manual/luatex-math.tex

   1 % language=uk
   2
   3 \environment luatex-style
   4 \environment luatex-logos
   5
   6 \startcomponent luatex-math
   7
   8 \startchapter[reference=math,title={Math}]
   9
  10 The handling of mathematics in \LUATEX\ differs quite a bit from how \TEX82 (and
  11 therefore \PDFTEX) handles math. First, \LUATEX\ adds primitives and extends some
  12 others so that \UNICODE\ input can be used easily. Second, all of \TEX82's
  13 internal special values (for example for operator spacing) have been made
  14 accessible and changeable via control sequences. Third, there are extensions that
  15 make it easier to use \OPENTYPE\ math fonts. And finally, there are some
  16 extensions that have been proposed or considered in the past that are now added
  17 to the engine.
  18
  19 \section{The current math style}
  20
  21 It is possible to discover the math style that will be used for a formula in an
  22 expandable fashion (while the math list is still being read). To make this
  23 possible, \LUATEX\ adds the new primitive: \type {\mathstyle}. This is a \quote
  24 {convert command} like e.g. \type {\romannumeral}: its value can only be read,
  25 not set.
  26
  27 \subsection{\type {\mathstyle}}
  28
  29 The returned value is between 0 and 7 (in math mode), or $-1$ (all other modes).
  30 For easy testing, the eight math style commands have been altered so that the can
  31 be used as numeric values, so you can write code like this:
  32
  33 \starttyping
  34 \ifnum\mathstyle=\textstyle
  35     \message{normal text style}
  36 \else \ifnum\mathstyle=\crampedtextstyle
  37     \message{cramped text style}
  38 \fi \fi
  39 \stoptyping
  40
  41 \subsection{\type {\Ustack}}
  42
  43 There are a few math commands in \TEX\ where the style that will be used is not
  44 known straight from the start. These commands (\type {\over}, \type {\atop},
  45 \type {\overwithdelims}, \type {\atopwithdelims}) would therefore normally return
  46 wrong values for \type {\mathstyle}. To fix this, \LUATEX\ introduces a special
  47 prefix command: \type {\Ustack}:
  48
  49 \starttyping
  50 $\Ustack {a \over b}$
  51 \stoptyping
  52
  53 The \type {\Ustack} command will scan the next brace and start a new math group
  54 with the correct (numerator) math style.
  55
  56 \section{Unicode math characters}
  57
  58 Character handling is now extended up to the full \UNICODE\ range (the \type {\U}
  59 prefix), which is compatible with \XETEX.
  60
  61 The math primitives from \TEX\ are kept as they are, except for the ones that
  62 convert from input to math commands: \type {mathcode}, and \type {delcode}. These
  63 two now allow for a 21-bit character argument on the left hand side of the equals
  64 sign.
  65
  66 Some of the new \LUATEX\ primitives read more than one separate value. This is
  67 shown in the tables below by a plus sign in the second column.
  68
  69 The input for such primitives would look like this:
  70
  71 \starttyping
  72 \def\overbrace{\Umathaccent 0 1 "23DE }
  73 \stoptyping
  74
  75 The altered \TEX82 primitives are:
  76
  77 \starttabulate[|l|l|r|c|l|r|]
  78 \NC \bf primitive     \NC \bf min \NC \bf max \NC \kern 2em  \NC \bf min \NC \bf max \NC \NR
  79 \NC \type {\mathcode} \NC 0       \NC 10FFFF  \NC =          \NC 0       \NC 8000    \NC \NR
  80 \NC \type {\delcode}  \NC 0       \NC 10FFFF  \NC =          \NC 0       \NC FFFFFF  \NC \NR
  81 \stoptabulate
  82
  83 The unaltered ones are:
  84
  85 \starttabulate[|l|l|r|]
  86 \NC \bf primitive        \NC \bf min \NC \bf max \NC \NR
  87 \NC \type {\mathchardef} \NC 0       \NC    8000 \NC \NR
  88 \NC \type {\mathchar}    \NC 0       \NC    7FFF \NC \NR
  89 \NC \type {\mathaccent}  \NC 0       \NC    7FFF \NC \NR
  90 \NC \type {\delimiter}   \NC 0       \NC 7FFFFFF \NC \NR
  91 \NC \type {\radical}     \NC 0       \NC 7FFFFFF \NC \NR
  92 \stoptabulate
  93
  94 For practical reasons \type {\mathchardef} will silently accept values larger
  95 that \type {0x8000} and interpret it as \type {\Umathcharnumdef}. This is needed
  96 to satisfy older macro packages.
  97
  98 The following new primitives are compatible with \XETEX:
  99
 100 % somewhat fuzzy:
 101
 102 \starttabulate[|l|l|r|c|l|r|]
 103 \NC \bf primitive                           \NC \bf min   \NC \bf max             \NC \kern 2em  \NC \bf min   \NC \bf max                    \NC \NR
 104 \NC \type {\Umathchardef}                   \NC 0+0+0     \NC 7+FF+10FFFF\rlap{\high{1}}   \NC   \NC           \NC                            \NC \NR
 105 \NC \type {\Umathcharnumdef}\rlap{\high{5}} \NC -80000000 \NC    7FFFFFFF\rlap{\high{3}}   \NC   \NC           \NC                            \NC \NR
 106 \NC \type {\Umathcode}                      \NC 0         \NC      10FFFF                  \NC = \NC 0+0+0     \NC 7+FF+10FFFF\rlap{\high{1}} \NC \NR
 107 \NC \type {\Udelcode}                       \NC 0         \NC      10FFFF                  \NC = \NC 0+0       \NC   FF+10FFFF\rlap{\high{2}} \NC \NR
 108 \NC \type {\Umathchar}                      \NC 0+0+0     \NC 7+FF+10FFFF                  \NC   \NC           \NC                            \NC \NR
 109 \NC \type {\Umathaccent}                    \NC 0+0+0     \NC 7+FF+10FFFF\rlap{\high{2,4}} \NC   \NC           \NC                            \NC \NR
 110 \NC \type {\Udelimiter}                     \NC 0+0+0     \NC 7+FF+10FFFF\rlap{\high{2}}   \NC   \NC           \NC                            \NC \NR
 111 \NC \type {\Uradical}                       \NC 0+0       \NC   FF+10FFFF\rlap{\high{2}}   \NC   \NC           \NC                            \NC \NR
 112 \NC \type {\Umathcharnum}                   \NC -80000000 \NC    7FFFFFFF\rlap{\high{3}}   \NC   \NC           \NC                            \NC \NR
 113 \NC \type {\Umathcodenum}                   \NC 0         \NC      10FFFF                  \NC = \NC -80000000 \NC    7FFFFFFF\rlap{\high{3}} \NC \NR
 114 \NC \type {\Udelcodenum}                    \NC 0         \NC      10FFFF                  \NC = \NC -80000000 \NC    7FFFFFFF\rlap{\high{3}} \NC \NR
 115 \stoptabulate
 116
 117 Specifications typically look like:
 118
 119 \starttyping
 120 \Umathchardef\xx="1"0"456
 121 \Umathcode   123="1"0"789
 122 \stoptyping
 123
 124 Note 1: The new primitives that deal with delimiter|-|style objects do not set up a
 125 \quote {large family}. Selecting a suitable size for display purposes is expected
 126 to be dealt with by the font via the \type {\Umathoperatorsize} parameter (more
 127 information can be found in a following section).
