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diff --git a/Master/texmf-dist/doc/luatex/base/luatex-math.tex b/Master/texmf-dist/doc/luatex/base/luatex-math.tex new file mode 100644 index 00000000000..cb8d198b1fc --- /dev/null +++ b/Master/texmf-dist/doc/luatex/base/luatex-math.tex @@ -0,0 +1,1049 @@ +% language=uk + +\environment luatex-style +\environment luatex-logos + +\startcomponent luatex-math + +\startchapter[reference=math,title={Math}] + +The handling of mathematics in \LUATEX\ differs quite a bit from how \TEX82 (and +therefore \PDFTEX) handles math. First, \LUATEX\ adds primitives and extends some +others so that \UNICODE\ input can be used easily. Second, all of \TEX82's +internal special values (for example for operator spacing) have been made +accessible and changeable via control sequences. Third, there are extensions that +make it easier to use \OPENTYPE\ math fonts. And finally, there are some +extensions that have been proposed or considered in the past that are now added +to the engine. + +\section{The current math style} + +It is possible to discover the math style that will be used for a formula in an +expandable fashion (while the math list is still being read). To make this +possible, \LUATEX\ adds the new primitive: \type {\mathstyle}. This is a \quote +{convert command} like e.g. \type {\romannumeral}: its value can only be read, +not set. + +\subsection{\type {\mathstyle}} + +The returned value is between 0 and 7 (in math mode), or $-1$ (all other modes). +For easy testing, the eight math style commands have been altered so that the can +be used as numeric values, so you can write code like this: + +\starttyping +\ifnum\mathstyle=\textstyle + \message{normal text style} +\else \ifnum\mathstyle=\crampedtextstyle + \message{cramped text style} +\fi \fi +\stoptyping + +\subsection{\type {\Ustack}} + +There are a few math commands in \TEX\ where the style that will be used is not +known straight from the start. These commands (\type {\over}, \type {\atop}, +\type {\overwithdelims}, \type {\atopwithdelims}) would therefore normally return +wrong values for \type {\mathstyle}. To fix this, \LUATEX\ introduces a special +prefix command: \type {\Ustack}: + +\starttyping +$\Ustack {a \over b}$ +\stoptyping + +The \type {\Ustack} command will scan the next brace and start a new math group +with the correct (numerator) math style. + +\section{Unicode math characters} + +Character handling is now extended up to the full \UNICODE\ range (the \type {\U} +prefix), which is compatible with \XETEX. + +The math primitives from \TEX\ are kept as they are, except for the ones that +convert from input to math commands: \type {mathcode}, and \type {delcode}. These +two now allow for a 21-bit character argument on the left hand side of the equals +sign. + +Some of the new \LUATEX\ primitives read more than one separate value. This is +shown in the tables below by a plus sign in the second column. + +The input for such primitives would look like this: + +\starttyping +\def\overbrace{\Umathaccent 0 1 "23DE } +\stoptyping + +The altered \TEX82 primitives are: + +\starttabulate[|l|l|r|c|l|r|] +\NC \bf primitive \NC \bf min \NC \bf max \NC \kern 2em \NC \bf min \NC \bf max \NC \NR +\NC \type {\mathcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC 8000 \NC \NR +\NC \type {\delcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC FFFFFF \NC \NR +\stoptabulate + +The unaltered ones are: + +\starttabulate[|l|l|r|] +\NC \bf primitive \NC \bf min \NC \bf max \NC \NR +\NC \type {\mathchardef} \NC 0 \NC 8000 \NC \NR +\NC \type {\mathchar} \NC 0 \NC 7FFF \NC \NR +\NC \type {\mathaccent} \NC 0 \NC 7FFF \NC \NR +\NC \type {\delimiter} \NC 0 \NC 7FFFFFF \NC \NR +\NC \type {\radical} \NC 0 \NC 7FFFFFF \NC \NR +\stoptabulate + +For practical reasons \type {\mathchardef} will silently accept values larger +that \type {0x8000} and interpret it as \type {\Umathcharnumdef}. This is needed +to satisfy older macro packages. + +The following new primitives are compatible with \XETEX: + +% somewhat fuzzy: + +\starttabulate[|l|l|r|c|l|r|] +\NC \bf primitive \NC \bf min \NC \bf max \NC \kern 2em \NC \bf min \NC \bf max \NC \NR +\NC \type {\Umathchardef} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{1}} \NC \NC \NC \NC \NR +\NC \type {\Umathcharnumdef}\rlap{\high{5}} \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NC \NC \NC \NR +\NC \type {\Umathcode} \NC 0 \NC 10FFFF \NC = \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{1}} \NC \NR +\NC \type {\Udelcode} \NC 0 \NC 10FFFF \NC = \NC 0+0 \NC FF+10FFFF\rlap{\high{2}} \NC \NR +\NC \type {\Umathchar} \NC 0+0+0 \NC 7+FF+10FFFF \NC \NC \NC \NC \NR +\NC \type {\Umathaccent} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{2,4}} \NC \NC \NC \NC \NR +\NC \type {\Udelimiter} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{2}} \NC \NC \NC \NC \NR +\NC \type {\Uradical} \NC 0+0 \NC FF+10FFFF\rlap{\high{2}} \NC \NC \NC \NC \NR +\NC \type {\Umathcharnum} \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NC \NC \NC \NR +\NC \type {\Umathcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NR +\NC \type {\Udelcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NR +\stoptabulate + +Specifications typically look like: + +\starttyping +\Umathchardef\xx="1"0"456 +\Umathcode 123="1"0"789 +\stoptyping + +Note 1: The new primitives that deal with delimiter|-|style objects do not set up a +\quote {large family}. Selecting a suitable size for display purposes is expected +to be dealt with by the font via the \type {\Umathoperatorsize} parameter (more +information can be found in a following section). + +Note 2: For these three primitives, all information is packed into a single +signed