diff options
| author | dos-reis <gdr@axiomatics.org> | 2011-02-06 04:58:02 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-02-06 04:58:02 +0000 |
| commit | 2eef476c721ed93b1acaaf1a77e20b5b7c73ed4f (patch) | |
| tree | 0a8dd6968553c1c45be0e2e66cc5a7a6660addea | |
| parent | 9c5ffc67bc7783bf0a93335ef6703a10a602ff37 (diff) | |
| download | open-axiom-2eef476c721ed93b1acaaf1a77e20b5b7c73ed4f.tar.gz | |
cleanup special hyperbolic builtins
| -rw-r--r-- | src/algebra/sf.spad.pamphlet | 30 | ||||
| -rw-r--r-- | src/algebra/strap/DFLOAT.lsp | 84 | ||||
| -rw-r--r-- | src/interp/boot-pkg.lisp | 11 | ||||
| -rw-r--r-- | src/interp/g-opt.boot | 8 | ||||
| -rw-r--r-- | src/interp/lisp-backend.boot | 18 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1334 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9128 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31516 |
10 files changed, 22163 insertions, 22176 deletions
diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index 55a4bd72..1a6f8266 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -313,26 +313,16 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, import %fcos: % -> % from Foreign Builtin import %ftan: % -> % from Foreign Builtin import %fcot: % -> % from Foreign Builtin - import %fsec: % -> % from Foreign Builtin - import %fcsc: % -> % from Foreign Builtin import %fasin: % -> % from Foreign Builtin import %facos: % -> % from Foreign Builtin import %fatan: % -> % from Foreign Builtin import %facot: % -> % from Foreign Builtin - import %fasec: % -> % from Foreign Builtin - import %facsc: % -> % from Foreign Builtin import %fsinh: % -> % from Foreign Builtin import %fcosh: % -> % from Foreign Builtin import %ftanh: % -> % from Foreign Builtin - import %fcsch: % -> % from Foreign Builtin - import %fcoth: % -> % from Foreign Builtin - import %fsech: % -> % from Foreign Builtin import %fasinh: % -> % from Foreign Builtin import %facosh: % -> % from Foreign Builtin import %fatanh: % -> % from Foreign Builtin - import %facsch: % -> % from Foreign Builtin - import %facoth: % -> % from Foreign Builtin - import %fasech: % -> % from Foreign Builtin import %fcstpi: () -> % from Foreign Builtin manexp: % -> MER @@ -416,26 +406,26 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, cos x == %fcos x tan x == %ftan x cot x == %fcot x - sec x == %fsec x - csc x == %fcsc x + sec x == 1/cos(x) + csc x == 1/sin(x) asin x == %fasin x acos x == %facos x atan x == %fatan x - acsc x == %facsc x + acsc x == asin(1/x) acot x == %facot x - asec x == %fasec x + asec x == acos(1/x) sinh x == %fsinh x cosh x == %fcosh x tanh x == %ftanh x - csch x == %fcsch x - coth x == %fcoth x - sech x == %fsech x + csch x == 1/sinh(x) + coth x == 1/tanh(x) + sech x == 1/cosh(x) asinh x == %fasinh x acosh x == %facosh x atanh x == %fatanh x - acsch x == %facsch x - acoth x == %facoth x - asech x == %fasech x + acsch x == asinh(1/x) + acoth x == atanh(1/x) + asech x == acosh(1/x) x:% / y:% == %fdiv(x,y) negative? x == x < 0 zero? x == x = 0 diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp index 21ed3bb1..3b21f1ba 100644 --- a/src/algebra/strap/DFLOAT.lsp +++ b/src/algebra/strap/DFLOAT.lsp @@ -209,13 +209,9 @@ (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;sec;2$;44|)) -(PUT '|DFLOAT;sec;2$;44| '|SPADreplace| '|%fsec|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;csc;2$;45|)) -(PUT '|DFLOAT;csc;2$;45| '|SPADreplace| '|%fcsc|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;asin;2$;46|)) @@ -234,8 +230,6 @@ (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;acsc;2$;49|)) -(PUT '|DFLOAT;acsc;2$;49| '|SPADreplace| '|%facsc|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;acot;2$;50|)) @@ -244,8 +238,6 @@ (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;asec;2$;51|)) -(PUT '|DFLOAT;asec;2$;51| '|SPADreplace| '|%fasec|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;sinh;2$;52|)) @@ -264,18 +256,12 @@ (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;csch;2$;55|)) -(PUT '|DFLOAT;csch;2$;55| '|SPADreplace| '|%fcsch|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;coth;2$;56|)) -(PUT '|DFLOAT;coth;2$;56| '|SPADreplace| '|%fcoth|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;sech;2$;57|)) -(PUT '|DFLOAT;sech;2$;57| '|SPADreplace| '|%fsech|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;asinh;2$;58|)) @@ -294,18 +280,12 @@ (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;acsch;2$;61|)) -(PUT '|DFLOAT;acsch;2$;61| '|SPADreplace| '|%facsch|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;acoth;2$;62|)) -(PUT '|DFLOAT;acoth;2$;62| '|SPADreplace| '|%facoth|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;asech;2$;63|)) -(PUT '|DFLOAT;asech;2$;63| '|SPADreplace| '|%fasech|) - (DECLAIM (FTYPE (FUNCTION (|%DoubleFloat| |%DoubleFloat| |%Shell|) |%DoubleFloat|) |DFLOAT;/;3$;64|)) @@ -403,6 +383,36 @@ (PUT '|DFLOAT;exp1;$;15| '|SPADreplace| '(XLAM NIL (|%fdiv| (|%i2f| 534625820200) (|%i2f| 196677847971)))) +(PUT '|DFLOAT;sec;2$;44| '|SPADreplace| + '(XLAM (|x|) (|%fdiv| (|%i2f| 1) (|%fcos| |x|)))) + +(PUT '|DFLOAT;csc;2$;45| '|SPADreplace| + '(XLAM (|x|) (|%fdiv| (|%i2f| 1) (|%fsin| |x|)))) + +(PUT '|DFLOAT;acsc;2$;49| '|SPADreplace| + '(XLAM (|x|) (|%fasin| (|%fdiv| (|%i2f| 1) |x|)))) + +(PUT '|DFLOAT;asec;2$;51| '|SPADreplace| + '(XLAM (|x|) (|%facos| (|%fdiv| (|%i2f| 1) |x|)))) + +(PUT '|DFLOAT;csch;2$;55| '|SPADreplace| + '(XLAM (|x|) (|%fdiv| (|%i2f| 1) (|%fsinh| |x|)))) + +(PUT '|DFLOAT;coth;2$;56| '|SPADreplace| + '(XLAM (|x|) (|%fdiv| (|%i2f| 1) (|%ftanh| |x|)))) + +(PUT '|DFLOAT;sech;2$;57| '|SPADreplace| + '(XLAM (|x|) (|%fdiv| (|%i2f| 1) (|%fcosh| |x|)))) + +(PUT '|DFLOAT;acsch;2$;61| '|SPADreplace| + '(XLAM (|x|) (|%fasinh| (|%fdiv| (|%i2f| 1) |x|)))) + +(PUT '|DFLOAT;acoth;2$;62| '|SPADreplace| + '(XLAM (|x|) (|%fatanh| (|%fdiv| (|%i2f| 1) |x|)))) + +(PUT '|DFLOAT;asech;2$;63| '|SPADreplace| + '(XLAM (|x|) (|%facosh| (|%fdiv| (|%i2f| 1) |x|)))) + (PUT '|DFLOAT;negative?;$B;65| '|SPADreplace| '(XLAM (|x|) (|%flt| |x| (|%i2f| 0)))) @@ -569,9 +579,13 @@ (DEFUN |DFLOAT;cot;2$;43| (|x| $) (DECLARE (IGNORE $)) (COT |x|)) -(DEFUN |DFLOAT;sec;2$;44| (|x| $) (DECLARE (IGNORE $)) (SEC |x|)) +(DEFUN |DFLOAT;sec;2$;44| (|x| $) + (DECLARE (IGNORE $)) + (/ 1.0 (COS |x|))) -(DEFUN |DFLOAT;csc;2$;45| (|x| $) (DECLARE (IGNORE $)) (CSC |x|)) +(DEFUN |DFLOAT;csc;2$;45| (|x| $) + (DECLARE (IGNORE $)) + (/ 1.0 (SIN |x|))) (DEFUN |DFLOAT;asin;2$;46| (|x| $) (DECLARE (IGNORE $)) @@ -585,13 +599,13 @@ (DEFUN |DFLOAT;acsc;2$;49| (|x| $) (DECLARE (IGNORE $)) - (C-TO-R (ACSC |x|))) + (C-TO-R (ASIN (/ 1.0 |x|)))) (DEFUN |DFLOAT;acot;2$;50| (|x| $) (DECLARE (IGNORE $)) (ACOT |x|)) (DEFUN |DFLOAT;asec;2$;51| (|x| $) (DECLARE (IGNORE $)) - (C-TO-R (ASEC |x|))) + (C-TO-R (ACOS (/ 1.0 |x|)))) (DEFUN |DFLOAT;sinh;2$;52| (|x| $) (DECLARE (IGNORE $)) (SINH |x|)) @@ -599,11 +613,17 @@ (DEFUN |DFLOAT;tanh;2$;54| (|x| $) (DECLARE (IGNORE $)) (TANH |x|)) -(DEFUN |DFLOAT;csch;2$;55| (|x| $) (DECLARE (IGNORE $)) (CSCH |x|)) +(DEFUN |DFLOAT;csch;2$;55| (|x| $) + (DECLARE (IGNORE $)) + (/ 1.0 (SINH |x|))) -(DEFUN |DFLOAT;coth;2$;56| (|x| $) (DECLARE (IGNORE $)) (COTH |x|)) +(DEFUN |DFLOAT;coth;2$;56| (|x| $) + (DECLARE (IGNORE $)) + (/ 1.0 (TANH |x|))) -(DEFUN |DFLOAT;sech;2$;57| (|x| $) (DECLARE (IGNORE $)) (SECH |x|)) +(DEFUN |DFLOAT;sech;2$;57| (|x| $) + (DECLARE (IGNORE $)) + (/ 1.0 (COSH |x|))) (DEFUN |DFLOAT;asinh;2$;58| (|x| $) (DECLARE (IGNORE $)) (ASINH |x|)) @@ -615,13 +635,17 @@ (DECLARE (IGNORE $)) (C-TO-R (ATANH |x|))) -(DEFUN |DFLOAT;acsch;2$;61| (|x| $) (DECLARE (IGNORE $)) (ACSCH |x|)) +(DEFUN |DFLOAT;acsch;2$;61| (|x| $) + (DECLARE (IGNORE $)) + (ASINH (/ 1.0 |x|))) (DEFUN |DFLOAT;acoth;2$;62| (|x| $) (DECLARE (IGNORE $)) - (C-TO-R (ACOTH |x|))) + (C-TO-R (ATANH (/ 1.0 |x|)))) -(DEFUN |DFLOAT;asech;2$;63| (|x| $) (DECLARE (IGNORE $)) (ASECH |x|)) +(DEFUN |DFLOAT;asech;2$;63| (|x| $) + (DECLARE (IGNORE $)) + (C-TO-R (ACOSH (/ 1.0 |x|)))) (DEFUN |DFLOAT;/;3$;64| (|x| |y| $) (DECLARE (IGNORE $)) (/ |x| |y|)) diff --git a/src/interp/boot-pkg.lisp b/src/interp/boot-pkg.lisp index b7b1cd56..aa16ed6f 100644 --- a/src/interp/boot-pkg.lisp +++ b/src/interp/boot-pkg.lisp @@ -71,17 +71,6 @@ ;; Contributed by Juergen Weiss from a suggestion by Arthur Norman. -(defun sec (x) (/ 1 (cos x))) -(defun csc (x) (/ 1 (sin x))) -(defun acsc (x) (asin (/ 1 x))) -(defun asec (x) (acos (/ 1 x))) -(defun csch (x) (/ 1 (sinh x))) -(defun coth (x) (* (cosh x) (csch x))) -(defun sech (x) (/ 1 (cosh x))) -(defun acsch (x) (asinh (/ 1 x))) -(defun acoth (x) (atanh (/ 1 x))) -(defun asech (x) (acosh (/ 1 x))) - (defun cot (a) (if (or (> a 1000.0) (< a -1000.0)) (/ (cos a) (sin a)) diff --git a/src/interp/g-opt.boot b/src/interp/g-opt.boot index d99f8c6a..f29ef062 100644 --- a/src/interp/g-opt.boot +++ b/src/interp/g-opt.boot @@ -408,10 +408,10 @@ $VMsideEffectFreeOperators == %feq %flt %fle %fgt %fge %fmul %fadd %fsub %fexp %fmin %fmax %float? %fpowi %fdiv %fneg %i2f %fminval %fmaxval %fbase %fprec %ftrunc %fsqrt %fpowf %flog %flog2 %flog10 %fmanexp - %fsin %fcos %ftan %fcot %fsec %fcsc - %fasin %facos %fatan %facot %fasec %facsc - %fsinh %fcosh %ftanh %fcsch %fcoth %fsech - %fasinh %facosh %fatanh %facsch %facoth %fasech + %fsin %fcos %ftan %fcot + %fasin %facos %fatan %facot + %fsinh %fcosh %ftanh + %fasinh %facosh %fatanh %val2z %z2val %zlit %zreal %zimag %zexp %zlog %zsin %zcos %ztan %zasin %zacos %zatan %zsinh %zcosh %ztanh %zasinh %zacosh %zatanh diff --git a/src/interp/lisp-backend.boot b/src/interp/lisp-backend.boot index 8a9a01d2..646dab26 100644 --- a/src/interp/lisp-backend.boot +++ b/src/interp/lisp-backend.boot @@ -293,12 +293,6 @@ expandFasin ['%fasin,x] == expandFacos ['%facos,x] == ['C_-TO_-R,['ACOS,expandToVMForm x]] -expandFasec ['%fasec,x] == - ['C_-TO_-R,['ASEC,expandToVMForm x]] - -expandFacsc ['%facsc,x] == - ['C_-TO_-R,['ACSC,expandToVMForm x]] - expandFacosh ['%facosh,x] == ['C_-TO_-R,['ACOSH,expandToVMForm x]] @@ -308,9 +302,6 @@ expandFatanh ['%fatanh,x] == expandFacoth ['%facoth,x] == ['C_-TO_-R,['ACOTH,expandToVMForm x]] -expandFasech ['%fasech,x] == - ['C_-TO_-R,['ASECH,expandToVMForm x]] - -- String operations @@ -522,19 +513,12 @@ for x in [ ['%fcos, :'COS], ['%ftan, :'TAN], ['%fcot, :'COT], - ['%fsec, :'SEC], - ['%fcsc, :'CSC], ['%fatan, :'ATAN], ['%facot, :'ACOT], ['%fsinh, :'SINH], ['%fcosh, :'COSH], ['%ftanh, :'TANH], - ['%fcsch, :'CSCH], - ['%fcoth, :'COTH], - ['%fsech, :'SECH], ['%fasinh, :'ASINH], - ['%fasech, :'ASECH], - ['%facsch, :'ACSCH], -- complex number operations ['%zlit, :'COMPLEX], @@ -641,8 +625,6 @@ for x in [ ['%flog10, :function expandFlog10], ['%fasin, :function expandFasin], ['%facos, :function expandFacos], - ['%fasec, :function expandFasec], - ['%facsc, :function expandFacsc], ['%facosh, :function expandFacosh], ['%fatanh, :function expandFatanh], ['%facoth, :function expandFacoth], diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 6575a97e..6f5eb3e8 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2301248 . 3505945375) +(2301248 . 3505955684) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1677) +(-32 R -1573) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -1677 UP UPUP -2845) +(-40 -1573 UP UPUP -2990) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2157 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2157 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2157 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2157 (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2157 (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-2157 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -1677) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2188 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2188 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2188 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2188 (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2188 (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-2188 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -1573) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -435) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4508 . T) (-4509 . T)) -((-2157 (-12 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#2|))))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-871))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#2|))))))) +((-2188 (-12 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#2|))))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-871))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1677) +(-54 |Base| R -1573) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -171,64 +171,64 @@ NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray's."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -4043) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -3820) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-62 -4043) +(-62 -3820) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -4043) +(-63 -3820) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-64 -4043) +(-64 -3820) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -4043) +(-65 -3820) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -4043) +(-66 -3820) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -4043) +(-67 -3820) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -4043) +(-68 -3820) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -4043) +(-69 -3820) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -4043) +(-70 -3820) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -4043) +(-71 -3820) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -4043) +(-72 -3820) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -4043) +(-73 -3820) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -4043) +(-74 -3820) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -4043) +(-75 -3820) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -240,51 +240,51 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives wrt \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -4043) +(-78 -3820) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -4043) +(-79 -3820) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -4043) +(-80 -3820) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -4043) +(-81 -3820) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -4043) +(-82 -3820) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -4043) +(-83 -3820) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -4043) +(-84 -3820) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -4043) +(-85 -3820) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -4043) +(-86 -3820) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -4043) +(-87 -3820) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -4043) +(-88 -3820) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-89 -4043) +(-89 -3820) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2157 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2188 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -396,7 +396,7 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -1677 UP) +(-117 -1573 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -407,7 +407,7 @@ NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2157 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|%listlit| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -298) (|%listlit| (QUOTE -118) (|devaluate| |#1|)) (|%listlit| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2188 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|%listlit| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%listlit| (QUOTE -298) (|%listlit| (QUOTE -118) (|devaluate| |#1|)) (|%listlit| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -423,7 +423,7 @@ NIL (-123 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -443,11 +443,11 @@ NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL @@ -455,7 +455,7 @@ NIL (-131) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130)))))) (-2157 (|HasCategory| (-130) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130)))))) (|HasCategory| (-130) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2157 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130)))))) +((-2188 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130)))))) (-2188 (|HasCategory| (-130) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130)))))) (|HasCategory| (-130) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2188 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%listlit| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -476,11 +476,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4510 "*") . T)) NIL -(-137 |minix| -3678 R) +(-137 |minix| -4081 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -3678 S T$) +(-138 |minix| -4081 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL @@ -503,7 +503,7 @@ NIL (-143) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4508 . T) (-4498 . T) (-4509 . T)) -((-2157 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) +((-2188 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (-144 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4505 . T)) NIL -(-150 -1677 UP UPUP) +(-150 -1573 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -568,7 +568,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-160 R -1677) +(-160 R -1573) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -602,7 +602,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4504)) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-168 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4501 -2157 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-2973 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4501 -2188 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-2857 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-169 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4501 -2157 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4504 |has| |#1| (-6 -4504)) (-4507 |has| |#1| (-6 -4507)) (-2973 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -1677) +(-191 R -1573) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -1677 UP UPUP R) +(-219 -1573 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-220 -1677 FP) +(-220 -1573 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) 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(|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -1677) +(-223 R -1573) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4505 . T)) NIL -(-228 R -1677) +(-228 R -1573) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-229) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2965 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2848 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-230) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -855,7 +855,7 @@ NIL (-231 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -904,19 +904,19 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-244 S -3678 R) +(-244 S -4081 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4505)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-1132)))) -(-245 -3678 R) +(-245 -4081 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4502 |has| |#2| (-1080)) (-4503 |has| |#2| (-1080)) (-4505 |has| |#2| (-6 -4505)) (-4508 . T)) NIL -(-246 -3678 R) +(-246 -4081 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. 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\\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) 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(-1080)))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|))))) (-261 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -1031,7 +1031,7 @@ NIL (-275 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1076,11 +1076,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-287 R -1677) +(-287 R -1573) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-288 R -1677) +(-288 R -1573) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1132,7 +1132,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-301 S R |Mod| -1562 -2026 |exactQuo|) +(-301 S R |Mod| -3860 -3892 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4505 -2157 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) -((|HasCategory| |#1| (QUOTE (-376))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2157 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2157 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2157 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2157 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) +((-4505 -2188 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) +((|HasCategory| |#1| (QUOTE (-376))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2188 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2188 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2188 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) (-306 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL @@ -1159,7 +1159,7 @@ NIL (-307 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#2|)))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#2|)))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102)))) (-308) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL @@ -1172,11 +1172,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -1677 S) +(-311 -1573 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -1677) +(-312 E -1573) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-322 -1677) +(-322 -1573) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1231,11 +1231,11 @@ NIL (-325 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1051))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871))) (-2157 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1182))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-1284 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(|HasCategory| $ (QUOTE (-147)))) (-2188 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| $ (QUOTE (-147)))))) (-326 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4505 -2157 (-12 (|has| |#1| (-571)) (-2157 (|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) -((-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-2157 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-1080))) (-2157 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-147)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-175)))) (-12 (|HasCategory| |#1| 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(|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) +((-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-2188 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-1080))) (-2188 (-12 (|HasCategory| |#1| 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(|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (-2188 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571)))) (-2188 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21)))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143)))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25)))) (-2188 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (-327 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -1677) +(-329 R -1573) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1255,7 +1255,7 @@ NIL (-331 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . 