@Section
   @Title { Summary }
   @Tag { mat_summ }
@Begin
@PP
This section is a complete list of the symbols provided by
{@Code "@Math"}.  We divide them into @I { helper }, @I { ordinary },
@I { variable-building }, @I { large operator }, @I { unary operator },
@I { binary operator }, @I { relation }, and @I { punctuation } symbols.
mathematics.precedence @SubIndex { precedence of symbols }
precedence.mathematics @Index { precedence of symbols (mathematics) }
The precedences of these symbols, where relevant, are as follows:
@ID @OneRow @Tbl
    mv { 0.5vx }
    aformat { @Cell ml { 0i } A | @Cell indent { ctr } B | @Cell mr { 0i } C }
    afont { Italic }
    bformat { @Cell ml { 0i } A | @Cell indent { ctr } B | @Cell mr { 0i } C }
{
@Rowa
   ma { 0i }
   A { Symbol type }
   B { Precedence }
   C { Symbols }
   rb { yes }
@Rowb
   A { Helper }
   B { 100 }
   C { @Code { "big" } @Code { "small" } @Code { "vctr" }
@Code { "@SuperScriptStyle" } etc.
# @Code { "@SubScriptStyle" }
# @Code { "@NumeratorStyle" } @Code { "@DenominatorStyle" }
# @Code { "@SquareRootStyle" }
}
@Rowb
    A { Variable-building }
    B { 84 }
    C { @Code { "dot" } @Code { "dotdot" } @Code { "hat" }
@Code { "tilde" } @Code { "vec" } @Code { "dyad" }
@Code { "overbar" } @Code { "underbar" }
}
@Rowb
    A { Variable-building }
    B { 82 }
    C { @Code { "sub" } @Code { "on" } @Code { "ton" } }
@Rowb
    A { Variable-building }
    B { 80 }
    C { @Code { "sup" } @Code { "supp" } }
@Rowb
    A { Unary operator }
    B { 70 }
    C { @Code { sqrt } @Code { root } @Code { zroot } @Code { matrix } etc. }
@Rowb
    A { Binary operator }
    B { 64 }
    C { @Code { "times" } @Code { "*" } }
@Rowb
    A { Binary operator }
    B { 62 }
    C { @Code { "div" } @Code { "frac" } @Code { "over" } }
@Rowb
    A { Binary operator }
    B { 60 }
    C { @Code { "bin" } @Code { "+" } @Code { "-" } and
all other binary operator symbols }
@Rowb
    A { Relation }
    B { 50 }
    C { @Code "rel" and all other relation symbols }
@Rowb
    A { Punctuation }
    B { 40 }
    C { @Code { "punct" }  @Code { ";" }  @Code { "," }  @Code { "col" } }
@Rowb
    A { Helper }
    B { 26 }
    C { @Code "non" }
@Rowb
    A { Helper }
    B { 24 }
    C { @Code { "above" } @Code { "below" } @Code { "wideabove" }
@Code { "widebelow" }
}
@Rowb
    A { Helper }
    B { 22 }
    C { @Code { "col" } @Code { "lcol" } @Code { "ccol" }
@Code { "rcol" } @Code { "mcol" } }
@Rowb
    A { Helper }
    B { 20 }
    C { @Code { "row" } @Code { "axisrow" } }
    rb { yes }
    mb { 0i }
}
Results are shown in display style in this section; the other styles
give more compressed results.
@BeginSubSections

@SubSection
    @Title { Helper symbols }
@Begin
@LP
The full list of helper symbols is
@ID @OneRow @Tbl
     mv { 0.5vx }
     aformat { @Cell ml { 0i } A | @Cell mr { 0i } B }
{
@Rowa
    ma { 0i }
    A { @Code "`" }
    B { Thin space, as after punctuation symbols }
@Rowa
    A { @Code "``" }
    B { Medium space, as around binary operator symbols }
@Rowa
    A { @Code "```" }
    B { Thick space, as around relation symbols }
@Rowa
    A { @Code "big x"
mathematics.big. @SubIndex { @Code "big" symbol }
big. @Index { @Code "big" symbol (mathematics) }
}
    B { Make @Code x larger }
@Rowa
    A { @Code "small x"
mathematics.small. @SubIndex { @Code "small" symbol }
small. @Index { @Code "small" symbol (mathematics) }
}
    B { Make @Code x smaller }
@Rowa
    A { @Code "vctr x"
mathematics.vctr. @SubIndex { @Code "vctr" symbol }
vctr. @Index { @Code "vctr" symbol (mathematics) }
}
    B { Centre @Code x vertically }
@Rowa
    A { @Code "@SuperScriptStyle x"
mathematics.superscriptstyle. @SubIndex { @Code "@SuperScriptStyle" }
superscriptstyle. @Index { @Code "@SuperScriptStyle" (mathematics) }
}
    B { Set @Code x in the style of a superscript }
@Rowa
    A { @Code "@SubScriptStyle x"
mathematics.subscriptstyle. @SubIndex { @Code "@SubScriptStyle" }
subscriptstyle. @Index { @Code "@SubScriptStyle" (mathematics) }
}
    B { Set @Code x in the style of a subscript }
@Rowa
    A { @Code "@NumeratorStyle x"
mathematics.numeratorstyle. @SubIndex { @Code "@NumeratorStyle" }
numeratorstyle. @Index { @Code "@NumeratorStyle" (mathematics) }
}
    B { Set @Code x in the style of a numerator }
@Rowa
    A { @Code "@DenominatorStyle x"
mathematics.denominatorstyle. @SubIndex { @Code "@DenominatorStyle" }
denominatorstyle. @Index { @Code "@DenominatorStyle" (mathematics) }
}
    B { Set @Code x in the style of a denominator }
@Rowa
    A { @Code "@SquareRootStyle x"
mathematics.squarerootstyle. @SubIndex { @Code "@SquareRootStyle" }
squarerootstyle. @Index { @Code "@SquareRootStyle" (mathematics) }
}
    B { Set @Code x in the style of a square root }
@Rowa
    A { @Code { above } @Code { below } @Code { wideabove }
@Code { widebelow } }
    B { Vertical stacking (see below) }
@Rowa
    A { @Code { "col" } @Code { "lcol" } @Code { "ccol" }
@Code { "rcol" } @Code { "mcol" } @Code { "row" } @Code { "axisrow" } }
    B { Used only within matrices (Section {@NumberOf matrices}) }
@Rowa
    A { @Code "non x" }
    B { Remove spaces from @Code x (see below) }
    mb { 0i }
}
where @Code "x" is arbitrary as usual.  The @Code "above" symbol prints
mathematics.above. @SubIndex { @Code "above" symbol }
above. @Index { @Code "above" symbol (mathematics) }
the preceding object above the following object, while the @Code "below"
mathematics.below. @SubIndex { @Code "below" symbol }
below. @Index { @Code "below" symbol (mathematics) }
symbol prints it below:
@ID { 
@Code @Verbatim { { a above f } + { z below b } }
|7ct
@Math { { a above f } + { z below b } }
}
Here is a larger example:
@ID { @Code @Verbatim {
sum from { { 1 <= i <= p } above
   { 1 <= j <= q } above { 1 <= k <= r } }
{ a sub ij b sub jk c sub ki }
}
||7ct
@Math {
  sum from { { 1 <= i <= p } above
             { 1 <= j <= q } above
             { 1 <= k <= r } }
  { a sub { ij } b sub { jk } c sub { ki } }
}
}
The @Code "wideabove" and @Code "widebelow" symbols are like @Code "above"
mathematics.wideabove. @SubIndex { @Code "wideabove" symbol }
wideabove. @Index { @Code "wideabove" symbol (mathematics) }
mathematics.widebelow. @SubIndex { @Code "widebelow" symbol }
widebelow. @Index { @Code "widebelow" symbol (mathematics) }
and @Code "below" except that they horizontally scale the right parameter
to the width of the left:
@IL

