
###############################################################################
#                                                                             #
#  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 Courts, 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" } }
