}   
---
---Kerning between a character subscript is controlled by `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%
---  {
---   #1 
---   #2 
---   \showglyphdata \switchtobodyfont[#2,17.3pt]`#3T_{f}`         
---   \showglyphdata \switchtobodyfont[#2,17.3pt]`#3\gamma_{e}`    
---   \showglyphdata \switchtobodyfont[#2,17.3pt]`#3\gamma_{ee}`   
---   \showglyphdata \switchtobodyfont[#2,17.3pt]`#3T_{\tf fluff}` 
---   \NR}
---
---    \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}
---    
---
---# Fixed scripts
---
---We have three parameters that are used for this fixed anchoring:
---
--- parameter  register 
--- `d`  `Umathsubshiftdown`    
--- `u`  `Umathsupshiftup`      
--- `s`  `Umathsubsupshiftdown` 
---
---When we set `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`}
---
--- mode  down           up             example        
---
--- 0     dynamic        dynamic        \SampleMath{0} 
--- 1     `d`            `u`            \SampleMath{1} 
--- 2     `s`            `u`            \SampleMath{2} 
--- 3     `s`            `u + s - d`    \SampleMath{3} 
--- 4     `d + (s-d)/2`  `u + (s-d)/2`  \SampleMath{4} 
--- 5     `d`            `u + s - d`    \SampleMath{5} 
---
---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
---
---# Penalties: `mathpenaltiesmode`
---
---Only in inline math penalties will be added in a math list. You can force
---penalties (also in display math) by setting:
---
---```
---\mathpenaltiesmode = 1
---```
---
---This primnitive is not really needed in *LuaTeX* because you can use the callback
---`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:
---
---```
---\prebinoppenalty = -100 % example value
---\prerelpenalty   =  900 % example value
---```
---
---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.
---
---# Equation spacing: `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*.
---
----------------------------------------------------------------


---
---# Math constructs
---
---\subsection {Unscaled fences}
---
---The `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 `mathitalicsmode` enabled).
---
---\starttexdefinition Whatever #1
---     `\mathdelimitersmode = #1`
---     \mathitalicsmode1\mathdelimitersmode#1\ruledhbox{\showglyphs\showfontkerns\showfontitalics`f(x)`}
---     \mathitalicsmode1\mathdelimitersmode#1\ruledhbox{\showglyphs\showfontkerns\showfontitalics`f\left(x\right)`}
---    
---\stoptexdefinition
---
---\start
---    \switchtobodyfont[cambria]
---    
---        \Whatever{0}\Whatever{1}\Whatever{2}\Whatever{3}%
---        \Whatever{4}\Whatever{5}\Whatever{6}\Whatever{7}%
---    
---\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 `left` and `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:
---
--- value   meaning 
---
--- `"01`  don't apply the usual shift 
--- `"02`  apply italic correction when possible 
--- `"04`  force an ordinary subformula 
--- `"08`  no shift when a base character 
--- `"10`  only shift when an extensible 
---
---The effect can depend on the font (and for Cambria one can use for instance `"16`).
---
---\subsection[mathacc]{Accent handling}
---
---*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 `Umathaccent`.
---
---The keyword `bottom` after `Umathaccent` signals that a bottom accent
---is needed, and the keyword `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 `fixed` keyword to indicate that a non-stretching
---variant is requested (in case of both accents, this step is repeated).
---
---A simple example:
---
---```
---\Umathaccent both fixed 0 0 "20D7 fixed 0 0 "20D7 {example}
---```
---
---If a math top accent has to be placed and the accentee is a character and has a
---non-zero `top_accent` value, then this value will be used to place the
---accent instead of the `skewchar` kern used by *TeX*82.
---
---The `top_accent` value represents a vertical line somewhere in the
---accentee. The accent will be shifted horizontally such that its own `top_accent` line coincides with the one from the accentee. If the `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 `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 `MathConstants` table, then `AccentBaseHeight` is used instead.
---
---The vertical placement of a bottom accent is straight below the accentee, no
---correction takes place.
---
---Possible locations are `top`, `bottom`, `both` and `center`. When no location is given `top` is assumed. An additional
---parameter `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
---`overlay` location. It also works for the other locations but then it
---concerns the width.
