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diff --git a/doc/context/sources/general/manuals/luatex/luatex-math.tex b/doc/context/sources/general/manuals/luatex/luatex-math.tex index 8ccae83f3..4623ce706 100644 --- a/doc/context/sources/general/manuals/luatex/luatex-math.tex +++ b/doc/context/sources/general/manuals/luatex/luatex-math.tex @@ -1,12 +1,15 @@ % language=uk \environment luatex-style -\environment luatex-logos \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 @@ -16,18 +19,133 @@ 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} +\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: \type {\mathstyle}. This is a \quote -{convert command} like e.g. \type {\romannumeral}: its value can only be read, +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. -\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 +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 @@ -48,16 +166,15 @@ thereby reusing numbers) because the number that got used is stored and used in the second pass (so changing \type {\fam 12} mid|-|formula spoils over to preceding use of that family). -The style switching primitives like \type {\textstyle} are turned into nodes so -the styles set there are frozen. The \type {\mathchoice} primitive results in -four lists being constructed of which one is used in the second pass. The fact -that some automatic styles are not yet known also means that the \type -{\mathstyle} primitive expands to the current style which can of course be -different from the one really used. It's a snapshot of the first pass state. As a -consequence in the following example you get a style number (first pass) typeset -that can actually differ from the used style (second pass). In the case of a math -choice used ungrouped, the chosen style is used after the choice too, unless you -group. +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 @@ -120,134 +237,39 @@ This gives: \blank $\displaystyle \getbuffer[1]$ \blank \blank $\textstyle \getbuffer[1]$ \blank -Using \type {\begingroup} \unknown\ \type {\endgroup} instead gives: +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 \type {\mathstyle} expanding +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{\type {\Ustack}} +\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 (\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}: +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 \type {\Ustack} command will scan the next brace and start a new math group +The \lpr {Ustack} command will scan the next brace and start a new math group with the correct (numerator) math style. -\section{Unicode math characters} - -Character handling is now extended up to the full \UNICODE\ range (the \type {\U} -prefix), which is compatible with \XETEX. - -The math primitives from \TEX\ are kept as they are, except for the ones that -convert from input to math commands: \type {mathcode}, and \type {delcode}. These -two now allow for a 21-bit character argument on the left hand side of the equals -sign. - -Some of the new \LUATEX\ primitives read more than one separate value. This is -shown in the tables below by a plus sign in the second column. - -The input for such primitives would look like this: - -\starttyping -\def\overbrace{\Umathaccent 0 1 "23DE } -\stoptyping - -The altered \TEX82 primitives are: - -\starttabulate[|l|l|r|c|l|r|] -\BC primitive \BC min \BC max \BC \kern 2em \BC min \BC max \NC \NR -\NC \type {\mathcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC 8000 \NC \NR -\NC \type {\delcode} \NC 0 \NC 10FFFF \NC = \NC 0 \NC FFFFFF \NC \NR -\stoptabulate - -The unaltered ones are: - -\starttabulate[|l|l|r|] -\BC primitive \BC min \BC max \NC \NR -\NC \type {\mathchardef} \NC 0 \NC 8000 \NC \NR -\NC \type {\mathchar} \NC 0 \NC 7FFF \NC \NR -\NC \type {\mathaccent} \NC 0 \NC 7FFF \NC \NR -\NC \type {\delimiter} \NC 0 \NC 7FFFFFF \NC \NR -\NC \type {\radical} \NC 0 \NC 7FFFFFF \NC \NR -\stoptabulate +\subsection{Cramped math styles} -For practical reasons \type {\mathchardef} will silently accept values larger -that \type {0x8000} and interpret it as \type {\Umathcharnumdef}. This is needed -to satisfy older macro packages. - -The following new primitives are compatible with \XETEX: - -% somewhat fuzzy: - -\starttabulate[|l|l|r|c|l|r|] -\BC primitive \BC min \BC max \BC \kern 2em \BC min \BC max \NC \NR -\NC \type {\Umathchardef} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{1}} \NC \NC \NC \NC \NR -\NC \type {\Umathcharnumdef}\rlap{\high{5}} \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NC \NC \NC \NR -\NC \type {\Umathcode} \NC 0 \NC 10FFFF \NC = \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{1}} \NC \NR -\NC \type {\Udelcode} \NC 0 \NC 10FFFF \NC = \NC 0+0 \NC FF+10FFFF\rlap{\high{2}} \NC \NR -\NC \type {\Umathchar} \NC 0+0+0 \NC 7+FF+10FFFF \NC \NC \NC \NC \NR -\NC \type {\Umathaccent} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{2,4}} \NC \NC \NC \NC \NR -\NC \type {\Udelimiter} \NC 0+0+0 \NC 7+FF+10FFFF\rlap{\high{2}} \NC \NC \NC \NC \NR -\NC \type {\Uradical} \NC 0+0 \NC FF+10FFFF\rlap{\high{2}} \NC \NC \NC \NC \NR -\NC \type {\Umathcharnum} \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NC \NC \NC \NR -\NC \type {\Umathcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NR -\NC \type {\Udelcodenum} \NC 0 \NC 10FFFF \NC = \NC -80000000 \NC 7FFFFFFF\rlap{\high{3}} \NC \NR -\stoptabulate - -Specifications typically look like: - -\starttyping -\Umathchardef\xx="1"0"456 -\Umathcode 123="1"0"789 -\stoptyping - -Note 1: The new primitives that deal with delimiter|-|style objects do not set up a -\quote {large family}. Selecting a suitable size for display purposes is expected -to be dealt with by the font via the \type {\Umathoperatorsize} parameter (more -information can be found in a following section). - -Note 2: For these three primitives, all information is packed into a single -signed integer. For the first two (\type {\Umathcharnum} and \type -{\Umathcodenum}), the lowest 21 bits are the character code, the 3 bits above -that represent the math class, and the family data is kept in the topmost bits -(This means that the values for math families 128--255 are actually negative). -For \type {\Udelcodenum} there is no math class. The math family information is -stored in the bits directly on top of the character code. Using these three -commands is not as natural as using the two- and three|-|value commands, so -unless you know exactly what you are doing and absolutely require the speedup -resulting from the faster input scanning, it is better to use the verbose -commands instead. - -Note 3: The \type {\Umathaccent} command accepts optional keywords to control -various details regarding math accents. See \in {section} [mathacc] below for -details. - -New primitives that exist in \LUATEX\ only (all of these will be explained -in following sections): - -\starttabulate[|l|l|] -\BC primitive \BC value range (in hex) \NC \NR -\NC \type {\Uroot} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Uoverdelimiter} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Uunderdelimiter} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Udelimiterover} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\NC \type {\Udelimiterunder} \NC 0+0--FF+10FFFF$^2$ \NC \NR -\stoptabulate - -\section{Cramped math styles} +\topicindex {math+styles} +\topicindex {math+spacing} +\topicindex {math+cramped} \LUATEX\ has four new primitives to set the cramped math styles directly: @@ -282,20 +304,23 @@ are described as follows: style if the original style was cramped. \stopitem \startitem - Formulas under a \type {\sqrt} or \type {\overline} are in cramped style. + 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. If we -force styles in the script using \type {\scriptstyle} and \type {\crampedscriptstyle} -we get this: +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 @@ -310,7 +335,7 @@ Now we set the following parameters \typebuffer[setup] -This gives: +This gives a different result: \start\getbuffer[setup,demo]\stop @@ -329,69 +354,77 @@ Now we get: \start\getbuffer[setup,demo]\stop -\section{Math parameter settings} +\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 accessible before. +has resulted in many more parameters than were not accessible before. \starttabulate -\BC primitive name \BC description \NC \NR -\NC \type {\Umathquad} \NC the width of 18 mu's \NC \NR -\NC \type {\Umathaxis} \NC height of the vertical center axis of +\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 \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 +\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: @@ -403,22 +436,9 @@ Each of the parameters in this section can be set by a command like this: they obey grouping, and you can use \type {\the\Umathquad\displaystyle} if needed. -\section{Skips around display math} +\subsection{Font|-|based math parameters} -The injection of \type {\abovedisplayskip} and \type {\belowdisplayskip} is not -symmetrical. An above one is always inserted, also when zero, but the below is -only inserted when larger than zero. Especially the later makes it sometimes hard -to fully control spacing. Therefore \LUATEX\ comes with a new directive: \type -{\mathdisplayskipmode}. The following values apply: - -\starttabulate -\NC 0 \NC normal \TEX\ behaviour \NC \NR -\NC 1 \NC always (same as 0) \NC \NR -\NC 2 \NC only when not zero \NC \NR -\NC 3 \NC never, not even when not zero \NC \NR -\stoptabulate - -\section{Font-based Math Parameters} +\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\ @@ -432,121 +452,118 @@ 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 +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. -\start +\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} -\switchtobodyfont[8pt] - -\starttabulate[|l|l|l|p|] -\BC variable \BC style \BC default value opentype \BC default value tfm \NC \NR -\NC \type {\Umathaxis} \NC -- \NC AxisHeight \NC axis_height \NC \NR -\NC \type {\Umathoperatorsize} \NC D, D' \NC DisplayOperatorMinHeight \NC $^6$ \NC \NR -\NC \type {\Umathfractiondelsize} \NC D, D' \NC FractionDelimiterDisplayStyleSize$^9$ \NC delim1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionDelimiterSize$^9$ \NC delim2 \NC \NR -\NC \type {\Umathfractiondenomdown} \NC D, D' \NC FractionDenominatorDisplayStyleShiftDown \NC denom1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionDenominatorShiftDown \NC denom2 \NC \NR -\NC \type {\Umathfractiondenomvgap} \NC D, D' \NC FractionDenominatorDisplayStyleGapMin \NC 3*default_rule_thickness \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionDenominatorGapMin \NC default_rule_thickness \NC \NR -\NC \type {\Umathfractionnumup} \NC D, D' \NC FractionNumeratorDisplayStyleShiftUp \NC num1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionNumeratorShiftUp \NC num2 \NC \NR -\NC \type {\Umathfractionnumvgap} \NC D, D' \NC FractionNumeratorDisplayStyleGapMin \NC 3*default_rule_thickness \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC FractionNumeratorGapMin \NC default_rule_thickness \NC \NR -\NC \type {\Umathfractionrule} \NC -- \NC FractionRuleThickness \NC default_rule_thickness \NC \NR -\NC \type {\Umathskewedfractionhgap} \NC -- \NC SkewedFractionHorizontalGap \NC math_quad/2 \NC \NR -\NC \type {\Umathskewedfractionvgap} \NC -- \NC SkewedFractionVerticalGap \NC math_x_height \NC \NR -\NC \type {\Umathlimitabovebgap} \NC -- \NC UpperLimitBaselineRiseMin \NC big_op_spacing3 \NC \NR -\NC \type {\Umathlimitabovekern} \NC -- \NC 0$^1$ \NC big_op_spacing5 \NC \NR -\NC \type {\Umathlimitabovevgap} \NC -- \NC UpperLimitGapMin \NC big_op_spacing1 \NC \NR -\NC \type {\Umathlimitbelowbgap} \NC -- \NC LowerLimitBaselineDropMin \NC big_op_spacing4 \NC \NR -\NC \type {\Umathlimitbelowkern} \NC -- \NC 0$^1$ \NC big_op_spacing5 \NC \NR -\NC \type {\Umathlimitbelowvgap} \NC -- \NC LowerLimitGapMin \NC big_op_spacing2 \NC \NR -\NC \type {\Umathoverdelimitervgap} \NC -- \NC StretchStackGapBelowMin \NC big_op_spacing1 \NC \NR -\NC \type {\Umathoverdelimiterbgap} \NC -- \NC StretchStackTopShiftUp \NC big_op_spacing3 \NC \NR -\NC \type {\Umathunderdelimitervgap} \NC-- \NC StretchStackGapAboveMin \NC big_op_spacing2 \NC \NR -\NC \type {\Umathunderdelimiterbgap} \NC-- \NC StretchStackBottomShiftDown \NC big_op_spacing4 \NC \NR -\NC \type {\Umathoverbarkern} \NC -- \NC OverbarExtraAscender \NC default_rule_thickness \NC \NR -\NC \type {\Umathoverbarrule} \NC -- \NC OverbarRuleThickness \NC default_rule_thickness \NC \NR -\NC \type {\Umathoverbarvgap} \NC -- \NC OverbarVerticalGap \NC 3*default_rule_thickness \NC \NR -\NC \type {\Umathquad} \NC -- \NC <font_size(f)>$^1$ \NC math_quad \NC \NR -\NC \type {\Umathradicalkern} \NC -- \NC RadicalExtraAscender \NC default_rule_thickness \NC \NR -\NC \type {\Umathradicalrule} \NC -- \NC RadicalRuleThickness \NC <not set>$^2$ \NC \NR -\NC \type {\Umathradicalvgap} \NC D, D' \NC RadicalDisplayStyleVerticalGap \NC (default_rule_thickness+\crlf - (abs(math_x_height)/4))$^3$ \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC RadicalVerticalGap \NC (default_rule_thickness+\crlf - (abs(default_rule_thickness)/4))$^3$ \NC \NR -\NC \type {\Umathradicaldegreebefore} \NC -- \NC RadicalKernBeforeDegree \NC <not set>$^2$ \NC \NR -\NC \type {\Umathradicaldegreeafter} \NC -- \NC RadicalKernAfterDegree \NC <not set>$^2$ \NC \NR -\NC \type {\Umathradicaldegreeraise} \NC -- \NC RadicalDegreeBottomRaisePercent \NC <not set>$^{2,7}$ \NC \NR -\NC \type {\Umathspaceafterscript} \NC -- \NC SpaceAfterScript \NC script_space$^4$ \NC \NR -\NC \type {\Umathstackdenomdown} \NC D, D' \NC StackBottomDisplayStyleShiftDown \NC denom1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC StackBottomShiftDown \NC denom2 \NC \NR -\NC \type {\Umathstacknumup} \NC D, D' \NC StackTopDisplayStyleShiftUp \NC num1 \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC StackTopShiftUp \NC num3 \NC \NR -\NC \type {\Umathstackvgap} \NC D, D' \NC StackDisplayStyleGapMin \NC 7*default_rule_thickness \NC \NR -\NC \NC T, T', S, S', SS, SS' \NC StackGapMin \NC 3*default_rule_thickness \NC \NR -\NC \type {\Umathsubshiftdown} \NC -- \NC SubscriptShiftDown \NC sub1 \NC \NR -\NC \type {\Umathsubshiftdrop} \NC -- \NC SubscriptBaselineDropMin \NC sub_drop \NC \NR -\NC \type {\Umathsubsupshiftdown} \NC -- \NC SubscriptShiftDownWithSuperscript$^8$ \NC \NC \NR -\NC \NC \NC \quad\ or SubscriptShiftDown \NC sub2 \NC \NR -\NC \type {\Umathsubtopmax} \NC -- \NC SubscriptTopMax \NC (abs(math_x_height * 4) / 5) \NC \NR -\NC \type {\Umathsubsupvgap} \NC -- \NC SubSuperscriptGapMin \NC 4*default_rule_thickness \NC \NR -\NC \type {\Umathsupbottommin} \NC -- \NC SuperscriptBottomMin \NC (abs(math_x_height) / 4) \NC \NR -\NC \type {\Umathsupshiftdrop} \NC -- \NC SuperscriptBaselineDropMax \NC sup_drop \NC \NR -\NC \type {\Umathsupshiftup} \NC D \NC SuperscriptShiftUp \NC sup1 \NC \NR -\NC \NC T, S, SS, \NC SuperscriptShiftUp \NC sup2 \NC \NR -\NC \NC D', T', S', SS' \NC SuperscriptShiftUpCramped \NC sup3 \NC \NR -\NC \type {\Umathsupsubbottommax} \NC -- \NC SuperscriptBottomMaxWithSubscript \NC (abs(math_x_height * 4) / 5) \NC \NR -\NC \type {\Umathunderbarkern} \NC -- \NC UnderbarExtraDescender \NC default_rule_thickness \NC \NR -\NC \type {\Umathunderbarrule} \NC -- \NC UnderbarRuleThickness \NC default_rule_thickness \NC \NR -\NC \type {\Umathunderbarvgap} \NC -- \NC UnderbarVerticalGap \NC 3*default_rule_thickness \NC \NR -\NC \type {\Umathconnectoroverlapmin} \NC -- \NC MinConnectorOverlap \NC 0$^5$ \NC \NR +\starttabulate[|l|l|] +\DB variable / style \BC tfm / opentype \NC \NR +\MathLine{\Umathaxis} {} {} {AxisHeight} {axis_height} +\MathLine{\Umathoperatorsize} {6} {D, D'} {DisplayOperatorMinHeight} {\emdash} +\MathLine{\Umathfractiondelsize} {9} {D, D'} {FractionDelimiterDisplayStyleSize} {delim1} +\MathLine{\Umathfractiondelsize} {9} {T, T', S, S', SS, SS'}{FractionDelimiterSize} {delim2} +\MathLine{\Umathfractiondenomdown} {} {D, D'} {FractionDenominatorDisplayStyleShiftDown}{denom1} +\MathLine{\Umathfractiondenomdown} {} {T, T', S, S', SS, SS'}{FractionDenominatorShiftDown} {denom2} +\MathLine{\Umathfractiondenomvgap} {} {D, D'} {FractionDenominatorDisplayStyleGapMin} {3*default_rule_thickness} +\MathLine{\Umathfractiondenomvgap} {} {T, T', S, S', SS, SS'}{FractionDenominatorGapMin} {default_rule_thickness} +\MathLine{\Umathfractionnumup} {} {D, D'} {FractionNumeratorDisplayStyleShiftUp} {num1} +\MathLine{\Umathfractionnumup} {} {T, T', S, S', SS, SS'}{FractionNumeratorShiftUp} {num2} +\MathLine{\Umathfractionnumvgap} {} {D, D'} {FractionNumeratorDisplayStyleGapMin} {3*default_rule_thickness} +\MathLine{\Umathfractionnumvgap} {} {T, T', S, S', SS, SS'}{FractionNumeratorGapMin} {default_rule_thickness} +\MathLine{\Umathfractionrule} {} {} {FractionRuleThickness} {default_rule_thickness} +\MathLine{\Umathskewedfractionhgap} {} {} {SkewedFractionHorizontalGap} {math_quad/2} +\MathLine{\Umathskewedfractionvgap} {} {} {SkewedFractionVerticalGap} {math_x_height} +\MathLine{\Umathlimitabovebgap} {} {} {UpperLimitBaselineRiseMin} {big_op_spacing3} +\MathLine{\Umathlimitabovekern} {1} {} {0} {big_op_spacing5} +\MathLine{\Umathlimitabovevgap} {} {} {UpperLimitGapMin} {big_op_spacing1} +\MathLine{\Umathlimitbelowbgap} {} {} {LowerLimitBaselineDropMin} {big_op_spacing4} +\MathLine{\Umathlimitbelowkern} {1} {} {0} {big_op_spacing5} +\MathLine{\Umathlimitbelowvgap} {} {} {LowerLimitGapMin} {big_op_spacing2} +\MathLine{\Umathoverdelimitervgap} {} {} {StretchStackGapBelowMin} {big_op_spacing1} +\MathLine{\Umathoverdelimiterbgap} {} {} {StretchStackTopShiftUp} {big_op_spacing3} +\MathLine{\Umathunderdelimitervgap} {} {} {StretchStackGapAboveMin} {big_op_spacing2} +\MathLine{\Umathunderdelimiterbgap} {} {} {StretchStackBottomShiftDown} {big_op_spacing4} +\MathLine{\Umathoverbarkern} {} {} {OverbarExtraAscender} {default_rule_thickness} +\MathLine{\Umathoverbarrule} {} {} {OverbarRuleThickness} {default_rule_thickness} +\MathLine{\Umathoverbarvgap} {} {} {OverbarVerticalGap} {3*default_rule_thickness} +\MathLine{\Umathquad} {1} {} {<font_size(f)>} {math_quad} +\MathLine{\Umathradicalkern} {} {} {RadicalExtraAscender} {default_rule_thickness} +\MathLine{\Umathradicalrule} {2} {} {RadicalRuleThickness} {<not set>} +\MathLine{\Umathradicalvgap} {3} {D, D'} {RadicalDisplayStyleVerticalGap} {default_rule_thickness+abs(math_x_height)/4} +\MathLine{\Umathradicalvgap} {3} {T, T', S, S', SS, SS'}{RadicalVerticalGap} {default_rule_thickness+abs(default_rule_thickness)/4} +\MathLine{\Umathradicaldegreebefore}{2} {} {RadicalKernBeforeDegree} {<not set>} +\MathLine{\Umathradicaldegreeafter} {2} {} {RadicalKernAfterDegree} {<not set>} +\MathLine{\Umathradicaldegreeraise} {2,7}{} {RadicalDegreeBottomRaisePercent} {<not