integer. For the first two (\type {\Umathcharnum} and \type +{\Umathcodenum}), the lowest 21 bits are the character code, the 3 bits above +that represent the math class, and the family data is kept in the topmost bits +(This means that the values for math families 128--255 are actually negative). +For \type {\Udelcodenum} there is no math class. The math family information is +stored in the bits directly on top of the character code. Using these three +commands is not as natural as using the two- and three|-|value commands, so +unless you know exactly what you are doing and absolutely require the speedup +resulting from the faster input scanning, it is better to use the verbose +commands instead. + +Note 3: The \type {\Umathaccent} command accepts optional keywords to control +various details regarding math accents. See \in {section} [mathacc] below for +details. + +New primitives that exist in \LUATEX\ only (all of these will be explained +in following sections): + +\starttabulate[|l|l|l|l|] +\NC \bf primitive \NC \bf value range (in hex) \NC \NR +\NC \type {\Uroot} \NC 0+0--FF+10FFFF$^2$ \NC \NR +\NC \type {\Uoverdelimiter} \NC 0+0--FF+10FFFF$^2$ \NC \NR +\NC \type {\Uunderdelimiter} \NC 0+0--FF+10FFFF$^2$ \NC \NR +\NC \type {\Udelimiterover} \NC 0+0--FF+10FFFF$^2$ \NC \NR +\NC \type {\Udelimiterunder} \NC 0+0--FF+10FFFF$^2$ \NC \NR +\stoptabulate + +\section{Cramped math styles} + +\LUATEX\ has four new primitives to set the cramped math styles directly: + +\starttyping +\crampeddisplaystyle +\crampedtextstyle +\crampedscriptstyle +\crampedscriptscriptstyle +\stoptyping + +These additional commands are not all that valuable on their own, but they come +in handy as arguments to the math parameter settings that will be added shortly. + +In Eijkhouts \quotation {\TEX\ by Topic} the rules for handling styles in scripts +are described as follows: + +\startitemize +\startitem + In any style superscripts and subscripts are taken from the next smaller style. + Exception: in display style they are taken in script style. +\stopitem +\startitem + Subscripts are always in the cramped variant of the style; superscripts are only + cramped if the original style was cramped. +\stopitem +\startitem + In an \type {..\over..} formula in any style the numerator and denominator are + taken from the next smaller style. +\stopitem +\startitem + The denominator is always in cramped style; the numerator is only in cramped + style if the original style was cramped. +\stopitem +\startitem + Formulas under a \type {\sqrt} or \type {\overline} are in cramped style. +\stopitem +\stopitemize + +In \LUATEX\ one can set the styles in more detail which means that you sometimes +have to set both normal and cramped styles to get the effect you want. If we +force styles in the script using \type {\scriptstyle} and \type {\crampedscriptstyle} +we get this: + +\startbuffer[demo] +\starttabulate +\NC default \NC $b_{x=xx}^{x=xx}$ \NC \NR +\NC script \NC $b_{\scriptstyle x=xx}^{\scriptstyle x=xx}$ \NC \NR +\NC crampedscript \NC $b_{\crampedscriptstyle x=xx}^{\crampedscriptstyle x=xx}$ \NC \NR +\stoptabulate +\stopbuffer + +\getbuffer[demo] + +Now we set the following parameters + +\startbuffer[setup] +\Umathordrelspacing\scriptstyle=30mu +\Umathordordspacing\scriptstyle=30mu +\stopbuffer + +\typebuffer[setup] + +This gives: + +\start\getbuffer[setup,demo]\stop + +But, as this is not what is expected (visually) we should say: + +\startbuffer[setup] +\Umathordrelspacing\scriptstyle=30mu +\Umathordordspacing\scriptstyle=30mu +\Umathordrelspacing\crampedscriptstyle=30mu +\Umathordordspacing\crampedscriptstyle=30mu +\stopbuffer + +\typebuffer[setup] + +Now we get: + +\start\getbuffer[setup,demo]\stop + +\section{Math parameter settings} + +In \LUATEX, the font dimension parameters that \TEX\ used in math typesetting are +now accessible via primitive commands. In fact, refactoring of the math engine +has resulted in many more parameters than were accessible before. + +\starttabulate +\NC \bf primitive name \NC \bf description \NC \NR +\NC \type {\Umathquad} \NC the width of 18 mu's \NC \NR +\NC \type {\Umathaxis} \NC height of the vertical center axis of + the math formula above the baseline \NC \NR +\NC \type {\Umathoperatorsize} \NC minimum size of large operators in display mode \NC \NR +\NC \type {\Umathoverbarkern} \NC vertical clearance above the rule \NC \NR +\NC \type {\Umathoverbarrule} \NC the width of the rule \NC \NR +\NC \type {\Umathoverbarvgap} \NC vertical clearance below the rule \NC \NR +\NC \type {\Umathunderbarkern} \NC vertical clearance below the rule \NC \NR +\NC \type {\Umathunderbarrule} \NC the width of the rule \NC \NR +\NC \type {\Umathunderbarvgap} \NC vertical clearance above the rule \NC \NR +\NC \type {\Umathradicalkern} \NC vertical clearance above the rule \NC \NR +\NC \type {\Umathradicalrule} \NC the width of the rule \NC \NR +\NC \type {\Umathradicalvgap} \NC vertical clearance below the rule \NC \NR +\NC \type {\Umathradicaldegreebefore}\NC the forward kern that takes place before placement of + the radical degree \NC \NR +\NC \type {\Umathradicaldegreeafter} \NC the backward kern that takes place after placement of + the radical degree \NC \NR +\NC \type {\Umathradicaldegreeraise} \NC this is the percentage of the total height and depth of + the radical sign that the degree is raised by; it is + expressed in \type {percents}, so 60\% is expressed as the + integer $60$ \NC \NR +\NC \type {\Umathstackvgap} \NC vertical clearance between the two + elements in a \type {\atop} stack \NC \NR +\NC \type {\Umathstacknumup} \NC numerator shift upward in \type {\atop} stack \NC \NR +\NC \type {\Umathstackdenomdown} \NC denominator shift downward in \type {\atop} stack \NC \NR +\NC \type {\Umathfractionrule} \NC the width of the rule in a \type {\over} \NC \NR +\NC \type {\Umathfractionnumvgap} \NC vertical clearance between the numerator and the rule \NC \NR +\NC \type {\Umathfractionnumup} \NC numerator shift upward in \type {\over} \NC \NR +\NC \type {\Umathfractiondenomvgap} \NC vertical clearance between the denominator and the rule \NC \NR +\NC \type {\Umathfractiondenomdown} \NC denominator shift downward in \type {\over} \NC \NR +\NC \type {\Umathfractiondelsize} \NC minimum delimiter size for \type {\...withdelims} \NC \NR +\NC \type {\Umathlimitabovevgap} \NC vertical clearance for limits above operators \NC \NR +\NC \type {\Umathlimitabovebgap} \NC vertical baseline clearance for limits above operators \NC \NR +\NC \type {\Umathlimitabovekern} \NC space reserved at the top of the limit \NC \NR +\NC \type {\Umathlimitbelowvgap} \NC vertical clearance for limits below operators \NC \NR +\NC \type {\Umathlimitbelowbgap} \NC vertical baseline clearance for limits below operators \NC \NR +\NC \type {\Umathlimitbelowkern} \NC space reserved at the bottom of the limit \NC \NR +\NC \type {\Umathoverdelimitervgap} \NC vertical clearance for limits above delimiters \NC \NR +\NC \type {\Umathoverdelimiterbgap} \NC vertical baseline clearance for limits above delimiters \NC \NR +\NC \type {\Umathunderdelimitervgap} \NC vertical clearance for limits below delimiters \NC \NR +\NC \type {\Umathunderdelimiterbgap} \NC vertical baseline clearance for limits below delimiters \NC \NR +\NC \type {\Umathsubshiftdrop} \NC subscript drop for boxes and subformulas \NC \NR +\NC \type {\Umathsubshiftdown} \NC subscript drop for characters \NC \NR +\NC \type {\Umathsupshiftdrop} \NC superscript drop (raise, actually) for boxes and subformulas \NC \NR +\NC \type {\Umathsupshiftup} \NC superscript raise for characters \NC \NR +\NC \type {\Umathsubsupshiftdown} \NC subscript drop in the presence of a superscript \NC \NR +\NC \type {\Umathsubtopmax} \NC the top of standalone subscripts cannot be higher than this + above the baseline \NC \NR +\NC \type {\Umathsupbottommin} \NC the bottom of standalone superscripts cannot be less than + this above the baseline \NC \NR +\NC \type {\Umathsupsubbottommax} \NC the bottom of the superscript of a combined super- and subscript + be at least as high as this above the baseline \NC \NR +\NC \type {\Umathsubsupvgap} \NC vertical clearance between super- and subscript \NC \NR +\NC \type {\Umathspaceafterscript} \NC additional space added after a super- or subscript \NC \NR +\NC \type {\Umathconnectoroverlapmin}\NC minimum overlap between parts in an extensible recipe \NC \NR +\stoptabulate + +Each of the parameters in this section can be set by a command like this: + +\starttyping +\Umathquad\displaystyle=1em +\stoptyping + +they obey grouping, and you can use \type {\the\Umathquad\displaystyle} if +needed. + +\section{Skips around display math} + +The injection of \type {\abovedisplayskip} and \type {\belowdisplayskip} is not +symmetrical. An above one is always inserted, also when zero, but the below is +only inserted when larger than zero. Especially the later mkes it sometimes hard +to fully control spacing. Therefore \LUATEX\ comes with a new directive: \type +{\mathdisplayskipmode}. The following values apply: + +\starttabulate +\NC 0 \NC normal \TEX\ behaviour: always above, only below when larger than zero \NC \NR +\NC 1 \NC always \NC \NR +\NC 2 \NC only when not zero \NC \NR +\NC 3 \NC never, not even when not zero \NC \NR +\stoptabulate + +\section{Font-based Math Parameters} + +While it is nice to have these math parameters available for tweaking, it would +be tedious to have to set each of them by hand. For this reason, \LUATEX\ +initializes a bunch of these parameters whenever you assign a font identifier to +a math family based on either the traditional math font dimensions in the font +(for assignments to math family~2 and~3 using \TFM|-|based fonts like \type +{cmsy} and \type {cmex}), or based on the named values in a potential \type +{MathConstants} table when the font is loaded via Lua. If there is a \type +{MathConstants} table, this takes precedence over font dimensions, and in that +case no attention is paid to which family is being assigned to: the \type +{MathConstants} tables in the last assigned family sets all parameters. + +In the table below, the one|-|letter style abbreviations and symbolic tfm font +dimension names match those using in the \TeX book. Assignments to \type +{\textfont} set the values for the cramped and uncramped display and text styles, +\type {\scriptfont} sets the script styles, and \type {\scriptscriptfont} sets +the scriptscript styles, so we have eight parameters for three font sizes. In the +\TFM\ case, assignments only happen in family~2 and family~3 (and of course only +for the parameters for which there are font dimensions). + +Besides the parameters below, \LUATEX\ also looks at the \quote {space} font +dimension parameter. For math fonts, this should be set to zero. + +\start + +\switchtobodyfont[8pt] + +\starttabulate[|l|l|l|p|] +\NC \bf variable \NC \bf style \NC \bf default value opentype \NC \bf default value tfm \NC \NR +\NC \type {\Umathaxis} \NC -- \NC AxisHeight \NC axis_height \NC \NR +\NC \type {\Umathoperatorsize} \NC D, D' \NC DisplayOperatorMinHeight \NC $^6$ \NC \NR +\NC \type {\Umathfractiondelsize} \NC D, D' \NC FractionDelimiterDisplayStyleSize$^9$ \NC delim1 \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC FractionDelimiterSize$^9$ \NC delim2 \NC \NR +\NC \type {\Umathfractiondenomdown} \NC D, D' \NC FractionDenominatorDisplayStyleShiftDown \NC denom1 \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC FractionDenominatorShiftDown \NC denom2 \NC \NR +\NC \type {\Umathfractiondenomvgap} \NC D, D' \NC FractionDenominatorDisplayStyleGapMin \NC 3*default_rule_thickness \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC FractionDenominatorGapMin \NC default_rule_thickness \NC \NR +\NC \type {\Umathfractionnumup} \NC D, D' \NC FractionNumeratorDisplayStyleShiftUp \NC num1 \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC FractionNumeratorShiftUp \NC num2 \NC \NR +\NC \type {\Umathfractionnumvgap} \NC D, D' \NC FractionNumeratorDisplayStyleGapMin \NC 3*default_rule_thickness \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC FractionNumeratorGapMin \NC default_rule_thickness \NC \NR +\NC \type {\Umathfractionrule} \NC -- \NC FractionRuleThickness \NC default_rule_thickness \NC \NR +\NC \type {\Umathskewedfractionhgap} \NC -- \NC SkewedFractionHorizontalGap \NC math_quad/2 \NC \NR +\NC \type {\Umathskewedfractionvgap} \NC -- \NC SkewedFractionVerticalGap \NC math_x_height \NC \NR +\NC \type {\Umathlimitabovebgap} \NC -- \NC UpperLimitBaselineRiseMin \NC big_op_spacing3 \NC \NR +\NC \type {\Umathlimitabovekern} \NC -- \NC 0$^1$ \NC big_op_spacing5 \NC \NR +\NC \type {\Umathlimitabovevgap} \NC -- \NC UpperLimitGapMin \NC big_op_spacing1 \NC \NR +\NC \type {\Umathlimitbelowbgap} \NC -- \NC LowerLimitBaselineDropMin \NC big_op_spacing4 \NC \NR +\NC \type {\Umathlimitbelowkern} \NC -- \NC 0$^1$ \NC big_op_spacing5 \NC \NR +\NC \type {\Umathlimitbelowvgap} \NC -- \NC LowerLimitGapMin \NC big_op_spacing2 \NC \NR +\NC \type {\Umathoverdelimitervgap} \NC -- \NC StretchStackGapBelowMin \NC big_op_spacing1 \NC \NR +\NC \type {\Umathoverdelimiterbgap} \NC -- \NC StretchStackTopShiftUp \NC big_op_spacing3 \NC \NR +\NC \type {\Umathunderdelimitervgap} \NC-- \NC StretchStackGapAboveMin \NC big_op_spacing2 \NC \NR +\NC \type {\Umathunderdelimiterbgap} \NC-- \NC StretchStackBottomShiftDown \NC big_op_spacing4 \NC \NR +\NC \type {\Umathoverbarkern} \NC -- \NC OverbarExtraAscender \NC default_rule_thickness \NC \NR +\NC \type {\Umathoverbarrule} \NC -- \NC OverbarRuleThickness \NC default_rule_thickness \NC \NR +\NC \type {\Umathoverbarvgap} \NC -- \NC OverbarVerticalGap \NC 3*default_rule_thickness \NC \NR +\NC \type {\Umathquad} \NC -- \NC <font_size(f)>$^1$ \NC math_quad \NC \NR +\NC \type {\Umathradicalkern} \NC -- \NC RadicalExtraAscender \NC default_rule_thickness \NC \NR +\NC \type {\Umathradicalrule} \NC -- \NC RadicalRuleThickness \NC <not set>$^2$ \NC \NR +\NC \type {\Umathradicalvgap} \NC D, D' \NC RadicalDisplayStyleVerticalGap \NC (default_rule_thickness+\crlf + (abs(math_x_height)/4))$^3$ \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC RadicalVerticalGap \NC (default_rule_thickness+\crlf + (abs(default_rule_thickness)/4))$^3$ \NC \NR +\NC \type {\Umathradicaldegreebefore} \NC -- \NC RadicalKernBeforeDegree \NC <not set>$^2$ \NC \NR +\NC \type {\Umathradicaldegreeafter} \NC -- \NC RadicalKernAfterDegree \NC <not set>$^2$ \NC \NR +\NC \type {\Umathradicaldegreeraise} \NC -- \NC RadicalDegreeBottomRaisePercent \NC <not set>$^{2,7}$ \NC \NR +\NC \type {\Umathspaceafterscript} \NC -- \NC SpaceAfterScript \NC script_space$^4$ \NC \NR +\NC \type {\Umathstackdenomdown} \NC D, D' \NC StackBottomDisplayStyleShiftDown \NC denom1 \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC StackBottomShiftDown \NC denom2 \NC \NR +\NC \type {\Umathstacknumup} \NC D, D' \NC StackTopDisplayStyleShiftUp \NC num1 \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC StackTopShiftUp \NC num3 \NC \NR +\NC \type {\Umathstackvgap} \NC D, D' \NC StackDisplayStyleGapMin \NC 7*default_rule_thickness \NC \NR +\NC \NC T, T', S, S', SS, SS' \NC StackGapMin \NC 3*default_rule_thickness \NC \NR +\NC \type {\Umathsubshiftdown} \NC -- \NC SubscriptShiftDown \NC sub1 \NC \NR +\NC \type {\Umathsubshiftdrop} \NC -- \NC SubscriptBaselineDropMin \NC sub_drop \NC \NR +\NC \type {\Umathsubsupshiftdown} \NC -- \NC SubscriptShiftDownWithSuperscript$^8$ \NC \NC \NR +\NC \NC \NC \quad\ or SubscriptShiftDown \NC sub2 \NC \NR +\NC \type {\Umathsubtopmax} \NC -- \NC SubscriptTopMax \NC (abs(math_x_height * 4) / 5) \NC \NR +\NC \type {\Umathsubsupvgap} \NC -- \NC SubSuperscriptGapMin \NC 4*default_rule_thickness \NC \NR +\NC \type {\Umathsupbottommin} \NC -- \NC SuperscriptBottomMin \NC (abs(math_x_height) / 4) \NC \NR +\NC \type {\Umathsupshiftdrop} \NC -- \NC SuperscriptBaselineDropMax \NC sup_drop \NC \NR +\NC \type {\Umathsupshiftup} \NC D \NC SuperscriptShiftUp \NC sup1 \NC \NR +\NC \NC T, S, SS, \NC SuperscriptShiftUp \NC sup2 \NC \NR +\NC \NC D', T', S', SS' \NC SuperscriptShiftUpCramped \NC sup3 \NC \NR +\NC \type {\Umathsupsubbottommax} \NC -- \NC SuperscriptBottomMaxWithSubscript \NC (abs(math_x_height * 4) / 5) \NC \NR +\NC \type {\Umathunderbarkern} \NC -- \NC UnderbarExtraDescender \NC default_rule_thickness \NC \NR +\NC \type {\Umathunderbarrule} \NC -- \NC UnderbarRuleThickness \NC default_rule_thickness \NC \NR +\NC \type {\Umathunderbarvgap} \NC -- \NC UnderbarVerticalGap \NC 3*default_rule_thickness \NC \NR +\NC \type {\Umathconnectoroverlapmin} \NC -- \NC MinConnectorOverlap \NC 0$^5$ \NC \NR +\stoptabulate + +\stop + +Note 1: \OPENTYPE\ fonts set \type {\Umathlimitabovekern} and \type +{\Umathlimitbelowkern} to zero and set \type {\Umathquad} to the font size of the +used font, because these are not supported in the \type {MATH} table, + +Note 2: Traditional \TFM\ fonts do not set \type {\Umathradicalrule} because +\TEX82\ uses the height of the radical instead. When this parameter is indeed not +set when \LUATEX\ has to typeset a radical, a backward compatibility mode will +kick in that assumes that an oldstyle \TEX\ font is