% language=uk \environment luametatex-style \startcomponent luametatex-math \startchapter[reference=math,title={Math}] \startsection[title={Traditional alongside \OPENTYPE}] \topicindex {math} At this point there is no difference between \LUAMETATEX\ and \LUATEX\ with respect to math. The handling of mathematics in \LUATEX\ differs quite a bit from how \TEX82 (and therefore \PDFTEX) handles math. First, \LUATEX\ adds primitives and extends some others so that \UNICODE\ input can be used easily. Second, all of \TEX82's internal special values (for example for operator spacing) have been made accessible and changeable via control sequences. Third, there are extensions that make it easier to use \OPENTYPE\ math fonts. And finally, there are some extensions that have been proposed or considered in the past that are now added to the engine. \stopsection \startsection[title={Unicode math characters}] \topicindex {math+\UNICODE} \topicindex {\UNICODE+math} Character handling is now extended up to the full \UNICODE\ range (the \type {\U} prefix), which is compatible with \XETEX. The math primitives from \TEX\ are kept as they are, except for the ones that convert from input to math commands: \type {mathcode}, and \type {delcode}. These two now allow for a 21-bit character argument on the left hand side of the equals sign. Some of the new \LUATEX\ primitives read more than one separate value. This is shown in the tables below by a plus sign. The input for such primitives would look like this: \starttyping \def\overbrace{\Umathaccent 0 1 "23DE } \stoptyping The altered \TEX82 primitives are: \starttabulate[|l|l|r|c|l|r|] \DB primitive \BC min \BC max \BC \kern 2em \BC min \BC max \NC \NR \TB \NC \prm {mathcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC 8000 \NC \NR \NC \prm {delcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC FFFFFF \NC \NR \LL \stoptabulate The unaltered ones are: \starttabulate[|l|l|r|] \DB primitive \BC min \BC max \NC \NR \TB \NC \prm {mathchardef} \NC 0 \NC 8000 \NC \NR \NC \prm {mathchar} \NC 0 \NC 7FFF \NC \NR \NC \prm {mathaccent} \NC 0 \NC 7FFF \NC \NR \NC \prm {delimiter} \NC 0 \NC 7FFFFFF \NC \NR \NC \prm {radical} \NC 0 \NC 7FFFFFF \NC \NR \LL \stoptabulate For practical reasons \prm {mathchardef} will silently accept values larger that \type {0x8000} and interpret it as \lpr {Umathcharnumdef}. This is needed to satisfy older macro packages. The following new primitives are compatible with \XETEX: % somewhat fuzzy: \starttabulate[|l|l|r|c|l|r|] \DB primitive \BC min \BC max \BC \kern 2em \BC min \BC max \NC \NR \TB \NC \lpr {Umathchardef} \NC 0+0+0 \NC 7+FF+10FFFF \NC \NC \NC \NC \NR \NC \lpr {Umathcharnumdef}\rlap{\high{5}} \NC -80000000 \NC 7FFFFFFF \NC \NC \NC \NC \NR \NC \lpr {Umathcode} \NC 0 \NC 10FFFF \NC = \NC 0+0+0 \NC 7+FF+10FFFF \NC \NR \NC \lpr {Udelcode} \NC 0 \NC 10FFFF \NC = \NC 0+0 \NC FF+10FFFF \NC \NR \NC \lpr {Umathchar} \NC 0+0+0 \NC 7+FF+10FFFF \NC \NC \NC \NC \NR \NC \lpr {Umathaccent} \NC 0+0+0 \NC 7+FF+10FFFF \NC \NC \NC \NC \NR \NC \lpr {Udelimiter} \NC 0+0+0 \NC 7+FF+10FFFF \NC \NC \NC \NC \NR \NC \lpr {Uradical} \NC 0+0 \NC FF+10FFFF \NC \NC \NC \NC \NR \NC \lpr {Umathcharnum} \NC -80000000 \NC 7FFFFFFF \NC \NC \NC \NC \NR \NC \lpr {Umathcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF \NC \NR \NC \lpr {Udelcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF \NC \NR \LL \stoptabulate Specifications typically look like: \starttyping \Umathchardef\xx="1"0"456 \Umathcode 123="1"0"789 \stoptyping The new primitives that deal with delimiter|-|style objects do not set up a \quote {large family}. Selecting a suitable size for display purposes is expected to be dealt with by the font via the \lpr {Umathoperatorsize} parameter. For some of these primitives, all information is packed into a single signed integer. For the first two (\lpr {Umathcharnum} and \lpr {Umathcodenum}), the lowest 21 bits are the character code, the 3 bits above that represent the math class, and the family data is kept in the topmost bits. This means that the values for math families 128--255 are actually negative. For \lpr {Udelcodenum} there is no math class. The math family information is stored in the bits directly on top of the character code. Using these three commands is not as natural as using the two- and three|-|value commands, so unless you know exactly what you are doing and absolutely require the speedup resulting from the faster input scanning, it is better to use the verbose commands instead. The \lpr {Umathaccent} command accepts optional keywords to control various details regarding math accents. See \in {section} [mathacc] below for details. There are more new primitives and all of these will be explained in following sections: \starttabulate[|l|l|] \DB primitive \BC value range (in hex) \NC \NR \TB \NC \lpr {Uroot} \NC 0 + 0--FF + 10FFFF \NC \NR \NC \lpr {Uoverdelimiter} \NC 0 + 0--FF + 10FFFF \NC \NR \NC \lpr {Uunderdelimiter} \NC 0 + 0--FF + 10FFFF \NC \NR \NC \lpr {Udelimiterover} \NC 0 + 0--FF + 10FFFF \NC \NR \NC \lpr {Udelimiterunder} \NC 0 + 0--FF + 10FFFF \NC \NR \LL \stoptabulate \stopsection \startsection[title={Math styles}] \subsection{\lpr {mathstyle}} \topicindex {math+styles} It is possible to discover the math style that will be used for a formula in an expandable fashion (while the math list is still being read). To make this possible, \LUATEX\ adds the new primitive: \lpr {mathstyle}. This is a \quote {convert command} like e.g. \prm {romannumeral}: its value can only be read, not set. Beware that contrary to \LUATEX\ this is now a proper number so you need to use \type {\number} o r\type {\the} in order to serialize it. 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:\number\mathstyle]\quad \bgroup \mathchoice {\bf \scriptstyle (x:d :\number\mathstyle)} {\bf \scriptscriptstyle (x:t :\number\mathstyle)} {\bf \scriptscriptstyle (x:s :\number\mathstyle)} {\bf \scriptscriptstyle (x:ss:\number\mathstyle)} \egroup \quad[b:\number\mathstyle]\quad \mathchoice {\bf \scriptstyle (y:d :\number\mathstyle)} {\bf \scriptscriptstyle (y:t :\number\mathstyle)} {\bf \scriptscriptstyle (y:s :\number\mathstyle)} {\bf \scriptscriptstyle (y:ss:\number\mathstyle)} \quad[c:\number\mathstyle]\quad \bgroup \mathchoice {\bf \scriptstyle (z:d :\number\mathstyle)} {\bf \scriptscriptstyle (z:t :\number\mathstyle)} {\bf \scriptscriptstyle (z:s :\number\mathstyle)} {\bf \scriptscriptstyle (z:ss:\number\mathstyle)} \egroup \quad[d:\number\mathstyle] \stopbuffer \startbuffer[2] [a:\number\mathstyle]\quad \begingroup \mathchoice {\bf \scriptstyle (x:d :\number\mathstyle)} {\bf \scriptscriptstyle (x:t :\number\mathstyle)} {\bf \scriptscriptstyle (x:s :\number\mathstyle)} {\bf \scriptscriptstyle (x:ss:\number\mathstyle)} \endgroup \quad[b:\number\mathstyle]\quad \mathchoice {\bf \scriptstyle (y:d :\number\mathstyle)} {\bf \scriptscriptstyle (y:t :\number\mathstyle)} {\bf \scriptscriptstyle (y:s :\number\mathstyle)} {\bf \scriptscriptstyle (y:ss:\number\mathstyle)} \quad[c:\number\mathstyle]\quad \begingroup \mathchoice {\bf \scriptstyle (z:d :\number\mathstyle)} {\bf \scriptscriptstyle (z:t :\number\mathstyle)} {\bf \scriptscriptstyle (z:s :\number\mathstyle)} {\bf \scriptscriptstyle (z:ss:\number\mathstyle)} \endgroup \quad[d:\number\mathstyle] \stopbuffer \typebuffer[1] % \typebuffer[2] This gives: \blank $\displaystyle \getbuffer[1]$ \blank \blank $\textstyle \getbuffer[1]$ \blank Using \prm {begingroup} \unknown\ \prm {endgroup} instead gives: \blank $\displaystyle \getbuffer[2]$ \blank \blank $\textstyle \getbuffer[2]$ \blank This might look wrong but it's just a side effect of \lpr {mathstyle} expanding to the current (first pass) style and the number being injected in the list that gets converted in the second pass. It all makes sense and it illustrates the importance of grouping. In fact, the math choice style being effective afterwards has advantages. It would be hard to get it otherwise. \subsection{\lpr {Ustack}} \topicindex {math+stacks} There are a few math commands in \TEX\ where the style that will be used is not known straight from the start. These commands (\prm {over}, \prm {atop}, \prm {overwithdelims}, \prm {atopwithdelims}) would therefore normally return wrong values for \lpr {mathstyle}. To fix this, \LUATEX\ introduces a special prefix command: \lpr {Ustack}: \starttyping $\Ustack {a \over b}$ \stoptyping The \lpr {Ustack} command will scan the next brace and start a new math group with the correct (numerator) math style. \subsection{The new \type {\cramped...style} commands} \topicindex {math+styles} \topicindex {math+spacing} \topicindex {math+cramped} \LUATEX\ has four new primitives to set the cramped math styles directly: \starttyping \crampeddisplaystyle \crampedtextstyle \crampedscriptstyle \crampedscriptscriptstyle \stoptyping These additional commands are not all that valuable on their own, but they come in handy as arguments to the math parameter settings that will be added shortly. In Eijkhouts \quotation {\TEX\ by Topic} the rules for handling styles in scripts are described as follows: \startitemize \startitem In any style superscripts and subscripts are taken from the next smaller style. Exception: in display style they are in script style. \stopitem \startitem Subscripts are always in the cramped variant of the style; superscripts are only cramped if the original style was cramped. \stopitem \startitem In an \type {..\over..} formula in any style the numerator and denominator are taken from the next smaller style. \stopitem \startitem The denominator is always in cramped style; the numerator is only in cramped style if the original style was cramped. \stopitem \startitem Formulas under a \type {\sqrt} or \prm {overline} are in cramped style. \stopitem \stopitemize In \LUATEX\ one can set the styles in more detail which means that you sometimes have to set both normal and cramped styles to get the effect you want. (Even) if we force styles in the script using \prm {scriptstyle} and \lpr {crampedscriptstyle} we get this: \startbuffer[demo] \starttabulate \DB style \BC example \NC \NR \TB \NC default \NC $b_{x=xx}^{x=xx}$ \NC \NR \NC script \NC $b_{\scriptstyle x=xx}^{\scriptstyle x=xx}$ \NC \NR \NC crampedscript \NC $b_{\crampedscriptstyle x=xx}^{\crampedscriptstyle x=xx}$ \NC \NR \LL \stoptabulate \stopbuffer \getbuffer[demo] Now we set the following parameters \startbuffer[setup] \Umathordrelspacing\scriptstyle=30mu \Umathordordspacing\scriptstyle=30mu \stopbuffer \typebuffer[setup] This gives a different result: \start\getbuffer[setup,demo]\stop But, as this is not what is expected (visually) we should say: \startbuffer[setup] \Umathordrelspacing\scriptstyle=30mu \Umathordordspacing\scriptstyle=30mu \Umathordrelspacing\crampedscriptstyle=30mu \Umathordordspacing\crampedscriptstyle=30mu \stopbuffer \typebuffer[setup] Now we get: \start\getbuffer[setup,demo]\stop \stopsection \startsection[title={Math parameter settings}] \subsection {Many new \lpr {Umath*} primitives} \topicindex {math+parameters} In \LUATEX, the font dimension parameters that \TEX\ used in math typesetting are now accessible via primitive commands. In fact, refactoring of the math engine has resulted in turning some hard codes properties into parameters. \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 an \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 {Umathspacebeforescript} \NC additional space added before a super- or subprescript (bonus setting) \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} {} {} {math_quad} \MathLine{\Umathradicalkern} {} {} {RadicalExtraAscender} {default_rule_thickness} \MathLine{\Umathradicalrule} {2} {} {RadicalRuleThickness} {} \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} {} \MathLine{\Umathradicaldegreeafter} {2} {} {RadicalKernAfterDegree} {} \MathLine{\Umathradicaldegreeraise} {2,7}{} {RadicalDegreeBottomRaisePercent} {} \MathLine{\Umathspaceafterscript} {4} {} {SpaceAfterScript} {script_space} \MathLine{\Umathstackdenomdown} {} {D, D'} {StackBottomDisplayStyleShiftDown} {denom1} \MathLine{\Umathstackdenomdown} {} {T, T', S, S', SS, SS'}{StackBottomShiftDown} {denom2} \MathLine{\Umathstacknumup} {} {D, D'} {StackTopDisplayStyleShiftUp} {num1} \MathLine{\Umathstacknumup} {} {T, T', S, S', SS, SS'}{StackTopShiftUp} {num3} \MathLine{\Umathstackvgap} {} {D, D'} {StackDisplayStyleGapMin} {7*default_rule_thickness} \MathLine{\Umathstackvgap} {} {T, T', S, S', SS, SS'}{StackGapMin} {3*default_rule_thickness} \MathLine{\Umathsubshiftdown} {} {} {SubscriptShiftDown} {sub1} \MathLine{\Umathsubshiftdrop} {} {} {SubscriptBaselineDropMin} {sub_drop} \MathLine{\Umathsubsupshiftdown} {8} {} {SubscriptShiftDownWithSuperscript} {\emdash} \MathLine{\Umathsubtopmax} {} {} {SubscriptTopMax} {abs(math_x_height*4)/5} \MathLine{\Umathsubsupvgap} {} {} {SubSuperscriptGapMin} {4*default_rule_thickness} \MathLine{\Umathsupbottommin} {} {} {SuperscriptBottomMin} {abs(math_x_height/4)} \MathLine{\Umathsupshiftdrop} {} {} {SuperscriptBaselineDropMax} {sup_drop} \MathLine{\Umathsupshiftup} {} {D} {SuperscriptShiftUp} {sup1} \MathLine{\Umathsupshiftup} {} {T, S, SS,} {SuperscriptShiftUp} {sup2} \MathLine{\Umathsupshiftup} {} {D', T', S', SS'} {SuperscriptShiftUpCramped} {sup3} \MathLine{\Umathsupsubbottommax} {} {} {SuperscriptBottomMaxWithSubscript} {abs(math_x_height*4)/5} \MathLine{\Umathunderbarkern} {} {} {UnderbarExtraDescender} {default_rule_thickness} \MathLine{\Umathunderbarrule} {} {} {UnderbarRuleThickness} {default_rule_thickness} \MathLine{\Umathunderbarvgap} {} {} {UnderbarVerticalGap} {3*default_rule_thickness} \MathLine{\Umathconnectoroverlapmin}{5} {} {MinConnectorOverlap} {0} \LL \stoptabulate Note 1: \OPENTYPE\ fonts set \lpr {Umathlimitabovekern} and \lpr {Umathlimitbelowkern} to zero and set \lpr {Umathquad} to the font size of the used font, because