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Diffstat (limited to 'include/include/mathf')
| -rw-r--r-- | include/include/mathf | 2944 |
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diff --git a/include/include/mathf b/include/include/mathf deleted file mode 100644 index 523504a..0000000 --- a/include/include/mathf +++ /dev/null @@ -1,2944 +0,0 @@ - -############################################################################### -# # -# Lout @Math package for formatting mathematics # -# # -# @Math is based on the earlier @Eq package. @Eq revision history: # -# # -# Version 1.0 by Jeffrey H. Kingston, December 1990. # -# Version 2.0 by Jeffrey H. Kingston, 22 December 1992. # -# Version 3.0 by Jeffrey H. Kingston and Robert Marsa, March 1996. # -# # -# @Math revision history: # -# # -# Version 4.0 by Ludovic Courtès, June 2007. # -# Version 5.0 by Jeffrey H. Kingston, September 2008. # -# # -# Acknowledgement: @Eq and @Math are based closely on the Eqn language # -# of B. W. Kernighan and L. L. Cherry; the spacing rules are similar to # -# those of the TeX system by D. E. Knuth. # -# # -# Version 4.0 makes use of `@SetContext' and `@GetContext' (introduced in # -# Lout 3.34) to better honor the typesetting conventions outlined by Knuth. # -# # -# This program is free software; you can redistribute it and/or modify # -# it under the terms of the GNU General Public License as published by # -# the Free Software Foundation; either Version 3, or (at your option) # -# any later version. # -# # -# This program is distributed in the hope that it will be useful, # -# but WITHOUT ANY WARRANTY; without even the implied warranty of # -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # -# GNU General Public License for more details. # -# # -# You should have received a copy of the GNU General Public License # -# along with this program; if not, write to the Free Software # -# Foundation, Inc., 59 Temple Place, Suite 330, Boston MA 02111-1307 USA # -# # -# As a special exception, when this file is read by Lout when processing # -# a Lout source document, you may use the result without restriction. # -# # -############################################################################### - -export - - # Helper symbols - above below wideabove widebelow - "`" "``" "```" non big small vctr - @SuperScriptStyle @SubScriptStyle @NumeratorStyle - @DenominatorStyle @SquareRootStyle - - # Ordinary symbols (Symbol font) - space exclam universal numbersign existential percent - ampersand suchthat parenleft parenright asteriskmath - plus comma minus period slash zero one two three four - five six seven eight nine colon semicolon less equal - greater question congruent Alpha Beta Chi Delta Epsilon - Phi Gamma Eta Iota thetaone Kappa Lambda Mu Nu Omicron - Pi Theta Rho Sigma Tau Upsilon sigmaone Omega Xi Psi Zeta - bracketleft therefore bracketright perpendicular underscore - radicalex alpha beta chi delta epsilon phi gamma eta iota - phione kappa lambda mu nu omicron pi theta rho sigma tau - upsilon omegaone omega xi psi zeta braceleft bar braceright - similar Upsilonone minute lessequal fraction infinity florin - club diamond heart spade arrowboth arrowleft arrowup - arrowright arrowdown degree plusminus second greaterequal - multiply proportional partialdiff bullet divide notequal - equivalence approxequal ellipsis arrowvertex arrowhorizex - carriagereturn aleph Ifraktur Rfraktur weierstrass - circlemultiply circleplus emptyset intersection union - propersuperset reflexsuperset notsubset propersubset - reflexsubset element notelement angle gradient registerserif - copyrightserif trademarkserif product radical dotmath - logicalnot logicaland logicalor arrowdblboth arrowdblleft - arrowdblup arrowdblright arrowdbldown lozenge angleleft - registersans copyrightsans trademarksans summation parenlefttp - parenleftex parenleftbt bracketlefttp bracketleftex - bracketleftbt bracelefttp braceleftmid braceleftbt braceex - angleright integral integraltp integralex integralbt - parenrighttp parenrightex parenrightbt bracketrighttp - bracketrightex bracketrightbt bracerighttp bracerightmid - bracerightbt - - # Ordinary symbols (arrows) - leftarrow longleftarrow dblleftarrow dbllongleftarrow - rightarrow longrightarrow dblrightarrow dbllongrightarrow - leftrightarrow longleftrightarrow dblleftrightarrow - dbllongleftrightarrow mapsto longmapsto hookleftarrow - hookrightarrow leadsto leftharpoonup rightharpoonup - leftharpoondown rightharpoondown rightleftharpoons - uparrow dbluparrow downarrow dbldownarrow updownarrow - dblupdownarrow nearrow searrow swarrow nwarrow - - # Ordinary symbols (to get Roman font) - arccos arcsin arctan arg cos cosh cot coth csc deg det dim exp - gcd hom inf ker lg lim liminf limsup ln log max min Pr sec sin - sinh supr tan tanh mod "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" - "!" "?" "%" "(" ")" "[" "]" - - # Ordinary symbols (for atleft and atright) - lpar blpar rpar brpar lbrack blbrack rbrack brbrack lbrace blbrace - rbrace brbrace lfloor blfloor rfloor brfloor lceil blceil - rceil brceil langle blangle rangle brangle - - # Ordinary symbols (miscellaneous) - hbar Re Im partial infty prime nabla surd top bot dbar triangle - backslash forall exists neg circle filledcircle square ldots cdots - vdots ddots del grad "..." ",...," "'" "''" "'''" "''''" empty - triangleup triangledown half third - - # Variable-building symbols - dot dotdot hat tilde vec dyad overbar underbar - sup sub tsub supp on ton - - # Large operator symbols - largeop sum prod coprod bcap bcup bvee bwedge bodot botimes - boplus buplus int oint - - # Unary operator symbols - sqrt root zroot - matrix pmatrix bmatrix brmatrix fmatrix cmatrix amatrix - - # Binary operator symbols - over frac - bin "+" "-" "+-" "-+" setminus cdot times "*" circ div - cap cup uplus sqcap sqcup triangleleft triangleright - wr bigcirc bigtriangleup bigtriangledown vee wedge oplus ominus - otimes oslash odot dagger daggerdbl amalg - - # Relation symbols - rel "<" ">" "=" "<=" prec preceq "<<" subset subseteq sqsubseteq - in vdash smile frown ">=" succ succeq ">>" supset supseteq - sqsupseteq ni dashv mid parallel "==" "~" "-~" asymp "~~" - "=~" bowtie propto models doteq trieq perp notsub notin "!=" - "<->" "<--" "-->" up down "<=>" "<==" "==>" dblup dbldown - ":" "::" ":=" - # not - - # Punctuation symbols - punct ";" "," col - -def @Math - named symbolfont { Symbol Base } - named basefont { Times Base } - named initialstyle { "display" } - named initiallycramped { "No" } - named initialspace { separate 0.05f } - body @Body -@Begin - - ################################################################### - # # - # Operator Precedences (private) # - # # - # All @Math symbols with parameters have explicit precedences # - # defined by invoking one of the following macros. Symbols # - # that are typically used to build variables have high # - # precedence (84-80), then come unary operators (70), then # - # binary operators (66-60), then relations and the rest. # - # See also http://en.wikipedia.org/wiki/Order_of_operations . # - # # - ################################################################### - - macro @MaxPrec { 100 } - macro @HatPrec { 84 } - macro @SubPrec { 82 } - macro @SupPrec { 80 } - macro @UnaryOpPrec { 70 } - macro @BinaryOpTimesPrec { 64 } - macro @BinaryOpDividePrec { 62 } - macro @BinaryOpPrec { 60 } - macro @RelationPrec { 50 } - macro @PunctuationPrec { 40 } - macro @HelperNonPrec { 26 } - macro @HelperAbovePrec { 24 } - macro @HelperColPrec { 22 } - macro @HelperRowPrec { 20 } - - - ################################################################### - # # - # Context-sensitive format changes (private) # - # # - # Equation formatting (according to