used. Also, they do not set +\type {\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type +{\Umathradicaldegreeraise}. These are then automatically initialized to +$5/18$quad, $-10/18$quad, and 60. + +Note 3: If \TFM\ fonts are used, then the \type {\Umathradicalvgap} is not set +until the first time \LUATEX\ has to typeset a formula because this needs +parameters from both family~2 and family~3. This provides a partial backward +compatibility with \TEX82, but that compatibility is only partial: once the \type +{\Umathradicalvgap} is set, it will not be recalculated any more. + +Note 4: When \TFM\ fonts are used a similar situation arises with respect to +\type {\Umathspaceafterscript}: it is not set until the first time \LUATEX\ has +to typeset a formula. This provides some backward compatibility with \TEX82. But +once the \type {\Umathspaceafterscript} is set, \type {\scriptspace} will never +be looked at again. + +Note 5: Traditional \TFM\ fonts set \type {\Umathconnectoroverlapmin} to zero +because \TEX82\ always stacks extensibles without any overlap. + +Note 6: The \type {\Umathoperatorsize} is only used in \type {\displaystyle}, and +is only set in \OPENTYPE\ fonts. In \TFM\ font mode, it is artificially set to +one scaled point more than the initial attempt's size, so that always the \quote +{first next} will be tried, just like in \TEX82. + +Note 7: The \type {\Umathradicaldegreeraise} is a special case because it is the +only parameter that is expressed in a percentage instead of as a number of scaled +points. + +Note 8: \type {SubscriptShiftDownWithSuperscript} does not actually exist in the +\quote {standard} \OPENTYPE\ math font Cambria, but it is useful enough to be +added. + +Note 9: \type {FractionDelimiterDisplayStyleSize} and \type +{FractionDelimiterSize} do not actually exist in the \quote {standard} \OPENTYPE\ +math font Cambria, but were useful enough to be added. + +\section{Math spacing setting} + +Besides the parameters mentioned in the previous sections, there are also 64 new +primitives to control the math spacing table (as explained in Chapter~18 of the +\TEX book). The primitive names are a simple matter of combining two math atom +types, but for completeness' sake, here is the whole list: + +\starttwocolumns +\starttyping +\Umathordordspacing +\Umathordopspacing +\Umathordbinspacing +\Umathordrelspacing +\Umathordopenspacing +\Umathordclosespacing +\Umathordpunctspacing +\Umathordinnerspacing +\Umathopordspacing +\Umathopopspacing +\Umathopbinspacing +\Umathoprelspacing +\Umathopopenspacing +\Umathopclosespacing +\Umathoppunctspacing +\Umathopinnerspacing +\Umathbinordspacing +\Umathbinopspacing +\Umathbinbinspacing +\Umathbinrelspacing +\Umathbinopenspacing +\Umathbinclosespacing +\Umathbinpunctspacing +\Umathbininnerspacing +\Umathrelordspacing +\Umathrelopspacing +\Umathrelbinspacing +\Umathrelrelspacing +\Umathrelopenspacing +\Umathrelclosespacing +\Umathrelpunctspacing +\Umathrelinnerspacing +\Umathopenordspacing +\Umathopenopspacing +\Umathopenbinspacing +\Umathopenrelspacing +\Umathopenopenspacing +\Umathopenclosespacing +\Umathopenpunctspacing +\Umathopeninnerspacing +\Umathcloseordspacing +\Umathcloseopspacing +\Umathclosebinspacing +\Umathcloserelspacing +\Umathcloseopenspacing +\Umathcloseclosespacing +\Umathclosepunctspacing +\Umathcloseinnerspacing +\Umathpunctordspacing +\Umathpunctopspacing +\Umathpunctbinspacing +\Umathpunctrelspacing +\Umathpunctopenspacing +\Umathpunctclosespacing +\Umathpunctpunctspacing +\Umathpunctinnerspacing +\Umathinnerordspacing +\Umathinneropspacing +\Umathinnerbinspacing +\Umathinnerrelspacing +\Umathinneropenspacing +\Umathinnerclosespacing +\Umathinnerpunctspacing +\Umathinnerinnerspacing +\stoptyping +\stoptwocolumns + +These parameters are of type \type {\muskip}, so setting a parameter can be done +like this: + +\starttyping +\Umathopordspacing\displaystyle=4mu plus 2mu +\stoptyping + +They are all initialized by \type {initex} to the values mentioned in the table +in Chapter~18 of the \TEX book. + +Note 1: for ease of use as well as for backward compatibility, \type +{\thinmuskip}, \type {\medmuskip} and \type {\thickmuskip} are treated +especially. In their case a pointer to the corresponding internal parameter is +saved, not the actual \type {\muskip} value. This means that any later changes to +one of these three parameters will be taken into account. + +Note 2: Careful readers will realise that there are also primitives for the items +marked \type {*} in the \TEX book. These will not actually be used as those +combinations of atoms cannot actually happen, but it seemed better not to break +orthogonality. They are initialized to zero. + +\section[mathacc]{Math accent handling} + +\LUATEX\ supports both top accents and bottom accents in math mode, and math +accents stretch automatically (if this is supported by the font the accent comes +from, of course). Bottom and combined accents as well as fixed-width math accents +are controlled by optional keywords following \type {\Umathaccent}. + +The keyword \type {bottom} after \type {\Umathaccent} signals that a bottom accent +is needed, and the keyword \type {both} signals that both a top and a bottom +accent are needed (in this case two accents need to be specified, of course). + +Then the set of three integers defining the accent is read. This set of integers +can be prefixed by the \type {fixed} keyword to indicate that a non-stretching +variant is requested (in case of both accents, this step is repeated). + +A simple example: + +\starttyping +\Umathaccent both fixed 0 0 "20D7 fixed 0 0 "20D7 {example} +\stoptyping + +If a math top accent has to be placed and the accentee is a character and has a +non-zero \type {top_accent} value, then this value will be used to place the +accent instead of the \type {\skewchar} kern used by \TEX82. + +The \type {top_accent} value represents a vertical line somewhere in the +accentee. The accent will be shifted horizontally such that its own \type +{top_accent} line coincides with the one from the accentee. If the \type +{top_accent} value of the accent is zero, then half the width of the accent +followed by its italic correction is used instead. + +The vertical placement of a top accent depends on the \type {x_height} of the +font of the accentee (as explained in the \TEX book), but if value that turns out +to be zero and the font had a \type {MathConstants} table, then \type +{AccentBaseHeight} is used instead. + +The vertical placement of a bottom accent is straight below the accentee, no +correction takes place. + +Possible locations are \type {top}, \type {bottom}, \type {both} and \type +{center}. When no location is given \type {top} is assumed. An additional +parameter \type {fraction} can be specified followed by a number; a value of for +instance 1200 means that the criterium is 1.2 times the width of the nuclues. The +fraction only applies to the stepwise selected shapes and is mostly meant for the +\type {overlay} location. It also works for the other locations but then it +concerns the width. + +\section{Math root extension} + +The new primitive \type {\Uroot} allows the construction of a radical noad +including a degree field. Its syntax is an extension of \type {\Uradical}: + +\starttyping +\Uradical <fam integer> <char integer> <radicand> +\Uroot <fam integer> <char integer> <degree> <radicand> +\stoptyping + +The placement of the degree is controlled by the math parameters \type +{\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type +{\Umathradicaldegreeraise}. The degree will be typeset in \type +{\scriptscriptstyle}. + +\section{Math kerning in super- and subscripts} + +The character fields in a \LUA|-|loaded \OPENTYPE\ math font can have a \quote +{mathkern} table. The format of this table is the same as the \quote {mathkern} +table that is returned by the \type {fontloader} library, except that all height +and kern values have to be specified in actual scaled points. + +When a super- or subscript has to be placed next to a math item, \LUATEX\ checks +whether the super- or subscript and the nucleus are both simple character items. +If they are, and if the fonts of both character items are \OPENTYPE\ fonts (as +opposed to legacy \TEX\ fonts), then \LUATEX\ will use the \OPENTYPE\ math +algorithm for deciding on the horizontal placement of the super- or subscript. + +This works as follows: + +\startitemize + \startitem + The vertical position of the script is calculated. + \stopitem + \startitem + The default horizontal position is flat next to the base character. + \stopitem + \startitem + For superscripts, the italic correction of the base character is added. + \stopitem + \startitem + For a superscript, two vertical values are calculated: the bottom of the + script (after shifting up), and the top of the base. For a subscript, the two + values are the top of the (shifted down) script, and the bottom of the base. + \stopitem + \startitem + For each of these two locations: + \startitemize + \startitem + find the math kern value at this height for the base (for a subscript + placement, this is the bottom_right corner, for a superscript + placement the top_right corner) + \stopitem + \startitem + find the math kern value at this height for the script (for a + subscript placement, this is the top_left corner, for a superscript + placement the bottom_left corner) + \stopitem + \startitem + add the found values together to get a preliminary result. + \stopitem + \stopitemize + \stopitem + \startitem + The horizontal kern to be applied is the smallest of the two results from + previous step. + \stopitem +\stopitemize + +The math kern value at a specific height is the kern value that is specified by the +next higher height and kern pair, or the highest one in the character (if there is no +value high enough in the character), or simply zero (if the character has no math kern +pairs at all). + +\section{Scripts on horizontally extensible items like arrows} + +The primitives \type {\Uunderdelimiter} and \type {\Uoverdelimiter} allow the +placement of a subscript or superscript on an automatically extensible item and +\type {\Udelimiterunder} and \type {\Udelimiterover} allow the placement of an +automatically extensible item as a subscript or superscript on a nucleus. The +input: + +% these produce radical noads .. in fact the code base has the numbers wrong for +% quite a while, so no one seems to use this + +\startbuffer +$\Uoverdelimiter 0 "2194 {\hbox{\strut overdelimiter}}$ +$\Uunderdelimiter 0 "2194 {\hbox{\strut underdelimiter}}$ +$\Udelimiterover 0 "2194 {\hbox{\strut delimiterover}}$ +$\Udelimiterunder 0 "2194 {\hbox{\strut delimiterunder}}$ +\stopbuffer + +\typebuffer will render this: + +\blank \startnarrower \getbuffer \stopnarrower \blank + +The vertical placements are controlled by \type {\Umathunderdelimiterbgap}, \type +{\Umathunderdelimitervgap}, \type {\Umathoverdelimiterbgap}, and \type +{\Umathoverdelimitervgap} in a similar way as limit placements on large operators. +The superscript in \type {\Uoverdelimiter} is typeset in a suitable scripted style, +the subscript in \type {\Uunderdelimiter} is cramped as well. + +These primitives accepts an option \type {width} specification. When used the +also optional keywords \type {left}, \type {middle} and \type {right} will +determine what happens when a requested size can't be met (which can happen when +we step to successive larger