 128
 129 Note 2: For these three primitives, all information is packed into a single
 130 signed integer. For the first two (\type {\Umathcharnum} and \type
 131 {\Umathcodenum}), the lowest 21 bits are the character code, the 3 bits above
 132 that represent the math class, and the family data is kept in the topmost bits
 133 (This means that the values for math families 128--255 are actually negative).
 134 For \type {\Udelcodenum} there is no math class. The math family information is
 135 stored in the bits directly on top of the character code. Using these three
 136 commands is not as natural as using the two- and three|-|value commands, so
 137 unless you know exactly what you are doing and absolutely require the speedup
 138 resulting from the faster input scanning, it is better to use the verbose
 139 commands instead.
 140
 141 Note 3: The \type {\Umathaccent} command accepts optional keywords to control
 142 various details regarding math accents. See \in {section} [mathacc] below for
 143 details.
 144
 145 New primitives that exist in \LUATEX\ only (all of these will be explained
 146 in following sections):
 147
 148 \starttabulate[|l|l|l|l|]
 149 \NC \bf primitive         \NC \bf value range (in hex) \NC \NR
 150 \NC \type {\Uroot}           \NC 0+0--FF+10FFFF$^2$       \NC \NR
 151 \NC \type {\Uoverdelimiter}  \NC 0+0--FF+10FFFF$^2$       \NC \NR
 152 \NC \type {\Uunderdelimiter} \NC 0+0--FF+10FFFF$^2$       \NC \NR
 153 \NC \type {\Udelimiterover}  \NC 0+0--FF+10FFFF$^2$       \NC \NR
 154 \NC \type {\Udelimiterunder} \NC 0+0--FF+10FFFF$^2$       \NC \NR
 155 \stoptabulate
 156
 157 \section{Cramped math styles}
 158
 159 \LUATEX\ has four new primitives to set the cramped math styles directly:
 160
 161 \starttyping
 162 \crampeddisplaystyle
 163 \crampedtextstyle
 164 \crampedscriptstyle
 165 \crampedscriptscriptstyle
 166 \stoptyping
 167
 168 These additional commands are not all that valuable on their own, but they come
 169 in handy as arguments to the math parameter settings that will be added shortly.
 170
 171 In Eijkhouts \quotation {\TEX\ by Topic} the rules for handling styles in scripts
 172 are described as follows:
 173
 174 \startitemize
 175 \startitem
 176     In any style superscripts and subscripts are taken from the next smaller style.
 177     Exception: in display style they are taken in script style.
 178 \stopitem
 179 \startitem
 180     Subscripts are always in the cramped variant of the style; superscripts are only
 181     cramped if the original style was cramped.
 182 \stopitem
 183 \startitem
 184     In an \type {..\over..} formula in any style the numerator and denominator are
 185     taken from the next smaller style.
 186 \stopitem
 187 \startitem
 188     The denominator is always in cramped style; the numerator is only in cramped
 189     style if the original style was cramped.
 190 \stopitem
 191 \startitem
 192     Formulas under a \type {\sqrt} or \type {\overline} are in cramped style.
 193 \stopitem
 194 \stopitemize
 195
 196 In \LUATEX\ one can set the styles in more detail which means that you sometimes
 197 have to set both normal and cramped styles to get the effect you want. If we
 198 force styles in the script using \type {\scriptstyle} and \type {\crampedscriptstyle}
 199 we get this:
 200
 201 \startbuffer[demo]
 202 \starttabulate
 203 \NC default       \NC $b_{x=xx}^{x=xx}$ \NC \NR
 204 \NC script        \NC $b_{\scriptstyle x=xx}^{\scriptstyle x=xx}$ \NC \NR
 205 \NC crampedscript \NC $b_{\crampedscriptstyle x=xx}^{\crampedscriptstyle x=xx}$ \NC \NR
 206 \stoptabulate
 207 \stopbuffer
 208
 209 \getbuffer[demo]
 210
 211 Now we set the following parameters
 212
 213 \startbuffer[setup]
 214 \Umathordrelspacing\scriptstyle=30mu
 215 \Umathordordspacing\scriptstyle=30mu
 216 \stopbuffer
 217
 218 \typebuffer[setup]
 219
 220 This gives:
 221
 222 \start\getbuffer[setup,demo]\stop
 223
 224 But, as this is not what is expected (visually) we should say:
 225
 226 \startbuffer[setup]
 227 \Umathordrelspacing\scriptstyle=30mu
 228 \Umathordordspacing\scriptstyle=30mu
 229 \Umathordrelspacing\crampedscriptstyle=30mu
 230 \Umathordordspacing\crampedscriptstyle=30mu
 231 \stopbuffer
 232
 233 \typebuffer[setup]
 234
 235 Now we get:
 236
 237 \start\getbuffer[setup,demo]\stop
 238
 239 \section{Math parameter settings}
 240
 241 In \LUATEX, the font dimension parameters that \TEX\ used in math typesetting are
 242 now accessible via primitive commands. In fact, refactoring of the math engine
 243 has resulted in many more parameters than were accessible before.
 244
 245 \starttabulate
 246 \NC \bf primitive name               \NC \bf description \NC \NR
 247 \NC \type {\Umathquad}               \NC the width of 18 mu's \NC \NR
 248 \NC \type {\Umathaxis}               \NC height of the vertical center axis of
 249                                          the math formula above the baseline \NC \NR
 250 \NC \type {\Umathoperatorsize}       \NC minimum size of large operators in display mode \NC \NR
 251 \NC \type {\Umathoverbarkern}        \NC vertical clearance above the rule \NC \NR
 252 \NC \type {\Umathoverbarrule}        \NC the width of the rule \NC \NR
 253 \NC \type {\Umathoverbarvgap}        \NC vertical clearance below the rule \NC \NR
 254 \NC \type {\Umathunderbarkern}       \NC vertical clearance below the rule \NC \NR
 255 \NC \type {\Umathunderbarrule}       \NC the width of the rule \NC \NR
 256 \NC \type {\Umathunderbarvgap}       \NC vertical clearance above the rule \NC \NR
 257 \NC \type {\Umathradicalkern}        \NC vertical clearance above the rule \NC \NR
 258 \NC \type {\Umathradicalrule}        \NC the width of the rule \NC \NR
 259 \NC \type {\Umathradicalvgap}        \NC vertical clearance below the rule \NC \NR
 260 \NC \type {\Umathradicaldegreebefore}\NC the forward kern that takes place before placement of
 261                                          the radical degree \NC \NR
 262 \NC \type {\Umathradicaldegreeafter} \NC the backward kern that takes place after placement of
 263                                          the radical degree \NC \NR
 264 \NC \type {\Umathradicaldegreeraise} \NC this is the percentage of the total height and depth of