Knuth) demands changes in # - # the appearance of equations depending on context. Knuth # - # distinguishes four major styles (the TeXbook, Ch. 17): # - # # - # display formulas displayed on lines by themselves # - # text formulas embedded in the text # - # script formulas used as superscripts or subscripts # - # scriptscript second-order superscripts or subscripts # - # # - # Each style has its own font size and spacing rules. # - # Additionally, each of these styles can be ``cramped'', # - # meaning that exponents are not raised as much. To these # - # four styles @Math adds a fifth: # - # # - # nohspace formulas enclosed in "non" # - # # - # which implements the "non" operator by causing all # - # style-dependent horizontal space to be 0. # - # # - ################################################################### - - macro @CurrStyleVar { "EqCurrStyle" } - macro @CrampedVar { "EqCramped?" } - - def @CurrStyle { @GetContext @CurrStyleVar } - def @Cramped { @GetContext @CrampedVar } - - def @EqDebug - { - # Uncomment the following line to get debugging information. - #{ { Helvetica Base 0.7f } @Font @CurrStyle } |0.2f - @Null - } - - def @WithStyle - named style { "display" } - named cramped { "No" } - right x - { - def @NewFontSize - { - @CurrStyle @Case { - "scriptscript" @Yield 1.0f # can't be smaller - "script" @Yield { - style @Case { - "script" @Yield 1.0f - else @Yield 0.8f } } - "text" @Yield { - style @Case { - "text" @Yield 1.0f - else @Yield 0.7f } } - "display" @Yield { - style @Case { - # display and text styles yield the same font size - { "display" "text" } @Yield 1.0f - else @Yield 0.7f } } - "nohspace" @Yield 1.0f - } - } - - - #{ Helvetica Base 0.4f } @Font { @CurrStyle -> style } |0.2f - @NewFontSize @Font - { @CurrStyleVar @Yield style } @SetContext { - { @CrampedVar @Yield cramped } @SetContext { - # FIXME: Space is not properly inherited, hence this - # `@Space' invocation. - { initialspace @Space x } - } - } - } - - def @CurrSuperScriptGap - { - @Cramped @Case { - "Yes" @Yield 0.23fk - "No" @Yield 0.35fk - } - } - - def @SubScriptGap { 0.35fk } - - # Space around relational operators. - def @CurrRelSpaceGap - { - @CurrStyle @Case { - { "display" "text" } @Yield 0.300fe - "nohspace" @Yield 0i - else @Yield 0.030ce - } - } - - # Space around binary operators. - def @CurrBinarySpaceGap - { - @CurrStyle @Case { - { "display" "text" } @Yield 0.240fe - "nohspace" @Yield 0i - else @Yield 0.024ce - } - } - - # Space around punctuation marks, including matrix braces. - def @CurrPunctSpaceGap - { - @CurrStyle @Case { - { "display" "text" } @Yield 0.180fe - "nohspace" @Yield 0i - else @Yield 0.018ce - } - } - - # Gap above/below math expressions (see, e.g., `to' and `from'). - def @AboveGap { 0.15f } - def @BelowGap { 0.15f } - - def @SkewGap { 0.05f } - def @ColGap { 0.8f } - def @RowGap { 0.5f } - - - ################################################################### - # # - # Miscellaneous helper definitions (private) # - # # - ################################################################### - - def @Base precedence @MaxPrec right x { basefont @Font x } - def @Sym precedence @MaxPrec right x { symbolfont @Font x } - - def @HLine - named line { @BackEnd @Case { PostScript @Yield { "0.05 ft setlinewidth" } PDF @Yield { "__mul(__loutf, 0.05) w" } } } - { - @BackEnd @Case { - PostScript @Yield { - { "0 0 moveto xsize 0 lineto" line "stroke" } @Graphic {} - } - PDF @Yield { # note re-arrangement of commands (setlinewidth (='w') not allowed in a path) - { line "0 0 m __xsize 0 l s" } @Graphic {} - } - } - } - - def @VLine - { - @BackEnd @Case { - PostScript @Yield { - "0 0 moveto 0 ysize lineto 0.05 ft setlinewidth stroke" @Graphic {} - } - PDF @Yield { - "__mul(__loutf, 0.05) w 0 0 m 0 __ysize l s" @Graphic {} - } - } - } - - def @Strut - precedence @MaxPrec - right x - { - @OneCol { x | @OneRow { 0.5f @High ^/ 0.5f @High } } - } - - def @OrDefault - left l - right r - { - l @Case { - "dft" @Yield r - else @Yield l - } - } - - - ################################################################### - # # - # Helper symbols (public, exc @ScriptStyle and @FractionStyle) # - # # - ################################################################### - - def above - precedence @HelperAbovePrec - associativity left - left x - named gap { @BelowGap } - named skew { 0c } - right y - { - @HContract @VContract - { |0.5rt x - //gap |0.5rt &skew y - } - } - - def below - precedence @HelperAbovePrec - associativity left - left x - named gap { @AboveGap } - named skew { 0c } - right y - { - @HContract @VContract - { |0.5rt &skew y - ^//gap |0.5rt x - } - } - - def wideabove - precedence @HelperAbovePrec - associativity left - left x - named gap { @BelowGap } - right y - { - @HContract @VContract - { - x //gap @HScale y - } - } - - def widebelow - precedence @HelperAbovePrec - associativity left - left x - named gap { @AboveGap } - right y - { - @HContract @VContract - { - @HScale y ^//gap x - } - } - - def "`" { &@CurrPunctSpaceGap } - def "``" { &@CurrBinarySpaceGap } - def "```" { &@CurrRelSpaceGap } - - def non - precedence @HelperNonPrec - right x - { - { @CurrStyleVar @Yield "nohspace" } @SetContext x - } - - def big - precedence @MaxPrec - right x - { - 1.3f @Font x - } - - def small - precedence @MaxPrec - right x - { - 0.6f @Font x - } - - def vctr - precedence @MaxPrec - right x - { - 0.5w @VShift x - } - - def @ScriptStyle - named level { "sup" } - right script - { - @WithStyle - style { @CurrStyle @Case { - { "display" "text" } @Yield "script" - { "script" "scriptscript" } @Yield "scriptscript" - "nohspace" @Yield "nohspace" - } } - cramped { level @Case { - "sub" @Yield "Yes" - "sup" @Yield @Cramped - } } - { script } - } - - def @SuperScriptStyle right superscript - { - @ScriptStyle level { "sup" } superscript - } - - def @SubScriptStyle right subscript - { - @ScriptStyle level { "sub" } subscript - } - - def @FractionStyle - named level { "numerator" } - right x - { - @WithStyle - style { @CurrStyle @Case { - "display" @Yield "text" - "text" @Yield "script" - { "script" "scriptscript" } @Yield "scriptscript" - "nohspace" @Yield "nohspace" - } } - cramped { level @Case { - "numerator" @Yield @Cramped - "denominator" @Yield "Yes" - } } - { x } - } - - def @NumeratorStyle right x - { - @FractionStyle level { "numerator" } x - } - - def @DenominatorStyle right x - { - @FractionStyle level { "denominator" } x - } - - def @SquareRootStyle right x - { - @WithStyle style { @CurrStyle } cramped { "Yes" } x - } - - ################################################################### - # # - # Ordinary symbols (Symbol font) # - # # - # These symbols and their names are taken directly from the # - # Adobe Systems Inc. Symbol font (see PostScript Language # - # Reference Manual, pp. 256-257). The only differences are: # - # # - # Adobe: theta1 @Math: thetaone # - # sigma1 sigmaone # - # phi1 phione # - # omega1 omegaone # - # Upsilon1 Upsilonone # - # # - # These were needed since Lout identifiers do not have digits. # - # # - ################################################################### - - def space { @Sym @Char "space" } - def exclam { @Sym @Char "exclam" } - def universal { @Sym @Char "universal" } - def numbersign { @Sym @Char "numbersign" } - def existential { @Sym @Char "existential" } - def percent { @Sym @Char "percent" } - def ampersand { @Sym @Char "ampersand" } - def suchthat { @Sym @Char "suchthat" } - def parenleft { @Sym @Char "parenleft" } - def parenright { @Sym @Char "parenright" } - def asteriskmath { @Sym @Char "asteriskmath" } - def plus { @Sym @Char "plus" } - def comma { @Sym @Char "comma" } - def minus { @Sym @Char "minus" } - def period { @Sym @Char "period" } - def slash { @Sym @Char "slash" } - def