set>} +\MathLine{\Umathspaceafterscript} {4} {} {SpaceAfterScript} {script_space} +\MathLine{\Umathstackdenomdown} {} {D, D'} {StackBottomDisplayStyleShiftDown} {denom1} +\MathLine{\Umathstackdenomdown} {} {T, T', S, S', SS, SS'}{StackBottomShiftDown} {denom2} +\MathLine{\Umathstacknumup} {} {D, D'} {StackTopDisplayStyleShiftUp} {num1} +\MathLine{\Umathstacknumup} {} {T, T', S, S', SS, SS'}{StackTopShiftUp} {num3} +\MathLine{\Umathstackvgap} {} {D, D'} {StackDisplayStyleGapMin} {7*default_rule_thickness} +\MathLine{\Umathstackvgap} {} {T, T', S, S', SS, SS'}{StackGapMin} {3*default_rule_thickness} +\MathLine{\Umathsubshiftdown} {} {} {SubscriptShiftDown} {sub1} +\MathLine{\Umathsubshiftdrop} {} {} {SubscriptBaselineDropMin} {sub_drop} +\MathLine{\Umathsubsupshiftdown} {8} {} {SubscriptShiftDownWithSuperscript} {\emdash} +\MathLine{\Umathsubtopmax} {} {} {SubscriptTopMax} {abs(math_x_height*4)/5} +\MathLine{\Umathsubsupvgap} {} {} {SubSuperscriptGapMin} {4*default_rule_thickness} +\MathLine{\Umathsupbottommin} {} {} {SuperscriptBottomMin} {abs(math_x_height/4)} +\MathLine{\Umathsupshiftdrop} {} {} {SuperscriptBaselineDropMax} {sup_drop} +\MathLine{\Umathsupshiftup} {} {D} {SuperscriptShiftUp} {sup1} +\MathLine{\Umathsupshiftup} {} {T, S, SS,} {SuperscriptShiftUp} {sup2} +\MathLine{\Umathsupshiftup} {} {D', T', S', SS'} {SuperscriptShiftUpCramped} {sup3} +\MathLine{\Umathsupsubbottommax} {} {} {SuperscriptBottomMaxWithSubscript} {abs(math_x_height*4)/5} +\MathLine{\Umathunderbarkern} {} {} {UnderbarExtraDescender} {default_rule_thickness} +\MathLine{\Umathunderbarrule} {} {} {UnderbarRuleThickness} {default_rule_thickness} +\MathLine{\Umathunderbarvgap} {} {} {UnderbarVerticalGap} {3*default_rule_thickness} +\MathLine{\Umathconnectoroverlapmin}{5} {} {MinConnectorOverlap} {0} +\LL \stoptabulate -\stop - -Note 1: \OPENTYPE\ fonts set \type {\Umathlimitabovekern} and \type -{\Umathlimitbelowkern} to zero and set \type {\Umathquad} to the font size of the +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 \type {\Umathradicalrule} because +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 -\type {\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type -{\Umathradicaldegreeraise}. These are then automatically initialized to +\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 \type {\Umathradicalvgap} is not set +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 \type -{\Umathradicalvgap} is set, it will not be recalculated any more. +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 -\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 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 \type {\Umathconnectoroverlapmin} to zero +Note 5: Traditional \TFM\ fonts set \lpr {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 +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 \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 +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 @@ -557,16 +574,198 @@ Note 9: \type {FractionDelimiterDisplayStyleSize} and \type {FractionDelimiterSize} do not actually exist in the \quote {standard} \OPENTYPE\ math font Cambria, but were useful enough to be added. -\section{Nolimit correction} +\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} -There are two extra math parameters \type {\Umathnolimitsupfactor} and \type -{\Umathnolimitsubfactor} that were added to provide some control over how limits +\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 \type {\mathnolimitsmode}. The half -corrections are what happens when scripts are placed on above and below. The +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, does 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|] @@ -609,13 +808,15 @@ When the mode is set to one, the math parameters are used. This way a macro package writer can decide what looks best. Given the current state of fonts in \CONTEXT\ we currently use mode 1 with factor 0 for the superscript and 750 for the subscripts. Positive values are used for both parameters but the subscript -shifts to the left. A \type {\mathnolimitsmode} larger that 15 is considered to +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. -\section{Math italic mess} +\subsection {Math italic mess} + +\topicindex {math+italics} -The \type {\mathitalicsmode} parameter can be set to~1 to force italic correction +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. @@ -641,20 +842,26 @@ example. This kind of parameters relate to the fact that italic correction in \OPENTYPE\ math is bound to fuzzy rules. So, control is the solution. -\section{Script boxes} +\subsection {Script and kerning} -If you want typeset text in math macro packages often provide something \type -{\text} which obeys the script sizes. As the definition can be anything there is -a good change that the kerning doesn't come out well when used in a script. Given -that the first glyph ends up in an \type {\hbox} we have some control over this. -And, as a bonus we also added control over the normal sublist kerning. The \type -{\mathscriptboxmode} parameter defaults to~1. +\topicindex {math+kerning} +\topicindex {math+scripts} -\starttabulate[|l|l|] +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 @@ -675,12 +882,12 @@ italics, while other fonts can lack kerns. \unexpanded\def\Show#1#2#3% {\doifelsenothing{#3} - {\small\typeinlinebuffer[#1]} + {\small\tx\typeinlinebuffer[#1]} {\doifelse{#3}{-} - {\small\type{mode #2}} + {\small\bf\tt mode #2} {\switchtobodyfont[#3]\showfontkerns\showglyphs\mathscriptboxmode#2\relax\inlinebuffer[#1]}}} -\starttabulate[|lT|c|c|c|c|c|] +\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 @@ -690,15 +897,129 @@ italics, while other fonts can lack kerns. \NC dejavu \NC \Show{1}{0}{dejavu} \NC\Show{1}{1}{dejavu} \NC \Show{2}{1}{dejavu} \NC \Show{2}{2}{dejavu} \NC \Show{3}{3}{dejavu} \NC \NR \stoptabulate -\section{Unscaled fences} +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 -The \type {\mathdelimitersmode} primitive is experimental and deals with the -following (potential) problems. Three bits can be set. The first bit prevents -an unwanted shift when the fence symbol is not scaled (a cambria side effect). The -second bit forces italic correction between a preceding character ordinal and -the fenced subformula, while the third bit turns that subformula into a ordinary -so that the same spacing applies as with unfenced variants. Here we show Cambria -(with \type {\mathitalicsmode} enabled). +\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} @@ -716,127 +1037,34 @@ so that the same spacing applies as with unfenced variants. Here we show Cambria \stop So, when set to 7 fenced subformulas with unscaled delimiters come out the same -as unfenced ones. This can be handy for cases where one is forced to use \type -{\left} and \type {\right} always because of unpredictable content. As said, it's -an experimental features (which somehow fits in the exceptional way fences are -dealt with in the engine). The full list of flags is given in the next table: - -\starttabulate[|T|l|] -\NC "01 \NC don't apply the usual shift \NC \NR -\NC "02 \NC apply italic correction when possible \NC \NR -\NC "04 \NC force a ordinary subformula \NC \NR -\NC "08 \NC no shift when a base character \NC \NR -\NC "10 \NC only shift when an extensible \NC \NR +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}). +The effect can depend on the font (and for Cambria one can use for instance \type {"16}). -\section{Math spacing setting} +\subsection[mathacc]{Accent handling} -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} +\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 \type {\Umathaccent}. +are controlled by optional keywords following \lpr {Umathaccent}. -The keyword \type {bottom} after \type {\Umathaccent} signals that a bottom accent +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). @@ -852,7 +1080,7 @@ A simple example: 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. +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 @@ -861,7 +1089,7 @@ accentee. The accent will be shifted horizontally such that its own \type 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 +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. @@ -870,28 +1098,30 @@ 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 +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. -\section{Math root extension} +\subsection{Radical extensions} + +\topicindex {math+radicals} -The new primitive \type {\Uroot} allows the construction of a radical noad -including a degree field. Its syntax is an extension of \type {\Uradical}: +The new primitive \lpr {Uroot} allows the construction of a radical noad +including a degree field. Its syntax is an extension of \lpr {Uradical}: \starttyping \Uradical <fam integer> <char integer> <radicand> \Uroot <fam integer> <char integer> <degree> <radicand> \stoptyping -The placement of the degree is controlled by the math parameters \type -{\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type -{\Umathradicaldegreeraise}. The degree will be typeset in \type -{\scriptscriptstyle}. +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}. -\section{Math kerning in super- and subscripts} +\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} @@ -950,11 +1180,15 @@ next higher height and kern pair, or the highest one in the character (if there 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} +\subsection{Scripts on extensibles} -The primitives \type {\Uunderdelimiter} and \type {\Uoverdelimiter} allow the +\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 -\type {\Udelimiterunder} and \type {\Udelimiterover} allow the placement of an +\lpr {Udelimiterunder} and \lpr {Udelimiterover} allow the placement of an automatically extensible item as a subscript or superscript on a nucleus. The input: @@ -972,18 +1206,18 @@ $\Udelimiterunder 0 "2194 {\hbox{\strut delimiterunder}}$ \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. +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 \type {\Uhextensible} is available that can be used like this: +An extra primitive \lpr {Uhextensible} is available that can be used like this: \startbuffer $\Uhextensible width 10cm 0 "2194$ @@ -1008,38 +1242,11 @@ $\Uhextensible width 1pt middle 0 "2194$ 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: +\subsection{Fractions} -\starttyping -\Umathcode 1 2 3 4 -\stoptyping - -then - -\starttyping -[\Umathcharclass1] [\Umathcharfam1] [\Umathcharslot1] -\stoptyping +\topicindex {math+fractions} -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 \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. @@ -1053,7 +1260,7 @@ 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}. +\lpr {Umathskewedfractionhgap} and \lpr {Umathskewedfractionvgap}. The syntax used here is: @@ -1064,7 +1271,7 @@ The syntax used here is: 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: +For Latin Modern the result looks as follows: \def\ShowA#1#2#3{$x + { {#1} \Uskewed / #3 {#2} } + x$} \def\ShowB#1#2#3{$x + { {#1} \Uskewedwithdelims / () #3 {#2} } + x$} @@ -1099,7 +1306,85 @@ For Latin Modern The result looks as follows: \stoptabulate \stop -\section {Last lines} +\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 @@ -1121,32 +1406,41 @@ get the length of the last line, the following will often work too: \relax} \stoptyping -\section {Other Math changes} +\stopsection + +\startsection[title={Math mode}] + +\subsection {Verbose versions of single|-|character math commands} -\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 {$$}: \starttabulate[|l|l|] -\BC primitive \BC explanation \NC \NR -\NC \type {\Usuperscript} \NC Duplicates the functionality of \type {^} \NC \NR -\NC \type {\Usubscript} \NC Duplicates the functionality of \type {_} \NC \NR -\NC \type {\Ustartmath} \NC Duplicates the functionality of \type {$}, % $ +\DB primitive \BC explanation \NC \NR +\TB +\NC \lpr {Usuperscript} \NC duplicates the functionality of \type {^} \NC \NR +\NC \lpr {Usubscript} \NC duplicates the functionality of \type {_} \NC \NR +\NC \lpr {Ustartmath} \NC duplicates the functionality of \type {$}, % $ when used in non-math mode. \NC \NR -\NC \type {\Ustopmath} \NC Duplicates the functionality of \type {$}, % $ +\NC \lpr {Ustopmath} \NC duplicates the functionality of \type {$}, % $ when used in inline math mode. \NC \NR -\NC \type {\Ustartdisplaymath} \NC Duplicates the functionality of \type {$$}, % $$ +\NC \lpr {Ustartdisplaymath} \NC duplicates the functionality of \type {$$}, % $$ when used in non-math mode. \NC \NR -\NC \type {\Ustopdisplaymath} \NC Duplicates the functionality of \type {$$}, % $$ +\NC \lpr {Ustopdisplaymath} \NC duplicates the functionality of \type {$$}, % $$ when used in display math mode. \NC \NR +\LL \stoptabulate -The \type {\Ustopmath} and \type {\Ustopdisplaymath} primitives check if the current +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 \type {\Unosuperscript} and \type {\Unosubscript}} +\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, @@ -1164,71 +1458,17 @@ $ results in \inlinebuffer[script]. +\subsection{Allowed math commands in non|-|math modes} -\subsection{Allowed math commands in non-math modes} - -The commands \type {\mathchar}, and \type {\Umathchar} and control sequences that -are the result of \type {\mathchardef} or \type {\Umathchardef} are also -acceptable in the horizontal and vertical modes. In those cases, the \type -{\textfont} from the requested math family is used. - -\section{Math surrounding skips} - -Inline math is surrounded by (optional) \type {\mathsurround} spacing but that is fixed -dimension. There is now an additional parameter \type {\mathsurroundskip}. When set to a -non|-|zero value (or zero with some stretch or shrink) this parameter will replace -\type {\mathsurround}. By using an additional parameter instead of changing the nature -of \type {\mathsurround}, we can remain compatible. In the meantime a bit more -control has been added via \type {\mathsurroundmode}. This directive can take 6 values -with zero being the default behaviour. - -\start +\topicindex {math+text} +\topicindex {text+math} -\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} +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. -\startbuffer -\mathsurround 10pt -\mathsurroundskip20pt -\stopbuffer - -\typebuffer \getbuffer - -\starttabulate[|c|c|c|pl|] -\HL -\BC mode \BC \type {x$x$x} \BC \type {x $x$ x} \BC effect \NC \NR -\HL -\OneLiner{0}{obey \type {\mathsurround} when \type {\mathsurroundskip} is 0pt} -\OneLiner{1}{only add skip to the left} -\OneLiner{2}{only add skip to the right} -\OneLiner{3}{add skip to the left and right} -\OneLiner{4}{ignore the skip setting, obey \type {\mathsurround}} -\OneLiner{5}{disable all spacing around math} -\OneLiner{6}{only apply \type {\mathsurroundskip} when also spacing} -\OneLiner{7}{only apply \type {\mathsurroundskip} when no spacing} -\HL -\stoptabulate - -\stop - -Method six omits the surround glue when there is (x)spacing glue present while -method seven does the opposite, the glue is only applied when there is (x)space -glue present too. Anything more fancy, like checking the begining or end of a -paragraph (or edges of a box) would not be robust anyway. If you want that you -can write a callback that runs over a list and analyzes a paragraph. Actually, in -that case you could also inject glue (or set the properties of a math node) -explicitly. So, these modes are in practice mostly useful for special purposes -and experiments (they originate in a tracker item). Keep in mind that this glue -is part of the math node and not always treated as normal glue: it travels with -the begin and end math nodes. Also, method 6 and 7 will zero the skip related -fields in a node when applicable in the first occasion that checks them -(linebreaking or packaging). - -% \section{Math todo} +% \startsection[title={Math todo}] % % The following items are still todo. % @@ -1249,194 +1489,158 @@ fields in a node when applicable in the first occasion that checks them % Support for multi|-|line displays using \MATHML\ style alignment points. % \stopitem % \stopitemize +% +% \stopsection -\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. +\stopsection -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. +\startsection[title={Goodies}] -\subsection{Fixed scripts} +\subsection {Flattening: \lpr {mathflattenmode}} -We have three parameters that are used for this fixed anchoring: +\topicindex {math+flattening} -\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 +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). -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. +\startbuffer[sample] +\switchtobodyfont[modern] +$V \mathbin{\mathbin{v}} V$\par +$V \mathord{\mathord{v}} V$\par +\stopbuffer -\def\SampleMath#1% - {$\mathscriptsmode#1\mathupright CH_2 + CH^+_2 + CH^2_2$} +\typebuffer[sample] -\starttabulate[|c|c|c|l|] -\BC mode \BC down \BC up \BC \NC \NR -\NC 0 \NC dynamic \NC dynamic \NC \SampleMath{0} \NC \NR -\NC 1 \NC $d$ \NC $u$ \NC \SampleMath{1} \NC \NR -\NC 2 \NC $s$ \NC $u$ \NC \SampleMath{2} \NC \NR -\NC 3 \NC $s$ \NC $u + s - d$ \NC \SampleMath{3} \NC \NR -\NC 4 \NC $d + (s-d)/2$ \NC $u + (s-d)/2$ \NC \SampleMath{4} \NC \NR -\NC 5 \NC $d$ \NC $u + s - d$ \NC \SampleMath{5} \NC \NR -\stoptabulate +This renders as: -The value of this parameter obeys grouping but applies to the whole current -formula. +\blank \start \mathflattenmode\plusone \getbuffer[sample] \stop \blank -% if needed we can put the value in stylenodes but maybe more should go there +When we set \lpr {mathflattenmode} to 31 we get: -\subsection{Penalties: \type {\mathpenaltiesmode}} +\blank \start \mathflattenmode\numexpr1+2+4+8+16\relax \getbuffer[sample] \stop \blank -Only in inline math penalties will be added in a math list. You can force -penalties (also in display math) by setting: +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. -\starttyping -\mathpenaltiesmode = 1 -\stoptyping - -This primnitive is not really needed in \LUATEX\ because you can use the callback -\type {mlist_to_hlist} to force penalties by just calling the regular routine -with forced penalties. However, as part of opening up and control this primitive -makes sense. As a bonus we also provide two extra penalties: +You can influence flattening by adding the appropriate number to the value of the +mode parameter. The default value is~1. -\starttyping -\prebinoppenalty = -100 % example value -\prerelpenalty = 900 % example value -\stoptyping +\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 -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 {Less Tracing} -\subsection {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} +\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 will be driven by options for which a new -primitive \type {\mathoption} has been introduced (so that we don't end up with -many new commands). The approach of options also permits us to see what effect a -specific solution has. - -\subsubsection {\type {\mathoption old}} +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 seens as bugs as they relate to font -properties. +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. - -\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}} +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. -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}} +% % 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. -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 |