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Diffstat (limited to 'include/mathf')
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diff --git a/include/mathf b/include/mathf new file mode 100644 index 0000000..8c395fd --- /dev/null +++ b/include/mathf @@ -0,0 +1,2114 @@ + +############################################################################### +# # +# Lout @Math package for equation formatting, based on @Eq. # +# # +# @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 1.0 by Ludovic Courtès, June 2007. # +# # +# See "Eq - a Lout package for typesetting mathematics" for user # +# information. Acknowledgement: the @Eq language is 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 # +# Basser Lout 3.34) to better honor the typesetting conventions outlined by # +# Knuth. # +# # +############################################################################### + +export "`" "``" "```" bin rel punct non vctr big small + + 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 + + hbar Re Im partial infty prime nabla surd top bot dbar + triangle backslash forall exists neg + circle filledcircle square + + "0" "1" "2" "3" "4" "5" "6" "7" "8" "9" + + sum prod coprod int oint bcap bcup bvee bwedge bodot botimes + boplus buplus + + "+" "-" "+-" "-+" 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 + + "<" ">" "=" "<=" 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 "!=" not + "<->" "<--" "-->" up down "<=>" "<==" "==>" dblup dbldown + ":" "::" ":=" + + lpar blpar rpar brpar lbrack blbrack rbrack brbrack lbrace blbrace + rbrace brbrace lfloor blfloor rfloor brfloor lceil blceil + rceil brceil langle blangle rangle brangle + + ";" "," col + + "!" "?" "%" "(" ")" "[" "]" + + 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 ldots cdots vdots ddots del grad + "..." ",...," "'" "''" "'''" "''''" empty + + triangleup triangledown + + 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 + + sup sub tsub supp on ton frac half third over + atop below wideatop widebelow + dot dotdot hat tilde vec dyad overbar underbar sqrt root zroot + matrix pmatrix bmatrix brmatrix fmatrix cmatrix amatrix + + @SuperScriptStyle @SubScriptStyle + @NumeratorStyle @DenominatorStyle + @SquareRootStyle + +def @Math + named symbolfont { Symbol Base } + named basefont { Times Base } + named initialstyle { "display" } + named initiallycramped { "No" } + named initialspace { separate 0.05f } + body @Body +@Begin + + + ################################################################### + # # + # Context-sensitive format changes. # + # # + # 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 style (formulas displayed on lines by themselves) # + # text style (formulas embedded in the text) # + # script style (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. # + # # + ################################################################### + + 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 } } + } + } + + + #{ 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. + { @EqDebug initialspace @Space x } + } + } + } + + def @CurrSuperScriptGap + { + @Cramped @Case { + "Yes" @Yield 0.23fk + "No" @Yield 0.35fk + } + } + + def @SubScriptGap { 0.35fk } + + + ################################################################### + # # + # Spacing rules. # + # # + ################################################################### + + # Space around relational operators. + def @CurrRelSpaceGap + { + @CurrStyle @Case { + { "display" "text" } @Yield 0.300fe + else @Yield 0.030ce + } + } + + # Space around binary operators. + def @CurrBinarySpaceGap + { + @CurrStyle @Case { + { "display" "text" } @Yield 0.240fe + else @Yield 0.024ce + } + } + + # Space around punctuation marks, including matrix braces. + def @CurrPunctSpaceGap + { + @CurrStyle @Case { + { "display" "text" } @Yield 0.180fe + else @Yield 0.018ce + } + } + + def "`" { &@CurrPunctSpaceGap } + def "``" { &@CurrBinarySpaceGap } + def "```" { &@CurrRelSpaceGap } + def bin left l named op { "binop" } right r + { l &@CurrBinarySpaceGap op &@CurrBinarySpaceGap r } + def rel left l named op { "relop" } right r + { l &@CurrRelSpaceGap op &@CurrRelSpaceGap r } + def punct left l named symbol { "punct" } right r + { l &0.0ce symbol &@CurrPunctSpaceGap r } + + # 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 } + + + ################################################################### + # # + # Major styles: scripts, fractions, and square roots. # + # # + ################################################################### + + def @ScriptStyle + named level { "sup" } + right script + { + @WithStyle + style { @CurrStyle @Case { + { "display" "text" } @Yield "script" + { "script" "scriptscript" } @Yield "scriptscript" } } + 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" } } + 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 + } + + + ################################################################### + # # + # Utilities: `big', `small', `@HLine', etc. # + # # + ################################################################### + + # XXX: Certainly not the best way to implement `non'. + def non right x { { @CurrStyleVar @Yield "script" } @SetContext x } + def big right x { 1.3f @Font x } + def small right x { 0.6f @Font x } + + def @Base right x { basefont @Font x } + def @Sym 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 vctr + right x + { + 0.5w @VShift x + } + + def @Strut right x + { + @OneCol { x | @OneRow { 0.5f @High ^/ 0.5f @High } } + } + + ################################################################### + # # + # Full names # + # # + # 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 Eq: thetaone # + # sigma1 sigmaone # + # phi1 phione # + # omega1 omegaone # + # # + # 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 "thetaone" } + 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 "sigmaone" } + 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 "phione" } + 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 "omegaone" } + 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 "Upsilonone" } + 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 @PureDot # dot with no extra space + { + @HContract { &0io 0.4w @HShift 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" } + + + ################################################################### + # # + # Short names # + # # + # These symbols, their names, and their spacing, are based on # + # the list in Appendix F of Donald E. Knuth's The TeXBook. # + # # + # Group 1 (lowercase Greek letters): see full names above # + # Group 2 (uppercase Greek letters): see full names above # + # Group 3 (calligraphic capitals): not provided by Eq # + # # + ################################################################### + + ################################################################### + # # + # Group 4 (miscellaneous Ord symbols) # + # # + # Not all of Knuth's symbols are available. The four suits # + # (heartsuit, etc.), have definitions above. # + # # + ################################################################### + + def hbar { @OneCol { &0.1f @Base "-" ^/0.25fo 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 } + } + } + } + + + ################################################################### + # # + # Layout primitives. # + # # + ################################################################### + + def atop + precedence 73 + 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 73 + associativity left + left x + named gap { @AboveGap } + named skew { 0c } + right y + { + @HContract @VContract + { |0.5rt &skew y + ^//gap |0.5rt x + } + } + + def wideatop + precedence 73 + associativity left + left x + named gap { @BelowGap } + right y + { + @HContract @VContract + { + x //gap @HScale y + } + } + + def widebelow + precedence 73 + associativity left + left x + named gap { @AboveGap } + right y + { + @HContract @VContract + { + @HScale y ^//gap x + } + } + + ################################################################### + # # + # Operator Precedence # + # # + # We use the precedence illustrated by the following macros # + # for the various operator groups. I.e., exponentiation and # + # square root precede multiplication and division, which in # + # turn precede addition and substraction, etc. # + # See http://en.wikipedia.org/wiki/Order_of_operations . # + # # + ################################################################### + + macro @PunctuationPrec { 13 } + + macro @EqualityPrec { 23 } + macro @OrderingPrec { 33 } + macro @AdditionPrec { 43 } + macro @MultiplicationPrec { 53 } + macro @DivisionPrec { 54 } + macro @ExponentPrec { 63 } + macro @FactorialPrec { 73 } + + + ################################################################### + # # + # 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 largeoperator + precedence 58 + 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 atop { @SuperScriptStyle from } + below { @SubScriptStyle to } + } + + limits @Case { + { "Yes" "yes" } @Yield @LimitsBody + { "No" "no" } @Yield @NoLimitsBody + } + } + + def simplelargeoperator + named symbol { "simplelargeop" } + named limits { "Auto" } + named from { } + named to { } + { + largeoperator symbol { @CurrStyle @Case { + "display" @Yield { big symbol } + else @Yield symbol } } + limits { limits @Case { + "Auto" @Yield { + @CurrStyle @Case { + "display" @Yield "Yes" + else @Yield "No" } } + else @Yield limits } } + from { from } + to { to } + } + + def sum named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { summation } limits { limits } + from { from } to { to } } + def prod named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { product } limits { limits } + from { from } to { to } } + def coprod named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { 180d @Rotate vctr product } + limits { limits } + from { from } to { to } } + def bcap named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { intersection } limits { limits } + from { from } to { to } } + def bcup named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { union } limits { limits } + from { from } to { to } } + def bvee named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { logicalor } limits { limits } + from { from } to { to } } + def bwedge named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { logicaland } limits { limits } + from { from } to { to } } + def bodot named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { & @HContract { + circle /0io &0.5rt @PureDot } } + limits { limits } + from { from } to { to } } + def botimes named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { circlemultiply } limits { limits } + from { from } to { to } } + def boplus named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { circleplus } limits { limits } + from { from } to { to } } + def buplus named from { } named to { } named limits { "Auto" } + { simplelargeoperator symbol { & @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 let users the possibility to override this. # + # # + ################################################################### + + 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 { } + { + integration symbol { vctr integral } + limits { limits } + from { from } + to { to } + } + + def oint + named limits { "No" } + named from { } + named to { } + { + integration symbol { @OneCol { vctr degree |0.015fo int } } + limits { limits } + from { from } + to { to } + } + + + + ################################################################### + # # + # 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 "+" precedence @AdditionPrec left l right r + { l bin op { plus } r } + def "-" precedence @AdditionPrec left l right r + { l bin op { minus } r } + def "+-" precedence @AdditionPrec left l right r + { l bin op { plusminus } r } + def "-+" precedence @AdditionPrec left l right r + { l bin op { 180d @Rotate plusminus } r } + def setminus precedence @AdditionPrec left l right r + { l bin op { backslash } r } + def cdot precedence @AdditionPrec left l right r + { l bin op { dotmath } r } + def times precedence @MultiplicationPrec left l right r + { l bin op { multiply } r } + def "*" precedence @MultiplicationPrec left l right r + { l bin op { asteriskmath } r } + #def diamond { name used above } + def circ precedence @MultiplicationPrec left l right r + { l bin op { circle } r } + #def bullet { name used above } + def div precedence @DivisionPrec left l right r + { l bin op { divide } r } + def cap precedence @MultiplicationPrec left l right r + { l bin op { intersection } r } + def cup precedence @MultiplicationPrec left l right r + { l bin op { union } r } + def uplus precedence @MultiplicationPrec left l right r + { l + bin op { @OneRow @HContract { &0.5rt 0.7f @Font plus ^/0.2fo union} } + r } + + def sqcap precedence @MultiplicationPrec left l right r + { l + bin op { @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 + } + } + } + } + r } + + def sqcup { 180d @Rotate sqcap } + def triangleleft left l right r + { l bin op { "90d" @Rotate 0.8f @Font triangle } r } + def triangleright left l right r + { l bin op { "-90d" @Rotate 0.8f @Font triangle } r } + def wr left l right r + { l bin op { vctr {90d @Rotate similar } } r } + def bigcirc left l right r + { l bin op { 1.2f @Font circle} r } + def bigtriangleup left l right r + { l bin op { 1.2f @Font triangle } r } + def bigtriangledown left l right r + { l bin op { 180d @Rotate 1.2f @Font triangle } r } + def vee left l right r + { l bin op { logicalor } r } + def wedge left l right r + { l bin op { logicaland } r } + def oplus left l right r + { l bin op { circleplus } r } + def ominus left l right r + { l bin op { @OneRow @HContract { circle /0io &0.5rt minus } } r } + def otimes left l right r + { l bin op { circlemultiply } r } + def oslash left l right r + { l + bin op { `vctr 60d @Rotate @HContract {circle /0io &0.5rt minus`} } + r } + def odot left l right r + { l bin op { @OneRow @HContract {circle /0io &0.5rt @PureDot } } r } + def dagger left l right r + { l bin op { @Base @Char "dagger" } r } + def daggerdbl left l right r + { l bin op { @Base @Char "daggerdbl" } r } + def amalg 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. # + # # + ################################################################### + + def "<" precedence @OrderingPrec left l right r + { l rel op { less } r } + def ">" precedence @OrderingPrec left l right r + { l rel op { greater } r } + def "=" precedence @EqualityPrec left l right r + { l rel op { equal } r } + def "<=" precedence @OrderingPrec left l right r + { l rel op { lessequal } r } + def prec left l right r + { l + rel op { 0.45f @Font "-90d" + @Rotate { parenrighttp ^| parenlefttp } } + r } + def preceq { rel { @OneRow non prec /0.1f minus } } + def "<<" precedence @OrderingPrec left l right r + { l rel op { less less } r } + def subset precedence @OrderingPrec left l right r + { l rel op { propersubset } r } + def subseteq precedence @OrderingPrec left l right r + { l rel op { reflexsubset } r } + def sqsubseteq precedence @OrderingPrec left l right r + { l + rel op { @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 + } + } + } + } + r } + + def in precedence @OrderingPrec left l right r + { l rel op { element } r } + def vdash precedence @OrderingPrec left l right r + { l rel op { vctr {"-90d" @Rotate perpendicular} } r } + def smile precedence @OrderingPrec left l right r + { l rel op { vctr 90d @Rotate parenleft } r } + def frown precedence @OrderingPrec left l right r + { l rel op { vctr 90d @Rotate parenright } r } + + def ">=" precedence @OrderingPrec left l right r + { l rel op { greaterequal } r } + def succ precedence @OrderingPrec left l right r + { l + rel op { 0.45f @Font 90d @Rotate + { parenrighttp ^| parenlefttp } } + r } + def succeq precedence @OrderingPrec left l right r + { l rel op { @OneRow non succ /0.1f minus } r } + def ">>" precedence @OrderingPrec left l right r + { l rel op { greater greater } r } + def supset precedence @OrderingPrec left l right r + { l rel op { propersuperset } r } + def supseteq precedence @OrderingPrec left l right r + { l rel op { reflexsuperset } r } + def sqsupseteq precedence @OrderingPrec left l right r + { l + rel op { @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 + } + } + } + } + r } + def ni precedence @OrderingPrec left l right r + { l rel op { 180d @Rotate element } r } + def dashv precedence @OrderingPrec left l right r + { l rel op { vctr {90d @Rotate perpendicular} } r } + def mid precedence @OrderingPrec left l right r + { l rel op { @Base "|" } r } + def parallel precedence @OrderingPrec left l right r + { l rel op { @Base "||" } r } + + def "==" precedence @EqualityPrec left l right r + { l rel op { equivalence } r } + def "~" precedence @EqualityPrec left l right r + { l rel op { similar } r } + def "-~" precedence @EqualityPrec left l right r + { l rel op { @OneRow{similar^/0.07f/0.07f minus} } r } + def asymp precedence @EqualityPrec left l right r + { l + rel op { 0.7f @Font @OneRow + { 90d @Rotate parenleft ^/0.008f + /0.008f 90d @Rotate parenright } } + r } + def "~~" precedence @EqualityPrec left l right r + { l rel op { approxequal } r } + def "=~" precedence @EqualityPrec left l right r + { l rel op { congruent } r } + def bowtie precedence @EqualityPrec left l right r + { l rel op { non triangleright non triangleleft } r } + def propto precedence @EqualityPrec left l right r + { l rel op { proportional } r } + def models precedence @EqualityPrec left l right r + { l rel op { @Base vctr "|" &0.05fo vctr equal } r } + def trieq precedence @EqualityPrec left l right r + { l + rel op { @OneRow @HContract {&0.5rt small triangle^/0.15f equal} } + r } + def doteq precedence @EqualityPrec left l right r + { l + rel op { @OneRow @HContract { &0.5rt dotmath^/0.15f equal } } + r } + def perp precedence @EqualityPrec left l right r + { l rel op { perpendicular } r } + + def notsub precedence @OrderingPrec left l right r + { l rel op { notsubset } r } + def notin precedence @OrderingPrec left l right r + { l rel op { notelement } r } + def "!=" precedence @EqualityPrec left l right r + { l rel op { notequal } r } + + def "<->" left l right r + { l rel op { arrowboth } r } + def "<--" left l right r + { l rel op { arrowleft } r } + def "-->" left l right r + { l rel op { arrowright } r } + def up left l right r + { l rel op { arrowup } r } + def down left l right r + { l rel op { arrowdown } r } + def "<=>" left l right r + { l rel op { arrowdblboth } r } + def "<==" left l right r + { l rel op { arrowdblleft } r } + def "==>" left l right r + { l rel op { arrowdblright } r } + def dblup left l right r + { l rel op { arrowdblup } r } + def dbldown left l right r + { l rel op { arrowdbldown } r } + + def ":" left l right r + { l rel op { colon } r } + def "::" left l right r + { l rel op { @OneCol {colon ` colon} } r } + def ":=" left l right r + { l rel op { colon{ //0.05fo equal } } r } + + def not right x { @HContract {@OneCol x /0co &0.5rt slash}} + + + ################################################################### + # # + # 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 } + } + } + } + + + ################################################################### + # # + # Group 13 - punctuation. # + # # + ################################################################### + + def ";" precedence @PunctuationPrec left l right r + { l punct symbol { semicolon } r } + def "," precedence @PunctuationPrec left l right r + { l punct symbol { comma } r } + def col precedence @PunctuationPrec left l right r + { l punct symbol { colon } r } + + + ################################################################### + # # + # Additional short symbols (Knuth p. 132) # + # # + ################################################################### + + def "!" { exclam } + def "?" { question } + def "%" { percent } + def "(" { parenleft } + def ")" { parenright } + def "[" { bracketleft } + def "]" { bracketright } + + + ################################################################### + # # + # Common mathematical functions (from Knuth p. 162). # + # mod is included, since @Rel mod is easily typed if needed. # + # # + ################################################################### + + 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" } + + + ################################################################### + # # + # Arrow symbols. # + # # + ################################################################### + + 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 } + + + ################################################################### + # # + # 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 } + + + + ################################################################### + # # + # Miscellaneous # + # # + ################################################################### + + def triangleup { 0.8f @Font triangle } + def triangledown { 180d @Rotate 0.8f @Font triangle } + + ################################################################### + # # + # Symbols with parameters. # + # # + # These symbols are essentially those of eqn, with some # + # changes and additions. # + # # + ################################################################### + + def @OrDefault + left l + right r + { + l @Case { + "dft" @Yield r + else @Yield l + } + } + + def sup + precedence @FactorialPrec + associativity left + left x + named gap { "dft" } + right y + { + @HContract @VContract + { | @SuperScriptStyle y + ^/{ gap @OrDefault @CurrSuperScriptGap } x + } + } + + def sub + precedence 72 + associativity left + left x + named gap { @SubScriptGap } + right y + { + @HContract @VContract + { + "." @KernShrink x + /gap | @SubScriptStyle y + } + } + + def tsub + precedence 72 + associativity left + left x + named gap { @SubScriptGap } + right y + { + @HContract @VContract + { + x + /gap | &0io 0.2f @HShift @SubScriptStyle y + } + } + + def supp + precedence @FactorialPrec + associativity left + left x + named gap { "dft" } + right y + { + @HContract @VContract + { + { ^/{ gap @OrDefault @CurrSuperScriptGap } x + /{ gap @OrDefault @CurrSuperScriptGap } } + | y + } + } + + def on + precedence 74 + associativity left + left x + right y + { + { @SuperScriptStyle x } ^/ / + { @SubScriptStyle y } + } + + def ton + precedence 74 + associativity left + left x + right y + { + @SuperScriptStyle x ^/ / + &0io 0.3f @HShift @SubScriptStyle y + } + + def frac + precedence @DivisionPrec + 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 { 1 frac 2 } + def third { 1 frac 3 } + + def over + precedence @DivisionPrec + 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 dot + precedence @FactorialPrec + left x + named gap { @AboveGap } + { + x below gap { gap } skew { @SkewGap } . + } + + def dotdot + precedence @FactorialPrec + left x + named gap { @AboveGap } + { + x below gap { gap } skew { @SkewGap } .. + } + + def hat + precedence @FactorialPrec + left x + named gap { @AboveGap } + { + x below gap { gap } skew { @SkewGap } @Base "^" + } + + def tilde + precedence @FactorialPrec + left x + named gap { @AboveGap } + { + x below gap { gap } skew { @SkewGap } @Base "~" + } + + def vec + precedence @FactorialPrec + left x + named gap { @AboveGap } + { + x below gap { gap } skew { @SkewGap } arrowright + } + + def dyad + precedence @FactorialPrec + left x + named gap { @AboveGap } + { + x below gap { gap } skew { @SkewGap } arrowboth + } + + def overbar + precedence @FactorialPrec + left x + named gap { @AboveGap } + { + { @WithStyle style { @CurrStyle } cramped { "Yes" } x } + widebelow gap { gap } minus + } + + def underbar + precedence @FactorialPrec + left x + named gap { @BelowGap } + { + x wideatop gap { gap } minus + } + + def sqrt + precedence @ExponentPrec + 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 @ExponentPrec + left x + right y + { + "" sup x &0io sqrt y + } + + def zroot + precedence @ExponentPrec + 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 100 + 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 50 + associativity left + left x + right y + { + x @Case { + "" @Yield { y | @Strut } + else @Yield { x /@RowGap y | @Strut } + } + } + + macro row { newrow "" } + + def newaxisrow + precedence 50 + associativity left + left x + right y + { + x @Case { + "" @Yield { y | @Strut } + else @Yield { x ^/@RowGap y | @Strut } + } + } + + macro axisrow { newaxisrow "" } + + def col + precedence 52 + 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 52 + associativity left + left x + right y + { + x col indent { 0i } y + } + + def ccol + precedence 52 + associativity left + left x + right y + { + x col indent { 0.5rt } y + } + + def rcol + precedence 52 + associativity left + left x + right y + { + x col indent { 1rt } y + } + + def mcol + precedence 52 + 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 } } + + + ################################################################### + # # + # Group 5 (digits) # + # # + ################################################################### + + 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 } + + + + 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" } } |