zero { @Sym @Char "zero" } - def one { @Sym @Char "one" } - def two { @Sym @Char "two" } - def three { @Sym @Char "three" } - def four { @Sym @Char "four" } - def five { @Sym @Char "five" } - def six { @Sym @Char "six" } - def seven { @Sym @Char "seven" } - def eight { @Sym @Char "eight" } - def nine { @Sym @Char "nine" } - def colon { @Sym @Char "colon" } - def semicolon { @Sym @Char "semicolon" } - def less { @Sym @Char "less" } - def equal { @Sym @Char "equal" } - def greater { @Sym @Char "greater" } - def question { @Sym @Char "question" } - def congruent { @Sym @Char "congruent" } - def Alpha { @Sym @Char "Alpha" } - def Beta { @Sym @Char "Beta" } - def Chi { @Sym @Char "Chi" } - def Delta { @Sym @Char "Delta" } - def Epsilon { @Sym @Char "Epsilon" } - def Phi { @Sym @Char "Phi" } - def Gamma { @Sym @Char "Gamma" } - def Eta { @Sym @Char "Eta" } - def Iota { @Sym @Char "Iota" } - def thetaone { @Sym @Char "theta1" } - def Kappa { @Sym @Char "Kappa" } - - def Lambda { @Sym @Char "Lambda" } - def Mu { @Sym @Char "Mu" } - def Nu { @Sym @Char "Nu" } - def Omicron { @Sym @Char "Omicron" } - def Pi { @Sym @Char "Pi" } - def Theta { @Sym @Char "Theta" } - def Rho { @Sym @Char "Rho" } - def Sigma { @Sym @Char "Sigma" } - def Tau { @Sym @Char "Tau" } - def Upsilon { @Sym @Char "Upsilon" } - def sigmaone { @Sym @Char "sigma1" } - def Omega { @Sym @Char "Omega" } - def Xi { @Sym @Char "Xi" } - def Psi { @Sym @Char "Psi" } - def Zeta { @Sym @Char "Zeta" } - def bracketleft { @Sym @Char "bracketleft" } - def therefore { @Sym @Char "therefore" } - def bracketright { @Sym @Char "bracketright" } - def perpendicular { @Sym @Char "perpendicular" } - def underscore { @Sym @Char "underscore" } - def radicalex { @Sym @Char "radicalex" } - def alpha { @Sym @Char "alpha" } - def beta { @Sym @Char "beta" } - def chi { @Sym @Char "chi" } - def delta { @Sym @Char "delta" } - def epsilon { @Sym @Char "epsilon" } - def phi { @Sym @Char "phi" } - def gamma { @Sym @Char "gamma" } - def eta { @Sym @Char "eta" } - def iota { @Sym @Char "iota" } - def phione { @Sym @Char "phi1" } - def kappa { @Sym @Char "kappa" } - def lambda { @Sym @Char "lambda" } - def mu { @Sym @Char "mu" } - def nu { @Sym @Char "nu" } - - def omicron { @Sym @Char "omicron" } - def pi { @Sym @Char "pi" } - def theta { @Sym @Char "theta" } - def rho { @Sym @Char "rho" } - def sigma { @Sym @Char "sigma" } - def tau { @Sym @Char "tau" } - def upsilon { @Sym @Char "upsilon" } - def omegaone { @Sym @Char "omega1" } - def omega { @Sym @Char "omega" } - def xi { @Sym @Char "xi" } - def psi { @Sym @Char "psi" } - def zeta { @Sym @Char "zeta" } - def braceleft { @Sym @Char "braceleft" } - def bar { @Sym @Char "bar" } - def braceright { @Sym @Char "braceright" } - def similar { @Sym @Char "similar" } - def Upsilonone { @Sym @Char "Upsilon1" } - def minute { @Sym @Char "minute" } - def lessequal { @Sym @Char "lessequal" } - def fraction { @Sym @Char "fraction" } - # For Adobe Symbol, `infinity' used to be "1.2f @Font { ... }" - def infinity { @Sym @Char "infinity" } - def florin { @Sym @Char "florin" } - def club { @Sym @Char "club" } - def diamond { @Sym @Char "diamond" } - def heart { @Sym @Char "heart" } - def spade { @Sym @Char "spade" } - def arrowboth { @Sym @Char "arrowboth" } - def arrowleft { @Sym @Char "arrowleft" } - def arrowup { @Sym @Char "arrowup" } - def arrowright { @Sym @Char "arrowright" } - def arrowdown { @Sym @Char "arrowdown" } - def degree { @Sym @Char "degree" } - def plusminus { @Sym @Char "plusminus" } - def second { @Sym @Char "second" } - def greaterequal { @Sym @Char "greaterequal" } - - def multiply { @Sym @Char "multiply" } - def proportional { @Sym @Char "proportional" } - def partialdiff { @Sym @Char "partialdiff" } - def bullet { @Sym @Char "bullet" } - def divide { @Sym @Char "divide" } - def notequal { @Sym @Char "notequal" } - def equivalence { @Sym @Char "equivalence" } - def approxequal { @Sym @Char "approxequal" } - def ellipsis { @Sym @Char "ellipsis" } - def arrowvertex { @Sym @Char "arrowvertex" } - def arrowhorizex { @Sym @Char "arrowhorizex" } - def carriagereturn { @Sym @Char "carriagereturn" } - def aleph { @Sym @Char "aleph" } - def Ifraktur { @Sym @Char "Ifraktur" } - def Rfraktur { @Sym @Char "Rfraktur" } - def weierstrass { @Sym @Char "weierstrass" } - def circlemultiply { @Sym @Char "circlemultiply" } - def circleplus { @Sym @Char "circleplus" } - def emptyset { @Sym @Char "emptyset" } - def intersection { @Sym @Char "intersection" } - def union { @Sym @Char "union" } - def propersuperset { @Sym @Char "propersuperset" } - def reflexsuperset { @Sym @Char "reflexsuperset" } - def notsubset { @Sym @Char "notsubset" } - def propersubset { @Sym @Char "propersubset" } - def reflexsubset { @Sym @Char "reflexsubset" } - def element { @Sym @Char "element" } - def notelement { @Sym @Char "notelement" } - def angle { @Sym @Char "angle" } - def gradient { @Sym @Char "gradient" } - def registerserif { @Sym @Char "registerserif" } - def copyrightserif { @Sym @Char "copyrightserif" } - def trademarkserif { @Sym @Char "trademarkserif" } - def product { @Sym @Char "product" } - def radical { @Sym @Char "radical" } - def dotmath { @Sym @Char "dotmath" } - def logicalnot { @Sym @Char "logicalnot" } - def logicaland { @Sym @Char "logicaland" } - def logicalor { @Sym @Char "logicalor" } - def arrowdblboth { @Sym @Char "arrowdblboth" } - def arrowdblleft { @Sym @Char "arrowdblleft" } - def arrowdblup { @Sym @Char "arrowdblup" } - def arrowdblright { @Sym @Char "arrowdblright" } - def arrowdbldown { @Sym @Char "arrowdbldown" } - def lozenge { @Sym @Char "lozenge" } - def angleleft { @Sym @Char "angleleft" } - def registersans { @Sym @Char "registersans" } - def copyrightsans { @Sym @Char "copyrightsans" } - def trademarksans { @Sym @Char "trademarksans" } - def summation { @Sym @Char "summation" } - def parenlefttp { @Sym @Char "parenlefttp" } - def parenleftex { @Sym @Char "parenleftex" } - def parenleftbt { @Sym @Char "parenleftbt" } - def bracketlefttp { @Sym @Char "bracketlefttp" } - def bracketleftex { @Sym @Char "bracketleftex" } - def bracketleftbt { @Sym @Char "bracketleftbt" } - def bracelefttp { @Sym @Char "bracelefttp" } - def braceleftmid { @Sym @Char "braceleftmid" } - def braceleftbt { @Sym @Char "braceleftbt" } - def braceex { @Sym @Char "braceex" } - def angleright { @Sym @Char "angleright" } - def integral { @Sym @Char "integral" } - def integraltp { @Sym @Char "integraltp" } - def integralex { @Sym @Char "integralex" } - def integralbt { @Sym @Char "integralbt" } - def parenrighttp { @Sym @Char "parenrighttp" } - def parenrightex { @Sym @Char "parenrightex" } - def parenrightbt { @Sym @Char "parenrightbt" } - def bracketrighttp { @Sym @Char "bracketrighttp" } - def bracketrightex { @Sym @Char "bracketrightex" } - def bracketrightbt { @Sym @Char "bracketrightbt" } - def bracerighttp { @Sym @Char "bracerighttp" } - def bracerightmid { @Sym @Char "bracerightmid" } - def bracerightbt { @Sym @Char "bracerightbt" } - - - ################################################################### - # # - # Ordinary symbols (arrows) # - # # - ################################################################### - - def leftarrow { arrowleft } - def longleftarrow { { 1.6 1 } @Scale arrowleft } - def dblleftarrow { arrowdblleft } - def dbllongleftarrow { { 1.6 1 } @Scale arrowdblleft } - def rightarrow { arrowright } - def longrightarrow { { 1.6 1 } @Scale arrowright } - def dblrightarrow { arrowdblright } - def dbllongrightarrow { { 1.6 1 } @Scale arrowdblright } - def leftrightarrow { arrowboth } - def longleftrightarrow { { 1.6 1 } @Scale arrowboth } - def dblleftrightarrow { arrowdblboth } - def dbllongleftrightarrow { { 1.6 1 } @Scale arrowdblboth } - - def mapsto - { - @HContract @VContract { - @BackEnd @Case { - PostScript @Yield { - "0 ymark 0.16 ft sub moveto 0 ymark 0.16 ft add lineto stroke" - @Graphic arrowright - } - PDF @Yield { - "0 __sub(__ymark, __mul(__loutf, 0.16)) m 0 __add(__ymark, __mul(__loutf, 0.16)) l S" - @Graphic arrowright - } - } - } - } - - def longmapsto - { - @HContract @VContract { - @BackEnd @Case { - PostScript @Yield { - "0 ymark 0.16 ft sub moveto 0 ymark 0.16 ft add lineto stroke" - @Graphic { { 1.6 1 } @Scale arrowright } - } - PDF @Yield { - "0 __sub(__ymark, __mul(__loutf, 0.16)) m 0 __add(__ymark, __mul(__loutf, 0.16)) l S" - @Graphic { { 1.6 1 } @Scale arrowright } - } - } - } - } - - def hookleftarrow - { - @HContract @VContract { - @BackEnd @Case { - - PostScript @Yield { - "xsize ymark moveto xsize ymark 0.1 ft add 0.1 ft -90 90 arc stroke" - @Graphic leftarrow - } - - PDF @Yield { -# -# VT: draws a counterclockwise 180 degree arc from -90 to +90 degree positions -# (straight down to straight up) with centre = (xsize, ymark + 0.1 ft) -# and radius = 0.1 ft -# -# the control points therefore are: -# pt1 = (xsize + (4/3 * 0.1 ft), ymark) and pt2 = (xsize + (4/3 * 0.1 ft), ymark + 0.2 ft) -# - { - "__xsize __ymark m" # pt0 - "__add(__xsize, __div(__mul(0.4, __loutf), 3)) __ymark" # pt1 - "__add(__xsize, __div(__mul(0.4, __loutf), 3)) __add(__ymark, __mul(0.2, __loutf))" # pt2 - "__xsize __add(__ymark, __mul(0.2, __loutf)) c S" # pt3 - } - @Graphic leftarrow - } - - } - } - } - - def hookrightarrow - { - @HContract @VContract { - @BackEnd @Case { - - PostScript @Yield { - "0 ymark moveto 0 0.1 ft ymark add 0.1 ft -90 90 arcn stroke" - @Graphic rightarrow - } - - PDF @Yield { -# -# VT: draws a clockwise 180 degree arc from -90 to +90 degree positions -# (straight down to straight up) with centre = (0, ymark + 0.1 ft) -# and radius = 0.1 ft -# -# the control points therefore are: -# pt1 = (-4/3 * 0.1 ft, ymark) and pt2 = (-4/3 * 0.1 ft, ymark + 0.2 ft) -# - { - "0 __ymark m" # pt0 - "__div(__mul(-0.4, __loutf), 3) __ymark" # pt1 - "__div(__mul(-0.4, __loutf), 3) __add(__ymark, __mul(0.2, __loutf))" # pt2 - "0 __add(__ymark, __mul(0.2, __loutf)) c S" # pt3 - } - @Graphic rightarrow - } - - } - } - } - - def @ClipToSize right x - { - @HContract @VContract - @BackEnd @Case { - PostScript @Yield { - { - "grestore newpath 0 0 moveto xsize 0 lineto xsize ysize lineto" - "0 ysize lineto closepath clip gsave" - } @Graphic x - } - PDF @Yield { - "Q n 0 0 __xsize __ysize re W n q" @Graphic x - } - } - } - - def @ClipAboveMark - left amount - right x - { - @ClipToSize { ^//{{amount}o} x } - } - - def @ClipBelowMark - left amount - right x - { - @ClipToSize { x //{{amount}o} } - } - - def leftharpoonup - { - 0.04f @ClipBelowMark leftarrow - } - - def rightharpoonup - { - 0.04f @ClipBelowMark rightarrow - } - - def leftharpoondown - { - 0.02f @ClipAboveMark leftarrow - } - - def rightharpoondown - { - 0.02f @ClipAboveMark rightarrow - } - - def rightleftharpoons - { - @HContract @VContract { - rightharpoonup - ^//0.1fo - //0.1fo - leftharpoondown - } - } - - def leadsto { @HContract { similar &0.4fo arrowright } } - - def uparrow { arrowup } - def dbluparrow { arrowdblup } - def downarrow { arrowdown } - def dbldownarrow { arrowdbldown } - def updownarrow { @HContract { arrowup &0io arrowdown } } - def dblupdownarrow { @VContract { arrowdblup ^//0.2fo arrowdbldown } } - def nearrow { 0.5w @VShift 0.5w @HShift 45d @Rotate arrowright } - def searrow { 0.5w @VShift 0.5w @HShift 315d @Rotate arrowright } - def swarrow { 0.5w @VShift 0.5w @HShift 225d @Rotate arrowright } - def nwarrow { 0.5w @VShift 0.5w @HShift 135d @Rotate arrowright } - - - ################################################################### - # # - # Ordinary symbols (to get Roman font) # - # # - # These symbols are defined to yield themselves, but in Roman # - # font rather than the Italic that would otherwise be used. # - # See Knuth p. 162 and 132. The definitions of "0" ... "9" # - # should logically appear here, but they have been moved to # - # the end since it is awkward to enter numeric lengths after # - # they are defined. # - # # - ################################################################### - - def arccos { @Base "arccos" } - def arcsin { @Base "arcsin" } - def arctan { @Base "arctan" } - def arg { @Base "arg" } - def cos { @Base "cos" } - def cosh { @Base "cosh" } - def cot { @Base "cot" } - def coth { @Base "coth" } - def csc { @Base "csc" } - def deg { @Base "deg" } - def det { @Base "det" } - def dim { @Base "dim" } - def exp { @Base "exp" } - def gcd { @Base "gcd" } - def hom { @Base "hom" } - def inf { @Base "inf" } - def ker { @Base "ker" } - def lg { @Base "lg" } - def lim { @Base "lim" } - def liminf { @OneCol { @Base "lim" ` @Base "inf" } } - def limsup { @OneCol { @Base "lim" ` @Base "sup" } } - def ln { @Base "ln" } - def log { @Base "log" } - def max { @Base "max" } - def min { @Base "min" } - def Pr { @Base "Pr" } - def sec { @Base "sec" } - def sin { @Base "sin" } - def sinh { @Base "sinh" } - def supr { @Base "sup" } - def tan { @Base "tan" } - def tanh { @Base "tanh" } - def mod { @Base "mod" } - def "!" { exclam } - def "?" { question } - def "%" { percent } - def "(" { parenleft } - def ")" { parenright } - def "[" { bracketleft } - def "]" { bracketright } - - - ################################################################### - # # - # Ordinary symbols (for atleft and atright) # - # These are Knuth's Groups 11 and 12 - openings and closings. # - # # - ################################################################### - - def lpar { parenleft } - def rpar { parenright } - def lbrack { bracketleft } - def rbrack { bracketright } - def lbrace { braceleft } - def rbrace { braceright } - def lfloor { ` "-0.15f" @VShift bracketleftbt } - def rfloor { "-0.15f" @VShift bracketrightbt ` } - def lceil { ` "-0.1f" @VShift bracketlefttp } - def rceil { "-0.1f" @VShift bracketrighttp ` } - def langle { angleleft } - def rangle { angleright } - - def blpar { @OneRow {parenlefttp ^/ parenleftex / parenleftbt } } - def brpar { @OneRow {parenrighttp ^/ parenrightex / parenrightbt } } - def blbrack { @OneRow {bracketlefttp ^/ bracketleftex / bracketleftbt } } - def brbrack { @OneRow {bracketrighttp ^/ bracketrightex / bracketrightbt} } - def blbrace { @OneRow {bracelefttp ^/ braceleftmid / braceleftbt } } - def brbrace { @OneRow {bracerighttp ^/ bracerightmid / bracerightbt } } - def blfloor { @OneRow {bracketleftex ^/ bracketleftex / bracketleftbt } } - def brfloor { @OneRow {bracketrightex ^/ bracketrightex / bracketrightbt} } - def blceil { @OneRow {bracketlefttp ^/ bracketleftex / bracketleftex } } - def brceil { @OneRow {bracketrighttp ^/ bracketrightex / bracketrightex} } - - def blangle - { - @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { "xsize 0 moveto 0 ysize 2 div lineto" - "xsize ysize lineto 0.04 ft setlinewidth stroke" - } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High } - } - PDF @Yield { - { "__mul(__loutf, 0.04) w __xsize 0 m" - "0 __div(__ysize, 2) l __xsize __ysize l S" - } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High } - } - } - } - - def brangle - { - @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { "0 0 moveto xsize ysize 2 div lineto" - "0 ysize lineto 0.04 ft setlinewidth stroke" - } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High } - } - PDF @Yield { - { "__mul(__loutf, 0.04) w 0 0 m" - "__xsize __div(__ysize, 2) l 0 __ysize l S" - } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High } - } - } - } - - - ################################################################### - # # - # Ordinary symbols (miscellaneous) # - # # - # Not all of Knuth's symbols are available. The four suits # - # (heartsuit, etc.), have