 265                                          the radical sign that the degree is raised by; it is
 266                                          expressed in \type {percents}, so 60\% is expressed as the
 267                                          integer $60$ \NC \NR
 268 \NC \type {\Umathstackvgap}          \NC vertical clearance between the two
 269                                          elements in a \type {\atop} stack \NC \NR
 270 \NC \type {\Umathstacknumup}         \NC numerator shift upward in \type {\atop} stack \NC \NR
 271 \NC \type {\Umathstackdenomdown}     \NC denominator shift downward in \type {\atop} stack \NC \NR
 272 \NC \type {\Umathfractionrule}       \NC the width of the rule in a \type {\over} \NC \NR
 273 \NC \type {\Umathfractionnumvgap}    \NC vertical clearance between the numerator and the rule \NC \NR
 274 \NC \type {\Umathfractionnumup}      \NC numerator shift upward in \type {\over} \NC \NR
 275 \NC \type {\Umathfractiondenomvgap}  \NC vertical clearance between the denominator and the rule \NC \NR
 276 \NC \type {\Umathfractiondenomdown}  \NC denominator shift downward in \type {\over} \NC \NR
 277 \NC \type {\Umathfractiondelsize}    \NC minimum delimiter size for \type {\...withdelims} \NC \NR
 278 \NC \type {\Umathlimitabovevgap}     \NC vertical clearance for limits above operators \NC \NR
 279 \NC \type {\Umathlimitabovebgap}     \NC vertical baseline clearance for limits above operators \NC \NR
 280 \NC \type {\Umathlimitabovekern}     \NC space reserved at the top of the limit \NC \NR
 281 \NC \type {\Umathlimitbelowvgap}     \NC vertical clearance for limits below operators \NC \NR
 282 \NC \type {\Umathlimitbelowbgap}     \NC vertical baseline clearance for limits below operators \NC \NR
 283 \NC \type {\Umathlimitbelowkern}     \NC space reserved at the bottom of the limit \NC \NR
 284 \NC \type {\Umathoverdelimitervgap}  \NC vertical clearance for limits above delimiters \NC \NR
 285 \NC \type {\Umathoverdelimiterbgap}  \NC vertical baseline clearance for limits above delimiters \NC \NR
 286 \NC \type {\Umathunderdelimitervgap} \NC vertical clearance for limits below delimiters \NC \NR
 287 \NC \type {\Umathunderdelimiterbgap} \NC vertical baseline clearance for limits below delimiters \NC \NR
 288 \NC \type {\Umathsubshiftdrop}       \NC subscript drop for boxes and subformulas \NC \NR
 289 \NC \type {\Umathsubshiftdown}       \NC subscript drop for characters \NC \NR
 290 \NC \type {\Umathsupshiftdrop}       \NC superscript drop (raise, actually) for boxes and subformulas \NC \NR
 291 \NC \type {\Umathsupshiftup}         \NC superscript raise for characters \NC \NR
 292 \NC \type {\Umathsubsupshiftdown}    \NC subscript drop in the presence of a superscript \NC \NR
 293 \NC \type {\Umathsubtopmax}          \NC the top of standalone subscripts cannot be higher than this
 294                                          above the baseline \NC \NR
 295 \NC \type {\Umathsupbottommin}       \NC the bottom of standalone superscripts cannot be less than
 296                                          this above the baseline \NC \NR
 297 \NC \type {\Umathsupsubbottommax}    \NC the bottom of the superscript of a combined super- and subscript
 298                                          be at least as high as this above the baseline \NC \NR
 299 \NC \type {\Umathsubsupvgap}         \NC vertical clearance between super- and subscript \NC \NR
 300 \NC \type {\Umathspaceafterscript}   \NC additional space added after a super- or subscript \NC \NR
 301 \NC \type {\Umathconnectoroverlapmin}\NC minimum overlap between parts in an extensible recipe \NC \NR
 302 \stoptabulate
 303
 304 Each of the parameters in this section can be set by a command like this:
 305
 306 \starttyping
 307 \Umathquad\displaystyle=1em
 308 \stoptyping
 309
 310 they obey grouping, and you can use \type {\the\Umathquad\displaystyle} if
 311 needed.
 312
 313 \section{Skips around display math}
 314
 315 The injection of \type {\abovedisplayskip} and \type {\belowdisplayskip} is not
 316 symmetrical. An above one is always inserted, also when zero, but the below is
 317 only inserted when larger than zero. Especially the later mkes it sometimes hard
 318 to fully control spacing. Therefore \LUATEX\ comes with a new directive: \type
 319 {\mathdisplayskipmode}. The following values apply:
 320
 321 \starttabulate
 322 \NC 0 \NC normal \TEX\ behaviour: always above, only below when larger than zero \NC \NR
 323 \NC 1 \NC always \NC \NR
 324 \NC 2 \NC only when not zero \NC \NR
 325 \NC 3 \NC never, not even when not zero \NC \NR
 326 \stoptabulate
 327
 328 \section{Font-based Math Parameters}
 329
 330 While it is nice to have these math parameters available for tweaking, it would
 331 be tedious to have to set each of them by hand. For this reason, \LUATEX\
 332 initializes a bunch of these parameters whenever you assign a font identifier to
 333 a math family based on either the traditional math font dimensions in the font
 334 (for assignments to math family~2 and~3 using \TFM|-|based fonts like \type
 335 {cmsy} and \type {cmex}), or based on the named values in a potential \type
 336 {MathConstants} table when the font is loaded via Lua. If there is a \type
 337 {MathConstants} table, this takes precedence over font dimensions, and in that
 338 case no attention is paid to which family is being assigned to: the \type
 339 {MathConstants} tables in the last assigned family sets all parameters.
 340
 341 In the table below, the one|-|letter style abbreviations and symbolic tfm font
 342 dimension names match those using in the \TeX book. Assignments to \type
 343 {\textfont} set the values for the cramped and uncramped display and text styles,
 344 \type {\scriptfont} sets the script styles, and \type {\scriptscriptfont} sets
 345 the scriptscript styles, so we have eight parameters for three font sizes. In the
 346 \TFM\ case, assignments only happen in family~2 and family~3 (and of course only
 347 for the parameters for which there are font dimensions).
 348
 349 Besides the parameters below, \LUATEX\ also looks at the \quote {space} font
 350 dimension parameter. For math fonts, this should be set to zero.
