path: root/include/mathf

###############################################################################
#                                                                             #
#  Lout @Math package for formatting mathematics                              #
#                                                                             #
#  @Math is based on the earlier @Eq package.  @Eq revision history:          #
#                                                                             #
#  Version 1.0 by Jeffrey H. Kingston, December 1990.                         #
#  Version 2.0 by Jeffrey H. Kingston, 22 December 1992.                      #
#  Version 3.0 by Jeffrey H. Kingston and Robert Marsa, March 1996.           #
#                                                                             #
#  @Math revision history:                                                    #
#                                                                             #
#  Version 4.0 by Ludovic Courtès, June 2007.                                 #
#  Version 5.0 by Jeffrey H. Kingston, September 2008.                        #
#                                                                             #
#  Acknowledgement:  @Eq and @Math are based closely on the Eqn language      #
#  of B. W. Kernighan and L. L. Cherry; the spacing rules are similar to      #
#  those of the TeX system by D. E. Knuth.                                    #
#                                                                             #
#  Version 4.0 makes use of `@SetContext' and `@GetContext' (introduced in    #
#  Lout 3.34) to better honor the typesetting conventions outlined by Knuth.  #
#                                                                             #
#  This program is free software; you can redistribute it and/or modify       #
#  it under the terms of the GNU General Public License as published by       #
#  the Free Software Foundation; either Version 3, or (at your option)        #
#  any later version.                                                         #
#                                                                             #
#  This program is distributed in the hope that it will be useful,            #
#  but WITHOUT ANY WARRANTY; without even the implied warranty of             #
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the              #
#  GNU General Public License for more details.                               #
#                                                                             #
#  You should have received a copy of the GNU General Public License          #
#  along with this program; if not, write to the Free Software                #
#  Foundation, Inc., 59 Temple Place, Suite 330, Boston MA 02111-1307 USA     #
#                                                                             #
#  As a special exception, when this file is read by Lout when processing     #
#  a Lout source document, you may use the result without restriction.        #
#                                                                             #
###############################################################################

export

        # Helper symbols
	above below wideabove widebelow
        "`" "``" "```" non big small vctr
	@SuperScriptStyle @SubScriptStyle @NumeratorStyle
	@DenominatorStyle @SquareRootStyle

        # Ordinary symbols (Symbol font)
	space exclam universal numbersign existential percent
	ampersand suchthat parenleft parenright asteriskmath
	plus comma minus period slash zero one two three four
	five six seven eight nine colon semicolon less equal
	greater question congruent Alpha Beta Chi Delta Epsilon
	Phi Gamma Eta Iota thetaone Kappa Lambda Mu Nu Omicron
	Pi Theta Rho Sigma Tau Upsilon sigmaone Omega Xi Psi Zeta
	bracketleft therefore bracketright perpendicular underscore
	radicalex alpha beta chi delta epsilon phi gamma eta iota
	phione kappa lambda mu nu omicron pi theta rho sigma tau
	upsilon omegaone omega xi psi zeta braceleft bar braceright
	similar Upsilonone minute lessequal fraction infinity florin
	club diamond heart spade arrowboth arrowleft arrowup
	arrowright arrowdown degree plusminus second greaterequal
	multiply proportional partialdiff bullet divide notequal
	equivalence approxequal ellipsis arrowvertex arrowhorizex
	carriagereturn aleph Ifraktur Rfraktur weierstrass
	circlemultiply circleplus emptyset intersection union
	propersuperset reflexsuperset notsubset propersubset
	reflexsubset element notelement angle gradient registerserif
	copyrightserif trademarkserif product radical dotmath
	logicalnot logicaland logicalor arrowdblboth arrowdblleft
	arrowdblup arrowdblright arrowdbldown lozenge angleleft
	registersans copyrightsans trademarksans summation parenlefttp
	parenleftex parenleftbt bracketlefttp bracketleftex
	bracketleftbt bracelefttp braceleftmid braceleftbt braceex
	angleright integral integraltp integralex integralbt
	parenrighttp parenrightex parenrightbt bracketrighttp
	bracketrightex bracketrightbt bracerighttp bracerightmid
	bracerightbt

        # Ordinary symbols (arrows)
	leftarrow longleftarrow dblleftarrow dbllongleftarrow
	rightarrow longrightarrow dblrightarrow dbllongrightarrow
	leftrightarrow longleftrightarrow dblleftrightarrow
	dbllongleftrightarrow mapsto longmapsto hookleftarrow
	hookrightarrow leadsto leftharpoonup rightharpoonup
	leftharpoondown rightharpoondown rightleftharpoons
	uparrow dbluparrow downarrow dbldownarrow updownarrow
	dblupdownarrow nearrow searrow swarrow nwarrow

        # Ordinary symbols (to get Roman font)
	arccos arcsin arctan arg cos cosh cot coth csc deg det dim exp
	gcd hom inf ker lg lim liminf limsup ln log max min Pr sec sin
	sinh supr tan tanh mod "0" "1" "2" "3" "4" "5" "6" "7" "8" "9"
	"!" "?" "%" "(" ")" "[" "]"

        # Ordinary symbols (for atleft and atright)
	lpar blpar rpar brpar lbrack blbrack rbrack brbrack lbrace blbrace
	rbrace brbrace lfloor blfloor rfloor brfloor lceil blceil
	rceil brceil langle blangle rangle brangle

        # Ordinary symbols (miscellaneous)
	hbar Re Im partial infty prime nabla surd top bot dbar triangle
	backslash forall exists neg circle filledcircle square ldots cdots
	vdots ddots del grad "..." ",...," "'" "''" "'''" "''''" empty
        triangleup triangledown half third

        # Variable-building symbols
	dot dotdot hat tilde vec dyad overbar underbar
	sup sub tsub supp on ton
	
        # Large operator symbols
	largeop sum prod coprod bcap bcup bvee bwedge bodot botimes
	boplus buplus int oint

        # Unary operator symbols
	sqrt root zroot
	matrix pmatrix bmatrix brmatrix fmatrix cmatrix amatrix

        # Binary operator symbols
	over frac
        bin "+" "-" "+-" "-+" setminus cdot times "*" circ div
	cap cup uplus sqcap sqcup triangleleft triangleright
	wr bigcirc bigtriangleup bigtriangledown vee wedge oplus ominus
	otimes oslash odot dagger daggerdbl amalg

        # Relation symbols
	rel "<" ">" "=" "<=" prec preceq "<<" subset subseteq sqsubseteq
	in vdash smile frown ">=" succ succeq ">>" supset supseteq
	sqsupseteq ni dashv mid parallel "==" "~" "-~" asymp "~~"
	"=~" bowtie propto models doteq trieq perp notsub notin "!="
	"<->" "<--" "-->" up down "<=>" "<==" "==>" dblup dbldown
	":" "::" ":="
        # not

        # Punctuation symbols
	punct ";" "," col

def @Math
    named symbolfont	{ Symbol Base }
    named basefont	{ Times Base  }
    named initialstyle  { "display" }
    named initiallycramped { "No" }
    named initialspace  { separate 0.05f }
    body @Body
@Begin

    ###################################################################
    #                                                                 #
    #   Operator Precedences (private)                                #
    #                                                                 #
    #   All @Math symbols with parameters have explicit precedences   #
    #   defined by invoking one of the following macros.  Symbols     #
    #   that are typically used to build variables have high          #
    #   precedence (84-80), then come unary operators (70), then      #
    #   binary operators (66-60), then relations and the rest.        #
    #   See also http://en.wikipedia.org/wiki/Order_of_operations .   #
    #                                                                 #
    ###################################################################

    macro @MaxPrec		{ 100 }
    macro @HatPrec		{  84 }
    macro @SubPrec		{  82 }
    macro @SupPrec		{  80 }
    macro @UnaryOpPrec		{  70 }
    macro @BinaryOpTimesPrec	{  64 }
    macro @BinaryOpDividePrec	{  62 }
    macro @BinaryOpPrec		{  60 }
    macro @RelationPrec		{  50 }
    macro @PunctuationPrec	{  40 }
    macro @HelperNonPrec	{  26 }
    macro @HelperAbovePrec	{  24 }
    macro @HelperColPrec	{  22 }
    macro @HelperRowPrec	{  20 }