---
---# Radical extensions
---
---The new primitive `Uroot` allows the construction of a radical noad
---including a degree field. Its syntax is an extension of `Uradical`:
---
---```
---\Uradical <fam integer> <char integer> <radicand>
---\Uroot    <fam integer> <char integer> <degree> <radicand>
---```
---
---The placement of the degree is controlled by the math parameters `Umathradicaldegreebefore`, `Umathradicaldegreeafter`, and `Umathradicaldegreeraise`. The degree will be typeset in `scriptscriptstyle`.
---
---# Super- and subscripts
---
---The character fields in a *Lua*-loaded *OpenType* math font can have a “mathkern” table. The format of this table is the same as the “mathkern”
---table that is returned by the `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:
---
---    * The vertical position of the script is calculated.
---    
---    * The default horizontal position is flat next to the base character.
---    
---    * For superscripts, the italic correction of the base character is added.
---    
---    * 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.
---    
---    * For each of these two locations:
---         * 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)  * 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)  * add the found values together to get a preliminary result. 
---        
---    
---    * The horizontal kern to be applied is the smallest of the two results from
---        previous step.
---    
---
---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).
---
---# Scripts on extensibles
---
---The primitives `Uunderdelimiter` and `Uoverdelimiter` allow the
---placement of a subscript or superscript on an automatically extensible item and
---`Udelimiterunder` and `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 `Umathunderdelimiterbgap`, `Umathunderdelimitervgap`, `Umathoverdelimiterbgap`, and `Umathoverdelimitervgap` in a similar way as limit placements on large operators.
---The superscript in `Uoverdelimiter` is typeset in a suitable scripted style,
---the subscript in `Uunderdelimiter` is cramped as well.
---
---These primitives accepts an option `width` specification. When used the
---also optional keywords `left`, `middle` and `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 `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* “MathVariants” as well as *tfm* “extensible recipes”. In most cases where
---font metrics are involved we have a different code path for traditional fonts end
---*OpenType* fonts.
---
---Sometimes you might want to act upon the size of a delimiter, something that is
---not really possible because of the fact that they are calculated {\em after} most
---has been typeset already. In the following example the all-zero specification
---is the trigger to make a fake box with the last delimiter dimensions and shift.
---It's an ugly hack but its relative simple and not intrusive implementation has no
---side effects. Any other heuristic solution would not satisfy possible demands
---anyway. Here is a rather low level example:
---
---\startbuffer
---\startformula
---\Uleft  \Udelimiter 5 0 "222B
---\frac{\frac{a}{b}}{\frac{c}{d}}
---\Uright \Udelimiter 5 0 "222B
---\kern-2\fontcharwd\textfont0 "222B
---\mathlimop{\Uvextensible \Udelimiter 0 0 0}_1^2 x
---\stopformula
---\stopbuffer
---
---\typebuffer
---
---The last line, by passing zero values, results in a fake operator that has the
---dimensions of the previous delimiter. We can then backtrack over the (presumed)
---width and the two numbers become limit operators. As said, it's not pretty but it
---works.
---
---# Fractions
---
---The `abovewithdelims` command accepts a keyword `exact`. When issued
---the extra space relative to the rule thickness is not added. One can of course
---use the `\Umathfraction..gap` commands to influence the spacing. Also the
---rule is still positioned around the math axis.
---
---```
---$` { {a} \abovewithdelims() exact 4pt {b} }``
---```
---
---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
---`Umathskewedfractionhgap` and `Umathskewedfractionvgap`.
---
---The syntax used here is:
---
---```
---{ {1} \Uskewed / <options> {2} }
---{ {1} \Uskewedwithdelims / () <options> {2} }
---```
---
---where the options can be `noaxis` and `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]
---    
---          \ShowA{a}{b}{}  \ShowA{1}{2}{}  \ShowB{a}{b}{}  \ShowB{1}{2}{} 
---        \NR
---         `exact`  \ShowA{a}{b}{exact}  \ShowA{1}{2}{exact}  \ShowB{a}{b}{exact}  \ShowB{1}{2}{exact} 
---        \NR
---         `noaxis`  \ShowA{a}{b}{noaxis}  \ShowA{1}{2}{noaxis}  \ShowB{a}{b}{noaxis}  \ShowB{1}{2}{noaxis} 
---        \NR
---         `exact noaxis`  \ShowA{a}{b}{exact noaxis}  \ShowA{1}{2}{exact noaxis}  \ShowB{a}{b}{exact noaxis}  \ShowB{1}{2}{exact noaxis} 
---        \NR
---    
---\stop
---
---The keyword `norule` will hide the rule with the above variants while
---keeping the rule related spacing.
