From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- systems/doc/luatex/luatex-math.tex | 1647 ++++++++++++++++++++++++++++++++++++ 1 file changed, 1647 insertions(+) create mode 100644 systems/doc/luatex/luatex-math.tex (limited to 'systems/doc/luatex/luatex-math.tex') diff --git a/systems/doc/luatex/luatex-math.tex b/systems/doc/luatex/luatex-math.tex new file mode 100644 index 0000000000..fd038150f5 --- /dev/null +++ b/systems/doc/luatex/luatex-math.tex @@ -0,0 +1,1647 @@ +% 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} {} {} {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{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 +\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} + +\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 / {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 + +\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 -- cgit v1.2.3