    ###################################################################
    #                                                                 #
    #   Context-sensitive format changes (private)                    #
    #                                                                 #
    #   Equation formatting (according to Knuth) demands changes in   #
    #   the appearance of equations depending on context.  Knuth      #
    #   distinguishes four major styles (the TeXbook, Ch. 17):        #
    #                                                                 #
    #     display        formulas displayed on lines by themselves    #
    #     text           formulas embedded in the text                #
    #     script         formulas used as superscripts or subscripts  #
    #     scriptscript   second-order superscripts or subscripts      #
    #                                                                 #
    #   Each style has its own font size and spacing rules.           #
    #   Additionally, each of these styles can be ``cramped'',        #
    #   meaning that exponents are not raised as much.  To these      #
    #   four styles @Math adds a fifth:                               #
    #                                                                 #
    #     nohspace       formulas enclosed in "non"                   #
    #                                                                 #
    #   which implements the "non" operator by causing all            #
    #   style-dependent horizontal space to be 0.                     #
    #                                                                 #
    ###################################################################

    macro @CurrStyleVar { "EqCurrStyle" }
    macro @CrampedVar   { "EqCramped?"  }

    def @CurrStyle { @GetContext @CurrStyleVar }
    def @Cramped   { @GetContext @CrampedVar   }

    def @EqDebug
    {
        # Uncomment the following line to get debugging information.
        #{ { Helvetica Base 0.7f } @Font @CurrStyle } |0.2f
        @Null
    }

    def @WithStyle
        named style   { "display" }
        named cramped { "No"      }
        right x
    {
        def @NewFontSize
        {
            @CurrStyle @Case {
               "scriptscript" @Yield 1.0f  # can't be smaller
               "script" @Yield {
                  style @Case {
                    "script" @Yield 1.0f
                    else     @Yield 0.8f  } }
               "text"   @Yield {
                  style @Case {
                    "text" @Yield 1.0f
                    else   @Yield 0.7f } }
               "display" @Yield {
                  style @Case {
                    # display and text styles yield the same font size
                    { "display" "text" } @Yield 1.0f
                    else                 @Yield 0.7f } }
               "nohspace" @Yield 1.0f
            }
        }


        #{ Helvetica Base 0.4f } @Font { @CurrStyle -> style } |0.2f
        @NewFontSize @Font
        { @CurrStyleVar @Yield style } @SetContext {
            { @CrampedVar @Yield cramped } @SetContext {
                 # FIXME: Space is not properly inherited, hence this
                 # `@Space' invocation.
                 { initialspace @Space x }
            }
        }
    }

    def @CurrSuperScriptGap
    {
        @Cramped @Case {
          "Yes" @Yield 0.23fk
          "No"  @Yield 0.35fk
        }
    }

    def @SubScriptGap { 0.35fk }

    # Space around relational operators.
    def @CurrRelSpaceGap
    {
        @CurrStyle @Case {
          { "display" "text" } @Yield 0.300fe
	  "nohspace"	       @Yield 0i
          else                 @Yield 0.030ce
        }
    }

    # Space around binary operators.
    def @CurrBinarySpaceGap
    {
        @CurrStyle @Case {
          { "display" "text" } @Yield 0.240fe
	  "nohspace"	       @Yield 0i
          else                 @Yield 0.024ce
        }
    }

    # Space around punctuation marks, including matrix braces.
    def @CurrPunctSpaceGap
    {
        @CurrStyle @Case {
          { "display" "text" } @Yield 0.180fe
	  "nohspace"	       @Yield 0i
          else                 @Yield 0.018ce
        }
    }

    # Gap above/below math expressions (see, e.g., `to' and `from').
    def @AboveGap   { 0.15f }
    def @BelowGap   { 0.15f }

    def @SkewGap  { 0.05f  }
    def @ColGap   { 0.8f   }
    def @RowGap   { 0.5f   }


    ###################################################################
    #                                                                 #
    #   Miscellaneous helper definitions (private)                    #
    #                                                                 #
    ###################################################################

    def @Base precedence @MaxPrec right x { basefont @Font x }
    def @Sym  precedence @MaxPrec right x { symbolfont @Font x }

    def @HLine
	named line { @BackEnd @Case { PostScript @Yield { "0.05 ft setlinewidth" } PDF @Yield { "__mul(__loutf, 0.05) w" } } }
    {
	@BackEnd @Case {
	  PostScript @Yield {
	    { "0 0 moveto xsize 0 lineto" line "stroke" } @Graphic {}
	  }
	  PDF @Yield {	# note re-arrangement of commands (setlinewidth (='w') not allowed in a path)
	    { line "0 0 m __xsize 0 l s" } @Graphic {}
	  }
	}
    }

    def @VLine
    {
	@BackEnd @Case {
	  PostScript @Yield {
	    "0 0 moveto 0 ysize lineto 0.05 ft setlinewidth stroke" @Graphic {}
	  }
	  PDF @Yield {
	    "__mul(__loutf, 0.05) w 0 0 m 0 __ysize l s" @Graphic {}
	  }
	}
    }

    def @Strut
        precedence @MaxPrec
	right x
    {
	@OneCol { x | @OneRow { 0.5f @High ^/ 0.5f @High } }
    }

    def @OrDefault
        left l
        right r
    {
        l @Case {
           "dft" @Yield r
           else  @Yield l
        }
    }


    ###################################################################
    #                                                                 #
    #   Helper symbols (public, exc @ScriptStyle and @FractionStyle)  #
    #                                                                 #
    ###################################################################

    def above
	precedence @HelperAbovePrec
	associativity left
	left x
	named gap { @BelowGap }
	named skew { 0c }
	right y
    {  
	@HContract @VContract
	{          |0.5rt x
	   //gap   |0.5rt &skew y
	}
    }

    def below
	precedence @HelperAbovePrec
	associativity left
	left x
	named gap { @AboveGap }
	named skew { 0c }
	right y
    {
	@HContract @VContract
	{          |0.5rt &skew y
	  ^//gap   |0.5rt x
	}
    }

    def wideabove
	precedence @HelperAbovePrec
	associativity left
	left x
	named gap { @BelowGap  }
	right y
    {
	@HContract @VContract
	{
	    x //gap @HScale y
	}
    }

    def widebelow
	precedence @HelperAbovePrec
	associativity left
	left x
	named gap { @AboveGap  }
	right y
    {
	@HContract @VContract
	{
	    @HScale y ^//gap x
	}
    }

    def "`"       { &@CurrPunctSpaceGap  }
    def "``"      { &@CurrBinarySpaceGap }
    def "```"     { &@CurrRelSpaceGap    }

    def non
        precedence @HelperNonPrec
        right x
    {
        { @CurrStyleVar @Yield "nohspace" } @SetContext x
    }

    def big
        precedence @MaxPrec
	right x
    {
	1.3f @Font x
    }

    def small
        precedence @MaxPrec
	right x
    {
        0.6f @Font x
    }

    def vctr
        precedence @MaxPrec
	right x
    {
	0.5w @VShift x
    }

    def @ScriptStyle
        named level { "sup" }
        right script
    {
        @WithStyle
            style { @CurrStyle @Case {
	        { "display" "text" }        @Yield "script"
	        { "script" "scriptscript" } @Yield "scriptscript"
	        "nohspace"                  @Yield "nohspace"
	    } }
            cramped { level @Case {
	        "sub" @Yield "Yes"
	        "sup" @Yield @Cramped
	    } }
        { script }
    }

    def @SuperScriptStyle right superscript
    {
        @ScriptStyle level { "sup" } superscript
    }

    def @SubScriptStyle right subscript
    {
        @ScriptStyle level { "sub" } subscript
    }

    def @FractionStyle
        named level { "numerator" }
        right x
    {
        @WithStyle
            style { @CurrStyle @Case {
		"display"                   @Yield "text"
		"text"                      @Yield "script"
		{ "script" "scriptscript" } @Yield "scriptscript"
		"nohspace"                  @Yield "nohspace"
	    } }
            cramped { level @Case {
		"numerator"    @Yield @Cramped
		"denominator"  @Yield "Yes"
	    } }
        { x }
    }

    def @NumeratorStyle right x
    {
        @FractionStyle level { "numerator" } x
    }

    def @DenominatorStyle right x
    {
        @FractionStyle level { "denominator" } x
    }

    def @SquareRootStyle right x
    {
        @WithStyle style { @CurrStyle } cramped { "Yes" } x
    }