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(|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1287,12 +1287,12 @@ NIL (-339 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1677) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -1573) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -1677) +(-341 -1573) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -1677 UP UPUP R) +(-346 -1573 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1320,11 +1320,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-348 S -1677 UP UPUP R) +(-348 S -1573 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-349 -1677 UP UPUP R) +(-349 -1573 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL @@ -1343,12 +1343,12 @@ NIL (-353 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) -(-354 S -1677 UP UPUP) +((-2188 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +(-354 S -1573 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -1677 UP UPUP) +(-355 -1573 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL @@ -1359,15 +1359,15 @@ NIL (-357 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2188 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2188 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2188 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1384,42 +1384,42 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-364 R UP -1677) +(-364 R UP -1573) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-365 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2188 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2188 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2188 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2188 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-370 -1677 GF) +(-370 -1573 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-371 -1677 FP FPP) +(-371 -1573 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2188 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) NIL @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4491 . T) (-4499 . T) (-2965 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4491 . T) (-4499 . T) (-2848 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-392 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1552,7 +1552,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-406 -1677 UP UPUP R) +(-406 -1573 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-412 -4043 |returnType| -1668 |symbols|) +(-412 -3820 |returnType| -2782 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-413 -1677 UP) +(-413 -1573 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4491)) (|HasAttribute| |#1| (QUOTE -4499))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2965 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2848 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-419 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and gcd are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2157 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2188 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) NIL @@ -1615,7 +1615,7 @@ NIL (-421 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4495 -12 (|has| |#1| (-6 -4506)) (|has| |#1| (-466)) (|has| |#1| (-6 -4495))) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-391)))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4495)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-391)))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4506)) (|HasAttribute| |#1| (QUOTE -4495)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -1677 UP A) +(-427 R -1573 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) ((-4505 . T)) NIL @@ -1644,7 +1644,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-429 R -1677 UP A |ibasis|) +(-429 R -1573 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL ((|HasCategory| |#4| (|%listlit| (QUOTE -1069) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (-435 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4505 -2157 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) +((-4505 -2188 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -1677) +(-442 R -1573) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1704,19 +1704,19 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4495 -12 (|has| |#1| (-6 -4495)) (|has| |#2| (-6 -4495))) (-4502 . T) (-4503 . T) (-4505 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4495)) (|HasAttribute| |#2| (QUOTE -4495)))) -(-444 R -1677) +(-444 R -1573) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-445 R -1677) +(-445 R -1573) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-446 R -1677) +(-446 R -1573) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-447 R -1677) +(-447 R -1573) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1724,7 +1724,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-449 R -1677 UP) +(-449 R -1573 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-457 R UP -1677) +(-457 R UP -1573) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1803,7 +1803,7 @@ NIL (-468 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2157 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2157 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2157 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2157 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2157 (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2188 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2188 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2188 (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) NIL @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-485 |lv| -1677 R) +(-485 |lv| -1573 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1883,11 +1883,11 @@ NIL (-488 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") 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The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4509 . T) (-4508 . T)) @@ -1903,7 +1903,7 @@ NIL (-493 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4508 . T) (-4509 . 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Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1911,11 +1911,11 @@ NIL (-495 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasAttribute| |#2| (QUOTE -4505)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-1080)))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|))))) (-497) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1923,8 +1923,8 @@ NIL (-498 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -1677 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -1573 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1935,7 +1935,7 @@ NIL (-501) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2157 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2188 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-502 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -1677 UP |AlExt| |AlPol|) +(-508 -1573 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1971,16 +1971,16 @@ NIL (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-511 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray's with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-513 R UP -1677) +(-513 R UP -1573) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -1677 |Expon| |VarSet| |DPoly|) +(-518 -1573 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%listlit| (QUOTE -633) (QUOTE (-1207))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2059,15 +2059,15 @@ NIL (-532 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((-2157 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-2188 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-535 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2079,7 +2079,7 @@ NIL (-537 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2112,7 +2112,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL ((-12 (|HasCategory| (-793) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132))))) -(-546 K -1677 |Par|) +(-546 K -1573 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2136,7 +2136,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-552 K -1677 |Par|) +(-552 K -1573 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2191,12 +2191,12 @@ NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#2|)))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102)))) -(-566 R -1677) +((-12 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#2|)))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102)))) +(-566 R -1573) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-567 R0 -1677 UP UPUP R) +(-567 R0 -1573 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2206,7 +2206,7 @@ NIL NIL (-569 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} <= \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2965 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2848 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-570 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2216,7 +2216,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-572 R -1677) +(-572 R -1573) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2228,7 +2228,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-575 R -1677 L) +(-575 R -1573 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (|%listlit| (QUOTE -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-577 -1677 UP UPUP R) +(-577 -1573 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-578 -1677 UP) +(-578 -1573 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL @@ -2248,15 +2248,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\tt numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\tt \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\tt \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\tt \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-580 R -1677 L) +(-580 R -1573 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (|%listlit| (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -1677) +(-581 R -1573) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -1677 UP) +(-582 -1573 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2264,27 +2264,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-584 -1677) +(-584 -1573) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-585 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2965 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2848 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-586) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-587 R -1677) +(-587 R -1573) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -1677 UP) +(-588 -1573 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-589 R -1677) +(-589 R -1573) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2316,15 +2316,15 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-597 -1677) +(-597 -1573) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over F?")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-1207))))) -(-598 E -1677) +(-598 E -1573) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL -(-599 R -1677) +(-599 R -1573) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2359,7 +2359,7 @@ NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (-2157 (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2157 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) +((-2188 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (-2188 (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2188 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (-608 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2367,7 +2367,7 @@ NIL (-609 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -2556) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4202) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) (((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -2384,7 +2384,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-614 R -1677 FG) +(-614 R -1573 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2395,7 +2395,7 @@ NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-617 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4505 -2157 (-1466 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2157 (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2188 (-1350 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2188 (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (QUOTE (-1189))) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (QUOTE (-1189))) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-102)))) (-628 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2464,7 +2464,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -1677 UP) +(-634 -1573 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2492,7 +2492,7 @@ NIL ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4505 . T)) NIL -(-641 R -1677) +(-641 R -1573) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-648 R -1677) +(-648 R -1573) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL @@ -2528,18 +2528,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-650 |lv| -1677) +(-650 |lv| -1573) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-651) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (QUOTE (-1189))) (|%listlit| (QUOTE |:|) (QUOTE -3168) (QUOTE (-51))))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%listlit| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (QUOTE (-1189))) (|%listlit| (QUOTE |:|) (QUOTE -3553) (QUOTE (-51))))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%listlit| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (QUOTE (-1132)))) (-652 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4505 -2157 (-1466 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2157 (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2188 (-1350 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2188 (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%listlit| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%listlit| (QUOTE -380) (|devaluate| |#1|)))) (-653 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2563,7 +2563,7 @@ NIL (-658 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'s exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-1452 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-2553 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) (-659 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) ((-4503 . T) (-4502 . T)) @@ -2583,7 +2583,7 @@ NIL (-663 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-664 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2607,7 +2607,7 @@ NIL (-669 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL @@ -2628,11 +2628,11 @@ NIL ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4503 . T) (-4502 . T)) ((|HasCategory| |#1| (QUOTE (-813)))) -(-675 R -1677 L) +(-675 R -1573 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-676 A -4020) +(-676 A -1497) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-681 -1677 UP) +(-681 -1573 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) @@ -2684,11 +2684,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4509 . T) (-4508 . T)) NIL -(-689 -1677 |Row| |Col| M) +(-689 -1573 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-690 -1677) +(-690 -1573) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2699,7 +2699,7 @@ NIL (-692 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4505 . T) (-4508 . T) (-4502 . T) (-4503 . T)) -((|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2157 (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2157 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2188 (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2188 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2719,7 +2719,7 @@ NIL (-697 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2775,7 +2775,7 @@ NIL (-711 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4508 . T) (-4509 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-712 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-714 S -1677 FLAF FLAS) +(-714 S -1573 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{ku+1},{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2794,8 +2794,8 @@ NIL NIL (-716) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4501 . T) (-4506 |has| (-721) (-376)) (-4500 |has| (-721) (-376)) (-2973 . T) (-4507 |has| (-721) (-6 -4507)) (-4504 |has| (-721) (-6 -4504)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-2848 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-722 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2840,7 +2840,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) 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(QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -1562 -2026 |exactQuo|) +(-737 R |Mod| -3860 -3892 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4505 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4503 . T) (-4502 . T)) NIL -(-740 -1677) +(-740 -1573) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) ((-4505 . T)) NIL @@ -2924,7 +2924,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-749 -1677 UP) +(-749 -1573 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2943,7 +2943,7 @@ NIL (-753 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2157 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2157 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2157 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2157 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2157 (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2188 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2188 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2188 (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -3076,11 +3076,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-787 -1677) +(-787 -1573) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-788 P -1677) +(-788 P -1573) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -1677) +(-790 UP -1573) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3104,7 +3104,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4510 "*") . T)) NIL -(-794 R -1677) +(-794 R -1573) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3124,7 +3124,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-799 -1677 |ExtF| |SUEx| |ExtP| |n|) +(-799 -1573 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3139,11 +3139,11 @@ NIL (-802 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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(QUOTE -1022) (QUOTE (-560))))))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-803 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{R^(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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(|%listlit| (QUOTE -421) (QUOTE (-560))))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-804 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3211,8 +3211,8 @@ NIL (-820 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2157 (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (-2157 (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) -(-821 -2157 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2188 (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (-2188 (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) +(-821 -2188 R OS S) ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL @@ -3220,11 +3220,11 @@ NIL ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-823 R -1677 L) +(-823 R -1573 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-824 R -1677) +(-824 R -1573) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3232,7 +3232,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE's.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-826 R -1677) +(-826 R -1573) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3240,11 +3240,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-828 -1677 UP UPUP R) +(-828 -1573 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-829 -1677 UP L LQ) +(-829 -1573 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3252,38 +3252,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-831 -1677 UP L LQ) +(-831 -1573 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-832 -1677 UP) +(-832 -1573 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-833 -1677 L UP A LO) +(-833 -1573 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-834 -1677 UP) +(-834 -1573 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-835 -1677 LO) +(-835 -1573 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-836 -1677 LODO) +(-836 -1573 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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(((-4510 "*") |has| |#2| (-376)) (-4501 |has| |#2| (-376)) (-4506 |has| |#2| (-376)) (-4500 |has| |#2| (-376)) (-4505 . T) (-4503 . T) (-4502 . T)) @@ -3347,7 +3347,7 @@ NIL (-854 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4505 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2157 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (-2157 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2188 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (-2188 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-855 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL @@ -3387,7 +3387,7 @@ NIL (-864 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4505 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2157 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (-2157 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2188 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (-2188 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-865 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3396,7 +3396,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-867 -3678 S) +(-867 -4081 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3440,11 +3440,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-878 R |sigma| -4428) +(-878 R |sigma| -2823) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-879 |x| R |sigma| -4428) +(-879 |x| R |sigma| -2823) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4502 . T) (-4503 . T) (-4505 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3511,15 +3511,15 @@ NIL (-895 |p|) ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2157 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|%listlit| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -298) (|%listlit| (QUOTE -893) (|devaluate| |#1|)) (|%listlit| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) +((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2188 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|%listlit| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%listlit| (QUOTE -298) (|%listlit| (QUOTE -893) (|devaluate| |#1|)) (|%listlit| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) (-896 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of Qp.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2157 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%listlit| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2188 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%listlit| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-897 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))))) (-898) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) NIL @@ -3579,7 +3579,7 @@ NIL (-912 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-1452 (|HasCategory| |#2| (QUOTE (-1080)))) (-1452 (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-1452 (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207))))) +((-12 (-2553 (|HasCategory| |#2| (QUOTE (-1080)))) (-2553 (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-2553 (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-1207))))) (-913 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL @@ -3592,7 +3592,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-916 R -3405) +(-916 R -1799) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3620,7 +3620,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-923 UP -1677) +(-923 UP -1573) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3651,11 +3651,11 @@ NIL (-930 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-931 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4505 . T)) -((-2157 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) +((-2188 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (-932 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3688,7 +3688,7 @@ NIL ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-940 R0 -1677 UP UPUP R) +(-940 R0 -1573 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3716,7 +3716,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-947 -1677) +(-947 -1573) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3732,11 +3732,11 @@ NIL ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL -(-951 |xx| -1677) +(-951 |xx| -1573) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) NIL NIL -(-952 -1677 P) +(-952 -1573 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3764,7 +3764,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-959 R -1677) +(-959 R -1573) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3772,7 +3772,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-961 S R -1677) +(-961 S R -1573) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3792,11 +3792,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (|%listlit| (QUOTE -911) (|devaluate| |#1|)))) -(-966 -3405) +(-966 -1799) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-967 R -1677 -3405) +(-967 R -1573 -1799) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL @@ -3819,7 +3819,7 @@ NIL (-972 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-973 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3831,7 +3831,7 @@ NIL (-975 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-976 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3848,7 +3848,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) NIL -(-980 E V R P -1677) +(-980 E V R P -1573) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3856,7 +3856,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-982 E V R P -1677) +(-982 E V R P -1573) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3871,7 +3871,7 @@ NIL (-985 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4506))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4506))) (-986 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL @@ -3879,7 +3879,7 @@ NIL (-987 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-988 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3888,7 +3888,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-990 -1677) +(-990 -1573) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3903,7 +3903,7 @@ NIL (-993 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) ((-4505 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-994) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3992,7 +3992,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1016 K R UP -1677) +(-1016 K R UP -1573) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -4039,7 +4039,7 @@ NIL (-1027 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4501 |has| |#1| (-302)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2157 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2188 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%listlit| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) (-1028 