definitions above. # - # # - ################################################################### - - def hbar { @HContract @VContract {&0.1f @Base "-" ^/0.30fo h }} - def Re { Rfraktur } - def Im { Ifraktur } - def partial { partialdiff } - def infty { infinity } - def prime { minute } - #def emptyset { defined above } - def nabla { gradient } - def surd { radical } - def top { 180d @Rotate perpendicular } - def bot { perpendicular } - def dbar { @Base "||" } - #def angle { defined above } - def backslash { "\\" } - def forall { universal } - def exists { existential } - def neg { logicalnot } - - def circle - { @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { - "xsize ysize 2 div moveto" - "xsize 2 div ysize 2 div xsize 2 div 0 360 arc" - "0.04 ft setlinewidth stroke" - } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High } - } - PDF @Yield { - # - # VT: draws a counterclockwise 360 degree arc from 0 to +360 - # degree positions (straight right to straight right) with - # centre = (xsize/2, ysize/2) and radius = xsize/2, - # implemented as two counterclockwise 180 degree arcs. - # start at (xsize, ysize/2); the control points are: - # - # pt1 = (xsize, ysize/2 + (4/3 * xsize/2)) - # pt2 = (0, ysize/2 + (4/3 * xsize/2)) - # - # end at (0, ysize/2). Then start at (0, ysize/2); control points - # - # pt1 = (0, ysize/2 - (4/3 * xsize/2)) - # pt2 = (xsize, ysize/2 - (4/3 * xsize/2)) - # - # and end at (xsize, ysize/2). - - { - "__mul(0.04, __loutf) w" - "__xsize __div(__ysize, 2) m" - "__xsize __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "0 __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "0 __div(__ysize, 2) c" - "0 __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "__xsize __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "__xsize __div(__ysize, 2) c S" - } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High } - } - } - } - - def filledcircle - { @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { - "xsize ysize 2 div moveto" - "xsize 2 div ysize 2 div xsize 2 div 0 360 arc" - "0.04 ft setlinewidth fill" - } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High } - } - PDF @Yield { - # - # JK: I don't know how to fill in PDF, so this doesn't! - # - # VT: draws a counterclockwise 360 degree arc from 0 to +360 - # degree positions (straight right to straight right) with - # centre = (xsize/2, ysize/2) and radius = xsize/2, - # implemented as two counterclockwise 180 degree arcs. - # start at (xsize, ysize/2); the control points are: - # - # pt1 = (xsize, ysize/2 + (4/3 * xsize/2)) - # pt2 = (0, ysize/2 + (4/3 * xsize/2)) - # - # end at (0, ysize/2). Then start at (0, ysize/2); control points - # - # pt1 = (0, ysize/2 - (4/3 * xsize/2)) - # pt2 = (xsize, ysize/2 - (4/3 * xsize/2)) - # - # and end at (xsize, ysize/2). - - { - "__mul(0.04, __loutf) w" - "__xsize __div(__ysize, 2) m" - "__xsize __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "0 __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "0 __div(__ysize, 2) c" - "0 __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "__xsize __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))" - "__xsize __div(__ysize, 2) c S" - } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High } - } - } - } - - def square - { @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { - "0 0 moveto xsize 0 lineto xsize ysize lineto" - "0 ysize lineto closepath" - "0.04 ft setlinewidth stroke" - } @Graphic { 0.6f @Wide 0.3f @High ^/ 0.3f @High } - } - PDF @Yield { - { - "__mul(__loutf, 0.04) w" - "0 0 m __xsize 0 l __xsize __ysize l" - "0 __ysize l s" - } @Graphic { 0.6f @Wide 0.3f @High ^/ 0.3f @High } - } - } - } - - def triangle - { @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { - "0 0 moveto xsize 0 lineto" - "xsize 2 div ysize lineto closepath" - "0.04 ft setlinewidth stroke" - } @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High } - } - PDF @Yield { - { - "__mul(__loutf, 0.04) w" - "0 0 m __xsize 0 l" - "__div(__xsize, 2) __ysize l s" - } @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High } - } - } - } - - # other symbols taken from TeX - def ldots { . &0.3f . &0.3f . } - def cdots { dotmath &0.3f dotmath &0.3f dotmath } - def vdots { @OneRow { dotmath ^/0.3f dotmath /0.3f dotmath } } - def ddots { @OneCol @OneRow - { dotmath - ^/0.3f |0.3f dotmath - /0.3f | |0.3f dotmath - } - } - - # symbols taken from eqn (Kernighan and Cherry 1975). # - def del { gradient } - def grad { gradient } - def "..." { ellipsis } - def ",...," { , ellipsis ``` , } - def "'" { minute } - def "''" { minute minute } - def "'''" { minute minute minute } - def "''''" { minute minute minute minute } - def empty { emptyset } - - # forget where these are from - def triangleup { 0.8f @Font triangle } - def triangledown { 180d @Rotate 0.8f @Font triangle } - - # half and third defined later, since they use frac - - - ################################################################### - # # - # Variable-building symbols # - # # - # These symbols are essentially those of eqn, with some # - # changes and additions. # - # # - ################################################################### - - def dot - precedence @HatPrec - left x - named gap { @AboveGap } - { - x below gap { gap } skew { @SkewGap } @SuperScriptStyle . - } - - def dotdot - precedence @HatPrec - left x - named gap { @AboveGap } - { - x below gap { gap } skew { @SkewGap } @SuperScriptStyle .. - } - - def hat - precedence @HatPrec - left x - named gap { @AboveGap } - { - x below gap { gap } skew { @SkewGap } @SuperScriptStyle @Base "^" - } - - def tilde - precedence @HatPrec - left x - named gap { @AboveGap } - { - x below gap { gap } skew { @SkewGap } @SuperScriptStyle @Base "~" - } - - def vec - precedence @HatPrec - left x - named gap { @AboveGap } - { - x below gap { gap } skew { @SkewGap } @SuperScriptStyle arrowright - } - - def dyad - precedence @HatPrec - left x - named gap { @AboveGap } - { - x below gap { gap } skew { @SkewGap } @SuperScriptStyle arrowboth - } - - def overbar - precedence @HatPrec - left x - named gap { @AboveGap } - { - { @WithStyle style { @CurrStyle } cramped { "Yes" } x } - widebelow gap { gap } @SuperScriptStyle minus - } - - def underbar - precedence @HatPrec - left x - named gap { @BelowGap } - { - x wideabove gap { gap } @SuperScriptStyle minus - } - - def sup - precedence @SupPrec - associativity left - left x - named gap { "dft" } - right y - { - @HContract @VContract - { | @SuperScriptStyle y - ^/{ gap @OrDefault @CurrSuperScriptGap } x - } - } - - def sub - precedence @SubPrec - associativity left - left x - named gap { @SubScriptGap } - right y - { - @HContract @VContract - { - "." @KernShrink x - /gap | @SubScriptStyle y - } - } - - def tsub - precedence @SubPrec - associativity left - left x - named gap { @SubScriptGap } - right y - { - @HContract @VContract - { - x - /gap | &0io 0.2f @HShift @SubScriptStyle y - } - } - - def supp - precedence @SupPrec - associativity left - left x - named gap { "dft" } - right y - { - @HContract @VContract - { - { ^/{ gap @OrDefault @CurrSuperScriptGap } x - /{ gap @OrDefault @CurrSuperScriptGap } } - | y - } - } - - def on - precedence @SubPrec - associativity left - left x - right y - { - { @SuperScriptStyle x } ^/ / - { @SubScriptStyle y } - } - - def ton - precedence @SubPrec - associativity left - left x - right y - { - @SuperScriptStyle x ^/ / - &0io 0.3f @HShift @SubScriptStyle y - } - - - ################################################################### - # # - # Large operator symbols (Knuth's Group 6 "Large" operators) # - # # - # Layout of large operators differs in several ways, depending # - # on whether they are in display mode or not. # - # # - # 1. The operator itself is larger