    ###################################################################
    #                                                                 #
    #   Ordinary symbols (Symbol font)                                #
    #                                                                 #
    #   These symbols and their names are taken directly from the     #
    #   Adobe Systems Inc. Symbol font (see PostScript Language       #
    #   Reference Manual, pp. 256-257).  The only differences are:    #
    #                                                                 #
    #      Adobe:  theta1     @Math:  thetaone                        #
    #              sigma1             sigmaone                        #
    #              phi1               phione                          #
    #              omega1             omegaone                        #
    #              Upsilon1           Upsilonone                      #
    #                                                                 #
    #   These were needed since Lout identifiers do not have digits.  #
    #                                                                 #
    ###################################################################

    def space           { @Sym @Char "space" }
    def exclam          { @Sym @Char "exclam" }
    def universal       { @Sym @Char "universal" }
    def numbersign      { @Sym @Char "numbersign" }
    def existential     { @Sym @Char "existential" }
    def percent         { @Sym @Char "percent" }
    def ampersand       { @Sym @Char "ampersand" }
    def suchthat        { @Sym @Char "suchthat" }
    def parenleft       { @Sym @Char "parenleft" }
    def parenright      { @Sym @Char "parenright" }
    def asteriskmath    { @Sym @Char "asteriskmath" }
    def plus            { @Sym @Char "plus" }
    def comma           { @Sym @Char "comma" }
    def minus           { @Sym @Char "minus" }
    def period          { @Sym @Char "period" }
    def slash           { @Sym @Char "slash" }
    def zero            { @Sym @Char "zero" }
    def one             { @Sym @Char "one" }
    def two             { @Sym @Char "two" }
    def three           { @Sym @Char "three" }
    def four            { @Sym @Char "four" }
    def five            { @Sym @Char "five" }
    def six             { @Sym @Char "six" }
    def seven           { @Sym @Char "seven" }
    def eight           { @Sym @Char "eight" }
    def nine            { @Sym @Char "nine" }
    def colon           { @Sym @Char "colon" }
    def semicolon       { @Sym @Char "semicolon" }
    def less            { @Sym @Char "less" }
    def equal           { @Sym @Char "equal" }
    def greater         { @Sym @Char "greater" }
    def question        { @Sym @Char "question" }
    def congruent       { @Sym @Char "congruent" }
    def Alpha           { @Sym @Char "Alpha" }
    def Beta            { @Sym @Char "Beta" }
    def Chi             { @Sym @Char "Chi" }
    def Delta           { @Sym @Char "Delta" }
    def Epsilon         { @Sym @Char "Epsilon" }
    def Phi             { @Sym @Char "Phi" }
    def Gamma           { @Sym @Char "Gamma" }
    def Eta             { @Sym @Char "Eta" }
    def Iota            { @Sym @Char "Iota" }
    def thetaone        { @Sym @Char "theta1" }
    def Kappa           { @Sym @Char "Kappa" }

    def Lambda          { @Sym @Char "Lambda" }
    def Mu              { @Sym @Char "Mu" }
    def Nu              { @Sym @Char "Nu" }
    def Omicron         { @Sym @Char "Omicron" }
    def Pi              { @Sym @Char "Pi" }
    def Theta           { @Sym @Char "Theta" }
    def Rho             { @Sym @Char "Rho" }
    def Sigma           { @Sym @Char "Sigma" }
    def Tau             { @Sym @Char "Tau" }
    def Upsilon         { @Sym @Char "Upsilon" }
    def sigmaone        { @Sym @Char "sigma1" }
    def Omega           { @Sym @Char "Omega" }
    def Xi              { @Sym @Char "Xi" }
    def Psi             { @Sym @Char "Psi" }
    def Zeta            { @Sym @Char "Zeta" }
    def bracketleft     { @Sym @Char "bracketleft" }
    def therefore       { @Sym @Char "therefore" }
    def bracketright    { @Sym @Char "bracketright" }
    def perpendicular   { @Sym @Char "perpendicular" }
    def underscore      { @Sym @Char "underscore" }
    def radicalex       { @Sym @Char "radicalex" }
    def alpha           { @Sym @Char "alpha" }
    def beta            { @Sym @Char "beta" }
    def chi             { @Sym @Char "chi" }
    def delta           { @Sym @Char "delta" }
    def epsilon         { @Sym @Char "epsilon" }
    def phi             { @Sym @Char "phi" }
    def gamma           { @Sym @Char "gamma" }
    def eta             { @Sym @Char "eta" }
    def iota            { @Sym @Char "iota" }
    def phione          { @Sym @Char "phi1" }
    def kappa           { @Sym @Char "kappa" }
    def lambda          { @Sym @Char "lambda" }
    def mu              { @Sym @Char "mu" }
    def nu              { @Sym @Char "nu" }

    def omicron         { @Sym @Char "omicron" }
    def pi              { @Sym @Char "pi" }
    def theta           { @Sym @Char "theta" }
    def rho             { @Sym @Char "rho" }
    def sigma           { @Sym @Char "sigma" }
    def tau             { @Sym @Char "tau" }
    def upsilon         { @Sym @Char "upsilon" }
    def omegaone        { @Sym @Char "omega1" }
    def omega           { @Sym @Char "omega" }
    def xi              { @Sym @Char "xi" }
    def psi             { @Sym @Char "psi" }
    def zeta            { @Sym @Char "zeta" }
    def braceleft       { @Sym @Char "braceleft" }
    def bar             { @Sym @Char "bar" }
    def braceright      { @Sym @Char "braceright" }
    def similar         { @Sym @Char "similar" }
    def Upsilonone      { @Sym @Char "Upsilon1" }
    def minute          { @Sym @Char "minute" }
    def lessequal       { @Sym @Char "lessequal" }
    def fraction        { @Sym @Char "fraction" }
    # For Adobe Symbol, `infinity' used to be "1.2f @Font { ... }"
    def infinity        { @Sym @Char "infinity" }
    def florin          { @Sym @Char "florin" }
    def club            { @Sym @Char "club" }
    def diamond         { @Sym @Char "diamond" }
    def heart           { @Sym @Char "heart" }
    def spade           { @Sym @Char "spade" }
    def arrowboth       { @Sym @Char "arrowboth" }
    def arrowleft       { @Sym @Char "arrowleft" }
    def arrowup         { @Sym @Char "arrowup" }
    def arrowright      { @Sym @Char "arrowright" }
    def arrowdown       { @Sym @Char "arrowdown" }
    def degree          { @Sym @Char "degree" }
    def plusminus       { @Sym @Char "plusminus" }
    def second          { @Sym @Char "second" }
    def greaterequal    { @Sym @Char "greaterequal" }

    def multiply        { @Sym @Char "multiply" }
    def proportional    { @Sym @Char "proportional" }
    def partialdiff     { @Sym @Char "partialdiff" }
    def bullet          { @Sym @Char "bullet" }
    def divide          { @Sym @Char "divide" }
    def notequal        { @Sym @Char "notequal" }
    def equivalence     { @Sym @Char "equivalence" }
    def approxequal     { @Sym @Char "approxequal" }
    def ellipsis        { @Sym @Char "ellipsis" }
    def arrowvertex     { @Sym @Char "arrowvertex" }
    def arrowhorizex    { @Sym @Char "arrowhorizex" }
    def carriagereturn  { @Sym @Char "carriagereturn" }
    def aleph           { @Sym @Char "aleph" }
    def Ifraktur        { @Sym @Char "Ifraktur" }
    def Rfraktur        { @Sym @Char "Rfraktur" }
    def weierstrass     { @Sym @Char "weierstrass" }
    def circlemultiply  { @Sym @Char "circlemultiply" }
    def circleplus      { @Sym @Char "circleplus" }
    def emptyset        { @Sym @Char "emptyset" }
    def intersection    { @Sym @Char "intersection" }
    def union           { @Sym @Char "union" }
    def propersuperset  { @Sym @Char "propersuperset" }
    def reflexsuperset  { @Sym @Char "reflexsuperset" }
    def notsubset       { @Sym @Char "notsubset" }
    def propersubset    { @Sym @Char "propersubset" }
    def reflexsubset    { @Sym @Char "reflexsubset" }
    def element         { @Sym @Char "element" }
    def notelement      { @Sym @Char "notelement" }
    def angle           { @Sym @Char "angle" }
    def gradient        { @Sym @Char "gradient" }
    def registerserif   { @Sym @Char "registerserif" }
    def copyrightserif  { @Sym @Char "copyrightserif" }
    def trademarkserif  { @Sym @Char "trademarkserif" }
    def product         { @Sym @Char "product" }
    def radical         { @Sym @Char "radical" }
    def dotmath         { @Sym @Char "dotmath" }
    def logicalnot      { @Sym @Char "logicalnot" }
    def logicaland      { @Sym @Char "logicaland" }
    def logicalor       { @Sym @Char "logicalor" }
    def arrowdblboth    { @Sym @Char "arrowdblboth" }
    def arrowdblleft    { @Sym @Char "arrowdblleft" }
    def arrowdblup      { @Sym @Char "arrowdblup" }
    def arrowdblright   { @Sym @Char "arrowdblright" }
    def arrowdbldown    { @Sym @Char "arrowdbldown" }
    def lozenge         { @Sym @Char "lozenge" }
    def angleleft       { @Sym @Char "angleleft" }
    def registersans    { @Sym @Char "registersans" }
    def copyrightsans   { @Sym @Char "copyrightsans" }
    def trademarksans   { @Sym @Char "trademarksans" }
    def summation       { @Sym @Char "summation" }
    def parenlefttp     { @Sym @Char "parenlefttp" }
    def parenleftex     { @Sym @Char "parenleftex" }
    def parenleftbt     { @Sym @Char "parenleftbt" }
    def bracketlefttp   { @Sym @Char "bracketlefttp" }
    def bracketleftex   { @Sym @Char "bracketleftex" }
    def bracketleftbt   { @Sym @Char "bracketleftbt" }
    def bracelefttp     { @Sym @Char "bracelefttp" }
    def braceleftmid    { @Sym @Char "braceleftmid" }
    def braceleftbt     { @Sym @Char "braceleftbt" }
    def braceex         { @Sym @Char "braceex" }
    def angleright      { @Sym @Char "angleright" }
    def integral        { @Sym @Char "integral" }
    def integraltp      { @Sym @Char "integraltp" }
    def integralex      { @Sym @Char "integralex" }
    def integralbt      { @Sym @Char "integralbt" }
    def parenrighttp    { @Sym @Char "parenrighttp" }
    def parenrightex    { @Sym @Char "parenrightex" }
    def parenrightbt    { @Sym @Char "parenrightbt" }
    def bracketrighttp  { @Sym @Char "bracketrighttp" }
    def bracketrightex  { @Sym @Char "bracketrightex" }
    def bracketrightbt  { @Sym @Char "bracketrightbt" }
    def bracerighttp    { @Sym @Char "bracerighttp" }
    def bracerightmid   { @Sym @Char "bracerightmid" }
    def bracerightbt    { @Sym @Char "bracerightbt" }