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4055,7 +4055,7 @@ NIL (-1031 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1032 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4064,14 +4064,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1034 -1677 UP UPUP |radicnd| |n|) +(-1034 -1573 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4501 |has| (-421 |#2|) (-376)) (-4506 |has| (-421 |#2|) (-376)) (-4500 |has| (-421 |#2|) (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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(|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2157 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2188 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (|%listlit| (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%listlit| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%listlit| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1036) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -4104,19 +4104,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) NIL -(-1044 R -1677) +(-1044 R -1573) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1045 R -1677) +(-1045 R -1573) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1046 -1677 UP) +(-1046 -1573 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1047 -1677 UP) +(-1047 -1573 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4151,8 +4151,8 @@ NIL (-1055 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4501 . T) (-4506 . T) (-4500 . T) (-4503 . T) (-4502 . T) ((-4510 "*") . T) (-4505 . T)) -((-2157 (|HasCategory| (-421 (-560)) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%listlit| (QUOTE -1069) (QUOTE (-560))))) -(-1056 -1677 L) +((-2188 (|HasCategory| (-421 (-560)) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%listlit| (QUOTE -1069) (QUOTE (-560))))) +(-1056 -1573 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4188,14 +4188,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1065 -1677 |Expon| |VarSet| |FPol| |LFPol|) +(-1065 -1573 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-1066) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (QUOTE (-1207))) (|%listlit| (QUOTE |:|) (QUOTE -3168) (QUOTE (-51))))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%listlit| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (QUOTE (-1207))) (|%listlit| (QUOTE |:|) (QUOTE -3553) (QUOTE (-51))))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%listlit| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-102)))) (-1067) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4252,7 +4252,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4505 . T)) NIL -(-1081 |xx| -1677) +(-1081 |xx| -1573) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4271,7 +4271,7 @@ NIL (-1085 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4508 . T) (-4503 . T) (-4502 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-2157 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%listlit| (QUOTE -632) (QUOTE (-887))))) +((|HasCategory| |#3| (QUOTE (-175))) (-2188 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%listlit| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-1086 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4307,7 +4307,7 @@ NIL (-1094) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (QUOTE (-1207))) (|%listlit| (QUOTE |:|) (QUOTE -3168) (QUOTE (-51))))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%listlit| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (QUOTE (-1207))) (|%listlit| (QUOTE |:|) (QUOTE -3553) (QUOTE (-51))))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%listlit| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (QUOTE (-102)))) (-1095 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4352,7 +4352,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1106 |Base| R -1677) +(-1106 |Base| R -1573) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL @@ -4360,7 +4360,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1108 |Base| R -1677) +(-1108 |Base| R -1573) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL @@ -4371,7 +4371,7 @@ NIL (-1110 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4501 |has| |#1| (-376)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . 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(|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4403,7 +4403,7 @@ NIL (-1118 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1119 (-1207)) (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1119 (-1207)) (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1119 (-1207)) (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) 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indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4443,7 +4443,7 @@ NIL (-1128 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) ((-4508 . T) (-4498 . T) (-4509 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-1129 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4520,7 +4520,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1148 R -1677) +(-1148 R -1573) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4555,16 +4555,16 @@ NIL (-1156 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2157 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1157 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1158 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4509 . T) (-4508 . T)) NIL -(-1159 UP -1677) +(-1159 UP -1573) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4619,11 +4619,11 @@ NIL (-1172 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}lt)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}ls)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in ls]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2157 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2157 (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2188 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2188 (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) (-1173 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4505 . T) (-4497 |has| |#2| (-6 (-4510 "*"))) (-4508 . T) (-4502 . T) (-4503 . T)) -((|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2157 (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2157 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (-2188 (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|))))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2188 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1174 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} >= \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} >= \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\"*\")} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4643,7 +4643,7 @@ NIL (-1178 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1179 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4655,7 +4655,7 @@ NIL (-1181 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#2|)))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#2|)))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132)))) (-1182) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}'s are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4671,7 +4671,7 @@ NIL (-1185 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1186 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL @@ -4687,11 +4687,11 @@ NIL (-1189) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (-2157 (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2157 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) +((-2188 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (-2188 (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2188 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%listlit| (QUOTE -321) (QUOTE (-146)))))) (-1190 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (QUOTE (-1189))) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#1|)))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 (-1189)) (|:| -3168 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (QUOTE (-1189))) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#1|)))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 (-1189)) (|:| -3553 |#1|)) (QUOTE (-102)))) (-1191 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4722,9 +4722,9 @@ NIL NIL (-1198 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4735,7 +4735,7 @@ NIL (-1201 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4747,11 +4747,11 @@ NIL (-1204 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . 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We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%listlit| (QUOTE -2556) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2157 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -1457) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4216) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4202) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3935) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3329) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1206) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4767,7 +4767,7 @@ NIL (-1209 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-6 -4506)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2157 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4506))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2188 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4506))) (-1210) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4807,7 +4807,7 @@ NIL (-1219 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4508 . T) (-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3913) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3168) (|devaluate| |#2|)))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2157 (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -321) (|%listlit| (QUOTE -2) (|%listlit| (QUOTE |:|) (QUOTE -3699) (|devaluate| |#1|)) (|%listlit| (QUOTE |:|) (QUOTE -3553) (|devaluate| |#2|)))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%listlit| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (-2188 (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (QUOTE (-102)))) (-1220 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4867,7 +4867,7 @@ NIL (-1234 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4509 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1235 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4876,7 +4876,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1237 R -1677) +(-1237 R -1573) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -4884,14 +4884,14 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1239 R -1677) +(-1239 R -1573) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (|%listlit| (QUOTE -633) (|%listlit| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%listlit| (QUOTE -911) (|devaluate| |#1|))))) (-1240 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1241 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL @@ -4912,7 +4912,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) -(-1246 -1677) +(-1246 -1573) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4958,8 +4958,8 @@ NIL NIL (-1257 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) 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(QUOTE -929) (QUOTE (-1207)))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-147)))))) (-1263 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4995,7 +4995,7 @@ NIL (-1266 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4510 "*") |has| |#2| (-175)) (-4501 |has| |#2| (-571)) (-4504 |has| |#2| (-376)) (-4506 |has| |#2| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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(|%listlit| (QUOTE -421) (QUOTE (-560))))) (-2188 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (|%listlit| (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2188 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1267 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -5031,7 +5031,7 @@ NIL (-1275 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%listlit| (QUOTE -2556) (|%listlit| (|devaluate| |#2|) (QUOTE (-1207)))))) +((|HasCategory| |#2| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%listlit| (QUOTE -4202) (|%listlit| (|devaluate| |#2|) (QUOTE (-1207)))))) (-1276 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -5043,7 +5043,7 @@ NIL (-1278 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2157 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%listlit| (QUOTE -2556) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (-2157 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -1457) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4216) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2188 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4202) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3935) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3329) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1279 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL @@ -5063,11 +5063,11 @@ NIL (-1283 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-376)) (-4500 |has| |#1| (-376)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2157 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%listlit| (QUOTE -2556) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (-2157 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -1457) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4216) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2188 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4202) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3935) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3329) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (-1284 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) (((-4510 "*") |has| (-1278 |#2| |#3| |#4|) (-175)) (-4501 |has| (-1278 |#2| |#3| |#4|) (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-175))) (-2157 (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-175))) (-2188 (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (|%listlit| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1278 |#2| |#3| |#4|) (QUOTE (-571)))) (-1285 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5079,7 +5079,7 @@ NIL (-1287 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2157 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%listlit| (QUOTE -2556) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2157 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -1457) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4216) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2188 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%listlit| (QUOTE *) (|%listlit| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%listlit| (QUOTE -4202) (|%listlit| (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (|%listlit| (QUOTE **) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2188 (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233)))) (-12 (|HasCategory| |#1| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3935) (|%listlit| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (|%listlit| (QUOTE -3329) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1288 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL @@ -5087,7 +5087,7 @@ NIL (-1289 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (|%listlit| (QUOTE -4216) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%listlit| (QUOTE -1457) (|%listlit| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%listlit| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (|%listlit| (QUOTE -3329) (|%listlit| (|%listlit| (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%listlit| (QUOTE -3935) (|%listlit| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (|%listlit| (QUOTE -38) (|%listlit| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1290 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4502 . T) (-4503 . T) (-4505 . T)) @@ -5096,7 +5096,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1292 -1677 UP L UTS) +(-1292 -1573 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-571)))) @@ -5119,7 +5119,7 @@ NIL (-1297 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4509 . T) (-4508 . T)) -((-2157 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2157 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2157 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2157 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) +((-2188 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-2188 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%listlit| (QUOTE -633) (QUOTE (-549)))) (-2188 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2188 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%listlit| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%listlit| (QUOTE -321) (|devaluate| |#1|))))) (-1298 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL @@ -5156,7 +5156,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1307 K R UP -1677) +(-1307 K R UP -1573) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5188,11 +5188,11 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1315 S -1677) +(-1315 S -1573) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1316 -1677) +(-1316 -1573) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 9682fe5a..594099d8 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205732 . 3505945380) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) #0#) |has| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (-321 (-2 (|:| -3913 |#1|) (|:| -3168 |#2|))))) -((((-560)) . T) (($) -2157 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +(205732 . 3505955689) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) #0#) |has| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (-321 (-2 (|:| -3699 |#1|) (|:| -3553 |#2|))))) +((((-560)) . T) (($) -2188 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2188 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-560)) . T)) -((($ $) -2157 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) +((($ $) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T)) -((($) -2157 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-939)) ((((-887)) . T)) ((((-887)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1189)) . T) (((-229)) . T) (((-391)) . T) (((-915 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-887)) . T)) -(-2157 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2157 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2188 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2188 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2157 (|has| |#1| (-21)) (|has| |#1| (-870))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2157 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) -(-2157 (|has| |#1| (-842)) (|has| |#1| (-871))) +(-2188 (|has| |#1| (-21)) (|has| |#1| (-870))) +((($ $) . T) ((#0=(-421 (-560)) #0#) -2188 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) +(-2188 (|has| |#1| (-842)) (|has| |#1| (-871))) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-326 |#1|)) . T) (((-560)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-560)) . T) (((-893 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((($) . T) (((-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2188 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-887)) . T)) ((((-1212)) . T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1212)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -(-2157 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2157 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(((|#2| (-496 (-2277 |#1|) (-793))) . T)) -((((-1207)) -2157 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +(-2188 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2188 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(((|#2| (-496 (-2187 |#1|) (-793))) . T)) +((((-1207)) -2188 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) (((|#1| (-545 (-1207))) . T)) ((((-1189)) . T) (((-987 (-130))) . T) (((-887)) . T)) ((((-887)) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((#0=(-893 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -2157 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2157 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -4084 |#1|) (|:| -3758 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -2188 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2188 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -3865 |#1|) (|:| -4016 |#2|))) . T)) ((($) . T)) ((((-887)) |has| |#1| (-632 (-887))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2157 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-560)) . T) (((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2188 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1207)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-887)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2157 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2188 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (|has| |#1| (-1132)) (((|#1|) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2157 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((($) -2157 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2188 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((($) -2188 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((((-118 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) @@ -116,14 +116,14 @@ ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2157 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2188 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2157 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1264 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -2157 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2188 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (((|#1| |#2|) . T)) ((((-887)) . T)) @@ -241,13 +241,13 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2157 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -((($ $) -2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T) (((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) (|has| |#1| (-843)) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1| $) |has| |#1| (-298 |#1| |#1|))) ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) @@ -1065,49 +1065,49 @@ (((|#4|) |has| |#4| (-1132))) (((|#3|) |has| |#3| (-1132))) (|has| |#3| (-381)) -((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-560)) . T)) +((($) |has| |#1| (-571)) ((|#1|) . T) (((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-560)) . T)) ((((-887)) . 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T)) -(-2157 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1080))) +(-2188 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1080))) (((|#1|) |has| |#1| (-175))) (|has| $ (-149)) (|has| $ (-149)) ((((-1212)) . T)) (((|#1|) |has| |#1| (-175))) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-887)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) ((($ $) |has| |#1| (-298 $ $)) ((|#1| $) |has| |#1| (-298 |#1| |#1|))) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1207)) . T)) (|has| |#1| (-571)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2277 |#1|) (-793)) (-888 |#1|)) . T)) +(((|#2| (-246 (-2187 |#1|) (-793)) (-888 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2157 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2157 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2188 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2188 (|has| |#1| (-363)) (|has| |#1| (-381))) ((((-1173 |#2| |#1|)) . T) ((|#1|) . T)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) -(((|#2|) . T) (((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (|has| |#3| (-815)) (|has| |#3| (-815)) ((((-887)) . T)) @@ -1176,18 +1176,18 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) -((((-1207)) -2157 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) +((((-1207)) -2188 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207)))) (((-1113)) . T)) (((|#1|) . T)) (((|#3|) . T) (((-630 $)) . T)) (((|#1| (-421 (-560))) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((($ (-1294 |#2|)) . T) (($ (-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) -((((-560)) -2157 (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1132)) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) +((((-560)) -2188 (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1132)) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1195,15 +1195,15 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#1|) . 