diff options
Diffstat (limited to 'Master/texmf-dist/doc/luatex/base/luatex-math.tex')
| -rw-r--r-- | Master/texmf-dist/doc/luatex/base/luatex-math.tex | 3079 |
1 files changed, 1647 insertions, 1432 deletions
diff --git a/Master/texmf-dist/doc/luatex/base/luatex-math.tex b/Master/texmf-dist/doc/luatex/base/luatex-math.tex index f29a3aed0a6..fd038150f59 100644 --- a/Master/texmf-dist/doc/luatex/base/luatex-math.tex +++ b/Master/texmf-dist/doc/luatex/base/luatex-math.tex @@ -1,1432 +1,1647 @@ -% language=uk - -\environment luatex-style -\environment luatex-logos - -\startcomponent luatex-math - -\startchapter[reference=math,title={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. - -\section{The current math style} - -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: \type {\mathstyle}. This is a \quote -{convert command} like e.g. \type {\romannumeral}: its value can only be read, -not set. - -\subsection{\type {\mathstyle}} - -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 the 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 \type {\textstyle} are turned into nodes so -the styles set there are frozen. The \type {\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 \type -{\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 \type {\begingroup} \unknown\ \type {\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 \type {\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{\type {\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 (\type {\over}, \type {\atop}, -\type {\overwithdelims}, \type {\atopwithdelims}) would therefore normally return -wrong values for \type {\mathstyle}. To fix this, \LUATEX\ introduces a special -prefix command: \type {\Ustack}: - -\starttyping -$\Ustack {a \over b}$ -\stoptyping - -The \type {\Ustack} command will scan the next brace and start a new math group -with the correct (numerator) math style. - -\section{Unicode math characters} - -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 in the second column. - -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|] -\BC primitive \BC min \BC max \BC \kern 2em \BC min \BC max \NC \NR -\NC \type {\mathcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC 8000 \NC \NR -\NC \type {\delcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC FFFFFF \NC \NR -\stoptabulate - -The unaltered ones are: - -\starttabulate[|l|l|r|] -\BC primitive \BC min \BC max \NC \NR -\NC \type {\mathchardef} \NC 0 \NC 8000 \NC \NR -\NC \type {\mathchar} \NC 0 \NC 7FFF \NC \NR -\NC \type {\mathaccent} \NC 0 \NC 7FFF \NC \NR -\NC \type {\delimiter} \NC 0 \NC 7FFFFFF \NC \NR -\NC \type {\radical} \NC 0 \NC 7FFFFFF \NC \NR -\stoptabulate - -For practical reasons \type {\mathchardef} will silently accept values larger -that \type {0x8000} and interpret it as \type {\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|] -\BC primitive \BC min \BC max \BC \kern 2em \BC min \BC max \NC \NR -\NC \type {\Umathchardef} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{1}} \NC \NC \NC \NC \NR -\NC \type {\Umathcharnumdef}\rlap{\high{5}} \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NC \NC \NC \NR -\NC \type {\Umathcode} \NC 0 \NC 10FFFF \NC = \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{1}} \NC \NR -\NC \type {\Udelcode} \NC 0 \NC 10FFFF \NC = \NC 0+0 \NC FF+10FFFF\rlap{\high{2}} \NC \NR -\NC \type {\Umathchar} \NC 0+0+0 \NC 7+FF+10FFFF \NC \NC \NC \NC \NR -\NC \type {\Umathaccent} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{2,4}} \NC \NC \NC \NC \NR -\NC \type {\Udelimiter} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{2}} \NC \NC \NC \NC \NR -\NC \type {\Uradical} \NC 0+0 \NC FF+10FFFF\rlap{\high{2}} \NC \NC \NC \NC \NR -\NC \type {\Umathcharnum} \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NC \NC \NC \NR -\NC \type {\Umathcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NR -\NC \type {\Udelcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NR -\stoptabulate - -Specifications typically look like: - -\starttyping -\Umathchardef\xx="1"0"456 -\Umathcode 123="1"0"789 -\stoptyping - -Note 1: 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 \type {\Umathoperatorsize} parameter (more -information can be found in a following section). - -Note 2: For these three primitives, all information is packed into a single -signed integer. For the first two (\type {\Umathcharnum} and \type -{\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 \type {\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. - -Note 3: The \type {\Umathaccent} command accepts optional keywords to control -various details regarding math accents. See \in {section} [mathacc] below for -details. - -New primitives that exist in \LUATEX\ only (all of these will be explained -in following sections): - -\starttabulate[|l|l|] -\BC primitive \BC value range (in hex) \NC \NR -\NC \type {\Uroot} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Uoverdelimiter} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Uunderdelimiter} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Udelimiterover} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Udelimiterunder} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\stoptabulate - -\section{Cramped math styles} - -\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 \type {\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. If we -force styles in the script using \type {\scriptstyle} and \type {\crampedscriptstyle} -we get this: - -\startbuffer[demo] -\starttabulate -\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 -\stoptabulate -\stopbuffer - -\getbuffer[demo] - -Now we set the following parameters - -\startbuffer[setup] -\Umathordrelspacing\scriptstyle=30mu -\Umathordordspacing\scriptstyle=30mu -\stopbuffer - -\typebuffer[setup] - -This gives: - -\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 - -\section{Math parameter settings} - -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 accessible before. - -\starttabulate -\BC primitive name \BC description \NC \NR -\NC \type {\Umathquad} \NC the width of 18 mu's \NC \NR -\NC \type {\Umathaxis} \NC height of the vertical center axis of - the math formula above the baseline \NC \NR -\NC \type {\Umathoperatorsize} \NC minimum size of large operators in display mode \NC \NR -\NC \type {\Umathoverbarkern} \NC vertical clearance above the rule \NC \NR -\NC \type {\Umathoverbarrule} \NC the width of the rule \NC \NR -\NC \type {\Umathoverbarvgap} \NC vertical clearance below the rule \NC \NR -\NC \type {\Umathunderbarkern} \NC vertical clearance below the rule \NC \NR -\NC \type {\Umathunderbarrule} \NC the width of the rule \NC \NR -\NC \type {\Umathunderbarvgap} \NC vertical clearance above the rule \NC \NR -\NC \type {\Umathradicalkern} \NC vertical clearance above the rule \NC \NR -\NC \type {\Umathradicalrule} \NC the width of the rule \NC \NR -\NC \type {\Umathradicalvgap} \NC vertical clearance below the rule \NC \NR -\NC \type {\Umathradicaldegreebefore}\NC the forward kern that takes place before placement of - the radical degree \NC \NR -\NC \type {\Umathradicaldegreeafter} \NC the backward kern that takes place after placement of - the radical degree \NC \NR -\NC \type {\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 \type {\Umathstackvgap} \NC vertical clearance between the two - elements in a \type {\atop} stack \NC \NR -\NC \type {\Umathstacknumup} \NC numerator shift upward in \type {\atop} stack \NC \NR -\NC \type {\Umathstackdenomdown} \NC denominator shift downward in \type {\atop} stack \NC \NR -\NC \type {\Umathfractionrule} \NC the width of the rule in a \type {\over} \NC \NR -\NC \type {\Umathfractionnumvgap} \NC vertical clearance between the numerator and the rule \NC \NR -\NC \type {\Umathfractionnumup} \NC numerator shift upward in \type {\over} \NC \NR -\NC \type {\Umathfractiondenomvgap} \NC vertical clearance between the denominator and the rule \NC \NR -\NC \type {\Umathfractiondenomdown} \NC denominator shift downward in \type {\over} \NC \NR -\NC \type {\Umathfractiondelsize} \NC minimum delimiter size for \type {\...withdelims} \NC \NR -\NC \type {\Umathlimitabovevgap} \NC vertical clearance for limits above operators \NC \NR -\NC \type {\Umathlimitabovebgap} \NC vertical baseline clearance for limits above operators \NC \NR -\NC \type {\Umathlimitabovekern} \NC space reserved at the top of the limit \NC \NR -\NC \type {\Umathlimitbelowvgap} \NC vertical clearance for limits below operators \NC \NR -\NC \type {\Umathlimitbelowbgap} \NC vertical baseline clearance for limits below operators \NC \NR -\NC \type {\Umathlimitbelowkern} \NC space reserved at the bottom of the limit \NC \NR -\NC \type {\Umathoverdelimitervgap} \NC vertical clearance for limits above delimiters \NC \NR -\NC \type {\Umathoverdelimiterbgap} \NC vertical baseline clearance for limits above delimiters \NC \NR -\NC \type {\Umathunderdelimitervgap} \NC vertical clearance for limits below delimiters \NC \NR -\NC \type {\Umathunderdelimiterbgap} \NC vertical baseline clearance for limits below delimiters \NC \NR -\NC \type {\Umathsubshiftdrop} \NC subscript drop for boxes and subformulas \NC \NR -\NC \type {\Umathsubshiftdown} \NC subscript drop for characters \NC \NR -\NC \type {\Umathsupshiftdrop} \NC superscript drop (raise, actually) for boxes and subformulas \NC \NR -\NC \type {\Umathsupshiftup} \NC superscript raise for characters \NC \NR -\NC \type {\Umathsubsupshiftdown} \NC subscript drop in the presence of a superscript \NC \NR -\NC \type {\Umathsubtopmax} \NC the top of standalone subscripts cannot be higher than this - above the baseline \NC \NR -\NC \type {\Umathsupbottommin} \NC the bottom of standalone superscripts cannot be less than - this above the baseline \NC \NR -\NC \type {\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 \type {\Umathsubsupvgap} \NC vertical clearance between super- and subscript \NC \NR -\NC \type {\Umathspaceafterscript} \NC additional space added after a super- or subscript \NC \NR -\NC \type {\Umathconnectoroverlapmin}\NC minimum overlap between parts in an extensible recipe \NC \NR -\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. - -\section{Skips around display math} - -The injection of \type {\abovedisplayskip} and \type {\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 later makes it sometimes hard -to fully control spacing. Therefore \LUATEX\ comes with a new directive: \type -{\mathdisplayskipmode}. The following values apply: - -\starttabulate -\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 -\stoptabulate - -\section{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 \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 using in the \TeX book. Assignments to \type -{\textfont} set the values for the cramped and uncramped display and text styles, -\type {\scriptfont} sets the script styles, and \type {\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. - -\start - -\switchtobodyfont[8pt] - -\starttabulate[|l|l|l|p|] -\BC variable \BC style \BC default value opentype \BC default value tfm \NC \NR -\NC \type {\Umathaxis} \NC -- \NC AxisHeight \NC axis_height \NC \NR -\NC \type {\Umathoperatorsize} \NC D, D' \NC DisplayOperatorMinHeight \NC $^6$ \NC \NR -\NC \type {\Umathfractiondelsize} \NC D, D' \NC FractionDelimiterDisplayStyleSize$^9$ \NC delim1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionDelimiterSize$^9$ \NC delim2 \NC \NR -\NC \type {\Umathfractiondenomdown} \NC D, D' \NC FractionDenominatorDisplayStyleShiftDown \NC denom1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionDenominatorShiftDown \NC denom2 \NC \NR -\NC \type {\Umathfractiondenomvgap} \NC D, D' \NC FractionDenominatorDisplayStyleGapMin \NC 3*default_rule_thickness \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionDenominatorGapMin \NC default_rule_thickness \NC \NR -\NC \type {\Umathfractionnumup} \NC D, D' \NC FractionNumeratorDisplayStyleShiftUp \NC num1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionNumeratorShiftUp \NC num2 \NC \NR -\NC \type {\Umathfractionnumvgap} \NC D, D' \NC FractionNumeratorDisplayStyleGapMin \NC 3*default_rule_thickness \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionNumeratorGapMin \NC default_rule_thickness \NC \NR -\NC \type {\Umathfractionrule} \NC -- \NC FractionRuleThickness \NC default_rule_thickness \NC \NR -\NC \type {\Umathskewedfractionhgap} \NC -- \NC SkewedFractionHorizontalGap \NC math_quad/2 \NC \NR -\NC \type {\Umathskewedfractionvgap} \NC -- \NC SkewedFractionVerticalGap \NC math_x_height \NC \NR -\NC \type {\Umathlimitabovebgap} \NC -- \NC UpperLimitBaselineRiseMin \NC big_op_spacing3 \NC \NR -\NC \type {\Umathlimitabovekern} \NC -- \NC 0$^1$ \NC big_op_spacing5 \NC \NR -\NC \type {\Umathlimitabovevgap} \NC -- \NC UpperLimitGapMin \NC big_op_spacing1 \NC \NR -\NC \type {\Umathlimitbelowbgap} \NC -- \NC LowerLimitBaselineDropMin \NC big_op_spacing4 \NC \NR -\NC \type {\Umathlimitbelowkern} \NC -- \NC 0$^1$ \NC big_op_spacing5 \NC \NR -\NC \type {\Umathlimitbelowvgap} \NC -- \NC LowerLimitGapMin \NC big_op_spacing2 \NC \NR -\NC \type {\Umathoverdelimitervgap} \NC -- \NC StretchStackGapBelowMin \NC big_op_spacing1 \NC \NR -\NC \type {\Umathoverdelimiterbgap} \NC -- \NC StretchStackTopShiftUp \NC big_op_spacing3 \NC \NR -\NC \type {\Umathunderdelimitervgap} \NC-- \NC StretchStackGapAboveMin \NC big_op_spacing2 \NC \NR -\NC \type {\Umathunderdelimiterbgap} \NC-- \NC StretchStackBottomShiftDown \NC big_op_spacing4 \NC \NR -\NC \type {\Umathoverbarkern} \NC -- \NC OverbarExtraAscender \NC default_rule_thickness \NC \NR -\NC \type {\Umathoverbarrule} \NC -- \NC OverbarRuleThickness \NC default_rule_thickness \NC \NR -\NC \type {\Umathoverbarvgap} \NC -- \NC OverbarVerticalGap \NC 3*default_rule_thickness \NC \NR -\NC \type {\Umathquad} \NC -- \NC <font_size(f)>$^1$ \NC math_quad \NC \NR -\NC \type {\Umathradicalkern} \NC -- \NC RadicalExtraAscender \NC default_rule_thickness \NC \NR -\NC \type {\Umathradicalrule} \NC -- \NC RadicalRuleThickness \NC <not set>$^2$ \NC \NR -\NC \type {\Umathradicalvgap} \NC D, D' \NC RadicalDisplayStyleVerticalGap \NC (default_rule_thickness+\crlf - (abs(math_x_height)/4))$^3$ \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC RadicalVerticalGap \NC (default_rule_thickness+\crlf - (abs(default_rule_thickness)/4))$^3$ \NC \NR -\NC \type {\Umathradicaldegreebefore} \NC -- \NC RadicalKernBeforeDegree \NC <not set>$^2$ \NC \NR -\NC \type {\Umathradicaldegreeafter} \NC -- \NC RadicalKernAfterDegree \NC <not set>$^2$ \NC \NR -\NC \type {\Umathradicaldegreeraise} \NC -- \NC RadicalDegreeBottomRaisePercent \NC <not set>$^{2,7}$ \NC \NR -\NC \type {\Umathspaceafterscript} \NC -- \NC SpaceAfterScript \NC script_space$^4$ \NC \NR -\NC \type {\Umathstackdenomdown} \NC D, D' \NC StackBottomDisplayStyleShiftDown \NC denom1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC StackBottomShiftDown \NC denom2 \NC \NR -\NC \type {\Umathstacknumup} \NC D, D' \NC StackTopDisplayStyleShiftUp \NC num1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC StackTopShiftUp \NC num3 \NC \NR -\NC \type {\Umathstackvgap} \NC D, D' \NC StackDisplayStyleGapMin \NC 7*default_rule_thickness \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC StackGapMin \NC 3*default_rule_thickness \NC \NR -\NC \type {\Umathsubshiftdown} \NC -- \NC SubscriptShiftDown \NC sub1 \NC \NR -\NC \type {\Umathsubshiftdrop} \NC -- \NC SubscriptBaselineDropMin \NC sub_drop \NC \NR -\NC \type {\Umathsubsupshiftdown} \NC -- \NC SubscriptShiftDownWithSuperscript$^8$ \NC \NC \NR -\NC \NC \NC \quad\ or SubscriptShiftDown \NC sub2 \NC \NR -\NC \type {\Umathsubtopmax} \NC -- \NC SubscriptTopMax \NC (abs(math_x_height * 4) / 5) \NC \NR -\NC \type {\Umathsubsupvgap} \NC -- \NC SubSuperscriptGapMin \NC 4*default_rule_thickness \NC \NR -\NC \type {\Umathsupbottommin} \NC -- \NC SuperscriptBottomMin \NC (abs(math_x_height) / 4) \NC \NR -\NC \type {\Umathsupshiftdrop} \NC -- \NC SuperscriptBaselineDropMax \NC sup_drop \NC \NR -\NC \type {\Umathsupshiftup} \NC D \NC SuperscriptShiftUp \NC sup1 \NC \NR -\NC \NC T, S, SS, \NC SuperscriptShiftUp \NC sup2 \NC \NR -\NC \NC D', T', S', SS' \NC