    ###################################################################
    #                                                                 #
    #  Ordinary symbols (arrows)                                      #
    #                                                                 #
    ###################################################################

    def leftarrow		{ arrowleft }
    def longleftarrow		{ { 1.6 1 } @Scale arrowleft }
    def dblleftarrow		{ arrowdblleft }
    def dbllongleftarrow	{ { 1.6 1 } @Scale arrowdblleft }
    def rightarrow		{ arrowright }
    def longrightarrow		{ { 1.6 1 } @Scale arrowright }
    def dblrightarrow		{ arrowdblright }
    def dbllongrightarrow	{ { 1.6 1 } @Scale arrowdblright }
    def leftrightarrow		{ arrowboth }
    def longleftrightarrow	{ { 1.6 1 } @Scale arrowboth }
    def dblleftrightarrow	{ arrowdblboth }
    def dbllongleftrightarrow	{ { 1.6 1 } @Scale arrowdblboth }

    def mapsto
    {
	@HContract @VContract {
	  @BackEnd @Case {
	    PostScript @Yield {
	      "0 ymark 0.16 ft sub moveto 0 ymark 0.16 ft add lineto stroke"
	      @Graphic arrowright
	    }
	    PDF @Yield {
		"0 __sub(__ymark, __mul(__loutf, 0.16)) m 0 __add(__ymark, __mul(__loutf, 0.16)) l S"
		@Graphic arrowright
	    }
	  }
	}
    }

    def longmapsto
    {
	@HContract @VContract {
	  @BackEnd @Case {
	    PostScript @Yield {
		"0 ymark 0.16 ft sub moveto 0 ymark 0.16 ft add lineto stroke"
		@Graphic { { 1.6 1 } @Scale arrowright }
	    }
	    PDF @Yield {
		"0 __sub(__ymark, __mul(__loutf, 0.16)) m 0 __add(__ymark, __mul(__loutf, 0.16)) l S"
		@Graphic { { 1.6 1 } @Scale arrowright }
	    }
	  }
	}
    }

    def hookleftarrow
    {
	@HContract @VContract {
	  @BackEnd @Case {

	    PostScript @Yield {
		"xsize ymark moveto xsize ymark 0.1 ft add 0.1 ft -90 90 arc stroke"
		@Graphic leftarrow
	    }

	    PDF @Yield {
#
# VT: draws a counterclockwise 180 degree arc from -90 to +90 degree positions
#     (straight down to straight up) with centre = (xsize, ymark + 0.1 ft)
#     and radius = 0.1 ft
#
# the control points therefore are:
#   pt1 = (xsize + (4/3 * 0.1 ft), ymark) and pt2 = (xsize + (4/3 * 0.1 ft), ymark + 0.2 ft)
#
		{
		  "__xsize __ymark m"											# pt0
		  "__add(__xsize, __div(__mul(0.4, __loutf), 3)) __ymark"					# pt1
		  "__add(__xsize, __div(__mul(0.4, __loutf), 3)) __add(__ymark, __mul(0.2, __loutf))"	# pt2
		  "__xsize __add(__ymark, __mul(0.2, __loutf)) c S"						# pt3
		}
		@Graphic leftarrow
	    }

	  }
	}
    }

    def hookrightarrow
    {
	@HContract @VContract {
	  @BackEnd @Case {

	    PostScript @Yield {
		"0 ymark moveto 0 0.1 ft ymark add 0.1 ft -90 90 arcn stroke"
		@Graphic rightarrow
	    }

	    PDF @Yield {
#
# VT: draws a clockwise 180 degree arc from -90 to +90 degree positions
#     (straight down to straight up) with centre = (0, ymark + 0.1 ft)
#     and radius = 0.1 ft
#
# the control points therefore are:
#   pt1 = (-4/3 * 0.1 ft, ymark) and pt2 = (-4/3 * 0.1 ft, ymark + 0.2 ft)
#
		{
		  "0 __ymark m"										# pt0
		  "__div(__mul(-0.4, __loutf), 3) __ymark"					# pt1
		  "__div(__mul(-0.4, __loutf), 3) __add(__ymark, __mul(0.2, __loutf))"	# pt2
		  "0 __add(__ymark, __mul(0.2, __loutf)) c S"					# pt3
		}
		@Graphic rightarrow
	    }

	  }
	}
    }

    def @ClipToSize right x
    {
	@HContract @VContract
	  @BackEnd @Case {
	    PostScript @Yield {
		{
		"grestore newpath 0 0 moveto xsize 0 lineto xsize ysize lineto"
		"0 ysize lineto closepath clip gsave"
		} @Graphic x
	    }
	    PDF @Yield {
		"Q n 0 0 __xsize __ysize re W n q" @Graphic x
	    }
	  }
    }

    def @ClipAboveMark
	left amount
	right x
    {
	@ClipToSize { ^//{{amount}o} x }
    }

    def @ClipBelowMark
	left amount
	right x
    {
	@ClipToSize { x //{{amount}o} }
    }

    def leftharpoonup
    {
	0.04f @ClipBelowMark leftarrow
    }

    def rightharpoonup
    {
	0.04f @ClipBelowMark rightarrow
    }

    def leftharpoondown
    {
	0.02f @ClipAboveMark leftarrow
    }

    def rightharpoondown
    {
	0.02f @ClipAboveMark rightarrow
    }

    def rightleftharpoons
    {
	@HContract @VContract {
		rightharpoonup
		^//0.1fo
		 //0.1fo
		leftharpoondown
	}
    }

    def leadsto		{ @HContract { similar &0.4fo arrowright } }

    def uparrow		{ arrowup }
    def dbluparrow	{ arrowdblup }
    def downarrow	{ arrowdown }
    def dbldownarrow	{ arrowdbldown }
    def updownarrow	{ @HContract { arrowup &0io arrowdown } }
    def dblupdownarrow	{ @VContract { arrowdblup ^//0.2fo arrowdbldown } }
    def nearrow		{ 0.5w @VShift 0.5w @HShift  45d @Rotate arrowright }
    def searrow		{ 0.5w @VShift 0.5w @HShift 315d @Rotate arrowright }
    def swarrow		{ 0.5w @VShift 0.5w @HShift 225d @Rotate arrowright }
    def nwarrow		{ 0.5w @VShift 0.5w @HShift 135d @Rotate arrowright }


    ###################################################################
    #                                                                 #
    #   Ordinary symbols (to get Roman font)                          #
    #                                                                 #
    #   These symbols are defined to yield themselves, but in Roman   #
    #   font rather than the Italic that would otherwise be used.     #
    #   See Knuth p. 162 and 132.  The definitions of "0" ... "9"     #
    #   should logically appear here, but they have been moved to     #
    #   the end since it is awkward to enter numeric lengths after    #
    #   they are defined.                                             #
    #                                                                 #
    ###################################################################

    def arccos	{ @Base "arccos"	}
    def arcsin	{ @Base "arcsin"	}
    def arctan	{ @Base "arctan"	}
    def arg	{ @Base "arg"		}
    def cos	{ @Base "cos"		}
    def cosh	{ @Base "cosh"		}
    def cot	{ @Base "cot"		}
    def coth	{ @Base "coth"		}
    def csc	{ @Base "csc"		}
    def deg	{ @Base "deg"		}
    def det	{ @Base "det"		}
    def dim	{ @Base "dim"		}
    def exp	{ @Base "exp"		}
    def gcd	{ @Base "gcd"		}
    def hom	{ @Base "hom"		}
    def inf	{ @Base "inf"		}
    def ker	{ @Base "ker"		}
    def lg	{ @Base "lg"		}
    def lim	{ @Base "lim"		}
    def liminf	{ @OneCol { @Base "lim" ` @Base "inf" }	}
    def limsup	{ @OneCol { @Base "lim" ` @Base "sup" }	}
    def ln	{ @Base "ln"		}
    def log	{ @Base "log"		}
    def max	{ @Base "max"		}
    def min	{ @Base "min"		}
    def Pr	{ @Base "Pr"		}
    def sec	{ @Base "sec"		}
    def sin	{ @Base "sin"		}
    def sinh	{ @Base "sinh"		}
    def supr	{ @Base "sup"		}
    def tan	{ @Base "tan"		}
    def tanh	{ @Base "tanh"		}
    def mod	{ @Base "mod"		}
    def "!"	{ exclam          }
    def "?"	{ question        }
    def "%"	{ percent         }
    def "("	{ parenleft       }
    def ")"	{ parenright      }
    def "["	{ bracketleft     }
    def "]"	{ bracketright    }