these are not supported in the \type {MATH} table, Note 2: Traditional \TFM\ fonts do not set \lpr {Umathradicalrule} because \TEX82\ uses the height of the radical instead. When this parameter is indeed not set when \LUATEX\ has to typeset a radical, a backward compatibility mode will kick in that assumes that an oldstyle \TEX\ font is used. Also, they do not set \lpr {Umathradicaldegreebefore}, \lpr {Umathradicaldegreeafter}, and \lpr {Umathradicaldegreeraise}. These are then automatically initialized to $5/18$quad, $-10/18$quad, and 60. Note 3: If \TFM\ fonts are used, then the \lpr {Umathradicalvgap} is not set until the first time \LUATEX\ has to typeset a formula because this needs parameters from both family~2 and family~3. This provides a partial backward compatibility with \TEX82, but that compatibility is only partial: once the \lpr {Umathradicalvgap} is set, it will not be recalculated any more. Note 4: When \TFM\ fonts are used a similar situation arises with respect to \lpr {Umathspaceafterscript}: it is not set until the first time \LUATEX\ has to typeset a formula. This provides some backward compatibility with \TEX82. But once the \lpr {Umathspaceafterscript} is set, \prm {scriptspace} will never be looked at again. Note 5: Traditional \TFM\ fonts set \lpr {Umathconnectoroverlapmin} to zero because \TEX82\ always stacks extensibles without any overlap. Note 6: The \lpr {Umathoperatorsize} is only used in \prm {displaystyle}, and is only set in \OPENTYPE\ fonts. In \TFM\ font mode, it is artificially set to one scaled point more than the initial attempt's size, so that always the \quote {first next} will be tried, just like in \TEX82. Note 7: The \lpr {Umathradicaldegreeraise} is a special case because it is the only parameter that is expressed in a percentage instead of a number of scaled points. Note 8: \type {SubscriptShiftDownWithSuperscript} does not actually exist in the \quote {standard} \OPENTYPE\ math font Cambria, but it is useful enough to be added. Note 9: \type {FractionDelimiterDisplayStyleSize} and \type {FractionDelimiterSize} do not actually exist in the \quote {standard} \OPENTYPE\ math font Cambria, but were useful enough to be added. \stopsection \startsection[title={Math spacing}] \subsection{Setting inline surrounding space with \lpr {mathsurround[skip]}} \topicindex {math+spacing} Inline math is surrounded by (optional) \prm {mathsurround} spacing but that is a fixed dimension. There is now an additional parameter \lpr {mathsurroundskip}. When set to a non|-|zero value (or zero with some stretch or shrink) this parameter will replace \prm {mathsurround}. By using an additional parameter instead of changing the nature of \prm {mathsurround}, we can remain compatible. In the meantime a bit more control has been added via \lpr {mathsurroundmode}. This directive can take 6 values with zero being the default behaviour. \start \def\MathHack#1{\mathsurroundmode#1\relax\inlinebuffer} \def\OneLiner#1#2% {\NC \type{#1} \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\hsize 100pt x$\MathHack{#1}x$x} \NC \dontleavehmode\inframed[align=normal,offset=0pt,frame=off]{\hsize 100pt x $\MathHack{#1}x$ x} \NC #2 \NC \NR} \startbuffer \mathsurround 10pt \mathsurroundskip20pt \stopbuffer \typebuffer \starttabulate[|c|c|c|pl|] \DB mode \BC x\$x\$x \BC x \$x\$ x \BC effect \NC \NR \TB \OneLiner{0}{obey \prm {mathsurround} when \lpr {mathsurroundskip} is 0pt} \OneLiner{1}{only add skip to the left} \OneLiner{2}{only add skip to the right} \OneLiner{3}{add skip to the left and right} \OneLiner{4}{ignore the skip setting, obey \prm {mathsurround}} \OneLiner{5}{disable all spacing around math} \OneLiner{6}{only apply \lpr {mathsurroundskip} when also spacing} \OneLiner{7}{only apply \lpr {mathsurroundskip} when no spacing} \LL \stoptabulate \stop Anything more fancy, like checking the beginning or end of a paragraph (or edges of a box) would not be robust anyway. If you want that you can write a callback that runs over a list and analyzes a paragraph. Actually, in that case you could also inject glue (or set the properties of a math node) explicitly. So, these modes are in practice mostly useful for special purposes and experiments (they originate in a tracker item). Keep in mind that this glue is part of the math node and not always treated as normal glue: it travels with the begin and end math nodes. Also, method 6 and 7 will zero the skip related fields in a node when applicable in the first occasion that checks them (linebreaking or packaging). \subsection{Pairwise spacing and \lpr {Umath...spacing} commands} \topicindex {math+spacing} Besides the parameters mentioned in the previous sections, there are also 64 new primitives to control the math spacing table (as explained in Chapter~18 of the \TEX book). The primitive names are a simple matter of combining two math atom types, but for completeness' sake, here is the whole list: \starttwocolumns \startlines \lpr {Umathordordspacing} \lpr {Umathordopspacing} \lpr {Umathordbinspacing} \lpr {Umathordrelspacing} \lpr {Umathordopenspacing} \lpr {Umathordclosespacing} \lpr {Umathordpunctspacing} \lpr {Umathordinnerspacing} \lpr {Umathopordspacing} \lpr {Umathopopspacing} \lpr {Umathopbinspacing} \lpr {Umathoprelspacing} \lpr {Umathopopenspacing} \lpr {Umathopclosespacing} \lpr {Umathoppunctspacing} \lpr {Umathopinnerspacing} \lpr {Umathbinordspacing} \lpr {Umathbinopspacing} \lpr {Umathbinbinspacing} \lpr {Umathbinrelspacing} \lpr {Umathbinopenspacing} \lpr {Umathbinclosespacing} \lpr {Umathbinpunctspacing} \lpr {Umathbininnerspacing} \lpr {Umathrelordspacing} \lpr {Umathrelopspacing} \lpr {Umathrelbinspacing} \lpr {Umathrelrelspacing} \lpr {Umathrelopenspacing} \lpr {Umathrelclosespacing} \lpr {Umathrelpunctspacing} \lpr {Umathrelinnerspacing} \lpr {Umathopenordspacing} \lpr {Umathopenopspacing} \lpr {Umathopenbinspacing} \lpr {Umathopenrelspacing} \lpr {Umathopenopenspacing} \lpr {Umathopenclosespacing} \lpr {Umathopenpunctspacing} \lpr {Umathopeninnerspacing} \lpr {Umathcloseordspacing} \lpr {Umathcloseopspacing} \lpr {Umathclosebinspacing} \lpr {Umathcloserelspacing} \lpr {Umathcloseopenspacing} \lpr {Umathcloseclosespacing} \lpr {Umathclosepunctspacing} \lpr {Umathcloseinnerspacing} \lpr {Umathpunctordspacing} \lpr {Umathpunctopspacing} \lpr {Umathpunctbinspacing} \lpr {Umathpunctrelspacing} \lpr {Umathpunctopenspacing} \lpr {Umathpunctclosespacing} \lpr {Umathpunctpunctspacing} \lpr {Umathpunctinnerspacing} \lpr {Umathinnerordspacing} \lpr {Umathinneropspacing} \lpr {Umathinnerbinspacing} \lpr {Umathinnerrelspacing} \lpr {Umathinneropenspacing} \lpr {Umathinnerclosespacing} \lpr {Umathinnerpunctspacing} \lpr {Umathinnerinnerspacing} \stoplines \stoptwocolumns These parameters are of type \prm {muskip}, so setting a parameter can be done like this: \starttyping \Umathopordspacing\displaystyle=4mu plus 2mu \stoptyping They are all initialized by \type {initex} to the values mentioned in the table in Chapter~18 of the \TEX book. Note 1: For ease of use as well as for backward compatibility, \prm {thinmuskip}, \prm {medmuskip} and \prm {thickmuskip} are treated specially. In their case a pointer to the corresponding internal parameter is saved, not the actual \prm {muskip} value. This means that any later changes to one of these three parameters will be taken into account. Note 2: Careful readers will realise that there are also primitives for the items marked \type {*} in the \TEX book. These will not actually be used as those combinations of atoms cannot actually happen, but it seemed better not to break orthogonality. They are initialized to zero. \subsection{Local \lpr {frozen} settings with} Math is processed in two passes. The first pass is needed to intercept for instance \type {\over}, one of the few \TEX\ commands that actually has a preceding argument. There are often lots of curly braces used in math and these can result in a nested run of the math sub engine. However, you need to be aware of the fact that some properties are kind of global to a formula and the last setting (for instance a family switch) wins. This also means that a change (or again, the last one) in math parameters affects the whole formula. In \LUAMETATEX\ we have changed this model a bit. One can argue that this introduces an incompatibility but it's hard to imagine a reason for setting the parameters at the end of a formula run and assume that they also influence what goes in front. \startbuffer $ x \Usubscript {-} \frozen\Umathsubshiftdown\textstyle 0pt x \Usubscript {0} {\frozen\Umathsubshiftdown\textstyle 5pt x \Usubscript {5}} x \Usubscript {0} {\frozen\Umathsubshiftdown\textstyle 15pt x \Usubscript {15}} x \Usubscript {0} {\frozen\Umathsubshiftdown\textstyle 20pt x \Usubscript {20}} x \Usubscript {0} \frozen\Umathsubshiftdown\textstyle 10pt x \Usubscript {10} x \Usubscript {0} $ \stopbuffer \typebuffer The \type {\frozen} prefix does the magic: it injects information in the math list about the set parameter. In \LUATEX\ 1.10+ the last setting, the \type {10pt} drop wins, but in \LUAMETATEX\ you will see each local setting taking effect. The implementation uses a new node type, parameters nodes, so you might encounter these in an unprocessed math list. The result looks as follows: \blank \getbuffer \blank \subsection{Checking a state with \lpr {ifmathparameter}} When you adapt math parameters it might make sense to see if they are set at all. When a parameter is unset its value has the maximum dimension value and you might for instance mistakenly multiply that value to open up things a bit, which gives unexpected side effects. For that reason there is a convenient checker: \lpr {ifmathparameter}. This test primitive behaves like an \prm {ifcase}, with: \starttabulate[|c|l|] \DB value \BC meaning \NC \NR \TB \NC 0 \NC the parameter value is zero \NC \NR \NC 1 \NC the parameter is set \NC \NR \NC 2 \NC the parameter is unset \NC \NR \LL \stoptabulate \subsection{Skips around display math and \lpr {mathdisplayskipmode}} \topicindex {math+spacing} The injection of \prm {abovedisplayskip} and \prm {belowdisplayskip} is not symmetrical. An above one is always inserted, also when zero, but the below is only inserted when larger than zero. Especially the latter makes it sometimes hard to fully control spacing. Therefore \LUATEX\ comes with a new directive: \lpr {mathdisplayskipmode}. The following values apply: \starttabulate[|c|l|] \DB value \BC meaning \NC \NR \TB \NC 0 \NC normal \TEX\ behaviour \NC \NR \NC 1 \NC always (same as 0) \NC \NR \NC 2 \NC only when not zero \NC \NR \NC 3 \NC never, not even when not zero \NC \NR \LL \stoptabulate \subsection {Nolimit correction with \lpr {mathnolimitsmode}} \topicindex {math+limits} There are two extra math parameters \lpr {Umathnolimitsupfactor} and \lpr {Umathnolimitsubfactor} that were added to provide some control over how limits are spaced (for example the position of super and subscripts after integral operators). They relate to an extra parameter \lpr {mathnolimitsmode}. The half corrections are what happens when scripts are placed above and below. The problem with italic corrections is that officially that correction italic is used for above|/|below placement while advanced kerns are used for placement at the right end. The question is: how often is this implemented, and if so, do the kerns assume correction too. Anyway, with this parameter one can control it. \starttabulate[|l|ck1|ck1|ck1|ck1|ck1|ck1|] \NC \NC \mathnolimitsmode0 $\displaystyle\int\nolimits^0_1$ \NC \mathnolimitsmode1 $\displaystyle\int\nolimits^0_1$ \NC \mathnolimitsmode2 $\displaystyle\int\nolimits^0_1$ \NC \mathnolimitsmode3 $\displaystyle\int\nolimits^0_1$ \NC \mathnolimitsmode4 $\displaystyle\int\nolimits^0_1$ \NC \mathnolimitsmode8000 $\displaystyle\int\nolimits^0_1$ \NC \NR \TB \BC mode \NC \tttf 0 \NC \tttf 1 \NC \tttf 2 \NC \tttf 3 \NC \tttf 4 \NC \tttf 8000 \NC \NR \BC superscript \NC 0 \NC font \NC 0 \NC 0 \NC +ic/2 \NC 0 \NC \NR \BC subscript \NC -ic \NC font \NC 0 \NC -ic/2 \NC -ic/2 \NC 8000ic/1000 \NC \NR \stoptabulate When the mode is set to one, the math parameters are used. This way a macro package writer can decide what looks best. Given the current state of fonts in \CONTEXT\ we currently use mode 1 with factor 0 for the superscript and 750 for the subscripts. Positive values are used for both parameters but the subscript shifts to the left. A \lpr {mathnolimitsmode} larger that 15 is considered to be a factor for the subscript correction. This feature can be handy when experimenting. \subsection {Controlling math italic mess with \lpr {mathitalicsmode}} \topicindex {math+italics} The \lpr {mathitalicsmode} parameter can be set to~1 to force italic correction before noads that represent some more complex structure (read: everything that is not an ord, bin, rel, open, close, punct or inner). We show a Cambria example. \starttexdefinition Whatever #1 \NC \type{\mathitalicsmode = #1} \NC \mathitalicsmode#1\ruledhbox{$\left|T^1\right|$} \NC \mathitalicsmode#1\ruledhbox{$\left|T\right|$} \NC \mathitalicsmode#1\ruledhbox{$T+1$} \NC \mathitalicsmode#1\ruledhbox{$T{1\over2}$} \NC \mathitalicsmode#1\ruledhbox{$T\sqrt{1}$} \NC \NR \stoptexdefinition \start \switchtobodyfont[cambria] \starttabulate[|c|c|c|c|c|c|] \Whatever{0}% \Whatever{1}% \stoptabulate \stop This kind of parameters relate to the fact that italic correction in \OPENTYPE\ math is bound to fuzzy rules. So, control is the solution. \subsection {Influencing script kerning with \lpr {mathscriptboxmode}} \topicindex {math+kerning} \topicindex {math+scripts} If you want to typeset text in math macro packages often provide something \type {\text} which obeys the script sizes. As the definition can be anything there is a good chance that the kerning doesn't come out well when used in a script. Given that the