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T)) -((((-1207)) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((((-1207)) -2188 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-843)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1120 |#1|) (-1132)) -(((|#2| |#2|) -2157 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) -(((|#2|) -2157 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2157 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2| |#2|) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) ((((-560)) . T)) ((((-1212)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-2157 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1212)) . T)) -(-2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-2157 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -((($) -2157 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -2157 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2188 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2188 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2188 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1207)) -2157 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((($ (-1207)) -2188 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-887)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1207) $) |has| |#1| (-528 (-1207) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1207) |#1|) |has| |#1| (-528 (-1207) |#1|))) ((((-1207)) |has| |#1| (-927 (-1207)))) -(-2157 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2188 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#2|) . T) (((-887)) . T)) ((((-887)) . T)) (((|#2|) . T)) ((((-935 |#1|)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2157 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2157 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2188 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2188 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-893 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -2157 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -2188 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2188 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (|has| |#2| (-1080)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1233)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) ((((-887)) . T)) ((((-935 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-870)) -((($) -2157 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2188 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2188 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-376)) (((|#1|) . T) (($) . T)) (|has| |#1| (-870)) -((($) . T) (((-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2188 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (|has| |#1| (-870)) ((((-520)) . T)) @@ -1443,7 +1443,7 @@ ((((-549)) . T)) ((((-887)) . T)) ((($) . T)) -((((-560) (-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T) (((-1264 (-560)) $) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T) (((-1264 (-560)) $) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-175))) @@ -1453,22 +1453,22 @@ (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#3|) . 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T)) -(((|#2|) -2157 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1069 (-421 (-560)))) (((-560)) |has| #0# (-1069 (-560))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-1027 |#1|)) . T) ((|#1|) . T)) -((((-1207)) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-840 (-1207))) . 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T)) -(-2157 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-2188 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-2157 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-2188 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1189) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1719,24 +1719,24 @@ (((|#3|) . T)) ((((-1287 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1205 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) ((((-887)) . T)) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) (|has| |#1| (-870)) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-987 |#1|)) . T)) -(((|#4|) -2157 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) -(((|#3|) -2157 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) +(((|#4|) -2188 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) +(((|#3|) -2188 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) (|has| |#2| (-376)) (((|#1|) |has| |#1| (-175))) -(((|#4|) -2157 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) -(((|#3|) -2157 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) +(((|#4|) -2188 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) +(((|#3|) -2188 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) (((|#2|) |has| |#2| (-1080))) (((|#2|) |has| |#2| (-1080))) ((((-1189) |#1|) . T)) @@ -1748,8 +1748,8 @@ ((((-402) (-1189)) . T)) ((($ (-1207)) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-887)) -2157 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1297 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3913 (-1189)) (|:| -3168 #0#))) . T)) +((((-887)) -2188 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1297 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3699 (-1189)) (|:| -3553 #0#))) . T)) (((|#1|) . T)) ((((-887)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) @@ -1758,7 +1758,7 @@ ((((-560)) . T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-2157 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2188 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (|has| |#1| (-376)) ((((-887)) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -1769,8 +1769,8 @@ (|has| |#1| (-870)) ((((-887)) . T)) (((|#2|) . T)) -((((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2157 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2157 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2188 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T) (((-560)) . T) (((-841 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1779,8 +1779,8 @@ ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(((|#2| (-496 (-2277 |#1|) (-793)) (-888 |#1|)) . T)) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(((|#2| (-496 (-2187 |#1|) (-793)) (-888 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1207)) (-1207)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3913 (-1189)) (|:| -3168 |#1|))) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3699 (-1189)) (|:| -3553 |#1|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3913 (-1207)) (|:| -3168 (-51)))) . T)) +((((-2 (|:| -3699 (-1207)) (|:| -3553 (-51)))) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) ((((-1207) (-51)) . T)) ((((-421 (-560)) |#1|) . T) (($ $) . T)) (((|#1| (-560)) . T)) ((((-935 |#1|)) . T)) -(((|#1|) -2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) -((((-1207)) -2157 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) +(((|#1|) -2188 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2188 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +((((-1207)) -2188 (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))))) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#3|) -2157 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2157 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-2157 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) -((($) -2157 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(((|#3|) -2188 (|has| |#3| (-175)) (|has| |#3| (-376)))) +((($) -2188 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(-2188 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) +((($) -2188 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((($ |#2|) . T)) -((($ (-1207)) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) +((($ (-1207)) -2188 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) ((((-560) |#2|) . T)) -(((|#2|) -2157 (|has| |#2| (-175)) (|has| |#2| (-376)))) +(((|#2|) -2188 (|has| |#2| (-175)) (|has| |#2| (-376)))) (|has| |#1| (-363)) (((|#3| |#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) (((|#2|) . T) (((-560)) . T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1|) . T)) -(-2157 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2188 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-870)) (|has| |#1| (-870)) (|has| |#1| (-870)) @@ -1860,14 +1860,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) ((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T)) (((|#1|) . T)) (|has| |#1| (-870)) -(((#0=(-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) #0#) |has| (-2 (|:| -3913 (-1189)) (|:| -3168 (-51))) (-321 (-2 (|:| -3913 (-1189)) (|:| -3168 (-51)))))) +(((#0=(-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) #0#) |has| (-2 (|:| -3699 (-1189)) (|:| -3553 (-51))) (-321 (-2 (|:| -3699 (-1189)) (|:| -3553 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (|has| |#1| (-1132)) ((((-887)) . T) (((-1212)) . T)) @@ -1891,14 +1891,14 @@ (((|#3|) . T)) (((|#1| (-793) (-1113)) . T)) ((((-146)) . T)) -((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2157 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2188 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) +((($) -2188 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239))))) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((((-1002)) . T)) ((((-1002)) . T) (((-887)) . T)) @@ -2058,7 +2058,7 @@ ((($) . T)) (((|#1|) . T)) ((((-114)) . T)) -(-2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) (((|#1| (-560)) . T)) ((($) . T)) @@ -2081,7 +2081,7 @@ (((|#1| (-1257 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) (|has| |#1| (-1132)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#1| (-793)) . T)) ((((-1189) |#1|) . T)) (((|#1|) . T)) @@ -2102,20 +2102,20 @@ ((((-560)) . T)) ((((-560)) . T)) ((((-887)) . T)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-363))) ((((-887)) . T)) (|has| |#1| (-149)) (((|#3|) . 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T)) @@ -2159,8 +2159,8 @@ (|has| |#1| (-870)) (|has| |#1| (-870)) (((|#1| (-560) (-1113)) . T)) -(-2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +(-2188 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#1| (-421 (-560)) (-1113)) . T)) (((|#1| (-793) (-1113)) . T)) (|has| |#1| (-871)) @@ -2174,41 +2174,41 @@ ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-1132)) ((((-421 (-560))) |has| |#2| (-376)) (($) . T) (((-560)) . T)) -((((-560)) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) +((((-560)) -2188 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)))) (((|#1|) . 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T)) (((|#3|) |has| |#3| (-1080))) @@ -2362,7 +2362,7 @@ ((((-1207)) |has| |#2| (-927 (-1207)))) (|has| |#1| (-871)) ((((-887)) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (|has| |#1| (-813)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -((($) -2157 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +((($) -2188 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2383,7 +2383,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-887)) . T)) (((|#2|) . T) (((-887)) . T)) -((($ (-1207)) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((($ (-1207)) -2188 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2393,18 +2393,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-871)) -((((-2 (|:| -3913 (-1189)) (|:| -3168 |#1|))) . T)) +((((-2 (|:| -3699 (-1189)) (|:| -3553 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) |has| (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)) (-321 (-2 (|:| -3913 |#1|) (|:| -3168 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) |has| (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)) (-321 (-2 (|:| -3699 |#1|) (|:| -3553 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-2157 (-12 (|has| (-1287 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2188 (-12 (|has| (-1287 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1287 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) @@ -2423,17 +2423,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-887)) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) ((($ $) . T) (((-630 $) $) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) ((($) . 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T)) -((((-1207)) -2157 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) +((((-1207)) -2188 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) ((((-663 (-802 |#1| (-888 |#2|)))) . T) (((-887)) . T)) ((((-549)) |has| (-802 |#1| (-888 |#2|)) (-633 (-549)))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -2442,17 +2442,17 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) (((|#1|) |has| |#1| (-175))) ((((-887)) . T)) -(-2157 (|has| |#2| (-466)) (|has| |#2| (-939))) +(-2188 (|has| |#2| (-466)) (|has| |#2| (-939))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) -2157 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,13 +2460,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1278 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . 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T) (($ $) -2157 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) +(((|#1| |#1|) . T) (($ $) -2188 (|has| |#1| (-302)) (|has| |#1| (-376))) ((#0=(-421 (-560)) #0#) |has| |#1| (-376))) ((((-975 |#1|)) . T)) -((((-2 (|:| -3913 (-1207)) (|:| -3168 (-51)))) . T)) +((((-2 (|:| -3699 (-1207)) (|:| -3553 (-51)))) . T)) ((($) . T)) ((((-560) |#1|) . T)) ((((-1207)) |has| (-421 |#2|) (-927 (-1207)))) -(((|#1|) . T) (($) -2157 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) +(((|#1|) . T) (($) -2188 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) ((((-549)) |has| |#2| (-633 (-549)))) ((((-711 |#2|)) . T) (((-887)) . T)) (((|#1|) . T)) @@ -2518,24 +2518,24 @@ (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-893 |#1|)) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2157 (|has| |#2| (-842)) (|has| |#2| (-871))) +(-2188 (|has| |#2| (-842)) (|has| |#2| (-871))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1207)) -2157 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2188 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T) (((-560)) . T)) -((((-2 (|:| -3913 (-1189)) (|:| -3168 (-51)))) . T)) +((((-2 (|:| -3699 (-1189)) (|:| -3553 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-2157 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2188 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-870)) @@ -2880,7 +2880,7 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-186)) . T) (((-887)) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -2897,8 +2897,8 @@ (|has| |#1| (-871)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3913 (-1189)) (|:| -3168 |#1|))) . 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T)) -((($) -2157 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2188 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2188 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1051)) ((($) . T)) (|has| |#1| (-939)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-935 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . 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T)) -(-2157 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) +(-2188 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-2277 |#1|) (-793))) . T)) +(((|#2| (-246 (-2187 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-2157 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2188 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((((-1189)) . T) (((-887)) . T)) -(((#0=(-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) #0#) |has| (-2 (|:| -3913 (-1207)) (|:| -3168 (-51))) (-321 (-2 (|:| -3913 (-1207)) (|:| -3168 (-51)))))) +(((#0=(-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) #0#) |has| (-2 (|:| -3699 (-1207)) (|:| -3553 (-51))) (-321 (-2 (|:| -3699 (-1207)) (|:| -3553 (-51)))))) ((((-1189)) . T)) (|has| |#1| (-939)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-2157 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2188 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -3109,12 +3109,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2157 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2188 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-843))) ((((-887)) . T)) (|has| |#1| (-376)) -((((-1207)) -2157 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) +((((-1207)) -2188 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) (|has| |#1| (-376)) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-421 (-560))) . T) (($) . T)) @@ -3126,13 +3126,13 @@ ((((-560) |#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (((|#1|) . T)) -(-2157 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2188 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2157 (|has| |#4| (-815)) (|has| |#4| (-871))) -(-2157 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2188 (|has| |#4| (-815)) (|has| |#4| (-871))) +(-2188 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3167,7 +3167,7 @@ (|has| |#1| (-871)) ((((-887)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3176,27 +3176,27 @@ (((|#3|) . T)) ((((-1189)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-2157 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2188 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1080)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) -((((-2 (|:| -3913 (-1189)) (|:| -3168 |#1|))) . T)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) +((((-2 (|:| -3699 (-1189)) (|:| -3553 |#1|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3212,7 +3212,7 @@ ((((-421 (-560))) |has| |#2| (-1069 (-560))) (((-560)) |has| |#2| (-1069 (-560))) (((-1207)) |has| |#2| (-1069 (-1207))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2157 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2188 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-887)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-1207)) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) +((((-1207)) -2188 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) (|has| |#1| (-813)) (|has| |#1| (-813)) ((((-887)) . T)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-887)) . T)) ((((-887)) . T)) -(-2157 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(-2188 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-887)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1207)) -2157 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +((((-1207)) -2188 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) ((((-887)) . T)) ((((-560)) . T)) -(-2157 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2188 (|has| |#2| (-815)) (|has| |#2| (-871))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-887)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-2157 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) (|has| |#1| (-1182)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-2157 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2188 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-887)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-887)) . T)) -((((-1207)) -2157 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2188 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1207) |#1|) . T)) -(((|#1|) -2157 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2188 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1207)) . T)) -(((|#1|) -2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) +(((|#1|) -2188 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3315,15 +3315,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1132)) ((((-802 |#1| (-888 |#2|))) |has| (-802 |#1| (-888 |#2|)) (-321 (-802 |#1| (-888 |#2|))))) -(-2157 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2188 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3332,17 +3332,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1119 (-1207)))) . 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T) (((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-1119 (-1207))) . T) (($) -2188 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1297 |#1|) (-1297 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3375,7 +3375,7 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-887)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2157 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2188 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -2157 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2157 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2188 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2188 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-2157 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2188 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1207)) . T) ((|#1|) . T)) @@ -3419,15 +3419,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-2157 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) +(-2188 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (((|#1|) . T)) (((|#1|) . T)) -(-2157 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2188 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . 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T) (((-421 (-560))) -2157 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -2188 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -2188 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-560)) |has| |#1| (-911 (-560))) (((-391)) |has| |#1| (-911 (-391)))) (((|#1|) . T)) @@ -3496,7 +3496,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-939))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#2|) -2157 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2188 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3510,12 +3510,12 @@ (((|#2| (-793)) . T)) ((((-1207)) . T)) ((((-893 |#1|)) . 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T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-2157 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-887)) . T)) (|has| |#2| (-939)) -((((-2 (|:| -3913 (-1207)) (|:| -3168 (-51)))) . T)) +((((-2 (|:| -3699 (-1207)) (|:| -3553 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560))))) ((((-887)) . T)) ((((-887)) . T)) @@ -3553,7 +3553,7 @@ ((((-1201 |#1|)) . T) (((-887)) . T)) ((((-887)) . T)) ((((-421 (-560))) |has| |#2| (-1069 (-421 (-560)))) (((-560)) |has| |#2| (-1069 (-560))) ((|#2|) . T) (((-888 |#1|)) . T)) -((((-1207)) -2157 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . 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T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1132)) (((-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) -(-2157 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2188 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-939)) @@ -4035,14 +4035,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1212)) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2157 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2188 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#2|) . T)) -(-2157 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2188 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-887)) -2157 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) +((((-887)) -2188 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4051,7 +4051,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-2157 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2188 (|has| |#3| (-815)) (|has| |#3| (-871))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4067,7 +4067,7 @@ ((((-1212)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1207)) -2157 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) +((((-1207)) -2188 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207))))) ((((-1207)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1207))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1171 |#1| |#2|)) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) -((((-2 (|:| -3913 (-1207)) (|:| -3168 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) +((((-2 (|:| -3699 (-1207)) (|:| -3553 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1051)) -(((|#2|) . T) (((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) ((($) . T)) ((((-887)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560)))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-391)) . #0=(|has| |#2| (-1051))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1207)) -2157 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2188 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) ((((-887)) . T)) (((|#2|) . T)) ((((-887)) . T)) @@ -4106,15 +4106,15 @@ ((((-1205 |#1| |#2| |#3|)) . T)) ((((-1205 |#1| |#2| |#3|)) . T) (((-1198 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2157 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) -(((|#2|) . T) ((|#3|) -2157 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2188 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) +(((|#2|) . T) ((|#3|) -2188 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4128,7 +4128,7 @@ ((((-186)) . T) (((-887)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-2157 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) +(-2188 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) ((($ (-1207)) |has| |#1| (-1080))) -(-2157 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2188 (|has| |#1| (-871)) (|has| |#1| (-1132))) ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -3913 (-1207)) (|:| -3168 (-51)))) . T)) +((((-2 (|:| -3699 (-1207)) (|:| -3553 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4158,8 +4158,8 @@ ((((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) -(-2157 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2157 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2188 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2188 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((($) . T)) (((|#2| (-545 (-888 |#1|))) . T)) ((((-1212)) . T)) @@ -4174,7 +4174,7 @@ ((((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-887)) -2157 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2188 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1189) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -3913 |#1|) (|:| -3168 |#2|))) . T)) +((((-2 (|:| -3699 |#1|) (|:| -3553 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4192,14 +4192,14 @@ ((((-560)) . T) (($) . 