in display mode. We # - # achieve this by automatically prepending `big' to the # - # operator's symbol when in display mode. # - # # - # 2. The "bounds" of these operators (i.e., `from' and `to') # - # are set as limits (i.e., above and below the operator # - # symbol) when in display mode, and displayed to the # - # right of the symbol otherwise. Integrations are an # - # exception (the only exception?). # - # # - # See ``The TeXbook'', Chapter 17. # - # # - ################################################################### - - def largeop - named symbol { "largeop" } - named limits { "dft" } # whether to set `from' and `to' as limits - named from { "" } - named to { "" } - { - def @Symbol - { - @CurrStyle @Case { - "display" @Yield { big symbol } - else @Yield symbol - } - } - - def @Limits - { - limits @OrDefault { - @CurrStyle @Case { - "display" @Yield "Yes" - else @Yield "No" } - } - } - - def @LimitsBody - { - @Symbol above { @SuperScriptStyle from } - below { @SubScriptStyle to } - } - - def @NoLimitsBody - { - 0.5w @VShift { - 1.0w @VShift @OneRow { - { | 0.3w @VShift @SuperScriptStyle to } - ^/0.0fo { 0w @VShift @Symbol | } - } - - /0.0fo - - { | 0.7w @VShift @SubScriptStyle from } - } - |{ @CurrPunctSpaceGap } - } - - @Limits @Case { - { "Yes" "yes" } @Yield @LimitsBody - { "No" "no" } @Yield @NoLimitsBody - } - } - - # Ludovic's symbol, no longer used - def largeoperator - named symbol { "largeop" } - named from { "" } - named to { "" } - named limits { "Yes" } # whether to set `from' and `to' as limits - { - def @NoLimitsBody { - 0.5w @VShift { - 1.0w @VShift @OneRow { - { | 0.3w @VShift @SuperScriptStyle to } - ^/0.0fo { 0w @VShift symbol | } - } - - /0.0fo - - { | 0.7w @VShift @SubScriptStyle from } - } - |{ @CurrPunctSpaceGap } - } - - def @LimitsBody { - symbol above { @SuperScriptStyle from } - below { @SubScriptStyle to } - } - - limits @Case { - { "Yes" "yes" } @Yield @LimitsBody - { "No" "no" } @Yield @NoLimitsBody - } - } - - # Ludovic's symbol, no longer used - def simplelargeoperator - named symbol { "simplelargeop" } - named limits { "dft" } - named from { } - named to { } - { - largeoperator - symbol { @CurrStyle @Case { - "display" @Yield { big symbol } - else @Yield symbol } - } - limits { limits @OrDefault { - @CurrStyle @Case { - "display" @Yield "Yes" - else @Yield "No" } - } - } - from { from } - to { to } - } - - def sum - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { summation } limits { limits } from { from } to { to } - } - - def prod - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { product } limits { limits } from { from } to { to } - } - - def coprod - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { 180d @Rotate vctr product } - limits { limits } from { from } to { to } - } - - def bcap - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { big intersection } limits { limits } from { from } to { to } - } - - def bcup - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { big union } limits { limits } from { from } to { to } - } - - def bvee - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { big logicalor } limits { limits } from { from } to { to } - } - - def bwedge - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { big logicaland } limits { limits } from { from } to { to } - } - - def circledot - { - def @PureDot # dot with no extra space - { - @HContract { &0io 0.4w @HShift dotmath } - } - - @OneRow @HContract { circle /0io &0.5rt @PureDot /0io circle } - } - - - def bodot - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { circledot } - limits { limits } from { from } to { to } - } - - def botimes - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { circlemultiply } limits { limits } from { from } to { to } - } - - def boplus - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { circleplus } limits { limits } from { from } to { to } - } - - def buplus - named limits { "dft" } - named from {} - named to {} - { - largeop - symbol { & big @HContract { &0.5rt 0.7f @Font plus ^/0.2fo union } } - limits { limits } from { from } to { to } - } - - - ################################################################### - # # - # Integrations are slightly different in that, according to # - # Knuth (Chapter 17, p. 144), ``superscripts and subscripts # - # are not set as limits, even in display style''. Still, as # - # in TeX, we give users the possibility to override this. # - # # - ################################################################### - - # Ludovic's symbol, no longer used - def integration - named symbol { "integration" } - named limits { "No" } - named from { } - named to { } - { - largeoperator - symbol { @CurrStyle @Case { - "display" @Yield { big symbol } - else @Yield symbol } - } - limits { limits } from { from } to { to } - } - - def int - named limits { "No" } - named from { } - named to { } - { - largeop - symbol { vctr big integral } limits { limits } from { from } to { to } - } - - def oint - named limits { "No" } - named from { } - named to { } - { - largeop - symbol { @OneCol { vctr degree |0.015fo big integral } } - limits { limits } from { from } to { to } - } - - - ################################################################### - # # - # Unary operator symbols # - # # - ################################################################### - - def sqrt - precedence @UnaryOpPrec - named gap { @AboveGap } - right x - { - @BackEnd @Case { - PostScript @Yield { - @HContract @VContract - { - @VScale surd | @OneRow - { - @HLine line { "0.03 ft setlinewidth 2 setlinecap" } - ^//gap |gap @SquareRootStyle @Strut x # //gap - } - } - } - PDF @Yield { - @HContract @VContract - { -# -# VT: this PDF is correct but it renders badly in Acrobat (?problem -# with scaling by fractional factors) -# In other words, the @VScale value comes through correctly but it -# looks ugly; GhostScript's translation actually expands the -# "draw surd" instruction into raw moveto's and lineto's which -# it presumably gets from the font's definition of the glyph! -# - @VScale surd | @OneRow - { - @HLine line { "__mul(__loutf, 0.03) w 2 J" } - ^//gap |gap @SquareRootStyle @Strut x # //gap - } - } - } - } - } - - def root - precedence @UnaryOpPrec - associativity left - left x - right y - { - "" sup x &0io sqrt y - } - - def zroot - precedence @UnaryOpPrec - associativity left - left x - right y - { - def zsup right x { "+0.3f" @VShift 0.5f @Font x } - - "-0.4f" @HShift { 1w @HShift { zsup x } } &0co sqrt y - } - - export row axisrow col lcol ccol rcol mcol - def matrix - precedence @UnaryOpPrec - named gap { @CurrBinarySpaceGap } - named strut - named no { } - named No { } - named yes { 0.5f } - named Yes { 0.5f } - { No } - named atleft {} - named atright {} - named userow { No } - named shiftdelim { Yes } - body x - { - def @Strut - { - strut @Case { - "" @Yield {} - else @Yield { @OneRow { strut @High ^/ strut @High } } - } - } - - def newrow - precedence @HelperRowPrec - associativity left - left x - right y - { - x @Case { - "" @Yield { y | @Strut } - else @Yield { x /@RowGap y | @Strut } - } - } - - macro row { newrow "" } - - def newaxisrow - precedence @HelperRowPrec - associativity left - left x - right y - { - x @Case { - "" @Yield { y | @Strut } - else @Yield { x ^/@RowGap y | @Strut } - } - } - - macro axisrow { newaxisrow "" } - - def col - precedence @HelperColPrec - associativity left - left x - named indent { 0.5rt } - right y - { - x @Case { - "" @Yield { &indent @OneCol y } - else @Yield { x |@ColGap &indent @OneCol y } - } - } - - def lcol - precedence @HelperColPrec - associativity left - left x - right y - { - x col indent { 0i } y - } - - def ccol - precedence @HelperColPrec - associativity left - left x - right y - { - x col indent { 