@LI {
@Code @Verbatim {
{a, ... , z} wideabove
{90d @Rotate blbrace}
}
||7ct
@Math { {a, ... , z} wideabove {90d @Rotate blbrace} }
}

@LI {
@Code "{a, ... , z} widebelow minus"
|7ct
@Math { {a, ... , z} widebelow minus }
}
@EL
The @Code "non" symbol prints the following object without the
mathematics.non. @SubIndex { @Code "non" symbol }
non. @Index { @Code "non" symbol (mathematics) }
horizontal spacing it would usually contain.  It has low precedence
so that, in examples like
@ID @Code @Verbatim {
The `@M { non <= }' operation is reflexive and transitive.
}
which produces
@ID {
The `@M { non <= }' operation is reflexive and transitive.
}
it is easy to use the familiar symbolic names for relations and
operators without getting the usual surrounding spaces, saving
the trouble of looking up the names of the characters.
@End @SubSection

@SubSection
    @Title { Ordinary symbols }
@Begin
@LP
Ordinary symbols are the simplest symbols.  They do not take objects
mathematics.ordinary. @SubIndex { ordinary symbols }
ordinary. @Index { ordinary symbols (mathematics) }
to their left or right, and they always look the same except for the
usual change of size in certain contexts (superscripts, subscripts, etc.).
There are hundreds of these symbols, so they are presented here in groups.
@PP
The first group consists of all the symbols from the Adobe Symbol font;
these are as for the @Code "@Sym" symbol of Section {@NumberOf characters},
but within @Code "@Math" you don't type {@Code "@Sym"}:
@DP
@Tbl
  mv { 0.5vx }
  aformat { @Cell ml {@DisplayIndent} indent {right} w {@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "space" } B { @Math { space } }
  C { "exclam" } D { @Math { exclam } }
  E { "universal" } F { @Math { universal } }
@Rowa
  A { "numbersign" } B { @Math { numbersign } }
  C { "existential" } D { @Math { existential } }
  E { "percent" } F { @Math { percent } }
@Rowa
  A { "ampersand" } B { @Math { ampersand } }
  C { "suchthat" } D { @Math { suchthat } }
  E { "parenleft" } F { @Math { parenleft } }
@Rowa
  A { "parenright" } B { @Math { parenright } }
  C { "asteriskmath" } D { @Math { asteriskmath } }
  E { "plus" } F { @Math { plus } }
@Rowa
  A { "comma" } B { @Math { comma } }
  C { "minus" } D { @Math { minus } }
  E { "period" } F { @Math { period } }
@Rowa
  A { "slash" } B { @Math { slash } }
  C { "zero" } D { @Math { zero } }
  E { "one" } F { @Math { one } }
@Rowa
  A { "two" } B { @Math { two } }
  C { "three" } D { @Math { three } }
  E { "four" } F { @Math { four } }
@Rowa
  A { "five" } B { @Math { five } }
  C { "six" } D { @Math { six } }
  E { "seven" } F { @Math { seven } }
@Rowa
  A { "eight" } B { @Math { eight } }
  C { "nine" } D { @Math { nine } }
  E { "colon" } F { @Math { colon } }
@Rowa
  A { "semicolon" } B { @Math { semicolon } }
  C { "less" } D { @Math { less } }
  E { "equal" } F { @Math { equal } }
@Rowa
  A { "greater" } B { @Math { greater } }
  C { "question" } D { @Math { question } }
  E { "congruent" } F { @Math { congruent } }
@Rowa
  A { "Alpha" } B { @Math { Alpha } }
  C { "Beta" } D { @Math { Beta } }
  E { "Chi" } F { @Math { Chi } }
@Rowa
  A { "Delta" } B { @Math { Delta } }
  C { "Epsilon" } D { @Math { Epsilon } }
  E { "Phi" } F { @Math { Phi } }
@Rowa
  A { "Gamma" } B { @Math { Gamma } }
  C { "Eta" } D { @Math { Eta } }
  E { "Iota" } F { @Math { Iota } }
@Rowa
  A { "thetaone" } B { @Math { thetaone } }
  C { "Kappa" } D { @Math { Kappa } }
  E { "Lambda" } F { @Math { Lambda } }
@Rowa
  A { "Mu" } B { @Math { Mu } }
  C { "Nu" } D { @Math { Nu } }
  E { "Omicron" } F { @Math { Omicron } }
@Rowa
  A { "Pi" } B { @Math { Pi } }
  C { "Theta" } D { @Math { Theta } }
  E { "Rho" } F { @Math { Rho } }
@Rowa
  A { "Sigma" } B { @Math { Sigma } }
  C { "Tau" } D { @Math { Tau } }
  E { "Upsilon" } F { @Math { Upsilon } }
@Rowa
  A { "sigmaone" } B { @Math { sigmaone } }
  C { "Omega" } D { @Math { Omega } }
  E { "Xi" } F { @Math { Xi } }
@Rowa
  A { "Psi" } B { @Math { Psi } }
  C { "Zeta" } D { @Math { Zeta } }
  E { "bracketleft" } F { @Math { bracketleft } }
@Rowa
  A { "therefore" } B { @Math { therefore } }
  C { "bracketright" } D { @Math { bracketright } }
  E { "perpendicular" } F { @Math { perpendicular } }
@Rowa
  A { "underscore" } B { @Math { underscore } }
  C { "radicalex" } D { @Math { radicalex } }
  E { "alpha" } F { @Math { alpha } }
@Rowa
  A { "beta" } B { @Math { beta } }
  C { "chi" } D { @Math { chi } }
  E { "delta" } F { @Math { delta } }
@Rowa
  A { "epsilon" } B { @Math { epsilon } }
  C { "phi" } D { @Math { phi } }
  E { "gamma" } F { @Math { gamma } }
@Rowa
  A { "eta" } B { @Math { eta } }
  C { "iota" } D { @Math { iota } }
  E { "phione" } F { @Math { phione } }
@Rowa
  A { "kappa" } B { @Math { kappa } }
  C { "lambda" } D { @Math { lambda } }
  E { "mu" } F { @Math { mu } }
@Rowa
  A { "nu" } B { @Math { nu } }
  C { "omicron" } D { @Math { omicron } }
  E { "pi" } F { @Math { pi } }
@Rowa
  A { "theta" } B { @Math { theta } }
  C { "rho" } D { @Math { rho } }
  E { "sigma" } F { @Math { sigma } }
@Rowa
  A { "tau" } B { @Math { tau } }
  C { "upsilon" } D { @Math { upsilon } }
  E { "omegaone" } F { @Math { omegaone } }
@Rowa
  A { "omega" } B { @Math { omega } }
  C { "xi" } D { @Math { xi } }
  E { "psi" } F { @Math { psi } }
@Rowa
  A { "zeta" } B { @Math { zeta } }
  C { "braceleft" } D { @Math { braceleft } }
  E { "bar" } F { @Math { bar } }
@Rowa
  A { "braceright" } B { @Math { braceright } }
  C { "similar" } D { @Math { similar } }
  E { "Upsilonone" } F { @Math { Upsilonone } }
@Rowa
  A { "minute" } B { @Math { minute } }
  C { "lessequal" } D { @Math { lessequal } }
  E { "fraction" } F { @Math { fraction } }
@Rowa
  A { "infinity" } B { @Math { infinity } }
  C { "florin" } D { @Math { florin } }
  E { "club" } F { @Math { club } }
@Rowa
  A { "diamond" } B { @Math { diamond } }
  C { "heart" } D { @Math { heart } }