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T) (($) -2188 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-1113)) . T) ((|#2|) . T) (((-421 (-560))) -2188 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560)))))) +((((-1027 |#1|)) . T) ((|#1|) . T) (((-560)) -2188 (|has| (-1027 |#1|) (-1069 (-560))) (|has| |#1| (-1069 (-560)))) (((-421 (-560))) -2188 (|has| (-1027 |#1|) (-1069 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560)))))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -4216,11 +4216,11 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1171 |#1| |#2|) #0#) |has| (-1171 |#1| |#2|) (-321 (-1171 |#1| |#2|)))) (((|#1|) . 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196913) ((-1201 . -670) 196802) ((-1156 . -670) 196691) ((-878 . -670) 196665) ((-740 . -632) 196647) ((-561 . -381) T) ((-1319 . -23) T) ((-716 . -929) NIL) ((-1318 . -23) T) ((-505 . -1132) T) ((-391 . -635) 196597) ((-391 . -637) 196579) ((-1065 . -1080) T) ((-889 . -102) T) ((-1219 . -298) 196558) ((-171 . -381) 196509) ((-1035 . -1247) T) ((-1002 . -1247) T) ((-943 . -1247) T) ((-856 . -635) 196463) ((-850 . -635) 196418) ((-44 . -23) T) ((-1327 . -102) T) ((-493 . -298) 196397) ((-597 . -1132) T) ((-1177 . -1140) 196366) ((-443 . -1247) T) ((-1134 . -1135) 196318) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1143) T) ((-1240 . -739) 196215) ((-1227 . -1132) T) ((-1035 . -909) 196197) ((-1035 . -911) 196179) ((-642 . -234) 196163) ((-642 . -274) 196147) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1035 . -1069) 196107) ((-733 . -739) 196072) ((-246 . -390) 196041) ((-391 . -1080) T) ((-227 . -1088) T) ((-119 . -274) 196018) ((-119 . -234) 195995) ((-58 . -298) 195947) 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T) ((-530 . -19) 194521) ((-510 . -19) 194505) ((-58 . -618) 194482) ((-1034 . -239) 194419) ((-930 . -102) 194369) ((-878 . -748) T) ((-803 . -1132) T) ((-530 . -618) 194346) ((-510 . -618) 194323) ((-802 . -1132) T) ((-802 . -1096) 194290) ((-475 . -1132) T) ((-468 . -1132) T) ((-597 . -739) 194265) ((-671 . -1132) T) ((-1287 . -47) 194242) ((-1284 . -102) T) ((-1278 . -47) 194212) ((-1257 . -47) 194189) ((-1240 . -175) 194140) ((-1204 . -319) 194119) ((-1198 . -319) 194098) ((-1127 . -635) 194079) ((-1122 . -635) 194060) ((-1110 . -571) 194011) ((-1110 . -1252) 193962) ((-1104 . -635) 193943) ((-1035 . -927) NIL) ((-1097 . -635) 193924) ((-692 . -133) T) ((-646 . -1143) T) ((-1067 . -635) 193905) ((-1050 . -635) 193886) ((-736 . -1087) 193856) ((-734 . -921) 193759) ((-721 . -668) 193709) ((-286 . -1132) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1087) 193693) ((-50 . -1132) T) ((-609 . -47) 193670) ((-229 . -670) 193635) ((-595 . -1132) T) ((-532 . -1132) T) 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T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1172 . -632) 190662) ((-1151 . -662) 190649) ((-1151 . -1082) 190636) ((-841 . -748) T) ((-841 . -881) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-935 . -632) 190487) ((-935 . -633) 190469) ((-400 . -748) T) ((-896 . -1087) 190421) ((-896 . -111) 190359) ((-736 . -1080) T) ((-734 . -1273) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -819) T) ((-170 . -1247) T) ((-227 . -1132) T) ((-391 . -814) T) ((-58 . -633) 190236) ((-229 . -816) T) ((-229 . -813) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1110 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1247) T) ((-895 . -939) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1247) T) ((-661 . -1132) T) ((-1257 . -351) 189637) ((-895 . -670) 189582) ((-1257 . -390) 189534) ((-993 . -133) 189389) ((-837 . -133) 189260) ((-45 . -874) NIL) ((-987 . -673) 189244) ((-1256 . -684) T) ((-1118 . -175) 189155) ((-987 . -385) 189139) ((-1093 . -816) T) ((-1093 . -813) T) ((-896 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-838 . -47) 188801) ((-1093 . -748) T) ((-339 . -503) 188785) ((-975 . -748) T) ((-1311 . -321) 188723) ((-1287 . -927) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1283 . -1087) 188334) ((-1278 . -927) 188240) ((-1262 . -1087) 188048) ((-495 . -748) T) ((-1257 . -927) 187881) ((-1240 . -302) 187860) ((-1217 . -1247) T) ((-1214 . -381) T) ((-1213 . -381) T) ((-1177 . -153) 187844) ((-1151 . -102) T) ((-1146 . -1132) T) ((-1110 . -23) T) ((-1110 . -1143) T) ((-1107 . -102) T) ((-1089 . -632) 187811) ((-1034 . -424) 187783) ((-954 . -984) T) ((-758 . -321) 187721) ((-76 . -1247) T) ((-686 . -397) 187693) ((-171 . -939) 187646) ((-30 . -984) T) ((-114 . -866) T) ((-1 . -632) 187628) ((-1027 . -921) 187549) ((-131 . -673) 187531) ((-50 . -640) 187515) ((-716 . -668) 187450) ((-609 . -927) 187363) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187345) ((-896 . -1080) T) ((-854 . -871) 187324) ((-81 . -1247) T) ((-733 . -302) T) ((-40 . -1088) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187306) ((-171 . -670) 187180) ((-521 . -632) 187162) ((-365 . -149) 187144) ((-365 . -147) T) ((-372 . -1143) T) ((-367 . -1143) T) ((-359 . -1143) T) ((-1035 . -319) T) ((-943 . -319) T) ((-896 . -250) T) ((-108 . -1143) T) ((-896 . -240) 187123) ((-1283 . -111) 186944) ((-1262 . -111) 186733) ((-252 . -1286) 186717) ((-560 . -870) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1035 . -1051) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1082) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1132) T) ((-678 . -662) 186541) ((-1284 . -38) 186433) ((-1266 . -939) 186412) ((-114 . -1132) T) ((-838 . -1247) T) ((-427 . -1247) T) ((-1066 . -102) T) ((-1266 . -670) 186301) ((-895 . -816) NIL) ((-879 . -670) 186275) ((-895 . -813) NIL) ((-838 . -911) NIL) ((-895 . -748) T) ((-1118 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-838 . -1069) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1283 . -635) 185618) ((-1262 . -635) 185366) ((-60 . -1247) T) ((-638 . -871) 185345) ((-514 . -684) T) ((-1177 . -1007) 185314) ((-1055 . -668) 185251) ((-1034 . -466) T) ((-721 . -870) T) ((-525 . -814) T) 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-1132) T) ((-918 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-879 . -748) T) ((-119 . -870) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1066 . -321) 183173) ((-900 . -504) 183154) ((-900 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1178 . -34) T) ((-972 . -1247) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1207 . -635) 182524) ((-343 . -1247) T) ((-488 . -1080) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1151 . -1182) T) ((-1278 . -319) 182433) ((-734 . -1082) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1257 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1247) T) ((-734 . -662) 181995) ((-1257 . -1051) NIL) ((-1110 . -133) T) ((-896 . -819) 181974) ((-146 . -102) T) ((-40 . -1132) T) ((-896 . -814) 181953) ((-663 . -1041) 181937) ((-594 . -1088) T) ((-560 . -1088) T) ((-509 . -1088) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1212 . -1132) T) ((-1151 . -38) 181869) ((-1120 . -632) 181836) ((-108 . -133) T) ((-983 . -1132) T) ((-948 . -1132) T) ((-793 . -1132) T) ((-694 . -1132) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1319 . -21) T) ((-1319 . -25) T) ((-1318 . -21) T) ((-1318 . -25) T) ((-686 . -1087) 181820) ((-545 . -871) T) ((-514 . -871) T) ((-377 . -1247) T) ((-368 . -1087) 181772) ((-366 . -1087) 181724) ((-358 . -1087) 181676) ((-260 . -1247) T) ((-259 . -1247) T) ((-275 . -1087) 181519) ((-255 . -1087) 181362) ((-686 . -111) 181341) ((-839 . -1252) 181320) ((-562 . -866) T) ((-326 . -929) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -929) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-931 . -874) 180693) ((-130 . -684) T) ((-837 . -660) 180599) ((-839 . -571) 180578) ((-501 . -874) T) ((-260 . -1069) 180405) ((-259 . -1069) 180232) ((-128 . -121) 180216) ((-221 . -874) T) ((-935 . -1087) 180181) ((-734 . -102) T) ((-721 . -1088) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-935 . -111) 179984) ((-40 . -739) 179929) ((-893 . -1132) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1132) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1247) T) ((-1262 . -814) 179062) 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177526) ((-1085 . -23) T) ((-1055 . -870) T) ((-935 . -1080) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1204 . -950) 177432) ((-1198 . -950) 177411) ((-1198 . -842) NIL) ((-1027 . -1082) 177307) ((-996 . -1247) T) ((-935 . -250) T) ((-839 . -376) 177286) ((-218 . -1132) T) ((-394 . -23) T) ((-129 . -1132) 177264) ((-123 . -1132) 177242) ((-935 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1027 . -662) 177155) ((-893 . -739) 177142) ((-1327 . -668) 177114) ((-1077 . -153) 177079) ((-1024 . -1247) T) ((-887 . -1247) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-856 . -670) 177008) ((-850 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1132) T) ((-560 . -1132) T) ((-509 . -1132) T) ((-1201 . -1247) T) ((-252 . -300) 176938) ((-1156 . -1247) T) ((-878 . -1247) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1253 . -874) T) ((-1201 . -911) NIL) ((-55 . -1132) T) ((-1156 . -911) 176719) ((-130 . -871) T) ((-1201 . -1069) 176599) ((-1156 . -1069) 176482) ((-187 . -632) 176464) ((-878 . -1069) 176360) ((-803 . -298) 176287) ((-839 . -1143) T) ((-1065 . -748) T) ((-1077 . -1007) 176216) ((-616 . -673) 176200) ((-1034 . -921) 176107) ((-1027 . -102) T) ((-839 . -23) T) ((-734 . -1182) 176085) ((-716 . -1088) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1300 . -1132) T) ((-256 . -1132) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1132) T) ((-721 . -1132) T) ((-374 . -487) T) ((-1240 . -632) 176051) ((-1201 . -390) 176035) ((-1156 . -390) 176019) ((-1055 . -426) 175981) ((-143 . -233) 175963) ((-391 . -816) T) ((-391 . -813) T) ((-893 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1297 . -1296) 175758) ((-365 . -416) T) ((-1297 . -1132) 175708) ((-1221 . -1132) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1284 . -668) 175537) ((-326 . -649) 175516) ((-856 . -748) T) 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T) ((-900 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1252) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1252) T) ((-421 . -921) 174525) ((-229 . -1069) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1088) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1093 . -1247) T) ((-975 . -1247) T) ((-735 . -1247) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1247) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1128 . -107) 173800) ((-1093 . -911) 173782) ((-975 . -911) 173707) ((-677 . -1143) T) ((-642 . -739) 173694) ((-495 . -911) NIL) ((-1177 . -102) T) ((-1120 . -637) 173678) ((-1093 . -1069) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-975 . -1069) 173522) ((-119 . -739) 173467) ((-734 . -929) 173374) ((-677 . -23) T) ((-495 . -1069) 173250) ((-1118 . -633) NIL) ((-1118 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1144 . -660) 172647) ((-820 . -874) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1066 . -233) 172397) ((-896 . -939) 172376) ((-128 . -34) T) ((-839 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1316) 172342) ((-366 . -1316) 172326) ((-358 . -1316) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -814) T) ((-526 . -819) T) ((-525 . -816) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1132) T) ((-896 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-975 . -390) 171946) ((-893 . -302) T) ((-50 . -632) 171928) ((-1151 . -668) 171900) 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169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1322 . -1317) 169581) ((-699 . -1069) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1266 . -1247) T) ((-137 . -484) 169520) ((-879 . -1247) T) ((-678 . -668) 169479) ((-48 . -1132) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-895 . -927) NIL) ((-585 . -1247) T) ((-1266 . -911) NIL) ((-913 . -102) T) ((-910 . -102) T) ((-661 . -632) 169429) ((-402 . -1132) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1266 . -1069) 169277) ((-879 . -1069) 169173) ((-1173 . -102) T) ((-1027 . -929) 169096) ((-677 . -133) T) ((-674 . -814) 169075) ((-674 . -819) 169054) ((-119 . -528) 168962) ((-585 . -1069) 168944) ((-305 . -1305) 168914) ((-1198 . -874) NIL) ((-890 . -102) T) ((-985 . -571) 168893) ((-1240 . -1087) 168776) ((-1034 . -1082) 168721) ((-496 . -660) 168627) ((-934 . -1132) T) ((-1055 . -739) 168564) ((-733 . -1087) 168529) ((-1034 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1178 . -1247) T) ((-1240 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -927) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1327 . -1088) T) ((-1266 . -390) 168084) ((-419 . -1252) 168062) ((-1146 . -632) 168044) ((-325 . -870) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1262 . -813) 167997) ((-1262 . -816) 167950) ((-1283 . -748) T) ((-1262 . -748) T) ((-48 . -739) 167915) ((-229 . -1051) T) ((-1284 . -426) 167881) ((-1266 . -927) 167824) ((-365 . -1305) 167801) ((-1240 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -874) 167644) ((-1144 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1321 . -1082) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1321 . -662) 167115) ((-642 . -302) T) ((-597 . -1087) 167090) 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-1247) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1321 . -102) T) ((-1229 . -1247) T) ((-1227 . -635) 166423) ((-1119 . -1247) T) ((-1118 . -1087) 166266) ((-1106 . -1247) T) ((-275 . -939) 166245) ((-255 . -939) 166224) ((-803 . -1087) 166047) ((-802 . -1087) 165890) ((-627 . -1247) T) ((-1195 . -632) 165872) ((-1118 . -111) 165701) ((-1077 . -102) T) ((-489 . -1247) T) ((-475 . -1087) 165672) ((-468 . -1087) 165515) ((-686 . -670) 165499) ((-895 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1189 . -871) T) ((-1119 . -1069) 164755) ((-1106 . -1069) 164732) ((-1035 . -874) T) ((-1031 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1002 . -874) T) ((-995 . -632) 164504) ((-987 . -1247) T) ((-985 . -1143) T) ((-128 . -1041) 164488) ((-872 . -1247) T) ((-895 . -1051) NIL) ((-757 . -1143) T) ((-737 . -1143) T) ((-676 . -635) 164406) ((-1297 . -503) 164390) ((-1215 . -1247) T) ((-1214 . -1247) T) ((-1173 . -38) 164350) ((-985 . -23) T) ((-935 . -670) 164315) ((-889 . -1132) T) ((-864 . -102) T) ((-839 . -21) T) ((-652 . -1082) 164299) ((-620 . -1082) 164283) ((-839 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1087) 164216) ((-532 . -1087) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1213 . -1247) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-890 . -38) 164089) ((-1118 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1143) T) ((-326 . -1088) 163600) ((-325 . -1088) T) ((-132 . -1247) T) ((-131 . -1247) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1080) T) ((-1327 . -1132) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1022) 162778) ((-118 . -894) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) 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-1132) T) ((-421 . -321) 161010) ((-1173 . -929) 160933) ((-893 . -632) 160915) ((-856 . -1069) 160884) ((-661 . -1087) 160868) ((-206 . -809) T) ((-205 . -809) T) ((-204 . -809) T) ((-203 . -809) T) ((-202 . -809) T) ((-201 . -809) T) ((-200 . -809) T) ((-199 . -809) T) ((-198 . -809) T) ((-197 . -809) T) ((-562 . -632) 160850) ((-509 . -1033) T) ((-285 . -861) T) ((-284 . -861) T) ((-283 . -861) T) ((-282 . -861) T) ((-48 . -302) T) ((-281 . -861) T) ((-280 . -861) T) ((-279 . -861) T) ((-196 . -809) T) ((-661 . -111) 160829) ((-630 . -871) T) ((-678 . -426) 160813) ((-692 . -239) 160764) ((-227 . -635) 160726) ((-110 . -871) T) ((-677 . -21) T) ((-677 . -25) T) ((-1321 . -38) 160696) ((-119 . -298) 160647) ((-1297 . -19) 160631) ((-1257 . -874) NIL) ((-1297 . -618) 160608) ((-1311 . -1132) T) ((-365 . -1082) 160553) ((-1108 . -1132) T) ((-1017 . -1132) T) ((-985 . -133) T) ((-839 . -236) 160540) ((-758 . -1132) T) ((-365 . -662) 160485) ((-757 . -133) T) ((-737 . -133) T) ((-526 . -815) T) ((-526 . -816) T) ((-467 . -133) T) ((-421 . -1182) 160463) ((-227 . -1080) T) ((-305 . -102) 160245) ((-143 . -1132) T) ((-721 . -1033) T) ((-1136 . -298) 160201) ((-91 . -1247) T) ((-218 . -632) 160183) ((-129 . -632) 160115) ((-123 . -632) 160047) ((-1327 . -175) T) ((-1204 . -376) 160026) ((-1198 . -376) 160005) ((-326 . -1132) T) ((-419 . -133) T) ((-325 . -1132) T) ((-421 . -38) 159957) ((-1164 . -102) T) ((-1284 . -739) 159849) ((-1166 . -1293) T) ((-1127 . -1247) T) ((-1122 . -1247) T) ((-678 . -1088) T) ((-1104 . -1247) T) ((-1097 . -1247) T) ((-1067 . -1247) T) ((-1050 . -1247) T) ((-331 . -147) 159828) ((-331 . -149) 159807) ((-141 . -1132) T) ((-137 . -1132) T) ((-115 . -1132) T) ((-882 . -102) T) ((-645 . -1247) T) ((-497 . -1247) T) ((-594 . -632) 159789) ((-560 . -633) 159688) ((-560 . -632) 159670) ((-509 . -632) 159652) ((-509 . -633) 159597) ((-499 . -23) T) ((-222 . -1247) T) ((-496 . -871) 159548) ((-501 . -660) 159530) ((-994 . -632) 159512) ((-1034 . 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-1132) 146013) ((-1255 . -866) T) ((-331 . -1004) 145975) ((-105 . -102) T) ((-48 . -1087) 145940) ((-895 . -874) NIL) ((-1322 . -102) T) ((-395 . -102) T) ((-1284 . -632) 145922) ((-1164 . -1165) 145906) ((-1035 . -660) 145888) ((-900 . -1247) T) ((-48 . -111) 145844) ((-703 . -1247) T) ((-698 . -1247) T) ((-674 . -1247) T) ((-837 . -921) 145711) ((-492 . -1247) T) ((-252 . -1247) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1305) 145695) ((-140 . -1247) T) ((-139 . -1247) T) ((-135 . -1247) T) ((-1248 . -102) T) ((-1055 . -635) 145632) ((-839 . -239) T) ((-1201 . -1252) 145611) ((-218 . -381) T) ((-353 . -635) 145541) ((-1156 . -1252) 145520) ((-246 . -25) 145353) ((-246 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1201 . -571) 145127) ((-1156 . -571) 145058) ((-1255 . -1132) T) ((-561 . -874) T) ((-1066 . -298) 145033) ((-1197 . -1114) T) ((-1025 . -1114) T) ((-838 . -133) T) ((-119 . -819) NIL) ((-119 . -814) NIL) ((-368 . -319) T) 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143042) ((-1219 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1224) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1151 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1151 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1257 . -660) 142704) ((-493 . -107) 142654) ((-1024 . -23) T) ((-1322 . -38) 142624) ((-1201 . -1143) T) ((-1156 . -1143) T) ((-1093 . -1252) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-878 . -1143) T) ((-975 . -1252) 142494) ((-495 . -1252) 142473) ((-1093 . -571) T) ((-975 . -571) 142404) ((-1201 . -23) T) ((-1183 . -1114) T) ((-1156 . -23) T) ((-878 . -23) T) ((-495 . -571) 142335) ((-1173 . -739) 142267) ((-692 . -1082) 142251) ((-1177 . -528) 142184) ((-692 . -662) 142168) ((-1066 . -633) NIL) ((-1066 . -632) 142150) ((-96 . -1114) T) ((-1327 . -1087) 142137) ((-890 . -739) 142107) ((-1327 . -111) 142092) ((-1240 . -47) 142061) ((-1198 . -871) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1134 . -1132) T) ((-1034 . -1132) T) ((-63 . -632) 142043) ((-1110 . -921) 141912) ((-1055 . -814) T) ((-1055 . -819) T) ((-1287 . -25) T) ((-1287 . -21) T) ((-1278 . -21) T) ((-1278 . -25) T) ((-893 . -670) 141899) ((-1257 . -21) T) ((-1257 . -25) T) ((-1058 . -153) 141883) ((-1035 . -236) 141870) ((-896 . -842) 141849) ((-896 . -950) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -921) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1247) T) ((-948 . -816) T) ((-948 . -748) T) ((-793 . -815) T) ((-793 . -816) T) ((-520 . -1132) T) ((-516 . -1132) T) ((-793 . -748) T) ((-229 . -376) T) ((-1319 . -1082) 141537) ((-1318 . -1082) 141521) ((-1319 . -662) 141491) ((-1185 . -1132) 141469) ((-895 . -1252) T) ((-1318 . -662) 141439) ((-1119 . -874) T) ((-678 . -632) 141421) ((-895 . -571) T) ((-716 . -381) NIL) ((-44 . -1082) 141405) ((-1327 . -635) 141387) ((-1321 . -1132) T) ((-692 . -102) T) ((-372 . -1305) 141371) ((-367 . -1305) 141355) ((-44 . -662) 141339) ((-359 . -1305) 141323) ((-563 . -102) T) ((-1240 . -1247) T) ((-534 . -871) 141302) ((-733 . -1247) T) ((-987 . -874) 141281) ((-872 . -874) T) ((-501 . -239) T) ((-221 . -239) T) ((-1077 . -1132) T) ((-839 . -466) 141260) ((-154 . -1082) 141244) ((-1077 . -1102) 141173) ((-1058 . -1007) 141142) ((-841 . -1143) T) ((-1034 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1143) T) ((-490 . -1007) 141040) ((-477 . -1007) 141009) ((-1214 . -874) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-918 . -632) 140955) ((-1213 . -874) T) ((-1110 . -746) 140934) ((-1327 . -1080) T) ((-838 . -660) 140882) ((-305 . -1088) 140824) ((-171 . -1252) 140729) ((-229 . -1143) T) ((-336 . -23) T) ((-1198 . -1022) 140681) ((-1284 . -1087) 140586) ((-864 . -1132) T) ((-131 . -874) T) ((-1157 . -762) 140565) ((-1283 . -950) 140544) ((-1262 . -950) 140523) ((-893 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1132) T) ((-270 . -1132) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1262 . -842) 140278) ((-1319 . -102) T) ((-505 . -1247) T) ((-353 . -1316) 140255) ((-1318 . -102) T) ((-1284 . -111) 140147) ((-1144 . -921) 140014) ((-837 . -1082) 139915) ((-837 . -662) 139837) ((-146 . -632) 139819) ((-1024 . -133) T) ((-44 . -102) T) ((-246 . -871) 139770) ((-597 . -1247) T) ((-1266 . -1252) 139749) ((-103 . -503) 139733) ((-1321 . -739) 139703) ((-1118 . -47) 139664) ((-1093 . -1143) T) ((-975 . -1143) T) ((-129 . -34) T) ((-123 . -34) T) ((-1266 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1227 . -1247) T) ((-1201 . -133) T) ((-353 . -381) T) ((-495 . -1143) T) ((-1156 . -133) T) ((-895 . -376) T) ((-468 . -47) 139503) ((-878 . -133) T) ((-334 . -874) 139482) ((-154 . -102) T) ((-1093 . -23) T) ((-975 . -23) T) ((-585 . -571) T) ((-838 . -25) T) ((-838 . -21) T) 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137363) ((-1118 . -1247) T) ((-1066 . -300) 137338) ((-594 . -748) T) ((-560 . -816) T) ((-171 . -376) 137289) ((-560 . -813) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1247) T) ((-802 . -1247) T) ((-1177 . -503) 137273) ((-475 . -1247) T) ((-468 . -1247) T) ((-1319 . -1320) 137249) ((-1118 . -911) NIL) ((-895 . -1143) T) ((-119 . -939) NIL) ((-1318 . -1320) 137228) ((-671 . -1247) T) ((-803 . -911) NIL) ((-802 . -911) 137087) ((-1313 . -25) T) ((-1313 . -21) T) ((-1245 . -102) 137065) ((-1137 . -410) T) ((-642 . -670) 137052) ((-468 . -911) NIL) ((-697 . -102) 137002) ((-1118 . -1069) 136829) ((-895 . -23) T) ((-803 . -1069) 136688) ((-802 . -1069) 136545) ((-119 . -670) 136490) ((-468 . -1069) 136366) ((-286 . -1247) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1247) T) ((-404 . -668) 135782) ((-671 . -1069) 135766) ((-646 . -102) T) ((-595 . -1247) T) ((-532 . -1247) T) ((-226 . -503) 135750) ((-1297 . -34) T) ((-638 . -668) 135709) ((-301 . -1082) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1151 . -1087) 135582) ((-86 . -632) 135564) ((-50 . -1069) 135548) ((-1118 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -816) T) ((-721 . -813) T) ((-60 . -57) 135478) ((-595 . -1069) 135465) ((-532 . -1069) 135442) ((-174 . -1247) T) ((-336 . -133) T) ((-326 . -1080) 135332) ((-325 . -1080) T) ((-171 . -1143) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1035 . -1022) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1132) 134993) ((-229 . -133) T) ((-1151 . -111) 134978) ((-171 . -23) T) ((-820 . -149) 134957) ((-820 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1185 . -528) 134647) ((-491 . -668) 134597) ((-657 . -866) T) ((-496 . -921) 134464) ((-1164 . -1132) T) ((-229 . -1091) T) ((-837 . -321) 134402) ((-1118 . -927) 134337) ((-803 . -927) 134280) ((-802 . -927) 134264) ((-1319 . -38) 134234) ((-1318 . -38) 134204) ((-1266 . -1143) T) ((-879 . -1143) T) ((-468 . -927) 134181) ((-882 . -1132) T) ((-1266 . -23) T) ((-1151 . -635) 134153) ((-1093 . -133) T) ((-879 . -23) T) ((-585 . -1143) T) ((-642 . -748) T) ((-525 . -874) T) ((-368 . -950) T) ((-366 . -950) T) ((-301 . -102) T) ((-358 . -950) T) ((-1001 . -1114) T) ((-975 . -133) T) ((-838 . -236) 134098) ((-119 . -816) NIL) ((-119 . -813) NIL) ((-119 . -748) T) ((-1077 . -528) 133999) ((-716 . -939) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1247) T) ((-657 . -1132) T) ((-652 . -783) T) ((-620 . -783) T) ((-1257 . -871) NIL) ((-1110 . -1082) 133798) ((-1034 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1132) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-935 . -950) T) ((-1110 . -662) 133600) ((-496 . -1305) 133570) ((-1151 . -1080) T) ((-733 . -319) T) ((-723 . -1088) T) ((-372 . -1082) 133522) ((-367 . -1082) 133474) ((-359 . -1082) 133426) ((-372 . -662) 133378) ((-227 . -1069) 133355) ((-367 . -662) 133307) ((-108 . -1082) 133257) ((-359 . -662) 133209) ((-305 . -739) 133151) ((-661 . -1247) T) ((-501 . -466) T) ((-421 . -528) 133063) ((-108 . -662) 133013) ((-221 . -466) T) ((-1151 . -240) T) ((-307 . -153) 132963) ((-1027 . -633) 132924) ((-1027 . -632) 132906) ((-1020 . -632) 132888) ((-118 . -1088) T) ((-678 . -1087) 132872) ((-229 . -507) T) ((-413 . -632) 132854) ((-413 . -633) 132831) ((-1085 . -1305) 132801) ((-678 . -111) 132780) ((-692 . -929) 132703) ((-1173 . -503) 132687) ((-1322 . -668) 132646) ((-395 . -668) 132615) ((-64 . -455) T) ((-64 . -410) T) ((-1190 . -102) T) ((-895 . -133) T) ((-498 . -102) 132565) ((-1146 . -1247) T) ((-1254 . -874) T) ((-1327 . -381) T) ((-1110 . -102) T) ((-1092 . -102) T) ((-365 . -739) 132510) ((-896 . -874) 132461) ((-753 . -149) 132440) ((-753 . -147) 132419) 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131166) ((-1189 . -102) T) ((-1266 . -133) T) ((-1262 . -874) 131065) ((-1201 . -25) T) ((-1201 . -21) T) ((-1190 . -321) 130860) ((-357 . -1247) T) ((-1156 . -25) T) ((-879 . -133) T) ((-407 . -1247) T) ((-1156 . -21) T) ((-878 . -25) T) ((-878 . -21) T) ((-803 . -319) 130839) ((-1185 . -503) 130823) ((-1181 . -153) 130773) ((-1177 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1177 . -633) 130646) ((-585 . -133) T) ((-638 . -870) 130625) ((-1055 . -813) T) ((-1055 . -816) T) ((-1055 . -748) T) ((-837 . -929) 130494) ((-734 . -1087) 130317) ((-616 . -874) 130296) ((-498 . -321) 130234) ((-467 . -432) 130204) ((-365 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1069) 129950) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -102) T) ((-205 . 