first glyph ends up in an \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 {3} \NC only kern math sub boxes with a boundary node present\NC \NR \LL \stoptabulate Here we show some examples. Of course this doesn't solve all our problems, if only because some fonts have characters with bounding boxes that compensate for italics, while other fonts can lack kerns. \startbuffer[1] $T_{\tf fluff}$ \stopbuffer \startbuffer[2] $T_{\text{fluff}}$ \stopbuffer \startbuffer[3] $T_{\text{\boundary1 fluff}}$ \stopbuffer \unexpanded\def\Show#1#2#3% {\doifelsenothing{#3} {\small\tx\typeinlinebuffer[#1]} {\doifelse{#3}{-} {\small\bf\tt mode #2} {\switchtobodyfont[#3]\showfontkerns\showglyphs\mathscriptboxmode#2\relax\inlinebuffer[#1]}}} \starttabulate[|lBT|c|c|c|c|c|] \NC \NC \Show{1}{0}{} \NC\Show{1}{1}{} \NC \Show{2}{1}{} \NC \Show{2}{2}{} \NC \Show{3}{3}{} \NC \NR \NC \NC \Show{1}{0}{-} \NC\Show{1}{1}{-} \NC \Show{2}{1}{-} \NC \Show{2}{2}{-} \NC \Show{3}{3}{-} \NC \NR \NC modern \NC \Show{1}{0}{modern} \NC\Show{1}{1}{modern} \NC \Show{2}{1}{modern} \NC \Show{2}{2}{modern} \NC \Show{3}{3}{modern} \NC \NR \NC lucidaot \NC \Show{1}{0}{lucidaot} \NC\Show{1}{1}{lucidaot} \NC \Show{2}{1}{lucidaot} \NC \Show{2}{2}{lucidaot} \NC \Show{3}{3}{lucidaot} \NC \NR \NC pagella \NC \Show{1}{0}{pagella} \NC\Show{1}{1}{pagella} \NC \Show{2}{1}{pagella} \NC \Show{2}{2}{pagella} \NC \Show{3}{3}{pagella} \NC \NR \NC cambria \NC \Show{1}{0}{cambria} \NC\Show{1}{1}{cambria} \NC \Show{2}{1}{cambria} \NC \Show{2}{2}{cambria} \NC \Show{3}{3}{cambria} \NC \NR \NC dejavu \NC \Show{1}{0}{dejavu} \NC\Show{1}{1}{dejavu} \NC \Show{2}{1}{dejavu} \NC \Show{2}{2}{dejavu} \NC \Show{3}{3}{dejavu} \NC \NR \stoptabulate Kerning between a character subscript is controlled by \lpr {mathscriptcharmode} which also defaults to~1. Here is another example. Internally we tag kerns as italic kerns or font kerns where font kerns result from the staircase kern tables. In 2018 fonts like Latin Modern and Pagella rely on cheats with the boundingbox, Cambria uses staircase kerns and Lucida a mixture. Depending on how fonts evolve we might add some more control over what one can turn on and off. \def\MathSample#1#2#3% {\NC #1 \NC #2 \NC \showglyphdata \switchtobodyfont[#2,17.3pt]$#3T_{f}$ \NC \showglyphdata \switchtobodyfont[#2,17.3pt]$#3\gamma_{e}$ \NC \showglyphdata \switchtobodyfont[#2,17.3pt]$#3\gamma_{ee}$ \NC \showglyphdata \switchtobodyfont[#2,17.3pt]$#3T_{\tf fluff}$ \NC \NR} \starttabulate[|Tl|Tl|l|l|l|l|] \FL \MathSample{normal}{modern} {\mr} \MathSample{} {pagella} {\mr} \MathSample{} {cambria} {\mr} \MathSample{} {lucidaot}{\mr} \ML \MathSample{bold} {modern} {\mb} \MathSample{} {pagella} {\mb} \MathSample{} {cambria} {\mb} \MathSample{} {lucidaot}{\mb} \LL \stoptabulate \subsection{Forcing fixed scripts with \lpr {mathscriptsmode}} We have three parameters that are used for this fixed anchoring: \starttabulate[|c|l|] \DB parameter \BC register \NC \NR \NC $d$ \NC \lpr {Umathsubshiftdown} \NC \NR \NC $u$ \NC \lpr {Umathsupshiftup} \NC \NR \NC $s$ \NC \lpr {Umathsubsupshiftdown} \NC \NR \LL \stoptabulate When we set \lpr {mathscriptsmode} to a value other than zero these are used for calculating fixed positions. This is something that is needed for instance for chemistry. You can manipulate the mentioned variables to achieve different effects. \def\SampleMath#1% {$\mathscriptsmode#1\mathupright CH_2 + CH^+_2 + CH^2_2$} \starttabulate[|c|c|c|p|] \DB mode \BC down \BC up \BC example \NC \NR \TB \NC 0 \NC dynamic \NC dynamic \NC \SampleMath{0} \NC \NR \NC 1 \NC $d$ \NC $u$ \NC \SampleMath{1} \NC \NR \NC 2 \NC $s$ \NC $u$ \NC \SampleMath{2} \NC \NR \NC 3 \NC $s$ \NC $u + s - d$ \NC \SampleMath{3} \NC \NR \NC 4 \NC $d + (s-d)/2$ \NC $u + (s-d)/2$ \NC \SampleMath{4} \NC \NR \NC 5 \NC $d$ \NC $u + s - d$ \NC \SampleMath{5} \NC \NR \LL \stoptabulate The value of this parameter obeys grouping but applies to the whole current formula. % if needed we can put the value in stylenodes but maybe more should go there \subsection{Penalties: \lpr {mathpenaltiesmode}} \topicindex {math+penalties} Only in inline math penalties will be added in a math list. You can force penalties (also in display math) by setting: \starttyping \mathpenaltiesmode = 1 \stoptyping This primnitive is not really needed in \LUATEX\ because you can use the callback \cbk {mlist_to_hlist} to force penalties by just calling the regular routine with forced penalties. However, as part of opening up and control this primitive makes sense. As a bonus we also provide two extra penalties: \starttyping \prebinoppenalty = -100 % example value \prerelpenalty = 900 % example value \stoptyping They default to inifinite which signals that they don't need to be inserted. When set they are injected before a binop or rel noad. This is an experimental feature. \subsection{Equation spacing: \lpr {matheqnogapstep}} By default \TEX\ will add one quad between the equation and the number. This is hard coded. A new primitive can control this: \startsyntax \matheqnogapstep = 1000 \stopsyntax Because a math quad from the math text font is used instead of a dimension, we use a step to control the size. A value of zero will suppress the gap. The step is divided by 1000 which is the usual way to mimmick floating point factors in \TEX. \stopsection \startsection[title={Math constructs}] \subsection {Unscaled fences and \lpr{mathdelimitersmode}} \topicindex {math+fences} The \lpr {mathdelimitersmode} primitive is experimental and deals with the following (potential) problems. Three bits can be set. The first bit prevents an unwanted shift when the fence symbol is not scaled (a cambria side effect). The second bit forces italic correction between a preceding character ordinal and the fenced subformula, while the third bit turns that subformula into an ordinary so that the same spacing applies as with unfenced variants. Here we show Cambria (with \lpr {mathitalicsmode} enabled). \starttexdefinition Whatever #1 \NC \type{\mathdelimitersmode = #1} \NC \mathitalicsmode1\mathdelimitersmode#1\ruledhbox{\showglyphs\showfontkerns\showfontitalics$f(x)$} \NC \mathitalicsmode1\mathdelimitersmode#1\ruledhbox{\showglyphs\showfontkerns\showfontitalics$f\left(x\right)$} \NC \NR \stoptexdefinition \start \switchtobodyfont[cambria] \starttabulate[|l|l|l|] \Whatever{0}\Whatever{1}\Whatever{2}\Whatever{3}% \Whatever{4}\Whatever{5}\Whatever{6}\Whatever{7}% \stoptabulate \stop So, when set to 7 fenced subformulas with unscaled delimiters come out the same as unfenced ones. This can be handy for cases where one is forced to use \prm {left} and \prm {right} always because of unpredictable content. As said, it's an experimental feature (which somehow fits in the exceptional way fences are dealt with in the engine). The full list of flags is given in the next table: \starttabulate[|c|l|] \DB value \BC meaning \NC \NR \TB \NC \type{"01} \NC don't apply the usual shift \NC \NR \NC \type{"02} \NC apply italic correction when possible \NC \NR \NC \type{"04} \NC force an ordinary subformula \NC \NR \NC \type{"08} \NC no shift when a base character \NC \NR \NC \type{"10} \NC only shift when an extensible \NC \NR \LL \stoptabulate The effect can depend on the font (and for Cambria one can use for instance \type {"16}). Sometimes you might want to act upon the size of a delimiter, something that is not really possible because of the fact that they are calculated {\em after} most has been typeset already. In the following example the all|-|zero specification is the trigger to make a fake box with the last delimiter dimensions and shift. It's an ugly hack but its relative simple and not intrusive implementation has no side effects. Any other heuristic solution would not satisfy possible demands anyway. Here is a rather low level example: \startbuffer \startformula \Uleft \Udelimiter 5 0 "222B \frac{\frac{a}{b}}{\frac{c}{d}} \Uright \Udelimiter 5 0 "222B \kern-2\fontcharwd\textfont0 "222B \mathlimop{\Uvextensible \Udelimiter 0 0 0}_1^2 x \stopformula \stopbuffer \typebuffer The last line, by passing zero values, results in a fake operator that has the dimensions of the previous delimiter. We can then backtrack over the (presumed) width and the two numbers become limit operators. As said, it's not pretty but it works. \getbuffer \subsection[mathacc]{Accent handling with \lpr {Umathaccent}} \topicindex {math+accents} \LUATEX\ supports both top accents and bottom accents in math mode, and math accents stretch automatically (if this is supported by the font the accent comes from, of course). Bottom and combined accents as well as fixed-width math accents are controlled by optional keywords following \lpr {Umathaccent}. The keyword \type {bottom} after \lpr {Umathaccent} signals that a bottom accent is needed, and the keyword \type {both} signals that both a top and a bottom accent are needed (in this case two accents need to be specified, of course). Then the set of three integers defining the accent is read. This set of integers can be prefixed by the \type {fixed} keyword to indicate that a non-stretching variant is requested (in case of both accents, this step is repeated). A simple example: \starttyping \Umathaccent both fixed 0 0 "20D7 fixed 0 0 "20D7 {example} \stoptyping If a math top accent has to be placed and the accentee is a character and has a non-zero \type {top_accent} value, then this value will be used to place the accent instead of the \prm {skewchar} kern used by \TEX82. The \type {top_accent} value represents a vertical line somewhere in the accentee. The accent will be shifted horizontally such that its own \type {top_accent} line coincides with the one from the accentee. If the \type {top_accent} value of the accent is zero, then half the width of the accent followed by its italic correction is used instead. The vertical placement of a top accent depends on the \type {x_height} of the font of the accentee (as explained in the \TEX book), but if a value turns out to be zero and the font had a \type {MathConstants} table, then \type {AccentBaseHeight} is used instead. The vertical placement of a bottom accent is straight below the accentee, no correction takes place. Possible locations are \type {top}, \type {bottom}, \type {both} and \type {center}. When no location is given \type {top} is assumed. An additional parameter \nod {fraction} can be specified followed by a number; a value of for instance 1200 means that the criterium is 1.2 times the width of the nucleus. The fraction only applies to the stepwise selected shapes and is mostly meant for the \type {overlay} location. It also works for the other locations but then it concerns the width. \subsection{Building radicals with \lpr {Uradical} and \lpr {Uroot}} \topicindex {math+radicals} The new primitive \lpr {Uroot} allows the construction of a radical noad including a degree field. Its syntax is an extension of \lpr {Uradical}: \starttyping \Uradical \Uroot \stoptyping The placement of the degree is controlled by the math parameters \lpr {Umathradicaldegreebefore}, \lpr {Umathradicaldegreeafter}, and \lpr {Umathradicaldegreeraise}. The degree will be typeset in \prm {scriptscriptstyle}. \subsection{Super- and subscripts} The character fields in a \LUA|-|loaded \OPENTYPE\ math font can have a \quote {mathkern} table. The format of this table is the same as the \quote {mathkern} table that is returned by the \type {fontloader} library, except that all height and kern values have to be specified in actual scaled points. When a super- or subscript has to be placed next to a math item, \LUATEX\ checks whether the super- or subscript and the nucleus are both simple character items. If they are, and if the fonts of both character items are \OPENTYPE\ fonts (as opposed to legacy \TEX\ fonts), then \LUATEX\ will use the \OPENTYPE\ math algorithm for deciding on the horizontal placement of the super- or subscript. This works as follows: \startitemize \startitem The vertical position of the script is calculated. \stopitem \startitem The default horizontal position is flat next to the base character. \stopitem \startitem For superscripts, the italic correction of the base character is added. \stopitem \startitem For a superscript, two vertical values are calculated: the bottom of the script (after shifting up), and the top of the base. For a subscript, the two values are the top of the (shifted down) script, and the bottom of the base. \stopitem \startitem For each of these two locations: \startitemize \startitem find the math kern value at this height for the base (for a subscript placement, this is the bottom_right corner, for a superscript placement the top_right corner) \stopitem \startitem find the math kern value at this height for the script (for a subscript placement, this is the top_left corner, for a superscript placement the bottom_left corner) \stopitem \startitem add the found values together to get a preliminary result. \stopitem \stopitemize \stopitem \startitem The horizontal kern to be applied is the smallest of the two results from previous step. \stopitem \stopitemize The math kern value at a specific height is the kern value that is specified by the next higher height and kern pair, or the highest one in the character (if there is no value high enough in the character), or simply zero (if the character has no math kern pairs at all). \subsection{Scripts on extensibles: \lpr {Uunderdelimiter}, \lpr {Uoverdelimiter}, \lpr {Udelimiterover}, \lpr {Udelimiterunder} and \lpr {Uhextensible}} \topicindex {math+scripts} \topicindex {math+delimiters} \topicindex {math+extensibles} The primitives \lpr {Uunderdelimiter} and \lpr {Uoverdelimiter} allow the placement of a subscript or superscript on an automatically extensible item and \lpr {Udelimiterunder} and \lpr {Udelimiterover} allow the placement of an automatically extensible item as a