    ###################################################################
    #                                                                 #
    #   Ordinary symbols (for atleft and atright)                     #
    #   These are Knuth's Groups 11 and 12 - openings and closings.   #
    #                                                                 #
    ###################################################################

    def lpar	{ parenleft				}
    def rpar	{ parenright				}
    def lbrack	{ bracketleft				}
    def rbrack	{ bracketright				}
    def lbrace	{ braceleft				}
    def rbrace	{ braceright				}
    def lfloor	{ ` "-0.15f" @VShift bracketleftbt	}
    def rfloor	{   "-0.15f" @VShift bracketrightbt `	}
    def lceil	{ ` "-0.1f"  @VShift bracketlefttp	}
    def rceil	{   "-0.1f"  @VShift bracketrighttp `	}
    def langle	{ angleleft				}
    def rangle	{ angleright				}

    def blpar	{ @OneRow {parenlefttp    ^/ parenleftex    / parenleftbt   } }
    def brpar	{ @OneRow {parenrighttp   ^/ parenrightex   / parenrightbt  } }
    def blbrack	{ @OneRow {bracketlefttp  ^/ bracketleftex  / bracketleftbt } }
    def brbrack	{ @OneRow {bracketrighttp ^/ bracketrightex / bracketrightbt} }
    def blbrace	{ @OneRow {bracelefttp    ^/ braceleftmid   / braceleftbt   } }
    def brbrace	{ @OneRow {bracerighttp   ^/ bracerightmid  / bracerightbt  } }
    def blfloor	{ @OneRow {bracketleftex  ^/ bracketleftex  / bracketleftbt } }
    def brfloor	{ @OneRow {bracketrightex ^/ bracketrightex / bracketrightbt} }
    def blceil	{ @OneRow {bracketlefttp  ^/ bracketleftex  / bracketleftex } }
    def brceil	{ @OneRow {bracketrighttp ^/ bracketrightex / bracketrightex} }

    def blangle
    {
        @HContract @VContract @BackEnd @Case {
	    PostScript @Yield {
	      { "xsize 0 moveto 0 ysize 2 div lineto"
		"xsize ysize lineto 0.04 ft setlinewidth stroke"
	      } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High }
	    }
	    PDF @Yield {
	      { "__mul(__loutf, 0.04) w __xsize 0 m"
		"0 __div(__ysize, 2) l __xsize __ysize l S"
	      } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High }
	    }
	}
    }

    def brangle
    {
        @HContract @VContract @BackEnd @Case {
	    PostScript @Yield {
	      { "0 0 moveto xsize ysize 2 div lineto"
		"0 ysize lineto 0.04 ft setlinewidth stroke"
	      } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High }
	    }
	    PDF @Yield {
	      { "__mul(__loutf, 0.04) w 0 0 m"
		"__xsize __div(__ysize, 2) l 0 __ysize l S"
	      } @Graphic { 0.5f @Wide 2f @High ^/ 2f @High }
	    }
	}
    }


    ###################################################################
    #                                                                 #
    #   Ordinary symbols (miscellaneous)                              #
    #                                                                 #
    #   Not all of Knuth's symbols are available.  The four suits     #
    #   (heartsuit, etc.), have definitions above.                    #
    #                                                                 #
    ###################################################################

    def hbar         { @HContract @VContract {&0.1f @Base "-" ^/0.30fo h }}
    def Re           { Rfraktur					}
    def Im           { Ifraktur					}
    def partial      { partialdiff				}
    def infty        { infinity					}
    def prime        { minute        				}
   #def emptyset     { defined above				}
    def nabla        { gradient					}
    def surd         { radical					}
    def top          { 180d @Rotate perpendicular		}
    def bot          { perpendicular				}
    def dbar         { @Base "||"                         	}
   #def angle        { defined above				}
    def backslash    { "\\"					}
    def forall       { universal				}
    def exists       { existential				}
    def neg          { logicalnot				}

    def circle
    { @HContract @VContract @BackEnd @Case {
	PostScript @Yield {
	  {
	    "xsize ysize 2 div moveto"
	    "xsize 2 div ysize 2 div xsize 2 div 0 360 arc"
	    "0.04 ft setlinewidth stroke"
	  } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High }
	}
	PDF @Yield {
	  #
	  # VT: draws a counterclockwise 360 degree arc from 0 to +360
	  # degree positions (straight right to straight right) with
	  # centre = (xsize/2, ysize/2) and radius = xsize/2, 
	  # implemented as two counterclockwise 180 degree arcs.
	  # start at (xsize, ysize/2); the control points are:
	  #
	  #     pt1 = (xsize, ysize/2 + (4/3 * xsize/2))
	  #     pt2 = (0, ysize/2 + (4/3 * xsize/2))
	  #
	  # end at (0, ysize/2).  Then start at (0, ysize/2); control points
	  #
	  #     pt1 = (0, ysize/2 - (4/3 * xsize/2))
	  #     pt2 = (xsize, ysize/2 - (4/3 * xsize/2))
	  #
	  # and end at (xsize, ysize/2).

	  {
	    "__mul(0.04, __loutf) w"
	    "__xsize __div(__ysize, 2) m"
	    "__xsize __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "0 __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "0 __div(__ysize, 2) c"
	    "0 __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "__xsize __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "__xsize __div(__ysize, 2) c S"
	  } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High }
	}
      }
    }

    def filledcircle
    { @HContract @VContract @BackEnd @Case {
	PostScript @Yield {
	  {
	    "xsize ysize 2 div moveto"
	    "xsize 2 div ysize 2 div xsize 2 div 0 360 arc"
	    "0.04 ft setlinewidth fill"
	  } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High }
	}
	PDF @Yield {
	  #
	  # JK: I don't know how to fill in PDF, so this doesn't!
	  #
	  # VT: draws a counterclockwise 360 degree arc from 0 to +360
	  # degree positions (straight right to straight right) with
	  # centre = (xsize/2, ysize/2) and radius = xsize/2, 
	  # implemented as two counterclockwise 180 degree arcs.
	  # start at (xsize, ysize/2); the control points are:
	  #
	  #     pt1 = (xsize, ysize/2 + (4/3 * xsize/2))
	  #     pt2 = (0, ysize/2 + (4/3 * xsize/2))
	  #
	  # end at (0, ysize/2).  Then start at (0, ysize/2); control points
	  #
	  #     pt1 = (0, ysize/2 - (4/3 * xsize/2))
	  #     pt2 = (xsize, ysize/2 - (4/3 * xsize/2))
	  #
	  # and end at (xsize, ysize/2).

	  {
	    "__mul(0.04, __loutf) w"
	    "__xsize __div(__ysize, 2) m"
	    "__xsize __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "0 __add(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "0 __div(__ysize, 2) c"
	    "0 __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "__xsize __sub(__div(__ysize, 2), __div(__mul(2, __xsize), 3))"
	    "__xsize __div(__ysize, 2) c S"
	  } @Graphic { 0.7f @Wide 0.3f @High ^/ 0.3f @High }
	}
      }
    }

    def square
    { @HContract @VContract @BackEnd @Case {
	PostScript @Yield {
	  {
	    "0 0 moveto xsize 0 lineto xsize ysize lineto"
	    "0 ysize lineto closepath"
	    "0.04 ft setlinewidth stroke"
	  } @Graphic { 0.6f @Wide 0.3f @High ^/ 0.3f @High }
	}
	PDF @Yield {
	  {
	    "__mul(__loutf, 0.04) w"
	    "0 0 m __xsize 0 l __xsize __ysize l"
	    "0 __ysize l s"
	  } @Graphic { 0.6f @Wide 0.3f @High ^/ 0.3f @High }
	}
      }
    }

    def triangle
    { @HContract @VContract @BackEnd @Case {
	PostScript @Yield {
	  {
	    "0 0 moveto xsize 0 lineto"
	    "xsize 2 div ysize lineto closepath"
	    "0.04 ft setlinewidth stroke"
	  } @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High }
	}
	PDF @Yield {
	  {
	    "__mul(__loutf, 0.04) w"
	    "0 0 m __xsize 0 l"
	    "__div(__xsize, 2) __ysize l s"
	  } @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High }
	}
      }
    }

    # other symbols taken from TeX
    def ldots { .       &0.3f .       &0.3f .			}
    def cdots { dotmath &0.3f dotmath &0.3f dotmath		}
    def vdots { @OneRow { dotmath ^/0.3f dotmath /0.3f dotmath } }
    def ddots { @OneCol @OneRow
	       {        dotmath
	         ^/0.3f |0.3f dotmath
                  /0.3f |     |0.3f dotmath
	       }
	      }