  E { "spade" } F { @Math { spade } }
@Rowa
  A { "arrowboth" } B { @Math { arrowboth } }
  C { "arrowleft" } D { @Math { arrowleft } }
  E { "arrowup" } F { @Math { arrowup } }
@Rowa
  A { "arrowright" } B { @Math { arrowright } }
  C { "arrowdown" } D { @Math { arrowdown } }
  E { "degree" } F { @Math { degree } }
@Rowa
  A { "plusminus" } B { @Math { plusminus } }
  C { "second" } D { @Math { second } }
  E { "greaterequal" } F { @Math { greaterequal } }
@Rowa
  A { "multiply" } B { @Math { multiply } }
  C { "proportional" } D { @Math { proportional } }
  E { "partialdiff" } F { @Math { partialdiff } }
@Rowa
  A { "bullet" } B { @Math { bullet } }
  C { "divide" } D { @Math { divide } }
  E { "notequal" } F { @Math { notequal } }
@Rowa
  A { "equivalence" } B { @Math { equivalence } }
  C { "approxequal" } D { @Math { approxequal } }
  E { "ellipsis" } F { @Math { ellipsis } }
@Rowa
  A { "arrowvertex" } B { @Math { arrowvertex } }
  C { "arrowhorizex" } D { @Math { arrowhorizex } }
  E { "carriagereturn" } F { @Math { carriagereturn } }
@Rowa
  A { "aleph" } B { @Math { aleph } }
  C { "Ifraktur" } D { @Math { Ifraktur } }
  E { "Rfraktur" } F { @Math { Rfraktur } }
@Rowa
  A { "weierstrass" } B { @Math { weierstrass } }
  C { "circlemultiply" } D { @Math { circlemultiply } }
  E { "circleplus" } F { @Math { circleplus } }
@Rowa
  A { "emptyset" } B { @Math { emptyset } }
  C { "intersection" } D { @Math { intersection } }
  E { "union" } F { @Math { union } }
@Rowa
  A { { 0.92 1.0 } @Scale "propersuperset" } B { @Math { propersuperset } }
  C { "reflexsuperset" } D { @Math { reflexsuperset } }
  E { "notsubset" } F { @Math { notsubset } }
@Rowa
  A { "propersubset" } B { @Math { propersubset } }
  C { "reflexsubset" } D { @Math { reflexsubset } }
  E { "element" } F { @Math { element } }
@Rowa
  A { "notelement" } B { @Math { notelement } }
  C { "angle" } D { @Math { angle } }
  E { "gradient" } F { @Math { gradient } }
@Rowa
  A { "registerserif" } B { @Math { registerserif } }
  C { "copyrightserif" } D { @Math { copyrightserif } }
  E { "trademarkserif" } F { @Math { trademarkserif } }
@Rowa
  A { "product" } B { @Math { product } }
  C { "radical" } D { @Math { radical } }
  E { "dotmath" } F { @Math { dotmath } }
@Rowa
  A { "logicalnot" } B { @Math { logicalnot } }
  C { "logicaland" } D { @Math { logicaland } }
  E { "logicalor" } F { @Math { logicalor } }
@Rowa
  A { "arrowdblboth" } B { @Math { arrowdblboth } }
  C { "arrowdblleft" } D { @Math { arrowdblleft } }
  E { "arrowdblup" } F { @Math { arrowdblup } }
@Rowa
  A { "arrowdblright" } B { @Math { arrowdblright } }
  C { "arrowdbldown" } D { @Math { arrowdbldown } }
  E { "lozenge" } F { @Math { lozenge } }
@Rowa
  A { "angleleft" } B { @Math { angleleft } }
  C { "registersans" } D { @Math { registersans } }
  E { "copyrightsans" } F { @Math { copyrightsans } }
@Rowa
  A { { 0.92 1.0 } @Scale "trademarksans" } B { @Math { trademarksans } }
  C { "summation" } D { @Math { summation } }
  E { "parenlefttp" } F { @Math { parenlefttp } }
@Rowa
  A { "parenleftex" } B { @Math { parenleftex } }
  C { "parenleftbt" } D { @Math { parenleftbt } }
  E { "bracketlefttp" } F { @Math { bracketlefttp } }
@Rowa
  A { "bracketleftex" } B { @Math { bracketleftex } }
  C { "bracketleftbt" } D { @Math { bracketleftbt } }
  E { "bracelefttp" } F { @Math { bracelefttp } }
@Rowa
  A { "braceleftmid" } B { @Math { braceleftmid } }
  C { "braceleftbt" } D { @Math { braceleftbt } }
  E { "braceex" } F { @Math { braceex } }
@Rowa
  A { "angleright" } B { @Math { angleright } }
  C { "integral" } D { @Math { integral } }
  E { "integraltp" } F { @Math { integraltp } }
@Rowa
  A { "integralex" } B { @Math { integralex } }
  C { "integralbt" } D { @Math { integralbt } }
  E { "parenrighttp" } F { @Math { parenrighttp } }
@Rowa
  A { "parenrightex" } B { @Math { parenrightex } }
  C { "parenrightbt" } D { @Math { parenrightbt } }
  E { "bracketrighttp" } F { @Math { bracketrighttp } }
@Rowa
  A { "bracketrightex" } B { @Math { bracketrightex } }
  C { "bracketrightbt" } D { @Math { bracketrightbt } }
  E { "bracerighttp" } F { @Math { bracerighttp } }
@Rowa
  A { "bracerightmid" } B { @Math { bracerightmid } }
  C { "bracerightbt" } D { @Math { bracerightbt } }
  mb { 0i }
}
@DP
The symbols that produce the Symbol font characters @Code { theta1 },
@Code { sigma1 }, @Code { phi1 }, @Code { omega1 }, and @Code { Upsilon1 }
are called @Code { thetaone }, @Code { sigmaone }, @Code { phione },
@Code { omegaone }, and @Code { Upsilonone }, since Lout symbol names
cannot contain both letters and digits.  The second group of ordinary
symbols produces arrows:
@ID @OneRow @Tbl
  mv { 0.5vx }
  aformat { @Cell ml{0i} indent{right} w{@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "leftarrow" } B { @Math { leftarrow } }
  C { "longleftarrow" } D { @Math { longleftarrow } }
  E { "dblleftarrow" } F { @Math { dblleftarrow } }
@Rowa
  A { "dbllongleftarrow" } B { @Math { dbllongleftarrow } }
  C { "rightarrow" } D { @Math { rightarrow } }
  E { "longrightarrow" } F { @Math { longrightarrow } }
@Rowa
  A { "dblrightarrow" } B { @Math { dblrightarrow } }
  C { "dbllongrightarrow" } D { @Math { dbllongrightarrow } }
  E { "leftrightarrow" } F { @Math { leftrightarrow } }
@Rowa
  A { "longleftrightarrow" } B { @Math { longleftrightarrow } }
  C { "dblleftrightarrow" } D { @Math { dblleftrightarrow } }
  E { { 0.85 1.0 } @Scale "dbllongleftrightarrow" }
  F { @Math { dbllongleftrightarrow } }
@Rowa
  A { "mapsto" } B { @Math { mapsto } }
  C { "longmapsto" } D { @Math { longmapsto } }
  E { "hookleftarrow" } F { @Math { hookleftarrow } }
@Rowa
  A { "hookrightarrow" } B { @Math { hookrightarrow } }
  C { "leadsto" } D { @Math { leadsto } }
  E { "leftharpoonup" } F { @Math { leftharpoonup } }
@Rowa
  A { "rightharpoonup" } B { @Math { rightharpoonup } }
  C { "leftharpoondown" } D { @Math { leftharpoondown } }