 351
 352 \start
 353
 354 \switchtobodyfont[8pt]
 355
 356 \starttabulate[|l|l|l|p|]
 357 \NC \bf variable                      \NC \bf style             \NC \bf default value opentype               \NC \bf default value tfm \NC \NR
 358 \NC \type {\Umathaxis}                \NC --                    \NC AxisHeight                               \NC axis_height \NC \NR
 359 \NC \type {\Umathoperatorsize}        \NC D, D'                 \NC DisplayOperatorMinHeight                 \NC $^6$ \NC \NR
 360 \NC \type {\Umathfractiondelsize}     \NC D, D'                 \NC FractionDelimiterDisplayStyleSize$^9$    \NC delim1 \NC \NR
 361 \NC                                   \NC T, T', S, S', SS, SS' \NC FractionDelimiterSize$^9$                \NC delim2 \NC \NR
 362 \NC \type {\Umathfractiondenomdown}   \NC D, D'                 \NC FractionDenominatorDisplayStyleShiftDown \NC denom1 \NC \NR
 363 \NC                                   \NC T, T', S, S', SS, SS' \NC FractionDenominatorShiftDown             \NC denom2 \NC \NR
 364 \NC \type {\Umathfractiondenomvgap}   \NC D, D'                 \NC FractionDenominatorDisplayStyleGapMin    \NC 3*default_rule_thickness \NC \NR
 365 \NC                                   \NC T, T', S, S', SS, SS' \NC FractionDenominatorGapMin                \NC default_rule_thickness \NC \NR
 366 \NC \type {\Umathfractionnumup}       \NC D, D'                 \NC FractionNumeratorDisplayStyleShiftUp     \NC num1 \NC \NR
 367 \NC                                   \NC T, T', S, S', SS, SS' \NC FractionNumeratorShiftUp                 \NC num2 \NC \NR
 368 \NC \type {\Umathfractionnumvgap}     \NC D, D'                 \NC FractionNumeratorDisplayStyleGapMin      \NC 3*default_rule_thickness \NC \NR
 369 \NC                                   \NC T, T', S, S', SS, SS' \NC FractionNumeratorGapMin                  \NC default_rule_thickness \NC \NR
 370 \NC \type {\Umathfractionrule}        \NC --                    \NC FractionRuleThickness                    \NC default_rule_thickness \NC \NR
 371 \NC \type {\Umathskewedfractionhgap}  \NC --                    \NC SkewedFractionHorizontalGap              \NC math_quad/2 \NC \NR
 372 \NC \type {\Umathskewedfractionvgap}  \NC --                    \NC SkewedFractionVerticalGap                \NC math_x_height \NC \NR
 373 \NC \type {\Umathlimitabovebgap}      \NC --                    \NC UpperLimitBaselineRiseMin                \NC big_op_spacing3 \NC \NR
 374 \NC \type {\Umathlimitabovekern}      \NC --                    \NC 0$^1$                                    \NC big_op_spacing5 \NC \NR
 375 \NC \type {\Umathlimitabovevgap}      \NC --                    \NC UpperLimitGapMin                         \NC big_op_spacing1 \NC \NR
 376 \NC \type {\Umathlimitbelowbgap}      \NC --                    \NC LowerLimitBaselineDropMin                \NC big_op_spacing4 \NC \NR
 377 \NC \type {\Umathlimitbelowkern}      \NC --                    \NC 0$^1$                                    \NC big_op_spacing5 \NC \NR
 378 \NC \type {\Umathlimitbelowvgap}      \NC --                    \NC LowerLimitGapMin                         \NC big_op_spacing2 \NC \NR
 379 \NC \type {\Umathoverdelimitervgap}   \NC --                    \NC StretchStackGapBelowMin                  \NC big_op_spacing1 \NC \NR
 380 \NC \type {\Umathoverdelimiterbgap}   \NC --                    \NC StretchStackTopShiftUp                   \NC big_op_spacing3 \NC \NR
 381 \NC \type {\Umathunderdelimitervgap}  \NC--                     \NC StretchStackGapAboveMin                  \NC big_op_spacing2 \NC \NR
 382 \NC \type {\Umathunderdelimiterbgap}  \NC--                     \NC StretchStackBottomShiftDown              \NC big_op_spacing4 \NC \NR
 383 \NC \type {\Umathoverbarkern}         \NC --                    \NC OverbarExtraAscender                     \NC default_rule_thickness \NC \NR
 384 \NC \type {\Umathoverbarrule}         \NC --                    \NC OverbarRuleThickness                     \NC default_rule_thickness \NC \NR
 385 \NC \type {\Umathoverbarvgap}         \NC --                    \NC OverbarVerticalGap                       \NC 3*default_rule_thickness \NC \NR
 386 \NC \type {\Umathquad}                \NC --                    \NC <font_size(f)>$^1$                       \NC math_quad \NC \NR
 387 \NC \type {\Umathradicalkern}         \NC --                    \NC RadicalExtraAscender                     \NC default_rule_thickness \NC \NR
 388 \NC \type {\Umathradicalrule}         \NC --                    \NC RadicalRuleThickness                     \NC <not set>$^2$ \NC \NR
 389 \NC \type {\Umathradicalvgap}         \NC D, D'                 \NC RadicalDisplayStyleVerticalGap           \NC (default_rule_thickness+\crlf
 390                                                                                                                  (abs(math_x_height)/4))$^3$ \NC \NR
 391 \NC                                   \NC T, T', S, S', SS, SS' \NC RadicalVerticalGap                       \NC (default_rule_thickness+\crlf
 392                                                                                                                  (abs(default_rule_thickness)/4))$^3$ \NC \NR
 393 \NC \type {\Umathradicaldegreebefore} \NC --                    \NC RadicalKernBeforeDegree                  \NC <not set>$^2$ \NC \NR
 394 \NC \type {\Umathradicaldegreeafter}  \NC --                    \NC RadicalKernAfterDegree                   \NC <not set>$^2$ \NC \NR
 395 \NC \type {\Umathradicaldegreeraise}  \NC --                    \NC RadicalDegreeBottomRaisePercent          \NC <not set>$^{2,7}$ \NC \NR
 396 \NC \type {\Umathspaceafterscript}    \NC --                    \NC SpaceAfterScript                         \NC script_space$^4$ \NC \NR
 397 \NC \type {\Umathstackdenomdown}      \NC D, D'                 \NC StackBottomDisplayStyleShiftDown         \NC denom1 \NC \NR
 398 \NC                                   \NC T, T', S, S', SS, SS' \NC StackBottomShiftDown                     \NC denom2 \NC \NR
 399 \NC \type {\Umathstacknumup}          \NC D, D'                 \NC StackTopDisplayStyleShiftUp              \NC num1 \NC \NR
 400 \NC                                   \NC T, T', S, S', SS, SS' \NC StackTopShiftUp                          \NC num3 \NC \NR
 401 \NC \type {\Umathstackvgap}           \NC D, D'                 \NC StackDisplayStyleGapMin                  \NC 7*default_rule_thickness \NC \NR
 402 \NC                                   \NC T, T', S, S', SS, SS' \NC StackGapMin                              \NC 3*default_rule_thickness \NC \NR
 403 \NC \type {\Umathsubshiftdown}        \NC --                    \NC SubscriptShiftDown                       \NC sub1 \NC \NR
 404 \NC \type {\Umathsubshiftdrop}        \NC --                    \NC SubscriptBaselineDropMin                 \NC sub_drop \NC \NR
 405 \NC \type {\Umathsubsupshiftdown}     \NC --                    \NC SubscriptShiftDownWithSuperscript$^8$    \NC \NC \NR
 406 \NC                                   \NC                       \NC \quad\ or SubscriptShiftDown             \NC sub2 \NC \NR
 407 \NC \type {\Umathsubtopmax}           \NC --                    \NC SubscriptTopMax                          \NC (abs(math_x_height * 4) / 5) \NC \NR
 408 \NC \type {\Umathsubsupvgap}          \NC --                    \NC SubSuperscriptGapMin                     \NC 4*default_rule_thickness \NC \NR
 409 \NC \type {\Umathsupbottommin}        \NC --                    \NC SuperscriptBottomMin                     \NC (abs(math_x_height) / 4) \NC \NR
 410 \NC \type {\Umathsupshiftdrop}        \NC --                    \NC SuperscriptBaselineDropMax               \NC sup_drop \NC \NR
 411 \NC \type {\Umathsupshiftup}          \NC D                     \NC SuperscriptShiftUp                       \NC sup1 \NC \NR
 412 \NC                                   \NC T, S, SS,             \NC SuperscriptShiftUp                       \NC sup2 \NC \NR
 413 \NC                                   \NC D', T', S', SS'       \NC SuperscriptShiftUpCramped                \NC sup3 \NC \NR
 414 \NC \type {\Umathsupsubbottommax}     \NC --                    \NC SuperscriptBottomMaxWithSubscript        \NC (abs(math_x_height * 4) / 5) \NC \NR
 415 \NC \type {\Umathunderbarkern}        \NC --                    \NC UnderbarExtraDescender                   \NC default_rule_thickness \NC \NR
 416 \NC \type {\Umathunderbarrule}        \NC --                    \NC UnderbarRuleThickness                    \NC default_rule_thickness \NC \NR
 417 \NC \type {\Umathunderbarvgap}        \NC --                    \NC UnderbarVerticalGap                      \NC 3*default_rule_thickness \NC \NR
 418 \NC \type {\Umathconnectoroverlapmin} \NC --                    \NC MinConnectorOverlap                      \NC 0$^5$ \NC \NR
 419 \stoptabulate
 420
 421 \stop
 422
 423 Note 1: \OPENTYPE\ fonts set \type {\Umathlimitabovekern} and \type
 424 {\Umathlimitbelowkern} to zero and set \type {\Umathquad} to the font size of the
 425 used font, because these are not supported in the \type {MATH} table,
 426
 427 Note 2: Traditional \TFM\ fonts do not set \type {\Umathradicalrule} because
 428 \TEX82\ uses the height of the radical instead. When this parameter is indeed not
 429 set when \LUATEX\ has to typeset a radical, a backward compatibility mode will
 430 kick in that assumes that an oldstyle \TEX\ font is used. Also, they do not set
 431 \type {\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type
 432 {\Umathradicaldegreeraise}. These are then automatically initialized to
 433 $5/18$quad, $-10/18$quad, and 60.
