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