  E { { 0.95 1.0 } @Scale "rightharpoondown" } F { @Math { rightharpoondown } }
@Rowa
  A { "rightleftharpoons" } B { @Math { rightleftharpoons } }
  C { "uparrow" } D { @Math { uparrow } }
  E { "dbluparrow" } F { @Math { dbluparrow } }
@Rowa
  A { "downarrow" } B { @Math { downarrow } }
  C { "dbldownarrow" } D { @Math { dbldownarrow } }
  E { "updownarrow" } F { @Math { updownarrow } }
@Rowa
  A { "dblupdownarrow" } B { @Math { dblupdownarrow } }
  C { "nearrow" } D { @Math { nearrow } }
  E { "searrow" } F { @Math { searrow } }
@Rowa
  A { "swarrow" } B { @Math { swarrow } }
  C { "nwarrow" } D { @Math { nwarrow } }
  mb { 0i }
}
The members of the third group of ordinary symbols stand for themselves,
but in Roman font rather than the Italic which is the default in
mathematics:
@ID @OneRow @Tbl
  mv { 0.45vx }
  aformat { @Cell ml {0i} indent {right} w {@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "arccos" } B { @Math { arccos } }
  C { "arcsin" } D { @Math { arcsin } }
  E { "arctan" } F { @Math { arctan } }
@Rowa
  A { "arg" } B { @Math { arg } }
  C { "cos" } D { @Math { cos } }
  E { "cosh" } F { @Math { cosh } }
@Rowa
  A { "cot" } B { @Math { cot } }
  C { "coth" } D { @Math { coth } }
  E { "csc" } F { @Math { csc } }
@Rowa
  A { "deg" } B { @Math { deg } }
  C { "det" } D { @Math { det } }
  E { "dim" } F { @Math { dim } }
@Rowa
  A { "exp" } B { @Math { exp } }
  C { "gcd" } D { @Math { gcd } }
  E { "hom" } F { @Math { hom } }
@Rowa
  A { "inf" } B { @Math { inf } }
  C { "ker" } D { @Math { ker } }
  E { "lg" } F { @Math { lg } }
@Rowa
  A { "lim" } B { @Math { lim } }
  C { "liminf" } D { @ZeroWidth @Math { liminf } }
  E { "limsup" } F { @Math { limsup } }
@Rowa
  A { "ln" } B { @Math { ln } }
  C { "log" } D { @Math { log } }
  E { "max" } F { @Math { max } }
@Rowa
  A { "min" } B { @Math { min } }
  C { "Pr" } D { @Math { Pr } }
  E { "sec" } F { @Math { sec } }
@Rowa
  A { "sin" } B { @Math { sin } }
  C { "sinh" } D { @Math { sinh } }
  E { "supr" } F { @Math { supr } }
@Rowa
  A { "tan" } B { @Math { tan } }
  C { "tanh" } D { @Math { tanh } }
  E { "mod" } F { @Math { mod } }
@Rowa
  A { "0" } B { @Math { 0 } }
  C { "1" } D { @Math { 1 } }
  E { "2" } F { @Math { 2 } }
@Rowa
  A { "3" } B { @Math { 3 } }
  C { "4" } D { @Math { 4 } }
  E { "5" } F { @Math { 5 } }
@Rowa
  A { "6" } B { @Math { 6 } }
  C { "7" } D { @Math { 7 } }
  E { "8" } F { @Math { 8 } }
@Rowa
  A { "9" } B { @Math { 9 } }
  C { "!" } D { @Math { ! } }
  E { "?" } F { @Math { ? } }
@Rowa
  A { "%" } B { @Math { % } }
  C { "(" } D { @Math { ( } }
  E { ")" } F { @Math { ) } }
@Rowa
  A { "[" } B { @Math { [ } }
  C { "]" } D { @Math { ] } }
  mb { 0i }
}
The fourth group make good values for the @Code "atleft" and
@Code "atright" options of @Code { matrix }:
@ID @OneRow @Tbl
  mv { 0.5vx }
  aformat { @Cell ml { 0i } indent { right } w {@LCodeWidth} @Code A | @Cell B | @Cell |
            @Cell           indent { right } @Code C | @Cell D | @Cell |
            @Cell           indent { right } @Code E | @Cell F | @Cell |
            @Cell           indent { right } @Code G | @Cell mr { 0i } H }
{
@Rowa
  ma { 0i }
  strut { 1.2f }
  A { "lpar" } B { @Math { lpar } }
  C { "rpar" } D { @Math { rpar } }
  E { "lbrack" } F { @Math { lbrack } }
  G { "rbrack" } H { @Math { rbrack } }
@Rowa
  strut { 1.2f }
  A { "lbrace" } B { @Math { lbrace } }
  C { "rbrace" } D { @Math { rbrace } }
  E { "lfloor" } F { @Math { lfloor } }
  G { "rfloor" } H { @Math { rfloor } }
@Rowa
  strut { 1.2f }
  A { "lceil" } B { @Math { lceil } }
  C { "rceil" } D { @Math { rceil } }
  E { "langle" } F { @Math { langle } }
  G { "rangle" } H { @Math { rangle } }
@Rowa
  strut { 3.5f }
  A { "blpar" } B { @Math { blpar } }
  C { "brpar" } D { @Math { brpar } }
  E { "blbrack" } F { @Math { blbrack } }
  G { "brbrack" } H { @Math { brbrack } }
@Rowa
  strut { 3.5f }
  A { "blbrace" } B { @Math { blbrace } }
  C { "brbrace" } D { @Math { brbrace } }
  E { "blfloor" } F { @Math { blfloor } }
  G { "brfloor" } H { @Math { brfloor } }
@Rowa
  strut { 3.5f }
  A { "blceil" } B { @Math { blceil } }
  C { "brceil" } D { @Math { brceil } }
  E { "blangle" } F { @Math { blangle } }
  G { "brangle" } H { @Math { brangle } }
  mb { 0i }
}
The last group is miscellaneous:
@DP
@RID @OneRow @Tbl
  mv { 0.5vx }
  aformat { @Cell ml {0i} indent {right} w {@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "hbar" } B { @Math { hbar } }
  C { "Re" } D { @Math { Re } }
  E { "Im" } F { @Math { Im } }
@Rowa
  A { "partial" } B { @Math { partial } }
  C { "infty" } D { @Math { infty } }
  E { "prime" } F { @Math { prime } }
@Rowa
  A { "nabla" } B { @Math { nabla } }
  C { "surd" } D { @Math { surd } }
  E { "top" } F { @Math { top } }
@Rowa
  A { "bot" } B { @Math { bot } }
  C { "dbar" } D { @Math { dbar } }
  E { "triangle" } F { @Math { triangle } }
@Rowa
  A { "backslash" } B { @Math { backslash } }
  C { "forall" } D { @Math { forall } }
  E { "exists" } F { @Math { exists } }
@Rowa
  A { "neg" } B { @Math { neg } }
  C { "circle" } D { @Math { circle } }
  E { "filledcircle" } F { @Math { filledcircle } }
@Rowa
  A { "square" } B { @Math { square } }
  C { "ldots" } D { @Math { ldots } }
  E { "cdots" } F { @Math { cdots } }
@Rowa
  A { "vdots" } B { @Math { vdots } }
  C { "ddots" } D { @Math { ddots } }
  E { "del" } F { @Math { del } }
@Rowa
  A { "grad" } B { @Math { grad } }
  C { "..." } D { @Math { ... } }
  E { ",...," } F { @Math { ,..., } }
@Rowa
  A { "'" } B { @Math { ' } }
  C { "''" } D { @Math { '' } }
  E { "'''" } F { @Math { ''' } }
@Rowa
  A { "''''" } B { @Math { '''' } }
  C { "empty" } D { @Math { empty } }
  E { "triangleup" } F { @Math { triangleup } }
@Rowa
  A { "triangledown" } B { @Math { triangledown } }
  C { "half" } D { @Math { half } }
  E { "third" } F { @Math { third } }
  mb { 0i }
}
@End @SubSection