 434
 435 Note 3: If \TFM\ fonts are used, then the \type {\Umathradicalvgap} is not set
 436 until the first time \LUATEX\ has to typeset a formula because this needs
 437 parameters from both family~2 and family~3. This provides a partial backward
 438 compatibility with \TEX82, but that compatibility is only partial: once the \type
 439 {\Umathradicalvgap} is set, it will not be recalculated any more.
 440
 441 Note 4: When \TFM\ fonts are used a similar situation arises with respect to
 442 \type {\Umathspaceafterscript}: it is not set until the first time \LUATEX\ has
 443 to typeset a formula. This provides some backward compatibility with \TEX82. But
 444 once the \type {\Umathspaceafterscript} is set, \type {\scriptspace} will never
 445 be looked at again.
 446
 447 Note 5: Traditional \TFM\ fonts set \type {\Umathconnectoroverlapmin} to zero
 448 because \TEX82\ always stacks extensibles without any overlap.
 449
 450 Note 6: The \type {\Umathoperatorsize} is only used in \type {\displaystyle}, and
 451 is only set in \OPENTYPE\ fonts. In \TFM\ font mode, it is artificially set to
 452 one scaled point more than the initial attempt's size, so that always the \quote
 453 {first next} will be tried, just like in \TEX82.
 454
 455 Note 7: The \type {\Umathradicaldegreeraise} is a special case because it is the
 456 only parameter that is expressed in a percentage instead of as a number of scaled
 457 points.
 458
 459 Note 8: \type {SubscriptShiftDownWithSuperscript} does not actually exist in the
 460 \quote {standard} \OPENTYPE\ math font Cambria, but it is useful enough to be
 461 added.
 462
 463 Note 9: \type {FractionDelimiterDisplayStyleSize} and \type
 464 {FractionDelimiterSize} do not actually exist in the \quote {standard} \OPENTYPE\
 465 math font Cambria, but were useful enough to be added.
 466
 467 \section{Math spacing setting}
 468
 469 Besides the parameters mentioned in the previous sections, there are also 64 new
 470 primitives to control the math spacing table (as explained in Chapter~18 of the
 471 \TEX book). The primitive names are a simple matter of combining two math atom
 472 types, but for completeness' sake, here is the whole list:
 473
 474 \starttwocolumns
 475 \starttyping
 476 \Umathordordspacing
 477 \Umathordopspacing
 478 \Umathordbinspacing
 479 \Umathordrelspacing
 480 \Umathordopenspacing
 481 \Umathordclosespacing
 482 \Umathordpunctspacing
 483 \Umathordinnerspacing
 484 \Umathopordspacing
 485 \Umathopopspacing
 486 \Umathopbinspacing
 487 \Umathoprelspacing
 488 \Umathopopenspacing
 489 \Umathopclosespacing
 490 \Umathoppunctspacing
 491 \Umathopinnerspacing
 492 \Umathbinordspacing
 493 \Umathbinopspacing
 494 \Umathbinbinspacing
 495 \Umathbinrelspacing
 496 \Umathbinopenspacing
 497 \Umathbinclosespacing
 498 \Umathbinpunctspacing
 499 \Umathbininnerspacing
 500 \Umathrelordspacing
 501 \Umathrelopspacing
 502 \Umathrelbinspacing
 503 \Umathrelrelspacing
 504 \Umathrelopenspacing
 505 \Umathrelclosespacing
 506 \Umathrelpunctspacing
 507 \Umathrelinnerspacing
 508 \Umathopenordspacing
 509 \Umathopenopspacing
 510 \Umathopenbinspacing
 511 \Umathopenrelspacing
 512 \Umathopenopenspacing
 513 \Umathopenclosespacing
 514 \Umathopenpunctspacing
 515 \Umathopeninnerspacing
 516 \Umathcloseordspacing
 517 \Umathcloseopspacing
 518 \Umathclosebinspacing
 519 \Umathcloserelspacing
 520 \Umathcloseopenspacing
 521 \Umathcloseclosespacing
 522 \Umathclosepunctspacing
 523 \Umathcloseinnerspacing
 524 \Umathpunctordspacing
 525 \Umathpunctopspacing
 526 \Umathpunctbinspacing
 527 \Umathpunctrelspacing
 528 \Umathpunctopenspacing
 529 \Umathpunctclosespacing
 530 \Umathpunctpunctspacing
 531 \Umathpunctinnerspacing
 532 \Umathinnerordspacing
 533 \Umathinneropspacing
 534 \Umathinnerbinspacing
 535 \Umathinnerrelspacing
 536 \Umathinneropenspacing
 537 \Umathinnerclosespacing
 538 \Umathinnerpunctspacing
 539 \Umathinnerinnerspacing
 540 \stoptyping
 541 \stoptwocolumns
 542
 543 These parameters are of type \type {\muskip}, so setting a parameter can be done
 544 like this:
 545
 546 \starttyping
 547 \Umathopordspacing\displaystyle=4mu plus 2mu
 548 \stoptyping
 549
 550 They are all initialized by \type {initex} to the values mentioned in the table
 551 in Chapter~18 of the \TEX book.
 552
 553 Note 1: for ease of use as well as for backward compatibility, \type
 554 {\thinmuskip}, \type {\medmuskip} and \type {\thickmuskip} are treated
 555 especially. In their case a pointer to the corresponding internal parameter is
 556 saved, not the actual \type {\muskip} value. This means that any later changes to
 557 one of these three parameters will be taken into account.
 558
 559 Note 2: Careful readers will realise that there are also primitives for the items
 560 marked \type {*} in the \TEX book. These will not actually be used as those
 561 combinations of atoms cannot actually happen, but it seemed better not to break
 562 orthogonality. They are initialized to zero.