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-874) T) ((-1205 . -35) 128490) ((-1205 . -95) 128456) ((-1205 . -1236) 128422) ((-1205 . -1233) 128388) ((-1204 . -1233) 128354) ((-1204 . -1236) 128320) ((-1204 . -95) 128286) ((-1204 . -35) 128252) ((-1198 . -1233) 128218) ((-1198 . -1236) 128184) ((-1189 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1110 . -1182) 128163) ((-40 . -1247) T) ((-1198 . -95) 128129) ((-1065 . -23) T) ((-1198 . -35) 128095) ((-585 . -507) T) ((-1157 . -35) 128061) ((-1157 . -95) 128027) ((-1157 . -1236) 127993) ((-1157 . -1233) 127959) ((-374 . -1143) T) ((-372 . -1182) 127938) ((-367 . -1182) 127917) ((-359 . -1182) 127896) ((-1134 . -298) 127852) ((-983 . -1247) T) ((-948 . -1247) T) ((-108 . -1182) T) ((-854 . -1088) 127831) ((-793 . -1247) T) ((-669 . -321) 127769) ((-651 . -321) 127620) ((-694 . -1247) T) ((-734 . -1080) T) ((-1093 . -660) 127602) ((-1110 . -38) 127470) ((-975 . -660) 127418) ((-1035 . -149) T) ((-1035 . -147) NIL) ((-391 . -1143) T) ((-336 . -25) T) ((-334 . -23) T) ((-972 . -871) 127397) ((-734 . -338) 127374) ((-495 . -660) 127322) ((-40 . -1069) 127210) ((-734 . -240) T) ((-723 . -739) 127197) ((-352 . -1132) T) ((-177 . -1132) T) ((-343 . -871) T) ((-419 . -466) 127147) ((-391 . -23) T) ((-372 . -38) 127112) ((-367 . -38) 127077) ((-359 . -38) 127042) ((-80 . -455) T) ((-80 . -410) T) ((-229 . -25) T) ((-229 . -21) T) ((-856 . -1143) T) ((-108 . -38) 126992) ((-850 . -1143) T) ((-795 . -1132) T) ((-118 . -739) 126979) ((-694 . -1069) 126963) ((-630 . -102) T) ((-856 . -23) T) ((-850 . -23) T) ((-1185 . -298) 126915) ((-1144 . -321) 126853) ((-496 . -1082) 126754) ((-1128 . -242) 126738) ((-61 . -411) T) ((-61 . -410) T) ((-1183 . -102) T) ((-110 . -102) T) ((-496 . -662) 126660) ((-40 . -390) 126637) ((-96 . -102) T) ((-677 . -876) 126621) ((-1201 . -236) 126608) ((-1166 . -1114) T) ((-1093 . -21) T) ((-1093 . -25) T) ((-1085 . -1082) 126592) ((-837 . -274) 126561) ((-837 . -234) 126530) ((-975 . -25) T) ((-975 . -21) T) ((-1151 . -381) T) ((-1085 . -662) 126472) ((-638 . -1088) T) ((-1058 . -321) 126410) ((-913 . -632) 126392) ((-692 . -668) 126351) ((-495 . -25) T) ((-495 . -21) T) ((-394 . -1082) 126335) ((-910 . -632) 126317) ((-893 . -1247) T) ((-537 . -528) 126250) ((-260 . -871) 126201) ((-259 . -871) 126152) ((-394 . -662) 126122) ((-895 . -660) 126099) ((-490 . -321) 126037) ((-562 . -1247) T) ((-477 . -321) 125975) ((-365 . -302) T) ((-1185 . -1286) 125959) ((-1173 . -632) 125921) ((-1173 . -633) 125882) ((-1171 . -102) T) ((-1027 . -1087) 125778) ((-40 . -927) 125730) ((-1185 . -618) 125707) ((-1327 . -670) 125694) ((-1094 . -153) 125640) ((-501 . -921) NIL) ((-890 . -504) 125617) ((-1027 . -111) 125499) ((-896 . -1252) T) ((-221 . -921) NIL) ((-352 . -739) 125483) ((-890 . -632) 125445) ((-177 . -739) 125377) ((-896 . -571) T) ((-421 . -298) 125335) ((-246 . -239) 125232) ((-108 . -414) 125214) ((-85 . -398) T) ((-85 . -410) T) ((-723 . -175) T) ((-636 . -632) 125196) ((-99 . -748) T) ((-496 . -102) 124928) ((-99 . 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-1233) 84069) ((-1283 . -1236) 84035) ((-1266 . -921) 83938) ((-1201 . -1082) 83761) ((-1173 . -1247) T) ((-1156 . -1082) 83604) ((-878 . -1082) 83588) ((-651 . -618) 83563) ((-1283 . -95) 83529) ((-1283 . -239) 83481) ((-1264 . -102) 83459) ((-1201 . -662) 83288) ((-1156 . -662) 83137) ((-878 . -662) 83107) ((-1262 . -1233) 83073) ((-1118 . -25) T) ((-564 . -1132) T) ((-1118 . -21) T) ((-985 . -1088) T) ((-545 . -814) T) ((-545 . -819) T) ((-119 . -1252) T) ((-890 . -1247) T) ((-642 . -571) T) ((-803 . -25) T) ((-803 . -21) T) ((-802 . -21) T) ((-802 . -25) T) ((-757 . -1088) T) ((-737 . -1088) T) ((-692 . -1087) 83057) ((-531 . -1114) T) ((-475 . -25) T) ((-119 . -571) T) ((-475 . -21) T) ((-468 . -25) T) ((-468 . -21) T) ((-1262 . -1236) 83023) ((-1183 . -93) T) ((-1173 . -1069) 82919) ((-839 . -302) 82898) ((-1262 . -239) 82757) ((-846 . -1132) T) ((-995 . -998) T) ((-692 . -111) 82736) ((-636 . -1247) T) ((-307 . -528) 82528) ((-1257 . -234) 82480) ((-1257 . -274) 82432) ((-1256 . -381) T) ((-260 . -321) 82370) ((-259 . -321) 82308) ((-1253 . -866) T) ((-1190 . -633) NIL) ((-1190 . -632) 82290) ((-1173 . -390) 82274) ((-1151 . -842) T) ((-1151 . -950) T) ((-96 . -93) T) ((-1144 . -618) 82251) ((-1110 . -633) 82235) ((-1110 . -632) 82217) ((-1035 . -668) 82167) ((-943 . -668) 82104) ((-837 . -300) 82081) ((-498 . -632) 82013) ((-627 . -153) 81960) ((-501 . -739) 81910) ((-419 . -1088) T) ((-496 . -503) 81894) ((-443 . -668) 81853) ((-339 . -871) 81832) ((-352 . -670) 81806) ((-50 . -21) T) ((-50 . -25) T) ((-221 . -739) 81756) ((-171 . -746) 81727) ((-177 . -670) 81659) ((-595 . -21) T) ((-595 . -25) T) ((-532 . -25) T) ((-532 . -21) T) ((-489 . -153) 81609) ((-1092 . -632) 81591) ((-1024 . -102) T) ((-887 . -102) T) ((-838 . -929) 81491) ((-820 . -426) 81454) ((-40 . -133) T) ((-721 . -376) T) ((-723 . -748) T) ((-723 . -816) T) ((-723 . -813) T) ((-215 . -922) T) ((-594 . -1143) T) ((-560 . -1143) T) ((-509 . -1143) T) ((-372 . -632) 81436) ((-367 . -632) 81418) ((-359 . -632) 81400) ((-66 . -411) T) ((-66 . -410) T) ((-108 . -633) 81330) ((-108 . -632) 81272) ((-214 . -922) T) ((-987 . -153) 81256) ((-793 . -133) T) ((-692 . -635) 81174) ((-136 . -748) T) ((-118 . -748) T) ((-1283 . -35) 81140) ((-1085 . -503) 81124) ((-594 . -23) T) ((-560 . -23) T) ((-509 . -23) T) ((-1262 . -95) 81090) ((-1262 . -35) 81056) ((-1201 . -102) T) ((-1156 . -102) T) ((-878 . -102) T) ((-231 . -503) 81040) ((-1319 . -111) 81019) ((-1318 . -111) 80998) ((-44 . -1087) 80982) ((-1321 . -1247) T) ((-1319 . -635) 80928) ((-1319 . -1080) T) ((-1318 . -635) 80857) ((-1318 . -1080) T) ((-1266 . -1273) 80841) ((-879 . -876) 80825) ((-1209 . -302) 80804) ((-1134 . -1247) T) ((-110 . -298) 80754) ((-1034 . -1247) T) ((-131 . -153) 80736) ((-1173 . -927) 80695) ((-44 . -111) 80674) ((-1253 . -1132) T) ((-1212 . -1293) T) ((-1198 . -870) NIL) ((-1197 . -504) 80655) ((-692 . -1080) T) ((-1197 . -632) 80621) ((-1189 . -632) 80603) ((-488 . -239) 80555) ((-1094 . -629) 80530) ((-1025 . -504) 80511) ((-74 . -455) T) ((-74 . -410) T) ((-1094 . -1132) T) ((-154 . -1087) 80495) ((-1025 . -632) 80461) ((-692 . -240) 80440) ((-585 . -569) 80424) ((-368 . -149) 80403) ((-368 . -147) 80354) ((-366 . -149) 80333) ((-366 . -147) 80284) ((-358 . -149) 80263) ((-358 . -147) 80214) ((-275 . -147) 80193) ((-275 . -149) 80172) ((-255 . -149) 80151) ((-119 . -376) T) ((-255 . -147) 80130) ((-1189 . -633) NIL) ((-154 . -111) 80109) ((-1034 . -1069) 79997) ((-1185 . -1247) T) ((-716 . -1252) T) ((-820 . -1088) T) ((-721 . -1143) T) ((-1034 . -390) 79974) ((-520 . -1247) T) ((-516 . -1247) T) ((-935 . -147) T) ((-935 . -149) 79956) ((-893 . -133) T) ((-837 . -1087) 79877) ((-721 . -23) T) ((-716 . -571) T) ((-229 . -1082) 79842) ((-669 . -632) 79774) ((-669 . -633) 79735) ((-651 . -633) NIL) ((-651 . -632) 79717) ((-501 . -175) T) ((-229 . -662) 79682) ((-221 . -175) T) ((-227 . -21) T) ((-227 . -25) T) ((-488 . -1236) 79648) ((-488 . -1233) 79614) ((-285 . -632) 79596) ((-284 . -632) 79578) ((-283 . -632) 79560) ((-282 . -632) 79542) ((-281 . -632) 79524) ((-514 . -673) 79506) ((-280 . -632) 79488) ((-352 . -748) T) ((-279 . -632) 79470) ((-110 . -19) 79452) ((-177 . -748) T) ((-514 . -385) 79434) ((-215 . -632) 79416) ((-534 . -1180) 79400) ((-514 . -125) T) ((-110 . -618) 79375) ((-214 . -632) 79357) ((-488 . -35) 79323) ((-488 . -95) 79289) ((-212 . -632) 79271) ((-211 . -632) 79253) ((-210 . -632) 79235) ((-209 . -632) 79217) ((-206 . -632) 79199) ((-205 . -632) 79181) ((-204 . -632) 79163) ((-203 . -632) 79145) ((-202 . -632) 79127) ((-201 . -632) 79109) ((-200 . -632) 79091) ((-549 . -1135) 79043) ((-199 . -632) 79025) ((-198 . -632) 79007) ((-45 . -503) 78944) ((-197 . -632) 78926) ((-196 . -632) 78908) ((-154 . -635) 78877) ((-1147 . -102) T) ((-837 . -111) 78793) ((-663 . -102) 78723) ((-661 . -21) T) ((-661 . -25) T) ((-496 . -298) 78700) ((-1321 . -1069) 78684) ((-1144 . -632) 78377) ((-1133 . -1132) T) ((-1077 . -1247) T) ((-1201 . -321) 78364) ((-1093 . -1082) 78351) ((-1166 . -1132) T) ((-975 . -1082) 78194) ((-1156 . -321) 78181) ((-1127 . -1114) T) ((-642 . -1143) T) ((-1093 . -662) 78168) ((-1122 . -1114) T) ((-975 . -662) 78017) ((-1118 . -236) 77962) ((-495 . -1082) 77805) ((-1104 . -1114) T) ((-1097 . -1114) T) ((-1067 . -1114) T) ((-1050 . -1114) T) ((-119 . -1143) T) ((-495 . -662) 77654) ((-803 . -236) 77641) ((-841 . -102) T) ((-645 . -1114) T) ((-642 . -23) T) ((-1181 . -528) 77433) ((-497 . -1114) T) ((-985 . -1132) T) ((-400 . -102) T) ((-336 . -102) T) ((-222 . -1114) T) ((-864 . -1247) T) ((-154 . -1080) T) ((-753 . -426) 77417) ((-119 . -23) T) ((-1034 . -927) 77369) ((-757 . -1132) T) ((-737 . -1132) T) ((-1287 . -668) 77279) ((-1278 . -668) 77161) ((-467 . -1132) T) ((-421 . -1247) T) ((-326 . -435) 77145) ((-606 . -93) T) ((-1058 . -633) 77106) ((-270 . -1247) T) ((-1055 . -1252) T) ((-229 . -102) T) ((-1058 . -632) 77068) ((-838 . -274) 77052) ((-838 . -234) 77036) ((-837 . -635) 76834) 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75010) ((-735 . -102) T) ((-307 . -503) 74947) ((-895 . -662) 74892) ((-495 . -102) T) ((-753 . -1088) T) ((-630 . -632) 74874) ((-630 . -633) 74735) ((-421 . -390) 74719) ((-421 . -351) 74703) ((-1201 . -38) 74532) ((-1156 . -38) 74381) ((-331 . -635) 74207) ((-935 . -239) T) ((-652 . -1247) T) ((-620 . -1247) T) ((-878 . -38) 74177) ((-404 . -670) 74161) ((-663 . -321) 74099) ((-1183 . -504) 74080) ((-1183 . -632) 74046) ((-985 . -739) 73943) ((-757 . -739) 73913) ((-638 . -670) 73887) ((-226 . -107) 73871) ((-45 . -298) 73771) ((-323 . -1132) T) ((-301 . -1087) 73758) ((-110 . -632) 73740) ((-110 . -633) 73722) ((-467 . -739) 73692) ((-838 . -262) 73631) ((-711 . -1132) 73609) ((-565 . -1132) T) ((-1205 . -1088) T) ((-1204 . -1088) T) ((-96 . -504) 73590) ((-1198 . -1088) T) ((-301 . -111) 73575) ((-1157 . -1088) T) ((-565 . -629) 73554) ((-96 . -632) 73520) ((-1035 . -870) T) ((-231 . -708) 73478) ((-716 . -1143) T) ((-1240 . -762) 73454) ((-1055 . -376) T) ((-860 . -858) 73436) 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T) ((-895 . -321) 69641) ((-677 . -298) 69620) ((-657 . -1247) T) ((-114 . -684) T) ((-365 . -1247) T) ((-372 . -635) 69557) ((-367 . -635) 69494) ((-359 . -635) 69431) ((-77 . -1247) T) ((-108 . -635) 69381) ((-114 . -113) T) ((-1093 . -38) 69368) ((-686 . -387) 69347) ((-975 . -38) 69196) ((-753 . -1132) T) ((-495 . -38) 69045) ((-82 . -1247) T) ((-606 . -504) 69026) ((-1257 . -870) NIL) ((-1205 . -1132) T) ((-585 . -296) T) ((-1204 . -1132) T) ((-606 . -632) 68992) ((-1198 . -1132) T) ((-1151 . -874) T) ((-1110 . -1080) T) ((-365 . -1069) 68969) ((-839 . -504) 68953) ((-1035 . -1088) T) ((-45 . -632) 68935) ((-45 . -633) NIL) ((-943 . -1088) T) ((-839 . -632) 68904) ((-1178 . -102) 68854) ((-1110 . -250) 68805) ((-443 . -1088) T) ((-372 . -1080) T) ((-367 . -1080) T) ((-377 . -378) 68782) ((-359 . -1080) T) ((-357 . -236) 68769) ((-260 . -245) 68748) ((-259 . -245) 68727) ((-1110 . -240) 68652) ((-1157 . -1132) T) ((-305 . -927) 68611) ((-108 . -1080) T) ((-716 . -133) T) ((-419 . -528) 68453) ((-372 . -240) 68432) ((-372 . -250) T) ((-44 . -742) T) ((-367 . -240) 68411) ((-367 . -250) T) ((-359 . -240) 68390) ((-359 . -250) T) ((-1197 . -635) 68371) ((-171 . -321) 68336) ((-108 . -250) T) ((-108 . -240) T) ((-1025 . -635) 68317) ((-331 . -814) T) ((-893 . -21) T) ((-893 . -25) T) ((-421 . -319) T) ((-514 . -34) T) ((-110 . -300) 68292) ((-1144 . -1087) 68213) ((-895 . -1182) NIL) ((-342 . -632) 68195) ((-421 . -1051) 68173) ((-1144 . -111) 68089) ((-713 . -1293) T) ((-451 . -1132) T) ((-258 . -1132) T) ((-1322 . -748) T) ((-64 . -632) 68071) ((-895 . -38) 68016) ((-616 . -153) 68000) ((-537 . -1247) T) ((-524 . -632) 67940) ((-1266 . -321) 67927) ((-753 . -739) 67776) ((-545 . -815) T) ((-545 . -816) T) ((-560 . -660) 67758) ((-509 . -660) 67718) ((-518 . -1247) T) ((-659 . -1305) 67702) ((-368 . -466) T) ((-366 . -466) T) ((-358 . -466) T) ((-275 . -466) 67653) ((-539 . -1132) T) ((-534 . -1132) 67603) ((-255 . -466) 67554) ((-1181 . -298) 67533) ((-1209 . 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. -1088) T) ((-1240 . -149) 63676) ((-334 . -1082) 63658) ((-1240 . -147) 63637) ((-1215 . -102) T) ((-1214 . -102) T) ((-1213 . -102) T) ((-1205 . -175) 63588) ((-334 . -662) 63570) ((-723 . -1247) T) ((-1204 . -175) 63501) ((-1198 . -175) 63432) ((-1183 . -635) 63413) ((-1157 . -175) 63364) ((-610 . -1088) T) ((-609 . -1088) T) ((-1035 . -1132) T) ((-1002 . -1132) T) ((-391 . -1082) 63329) ((-136 . -1247) T) ((-118 . -1247) T) ((-943 . -1132) T) ((-895 . -929) NIL) ((-391 . -662) 63294) ((-146 . -874) T) ((-820 . -818) 63278) ((-721 . -25) T) ((-721 . -21) T) ((-119 . -660) 63255) ((-723 . -911) 63237) ((-443 . -1132) T) ((-326 . -1252) 63216) ((-325 . -1252) T) ((-171 . -414) 63200) ((-856 . -1082) 63170) ((-488 . -1004) 63132) ((-72 . -632) 63114) ((-132 . -102) T) ((-131 . -102) T) ((-850 . -1082) 63098) ((-108 . -819) T) ((-108 . -814) T) ((-723 . -1069) 63080) ((-326 . -571) 63059) ((-325 . -571) T) ((-856 . -662) 63029) ((-850 . -662) 62999) ((-1327 . -23) T) ((-136 . -1069) 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. -921) 60880) ((-987 . -321) 60818) ((-856 . -102) T) ((-443 . -739) 60802) ((-229 . -843) T) ((-850 . -102) T) ((-847 . -102) T) ((-1319 . -670) 60776) ((-1283 . -1282) 60755) ((-493 . -153) 60705) ((-1283 . -1276) 60675) ((-1151 . -1252) T) ((-352 . -1069) 60642) ((-1283 . -1280) 60626) ((-1266 . -929) 60533) ((-1262 . -1261) 60512) ((-80 . -632) 60494) ((-931 . -632) 60476) ((-1262 . -1276) 60453) ((-1151 . -571) T) ((-948 . -871) T) ((-793 . -871) T) ((-694 . -871) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-391 . -296) T) ((-1262 . -1259) 60308) ((-1284 . -1143) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1094 . -618) 60154) ((-840 . -635) 60138) ((-560 . -236) 60125) ((-530 . -153) 60109) ((-58 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1316) 60048) ((-367 . -1316) 60032) ((-359 . -1316) 60016) ((-326 . -376) 59995) ((-325 . -376) T) ((-496 . -1080) 59973) ((-716 . -660) 59955) ((-1318 . -670) 59929) ((-131 . -321) NIL) ((-1284 . -23) T) 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|simpson| |rur| - |element?| |RemainderList| |reorder| |prinb| |component| |coordinates| - |cycleLength| |coefficient| |typeList| |sin2csc| |tablePow| |lyndon| - |lookup| |fractionFreeGauss!| |set| |frobenius| |scanOneDimSubspaces| - |OMgetApp| |removeDuplicates| |deepExpand| |just| |lambert| |solve| - |previous| |palgintegrate| |solid| |positive?| |setref| |bezoutMatrix| - |sturmSequence| |OMencodingUnknown| |getGoodPrime| |fmecg| - |nextSublist| |finiteBound| |rewriteIdealWithRemainder| - |reducedSystem| |solveLinearPolynomialEquationByRecursion| |wholePart| - |cyclic| |distance| |toseLastSubResultant| |matrixGcd| |isExpt| - |setchildren!| |singularitiesOf| |plus| |quotient| |f04adf| - |integralAtInfinity?| |redpps| |closedCurve?| |possiblyNewVariety?| - |iidsum| |selectNonFiniteRoutines| |iicos| |rootPower| |s14abf| - |euclideanNormalForm| |radicalSimplify| |isEquiv| |tanAn| - |iflist2Result| |elseBranch| |monicDivide| |numberOfHues| |pushup| - |expintegrate| |uniform01| |prevPrime| |cycleElt| |variable?| - |calcRanges| |radicalEigenvalues| |lp| |mapUnivariate| |times| - |genericLeftDiscriminant| |normalizeIfCan| |innerSolve1| |aromberg| - |mathieu12| |ldf2vmf| |atom?| |exptMod| |asinhIfCan| |unary?| - |interactiveEnv| |trigs2explogs| |null| |eulerE| - |ScanFloatIgnoreSpaces| |functionIsContinuousAtEndPoints| |back| - |maxPoints| |call| |matrixConcat3D| |elaboration| |not| |solveInField| - |stoseInvertible?sqfreg| |makeGraphImage| |getMeasure| |integrate| - |intersect| |currentScope| |symbolTable| |rationalPower| - |balancedBinaryTree| |count| |pushucoef| |bright| |and| |OMputObject| - |iiacoth| |nthRoot| |rightAlternative?| |green| |setvalue!| |member?| - |selectsecond| |monom| |or| |collectUpper| |complexElementary| - |e02def| |s15adf| |determinant| |pushFortranOutputStack| |lagrange| - |credPol| |selectPDERoutines| |backspace| |lyndonIfCan| |xor| - |asinIfCan| |reducedForm| |se2rfi| |prologue| |iiasin| |sumOfDivisors| - EQ |popFortranOutputStack| |color| 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|acsc| |ipow| |hostPlatform| |realZeros| |empty| - |setVariableOrder| |OMputEndAttr| |outputAsScript| |increase| - |numberOfFractionalTerms| |sinh| |setLength!| |chiSquare1| - |nextsousResultant2| |critMTonD1| |s14aaf| |nextPrime| |rationalIfCan| - |character?| |belong?| |cosh| |monicDecomposeIfCan| |biRank| - |definingInequation| |UpTriBddDenomInv| - |generalizedContinuumHypothesisAssumed?| |completeHensel| - |OMgetSymbol| |lazyPremWithDefault| |OMreadFile| |tanh| - |OMencodingXML| |rspace| |dfRange| |unknown| |minus!| |norm| - |changeBase| |stopTableInvSet!| |cyclotomicFactorization| |leftOne| - |upperCase!| |coth| |doubleComplex?| |chainSubResultants| - |selectAndPolynomials| |port| |OMputAtp| |showTheSymbolTable| |coord| - |extractIndex| |rowEch| |lhs| |OMUnknownSymbol?| |sech| - |idealiserMatrix| |mainMonomials| |drawToScale| |df2ef| |roughBase?| - |c06ecf| |rk4| |rhs| |acscIfCan| |ref| |csch| |cdr| - |jvmIntegerConstantTag| |s15aef| |isAtom| |addiag| |iisin| |cSech| - |asinh| |tanQ| |pseudoQuotient| |script| |tanNa| |t| |root| - |startTableGcd!| |nil| |f02axf| |selectODEIVPRoutines| |symbolIfCan| - |width| |algebraicSort| |acosh| |OMsend| |var1StepsDefault| |cyclic?| - |carriageReturn| |drawComplex| |getConstant| - |SturmHabichtCoefficients| |OMgetVariable| |create| |atanh| |heap| - |d02gbf| |computeInt| |f02xef| |halfExtendedResultant2| |bottom!| - |acoth| |newTypeLists| |iExquo| |RittWuCompare| |incrementKthElement| - |tex| |nthFlag| |useEisensteinCriterion?| |constDsolve| |approximate| - |setStatus!| |plus!| |algDsolve| |asech| |polarCoordinates| - |normalDenom| |regime| |complex| |lllip| |viewport2D| FG2F |rotate!| - |dn| |odd?| |flexibleArray| |stFuncN| |lieAlgebra?| |rootProduct| - |ranges| |factorPolynomial| |mainValue| |removeConstantTerm| |pile| - |multiple| |assign| |companionBlocks| |trapezoidalo| |sub| - |increasePrecision| |d03faf| |applyQuote| |optional| |beauzamyBound| - |asimpson| |degreeSubResultantEuclidean| |negative?| - |probablyZeroDim?| |multiEuclidean| |printInfo!| |listYoungTableaus| - |SturmHabichtMultiple| |pascalTriangle| |leftDivide| |minPoly| - |cotIfCan| |sequence| |sayLength| |weighted| |f01qdf| |bumprow| - |flatten| |decrease| |bumptab1| |seriesSolve| |mkAnswer| - |internalLastSubResultant| |attributeData| |bumptab| |mapdiv| - |reduced?| |formfeed| |f04maf| |ruleset| |partialDenominators| - |karatsuba| |blue| |OMclose| |row| |cAcot| |setTopPredicate| - |selectMultiDimensionalRoutines| |puiseux| |extractTop!| |tube| - |getIdentifier| |toseInvertible?| |makeSeries| |extension| |iCompose| - |gramschmidt| |initiallyReduce| |makeViewport2D| |zeroSquareMatrix| - |s13acf| |iiperm| |setFieldInfo| |factorOfDegree| |approximants| - |rk4a| |createNormalElement| |irreducibleFactor| |dimensionsOf| |inv| - |quadraticForm| |suchThat| |outputAsTex| |pushdterm| |normalise| - |e01bhf| |mapGen| |meshPar1Var| |d02raf| |cos2sec| |ground?| |isAnd| - |modularGcdPrimitive| |derivationCoordinates| |linearAssociatedExp| - |d02ejf| |duplicates| |dom| |cAcoth| |eigenMatrix| |mapExponents| - |rectangularMatrix| |sylvesterMatrix| |ground| |checkForZero| - |maxColIndex| |setright!| |f04asf| |pr2dmp| |obj| |lexico| - |lazyIrreducibleFactors| |groebnerFactorize| |algintegrate| - |semiResultantReduitEuclidean| |leadingMonomial| |integralCoordinates| - |npcoef| |outputArgs| |integer?| |concat!| |imagJ| |readIfCan!| - |associative?| |rCoord| |permutationGroup| |leadingCoefficient| - |extendedIntegrate| |numberOfChildren| |index?| |showArrayValues| - |vconcat| |polar| |qfactor| |fprindINFO| |collectQuasiMonic| - |primitiveMonomials| |taylorIfCan| |op| |outerProduct| |qelt| - |applyRules| |showScalarValues| |rowEchelonLocal| |leftFactorIfCan| - |lazyPquo| |nthRootIfCan| |pdf2ef| |rightGcd| |setProperties| - |completeEval| |cAtanh| |reductum| |qsetelt| |fortranReal| - |continuedFraction| |forLoop| |laurentIfCan| |nonQsign| |chebyshevU| - |jvmInterface| |trailingCoefficient| |rightRegularRepresentation| - |leftRankPolynomial| |radicalEigenvector| |xRange| |setMaxPoints3D| - |cosIfCan| |OMopenString| |preprocess| |corrPoly| |sechIfCan| |s18def| - |besselK| |outputFixed| |s17ahf| |inverseLaplace| |alphanumeric?| - |yRange| |testDim| |times!| |datalist| |quoted?| |oblateSpheroidal| - |associatorDependence| |coefChoose| |separateFactors| |zCoord| - |aLinear| |entry| |zRange| |removeSinSq| |removeZero| |jvmFinal| - |interpolate| |divide| |linear| |GospersMethod| |e02bcf| |s19abf| - |compose| |numberOfComposites| |map!| |separateDegrees| |printStats!| - |cCos| |internalAugment| LODO2FUN |comparison| |reciprocalPolynomial| - |allRootsOf| |btwFact| |fintegrate| |zeroDimensional?| |point| - |qsetelt!| |readable?| |startStats!| |close!| |OMputInteger| |sec2cos| - |polynomial| |rightExactQuotient| |overbar| |pol| |interpretString| - |subresultantSequence| |parameters| |createIrreduciblePoly| |s17acf| - |redPol| |rightMult| |isOpen?| |dequeue| |external?| |style| |trim| - |nthExponent| |isOr| |innerEigenvectors| |LyndonBasis| - |createGenericMatrix| |transform| |one?| |mapMatrixIfCan| - |palgextint0| |series| |operators| |imagj| |wrregime| |smith| - |setScreenResolution| |nilFactor| |polyRDE| |mapCoef| |square?| - |central?| |palgextint| |c06fpf| - |rewriteIdealWithQuasiMonicGenerators| - |zeroSetSplitIntoTriangularSystems| |antiAssociative?| |lflimitedint| - |multMonom| |primPartElseUnitCanonical!| |acsch| |e02ddf| |unitVector| - |flexible?| |primeFactor| |knownInfBasis| |update| |OMgetEndAtp| - |adjoint| |midpoint| |mightHaveRoots| |stFunc2| |replace| - |constantOpIfCan| |zeroMatrix| |bracket| |argumentList!| |plotPolar| - |lfextlimint| |unrankImproperPartitions0| |exprHasLogarithmicWeights| - |coHeight| |OMencodingSGML| |min| |extendedResultant| - |viewThetaDefault| |invertibleElseSplit?| |internalInfRittWu?| - |padicFraction| |top| |has?| |fullDisplay| |child| |unit?| - |lazyPseudoRemainder| |elaborate| |setProperty| |polygamma| |continue| - |purelyTranscendental?| |exprex| |explicitlyFinite?| |addBadValue| - |makeFR| |jvmSynchronized| |adaptive| |axesColorDefault| |void| - |iiacosh| |delay| |iicsc| |f01qcf| |power!| |genericRightTrace| - |e02bef| |substring?| |readUInt32!| |pointPlot| |hash| |anfactor| - |wordInStrongGenerators| |df2fi| |readBytes!| |iicot| |category| - |limitedint| |mantissa| |comp| |lexGroebner| |branchPointAtInfinity?| - |lfinfieldint| |dequeue!| |setsubMatrix!| |LiePolyIfCan| |underscore| - |rdregime| |makeCos| |equality| |domain| |d01anf| |suffix?| - |numberOfNormalPoly| |extendIfCan| |divergence| |ignore?| - |OMgetEndApp| |block| |LiePoly| |rootKerSimp| |package| |parametric?| - |quoByVar| |bandedHessian| |normInvertible?| |any?| |expPot| - |mainPrimitivePart| |permutation| |maxrank| |numberOfCycles| |nor| - |elementary| |prefix?| |c06gsf| |OMputError| |jvmStatic| |merge!| - |LowTriBddDenomInv| |getBadValues| |mainMonomial| |withPredicates| - |mpsode| |principalAncestors| |rational| |mesh?| |sincos| - |OMconnInDevice| |newline| |pmComplexintegrate| |accuracyIF| |region| - |euclideanSize| |triangSolve| |toroidal| |besselJ| |acothIfCan| |sign| - |representationType| |monomial?| |divisor| |stoseInvertibleSetreg| - |nextPrimitivePoly| |makeYoungTableau| |linefeed| |bivariateSLPEBR| - |numeric| |writable?| |primaryDecomp| |rotatez| |mvar| |ravel| |cycle| - |copy!| |rightZero| |multiset| |lowerCase| |extractProperty| |Ei| - |iitan| |radical| |debug| |OMgetBind| |domainTemplate| - |createPrimitivePoly| |reshape| |Nul| |SturmHabichtSequence| - |gradient| |rewriteSetByReducingWithParticularGenerators| - |relativeApprox| |char| D |supersub| |subPolSet?