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diff --git a/doc/user/mat_summ b/doc/user/mat_summ new file mode 100644 index 0000000..f6bf1a2 --- /dev/null +++ b/doc/user/mat_summ @@ -0,0 +1,1314 @@ +@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) } +options which work as described for the @Code "sum" symbol +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 |