SuperscriptShiftUpCramped \NC sup3 \NC \NR -\NC \type {\Umathsupsubbottommax} \NC -- \NC SuperscriptBottomMaxWithSubscript \NC (abs(math_x_height * 4) / 5) \NC \NR -\NC \type {\Umathunderbarkern} \NC -- \NC UnderbarExtraDescender \NC default_rule_thickness \NC \NR -\NC \type {\Umathunderbarrule} \NC -- \NC UnderbarRuleThickness \NC default_rule_thickness \NC \NR -\NC \type {\Umathunderbarvgap} \NC -- \NC UnderbarVerticalGap \NC 3*default_rule_thickness \NC \NR -\NC \type {\Umathconnectoroverlapmin} \NC -- \NC MinConnectorOverlap \NC 0$^5$ \NC \NR -\stoptabulate - -\stop - -Note 1: \OPENTYPE\ fonts set \type {\Umathlimitabovekern} and \type -{\Umathlimitbelowkern} to zero and set \type {\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 \type {\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 -\type {\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type -{\Umathradicaldegreeraise}. These are then automatically initialized to -$5/18$quad, $-10/18$quad, and 60. - -Note 3: If \TFM\ fonts are used, then the \type {\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 \type -{\Umathradicalvgap} is set, it will not be recalculated any more. - -Note 4: When \TFM\ fonts are used a similar situation arises with respect to -\type {\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 \type {\Umathspaceafterscript} is set, \type {\scriptspace} will never -be looked at again. - -Note 5: Traditional \TFM\ fonts set \type {\Umathconnectoroverlapmin} to zero -because \TEX82\ always stacks extensibles without any overlap. - -Note 6: The \type {\Umathoperatorsize} is only used in \type {\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 \type {\Umathradicaldegreeraise} is a special case because it is the -only parameter that is expressed in a percentage instead of as 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. - -\section{Nolimit correction} - -There are two extra math parameters \type {\Umathnolimitsupfactor} and \type -{\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 \type {\mathnolimitsmode}. The half -corrections are what happens when scripts are placed on 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, does 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 \type {\mathnolimitsmode} larger that 15 is considered to -be a factor for the subscript correction. This feature can be handy when -experimenting. - -\section{Math italic mess} - -The \type {\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. - -\section{Script boxes} - -If you want 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 change that the kerning doesn't come out well when used in a script. Given -that the first glyph ends up in an \type {\hbox} we have some control over this. -And, as a bonus we also added control over the normal sublist kerning. The \type -{\mathscriptboxmode} parameter defaults to~1. - -\starttabulate[|l|l|] -\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 -\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\typeinlinebuffer[#1]} - {\doifelse{#3}{-} - {\small\type{mode #2}} - {\switchtobodyfont[#3]\showfontkerns\showglyphs\mathscriptboxmode#2\relax\inlinebuffer[#1]}}} - -\starttabulate[|lT|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 - -\section{Unscaled fences} - -The \type {\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 a ordinary -so that the same spacing applies as with unfenced variants. Here we show Cambria -(with \type {\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 \type -{\left} and \type {\right} always because of unpredictable content. As said, it's -an experimental features (which somehow fits in the exceptional way fences are -dealt with in the engine). - -\section{Math spacing setting} - -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 -\starttyping -\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 -\stoptyping -\stoptwocolumns - -These parameters are of type \type {\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, \type -{\thinmuskip}, \type {\medmuskip} and \type {\thickmuskip} are treated -especially. In