| |prepareSubResAlgo| - |rewriteSetWithReduction| |doubleRank| |createRandomElement| - |extract!| |principalIdeal| |signAround| |maxIndex| |intChoose| - |infix?| |outputGeneral| |open?| |genericRightTraceForm| - |isConnected?| |bandedJacobian| |makeViewport3D| |s20adf| |mask| - |constantIfCan| |lowerCase!| |explogs2trigs| |composites| |sqfrFactor| - |repeating?| |pushuconst| |rightRemainder| |d01apf| |spherical| - |euclideanGroebner| |selectIntegrationRoutines| |viewSizeDefault| - |lift| |setLabelValue| |hasoln| |factorSquareFreeByRecursion| - |baseRDE| |infRittWu?| |fibonacci| |s18acf| |ellipticCylindrical| - |inverse| |reduce| |in?| |returnType!| |intermediateResultsIF| - |createMultiplicationMatrix| |dflist| |doublyTransitive?| |minIndex| - |inputOutputBinaryFile| |minRowIndex| |sumSquares| |leftReducedSystem| - |upperCase?| |lazyEvaluate| |oddInfiniteProduct| |s17aff| |lex| - |OMputFloat| |nil?| |homogeneous?| |stronglyReduce| |useNagFunctions| - |setnext!| |updatF| |gcdcofact| |OMgetBVar| |iidprod| |f02aef| - |s18aff| |nullary?| |integerIfCan| |headReduced?| |irreducible?| - |invertIfCan| |position| |numberOfVariables| |separant| |gensym| - |eigenvalues| |leastPower| |primextendedint| |print| |noValueMode| - |support| |iisqrt3| |mat| |viewDeltaYDefault| |dmpToP| |resolve| - |createMultiplicationTable| |outputBinaryFile| |ptFunc| |OMwrite| - |clearCache| |removeSuperfluousQuasiComponents| |options| - |countRealRootsMultiple| |roughSubIdeal?| |evenInfiniteProduct| - |constructor| |consnewpol| |twoFactor| |find| |setleaves!| - |karatsubaDivide| |setPredicates| |stiffnessAndStabilityOfODEIF| - |tanh2trigh| |signatureAst| |sts2stst| |normDeriv2| |numFunEvals3D| - |rational?| |string| |leftUnits| |wreath| |palglimint0| |associates?| - |divisors| |init| |nonLinearPart| |dot| |PollardSmallFactor| |s01eaf| - |compiledFunction| |commaSeparate| |exp1| |pointData| |truncate| |box| - |lastSubResultant| |orbit| |setAdaptive3D| - |stoseIntegralLastSubResultant| |mesh| |nextPrimitiveNormalPoly| - |hermiteH| |coshIfCan| |structuralConstants| |alphabetic| - |multinomial| |po| |pointSizeDefault| |measure| |jvmProtected| - |coerceImages| |f02ajf| |delete| |iicosh| |hitherPlane| |byte| - |totalGroebner| |changeName| |modifyPointData| |aQuadratic| |reopen!| - |rarrow| |tValues| |setEmpty!| |shiftRight| |generic| |nthr| - |integers| |constantOperator| |makeSin| |monomials| |enqueue!| - |generalInfiniteProduct| |graphs| |push!| |littleEndian| |coleman| - |generalPosition| |iiacsch| |ip4Address| |mapDown!| |cycleRagits| - |polyPart| |identity| |slash| |mathieu24| |nextLatticePermutation| - |rotatey| |intPatternMatch| |id| |messagePrint| |routines| |aQuartic| - |prefixRagits| |associatedSystem| |pack!| |tanIfCan| |diagonal?| - |binaryFunction| |rule| |lo| |createLowComplexityTable| |invmod| - |mindeg| |environment| |stoseInternalLastSubResultant| - |algebraicCoefficients?| |insertTop!| |infieldIntegrate| - |physicalLength| |e01baf| |step| |tab| |pleskenSplit| |point?| - |edf2df| |boundOfCauchy| |voidMode| |genericLeftNorm| |squareFreePart| - |perfectNthRoot| |setEpilogue!| |cache| |int| |ListOfTerms| - |totalfract| |setStatus| |ord| |Frobenius| |s21baf| |primextintfrac| - |conjug| |indiceSubResultantEuclidean| |typeLists| |cTan| |geometric| - |patternMatchTimes| |radix| |graeffe| |explicitEntries?| |OMlistCDs| - |readLineIfCan!| |specialTrigs| |permutationRepresentation| - |resultant| |exponentialOrder| |expandLog| |points| - |semicolonSeparate| |tRange| |factorials| |repeatUntilLoop| |f04jgf| - |rightExtendedGcd| |fglmIfCan| |countable?| |binomThmExpt| |entries| - |s18dcf| |invertibleSet| |shift| |retract| |createPrimitiveNormalPoly| - |c06frf| |resultantEuclideannaif| |removeCosSq| |units| |limit| - |shanksDiscLogAlgorithm| |extensionDegree| |algint| |diagonals| - |c06fqf| |s17dgf| |dim| |cycles| |legendre| |cartesian| - |inputBinaryFile| |hasTopPredicate?| |bezoutDiscriminant| - |prepareDecompose| |mapUp!| |nlde| |Aleph| |d02gaf| |log10| |f04mbf| - |hostByteOrder| |divisorCascade| |fi2df| |ScanFloatIgnoreSpacesIfCan| - |useSingleFactorBound?| |findCycle| |besselY| |tanh2coth| - |primitiveElement| |extractIfCan| |bitand| |e01daf| |numericIfCan| - |setPosition| |mappingAst| |ParCond| |integerBound| |areEquivalent?| - |move| |showSummary| |infieldint| |setfirst!| |readLine!| |bitior| - |f01bsf| |whatInfinity| |factorSquareFreePolynomial| |axes| - |supDimElseRittWu?| |mainKernel| |eof?| |complexEigenvectors| - |OMgetEndObject| |multiEuclideanTree| |toseInvertibleSet| - |parabolicCylindrical| |code| |leftCharacteristicPolynomial| - |nonSingularModel| |f07aef| |rootSplit| |search| |mkcomm| - |showAttributes| |elColumn2!| |rootDirectory| |transcendenceDegree| - |iisech| |resultantnaif| |thenBranch| |perfectSquare?| |scripted?| - |setrest!| |setleft!| |tubePlot| |imagI| |basisOfRightNucloid| - |limitPlus| |module| |augment| |padecf| |setMinPoints3D| - |quasiComponent| |cAtan| |f04axf| |HenselLift| |exponent| |e02gaf| - |f04arf| |revert| |medialSet| |insertMatch| |signature| |generic?| - |bfKeys| |clipWithRanges| |f04mcf| |cyclePartition| |yCoord| |digit?| - |complexForm| |pointColorPalette| |write!| |extractClosed| |ode| - |polyRicDE| |nextPartition| |power| |mapBivariate| - |lastSubResultantEuclidean| |maxRowIndex| |normalized?| |putProperty| - |numberOfIrreduciblePoly| |coerceListOfPairs| |property| |hexDigit?| - |OMParseError?| |bindings| |traceMatrix| |taylorQuoByVar| F2FG |euler| - |someBasis| |initials| |alternatingGroup| |pseudoDivide| - |extractBottom!| |iiacos| |rename!| |more?| |ratDsolve| - |removeRedundantFactorsInContents| |build| |imagk| |adaptive3D?| - |symbol?| |degreePartition| |permanent| |strongGenerators| - |dominantTerm| |zeroOf| |startPolynomial| |lexTriangular| |expt| - |combineFeatureCompatibility| |irreducibleRepresentation| |singRicDE| - |goodnessOfFit| |tubeRadius| |lquo| |sumOfSquares| |leadingExponent| - |d01akf| |minimumDegree| |printInfo| |univariatePolynomial| - |OMputBind| |erf| |c06fuf| |leftRank| |reducedQPowers| |uniform| - |fixPredicate| |declare| |dark| |mathieu23| |lazyIntegrate| - |pointColorDefault| |exteriorDifferential| |airyAi| |integral| - |stoseInvertible?reg| |reindex| |topFortranOutputStack| - |lazyGintegrate| |compound?| |digit| |denomRicDE| |rootSimp| - |conditionP| |cAsin| |explicitlyEmpty?| |goodPoint| |oddintegers| - |chineseRemainder| |second| |qinterval| |mainContent| - |antiCommutative?| |fortranComplex| |bit?| |leastAffineMultiple| - |dilog| |genericLeftTraceForm| |close| |factorSquareFree| |drawCurves| - |e04dgf| |OMgetEndBind| |third| |realSolve| |groebner| |changeMeasure| - |generalizedInverse| |viewpoint| |outlineRender| |sin| Y |superscript| - |leadingCoefficientRicDE| |OMmakeConn| |OMreadStr| |rightQuotient| - |clikeUniv| |pToDmp| |lastSubResultantElseSplit| |setIntersection| - |cosh2sech| |recur| |key?| |cos| |symmetricPower| |display| - |LagrangeInterpolation| |equiv| |horizontalTab| |internalIntegrate0| - |cylindrical| |iisinh| |nthCoef| |setPoly| |OMunhandledSymbol| |tower| - |patternMatch| |tan| |OMputString| |besselI| |graphImage| - |quotedOperators| |showAllElements| |key| |rightUnit| |expandPower| - |cross| |jvmMethodrefConstantTag| |OMReadError?| |SturmHabicht| |cot| - |cCoth| |head| |monicModulo| |separate| |parabolic| - |resetAttributeButtons| |imaginary| |shallowExpand| |cCot| - |OMgetObject| |cLog| |sec| |pole?| |outputFloating| |diagonalMatrix| - |setRealSteps| |filename| |collectUnder| |quasiAlgebraicSet| - |completeSmith| |mainCoefficients| |squareMatrix| |unaryFunction| - |generator| |csc| |iicoth| |binaryTournament| |OMgetEndError| - |hdmpToDmp| |stop| |leftTrace| |repSq| |setValue!| |curveColor| - |ldf2lst| |fortranLiteralLine| |asin| |input| |rightScalarTimes!| - |distribute| |removeSinhSq| |iiacot| |parse| |iiGamma| |elRow2!| - |selectFiniteRoutines| |product| |OMreceive| |retractIfCan| - |coordinate| |acos| |library| |expressIdealMember| |df2st| |lighting| - |sup| |any| |listOfMonoms| |bounds| |fortranLogical| |numberOfFactors| - |jvmPrivate| |complexNumeric| |atan| |elaborateFile| |unit| - |autoReduced?| |quote| ** |degreeSubResultant| |getPickedPoints| - |jvmNative| |leftScalarTimes!| |OMgetInteger| |acot| |isList| - |noncommutativeJordanAlgebra?| |thetaCoord| |Lazard2| |byteBuffer| - |OMputAttr| |trueEqual| |prime| |kernels| |raisePolynomial| |asec| - |scalarTypeOf| |mainVariables| |closeComponent| |quickSort| |cSinh| - |result| |initiallyReduced?| |basisOfLeftNucloid| |unvectorise| - |jvmStringConstantTag| |operator| |monomialIntegrate| |summation| - |diff| |irreducibleFactors| |makeSketch| |yCoordinates| - |factorGroebnerBasis| |OMputEndBind| |nextItem| |kind| |writeBytes!| - |zeroVector| |root?| |frst| |jvmClassConstantTag| |commutator| - |retractable?| |matrix| |round| |leviCivitaSymbol| |univariate| - |paren| |laplace| |s18adf| |cyclicGroup| |name| |dAndcExp| |f04atf| - |cschIfCan| |high| |graphStates| |readInt8!| |rightRank| - |nextNormalPoly| |localReal?| |keys| |acschIfCan| |defineProperty| - |atanIfCan| |characteristicSerie| |OMlistSymbols| - |linearlyDependentOverZ?| |getExplanations| |gderiv| |idealSimplify| - |tree| |moebiusMu| |imagi| |iiabs| |leadingIdeal| |s17dlf| |factor| - |resize| |setAttributeButtonStep| |createPrimitiveElement| |red| - |lazy?| |subscript| |moduloP| |viewZoomDefault| |linearMatrix| |sqrt| - |cap| |iFTable| |powers| |gcdprim| |index| |complexRoots| |moduleSum| - |f01brf| |parts| |f01rdf| |drawStyle| |real| |remove| |e01sbf| - |rightLcm| |reducedDiscriminant| |incr| |nextNormalPrimitivePoly| - |d02bhf| |internalZeroSetSplit| |open| |wordsForStrongGenerators| - |irDef| |imag| |minPol| |dmp2rfi| |subNodeOf?| |primeFrobenius| |hi| - |directProduct| |pdf2df| |critB| |prindINFO| |palgint0| - |fortranTypeOf| |s17adf| |last| |OMputVariable| |show| |safeFloor| - |f02bbf| |argument| |pair| |assoc| |schwerpunkt| |clip| |addMatch| - |Lazard| |vark| |hdmpToP| |solveLinearPolynomialEquationByFractions| - |coercePreimagesImages| |shape| |lowerPolynomial| |setErrorBound| - |removeDuplicates!| |screenResolution3D| |acoshIfCan| |brace| - |subHeight| |trace| |genericPosition| |pseudoRemainder| |sample| - |d01alf| |symFunc| |operations| |quasiRegular| |e01sff| |traverse| - |primlimintfrac| |destruct| |topPredicate| |doubleResultant| |ksec| - |firstNumer| |insert!| |subResultantGcd| |f01ref| |realElementary| - |printStatement| |integralRepresents| |rightTrim| |cSec| |ffactor| - |totalLex| |maximumExponent| |OMgetType| - |semiIndiceSubResultantEuclidean| |semiDegreeSubResultantEuclidean| - |length| |goto| |anticoord| |sparsityIF| |leftTrim| |partialFraction| - |ridHack1| |roughEqualIdeals?| |putGraph| |scripts| |e02baf| - |getSyntaxFormsFromFile| |functorData| |integralBasisAtInfinity| - |interpret| |s17def| |asechIfCan| |fracPart| |critM| |splitNodeOf!| - |stopMusserTrials| |prime?| |pomopo!| |monomial| |zoom| |super| - |palginfieldint| |mainDefiningPolynomial| |resultantReduitEuclidean| - |BumInSepFFE| |jokerMode| |aspFilename| |parseString| |pureLex| - |sort!| |multivariate| |nand| |Vectorise| |symmetric?| - |completeEchelonBasis| |rightNorm| |monicCompleteDecompose| - |increment| |conjugate| |level| |rk4f| |variables| |infix| |iiexp| - |leftMinimalPolynomial| |union| |colorFunction| |irForm| |f2st| - |definingPolynomial| |putProperties| |transpose| |getCode| |makeprod| - |evaluate| |freeOf?| |constantKernel| |startTableInvSet!| |option| - |reduceBasisAtInfinity| |isQuotient| |logpart| |create3Space| - |laplacian| |fractRadix| |getOperator| |unmakeSUP| |iiasec| - |cyclicSubmodule| |quasiMonic?| |readInt32!| |rubiksGroup| |entry?| - |df2mf| |generate| |resultantEuclidean| |terms| |viewDeltaXDefault| - |simplifyLog| |approxNthRoot| |errorKind| |factorsOfDegree| |cTanh| - |transcendentalDecompose| |rischNormalize| |plenaryPower| |hconcat| - |listLoops| |localAbs| |monicLeftDivide| |parent| - |basisOfMiddleNucleus| |padicallyExpand| |lifting1| |incrementBy| - |c06ebf| |halfExtendedResultant1| |createNormalPoly| |minColIndex| - |genericRightMinimalPolynomial| |taylor| |maxPoints3D| - |createLowComplexityNormalBasis| |numerator| |eigenvectors| - |asecIfCan| |expand| |factorAndSplit| |evenlambert| |pointLists| - |e01bef| |divideIfCan!| |laurent| |getStream| |noLinearFactor?| - |scale| |capacity| |e04gcf| |height| |filterWhile| |zeroDimPrimary?| - |hue| |newLine| |conjugates| |linearDependence| |fixedPointExquo| - |showClipRegion| |arbitrary| |partialNumerators| |filterUntil| - |chebyshevT| |Hausdorff| |e04naf| |primPartElseUnitCanonical| - |complexLimit| |qroot| |stack| |iiatan| |leftUnit| |constantLeft| - |select| |s19acf| |over| |basisOfRightNucleus| |LyndonWordsList| - |c05adf| |mirror| |computeBasis| |orbits| |romberg| |addPoint| - |exprToUPS| |ode1| |rightDivide| |stopTableGcd!| |intcompBasis| - |complexSolve| |sncndn| |packageCall| |unexpand| |makeVariable| - |plusInfinity| |formula| |horizConcat| |bits| |monomialIntPoly| - |bernoulli| |represents| |getButtonValue| |e04fdf| |leaves| - |printingInfo?| |minusInfinity| |oddlambert| |dimension| |varselect| - |bat1| |zero?| SEGMENT |branchPoint?| |predicate| |unknownEndian| - |prolateSpheroidal| |polCase| |checkPrecision| |groebSolve| - |leftQuotient| |exportedOperators| |f02abf| |basisOfNucleus| - |leftRegularRepresentation| |musserTrials| |complexIntegrate| - |stoseInvertibleSet| |triangulate| |generalSqFr| |contains?| |f01rcf| - |leftZero| |sn| |gethi| |fortranLinkerArgs| |normalDeriv| |isNot| - |apply| |solveLinearlyOverQ| |setFormula!| |makeRecord| - |OMsupportsSymbol?| |isPower| |pattern| |mapmult| |nrows| - |genericRightNorm| |normal?| |badNum| |algebraicOf| |nextColeman| - |mix| |first| |isMult| |bothWays| |makingStats?| |tan2trig| |ncols| - |purelyAlgebraic?| |nary?| |pointColor| |infinityNorm| |categories| - |f02fjf| |primitivePart| |rest| |type| |reducedContinuedFraction| - |ScanRoman| |nthFactor| |weierstrass| |d01asf| |cyclicCopy| |double?| - |f02aaf| |surface| |absolutelyIrreducible?| |jacobian| |setRow!| - |d01ajf| |overlap| |precision| |inR?| |compdegd| |clearTheIFTable| - |elliptic?| |delta| |leadingBasisTerm| |bivariatePolynomials| - |totalDifferential| |notelem| |numberOfMonomials| |size?| - |unrankImproperPartitions1| |indicialEquations| |cot2trig| |concat| - |qqq| |varList| |makeUnit| |is?| |var2Steps| |leftMult| |cPower| - |edf2efi| |flagFactor| |jvmVolatile| |expr| |positiveSolve| - |splitDenominator| |node?| |lprop| |substitute| |stronglyReduced?| - |shuffle| |tail| |linearAssociatedOrder| |semiResultantEuclidean2| - |An| |indiceSubResultant| |quotientByP| |lfunc| |inHallBasis?| - |clipParametric| |charthRoot| |modularFactor| |hasHi| - |identitySquareMatrix| |testModulus| |totolex| |normalizedDivide| - |generalizedEigenvectors| |dec| |janko2| |fixedDivisor| |predicates| - |doubleDisc| |escape| |trunc| |isImplies| |wholeRadix| |extractPoint| - |logical?| |palgLODE| |queue| |polygon?| |ParCondList| |nil| + |Enumeration| |Mapping| |Record| |Union| |stopTableGcd!| |indices| + |presub| |makeYoungTableau| |OMputAttr| |e04ycf| |reduce| + |particularSolution| |outputAsTex| |eulerE| |prepareDecompose| + |intcompBasis| |value| |decompose| |linefeed| |subQuasiComponent?| + |trueEqual| |pushdterm| |and| |composite| |mapUp!| |dimensions| + |complexSolve| |basisOfLeftNucleus| |top!| |bivariateSLPEBR| |prime| + |collectUpper| |or| |normalise| |clearTheSymbolTable| |generators| + |nlde| |sncndn| |unknown| |minordet| |writable?| |ScanArabic| + |raisePolynomial| |complexElementary| |backOldPos| |e01bhf| |xor| + |Aleph| |diagonalProduct| |packageCall| |submod| |primaryDecomp| + |c02agf| |scalarTypeOf| |e02def| |mapGen| |case| |inverseColeman| + |d02gaf| |crest| |iiacoth| |unexpand| |quasiRegular?| |rotatez| + |removeIrreducibleRedundantFactors| |mainVariables| |ideal| |center| + |meshPar1Var| |Zero| |f01qef| |f04mbf| |makeVariable| + |rationalFunction| |swapColumns!| |mvar| |closeComponent| |isQuotient| + |d02raf| |One| |viewWriteDefault| |subResultantsChain| |hostByteOrder| + |horizConcat| |level| |algSplitSimple| |cycle| |newSubProgram| + |quickSort| |delete| |finite?| |cos2sec| |divisorCascade| + |expextendedint| |bits| |setelt!| |copy!| |hasPredicate?| |cSinh| + |fi2df| |principal?| |isAnd| |irCtor| |ScanFloatIgnoreSpaces| + |monomialIntPoly| |orthonormalBasis| |rightZero| + |removeRoughlyRedundantFactorsInContents| |initiallyReduced?| + |functionIsContinuousAtEndPoints| |recolor| |modularGcdPrimitive| + |hyperelliptic| |ScanFloatIgnoreSpacesIfCan| |bernoulli| + |toseSquareFreePart| |bezoutResultant| |multiset| |basisOfLeftNucloid| + |useSingleFactorBound?| |readInt16!| |derivationCoordinates| |back| + |maxdeg| |represents| |zeroDim?| |trivialIdeal?| |lowerCase| |union| + |unvectorise| |generalizedContinuumHypothesisAssumed| + |linearAssociatedExp| |elt| |polynomialZeros| |findCycle| + |getButtonValue| |overset?| |cCosh| |extractProperty| + |jvmStringConstantTag| |d02ejf| |acotIfCan| |normalize| |besselY| + |e04fdf| |semiSubResultantGcdEuclidean1| |Ei| |minPoints| + |monomialIntegrate| |byte| |duplicates| |symmetricTensors| + |alternating| |tanh2coth| |printingInfo?| |cosSinInfo| |iitan| |latex| + |summation| |factorsOfCyclicGroupSize| |cAcoth| |primitiveElement| + |rewriteIdealWithHeadRemainder| |oddlambert| |OMgetBind| EQ + |OMputEndAtp| |resetVariableOrder| |rquo| |diff| + |numericalOptimization| |eigenMatrix| |f04faf| |extractIfCan| + |dimension| |adaptive?| |domainTemplate| |hcrf| |irreducibleFactors| + |exponents| |mapExponents| |e01daf| |fractRagits| |varselect| + |removeRoughlyRedundantFactorsInPol| |createPrimitivePoly| |OMputBVar| + |makeSketch| |read!| |rectangularMatrix| |numericIfCan| |enterInCache| + |bat1| |returns| |Nul| |expIfCan| |yCoordinates| |sylvesterMatrix| + |unparse| |setPosition| |normalizeAtInfinity| |zero?| |palgRDE0| + |SturmHabichtSequence| |usingTable?| |factorGroebnerBasis| + |checkForZero| |makeResult| |mappingAst| |OMserve| |branchPoint?| + |inverseIntegralMatrix| |critBonD| |leadingSupport| |gradient| + |OMputEndBind| |int| |whileLoop| |maxColIndex| |figureUnits| |ParCond| + |unknownEndian| |upDateBranches| |univariate?| + |rewriteSetByReducingWithParticularGenerators| |nextItem| |setright!| + |removeRedundantFactors| |integerBound| |diag| |prolateSpheroidal| + |search| |yellow| |showSummary| |relativeApprox| |writeBytes!| + |f04asf| |stripCommentsAndBlanks| |areEquivalent?| |split| |polCase| + |algebraicDecompose| |bipolar| |supersub| |zeroVector| F + |singleFactorBound| |pr2dmp| |leftLcm| |move| |groebSolve| |tab1| + |showAttributes| |s17aef| |subPolSet?| |root?| |lfextendedint| + |lexico| |infieldint| |maxrow| |leftQuotient| |leastMonomial| + |prepareSubResAlgo| |viewDefaults| |frst| |matrix| |varList| + |internalSubPolSet?| |setfirst!| |exportedOperators| |kovacic| + |s17dcf| |shallowCopy| |rewriteSetWithReduction| |jvmClassConstantTag| + |iicsch| |useEisensteinCriterion?| |recip| |readLine!| |f02abf| + |coerceL| |doubleRank| |f01mcf| |optpair| |commutator| |constantRight| + |constDsolve| |f01bsf| |meatAxe| |basisOfNucleus| |internal?| |bag| + |createRandomElement| |mainExpression| |retractable?| |multiple?| + |setStatus!| |whatInfinity| |ceiling| |leftRegularRepresentation| + |OMputSymbol| |round| |plus!| |mathieu11| |ramified?| + |factorSquareFreePolynomial| |musserTrials| |heapSort| + |componentUpperBound| |purelyTranscendental?| |leviCivitaSymbol| + |rightPower| |algDsolve| |numberOfDivisors| |axes| |complexIntegrate| + |jvmFieldrefConstantTag| |reflect| |exprex| |sn| |paren| + |polarCoordinates| |polyred| |jvmNameAndTypeConstantTag| + |supDimElseRittWu?| |stoseInvertibleSet| |cscIfCan| |dual| + |explicitlyFinite?| |laplace| |normalDenom| |tanSum| |ptree| + |triangulate| |myDegree| |directSum| |addBadValue| |s18adf| |regime| + |generalTwoFactor| |aQuartic| |children| |generalSqFr| + |realEigenvalues| |makeFR| |controlPanel| |cyclicGroup| |option?| + |lllip| |idealiser| |prefixRagits| |contains?| |replaceKthElement| + |palglimint| |jvmSynchronized| |dAndcExp| |plus| + |exprHasWeightCosWXorSinWX| |viewport2D| |associatedSystem| + |functionIsFracPolynomial?| |f01rcf| |addMatchRestricted| |adaptive| + |LazardQuotient2| |credPol| |splitConstant| FG2F |pack!| |rules| + |birth| |leftZero| |log| |dualSignature| |rootNormalize| + |normalizeIfCan| |axesColorDefault| |patternMatch| |size| + |selectPDERoutines| |mkIntegral| |rotate!| |problemPoints| |tanIfCan| + |gethi| |sum| |split!| |iiacosh| |makeEq| |innerSolve1| |OMputString| + |backspace| |stirling1| |times| |dn| |fortranLiteral| |diagonal?| + |top| |fortranLinkerArgs| |s17akf| |swapRows!| |delay| |besselI| + |prevPrime| |continue| |binaryFunction| |odd?| |deleteRoutine!| + |digits| UP2UTS |exprToXXP| |iicsc| |polygon| |graphImage| + |flexibleArray| |sinh2csch| |numerators| |createLowComplexityTable| + |entry?| |factor1| |f01qcf| |stoseLastSubResultant| |quotedOperators| + |cycleElt| |rotatex| |errorInfo| |stFuncN| |invmod| |whitePoint| + |df2mf| |leftRecip| |positiveRemainder| |power!| |showAllElements| + |variable?| |insertBottom!| |monom| |lieAlgebra?| |leftExtendedGcd| + |headReduce| |mindeg| |resultantEuclidean| |subspace| |copyInto!| + |genericRightTrace| |rightUnit| |calcRanges| |rootProduct| + |environment| |powerAssociative?| |critT| |midpoints| |terms| + |mainCharacterization| |cAcsc| |e02bef| |expandPower| |ranges| + |physicalLength!| |primintfldpoly| |stoseInternalLastSubResultant| + |debug| |viewDeltaXDefault| |decimal| |readUInt32!| |makeTerm| |cross| + |algebraicCoefficients?| |factorPolynomial| |ReduceOrder| |curve?| D + |simplifyLog| |exponential1| |pointPlot| |changeWeightLevel| |node| + |jvmMethodrefConstantTag| |pToHdmp| |mainValue| |insertTop!| + |remainder| |approxNthRoot| |title| |removeSuperfluousCases| + |anfactor| |lyndon?| |OMReadError?| |removeConstantTerm| |setlast!| + |infieldIntegrate| |triangularSystems| |arg1| |errorKind| |stop| + |leftDiscriminant| |wordInStrongGenerators| |rischDE| |close| + |SturmHabicht| |pile| |acosIfCan| |discreteLog| |physicalLength| + |factorsOfDegree| |arg2| |iprint| |df2fi| |simplifyExp| |cCoth| + |lyndonIfCan| |assign| |viewWriteAvailable| |e01baf| |deepCopy| |e| + |cTanh| |constantToUnaryFunction| |readBytes!| |cSin| |result| + |display| |head| |asinIfCan| |rowEchLocal| |ODESolve| + |companionBlocks| |Beta| |tab| |conditions| |transcendentalDecompose| + |e02agf| |iicot| |contractSolve| |monicModulo| |reducedForm| + |pleskenSplit| |trapezoidalo| |subset?| |OMbindTCP| |binomial| + |rischNormalize| |match| |cyclicParents| |limitedint| |exactQuotient!| + |macroExpand| |separate| |rightCharacteristicPolynomial| |pow| |sub| + |null?| |point?| |plenaryPower| |remove| |sequences| |ddFact| + |lexGroebner| |parabolic| |deleteProperty!| |increasePrecision| + |edf2df| |completeHermite| |hconcat| |setImagSteps| + |branchPointAtInfinity?| |quartic| |resetAttributeButtons| |c06ekf| + |d03faf| |s19adf| |boundOfCauchy| |print| |listLoops| |last| |f02awf| + |lfinfieldint| |quasiMonicPolynomials| |imaginary| |setClipValue| + |beauzamyBound| |resolve| |voidMode| |aCubic| |localAbs| |assoc| + |OMputApp| |output| |dequeue!| |hermite| |shallowExpand| |swap| + |asimpson| |genericLeftNorm| |OMcloseConn| |monicLeftDivide| |fortran| + |test| |addPoint2| |iroot| |setsubMatrix!| |cCot| + |degreeSubResultantEuclidean| |cothIfCan| |isOp| |squareFreePart| + |parent| |outputSpacing| |doubleFloatFormat| |LiePolyIfCan| + |OMgetObject| |negative?| |order| |perfectNthRoot| |roughUnitIdeal?| + |basisOfMiddleNucleus| |partition| |underscore| |push| |cLog| + |equation| |inspect| |label| |probablyZeroDim?| |setEpilogue!| + |coefficients| |padicallyExpand| |zeroDimPrime?| |rdregime| + |csch2sinh| |pole?| |multiEuclidean| |ListOfTerms| |interReduce| + |clearCache| |characteristicSet| |lifting1| |numberOfComputedEntries| + |message| |makeCos| |cCsc| |outputFloating| |commutativeEquality| + |printInfo!| |readUInt8!| |totalfract| |c06ebf| |binary| |equality| + |nodes| |diagonalMatrix| |linSolve| |listYoungTableaus| |makeMulti| + |setStatus| |halfExtendedResultant1| |init| |unitCanonical| |d01anf| + |torsion?| |setRealSteps| |loadNativeModule| |octon| + |SturmHabichtMultiple| |ord| |skewSFunction| |createNormalPoly| + |numberOfNormalPoly| |lazyPrem| |closedCurve?| |argumentListOf| + |collectUnder| |pascalTriangle| |digamma| |countRealRoots| |Frobenius| + |minColIndex| |direction| |possiblyNewVariety?| |wronskianMatrix| + |extendIfCan| |quasiAlgebraicSet| |leftDivide| |externalList| + |rootRadius| |s21baf| |genericRightMinimalPolynomial| |iidsum| + |edf2ef| |divergence| |f01maf| |completeSmith| |option| |minPoly| + |box| |zag| |rightTrace| |primextintfrac| |maxPoints3D| |ignore?| + |leftFactor| |readUInt16!| |table| |mainCoefficients| |cotIfCan| + |mindegTerm| |subMatrix| |conjug| |createLowComplexityNormalBasis| + |sorted?| |new| |denomLODE| |OMgetEndApp| |squareMatrix| |log2| + |sequence| |indiceSubResultantEuclidean| |iterationVar| |numerator| + |script| |csubst| |block| |makeCrit| |unaryFunction| |normFactors| + |sayLength| |elements| |satisfy?| |typeLists| |eigenvectors| |edf2fi| + |LiePoly| |listexp| |iicoth| |rightFactorCandidate| |weighted| |cTan| + |compactFraction| |asecIfCan| |rootKerSimp| |encodingDirectory| + |selectNonFiniteRoutines| |atrapezoidal| |binaryTournament| |delete!