0.5rt } y - } - - def rcol - precedence @HelperColPrec - associativity left - left x - right y - { - x col indent { 1rt } y - } - - def mcol - precedence @HelperColPrec - associativity left - left x - right y - { - x @Case { - "" @Yield { @OneCol y } - else @Yield { x |@ColGap @OneCol y } - } - } - - def delim right x - { - x @Case - { - "" @Yield @Null - else @Yield - { - shiftdelim @Case { - { Yes yes } @Yield { @VScale x } - else @Yield { @VCover x } - } - } - } - } - - @HContract @VContract { - delim atleft &@CurrPunctSpaceGap - userow @Case { - {Yes yes} @Yield @HContract @VContract {^//gap @OneRow x //gap} - else @Yield vctr @HContract @VContract { //gap x //gap } - } - &@CurrPunctSpaceGap delim atright - } - } - - macro pmatrix { matrix atleft {1.5f @Font (} atright {1.5f @Font )} } - macro bmatrix { matrix atleft { blbrack } atright { brbrack } } - macro brmatrix { matrix atleft { blbrace } atright { brbrace } } - macro fmatrix { matrix atleft { blfloor } atright { brfloor } } - macro cmatrix { matrix atleft { blceil } atright { brceil } } - macro amatrix { matrix atleft { blangle } atright { brangle } } - - - ################################################################### - # # - # Binary operator symbols # - # # - ################################################################### - - ################################################################### - # # - # over and frac (also half and third) # - # # - ################################################################### - - def over - precedence @BinaryOpDividePrec - associativity left - left x - named gap { "dft" } - named belowgap { "dft" } - right y - { - def @AboveLineGap - { - gap @Case { - "dft" @Yield { - @CurrStyle @Case { - "display" @Yield 0.20f - else @Yield 0.10f - } - } - else @Yield gap - } - } - - def @BelowLineGap - { - belowgap @Case { - "dft" @Yield { - @CurrStyle @Case { - "display" @Yield 0.15f - else @Yield 0.09f - } - } - else @Yield belowgap - } - } - - @HContract @VContract - { |0.5rt @OneCol @NumeratorStyle x - ^//@AboveLineGap @HLine - //@BelowLineGap |0.5rt @OneCol @DenominatorStyle @Strut y - } - } - - def frac - precedence @BinaryOpDividePrec - associativity left - left x - named gap { 0.2f } - right y - { - @HContract @VContract - { 1w @VShift { @SuperScriptStyle { x } /gap } - | fraction &0io - | 0w @VShift { |gap @SubScriptStyle { y } } - } - } - - def half { one frac two } - def third { one frac three } - - - ################################################################### - # # - # Knuth's Group 7 (binary operations) # - # # - # All of Knuth's symbols are available except \star, \diamond # - # and \bullet; a few have been given more mnemonic names. # - # # - ################################################################### - - def bin - precedence @BinaryOpPrec - associativity left - left l - named op { "binop" } - right r - { - l &@CurrBinarySpaceGap op &@CurrBinarySpaceGap r - } - - def "+" - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { plus } r - } - - def "-" - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { minus } r - } - - def "+-" - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { plusminus } r - } - - def "-+" - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { 180d @Rotate plusminus } r - } - - def setminus - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { backslash } r - } - - def cdot - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { dotmath } r - } - - def times - precedence @BinaryOpTimesPrec - associativity left - left l - right r - { - l bin op { multiply } r - } - - def "*" - precedence @BinaryOpTimesPrec - associativity left - left l - right r - { - l bin op { asteriskmath } r - } - - #def diamond { name used above } - - def circ - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { circle } r - } - - #def bullet { name used above } - - def div - precedence @BinaryOpDividePrec - associativity left - left l - right r - { - l bin op { divide } r - } - - def cap - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { intersection } r - } - - def cup - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { union } r - } - - def uplus - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op {@OneRow @HContract { &0.5rt 0.7f @Font plus ^/0.2fo union}} r - } - - def sqcapshape - { - @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { "0 0 moveto 0 ysize lineto xsize ysize lineto" - "xsize 0 lineto 0.04 ft setlinewidth stroke" - } - @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High } - } - PDF @Yield { - { "__mul(__loutf, 0.04) w" - "0 0 m 0 __ysize l __xsize __ysize l __xsize 0 l s" - } - @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High } - } - } - } - - def sqcap - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { sqcapshape } r - } - - def sqcup - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { "180d" @Rotate sqcapshape } r - } - - def triangleleft - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { "90d" @Rotate 0.8f @Font triangle } r - } - - def triangleright - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { "-90d" @Rotate 0.8f @Font triangle } r - } - - def wr - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { vctr {90d @Rotate similar } } r - } - - def bigcirc - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { 1.2f @Font circle} r - } - - def bigtriangleup - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { 1.2f @Font triangle } r - } - - def bigtriangledown - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { 180d @Rotate 1.2f @Font triangle } r - } - - def vee - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { logicalor } r - } - - def wedge - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { logicaland } r - } - - def oplus - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { circleplus } r - } - - def ominus - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { @OneRow @HContract { circle /0io &0.5rt minus } } r - } - - def otimes - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { circlemultiply } r - } - - def oslash - precedence @BinaryOpPrec - associativity left - left l - right r - { - #l bin op { `vctr 60d @Rotate @HContract {circle /0io &0.5rt minus`} } r - l bin op {@OneRow @HContract {circle /0io &0.5rt "-0.1f" @VShift slash}} r - } - - def odot - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { circledot } r - } - - def dagger - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { @Base @Char "dagger" } r - } - - def daggerdbl - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { @Base @Char "daggerdbl" } r - } - - def amalg - precedence @BinaryOpPrec - associativity left - left l - right r - { - l bin op { 180d @Rotate vctr product } r - } - - - ################################################################### - # # - # Group 8 (relations) # - # # - # All Knuth's operators are available, but many have been # - # given different, more mnemonic names. Also included is # - # a not operator for negating the relations. # - # # - ################################################################### - - # "not" done by an option now - # def not right x { @HContract {@OneCol x /0co &0.5rt slash}} - - def rel - precedence @RelationPrec - associativity left - left l - named op { "relop" } - named neg { "no" } - right r - { - - def @Op - { - neg @Case { - { "No" "no" } @Yield op - { "Yes" "yes" } @Yield - { @HContract {@OneCol { & op } /0co &0.5rt slash} } - } - } - - l &@CurrRelSpaceGap @Op &@CurrRelSpaceGap r - } - - def "<" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { less } r - } - - def ">" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { greater } r - } - - def "=" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { equal } r - } - - def "<=" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { lessequal } r - } - - def precsym - { - 0i @HShift 0.45f @Font "-90d" @Rotate {parenrighttp ^| parenlefttp} - } - - def prec - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { precsym } r - } - - def preceq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { @VContract { precsym /0.1f minus } } r - } - - def "<<" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { less less } r - } - - def subset - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { propersubset } r - } - - def subseteq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { reflexsubset } r - } - - def sqsubsetshape - { - @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { "xsize 0 moveto 0 0 lineto 0 ysize lineto" - "xsize ysize lineto 0.04 ft setlinewidth stroke" - } - @Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High } - /0.1f minus - } - PDF @Yield { - { "__mul(__loutf, 0.04) w __xsize 0 m 0 0 l" - "0 __ysize l __xsize __ysize l s" - } - @Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High } - /0.1f minus - } - } - } - - def sqsubseteq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { sqsubsetshape } r - } - - def in - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { element } r - } - - def vdash - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { vctr {"-90d" @Rotate perpendicular} } r - } - - def smile - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { vctr 90d @Rotate parenleft } r - } - - def frown - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { vctr 90d @Rotate parenright } r - } - - def ">=" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { greaterequal } r - } - - def succsym - { - 0.45f @Font 90d @Rotate { parenrighttp ^| parenlefttp } - } - - def succ - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { succsym } r - } - - def succeq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { @OneRow non succ /0.1f minus } r - } - - def ">>" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { greater greater } r - } - - def supset - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { propersuperset } r - } - - def supseteq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { reflexsuperset } r - } - - def sqsupseteqshape - { - @HContract @VContract @BackEnd @Case { - PostScript @Yield { - { "0 0 moveto xsize 0 lineto xsize ysize lineto" - "0 ysize lineto 0.04 ft setlinewidth stroke" - } @Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High } - /0.1f minus - } - PDF @Yield { - { "__mul(__loutf, 0.04) w 0 0 m __xsize 0 l" - "__xsize __ysize l 0 __ysize l s" - } @Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High } - /0.1f minus - } - } - } - - def sqsupseteq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { sqsupseteqshape } r - } - - def ni - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { 180d @Rotate element } r - } - - def dashv - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { vctr {90d @Rotate perpendicular} } r - } - - def mid - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { @Base "|" } r - } - - def parallel - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { @Base "||" } r - } - - def "==" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { equivalence } r - } - - def "~" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { similar } r - } - - def "-~" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { @OneRow { similar ^/0.07f /0.07f minus } } r - } - - def asymp - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { l - rel neg { neg } op { 0.7f @Font @OneRow - { 90d @Rotate parenleft ^/0.008f - /0.008f 90d @Rotate parenright } } - r - } - - def "~~" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { approxequal } r - } - - def "=~" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { congruent } r - } - - def bowtie - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { non triangleright non triangleleft } r - } - - def propto - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { proportional } r - } - - def models - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { @Base vctr "|" &0.05fo vctr equal } r - } - - def trieqsym - { - @OneRow @HContract {&0.5rt small triangle^/0.15f equal} - } - - def trieq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { trieqsym } r - } - - def doteqsym - { - @OneRow @HContract { &0.5rt dotmath^/0.15f equal } - } - - def doteq - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { doteqsym } r - } - - def perp - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { perpendicular } r - } - - def notsub - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { notsubset } r - } - - def notin - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { notelement } r - } - - def "!=" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { notequal } r - } - - def "<->" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowboth } r - } - - def "<--" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowleft } r - } - - def "-->" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowright } r - } - - def up - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowup } r - } - - def down - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowdown } r - } - - def "<=>" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowdblboth } r - } - - def "<==" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowdblleft } r - } - - def "==>" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowdblright } r - } - - def dblup - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowdblup } r - } - - def dbldown - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { arrowdbldown } r - } - - def ":" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { colon } r - } - - def "::" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { @OneCol {colon ` colon} } r - } - - def ":=" - precedence @RelationPrec - associativity left - left l - named neg { "no" } - right r - { - l rel neg { neg } op { colon{ //0.05fo equal } } r - } - - - ################################################################### - # # - # Punctuation symbols (Knuth's Group 13) # - # # - ################################################################### - - def punct - precedence @PunctuationPrec - associativity left - left l - named symbol { "punct" } - right r - { - l &0.0ce symbol &@CurrPunctSpaceGap r - } - - def ";" - precedence @PunctuationPrec - associativity left - left l - right r - { - l punct symbol { semicolon } r - } - - def "," - precedence @PunctuationPrec - associativity left - left l - right r - { - l punct symbol { comma } r - } - - def col - precedence @PunctuationPrec - associativity left - left l - right r - { - l punct symbol { colon } r - } - - - ################################################################### - # # - # Ordinary symbols (to get Roman font) - continued # - # # - ################################################################### - - def "0" { zero } - def "1" { one } - def "2" { two } - def "3" { three } - def "4" { four } - def "5" { five } - def "6" { six } - def "7" { seven } - def "8" { eight } - def "9" { nine } - - - ################################################################### - # # - # The result object # - # # - ################################################################### - - basefont @Font - { Slope xheight2mark nostrut } @Font { initialspace } @Space - { @CurrStyleVar @Yield initialstyle } @SetContext { - { @CrampedVar @Yield initiallycramped } @SetContext { - @Body - } - } - -@End @Math - - -############################################################################### -# # -# In-line equations # -# # -############################################################################### - -macro @M { @HContract @VContract @Math initialstyle { "text" } } |