 563
 564 \section[mathacc]{Math accent handling}
 565
 566 \LUATEX\ supports both top accents and bottom accents in math mode, and math
 567 accents stretch automatically (if this is supported by the font the accent comes
 568 from, of course). Bottom and combined accents as well as fixed-width math accents
 569 are controlled by optional keywords following \type {\Umathaccent}.
 570
 571 The keyword \type {bottom} after \type {\Umathaccent} signals that a bottom accent
 572 is needed, and the keyword \type {both} signals that both a top and a bottom
 573 accent are needed (in this case two accents need to be specified, of course).
 574
 575 Then the set of three integers defining the accent is read. This set of integers
 576 can be prefixed by the \type {fixed} keyword to indicate that a non-stretching
 577 variant is requested (in case of both accents, this step is repeated).
 578
 579 A simple example:
 580
 581 \starttyping
 582 \Umathaccent both fixed 0 0 "20D7 fixed 0 0 "20D7 {example}
 583 \stoptyping
 584
 585 If a math top accent has to be placed and the accentee is a character and has a
 586 non-zero \type {top_accent} value, then this value will be used to place the
 587 accent instead of the \type {\skewchar} kern used by \TEX82.
 588
 589 The \type {top_accent} value represents a vertical line somewhere in the
 590 accentee. The accent will be shifted horizontally such that its own \type
 591 {top_accent} line coincides with the one from the accentee. If the \type
 592 {top_accent} value of the accent is zero, then half the width of the accent
 593 followed by its italic correction is used instead.
 594
 595 The vertical placement of a top accent depends on the \type {x_height} of the
 596 font of the accentee (as explained in the \TEX book), but if value that turns out
 597 to be zero and the font had a \type {MathConstants} table, then \type
 598 {AccentBaseHeight} is used instead.
 599
 600 The vertical placement of a bottom accent is straight below the accentee, no
 601 correction takes place.
 602
 603 Possible locations are \type {top}, \type {bottom}, \type {both} and \type
 604 {center}. When no location is given \type {top} is assumed. An additional
 605 parameter \type {fraction} can be specified followed by a number; a value of for
 606 instance 1200 means that the criterium is 1.2 times the width of the nuclues. The
 607 fraction only applies to the stepwise selected shapes and is mostly meant for the
 608 \type {overlay} location. It also works for the other locations but then it
 609 concerns the width.
 610
 611 \section{Math root extension}
 612
 613 The new primitive \type {\Uroot} allows the construction of a radical noad
 614 including a degree field. Its syntax is an extension of \type {\Uradical}:
 615
 616 \starttyping
 617 \Uradical <fam integer> <char integer> <radicand>
 618 \Uroot    <fam integer> <char integer> <degree> <radicand>
 619 \stoptyping
 620
 621 The placement of the degree is controlled by the math parameters \type
 622 {\Umathradicaldegreebefore}, \type {\Umathradicaldegreeafter}, and \type
 623 {\Umathradicaldegreeraise}. The degree will be typeset in \type
 624 {\scriptscriptstyle}.
 625
 626 \section{Math kerning in super- and subscripts}
 627
 628 The character fields in a \LUA|-|loaded \OPENTYPE\ math font can have a \quote
 629 {mathkern} table. The format of this table is the same as the \quote {mathkern}
 630 table that is returned by the \type {fontloader} library, except that all height
 631 and kern values have to be specified in actual scaled points.
 632
 633 When a super- or subscript has to be placed next to a math item, \LUATEX\ checks
 634 whether the super- or subscript and the nucleus are both simple character items.
 635 If they are, and if the fonts of both character items are \OPENTYPE\ fonts (as
 636 opposed to legacy \TEX\ fonts), then \LUATEX\ will use the \OPENTYPE\ math
 637 algorithm for deciding on the horizontal placement of the super- or subscript.
 638
 639 This works as follows:
 640
 641 \startitemize
 642     \startitem
 643         The vertical position of the script is calculated.
 644     \stopitem
 645     \startitem
 646         The default horizontal position is flat next to the base character.
 647     \stopitem
 648     \startitem
 649         For superscripts, the italic correction of the base character is added.
 650     \stopitem
 651     \startitem
 652         For a superscript, two vertical values are calculated: the bottom of the
 653         script (after shifting up), and the top of the base. For a subscript, the two
 654         values are the top of the (shifted down) script, and the bottom of the base.
 655     \stopitem
 656     \startitem
 657         For each of these two locations:
 658         \startitemize
 659             \startitem
 660                 find the math kern value at this height for the base (for a subscript
 661                 placement, this is the bottom_right corner, for a superscript
 662                 placement the top_right corner)
 663             \stopitem
 664             \startitem
 665                 find the math kern value at this height for the script (for a
 666                 subscript placement, this is the top_left corner, for a superscript
 667                 placement the bottom_left corner)
 668             \stopitem
 669             \startitem
 670                 add the found values together to get a preliminary result.
 671             \stopitem
 672         \stopitemize
 673     \stopitem
 674     \startitem
 675         The horizontal kern to be applied is the smallest of the two results from
 676         previous step.
 677     \stopitem
 678 \stopitemize
 679
 680 The math kern value at a specific height is the kern value that is specified by the
 681 next higher height and kern pair, or the highest one in the character (if there is no
 682 value high enough in the character), or simply zero (if the character has no math kern
 683 pairs at all).
 684
 685 \section{Scripts on horizontally extensible items like arrows}
 686
 687 The primitives \type {\Uunderdelimiter} and \type {\Uoverdelimiter} allow the
 688 placement of a subscript or superscript on an automatically extensible item and
 689 \type {\Udelimiterunder} and \type {\Udelimiterover} allow the placement of an
 690 automatically extensible item as a subscript or superscript on a nucleus. The
 691 input:
 692
 693 % these produce radical noads .. in fact the code base has the numbers wrong for
 694 % quite a while, so no one seems to use this
 695
 696 \startbuffer
 697 $\Uoverdelimiter  0 "2194 {\hbox{\strut  overdelimiter}}$
 698 $\Uunderdelimiter 0 "2194 {\hbox{\strut underdelimiter}}$
 699 $\Udelimiterover  0 "2194 {\hbox{\strut  delimiterover}}$
 700 $\Udelimiterunder 0 "2194 {\hbox{\strut delimiterunder}}$
 701 \stopbuffer
 702
 703 \typebuffer will render this:
 704
 705 \blank \startnarrower \getbuffer \stopnarrower \blank
 706
 707 The vertical placements are controlled by \type {\Umathunderdelimiterbgap}, \type
 708 {\Umathunderdelimitervgap}, \type {\Umathoverdelimiterbgap}, and \type
 709 {\Umathoverdelimitervgap} in a similar way as limit placements on large operators.
 710 The superscript in \type {\Uoverdelimiter} is typeset in a suitable scripted style,
 711 the subscript in \type {\Uunderdelimiter} is cramped as well.
 712
 713 These primitives accepts an option \type {width} specification. When used the
 714 also optional keywords \type {left}, \type {middle} and \type {right} will
 715 determine what happens when a requested size can't be met (which can happen when
 716 we step to successive larger variants).