    # symbols taken from eqn (Kernighan and Cherry 1975).           #
    def del	{ gradient			}
    def grad	{ gradient			}
    def "..."	{ ellipsis			}
    def ",...,"	{ , ellipsis ``` ,		}
    def "'"	{ minute			}
    def "''"	{ minute minute			}
    def "'''"	{ minute minute minute		}
    def "''''"	{ minute minute minute minute	}
    def empty	{ emptyset			}

    # forget where these are from
    def triangleup	{ 0.8f @Font triangle	}
    def triangledown	{ 180d @Rotate 0.8f @Font triangle	}

    # half and third defined later, since they use frac


    ###################################################################
    #                                                                 #
    #   Variable-building symbols                                     #
    #                                                                 #
    #   These symbols are essentially those of eqn, with some         #
    #   changes and additions.                                        #
    #                                                                 #
    ###################################################################

    def dot
	precedence @HatPrec
	left x
	named gap { @AboveGap }
    {
	x below gap { gap } skew { @SkewGap } @SuperScriptStyle .
    }

    def dotdot
	precedence @HatPrec
	left x
	named gap { @AboveGap }
    {
	x below gap { gap } skew { @SkewGap } @SuperScriptStyle ..
    }

    def hat
	precedence @HatPrec
	left x
	named gap { @AboveGap }
    {
	x below gap { gap } skew { @SkewGap } @SuperScriptStyle @Base "^"
    }

    def tilde
	precedence @HatPrec
	left x
	named gap { @AboveGap }
    {
	x below gap { gap } skew { @SkewGap } @SuperScriptStyle @Base "~"
    }

    def vec
	precedence @HatPrec
	left x
	named gap { @AboveGap }
    {
	x below gap { gap } skew { @SkewGap } @SuperScriptStyle arrowright
    }

    def dyad
	precedence @HatPrec
	left x
	named gap { @AboveGap }
    {
	x below gap { gap } skew { @SkewGap } @SuperScriptStyle arrowboth
    }

    def overbar
	precedence @HatPrec
	left x
	named gap { @AboveGap }
    {
	{ @WithStyle style { @CurrStyle } cramped { "Yes" } x }
        widebelow gap { gap } @SuperScriptStyle minus
    }

    def underbar
	precedence @HatPrec
	left x
	named gap { @BelowGap }
    {
	x wideabove gap { gap } @SuperScriptStyle minus
    }

    def sup
	precedence @SupPrec
	associativity left
	left x
	named gap { "dft" }
	right y
    {
	@HContract @VContract
	{          | @SuperScriptStyle y
	  ^/{ gap @OrDefault @CurrSuperScriptGap }  x
	}
    }

    def sub
	precedence @SubPrec
	associativity left
	left x
	named gap { @SubScriptGap }
	right y
    {
	@HContract @VContract
	{
	       "." @KernShrink x
	  /gap  |  @SubScriptStyle y
	}
    }

    def tsub
	precedence @SubPrec
	associativity left
	left x
	named gap { @SubScriptGap }
	right y
    {
	@HContract @VContract
	{
	       x
	  /gap    |  &0io 0.2f @HShift @SubScriptStyle y
	}
    }

    def supp
	precedence @SupPrec
	associativity left
	left x
	named gap { "dft" }
	right y
    {
	@HContract @VContract
	{
	    { ^/{ gap @OrDefault @CurrSuperScriptGap } x
               /{ gap @OrDefault @CurrSuperScriptGap } }
            | y
	}
    }

    def on
	precedence @SubPrec
	associativity left
	left x
	right y
    {
	{ @SuperScriptStyle x } ^/  /
	{ @SubScriptStyle y }
    }

    def ton
	precedence @SubPrec
	associativity left
	left x
	right y
    {
	@SuperScriptStyle x ^/  /
	&0io 0.3f @HShift @SubScriptStyle y
    }


    ###################################################################
    #                                                                 #
    #   Large operator symbols (Knuth's Group 6 "Large" operators)    #
    #                                                                 #
    #   Layout of large operators differs in several ways, depending  #
    #   on whether they are in display mode or not.                   #
    #                                                                 #
    #     1. The operator itself is larger in display mode.  We       #
    #        achieve this by automatically prepending `big' to the    #
    #        operator's symbol when in display mode.                  #
    #                                                                 #
    #     2. The "bounds" of these operators (i.e., `from' and `to')  #
    #        are set as limits (i.e., above and below the operator    #
    #        symbol) when in display mode, and displayed to the       #
    #        right of the symbol otherwise.  Integrations are an      #
    #        exception (the only exception?).                         #
    #                                                                 #
    #   See ``The TeXbook'', Chapter 17.                              #
    #                                                                 #
    ###################################################################

    def largeop
	named symbol { "largeop" }
        named limits { "dft" } # whether to set `from' and `to' as limits
	named from   { "" }
	named to     { "" }
    {
        def @Symbol
	{
	    @CurrStyle @Case {
	        "display" @Yield { big symbol }
	        else      @Yield symbol
	    }
	}

	def @Limits
	{
	    limits @OrDefault {
		 @CurrStyle @Case {
		    "display" @Yield "Yes"
		     else     @Yield "No" }
	    }
	}

        def @LimitsBody
	{
            @Symbol above { @SuperScriptStyle from }
                    below { @SubScriptStyle to }
        }

        def @NoLimitsBody
	{
	    0.5w @VShift {
	      1.0w @VShift @OneRow {
		      { |  0.3w @VShift @SuperScriptStyle to }
	      ^/0.0fo { 0w @VShift @Symbol | }
	      }

	      /0.0fo

	      { | 0.7w @VShift @SubScriptStyle from }
	    }
	    |{ @CurrPunctSpaceGap }
        }

        @Limits @Case {
            { "Yes" "yes" } @Yield @LimitsBody
            { "No" "no" }   @Yield @NoLimitsBody
        }
    }

    # Ludovic's symbol, no longer used
    def largeoperator
	named symbol { "largeop" }
	named from   { "" }
	named to     { "" }
        named limits { "Yes" } # whether to set `from' and `to' as limits
    {
        def @NoLimitsBody {
	    0.5w @VShift {
	      1.0w @VShift @OneRow {
		      { |  0.3w @VShift @SuperScriptStyle to }
	      ^/0.0fo { 0w @VShift symbol | }
	      }

	      /0.0fo

	      { | 0.7w @VShift @SubScriptStyle from }
	    }
	    |{ @CurrPunctSpaceGap }
        }

        def @LimitsBody {
            symbol above  { @SuperScriptStyle from }
                   below { @SubScriptStyle to }
        }

        limits @Case {
            { "Yes" "yes" } @Yield @LimitsBody
            { "No" "no" }   @Yield @NoLimitsBody
        }
    }

    # Ludovic's symbol, no longer used
    def simplelargeoperator
        named symbol { "simplelargeop" }
        named limits { "dft" }
        named from   { }
        named to     { }
    {
        largeoperator
	  symbol { @CurrStyle @Case {
	    "display" @Yield { big symbol }
	    else      @Yield symbol }
	  }
	  limits { limits @OrDefault {
	       @CurrStyle @Case {
		  "display" @Yield "Yes"
		   else     @Yield "No" }
	       }
	  }
	  from   { from }
	  to     { to }
    }

    def sum
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { summation } limits { limits } from { from } to { to }
    }

    def prod
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { product } limits { limits } from { from } to { to }
    }

    def coprod
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { 180d @Rotate vctr product }
	  limits { limits } from { from } to { to }
    }

    def bcap
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { big intersection } limits { limits } from { from } to { to }
    }

    def bcup
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { big union } limits { limits } from { from } to { to }
    }

    def bvee
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { big logicalor } limits { limits } from { from } to { to }
    }

    def bwedge
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { big logicaland } limits { limits } from { from } to { to }
    }

    def circledot
    {
	def @PureDot   # dot with no extra space
	{
	    @HContract { &0io 0.4w @HShift dotmath }
	}

        @OneRow @HContract { circle /0io &0.5rt @PureDot /0io circle } 
    }


    def bodot
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { circledot }
	  limits { limits } from { from } to { to }
    }

    def botimes
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { circlemultiply } limits { limits } from { from } to { to }
    }

    def boplus
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { circleplus } limits { limits } from { from } to { to }
    }

    def buplus
	named limits { "dft" }
        named from {}
	named to {}
    {
        largeop
	  symbol { & big @HContract { &0.5rt 0.7f @Font plus ^/0.2fo union } }
	  limits { limits } from { from } to { to }
    }


    ###################################################################
    #                                                                 #
    #   Integrations are slightly different in that, according to     #
    #   Knuth (Chapter 17, p. 144), ``superscripts and subscripts     #
    #   are not set as limits, even in display style''.   Still, as   #
    #   in TeX, we give users the possibility to override this.       #
    #                                                                 #
    ###################################################################