their case a pointer to the corresponding internal parameter is -saved, not the actual \type {\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. - -\section[mathacc]{Math 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 \type {\Umathaccent}. - -The keyword \type {bottom} after \type {\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 \type {\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 value that 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 \type {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. - -\section{Math root extension} - -The new primitive \type {\Uroot} allows the construction of a radical noad -including a degree field. Its syntax is an extension of \type {\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 \type -{\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type -{\Umathradicaldegreeraise}. The degree will be typeset in \type -{\scriptscriptstyle}. - -\section{Math kerning in 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). - -\section{Scripts on horizontally extensible items like arrows} - -The primitives \type {\Uunderdelimiter} and \type {\Uoverdelimiter} allow the -placement of a subscript or superscript on an automatically extensible item and -\type {\Udelimiterunder} and \type {\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 \type {\Umathunderdelimiterbgap}, \type -{\Umathunderdelimitervgap}, \type {\Umathoverdelimiterbgap}, and \type -{\Umathoverdelimitervgap} in a similar way as limit placements on large operators. -The superscript in \type {\Uoverdelimiter} is typeset in a suitable scripted style, -the subscript in \type {\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 \type {\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. - -\section {Extracting values} - -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 came 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 - -\section{fractions} - -The \type {\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 -\type {\Umathskewedfractionhgap} and \type {\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 - -\section {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: - -\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 - -\section {Other Math changes} - -\subsection {Verbose versions of single-character math commands} - -\LUATEX\ defines six new primitives that have the same function as -\type {^}, \type {_}, \type {$}, and \type {$$}: - -\starttabulate[|l|l|] -\BC primitive \BC explanation \NC \NR -\NC \type {\Usuperscript} \NC Duplicates the functionality of \type {^} \NC \NR -\NC \type {\Usubscript} \NC Duplicates the functionality of \type {_} \NC \NR -\NC \type {\Ustartmath} \NC Duplicates the functionality of \type {$}, % $ - when used in non-math mode. \NC \NR -\NC \type {\Ustopmath} \NC Duplicates the functionality of \type {$}, % $ - when used in inline math mode. \NC \NR -\NC \type {\Ustartdisplaymath} \NC Duplicates the functionality of \type {$$}, % $$ - when used in non-math mode. \NC \NR -\NC \type {\Ustopdisplaymath} \NC Duplicates the functionality of \type {$$}, % $$ - when used in display math mode. \NC \NR -\stoptabulate - -The \type {\Ustopmath} and \type {\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 \type {\Unosuperscript} and \type {\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 - -results in \inlinebuffer[script]. - - -\subsection{Allowed math commands in non-math modes} - -The commands \type {\mathchar}, and \type {\Umathchar} and control sequences that -are the result of \type {\mathchardef} or \type {\Umathchardef} are also -acceptable in the horizontal and vertical modes. In those cases, the \type -{\textfont} from the requested math family is used. - -\section{Math surrounding skips} - -Inline math is surrounded by (optional) \type {\mathsurround} spacing but that is fixed -dimension. There is now an additional parameter \type {\mathsurroundskip}. When set to a -non|-|zero value (or zero with some stretch or shrink) this parameter will replace -\type {\mathsurround}. By