variants). + +An extra primitive \type {\Uhextensible} is available that can be used like this: + +\startbuffer +$\Uhextensible width 10cm 0 "2194$ +\stopbuffer + +\typebuffer This will render this: + +\blank \startnarrower \getbuffer \stopnarrower \blank + +Here you can also pass options, like: + +\startbuffer +$\Uhextensible width 1pt middle 0 "2194$ +\stopbuffer + +\typebuffer This gives: + +\blank \startnarrower \getbuffer \stopnarrower \blank + +\LUATEX\ internally uses a structure that supports \OPENTYPE\ \quote +{MathVariants} as well as \TFM\ \quote {extensible recipes}. In most cases where +font metrics are involved we have a different code path for traditional fonts end +\OPENTYPE\ fonts. + +\section {Extracting values} + +You can extract the components of a math character. Say that we have defined: + +\starttyping +\Umathcode 1 2 3 4 +\stoptyping + +then + +\starttyping +[\Umathcharclass1] [\Umathcharfam1] [\Umathcharslot1] +\stoptyping + +will return: + +\starttyping +[2] [3] [4] +\stoptyping + +These commands are provides as convenience. Before they came available you could +do the following: + +\starttyping +\def\Umathcharclass{\directlua{tex.print(tex.getmathcode(token.scan_int())[1])}} +\def\Umathcharfam {\directlua{tex.print(tex.getmathcode(token.scan_int())[2])}} +\def\Umathcharslot {\directlua{tex.print(tex.getmathcode(token.scan_int())[3])}} +\stoptyping + +\section{fractions} + +The \type {\abovewithdelims} command accepts a keyword \type {exact}. When issued +the extra space relative to the rule thickness is not added. One can of course +use the \type {\Umathfraction..gap} commands to influence the spacing. Also the +rule is still positioned around the math axis. + +\starttyping +$$ { {a} \abovewithdelims() exact 4pt {b} }$$ +\stoptyping + +The math parameter table contains some parameters that specify a horizontal and +vertical gap for skewed fractions. Of course some guessing is needed in order to +implement something that uses them. And so we now provide a primitive similar to the +other fraction related ones but with a few options so that one can influence the +rendering. Of course a user can also mess around a bit with the parameters +\type {\Umathskewedfractionhgap} and \type {\Umathskewedfractionvgap}. + +The syntax used here is: + +\starttyping +{ {1} \Uskewed / <options> {2} } +{ {1} \Uskewedwithdelims / () <options> {2} } +\stoptyping + +where the options can be \type {noaxis} and \type {exact}. By default we add half +the axis to the shifts and by default we zero the width of the middle character. +For Latin Modern The result looks as follows: + +\def\ShowA#1#2#3{$x + { {#1} \Uskewed / #3 {#2} } + x$} +\def\ShowB#1#2#3{$x + { {#1} \Uskewedwithdelims / () #3 {#2} } + x$} + +\start + \switchtobodyfont[modern] + \starttabulate[||||||] + \NC \NC + \ShowA{a}{b}{} \NC + \ShowA{1}{2}{} \NC + \ShowB{a}{b}{} \NC + \ShowB{1}{2}{} \NC + \NR + \NC \type{exact} \NC + \ShowA{a}{b}{exact} \NC + \ShowA{1}{2}{exact} \NC + \ShowB{a}{b}{exact} \NC + \ShowB{1}{2}{exact} \NC + \NR + \NC \type{noaxis} \NC + \ShowA{a}{b}{noaxis} \NC + \ShowA{1}{2}{noaxis} \NC + \ShowB{a}{b}{noaxis} \NC + \ShowB{1}{2}{noaxis} \NC + \NR + \NC \type{exact noaxis} \NC + \ShowA{a}{b}{exact noaxis} \NC + \ShowA{1}{2}{exact noaxis} \NC + \ShowB{a}{b}{exact noaxis} \NC + \ShowB{1}{2}{exact noaxis} \NC + \NR + \stoptabulate +\stop + +\section {Other Math changes} + +\subsection {Verbose versions of single-character math commands} + +\LUATEX\ defines six new primitives that have the same function as +\type {^}, \type {_}, \type {$}, and \type {$$}: %$ + +\starttabulate[|l|l|l|l|] +\NC \bf primitive \NC \bf explanation \NC \NR +\NC \type {\Usuperscript} \NC Duplicates the functionality of \type {^} \NC \NR +\NC \type {\Usubscript} \NC Duplicates the functionality of \type {_} \NC \NR +\NC \type {\Ustartmath} \NC Duplicates the functionality of \type {$}, % $ + when used in non-math mode. \NC \NR +\NC \type {\Ustopmath} \NC Duplicates the functionality of \type {$}, % $ + when used in inline math mode. \NC \NR +\NC \type {\Ustartdisplaymath} \NC Duplicates the functionality of \type {$$}, % $$ + when used in non-math mode. \NC \NR +\NC \type {\Ustopdisplaymath} \NC Duplicates the functionality of \type {$$}, % $$ + when used in display math mode. \NC \NR +\stoptabulate + +The \type {\Ustopmath} and \type {\Ustopdisplaymath} primitives check if the current +math mode is the correct one (inline vs.\ displayed), but you can freely intermix +the four mathon|/|mathoff commands with explicit dollar sign(s). + +\subsection{Allowed math commands in non-math modes} + +The commands \type {\mathchar}, and \type {\Umathchar} and control sequences that +are the result of \type {\mathchardef} or \type {\Umathchardef} are also +acceptable in the horizontal and vertical modes. In those cases, the \type +{\textfont} from the requested math family is used. + +\section{Math surrounding skips} + +Inline math is surrounded by (optional) \type {\mathsurround} spacing but that is fixed +dimension. There is now an additional parameter \type {\mathsurroundskip}. When set to a +non|-|zero value (or zero with some stretch or shrink) this parameter will replace +\type {\mathsurround}. By using an additional parameter instead of changing the nature +of \type {\mathsurround}, we can remain compatible. + +% \section{Math todo} +% +% The following items are still todo. +% +% \startitemize +% \startitem +% Pre-scripts. +% \stopitem +% \startitem +% Multi-story stacks. +% \stopitem +% \startitem +% Flattened accents for high characters (maybe). +% \stopitem +% \startitem +% Better control over the spacing around displays and handling of equation numbers. +% \stopitem +% \startitem +% Support