@SubSection
    @Title { Variable-building symbols }
@Begin
@LP
Under this category are symbols that are mainly used to build
mathematics.variablebuilding. @SubIndex { variable-building symbols }
variablebuilding. @Index { variable-building symbols (mathematics) }
variables.  However, as usual in Lout, the objects they link
together may in fact be arbitrary.  First we have symbols that
place a mark over or under an object:
mathematics.dot. @SubIndex { @Code "dot" symbol }
dot. @Index { @Code "dot" symbol (mathematics) }
mathematics.dotdot. @SubIndex { @Code "dotdot" symbol }
dotdot. @Index { @Code "dotdot" symbol (mathematics) }
mathematics.hat. @SubIndex { @Code "hat" symbol }
hat. @Index { @Code "hat" symbol (mathematics) }
mathematics.tilde. @SubIndex { @Code "tilde" symbol }
tilde. @Index { @Code "tilde" symbol (mathematics) }
mathematics.vec. @SubIndex { @Code "vec" symbol }
vec. @Index { @Code "vec" symbol (mathematics) }
mathematics.dyad. @SubIndex { @Code "dyad" symbol }
dyad. @Index { @Code "dyad" symbol (mathematics) }
mathematics.overbar. @SubIndex { @Code "overbar" symbol }
overbar. @Index { @Code "overbar" symbol (mathematics) }
mathematics.underbar. @SubIndex { @Code "underbar" symbol }
underbar. @Index { @Code "underbar" symbol (mathematics) }
@ID @Tbl
  mv { 0.5vx }
  aformat { @Cell ml{0i} indent{right} w{@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "x dot" } B { @Math { x dot } }
  C { "x dotdot" } D { @Math { x dotdot } }
  E { "x hat" } F { @Math { x hat } }
@Rowa
  A { "x tilde" } B { @Math { x tilde } }
  C { "x vec" } D { @Math { x vec } }
  E { "x dyad" } F { @Math { x dyad } }
@Rowa
  A { "{x + y} overbar" } B { @Math { {x + y} overbar } }
  C { "{x + y} underbar" } D { @Math { {x + y} underbar } }
  mb { 0i }
}
These marks are centred, with a small skew to allow for italic
slant, except the last two which are extended to the width of
the object.
@PP
The remaining variable-building symbols produce superscripts and
subscripts:
# These differ in appearance depending on the style,
mathematics.sup. @SubIndex { @Code "sup" symbol }
sup. @Index { @Code "sup" symbol (mathematics) }
mathematics.sub. @SubIndex { @Code "sub" symbol }
sub. @Index { @Code "sub" symbol (mathematics) }
mathematics.tsub. @SubIndex { @Code "tsub" symbol }
tsub. @Index { @Code "tsub" symbol (mathematics) }
mathematics.supp. @SubIndex { @Code "supp" symbol }
supp. @Index { @Code "supp" symbol (mathematics) }
mathematics.on. @SubIndex { @Code "on" symbol }
on. @Index { @Code "on" symbol (mathematics) }
mathematics.ton. @SubIndex { @Code "ton" symbol }
ton. @Index { @Code "ton" symbol (mathematics) }
so the results are shown in both display and text style:
@ID @Tbl
    mv { 0.6vx }
  # aformat { @Cell ml {0i} indent {right} @Code A | @Cell B | @Cell C | @Cell |
  #           @Cell         indent {right} @Code D | @Cell E | @Cell F | @Cell |
  #           @Cell         indent {right} @Code G | @Cell H | @Cell mr {0i} I }
    aformat { @Cell ml {0i} indent {right} @Code A | @Cell B | @Cell |
              @Cell         indent {right} @Code D | @Cell E |  @Cell |
              @Cell         indent {right} @Code G | @Cell mr {0i} H }
{
@Rowa
  ma { 0i }
  A { "x sup y" } B { @Math { x sup y } } C { @M { x sup y } }
  D { "x sub y" } E { @Math { x sub y } } F { @M { x sub y } }
  G { "W tsub y" } H { @Math { W tsub y } } I { @M { W tsub y } }
@Rowa
  A { "x supp y on z"  } B { @Math {x supp y on z } } C { @M {x supp y on z } }
  D { "W supp y ton z" } E { @Math {W supp y ton z} } F { @M {W supp y ton z} }
  mb { 0i }
}
The @Code "supp" and @Code "on" (or {@Code "ton"}) symbols must be
used together as shown; @Code "tsub" and @Code "ton" are exactly like
@Code "sub" and @Code "on" except that the subscript is tucked in.
@End @SubSection