    # Ludovic's symbol, no longer used
    def integration
        named symbol { "integration" }
        named limits { "No" }
        named from   { }
        named to     { }
    {
        largeoperator
	  symbol { @CurrStyle @Case {
	    "display" @Yield { big symbol }
	    else      @Yield symbol }
	  }
	  limits { limits } from { from } to { to }
    }

    def int
        named limits { "No" }
        named from   { }
        named to     { }
    {
        largeop
	  symbol { vctr big integral } limits { limits } from { from } to { to }
    }

    def oint
        named limits { "No" }
        named from   { }
        named to     { }
    {
        largeop
	  symbol { @OneCol { vctr degree |0.015fo big integral } }
	  limits { limits } from { from } to { to }
    }


    ###################################################################
    #                                                                 #
    #   Unary operator symbols                                        #
    #                                                                 #
    ###################################################################

    def sqrt
	precedence @UnaryOpPrec
	named gap { @AboveGap }
	right x
    {
	@BackEnd @Case {
	  PostScript @Yield {
	    @HContract @VContract
		{
		    @VScale surd | @OneRow
		    {
			@HLine line { "0.03 ft setlinewidth 2 setlinecap" }
			^//gap  |gap  @SquareRootStyle @Strut x # //gap
		    }
		}
	  }
	  PDF @Yield {
		@HContract @VContract
		{
#
#	VT: this PDF is correct but it renders badly in Acrobat (?problem
#	    with scaling by fractional factors)
#	In other words, the @VScale value comes through correctly but it
#	    looks ugly; GhostScript's translation actually expands the
#	    "draw surd" instruction into raw moveto's and lineto's which
#	    it presumably gets from the font's definition of the glyph!
#
		    @VScale surd | @OneRow
		    {
			@HLine line { "__mul(__loutf, 0.03) w 2 J" }
			^//gap  |gap  @SquareRootStyle @Strut x # //gap
		    }
		}
	  }
	}
    }

    def root
	precedence @UnaryOpPrec
	associativity left
	left x
	right y
    {
	"" sup x &0io sqrt y
    }

    def zroot
	precedence @UnaryOpPrec
	associativity left
	left x
	right y
    {
	def zsup right x { "+0.3f" @VShift 0.5f @Font x }

	"-0.4f" @HShift { 1w @HShift { zsup x } }  &0co sqrt y
    }

    export row axisrow col lcol ccol rcol mcol
    def matrix
	precedence @UnaryOpPrec
	named gap { @CurrBinarySpaceGap }
	named strut
	    named no  { }
	    named No  { }
	    named yes { 0.5f }
	    named Yes { 0.5f }
	{ No }
	named atleft {}
	named atright {}
	named userow { No }
	named shiftdelim { Yes }
	body x
    { 
	def @Strut
	{
	    strut @Case {
		"" @Yield {}
		else @Yield { @OneRow { strut @High ^/ strut @High } }
	    }
	}

	def newrow
	    precedence @HelperRowPrec
	    associativity left
	    left x
	    right y
	{
	    x @Case {
		"" @Yield { y | @Strut }
		else @Yield { x /@RowGap y | @Strut }
	    }
	}

	macro row { newrow "" }

	def newaxisrow
	    precedence @HelperRowPrec
	    associativity left
	    left x
	    right y
	{
	    x @Case {
		"" @Yield { y | @Strut }
		else @Yield { x ^/@RowGap y | @Strut }
	    }
	}

	macro axisrow { newaxisrow "" }

	def col
	    precedence @HelperColPrec
	    associativity left
	    left x
	    named indent { 0.5rt }
	    right y
	{
	    x @Case {
		""   @Yield {            &indent @OneCol y }
		else @Yield { x |@ColGap &indent @OneCol y }
	    }
	}

	def lcol
	    precedence @HelperColPrec
	    associativity left
	    left x
	    right y
	{
	    x col indent { 0i } y
	}

	def ccol
	    precedence @HelperColPrec
	    associativity left
	    left x
	    right y
	{
	    x col indent { 0.5rt } y
	}

	def rcol
	    precedence @HelperColPrec
	    associativity left
	    left x
	    right y
	{
	    x col indent { 1rt } y
	}

	def mcol
	    precedence @HelperColPrec
	    associativity left
	    left x
	    right y
	{
	    x @Case {
		""   @Yield {            @OneCol y }
		else @Yield { x |@ColGap @OneCol y }
	    }
	}

	def delim right x
	{
	    x @Case
	    {
		""   @Yield @Null
		else @Yield
		{
		    shiftdelim @Case {
		    { Yes yes } @Yield { @VScale x }
		    else        @Yield { @VCover x }
		    }
		}
	    }
	}

	@HContract @VContract {
	    delim atleft &@CurrPunctSpaceGap
	    userow @Case {
		{Yes yes} @Yield @HContract @VContract {^//gap @OneRow x //gap}
		else      @Yield vctr @HContract @VContract { //gap x //gap }
	    }
	    &@CurrPunctSpaceGap delim atright
	}
    }

    macro pmatrix  { matrix atleft {1.5f @Font (} atright {1.5f @Font )} }
    macro bmatrix  { matrix atleft { blbrack } atright { brbrack } }
    macro brmatrix { matrix atleft { blbrace } atright { brbrace } }
    macro fmatrix  { matrix atleft { blfloor } atright { brfloor } }
    macro cmatrix  { matrix atleft { blceil  } atright { brceil  } }
    macro amatrix  { matrix atleft { blangle } atright { brangle } }


    ###################################################################
    #                                                                 #
    #   Binary operator symbols                                       #
    #                                                                 #
    ###################################################################

    ###################################################################
    #                                                                 #
    #  over and frac (also half and third)                            #
    #                                                                 #
    ###################################################################

    def over
	precedence @BinaryOpDividePrec
	associativity left
	left x
	named gap { "dft" }
        named belowgap { "dft" }
	right y
    {  
        def @AboveLineGap
        {
            gap @Case {
              "dft" @Yield {
		 @CurrStyle @Case {
		    "display" @Yield 0.20f
		    else      @Yield 0.10f
		 }
              }
              else  @Yield gap
            }
        }

        def @BelowLineGap
        {
            belowgap @Case {
              "dft" @Yield {
		 @CurrStyle @Case {
		    "display" @Yield 0.15f
		    else      @Yield 0.09f
		 }
              }
              else  @Yield belowgap
            }
        }

	@HContract @VContract
	{                  |0.5rt @OneCol @NumeratorStyle x
	  ^//@AboveLineGap @HLine
	   //@BelowLineGap |0.5rt @OneCol @DenominatorStyle @Strut y
	}
    }

    def frac
	precedence @BinaryOpDividePrec
	associativity left
	left x
	named gap { 0.2f }
	right y
    {
	@HContract @VContract
	{ 1w @VShift { @SuperScriptStyle { x } /gap }
          | fraction &0io
          | 0w @VShift { |gap @SubScriptStyle { y } }
	}
    }

    def half { one frac two }
    def third { one frac three }


    ###################################################################
    #                                                                 #
    #   Knuth's Group 7 (binary operations)                           #
    #                                                                 #
    #   All of Knuth's symbols are available except \star, \diamond   #
    #   and \bullet; a few have been given more mnemonic names.       #
    #                                                                 #
    ###################################################################

    def bin
        precedence @BinaryOpPrec
        associativity left
        left l
        named op { "binop" }
        right r
    {
        l &@CurrBinarySpaceGap op &@CurrBinarySpaceGap r
    }

    def "+"
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { plus } r
    }

    def "-"
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { minus } r
    }

    def "+-"
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { plusminus } r
    }

    def "-+"
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { 180d @Rotate plusminus } r
    }

    def setminus
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { backslash } r
    }

    def cdot
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { dotmath } r
    }

    def times
        precedence @BinaryOpTimesPrec
	associativity left
	left l
	right r
    {
        l bin op { multiply } r
    }

    def "*"
        precedence @BinaryOpTimesPrec
	associativity left
	left l
	right r
    {
        l bin op { asteriskmath } r
    }