---
---\subsection {Delimiters: `\Uleft`, `Umiddle` and `Uright`}
---
---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) `\big` need use this feature. In *LuaTeX* we provide a bit more control
---by three variants that support optional parameters `height`, `depth`
---and `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 `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 `noaxis` command can be used to prevent shifting over the axis.
---
---You can influence the final class with the keyword `class` which will
---influence the spacing. The numbers are the same as for character classes.
---
----------------------------------------------------------------


---
---# Extracting values
---
---# Codes
---
---You can extract the components of a math character. Say that we have defined:
---
---```
---\Umathcode 1 2 3 4
---```
---
---then
---
---```
---[\Umathcharclass1] [\Umathcharfam1] [\Umathcharslot1]
---```
---
---will return:
---
---```
---[2] [3] [4]
---```
---
---These commands are provides as convenience. Before they come available you could
---do the following:
---
---```
---\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])}}
---```
---
---\subsection {Last lines}
---
---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:
---
---```
---\predisplaygapfactor=2000
---```
---
---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:
---
---```
---\def\lastlinelength{\dimexpr
---    \directlua {tex.sprint (
---        (nodes.dimensions(node.tail(tex.lists.page_head).list))
---    )}sp
---\relax}
---```
---
----------------------------------------------------------------


---
---# Math mode
---
---\subsection {Verbose versions of single-character math commands}
---
---*LuaTeX* defines six new primitives that have the same function as
---`^`, `_`, ```, and `$``:
---
--- primitive                   explanation 
---
--- `Usuperscript`       duplicates the functionality of `^` 
--- `Usubscript`         duplicates the functionality of `_` 
--- `Ustartmath`         duplicates the functionality of ```, % ` when used in non-math mode. 
--- `Ustopmath`          duplicates the functionality of ```, % ` when used in inline math mode. 
--- `Ustartdisplaymath`  duplicates the functionality of ````, % `` when used in non-math mode. 
--- `Ustopdisplaymath`   duplicates the functionality of ````, % `` when used in display math mode. 
---
---The `Ustopmath` and `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).
---
---# Script commands `Unosuperscript` and `Unosubscript`
---
---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[script]
---
---results in \inlinebuffer[script].
---
---# Allowed math commands in non-math modes
---
---The commands `mathchar`, and `Umathchar` and control sequences that are
---the result of `mathchardef` or `Umathchardef` are also acceptable in
---the horizontal and vertical modes. In those cases, the `textfont` from the
---requested math family is used.
---
---% # Math todo
---%
---% The following items are still todo.
---%
---% 
---% * %     Pre-scripts.
---% 
---% * %     Multi-story stacks.
---% 
---% * %     Flattened accents for high characters (maybe).
---% 
---% * %     Better control over the spacing around displays and handling of equation numbers.
---% 
---% * %     Support for multi-line displays using \MATHML\ style alignment points.
---% 
---% 
---%
---% \stopsection
---
----------------------------------------------------------------


---
---# Goodies
---
---\subsection {Flattening: `mathflattenmode`}
---
---The *TeX* math engine collapses `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 `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.
---
--- mode  class 
---
---  1    ord   
---  2    bin   
---  4    rel   
---  8    punct 
--- 16    inner 
---
---\subsection {Less Tracing}
---
---Because there are quite some math related parameters and values, it is possible
---to limit tracing. Only when `tracingassigns` and/or `tracingrestores` are set to 2 or more they will be traced.