 717
 718 An extra primitive \type {\Uhextensible} is available that can be used like this:
 719
 720 \startbuffer
 721 $\Uhextensible width 10cm 0 "2194$
 722 \stopbuffer
 723
 724 \typebuffer This will render this:
 725
 726 \blank \startnarrower \getbuffer \stopnarrower \blank
 727
 728 Here you can also pass options, like:
 729
 730 \startbuffer
 731 $\Uhextensible width 1pt middle 0 "2194$
 732 \stopbuffer
 733
 734 \typebuffer This gives:
 735
 736 \blank \startnarrower \getbuffer \stopnarrower \blank
 737
 738 \LUATEX\ internally uses a structure that supports \OPENTYPE\ \quote
 739 {MathVariants} as well as \TFM\ \quote {extensible recipes}. In most cases where
 740 font metrics are involved we have a different code path for traditional fonts end
 741 \OPENTYPE\ fonts.
 742
 743 \section {Extracting values}
 744
 745 You can extract the components of a math character. Say that we have defined:
 746
 747 \starttyping
 748 \Umathcode 1 2 3 4
 749 \stoptyping
 750
 751 then
 752
 753 \starttyping
 754 [\Umathcharclass1] [\Umathcharfam1] [\Umathcharslot1]
 755 \stoptyping
 756
 757 will return:
 758
 759 \starttyping
 760 [2] [3] [4]
 761 \stoptyping
 762
 763 These commands are provides as convenience. Before they came available you could
 764 do the following:
 765
 766 \starttyping
 767 \def\Umathcharclass{\directlua{tex.print(tex.getmathcode(token.scan_int())[1])}}
 768 \def\Umathcharfam  {\directlua{tex.print(tex.getmathcode(token.scan_int())[2])}}
 769 \def\Umathcharslot {\directlua{tex.print(tex.getmathcode(token.scan_int())[3])}}
 770 \stoptyping
 771
 772 \section{fractions}
 773
 774 The \type {\abovewithdelims} command accepts a keyword \type {exact}. When issued
 775 the extra space relative to the rule thickness is not added. One can of course
 776 use the \type {\Umathfraction..gap} commands to influence the spacing. Also the
 777 rule is still positioned around the math axis.
 778
 779 \starttyping
 780 $$ { {a} \abovewithdelims() exact 4pt {b} }$$
 781 \stoptyping
 782
 783 The math parameter table contains some parameters that specify a horizontal and
 784 vertical gap for skewed fractions. Of course some guessing is needed in order to
 785 implement something that uses them. And so we now provide a primitive similar to the
 786 other fraction related ones but with a few options so that one can influence the
 787 rendering. Of course a user can also mess around a bit with the parameters
 788 \type {\Umathskewedfractionhgap} and \type {\Umathskewedfractionvgap}.
 789
 790 The syntax used here is:
 791
 792 \starttyping
 793 { {1} \Uskewed / <options> {2} }
 794 { {1} \Uskewedwithdelims / () <options> {2} }
 795 \stoptyping
 796
 797 where the options can be \type {noaxis} and \type {exact}. By default we add half
 798 the axis to the shifts and by default we zero the width of the middle character.
 799 For Latin Modern The result looks as follows:
 800
 801 \def\ShowA#1#2#3{$x + { {#1} \Uskewed           /    #3 {#2} } + x$}
 802 \def\ShowB#1#2#3{$x + { {#1} \Uskewedwithdelims / () #3 {#2} } + x$}
 803
 804 \start
 805     \switchtobodyfont[modern]
 806     \starttabulate[||||||]
 807         \NC \NC
 808             \ShowA{a}{b}{} \NC
 809             \ShowA{1}{2}{} \NC
 810             \ShowB{a}{b}{} \NC
 811             \ShowB{1}{2}{} \NC
 812         \NR
 813         \NC \type{exact} \NC
 814             \ShowA{a}{b}{exact} \NC
 815             \ShowA{1}{2}{exact} \NC
 816             \ShowB{a}{b}{exact} \NC
 817             \ShowB{1}{2}{exact} \NC
 818         \NR
 819         \NC \type{noaxis} \NC
 820             \ShowA{a}{b}{noaxis} \NC
 821             \ShowA{1}{2}{noaxis} \NC
 822             \ShowB{a}{b}{noaxis} \NC
 823             \ShowB{1}{2}{noaxis} \NC
 824         \NR
 825         \NC \type{exact noaxis} \NC
 826             \ShowA{a}{b}{exact noaxis} \NC
 827             \ShowA{1}{2}{exact noaxis} \NC
 828             \ShowB{a}{b}{exact noaxis} \NC
 829             \ShowB{1}{2}{exact noaxis} \NC
 830         \NR
 831     \stoptabulate
 832 \stop
 833
 834 \section {Other Math changes}
 835
 836 \subsection {Verbose versions of single-character math commands}
 837
 838 \LUATEX\ defines six new primitives that have the same function as
 839 \type {^}, \type {_}, \type {$}, and \type {$$}: %$
 840
 841 \starttabulate[|l|l|l|l|]
 842 \NC \bf primitive           \NC \bf explanation \NC \NR
 843 \NC \type {\Usuperscript}      \NC Duplicates the functionality of \type {^} \NC \NR
 844 \NC \type {\Usubscript}        \NC Duplicates the functionality of \type {_} \NC \NR
 845 \NC \type {\Ustartmath}        \NC Duplicates the functionality of \type {$}, % $
 846                                    when used in non-math mode. \NC \NR
 847 \NC \type {\Ustopmath}         \NC Duplicates the functionality of \type {$}, % $
 848                                    when used in inline math mode. \NC \NR
 849 \NC \type {\Ustartdisplaymath} \NC Duplicates the functionality of \type {$$}, % $$
 850                                    when used in non-math mode. \NC \NR
 851 \NC \type {\Ustopdisplaymath}  \NC Duplicates the functionality of \type {$$}, % $$
 852                                    when used in display math mode. \NC \NR
 853 \stoptabulate
 854
 855 The \type {\Ustopmath} and \type {\Ustopdisplaymath} primitives check if the current
 856 math mode is the correct one (inline vs.\ displayed), but you can freely intermix
 857 the four mathon|/|mathoff commands with explicit dollar sign(s).
 858
 859 \subsection{Allowed math commands in non-math modes}
 860
 861 The commands \type {\mathchar}, and \type {\Umathchar} and control sequences that
 862 are the result of \type {\mathchardef} or \type {\Umathchardef} are also
 863 acceptable in the horizontal and vertical modes. In those cases, the \type
 864 {\textfont} from the requested math family is used.
 865
 866 \section{Math surrounding skips}
 867
 868 Inline math is surrounded by (optional) \type {\mathsurround} spacing but that is fixed
 869 dimension. There is now an additional parameter \type {\mathsurroundskip}. When set to a
 870 non|-|zero value (or zero with some stretch or shrink) this parameter will replace
 871 \type {\mathsurround}. By using an additional parameter instead of changing the nature
 872 of \type {\mathsurround}, we can remain compatible.
 873
 874 % \section{Math todo}
 875 %
 876 % The following items are still todo.
 877 %
 878 % \startitemize
 879 % \startitem
 880 %     Pre-scripts.
 881 % \stopitem
 882 % \startitem
 883 %     Multi-story stacks.
 884 % \stopitem
 885 % \startitem
 886 %     Flattened accents for high characters (maybe).
 887 % \stopitem
 888 % \startitem
 889 %     Better control over the spacing around displays and handling of equation numbers.
 890 % \stopitem
 891 % \startitem
 892 %     Support for multi|-|line displays using \MATHML\ style alignment points.