@SubSection
    @Title { Large operator symbols }
@Begin
@LP
Large operator symbols have @Code "from" and @Code "to"
mathematics.large.operators. @SubIndex { large operators }
large.operators. @Index { large operators (mathematics) }
options which work as described for the @Code "sum" symbol
in Section {@NumberOf mat_comm}.  Here they all are, with
their results in both display style and text style:
@CD @OneRow @Tbl
  mv { 0.7vx }
  strut { 2.5f }
  aformat { @Cell ml {0i} indent {right} @Code A | @Cell B | @Cell C | @Cell |
            @Cell         indent {right} @Code D | @Cell E | @Cell mr {0i} F }
{
@Rowa
  ma { 0i }
  A { "sum from { a } to { b } x" }
  B { @Math { sum from { a } to { b } x } }
  C { @M { sum from { a } to { b } x } }
  D { "prod from { a } to { b } x" }
  E { @Math { prod from { a } to { b } x } }
  F { @M { prod from { a } to { b } x } }
@Rowa
  A { "coprod from { a } to { b } x" }
  B { @Math { coprod from { a } to { b } x } }
  C { @M { coprod from { a } to { b } x } }
  D { "bcap from { a } to { b } x" }
  E { @Math { bcap from { a } to { b } x } }
  F { @M { bcap from { a } to { b } x } }
@Rowa
  A { "bcup from { a } to { b } x" }
  B { @Math { bcup from { a } to { b } x } }
  C { @M { bcup from { a } to { b } x } }
  D { "bvee from { a } to { b } x" }
  E { @Math { bvee from { a } to { b } x } }
  F { @M { bvee from { a } to { b } x } }
@Rowa
  A { "bwedge from { a } to { b } x" }
  B { @Math { bwedge from { a } to { b } x } }
  C { @M { bwedge from { a } to { b } x } }
  D { "bodot from { a } to { b } x" }
  E { @Math { bodot from { a } to { b } x } }
  F { @M { bodot from { a } to { b } x } }
@Rowa
  A { "botimes from { a } to { b } x" }
  B { @Math { botimes from { a } to { b } x } }
  C { @M { botimes from { a } to { b } x } }
  D { "boplus from { a } to { b } x" }
  E { @Math { boplus from { a } to { b } x } }
  F { @M { boplus from { a } to { b } x } }
@Rowa
  A { "buplus from { a } to { b } x" }
  B { @Math { buplus from { a } to { b } x } }
  C { @M { buplus from { a } to { b } x } }
  D { "int from { a } to { b } x" }
  E { @Math { int from { a } to { b } x } }
  F { @M { int from { a } to { b } x } }
@Rowa
  A { "oint from { a } to { b } x" }
  B { @Math { oint from { a } to { b } x } }
  C { @M { oint from { a } to { b } x } }
  mb { 0i }
}
All these symbols also have a @Code "limits" option; when set to
@Code "yes" it causes the limits to be shown above and below the
symbol, when @Code "no" it causes them to be shown as superscripts and
subscripts, and when omitted it defaults to @Code "yes" in display style
and @Code "no" otherwise, except for integrals, where the default is
uniformly @Code "no" as required by mathematical convention.
@PP
The @Code "largeop" symbol causes an arbitrary object to be treated
mathematics.largeop. @SubIndex { @Code "largeop" symbol }
largeop. @Index { @Code "largeop" symbol (mathematics) }
as a large operator:
@ID {
@Code @Verbatim { largeop symbol { diamond } from { a } to { b } x }
|10ct
@Math { largeop symbol { diamond } from { a } to { b } x }
}
In addition to {@Code "limits"}, {@Code "from"}, and {@Code "to"}
options, @Code "largeop" has a @Code "symbol" option holding the
object to be made into a large operator.  In display style, this
object is enlarged using the @Code "big" helper function.
@End @SubSection