for multi|-|line displays using \MATHML\ style alignment points. +% \stopitem +% \stopitemize + +\subsection {Delimiters: \type{\Uleft}, \type {\Umiddle} and \type {\Uright}} + +Normally you will force delimiters to certain sizes by putting an empty box or +rule next to it. The resulting delimiter will either be a character from the +stepwise size range or an extensible. The latter can be quite differently +positioned that the characters as it depends on the fit as well as the fact if +the used characters in the font have depth or height. Commands like (plain \TEX +s) \type {\big} need use this feature. In \LUATEX\ we provide a bit more control +by three variants that supporting optional parameters \type {height}, \type +{depth} and \type {axis}. The following example uses this: + +\startbuffer +\Uleft height 30pt depth 10pt \Udelimiter "0 "0 "000028 +\quad x\quad +\Umiddle height 40pt depth 15pt \Udelimiter "0 "0 "002016 +\quad x\quad +\Uright height 30pt depth 10pt \Udelimiter "0 "0 "000029 +\quad \quad \quad +\Uleft height 30pt depth 10pt axis \Udelimiter "0 "0 "000028 +\quad x\quad +\Umiddle height 40pt depth 15pt axis \Udelimiter "0 "0 "002016 +\quad x\quad +\Uright height 30pt depth 10pt axis \Udelimiter "0 "0 "000029 +\stopbuffer + +\typebuffer + +\startlinecorrection +\ruledhbox{\mathematics{\getbuffer}} +\stoplinecorrection + +The keyword \type {exact} can be used as directive that the real dimensions +should be applied when the criteria can't be met which can happen when we're +still stepping through the successively larger variants. When no dimensions are +given the \type {noaxis} command can be used to prevent shifting over the axis. + +You can influence the final class with the keyword \type {class} which will +influence the spacing. + +\subsection{Fixed scripts} + +We have three parameters that are used for this fixed anchoring: + +\starttabulate[|l|l|] +\NC $d$ \NC \type {\Umathsubshiftdown} \NC \NR +\NC $u$ \NC \type {\Umathsupshiftup} \NC \NR +\NC $s$ \NC \type {\Umathsubsupshiftdown} \NC \NR +\stoptabulate + +When we set \type {\mathscriptsmode} to a value other than zero these are used +for calculating fixed positions. This is something that is needed for instance +for chemistry. You can manipulate the mentioned variables to achive different +effects. + +\def\SampleMath#1% + {$\mathscriptsmode#1\mathupright CH_2 + CH^+_2 + CH^2_2$} + +\starttabulate[|c|c|c|l|] +\NC \bf mode \NC \bf down \NC \bf up \NC \NC \NR +\NC 0 \NC dynamic \NC dynamic \NC \SampleMath{0} \NC \NR +\NC 1 \NC $d$ \NC $u$ \NC \SampleMath{1} \NC \NR +\NC 2 \NC $s$ \NC $u$ \NC \SampleMath{2} \NC \NR +\NC 3 \NC $s$ \NC $u + s - d$ \NC \SampleMath{3} \NC \NR +\NC 4 \NC $d + (s-d)/2$ \NC $u + (s-d)/2$ \NC \SampleMath{4} \NC \NR +\NC 5 \NC $d$ \NC $u + s - d$ \NC \SampleMath{5} \NC \NR +\stoptabulate + +The value of this parameter obeys grouping but applies to the whole current +formula. + +% if needed we can put the value in stylenodes but maybe more should go there + +\subsection {Tracing} + +Because there are quite some math related parameters and values, it is possible +to limit tracing. Only when \type {tracingassigns} and|/|or \type +{tracingrestores} are set to~2 or more they will be traced. + +\subsection {Math options} + +The logic in the math engine is rather complex and there are often no universal +solutions (read: what works out well for one font, fails for another). Therefore +some variations in the implementation will be driven by options for which a new +primitive \type {\mathoption} has been introduced (so that we don't end up with +many new commands). The approach of options also permits us to see what effect a +specific solution has. + +\subsubsection {\type {\mathoption noitaliccompensation}} + +This option compensates placement for characters with a built|-|in italic +correction. + +\startbuffer +{\showboxes\int}\quad +{\showboxes\int_{|}^{|}}\quad +{\showboxes\int\limits_{|}^{|}} +\stopbuffer + +\typebuffer + +Gives (with computer modern that has such italics): + +\startlinecorrection[blank] + \switchtobodyfont[modern] + \startcombination[nx=2,ny=2,distance=5em] + {\mathoption noitaliccompensation 0\relax \mathematics{\getbuffer}} + {\nohyphens\type{0:inline}} + {\mathoption noitaliccompensation 0\relax \mathematics{\displaymath\getbuffer}} + {\nohyphens\type{0:display}} + {\mathoption noitaliccompensation 1\relax \mathematics{\getbuffer}} + {\nohyphens\type{1:inline}} + {\mathoption noitaliccompensation 1\relax \mathematics{\displaymath\getbuffer}} + {\nohyphens\type{1:display}} + \stopcombination +\stoplinecorrection + +\subsubsection {\type {\mathoption nocharitalic}} + +When two characters follow each other italic correction can interfere. The +following example shows what this option does: + +\startbuffer +\catcode"1D443=11 +\catcode"1D444=11 +\catcode"1D445=11 +P( PP PQR +\stopbuffer + +\typebuffer + +Gives (with computer modern that has such italics): + +\startlinecorrection[blank] + \switchtobodyfont[modern] + \startcombination[nx=2,ny=2,distance=5em] + {\mathoption nocharitalic 0\relax \mathematics{\getbuffer}} + {\nohyphens\type{0:inline}} + {\mathoption nocharitalic 0\relax \mathematics{\displaymath\getbuffer}} + {\nohyphens\type{0:display}} + {\mathoption nocharitalic 1\relax \mathematics{\getbuffer}} + {\nohyphens\type{1:inline}} + {\mathoption nocharitalic 1\relax \mathematics{\displaymath\getbuffer}} + {\nohyphens\type{1:display}} + \stopcombination +\stoplinecorrection + +\subsubsection {\type {\mathoption useoldfractionscaling}} + +This option has been introduced as solution for tracker item 604 for fuzzy cases +around either or not present fraction related settings for new fonts. + +\stopchapter + +\stopcomponent |