---
---\subsection {Math options with `mathdefaultsmode`}
---
---This option has been introduced because \LATEX\ developers wanted some of the
---defaults to be different from the ones that were set in stone when we froze
---*LuaTeX*. The default values are:
--- scanning  rendering 
---
--- radical/root     cramped   cramped   
--- under delimiter  cramped   supstyle  
--- over delimiter   cramped   substyle  
--- delimiter under  cramped   current   
--- delimiter over   cramped   current   
---
---When `\mathdefaultsmode` is larger than zero, we have:
--- scanning  rendering 
---
--- radical/root     cramped   cramped   
--- under delimiter  substyle  substyle  
--- over delimiter   supstyle  supstyle  
--- delimiter under  current   current   
--- delimiter over   cramped   cramped   
---
---It is outside the scope of this manual to discuss the rationale behind these
---defaults. The zero values date back from the early times. If needed you can
---explicitly set the style in the content argument.
---
---\subsection {Math options with `mathoption`}
---
---The logic in the math engine is rather complex and there are often no universal
---solutions (read: what works out well for one font, fails for another). Therefore
---some variations in the implementation are driven by parameters (modes). In
---addition there is a new primitive `mathoption` which will be used for
---testing. Don't rely on any option to be there in a production version as they are
---meant for development.
---
---This option was introduced for testing purposes when the math engine got split
---code paths and it forces the engine to treat new fonts as old ones with respect
---to italic correction etc. There are no guarantees given with respect to the final
---result and unexpected side effects are not seen as bugs as they relate to font
---properties. There is currently only one option:
---
---\startbuffer
---\mathoption old 1
---\stopbuffer
---
---The `oldmath` boolean flag in the *Lua* font table is the official way to
---force old treatment as it's bound to fonts. Like with all options we may
---temporarily introduce with this command this feature is not meant for production.
---
---% % obsolete:
---%
---% \subsubsection {`\mathoption noitaliccompensation`}
---%
---% This option compensates placement for characters with a built-in italic
---% correction.
---%
---% \startbuffer
---% {\showboxes\int}\quad
---% {\showboxes\int_{|}^{|}}\quad
---% {\showboxes\int\limits_{|}^{|}}
---% \stopbuffer
---%
---% \typebuffer
---%
---% Gives (with computer modern that has such italics):
---%
---% \startlinecorrection[blank]
---%     \switchtobodyfont[modern]
---%     \startcombination[nx=2,ny=2,distance=5em]
---%         {\mathoption noitaliccompensation 0\relax \mathematics{\getbuffer}}
---%             {\nohyphens`0:inline`}
---%         {\mathoption noitaliccompensation 0\relax \mathematics{\displaymath\getbuffer}}
---%             {\nohyphens`0:display`}
---%         {\mathoption noitaliccompensation 1\relax \mathematics{\getbuffer}}
---%             {\nohyphens`1:inline`}
---%         {\mathoption noitaliccompensation 1\relax \mathematics{\displaymath\getbuffer}}
---%             {\nohyphens`1:display`}
---%     \stopcombination
---% \stoplinecorrection
---
---% % obsolete:
---%
---% \subsubsection {`\mathoption nocharitalic`}
---%
---% When two characters follow each other italic correction can interfere. The
---% following example shows what this option does:
---%
---% \startbuffer
---% \catcode"1D443=11
---% \catcode"1D444=11
---% \catcode"1D445=11
---% P( PP PQR
---% \stopbuffer
---%
---% \typebuffer
---%
---% Gives (with computer modern that has such italics):
---%
---% \startlinecorrection[blank]
---%     \switchtobodyfont[modern]
---%     \startcombination[nx=2,ny=2,distance=5em]
---%         {\mathoption nocharitalic 0\relax \mathematics{\getbuffer}}
---%             {\nohyphens`0:inline`}
---%         {\mathoption nocharitalic 0\relax \mathematics{\displaymath\getbuffer}}
---%             {\nohyphens`0:display`}
---%         {\mathoption nocharitalic 1\relax \mathematics{\getbuffer}}
---%             {\nohyphens`1:inline`}
---%         {\mathoption nocharitalic 1\relax \mathematics{\displaymath\getbuffer}}
---%             {\nohyphens`1:display`}
---%     \stopcombination
---% \stoplinecorrection
---
---% % obsolete:
---%
---% \subsubsection {`\mathoption useoldfractionscaling`}
---%
---% This option has been introduced as solution for tracker item 604 for fuzzy cases
---% around either or not present fraction related settings for new fonts.
---
----------------------------------------------------------------


---
---\stopchapter
---
---\stopcomponent
---