    #def diamond { name used above }

    def circ
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { circle } r
    }

    #def bullet	{ name used above }

    def div
        precedence @BinaryOpDividePrec
	associativity left
	left l
	right r
    {
        l bin op { divide } r
    }

    def cap
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { intersection } r
    }

    def cup
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { union } r
    }

    def uplus
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op {@OneRow @HContract { &0.5rt 0.7f @Font plus ^/0.2fo union}} r
    }

    def sqcapshape
    {
        @HContract @VContract @BackEnd @Case {
	    PostScript @Yield {
	      {	"0 0 moveto 0 ysize lineto xsize ysize lineto"
		  "xsize 0 lineto 0.04 ft setlinewidth stroke"
	      }
	      @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High }
	    }
	    PDF @Yield {
	      {	"__mul(__loutf, 0.04) w"
		  "0 0 m 0 __ysize l __xsize __ysize l __xsize 0 l s"
	      }
	      @Graphic { 0.3f @Wide 0.3f @High ^| ^/ 0.3f @Wide 0.3f @High }
	    }
	}
    }

    def sqcap
        precedence @BinaryOpPrec
	associativity left
	left l
	right r
    {
        l bin op { sqcapshape } r
    }

    def sqcup
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { "180d" @Rotate sqcapshape } r
    }

    def triangleleft
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
       l bin op { "90d" @Rotate 0.8f @Font triangle } r
    }

    def triangleright
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { "-90d" @Rotate 0.8f @Font triangle } r
    }

    def wr
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { vctr {90d @Rotate similar } } r
    }

    def bigcirc
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { 1.2f @Font circle} r
    }

    def bigtriangleup
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { 1.2f @Font triangle } r
    }

    def bigtriangledown
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { 180d @Rotate 1.2f @Font triangle } r
    }

    def vee
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { logicalor } r
    }

    def wedge
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { logicaland } r
    }

    def oplus
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { circleplus } r
    }

    def ominus
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { @OneRow @HContract { circle /0io &0.5rt minus } } r
    }

    def otimes
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { circlemultiply } r
    }

    def oslash
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        #l bin op { `vctr 60d @Rotate @HContract {circle /0io &0.5rt minus`} } r
        l bin op {@OneRow @HContract {circle /0io &0.5rt "-0.1f" @VShift slash}} r
    }

    def odot
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { circledot } r
    }

    def dagger
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { @Base @Char "dagger" } r
    }

    def daggerdbl
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { @Base @Char "daggerdbl" } r
    }

    def amalg
        precedence @BinaryOpPrec
	associativity left
       	left l
	right r
    {
        l bin op { 180d @Rotate vctr product } r
    }


    ###################################################################
    #                                                                 #
    #   Group 8 (relations)                                           #
    #                                                                 #
    #   All Knuth's operators are available, but many have been       #
    #   given different, more mnemonic names.  Also included is       #
    #   a not operator for negating the relations.                    #
    #                                                                 #
    ###################################################################

    # "not" done by an option now
    # def not right x	{ @HContract {@OneCol x /0co &0.5rt slash}}

    def rel
        precedence @RelationPrec
        associativity left
        left l
        named op { "relop" }
	named neg { "no" }
        right r
    {

        def @Op
	{
	  neg @Case {
	      { "No" "no" } @Yield op
	      { "Yes" "yes"   } @Yield
	        { @HContract {@OneCol { & op } /0co &0.5rt slash} }
	  }
	}

        l &@CurrRelSpaceGap @Op &@CurrRelSpaceGap r 
    }

    def "<"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { less } r
    }

    def ">"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { greater } r
    }

    def "="
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { equal } r
    }

    def "<="
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { lessequal } r
    }

    def precsym
    {
        0i @HShift 0.45f @Font "-90d" @Rotate {parenrighttp ^| parenlefttp}
    }

    def prec
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { precsym } r
    }

    def preceq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { @VContract { precsym /0.1f minus } } r
    }

    def "<<"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { less less } r
    }

    def subset
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { propersubset } r
    }

    def subseteq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { reflexsubset } r
    }

    def sqsubsetshape
    {
        @HContract @VContract @BackEnd @Case {
	    PostScript @Yield {
	        { "xsize 0 moveto 0 0 lineto 0 ysize lineto"
		  "xsize ysize lineto 0.04 ft setlinewidth stroke"
		}
		@Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High }
		/0.1f minus
	    }
	    PDF @Yield {
		{ "__mul(__loutf, 0.04) w __xsize 0 m 0 0 l"
		  "0 __ysize l __xsize __ysize l s"
		}
		@Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High }
		/0.1f minus
	    }
	}
    }

    def sqsubseteq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { sqsubsetshape } r
    }

    def in
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { element } r
    }

    def vdash
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { vctr {"-90d" @Rotate perpendicular} } r
    }

    def smile
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { vctr 90d @Rotate parenleft } r
    }

    def frown
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { vctr 90d @Rotate parenright } r
    }

    def ">="
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { greaterequal } r
    }

    def succsym
    {
        0.45f @Font 90d @Rotate { parenrighttp ^| parenlefttp }
    }

    def succ
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { succsym } r
    }

    def succeq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { @OneRow non succ /0.1f minus } r
    }

    def ">>"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { greater greater } r
    }

    def supset
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { propersuperset } r
    }

    def supseteq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { reflexsuperset } r
    }

    def sqsupseteqshape
    {
        @HContract @VContract @BackEnd @Case {
	    PostScript @Yield {
	     	{ "0 0 moveto xsize 0 lineto xsize ysize lineto"
		   "0 ysize lineto 0.04 ft setlinewidth stroke"
	        } @Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High }
	        /0.1f minus
	    }
	    PDF @Yield {
	     	{ "__mul(__loutf, 0.04) w 0 0 m __xsize 0 l"
		  "__xsize __ysize l 0 __ysize l s"
		} @Graphic { 0.5f @Wide 0.25f @High ^/ 0.25f @High }
	        /0.1f minus
	     }
	}
    }

    def sqsupseteq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { sqsupseteqshape } r
    }

    def ni
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { 180d @Rotate element } r
    }

    def dashv
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { vctr {90d @Rotate perpendicular} } r
    }

    def mid
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { @Base "|" } r
    }

    def parallel
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { @Base "||" } r
    }

    def "=="
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { equivalence } r
    }

    def "~"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { similar } r
    }

    def "-~"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { @OneRow { similar ^/0.07f /0.07f minus } } r
    }

    def asymp
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {  l
       rel neg { neg } op { 0.7f @Font @OneRow
		   { 90d @Rotate parenleft ^/0.008f
		   /0.008f 90d @Rotate parenright } }
       r
    }

    def "~~"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { approxequal } r
    }

    def "=~"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { congruent } r
    }

    def bowtie
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { non triangleright non triangleleft } r
    }

    def propto
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { proportional } r
    }

    def models
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { @Base vctr "|" &0.05fo vctr equal } r
    }

    def trieqsym
    {
        @OneRow @HContract {&0.5rt small triangle^/0.15f equal}
    }

    def trieq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { trieqsym } r
    }

    def doteqsym
    {
        @OneRow @HContract { &0.5rt dotmath^/0.15f equal }
    }

    def doteq
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { doteqsym } r
    }

    def perp
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { perpendicular } r
    }

    def notsub
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { notsubset } r
    }

    def notin
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { notelement } r
    }

    def "!="
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { notequal } r
    }

    def "<->"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowboth } r
    }

    def "<--"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowleft } r
    }

    def "-->"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowright } r
    }

    def up
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowup } r
    }

    def down
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowdown } r
    }

    def "<=>"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowdblboth } r
    }

    def "<=="
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowdblleft } r
    }

    def "==>"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowdblright } r
    }

    def dblup
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowdblup } r
    }

    def dbldown
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { arrowdbldown } r
    }

    def ":"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { colon } r
    }

    def "::"
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { @OneCol {colon ` colon} } r
    }

    def ":="
        precedence @RelationPrec
	associativity left
       	left l
	named neg { "no" }
	right r
    {
        l rel neg { neg } op { colon{ //0.05fo equal } } r
    }


    ###################################################################
    #                                                                 #
    #   Punctuation symbols (Knuth's Group 13)                        #
    #                                                                 #
    ###################################################################

    def punct
       precedence @PunctuationPrec
       associativity left
       left l
       named symbol { "punct" }
       right r
    {
        l &0.0ce symbol &@CurrPunctSpaceGap r
    }

    def ";"
        precedence @PunctuationPrec
	associativity left
	left l
	right r
    {
        l punct symbol { semicolon } r
    }

    def ","
        precedence @PunctuationPrec
	associativity left
	left l
	right r
    {
        l punct symbol { comma } r
    }

    def col
        precedence @PunctuationPrec
	associativity left
	left l
	right r
    {
        l punct symbol { colon } r
    }


    ###################################################################
    #                                                                 #
    #   Ordinary symbols (to get Roman font) - continued              #
    #                                                                 #
    ###################################################################

    def "0" { zero            }
    def "1" { one             }
    def "2" { two             }
    def "3" { three           }
    def "4" { four            }
    def "5" { five            }
    def "6" { six             }
    def "7" { seven           }
    def "8" { eight           }
    def "9" { nine            }


    ###################################################################
    #                                                                 #
    #   The result object                                             #
    #                                                                 #
    ###################################################################

    basefont @Font
    { Slope xheight2mark nostrut } @Font { initialspace } @Space
    { @CurrStyleVar @Yield initialstyle } @SetContext {
      { @CrampedVar @Yield initiallycramped } @SetContext {
        @Body
      }
    }

@End @Math


###############################################################################
#                                                                             #
#   In-line equations                                                         #
#                                                                             #
###############################################################################

macro @M { @HContract @VContract @Math initialstyle { "text" } }