 893 % \stopitem
 894 % \stopitemize
 895
 896 \subsection {Delimiters: \type{\Uleft}, \type {\Umiddle} and \type {\Uright}}
 897
 898 Normally you will force delimiters to certain sizes by putting an empty box or
 899 rule next to it. The resulting delimiter will either be a character from the
 900 stepwise size range or an extensible. The latter can be quite differently
 901 positioned that the characters as it depends on the fit as well as the fact if
 902 the used characters in the font have depth or height. Commands like (plain \TEX
 903 s) \type {\big} need use this feature. In \LUATEX\ we provide a bit more control
 904 by three variants that supporting optional parameters \type {height}, \type
 905 {depth} and \type {axis}. The following example uses this:
 906
 907 \startbuffer
 908 \Uleft   height 30pt depth 10pt      \Udelimiter "0 "0 "000028
 909 \quad x\quad
 910 \Umiddle height 40pt depth 15pt      \Udelimiter "0 "0 "002016
 911 \quad x\quad
 912 \Uright  height 30pt depth 10pt      \Udelimiter "0 "0 "000029
 913 \quad \quad \quad
 914 \Uleft   height 30pt depth 10pt axis \Udelimiter "0 "0 "000028
 915 \quad x\quad
 916 \Umiddle height 40pt depth 15pt axis \Udelimiter "0 "0 "002016
 917 \quad x\quad
 918 \Uright  height 30pt depth 10pt axis \Udelimiter "0 "0 "000029
 919 \stopbuffer
 920
 921 \typebuffer
 922
 923 \startlinecorrection
 924 \ruledhbox{\mathematics{\getbuffer}}
 925 \stoplinecorrection
 926
 927 The keyword \type {exact} can be used as directive that the real dimensions
 928 should be applied when the criteria can't be met which can happen when we're
 929 still stepping through the successively larger variants. When no dimensions are
 930 given the \type {noaxis} command can be used to prevent shifting over the axis.
 931
 932 You can influence the final class with the keyword \type {class} which will
 933 influence the spacing.
 934
 935 \subsection{Fixed scripts}
 936
 937 We have three parameters that are used for this fixed anchoring:
 938
 939 \starttabulate[|l|l|]
 940 \NC $d$ \NC \type {\Umathsubshiftdown}    \NC \NR
 941 \NC $u$ \NC \type {\Umathsupshiftup}      \NC \NR
 942 \NC $s$ \NC \type {\Umathsubsupshiftdown} \NC \NR
 943 \stoptabulate
 944
 945 When we set \type {\mathscriptsmode} to a value other than zero these are used
 946 for calculating fixed positions. This is something that is needed for instance
 947 for chemistry. You can manipulate the mentioned variables to achive different
 948 effects.
 949
 950 \def\SampleMath#1%
 951   {$\mathscriptsmode#1\mathupright CH_2 + CH^+_2 + CH^2_2$}
 952
 953 \starttabulate[|c|c|c|l|]
 954 \NC \bf mode \NC \bf down      \NC \bf up        \NC                \NC \NR
 955 \NC 0        \NC dynamic       \NC dynamic       \NC \SampleMath{0} \NC \NR
 956 \NC 1        \NC $d$           \NC $u$           \NC \SampleMath{1} \NC \NR
 957 \NC 2        \NC $s$           \NC $u$           \NC \SampleMath{2} \NC \NR
 958 \NC 3        \NC $s$           \NC $u + s - d$   \NC \SampleMath{3} \NC \NR
 959 \NC 4        \NC $d + (s-d)/2$ \NC $u + (s-d)/2$ \NC \SampleMath{4} \NC \NR
 960 \NC 5        \NC $d$           \NC $u + s - d$   \NC \SampleMath{5} \NC \NR
 961 \stoptabulate
 962
 963 The value of this parameter obeys grouping but applies to the whole current
 964 formula.
 965
 966 % if needed we can put the value in stylenodes but maybe more should go there
 967
 968 \subsection {Tracing}
 969
 970 Because there are quite some math related parameters and values, it is possible
 971 to limit tracing. Only when \type {tracingassigns} and|/|or \type
 972 {tracingrestores} are set to~2 or more they will be traced.
 973
 974 \subsection {Math options}
 975
 976 The logic in the math engine is rather complex and there are often no universal
 977 solutions (read: what works out well for one font, fails for another). Therefore
 978 some variations in the implementation will be driven by options for which a new
 979 primitive \type {\mathoption} has been introduced (so that we don't end up with
 980 many new commands). The approach of options also permits us to see what effect a
 981 specific solution has.
 982
 983 \subsubsection {\type {\mathoption noitaliccompensation}}
 984
 985 This option compensates placement for characters with a built|-|in italic
 986 correction.
 987
 988 \startbuffer
 989 {\showboxes\int}\quad
 990 {\showboxes\int_{|}^{|}}\quad
 991 {\showboxes\int\limits_{|}^{|}}
 992 \stopbuffer
 993
 994 \typebuffer
 995
 996 Gives (with computer modern that has such italics):
 997
 998 \startlinecorrection[blank]
 999     \switchtobodyfont[modern]
1000     \startcombination[nx=2,ny=2,distance=5em]
1001         {\mathoption noitaliccompensation 0\relax \mathematics{\getbuffer}}
1002             {\nohyphens\type{0:inline}}
1003         {\mathoption noitaliccompensation 0\relax \mathematics{\displaymath\getbuffer}}
1004             {\nohyphens\type{0:display}}
1005         {\mathoption noitaliccompensation 1\relax \mathematics{\getbuffer}}
1006             {\nohyphens\type{1:inline}}
1007         {\mathoption noitaliccompensation 1\relax \mathematics{\displaymath\getbuffer}}
1008             {\nohyphens\type{1:display}}
1009     \stopcombination
1010 \stoplinecorrection
1011
1012 \subsubsection {\type {\mathoption nocharitalic}}
1013
1014 When two characters follow each other italic correction can interfere. The
1015 following example shows what this option does:
1016
1017 \startbuffer
1018 \catcode"1D443=11
1019 \catcode"1D444=11
1020 \catcode"1D445=11
1021 P( PP PQR
1022 \stopbuffer
1023
1024 \typebuffer
1025
1026 Gives (with computer modern that has such italics):
1027
1028 \startlinecorrection[blank]
1029     \switchtobodyfont[modern]
1030     \startcombination[nx=2,ny=2,distance=5em]
1031         {\mathoption nocharitalic 0\relax \mathematics{\getbuffer}}
1032             {\nohyphens\type{0:inline}}
1033         {\mathoption nocharitalic 0\relax \mathematics{\displaymath\getbuffer}}
1034             {\nohyphens\type{0:display}}
1035         {\mathoption nocharitalic 1\relax \mathematics{\getbuffer}}
1036             {\nohyphens\type{1:inline}}
1037         {\mathoption nocharitalic 1\relax \mathematics{\displaymath\getbuffer}}
1038             {\nohyphens\type{1:display}}
1039     \stopcombination
1040 \stoplinecorrection
1041
1042 \subsubsection {\type {\mathoption useoldfractionscaling}}
1043
1044 This option has been introduced as solution for tracker item 604 for fuzzy cases
1045 around either or not present fraction related settings for new fonts.
1046
1047 \stopchapter
1048
1049 \stopcomponent