@SubSection
    @Title { Unary operator symbols }
@Begin
@LP
This category mainly contains symbols that take one object on the right
mathematics.unaryoperator. @SubIndex { unary operators }
unaryoperator. @Index { unary operators (mathematics) }
and transform it.
@IL

@LI {
@Code "sqrt {x over y}"
|7ct
@Math { sqrt {x over y} }
mathematics.sqrt. @SubIndex { @Code "sqrt" symbol }
sqrt. @Index { @Code "sqrt" symbol (mathematics) }
}

@LI {
@Code "3 root {x over y}"
|7ct
@Math { 3 root {x over y} }
mathematics.root @SubIndex { @Code "root" symbol }
root.mathematics @Index { @Code "root" symbol (mathematics) }
}

@LI {
@Code @Verbatim { matrix atleft { ( } atright { ) } { x } }
|7ct @Math { matrix atleft { ( } atright { ) } { x } }
}

@EL
As usual, any object may appear to the left of {@Code "root"}.
The @Code "matrix" symbol produces matrices, as explained in
detail in Section {@NumberOf matrices}.  Its following object
must be enclosed in braces.
@PP
There are symbols which produce `matrices' with commonly needed
@Code atleft and @Code atright options already set for you.  Here are
these symbols, on the left, with the equivalent @Code matrix symbol
and, on the right, the result produced:
@ID @Tbl
    aformat { @Cell ml { 0i } @Code A | @Cell | @Cell @Code B |
    @Cell | @Cell mr { 0i }  C }
{
@Rowa
    ma { 0i }
    A { "pmatrix { M }" }
    B { "matrix atleft { ( } atright { ) } { M }" }
    C { @Math { pmatrix { M } }
mathematics.pmatrix @SubIndex { @Code "pmatrix" symbol }
pmatrix.mathematics @Index { @Code "pmatrix" symbol (mathematics) }
}
@Rowa
    A { "bmatrix { M }" }
    B { "matrix atleft { blbrack } atright { brbrack } { M }" }
    C { @Math { bmatrix { M } }
mathematics.bmatrix @SubIndex { @Code "bmatrix" symbol }
bmatrix.mathematics @Index { @Code "bmatrix" symbol (mathematics) }
}
@Rowa
    A { "brmatrix { M }" }
    B { "matrix atleft { blbrace } atright { brbrace } { M }" }
    C { @Math { brmatrix { M } }
mathematics.brmatrix @SubIndex { @Code "brmatrix" symbol }
brmatrix.mathematics @Index { @Code "brmatrix" symbol (mathematics) }
}
@Rowa
    A { "fmatrix { M }" }
    B { "matrix atleft { blfloor } atright { brfloor } { M }" }
    C { @Math { fmatrix { M } }
mathematics.fmatrix @SubIndex { @Code "fmatrix" symbol }
fmatrix.mathematics @Index { @Code "fmatrix" symbol (mathematics) }
}
@Rowa
    A { "cmatrix { M }" }
    B { "matrix atleft { blceil } atright { brceil } { M }" }
    C { @Math { cmatrix { M } }
mathematics.cmatrix @SubIndex { @Code "cmatrix" symbol }
cmatrix.mathematics @Index { @Code "cmatrix" symbol (mathematics) }
}
@Rowa
    A { "amatrix { M }" }
    B { "matrix atleft { blangle } atright { brangle } { M }" }
    C { @Math { amatrix { M } }
mathematics.amatrix @SubIndex { @Code "amatrix" symbol }
amatrix.mathematics @Index { @Code "amatrix" symbol (mathematics) }
}
    mb { 0i }
}
These are very useful for getting large scaled delimiters around things
that aren't necessarily matrices at all.
@End @SubSection

@SubSection
    @Title { Binary operator symbols }
@Begin
@LP
The symbols in this category take an object on the left and on
mathematics.binary.operators. @SubIndex { binary operators }
binary.operators. @Index { binary operators (mathematics) }
the right.  The first two produce built-up fractions:
mathematics.over. @SubIndex { @Code "over" symbol }
over. @Index { @Code "over" symbol (mathematics) }
mathematics.frac @SubIndex { @Code "frac" symbol }
frac.mathematics @Index { @Code "frac" symbol (mathematics) }
@ID @Tbl
    aformat { @Cell ml { 0i } indent { right } @Code A | @Cell B | @Cell |
              @Cell           indent { right } @Code C | @Cell mr { 0i } D }
{
@Rowa
    ma { 0i }
    A { "x over y" } B { @Math { x over y } }
    C { "x frac y" } D { @Math { x frac y } }
    mb { 0i }
}
The remaining binary operator symbols print the objects to the
left and right separated by the operator with a medium-width
space on each side.  Most have precedence 80, but a few (those
representing multiplication and division operations) have higher
precedence in accordance with mathematical convention.  Here is
the full list of these operators:
@ID @Tbl
  mv { 0.5vx }
  aformat { @Cell ml{0i} indent{right} w{@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "x + y" } B { @Math { x + y } }
  C { "x - y" } D { @Math { x - y } }
  E { "x +- y" } F { @Math { x +- y } }
@Rowa
  A { "x -+ y" } B { @Math { x -+ y } }
  C { "x setminus y" } D { @Math { x setminus y } }
  E { "x cdot y" } F { @Math { x cdot y } }
@Rowa
  A { "x times y" } B { @Math { x times y } }
  C { "x * y" } D { @Math { x * y } }
  E { "x circ y" } F { @Math { x circ y } }
@Rowa
  A { "x div y" } B { @Math { x div y } }
  C { "x cap y" } D { @Math { x cap y } }
  E { "x cup y" } F { @Math { x cup y } }
@Rowa
  A { "x uplus y" } B { @Math { x uplus y } }
  C { "x sqcap y" } D { @Math { x sqcap y } }
  E { "x sqcup y" } F { @Math { x sqcup y } }
@Rowa
  A { "x triangleleft y" } B { @Math { x triangleleft y } }
  C { "x triangleright y" } D { @Math { x triangleright y } }
  E { "x wr y" } F { @Math { x wr y } }
@Rowa
  A { "x bigcirc y" } B { @Math { x bigcirc y } }
  C { "x bigtriangleup y" } D { @Math { x bigtriangleup y } }
  E { { 0.85 1.0 } @Scale "x bigtriangledown y" }
  F { @Math { x bigtriangledown y } }
@Rowa
  A { "x vee y" } B { @Math { x vee y } }
  C { "x wedge y" } D { @Math { x wedge y } }
  E { "x oplus y" } F { @Math { x oplus y } }
@Rowa
  A { "x ominus y" } B { @Math { x ominus y } }
  C { "x otimes y" } D { @Math { x otimes y } }
  E { "x oslash y" } F { @Math { x oslash y } }
@Rowa
  A { "x odot y" } B { @Math { x odot y } }
  C { "x dagger y" } D { @Math { x dagger y } }
  E { "x daggerdbl y" } F { @Math { x daggerdbl y } }
@Rowa
  A { "x amalg y" } B { @Math { x amalg y } }
  mb { 0i }
}
The @Code "bin" symbol causes an arbitrary object to be treated
mathematics.bin @SubIndex { @Code "bin" symbol }
bin.mathematics @Index { @Code "bin" symbol (mathematics) }
as a binary operator:
@ID {
@Code @Verbatim { x bin op { diamond } y }
|7ct
@Math { x bin op { diamond } y }
}
The @Code "op" option following @Code "bin" contains the object
to be treated as a binary operator; its two parameters precede
and follow @Code "bin" as usual.
@End @SubSection