subscript or superscript on a nucleus. The input: % these produce radical noads .. in fact the code base has the numbers wrong for % quite a while, so no one seems to use this \startbuffer $\Uoverdelimiter 0 "2194 {\hbox{\strut overdelimiter}}$ $\Uunderdelimiter 0 "2194 {\hbox{\strut underdelimiter}}$ $\Udelimiterover 0 "2194 {\hbox{\strut delimiterover}}$ $\Udelimiterunder 0 "2194 {\hbox{\strut delimiterunder}}$ \stopbuffer \typebuffer will render this: \blank \startnarrower \getbuffer \stopnarrower \blank The vertical placements are controlled by \lpr {Umathunderdelimiterbgap}, \lpr {Umathunderdelimitervgap}, \lpr {Umathoverdelimiterbgap}, and \lpr {Umathoverdelimitervgap} in a similar way as limit placements on large operators. The superscript in \lpr {Uoverdelimiter} is typeset in a suitable scripted style, the subscript in \lpr {Uunderdelimiter} is cramped as well. These primitives accepts an optional \type {width} specification. When used the also optional keywords \type {left}, \type {middle} and \type {right} will determine what happens when a requested size can't be met (which can happen when we step to successive larger variants). An extra primitive \lpr {Uhextensible} is available that can be used like this: \startbuffer $\Uhextensible width 10cm 0 "2194$ \stopbuffer \typebuffer This will render this: \blank \startnarrower \getbuffer \stopnarrower \blank Here you can also pass options, like: \startbuffer $\Uhextensible width 1pt middle 0 "2194$ \stopbuffer \typebuffer This gives: \blank \startnarrower \getbuffer \stopnarrower \blank \LUATEX\ internally uses a structure that supports \OPENTYPE\ \quote {MathVariants} as well as \TFM\ \quote {extensible recipes}. In most cases where font metrics are involved we have a different code path for traditional fonts end \OPENTYPE\ fonts. \subsection{Fractions and the new \lpr {Uskewed} and \lpr {Uskewedwithdelims}} \topicindex {math+fractions} The \prm {abovewithdelims} command accepts a keyword \type {exact}. When issued the extra space relative to the rule thickness is not added. One can of course use the \type {\Umathfraction..gap} commands to influence the spacing. Also the rule is still positioned around the math axis. \starttyping $$ { {a} \abovewithdelims() exact 4pt {b} }$$ \stoptyping The math parameter table contains some parameters that specify a horizontal and vertical gap for skewed fractions. Of course some guessing is needed in order to implement something that uses them. And so we now provide a primitive similar to the other fraction related ones but with a few options so that one can influence the rendering. Of course a user can also mess around a bit with the parameters \lpr {Umathskewedfractionhgap} and \lpr {Umathskewedfractionvgap}. The syntax used here is: \starttyping { {1} \Uskewed / {2} } { {1} \Uskewedwithdelims / () {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 The \type {\over} and related primitives have the form: \starttyping {{top}\over{bottom}} \stoptyping For convenience, which also avoids some of the trickery that makes this \quote {looking back} possible, the \LUAMETATEX\ also provides this variant: \starttyping \Uover{top}{bottom} \stoptyping The optional arguments are also supported but we have one extra option: \type {style}. The style is applied to the numerator and denominator. \starttyping \Uover style \scriptstyle {top} {bottom} \stoptyping The complete list of these commands is: \lpr {Uabove}, \lpr {Uatop}, \lpr {Uover}, \lpr {Uabovewithdelims}, \lpr {Uatopwithdelims}, \lpr {Uoverwithdelims}, \lpr {UUskewed}, \lpr {UUskewedwithdelims}. As with other extensions we use a leading \type {U} and because we already had extra skew related primitives we end up with a \type {UU} there. This obscurity is not that big an issue because normally such primitives are wrapped in a macro. Here are a few examples: \startbuffer $\Uover { 1234} { 5678} $\quad $\Uover {\textstyle 1234} {\textstyle 5678} $\quad $\Uover {\scriptstyle 1234} {\scriptstyle 5678} $\quad $\Uover {\scriptscriptstyle 1234} {\scriptscriptstyle 5678} $\blank $\Uover {1234} {5678} $\quad $\Uover style \textstyle {1234} {5678} $\quad $\Uover style \scriptstyle {1234} {5678} $\quad $\Uover style \scriptscriptstyle {1234} {5678} $\blank \stopbuffer \typebuffer These render as: \getbuffer \subsection {Math styles: \lpr {Ustyle}} This primitive accepts a style identifier: \starttyping \Ustyle \displaystyle \stoptyping This in itself is not spectacular because it is equivalent to \starttyping \displaystyle \stoptyping Both commands inject a style node and change the current style. However, as in other places where \LUAMETATEX\ expects a style you can also pass a number in the range zero upto seven (like the ones reported by the primitive \lpr {mathstyle}). So, the next few lines give identical results: \startbuffer $\Ustyle0 \number\mathstyle \Ustyle7 \number\mathstyle$ $\Ustyle\displaystyle \number\mathstyle \Ustyle\crampedscriptscriptstyle \number\mathstyle$ $ \displaystyle \number\mathstyle \crampedscriptscriptstyle \number\mathstyle$ \stopbuffer Like: \inlinebuffer . Values outside the valid range are ignored. \subsection {Delimiters: \type{\Uleft}, \lpr {Umiddle} and \lpr {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 whether the used characters in the font have depth or height. Commands like (plain \TEX s) \type {\big} need to use this feature. In \LUATEX\ we provide a bit more control by three variants that support optional parameters \type {height}, \type {depth} and \type {axis}. The following example uses this: \startbuffer \Uleft height 30pt depth 10pt \Udelimiter "0 "0 "000028 \quad x\quad \Umiddle height 40pt depth 15pt \Udelimiter "0 "0 "002016 \quad x\quad \Uright height 30pt depth 10pt \Udelimiter "0 "0 "000029 \quad \quad \quad \Uleft height 30pt depth 10pt axis \Udelimiter "0 "0 "000028 \quad x\quad \Umiddle height 40pt depth 15pt axis \Udelimiter "0 "0 "002016 \quad x\quad \Uright height 30pt depth 10pt axis \Udelimiter "0 "0 "000029 \stopbuffer \typebuffer \startlinecorrection \ruledhbox{\mathematics{\getbuffer}} \stoplinecorrection The keyword \type {exact} can be used as directive that the real dimensions should be applied when the criteria can't be met which can happen when we're still stepping through the successively larger variants. When no dimensions are given the \type {noaxis} command can be used to prevent shifting over the axis. You can influence the final class with the keyword \type {class} which will influence the spacing. The numbers are the same as for character classes. \subsection {Accents: \type{\mathlimitsmode}} \topicindex {math+accents} When you use \type {\limits} or \type {\nolimits} without scripts spacing might get messed up. This can be prevented by setting \type {\mathlimitsmode} to a non|-|zero value. \stopsection \startsection[title={Extracting values}] \subsection{Codes and using \lpr {Umathcode}, \lpr {Umathcharclass}, \lpr {Umathcharfam} and \lpr {Umathcharslot}} \topicindex {math+codes} You can extract the components of a math character. Say that we have defined: \starttyping \Umathcode 1 2 3 4 \stoptyping then \starttyping [\Umathcharclass1] [\Umathcharfam1] [\Umathcharslot1] \stoptyping will return: \starttyping [2] [3] [4] \stoptyping These commands are provided as convenience. Before they come available you could do the following: \starttyping \def\Umathcharclass{\numexpr \directlua{tex.print(tex.getmathcode(token.scan_int())[1])} \relax} \def\Umathcharfam{\numexpr \directlua{tex.print(tex.getmathcode(token.scan_int())[2])} \relax} \def\Umathcharslot{\numexpr \directlua{tex.print(tex.getmathcode(token.scan_int())[3])} \relax} \stoptyping \subsection {Last lines and \lpr{predisplaygapfactor}} \topicindex {math+last line} There is a new primitive to control the overshoot in the calculation of the previous line in mid|-|paragraph display math. The default value is 2 times the em width of the current font: \starttyping \predisplaygapfactor=2000 \stoptyping If you want to have the length of the last line independent of math i.e.\ you don't want to revert to a hack where you insert a fake display math formula in order to get the length of the last line, the following will often work too: \starttyping \def\lastlinelength{\dimexpr \directlua {tex.sprint ( (nodes.dimensions(node.tail(tex.lists.page_head).list)) )}sp \relax} \stoptyping \stopsection \startsection[title={Math mode}] \subsection {Verbose versions of single|-|character math commands like \lpr {Usuperscript} and \lpr {Usubscript}} \topicindex {math+styles} \LUATEX\ defines six new primitives that have the same function as \type {^}, \type {_}, \type {$}, and \type {$$}: \starttabulate[|l|l|] \DB primitive \BC explanation \NC \NR \TB \NC \lpr {Usuperscript} \NC duplicates the functionality of \type {^} \NC \NR \NC \lpr {Usubscript} \NC duplicates the functionality of \type {_} \NC \NR \NC \lpr {Ustartmath} \NC duplicates the functionality of \type {$}, % $ when used in non-math mode. \NC \NR \NC \lpr {Ustopmath} \NC duplicates the functionality of \type {$}, % $ when used in inline math mode. \NC \NR \NC \lpr {Ustartdisplaymath} \NC duplicates the functionality of \type {$$}, % $$ when used in non-math mode. \NC \NR \NC \lpr {Ustopdisplaymath} \NC duplicates the functionality of \type {$$}, % $$ when used in display math mode. \NC \NR \LL \stoptabulate The \lpr {Ustopmath} and \lpr {Ustopdisplaymath} primitives check if the current math mode is the correct one (inline vs.\ displayed), but you can freely intermix the four mathon|/|mathoff commands with explicit dollar sign(s). \subsection{Script commands \lpr {Unosuperscript} and \lpr {Unosubscript}} \topicindex {math+styles} \topicindex {math+scripts} These two commands result in super- and subscripts but with the current style (at the time of rendering). So, \startbuffer[script] $ x\Usuperscript {1}\Usubscript {2} = x\Unosuperscript{1}\Unosubscript{2} = x\Usuperscript {1}\Unosubscript{2} = x\Unosuperscript{1}\Usubscript {2} $ \stopbuffer \typebuffer[script] results in \inlinebuffer[script]. \subsection{Allowed math commands in non|-|math modes} \topicindex {math+text} \topicindex {text+math} The commands \prm {mathchar}, and \lpr {Umathchar} and control sequences that are the result of \prm {mathchardef} or \lpr {Umathchardef} are also acceptable in the horizontal and vertical modes. In those cases, the \prm {textfont} from the requested math family is used. \stopsection \startsection[title={Goodies}] \subsection {Flattening: \lpr {mathflattenmode}} \topicindex {math+flattening} The \TEX\ math engine collapses \type {ord} noads without sub- and superscripts and a character as nucleus, which has the side effect that in \OPENTYPE\ mode italic corrections are applied (given that they are enabled). \startbuffer[sample] \switchtobodyfont[modern] $V \mathbin{\mathbin{v}} V$\par $V \mathord{\mathord{v}} V$\par \stopbuffer \typebuffer[sample] This renders as: \blank \start \mathflattenmode\plusone \getbuffer[sample] \stop \blank When we set \lpr {mathflattenmode} to 31 we get: \blank \start \mathflattenmode\numexpr1+2+4+8+16\relax \getbuffer[sample] \stop \blank When you see no difference, then the font probably has the proper character dimensions and no italic correction is needed. For Latin Modern (at least till 2018) there was a visual difference. In that respect this parameter is not always needed unless of course you want efficient math lists anyway. You can influence flattening by adding the appropriate number to the value of the mode parameter. The default value is~1. \starttabulate[|Tc|c|] \DB mode \BC class \NC \NR \TB \NC 1 \NC ord \NC \NR \NC 2 \NC bin \NC \NR \NC 4 \NC rel \NC \NR \NC 8 \NC punct \NC \NR \NC 16 \NC inner \NC \NR \LL \stoptabulate \subsection {Less Tracing} \topicindex {math+tracing} Because there are quite some math related parameters and values, it is possible to limit tracing. Only when \type {tracingassigns} and|/|or \type {tracingrestores} are set to~2 or more they will be traced. \stopsection \startsection[title={Experiments}] There are a couple of experimental features. They will stay but details might change, for instance more control over spacing. We just show some examples and let your imagination work it out. First we have prescripts: \subsection {Prescripts with \lpr {Usuperprescript} and {Usubprescript}} \startbuffer \hbox{$ {\tf X}^1_2^^3__4 \quad {\tf X}^1 ^^3 \quad {\tf X} _1 __4 \quad {\tf X} ^^3 \quad {\tf X} __4 \quad {\tf X}^^3 __4 $} \stopbuffer \typebuffer The question is: are these double super and subscript triggers the way to go? Anyway, you need to have them either being active (which in \CONTEXT\ then boils down to them being other characters), or say \type {\supmarkmode = 1} to disable the normal multiple \type {^} treatment (a value larger than 1 will also disable that in text mode). \blank \getbuffer \blank The more explicit commands are: \startbuffer \hbox{$ {\tf X}\Usuperscript{1} \quad {\tf X} \Usubscript{2} \quad {\tf X}\Usuperscript{1}\Usubscript{2} \quad {\tf X}\Usuperscript{1} \Usuperprescript{3} \quad {\tf X} \Usubscript{2} \Usubprescript{4}\quad {\tf X}\Usuperscript{1}\Usubscript{2}\Usuperprescript{3}\Usubprescript{4}\quad {\tf X} \Usuperprescript{3} \quad {\tf X} \Usubprescript{4}\quad {\tf X} \Usuperprescript{3}\Usubprescript{4} $} \stopbuffer \typebuffer These more verbose triggers can be used to build interfaces: \blank \getbuffer \blank \subsection {Prescripts with \lpr {Usuperprescript} and {Usubprescript}} You can change the class of a math character on the fly: \startbuffer $x\mathopen {!}+123+\mathclose {!}x$ $x\Umathclass4 ! +123+\Umathclass5 ! x$ $x ! +123+ ! x$ $x\mathclose {!}+123+\mathopen {!}x$ $x\Umathclass5 ! +123+\Umathclass4 ! x$ \stopbuffer \typebuffer Watch how the spacing changes: \startlines \getbuffer \stoplines \stopsection \stopchapter \stopcomponent