using an additional parameter instead of changing the nature -of \type {\mathsurround}, we can remain compatible. In the meantime a bit more -control has been added via \type {\mathsurroundmode}. This directive can take 6 values -with zero being the default behaviour. - -\start - -\def\OneLiner#1#2% - {\NC \type{#1} - \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\mathsurroundmode#1\relax\hsize 100pt x$x$x} - \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\mathsurroundmode#1\relax\hsize 100pt x $x$ x} - \NC #2 - \NC \NR} - -\startbuffer -\mathsurround 10pt -\mathsurroundskip20pt -\stopbuffer - -\typebuffer \getbuffer - -\starttabulate[|c|c|c|pl|] -\HL -\BC mode \BC \type {x$x$x} \BC \type {x $x$ x} \BC effect \NC \NR -\HL -\OneLiner{0}{obey \type {\mathsurround} when \type {\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 \type {\mathsurround}} -\OneLiner{5}{disable all spacing around math} -\OneLiner{6}{only apply \type {\mathsurroundskip} when also spacing} -\OneLiner{7}{only apply \type {\mathsurroundskip} when no spacing} -\HL -\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). - -% \section{Math todo} -% -% The following items are still todo. -% -% \startitemize -% \startitem -% Pre-scripts. -% \stopitem -% \startitem -% Multi-story stacks. -% \stopitem -% \startitem -% Flattened accents for high characters (maybe). -% \stopitem -% \startitem -% Better control over the spacing around displays and handling of equation numbers. -% \stopitem -% \startitem -% Support for multi|-|line displays using \MATHML\ style alignment points. -% \stopitem -% \stopitemize - -\subsection {Delimiters: \type{\Uleft}, \type {\Umiddle} and \type {\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 that 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 supporting 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{Fixed scripts} - -We have three parameters that are used for this fixed anchoring: - -\starttabulate[|l|l|] -\NC $d$ \NC \type {\Umathsubshiftdown} \NC \NR -\NC $u$ \NC \type {\Umathsupshiftup} \NC \NR -\NC $s$ \NC \type {\Umathsubsupshiftdown} \NC \NR -\stoptabulate - -When we set \type {\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 achive different -effects. - -\def\SampleMath#1% - {$\mathscriptsmode#1\mathupright CH_2 + CH^+_2 + CH^2_2$} - -\starttabulate[|c|c|c|l|] -\BC mode \BC down \BC up \BC \NC \NR -\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 -\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: \type {\mathpenaltiesmode}} - -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 -\type {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 {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. - -\subsection {Math options} - -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 will be driven by options for which a new -primitive \type {\mathoption} has been introduced (so that we don't end up with -many new commands). The approach of options also permits us to see what effect a -specific solution has. - -\subsubsection {\type {\mathoption old}} - -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 seens as bugs as they relate to font -properties. - -\startbuffer -\mathoption old 1 -\stopbuffer - -The \type {oldmath} boolean flag in the \LUA\ font table is the official way to -force old treatment as it's bound to fonts. - -\subsubsection {\type {\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\type{0:inline}} - {\mathoption noitaliccompensation 0\relax \mathematics{\displaymath\getbuffer}} - {\nohyphens\type{0:display}} - {\mathoption noitaliccompensation 1\relax \mathematics{\getbuffer}} - {\nohyphens\type{1:inline}} - {\mathoption noitaliccompensation 1\relax \mathematics{\displaymath\getbuffer}} - {\nohyphens\type{1:display}} - \stopcombination -\stoplinecorrection - -\subsubsection {\type {\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\type{0:inline}} - {\mathoption nocharitalic 0\relax \mathematics{\displaymath\getbuffer}} - {\nohyphens\type{0:display}} - {\mathoption nocharitalic 1\relax \mathematics{\getbuffer}} - {\nohyphens\type{1:inline}} - {\mathoption nocharitalic 1\relax \mathematics{\displaymath\getbuffer}} - {\nohyphens\type{1:display}} - \stopcombination -\stoplinecorrection - -\subsubsection {\type {\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 +% language=uk