@SubSection
    @Title { Relation symbols }
@Begin
@LP
These symbols represent relations.  They take an object on
mathematics.relation. @SubIndex { relation symbols }
relation.symbols. @Index { relation symbols (mathematics) }
the left and on the right, and print them separated by the
relation symbol, with a slightly wider space on each side than
is used for binary operators.  They have lower precedence than
binary operators, in accordance with mathematical convention.  Here
is the full list of these relations:
@ID @Tbl
  mv { 0.5vx }
  aformat { @Cell ml{0i} indent{right} w{@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "x < y" } B { @Math { x < y } }
  C { "x > y" } D { @Math { x > y } }
  E { "x = y" } F { @Math { x = y } }
@Rowa
  A { "x <= y" } B { @Math { x <= y } }
  C { "x prec y" } D { @Math { x prec y } }
  E { "x preceq y" } F { @Math { x preceq y } }
@Rowa
  A { "x << y" } B { @Math { x << y } }
  C { "x subset y" } D { @Math { x subset y } }
  E { "x subseteq y" } F { @Math { x subseteq y } }
@Rowa
  A { "x sqsubseteq y" } B { @Math { x sqsubseteq y } }
  C { "x in y" } D { @Math { x in y } }
  E { "x vdash y" } F { @Math { x vdash y } }
@Rowa
  A { "x smile y" } B { @Math { x smile y } }
  C { "x frown y" } D { @Math { x frown y } }
  E { "x >= y" } F { @Math { x >= y } }
@Rowa
  A { "x succ y" } B { @Math { x succ y } }
  C { "x succeq y" } D { @Math { x succeq y } }
  E { "x >> y" } F { @Math { x >> y } }
@Rowa
  A { "x supset y" } B { @Math { x supset y } }
  C { "x supseteq y" } D { @Math { x supseteq y } }
  E { "x sqsupseteq y" } F { @Math { x sqsupseteq y } }
@Rowa
  A { "x ni y" } B { @Math { x ni y } }
  C { "x dashv y" } D { @Math { x dashv y } }
  E { "x mid y" } F { @Math { x mid y } }
@Rowa
  A { "x parallel y" } B { @Math { x parallel y } }
  C { "x == y" } D { @Math { x == y } }
  E { "x ~ y" } F { @Math { x ~ y } }
@Rowa
  A { "x -~ y" } B { @Math { x -~ y } }
  C { "x asymp y" } D { @Math { x asymp y } }
  E { "x ~~ y" } F { @Math { x ~~ y } }
@Rowa
  A { "x =~ y" } B { @Math { x =~ y } }
  C { "x bowtie y" } D { @Math { x bowtie y } }
  E { "x propto y" } F { @Math { x propto y } }
@Rowa
  A { "x models y" } B { @Math { x models y } }
  C { "x trieq y" } D { @Math { x trieq y } }
  E { "x doteq y" } F { @Math { x doteq y } }
@Rowa
  A { "x perp y" } B { @Math { x perp y } }
  C { "x notsub y" } D { @Math { x notsub y } }
  E { "x notin y" } F { @Math { x notin y } }
@Rowa
  A { "x != y" } B { @Math { x != y } }
  C { "x <-> y" } D { @Math { x <-> y } }
  E { "x <-- y" } F { @Math { x <-- y } }
@Rowa
  A { "x --> y" } B { @Math { x --> y } }
  C { "x up y" } D { @Math { x up y } }
  E { "x down y" } F { @Math { x down y } }
@Rowa
  A { "x <=> y" } B { @Math { x <=> y } }
  C { "x <== y" } D { @Math { x <== y } }
  E { "x ==> y" } F { @Math { x ==> y } }
@Rowa
  A { "x dblup y" } B { @Math { x dblup y } }
  C { "x dbldown y" } D { @Math { x dbldown y } }
  E { "x : y" } F { @Math { x : y } }
@Rowa
  A { "x :: y" } B { @Math { x :: y } }
  C { "x := y" } D { @Math { x := y } }
  mb { 0i }
}
All of these symbols have a @Code "neg" option which, when set
to {@Code "yes"}, causes a slash to overstrike the relation
symbol:
@ID {
@Code @Verbatim { x ==> neg { yes } y }
|7ct
@Math { x ==> neg { yes } y }
}
The slash is horizontally centred over the relation symbol,
which is not always best.
@PP
The @Code "rel" symbol causes an arbitrary object to be treated
mathematics.rel @SubIndex { @Code "rel" symbol }
rel.mathematics @Index { @Code "rel" symbol (mathematics) }
as a relation:
@ID {
@Code @Verbatim { x rel op { diamond } y }
|7ct
@Math { x rel op { diamond } y }
}
The @Code "op" option following @Code "rel" contains the object
to be treated as a relation; @Code "rel" also has the @Code "neg"
option, plus the left and right parameters as usual.
@End @SubSection

@SubSection
    @Title { Punctuation symbols }
@Begin
@LP
These symbols represent punctuation.  They take an object on
mathematics.punctuation. @SubIndex { punctuation symbols }
punctuation.mathematics @Index { punctuation symbols (mathematics) }
the left and on the right, and print them separated by the
punctuation symbol, with no space to the left and a thin
space to the right.  Here is the full list of these symbols:
@ID @Tbl
  aformat { @Cell ml{0i} indent{right} w{@LCodeWidth} @Code A |
            @Cell w {@ResultWidth} B |
            @Cell indent {right} w {@CodeWidth} @Code C |
            @Cell w {@ResultWidth} D |
            @Cell indent {right} w {@CodeWidth} @Code E |
            @Cell w {@ResultWidth} mr { 0i } F }
{
@Rowa
  ma { 0i }
  A { "x ; y" } B { @Math { x ; y } }
  C { "x , y" } D { @Math { x , y } }
  E { "x col y" } F { @Math { x col y } }
  mb { 0i }
}
The @Code "punct" symbol causes an arbitrary object to be treated
mathematics.punct @SubIndex { @Code "punct" symbol }
punct.mathematics @Index { @Code "punct" symbol (mathematics) }
as punctuation:
@ID {
@Code @Verbatim { x punct symbol { diamond } y }
|7ct
@Math { x punct symbol { diamond } y }
}
The @Code "symbol" option following @Code "punct" contains the object
to be treated as punctuation; its two parameters precede and follow
@Code "punct" as usual.
@End @SubSection

@EndSubSections
@End @Section