+
+\environment luatex-style
+
+\startcomponent luatex-math
+
+\startchapter[reference=math,title={Math}]
+
+\startsection[title={Traditional alongside \OPENTYPE}]
+
+\topicindex {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{Cramped math styles}
+
+\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{Inline surrounding space}
+
+\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\OneLiner#1#2%
+ {\NC \type{#1}
+ \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\mathsurroundmode#1\relax\hsize 100pt x$x$x}
+ \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\mathsurroundmode#1\relax\hsize 100pt x $x$ x}
+ \NC #2
+ \NC \NR}
+
+\startbuffer
+\mathsurround 10pt
+\mathsurroundskip20pt
+\stopbuffer
+
+\typebuffer \getbuffer
+
+\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}
+
+\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{Skips around display math}
+
+\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}
+
+\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 {Math italic mess}
+
+\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 {Script and kerning}
+
+\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{Fixed scripts}
+
+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}
+
+\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}
+
+\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{Radical extensions}
+
+\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}
+
+\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}
+
+\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.
+
+\stopsection
+
+\startsection[title={Extracting values}]
+
+\subsection{Codes}
+
+\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}
+
+\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}
+
+\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.
+
+% \startsection[title={Math todo}]
+%
+% The following items are still todo.
+%
+% \startitemize
+% \startitem
+% Pre-scripts.
+% \stopitem
+% \startitem
+% Multi-story stacks.
+% \stopitem
+% \startitem
+% Flattened accents for high characters (maybe).
+% \stopitem
+% \startitem
+% Better control over the spacing around displays and handling of equation numbers.
+% \stopitem
+% \startitem
+% Support for multi|-|line displays using \MATHML\ style alignment points.
+% \stopitem
+% \stopitemize
+%
+% \stopsection
+
+\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.
+
+\subsection {Math options with \lpr {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 \lpr {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. Ther eis currently only one option:
+
+\startbuffer
+\mathoption old 1
+\stopbuffer
+
+The \type {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 {\type {\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\type{0:inline}}
+% {\mathoption noitaliccompensation 0\relax \mathematics{\displaymath\getbuffer}}
+% {\nohyphens\type{0:display}}
+% {\mathoption noitaliccompensation 1\relax \mathematics{\getbuffer}}
+% {\nohyphens\type{1:inline}}
+% {\mathoption noitaliccompensation 1\relax \mathematics{\displaymath\getbuffer}}
+% {\nohyphens\type{1:display}}
+% \stopcombination
+% \stoplinecorrection
+
+% % obsolete:
+%
+% \subsubsection {\type {\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\type{0:inline}}
+% {\mathoption nocharitalic 0\relax \mathematics{\displaymath\getbuffer}}
+% {\nohyphens\type{0:display}}
+% {\mathoption nocharitalic 1\relax \mathematics{\getbuffer}}
+% {\nohyphens\type{1:inline}}
+% {\mathoption nocharitalic 1\relax \mathematics{\displaymath\getbuffer}}
+% {\nohyphens\type{1:display}}
+% \stopcombination
+% \stoplinecorrection
+
+% % obsolete:
+%
+% \subsubsection {\type {\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.
+
+\stopsection
+
+\stopchapter
+
+\stopcomponent
|