| + |f01qdf| |geometric| |getOrder| |factorAndSplit| |tex| |iicos| + |cardinality| |parametric?| |upperBound| |OMgetEndError| |duplicates?| + |bumprow| |patternMatchTimes| |standardBasisOfCyclicSubmodule| + |evenlambert| |rootPower| |alphabetic?| |writeUInt8!| |categories| + |quoByVar| |hdmpToDmp| BY |decrease| |quadratic?| |dihedral| |radix| + |pointLists| |setOrder| |bandedHessian| |subNode?| |leftTrace| + |flatten| |subst| |bsolve| |bumptab1| |graeffe| |UP2ifCan| |e01bef| + SEGMENT |f07adf| |normInvertible?| |rem| |writeInt8!| |repSq| |se2rfi| + |seriesSolve| |setCondition!| |checkRur| |explicitEntries?| + |divideIfCan!| |any?| |clearTable!| |quo| |subSet| |setValue!| + |prologue| |mkAnswer| |string?| |OMlistCDs| + |unprotectedRemoveRedundantFactors| |getStream| |curveColor| + |numberOfPrimitivePoly| |expPot| |left| |youngDiagram| |apply| + |leaves| |iiasin| |lepol| |internalLastSubResultant| + |numberOfImproperPartitions| |shift| |readLineIfCan!| + |noLinearFactor?| |ocf2ocdf| |ldf2lst| |elliptic| |div| |right| + |mainPrimitivePart| |first| |mr| |objects| |attributeData| |epilogue| + |specialTrigs| |setUnion| |scale| |permutation| |exquo| |multisect| + |fortranLiteralLine| |rest| |directory| |rightRankPolynomial| |base| + |primitivePart!| |bumptab| |permutationRepresentation| |pattern| + |capacity| |cyclotomicDecomposition| NOT ~= |maxrank| + |rightScalarTimes!| |aromberg| |LyndonWordsList1| |mapdiv| + |rowEchelon| |resultant| |e04gcf| |formula| |#| OR |numberOfCycles| + |gcdPrimitive| |distribute| |mathieu12| |binaryTree| |coerceS| + |reduced?| |exponentialOrder| |twist| |zeroDimPrimary?| |function| + |nor| AND |complement| ~ |ldf2vmf| |removeSinhSq| |expint| |expandLog| + |algebraic?| |hue| |elementary| |redPo| |expr| |iiacot| |outerProduct| + |leftOne| |max| |squareFreePolynomial| |psolve| |points| |newLine| + |c06gsf| |mathieu22| |iiGamma| |concat| |airyBi| |upperCase!| + |semicolonSeparate| |B1solve| |conjugates| |every?| |/\\| + |matrixConcat3D| |nrows| |OMputError| |elRow2!| |solid?| + |doubleComplex?| |signature| |tRange| |mainVariable| + |linearDependence| |\\/| |ncols| |selectFiniteRoutines| |copies| + |chainSubResultants| |factorials| |paraboloidal| |fixedPointExquo| + |transform| |f02wef| |exponential| |product| |nextIrreduciblePoly| + |selectAndPolynomials| |repeatUntilLoop| |gbasis| |showClipRegion| + |qelt| |one?| |abs| |OMreceive| |OMputAtp| |squareFreeFactors| + |leadingIndex| |dec| |f04jgf| |arbitrary| |qsetelt| + |basisOfRightAnnihilator| |mapMatrixIfCan| |symbol| |coordinate| + |relationsIdeal| |showTheSymbolTable| |partialNumerators| |xRange| + |palgextint0| |enumerate| |expression| |expressIdealMember| |previous| + |critMonD1| |coord| |bytes| |pointData| |chebyshevT| |operators| + |yRange| |OMgetFloat| * |integer| |df2st| |OMencodingBinary| + |extractIndex| |stosePrepareSubResAlgo| |truncate| |Hausdorff| + |zRange| |imagj| |clearDenominator| |lighting| |rowEch| + |numberOfComponents| |hessian| |lastSubResultant| |e04naf| |lcm| + |map!| |wrregime| |univariatePolynomialsGcds| |s14abf| + |OMUnknownSymbol?| |halfExtendedSubResultantGcd1| |orbit| |argscript| + |exteriorDifferential| |primPartElseUnitCanonical| |weight| |qsetelt!| + |euclideanNormalForm| |smith| |OMputEndError| = |idealiserMatrix| + |viewPosDefault| |ran| |setAdaptive3D| |solve| |weights| + |complexLimit| |comment| |append| |variationOfParameters| + |setScreenResolution| |airyAi| |radicalSimplify| |outputList| + |isEquiv| |imagE| |mainMonomials| |d01amf| + |stoseIntegralLastSubResultant| |palgintegrate| |nilFactor| |qroot| + |d02cjf| |gcd| |integral| |fractionPart| |target| < |drawToScale| + |monomRDEsys| |tanAn| |OMgetEndAttr| |mesh| |solid| |complexExpand| + |false| |stoseInvertible?reg| |polyRDE| |commonDenominator| > + |iflist2Result| |df2ef| |front| |nextPrimitiveNormalPoly| + |subResultantGcdEuclidean| |functorData| |cond| |reindex| |mapCoef| + |content| |var1Steps| <= |roughBase?| |cot2tan| |e02bbf| |hermiteH| + |integralBasisAtInfinity| |topFortranOutputStack| |erf| |comp| |acsch| + |removeRedundantFactorsInPols| |square?| |d01gbf| >= + |regularRepresentation| |c06ecf| |coshIfCan| |rightFactorIfCan| + |s17def| |central?| |lazyGintegrate| |writeByte!| |closed?| |true| + |reverse!| |rk4| |subscriptedVariables| |structuralConstants| + |asechIfCan| |palgextint| |vectorise| |rootsOf| |compound?| |curry| + |acscIfCan| |alphabetic| |antisymmetric?| |fracPart| |digit| |dilog| + |c06fpf| |deepestTail| |rationalPoint?| + |factorset| |ref| + |multinomial| |powerSum| |critM| |setelt| |iisqrt2| |sin| |socf2socdf| + |rewriteIdealWithQuasiMonicGenerators| |denomRicDE| - |cdr| |degree| + |cExp| |po| |splitNodeOf!| |rootSimp| |cos| |dmpToHdmp| + |zeroSetSplitIntoTriangularSystems| |bringDown| / + |jvmIntegerConstantTag| |squareFree| |OMsupportsCD?| + |pointSizeDefault| |stopMusserTrials| |copy| |antiAssociative?| + |insertionSort!| |tan| |jvmFloatConstantTag| |set| |getMatch| + |conditionP| |arrayStack| |s15aef| |measure| |scalarMatrix| |prime?| + |readByte!| |cot| |inRadical?| |lflimitedint| |cAsin| + |currentCategoryFrame| |isAtom| |noKaratsuba| |iiatanh| |jvmProtected| + |pomopo!| |autoCoerce| |cRationalPower| |sec| |multMonom| |largest| + |explicitlyEmpty?| |intensity| |rightOne| |addiag| |e02dff| + |coerceImages| |zoom| |chvar| |csc| |setAdaptive| + |primPartElseUnitCanonical!| |goodPoint| |e02dcf| |iisin| + |isAbsolutelyIrreducible?| |f02ajf| |htrigs| |palginfieldint| |asin| + |var2StepsDefault| |e02ddf| |csc2sin| |tubePoints| |oddintegers| + |iifact| |cSech| |condition| |iicosh| |stFunc1| + |mainDefiningPolynomial| |unitNormalize| |acos| + |fortranCarriageReturn| |unitVector| |chineseRemainder| |OMUnknownCD?| + |tanQ| |fortranCompilerName| |ratpart| |hitherPlane| + |resultantReduitEuclidean| |jacobiIdentity?| |atan| |flexible?| + |atoms| |qinterval| |c06gcf| |mainSquareFreePart| |pseudoQuotient| + |s13aaf| |totalGroebner| |BumInSepFFE| |e02ahf| |acot| |eigenvector| + |primeFactor| |factorFraction| |mainContent| |depth| |changeName| + |interval| |tanNa| |null| |refine| |jokerMode| |knownInfBasis| + |lazyPseudoQuotient| |asec| |antiCommutative?| |setOfMinN| + |mergeFactors| |match?| |squareFreePrim| |root| |OMconnOutDevice| + |modifyPointData| |not| |aspFilename| |cAcosh| |acsc| |OMgetEndAtp| + |stoseInvertible?| |fortranComplex| |firstUncouplingMatrix| + |systemSizeIF| |startTableGcd!| |aQuadratic| |lllp| |parseString| + |contours| |sinh| |adjoint| |factorSFBRlcUnit| |prinpolINFO| |bit?| + |d01aqf| |f02axf| |reopen!| |fortranDouble| |pureLex| |simpson| |cosh| + |midpoint| |sh| |leastAffineMultiple| |optional?| |vertConcat| + |selectODEIVPRoutines| |headAst| |rarrow| |sort!| |rur| |tanh| + |brillhartTrials| |mightHaveRoots| |genericLeftTraceForm| |constant?| + |symbolIfCan| |tanhIfCan| |s21bbf| |tValues| |nand| |element?| |coth| + |pastel| |stFunc2| |setprevious!| |factorSquareFree| |cAsech| + |algebraicSort| |setEmpty!| |extend| |Vectorise| |sech| + |RemainderList| |replace| |rotate| |rightDiscriminant| |drawCurves| + |lhs| |meshPar2Var| |OMsend| |scopes| |shiftRight| |symmetric?| + |reorder| |csch| |constantOpIfCan| |approxSqrt| |e04dgf| |f02bjf| + |rhs| |rst| |var1StepsDefault| |generic| |powmod| + |completeEchelonBasis| |prinb| |asinh| |integralMatrix| |zeroMatrix| + |computeCycleLength| |OMgetEndBind| |basisOfLeftAnnihilator| |cyclic?| + |e01bgf| |nthr| |rightNorm| |getMultiplicationTable| |component| + |acosh| |length| |bracket| |real?| |realSolve| |width| + |carriageReturn| |generalLambert| |localUnquote| |integers| + |monicCompleteDecompose| |failed| |coordinates| |atanh| |scripts| + |argumentList!| |coth2tanh| |bigEndian| |groebner| |drawComplex| + |curryRight| |constantOperator| |unravel| |increment| |acoth| + |cycleLength| |iipow| |plotPolar| |hexDigit| |changeMeasure| + |getConstant| |jordanAlgebra?| |compile| |eyeDistance| |makeSin| + |toseLastSubResultant| |conjugate| |asech| |coefficient| |lfextlimint| + |zeroSetSplit| |generalizedInverse| |hspace| |exists?| |matrixGcd| + |SturmHabichtCoefficients| |monomials| |chiSquare| |rk4f| |typeList| + |linkToFortran| |unrankImproperPartitions0| |youngGroup| |viewpoint| + |differentialVariables| |complexEigenvalues| |OMgetVariable| |eval| + |isExpt| |enqueue!| |infix| |multiple| |sin2csc| + |exprHasLogarithmicWeights| |s17agf| |curveColorPalette| + |outlineRender| |showTheFTable| |create| |f02adf| + |generalInfiniteProduct| |iiexp| |applyQuote| |tablePow| + |symmetricSquare| |coHeight| |semiDiscriminantEuclidean| |superscript| + |optional| |heap| |purelyAlgebraicLeadingMonomial?| + |clearFortranOutputStack| |graphs| |leftMinimalPolynomial| |lyndon| + |rightUnits| |OMencodingSGML| |jvmPublic| |leadingCoefficientRicDE| + |d02gbf| |indicialEquationAtInfinity| |fill!| |push!| |colorFunction| + |lookup| |extendedResultant| |legendreP| |OMmakeConn| |makeop| + |computeInt| |fillPascalTriangle| |littleEndian| |jvmAbstract| + |irForm| |fractionFreeGauss!| |ruleset| |taylorRep| |viewThetaDefault| + |iiasinh| |OMreadStr| |f02xef| |shufflein| |coleman| + |nativeModuleExtension| |f2st| |frobenius| |simpsono| + |invertibleElseSplit?| |rightQuotient| |getVariableOrder| |Ci| + |halfExtendedResultant2| |generalPosition| |radicalRoots| + |definingPolynomial| |scanOneDimSubspaces| |updatD| + |internalInfRittWu?| |antiCommutator| |clikeUniv| |bottom!| + |FormatRoman| |iiacsch| |selectSumOfSquaresRoutines| |putProperties| + |arguments| |OMgetApp| |suchThat| |padicFraction| |phiCoord| + |resetBadValues| |pToDmp| |complexNumericIfCan| |newTypeLists| + |ip4Address| |printTypes| |transpose| |removeDuplicates| |has?| + |s21bcf| |lastSubResultantElseSplit| |mapSolve| |iExquo| |prod| + |mapDown!| |internalSubQuasiComponent?| |getCode| |compBound| + |fullDisplay| |setIntersection| |members| |factorial| |RittWuCompare| + |cycleRagits| |scan| |makeprod| |dom| |jvmTransient| |nil| |child| + |nullSpace| |cosh2sech| |polyPart| |nullity| |incrementKthElement| + |logIfCan| |delta| |evaluate| |obj| |unit?| |insert| |OMread| |recur| + |subResultantChain| |expenseOfEvaluationIF| |initial| |nthFlag| + |identity| |s14baf| |freeOf?| |lazyPseudoRemainder| |secIfCan| + |convert| |clipPointsDefault| |key?| |slash| |cyclotomic| + |constantKernel| |elaborate| |symmetricPower| |badValues| + |approximate| |op| |algebraicVariables| |jordanAdmissible?| + |partitions| |mathieu24| |solveRetract| |startTableInvSet!| + |setProperty| |complex| |printHeader| |LagrangeInterpolation| + |clipSurface| |listConjugateBases| |jacobi| |HermiteIntegrate| + |nextLatticePermutation| |reduceBasisAtInfinity| |numer| |OMgetAtp| + |polygamma| |arity| |equiv| |e02zaf| |viewPhiDefault| |rotatey| + |f07fef| |logpart| |denom| |horizontalTab| |trace2PowMod| + |genericLeftMinimalPolynomial| |pushdown| |balancedFactorisation| + |intPatternMatch| |create3Space| |processTemplate| |inverseLaplace| + |internalIntegrate0| |c05pbf| |imagK| |cyclicEntries| |lambda| + |messagePrint| |multiplyExponents| |laplacian| |pi| |alphanumeric?| + |setLegalFortranSourceExtensions| |cylindrical| |firstDenom| |sin?| + |rightMinimalPolynomial| |curryLeft| |rootPoly| |routines| + |fractRadix| |infinity| |testDim| |makeFloatFunction| |iisinh| + |measure2Result| |colorDef| |fixedPoints| |poisson| |getOperator| + |times!| |resultantReduit| |nthCoef| |useSingleFactorBound| + |singular?| |updatF| |totalDegree| |c06gqf| |maxPoints| + |sturmSequence| |unmakeSUP| |quoted?| |infLex?| |irVar| |setPoly| + |binding| |call| |realEigenvectors| |gcdcofact| |e02daf| |iiasec| + |OMencodingUnknown| |kernel| |oblateSpheroidal| |diagonal| + |OMgetError| |OMunhandledSymbol| |numFunEvals| |graphCurves| + |OMgetBVar| |closedCurve| |getGoodPrime| |cyclicSubmodule| |declare| + |list| |associatorDependence| |linGenPos| |hMonic| |connectTo| + |iidprod| |sizeMultiplication| |quasiMonic?| |draw| |update| + |coefChoose| |OMsetEncoding| |integralDerivationMatrix| + |lastSubResultantEuclidean| |currentEnv| |ef2edf| |blankSeparate| + |f02aef| |graphState| |readInt32!| |separateFactors| |sinhIfCan| + |charClass| |maxRowIndex| |iilog| |d03edf| + |inverseIntegralMatrixAtInfinity| |s18aff| |rubiksGroup| |zCoord| + |empty?| |att2Result| |normalized?| |mapUnivariateIfCan| + |definingEquations| |nullary?| |coth2trigh| |vedf2vef| |aLinear| + |putProperty| |selectOptimizationRoutines| |integerIfCan| |modulus| + |stoseInvertibleSetsqfreg| |substring?| |showIntensityFunctions| + |fortranTypeOf| |makeObject| |tanintegrate| |removeSinSq| + |numberOfIrreduciblePoly| |magnitude| |createNormalPrimitivePoly| + |shiftLeft| |closed| |headReduced?| |s17adf| |mantissa| |coef| + |appendPoint| |removeZero| |jvmUTF8ConstantTag| |coerceListOfPairs| + |properties| |hash| |irreducible?| |reify| + |tryFunctionalDecomposition| |trapezoidal| |suffix?| |laguerreL| + |OMputVariable| |jvmFinal| |selectOrPolynomials| |property| + |discriminantEuclidean| |count| |iibinom| |minGbasis| |jvmSuper| + |translate| |invertIfCan| |OMputEndApp| |safeFloor| + |expenseOfEvaluation| |interpolate| |hexDigit?| |createZechTable| + |edf2efi| |generator| |rk4qc| |prefix?| |child?| |subTriSet?| + |numberOfVariables| |f02bbf| |OMputEndBVar| |divide| |optimize| + |OMParseError?| |infiniteProduct| |flagFactor| |tracePowMod| |solveid| + |separant| |repeating| |argument| |conical| |GospersMethod| + |setchildren!| |traceMatrix| |semiSubResultantGcdEuclidean2| + |jvmVolatile| |complexNumeric| |torsionIfCan| |sinIfCan| + |fortranInteger| |gensym| |schwerpunkt| |li| |singularitiesOf| + |finiteBasis| |e02bcf| |fortranDoubleComplex| |taylorQuoByVar| + |positiveSolve| |ipow| |floor| |eigenvalues| |debug3D| |clip| |ravel| + |quotient| |s17ajf| |s19abf| F2FG |deepestInitial| |kernels| + |splitDenominator| |extendedint| |hostPlatform| |leastPower| |rename| + |addMatch| |nthRoot| |reshape| |primes| |compose| |indicialEquation| + |euler| |node?| |operator| |primextendedint| |inconsistent?| + |realZeros| |rischDEsys| |symbolTable| |rightAlternative?| |Lazard| + |part?| |numberOfComposites| |someBasis| |changeThreshhold| |lprop| + |noValueMode| |empty| |complexNormalize| |leaf?| |infix?| |vark| + |green| |separateDegrees| |listOfLists| |endSubProgram| |initials| + |substitute| |univariate| |bfEntry| |pushFortranOutputStack| |froot| + |setVariableOrder| |mask| |support| |hdmpToP| |char| |printStats!| + |expandTrigProducts| |even?| |alternatingGroup| |stronglyReduced?| + |iisqrt3| |cCsch| |OMputEndAttr| |select!| |popFortranOutputStack| + |solveLinearPolynomialEquationByFractions| |rangePascalTriangle| + |cCos| |characteristic| |pseudoDivide| |shuffle| |mat| |incr| + |LyndonCoordinates| |outputAsScript| |pair?| |outputAsFortran| + |coercePreimagesImages| |tree| |lfintegrate| |internalAugment| + |extractBottom!| |gcdPolynomial| |linearAssociatedOrder| |factor| |hi| + |increase| |Gamma| |setTex!| |viewDeltaYDefault| |shape| + |sumOfDivisors| |karatsubaOnce| LODO2FUN |iiacos| |components| + |semiResultantEuclidean2| |sqrt| |morphism| |numberOfFractionalTerms| + |dmpToP| |pop!| |lowerPolynomial| |color| |float| |comparison| + |iiacsc| |groebner?| |rename!| |An| |real| |setLength!| |getlo| + |createMultiplicationTable| |groebnerIdeal| |setErrorBound| |category| + |say| |reciprocalPolynomial| |squareTop| |symmetricProduct| |more?| + |indiceSubResultant| |imag| |chiSquare1| |middle| |groebgen| + |outputBinaryFile| |removeDuplicates!| |domain| |directProduct| + |iisec| |allRootsOf| |charpol| |ratDsolve| |quotientByP| |position| + |nextsousResultant2| |rootOf| |ptFunc| |d02bbf| |screenResolution3D| + |package| |btwFact| |eq| |modularGcd| |parts| + |solveLinearPolynomialEquation| |removeRedundantFactorsInContents| + |lfunc| |critMTonD1| |baseRDEsys| |d02kef| |OMwrite| |acoshIfCan| + |iter| |iomode| |fintegrate| |build| |s21bdf| |inHallBasis?| |brace| + |fortranCharacter| |s14aaf| |listRepresentation| + |removeSuperfluousQuasiComponents| |prefix| |subHeight| |fmecg| + |zeroDimensional?| |mdeg| |imagk| |untab| |clipParametric| |destruct| + |getRef| |nextPrime| |number?| |countRealRootsMultiple| + |genericPosition| |nextSublist| |readable?| |d03eef| |perfectSqrt| + |adaptive3D?| |charthRoot| |kroneckerDelta| |rationalIfCan| + |modifyPoint| |roughSubIdeal?| |options| |pseudoRemainder| + |finiteBound| |constructor| |monic?| |startStats!| |lazyVariations| + |symbol?| |modularFactor| |lowerCase?| |character?| |lazyResidueClass| + |evenInfiniteProduct| |vector| |sample| GE |close!| |headRemainder| + |degreePartition| |addmod| |hasHi| |before?| |verticalTab| |belong?| + |consnewpol| |string| |differentiate| |d01alf| GT |OMputInteger| + |reseed| |permanent| |exactQuotient| |identitySquareMatrix| |monomial| + |interpret| |OMgetAttr| |monicDecomposeIfCan| |OMopenFile| |twoFactor| + |symFunc| LE |exp| |alphanumeric| |sec2cos| |matrixDimensions| + |strongGenerators| |testModulus| |multivariate| |generate| |biRank| + |partialQuotients| |find| |setPrologue!| |quasiRegular| LT |shellSort| + |rightExactQuotient| |computeCycleEntry| |dominantTerm| |totolex| + |variables| |cup| |definingInequation| |setleaves!| |innerint| + |e01sff| |associator| |overbar| |zeroOf| |xn| |normalizedDivide| + |scaleRoots| |incrementBy| |elRow1!| |UpTriBddDenomInv| |alternative?| + |karatsubaDivide| |traverse| |pol| |list?| |startPolynomial| + |addPointLast| |generalizedEigenvectors| + |generalizedContinuumHypothesisAssumed?| |expand| |bitCoef| + |sech2cosh| |setPredicates| |setClosed| |primlimintfrac| |prinshINFO| + |interpretString| |putColorInfo| |lexTriangular| |janko2| |derivative| + |filterWhile| |shiftRoots| |completeHensel| |insertRoot!| + |stiffnessAndStabilityOfODEIF| |topPredicate| GF2FG + |subresultantSequence| |tensorProduct| |expt| |fixedDivisor| + |filterUntil| |OMgetSymbol| |simplify| |mainVariable?| |tanh2trigh| + |doubleResultant| |createIrreduciblePoly| |Is| |brillhartIrreducible?| + |combineFeatureCompatibility| |predicates| |taylor| |firstSubsetGray| + |select| |cAcsch| |lazyPremWithDefault| |hasSolution?| |signatureAst| + |ksec| |height| |s17acf| |stoseSquareFreePart| |printCode| + |irreducibleRepresentation| |doubleDisc| |laurent| |reduceLODE| + |OMreadFile| |cycleEntry| |sts2stst| |cAsec| |firstNumer| + |tryFunctionalDecomposition?| |zero| |redPol| |cache| |singRicDE| + |getDatabase| |escape| |puiseux| |stack| |OMencodingXML| |normal01| + |maxint| |normDeriv2| |check| |insert!| |rightMult| |id| + |showTheIFTable| |restorePrecision| |goodnessOfFit| |trunc| + |associatedEquations| |rspace| |opeval| |numFunEvals3D| |setMinPoints| + |subResultantGcd| |tubeRadius| |And| |safetyMargin| |isOpen?| |lo| + |quatern| |inv| |isImplies| |dfRange| |sturmVariationsOf| |ratDenom| + |rational?| |f01ref| |dequeue| |Or| |linears| |LazardQuotient| |step| + |lquo| |ground?| |wholeRadix| |const| |minus!| |leftUnits| |laguerre| + |realElementary| |rationalApproximation| |external?| |Not| + |systemCommand| |units| |sumOfSquares| |eisensteinIrreducible?| + |ground| |extractPoint| |norm| |bat| |wreath| |relerror| + |printStatement| |style| |seed| |leadingExponent| |difference| + |logical?| |leadingMonomial| |unitNormal| |changeBase| |solve1| + |palglimint0| |integralRepresents| |weakBiRank| |nthExpon| |normal| + |trim| |palgLODE| |d01akf| |double| |leadingCoefficient| + |linearElement| |stopTableInvSet!| |associates?| |wholeRagits| |cSec| + |s15adf| |parents| |nthExponent| |cycleTail| |rightRecip| + |minimumDegree| |primitiveMonomials| |queue| |cyclotomicFactorization| + |userOrdered?| |commutative?| |divisors| |ffactor| |log10| + |determinant| |isOr| |henselFact| |genericLeftTrace| + |univariatePolynomial| |polygon?| |reductum| |nonLinearPart| |e04jaf| + |makeRecord| |totalLex| |bitand| |lagrange| |code| |innerEigenvectors| + |selectfirst| |OMputBind| |setMaxPoints| |elseBranch| |ParCondList| + |f02agf| |exprHasAlgebraicWeight| |dot| |maximumExponent| |bitior| + |LyndonBasis| |rroot| |modTree| |c06fuf| |monicDivide| |deref| + |getProperty| |PollardSmallFactor| |OMgetType| |createGenericMatrix| + |showTheRoutinesTable| |leftRank| |leftPower| |numberOfHues| + |bipolarCylindrical| |entry| |s01eaf| |s19aaf| + |semiIndiceSubResultantEuclidean| |cn| |iitanh| |reducedQPowers| + |quadratic| |removeRoughlyRedundantFactorsInPols| |elem?| + |compiledFunction| |semiDegreeSubResultantEuclidean| + |lazyIrreducibleFactors| |curve| |s17dhf| |uniform| |KrullNumber| + |cons| |declare!| |tail| |minimize| |SFunction| |commaSeparate| |goto| + |groebnerFactorize| |OMgetEndBVar| |clipBoolean| |c06eaf| + |fixPredicate| |univcase| |datalist| |exp1| |monomRDE| |anticoord| + |algintegrate| |lifting| |dark| |float?| + |semiLastSubResultantEuclidean| |normalizedAssociate| |sparsityIF| + |c02aff| |semiResultantReduitEuclidean| |callForm?| + |fullPartialFraction| |mathieu23| |deriv| |extract!| |contract| + |partialFraction| |setvalue!| |integralCoordinates| + |linearlyDependent?| |FormatArabic| |lazyIntegrate| + |localIntegralBasis| |eq?| |factors| |reverse| |principalIdeal| + |ridHack1| |member?| |minimalPolynomial| |npcoef| |distdfact| |source| + |pointColorDefault| |failed?| |parametersOf| |signAround| + |returnTypeOf| |selectsecond| |roughEqualIdeals?| |outputArgs| + |sinhcosh| |basicSet| |pushup| |hclf| |basisOfCentroid| |maxIndex| + |putGraph| |mainKernel| |integer?| |updateStatus!| |distFact| + |printInfo| |dimensionOfIrreducibleRepresentation| |expintegrate| + |segment| |perspective| |bitTruth| |intChoose| |e02baf| |point| + |getCurve| |concat!| |eof?| |characteristicPolynomial| |subtractIfCan| + |outputGeneral| |uniform01| |virtualDegree| |void| |outputForm| + |positive?| |getSyntaxFormsFromFile| |harmonic| |imagJ| + |sizePascalTriangle| |complexEigenvectors| |permutations| |inc| + |seriesToOutputForm| |presuper| |open?| |setref| |sylvesterSequence| + |readIfCan!| |integralMatrixAtInfinity| |OMgetEndObject| |llprop| Y + |bezoutMatrix| |mappingMode| |sizeLess?| |genericRightTraceForm| + |f04atf| |series| |associative?| |bernoulliB| |multiEuclideanTree| + |exprToGenUPS| |tan2cot| |resetNew| |randomLC| |isConnected?| + |cschIfCan| |rCoord| |linearDependenceOverZ| |basisOfCenter| + |toseInvertibleSet| |removeZeroes| |tubePointsDefault| |iiasech| + |bandedJacobian| |high| |key| |parabolicCylindrical| + |permutationGroup| |supRittWu?| |atom?| |connect| |bivariate?| + |nullary| |safeCeiling| |makeViewport3D| |graphStates| |getZechTable| + |leftCharacteristicPolynomial| |extendedIntegrate| |OMputEndObject| + |nothing| |exptMod| |normalDeriv| |e02ajf| |pmintegrate| + |setButtonValue| |s20adf| |filename| |readInt8!| |min| + |nonSingularModel| |powern| |numberOfChildren| |fixedPoint| + |asinhIfCan| |isNot| |PDESolve| |recoverAfterFail| |newReduc| + |constantIfCan| |rightRank| |gcdcofactprim| |index?| |mapExpon| + |f07aef| |solveLinearlyOverQ| |antisymmetricTensors| |hex| |cubic| + |bitLength| |lowerCase!| |nextNormalPoly| |parse| |moebius| + |showArrayValues| |rootSplit| |listBranches| |setFormula!| |infinite?| + |limitedIntegrate| |crushedSet| |explogs2trigs| |c06gbf| |localReal?| + |vconcat| |normalForm| |mkcomm| |lSpaceBasis| |OMsupportsSymbol?| + |redmat| |ratPoly| |jvmStrict| |prem| |composites| |acschIfCan| + |polar| |categoryMode| |setDifference| |elColumn2!| |swap!| |isPower| + |radicalSolve| |uncouplingMatrices| |sqfrFactor| |defineProperty| + |common| |singularAtInfinity?| |qfactor| |c05nbf| |rootDirectory| + |mapmult| |qualifier| |makeSUP| |identification| |repeating?| + |atanIfCan| |genus| |fprindINFO| |f02akf| |transcendenceDegree| + |genericRightNorm| |linearPolynomials| |sPol| |pushuconst| |ricDsolve| + |characteristicSerie| |e02adf| |collectQuasiMonic| |iisech| |s13adf| + |normal?| |rombergo| |cAcos| |drawComplexVectorField| |rightRemainder| + |OMlistSymbols| |f02aff| |taylorIfCan| |semiResultantEuclidean1| + |resultantnaif| |perfectNthPower?| |badNum| |palgLODE0| |d01apf| + |cycleSplit!| |linearlyDependentOverZ?| |name| |applyRules| + |evaluateInverse| |bombieriNorm| |thenBranch| |trigs| |algebraicOf| + |selectPolynomials| |spherical| |changeVar| |getExplanations| |body| + |internalIntegrate| |showScalarValues| |perfectSquare?| |invertible?| + |leftNorm| |nextColeman| |linearForm| |coerceP| |euclideanGroebner| + |gderiv| |keys| |rowEchelonLocal| |showRegion| |quadraticNorm| + |scripted?| |hypergeometric0F1| |mix| |postfix| |dictionary| + |selectIntegrationRoutines| |idealSimplify| |deepExpand| |open| + |position!| |leftFactorIfCan| |e02akf| |setrest!| |isMult| |reduction| + |lazyPseudoDivide| |shrinkable| |viewSizeDefault| |moebiusMu| |index| + |just| |range| |lazyPquo| |setleft!| |d01fcf| |bothWays| + |monicRightFactorIfCan| |loopPoints| |setLabelValue| |cAsinh| |imagi| + |lambert| |inf| |nthRootIfCan| |tubePlot| |tableForDiscreteLogarithm| + |identityMatrix| |makingStats?| |input| |integralBasis| |rank| + |hasoln| |removeCoshSq| |iiabs| |pair| |pdf2ef| |merge| |imagI| + |divideExponents| |s18aef| |tan2trig| |library| |status| + |factorSquareFreeByRecursion| |stopTable!| |error| |leadingIdeal| + |basisOfRightNucloid| |operations| |rangeIsFinite| |rightGcd| + |makeGraphImage| |UnVectorise| |BasicMethod| |purelyAlgebraic?| |ode2| + |lookupFunction| |baseRDE| |s17dlf| |setProperties| |nary?| + |meshFun2Var| |shade| |f04qaf| |limitPlus| |getMeasure| |rightTrim| + |setColumn!| |conjunction| |infRittWu?| |resize| |pointColor| + |completeEval| |port| |module| |nodeOf?| |diophantineSystem| |minrank| + |leftTrim| |integrate| |divideIfCan| |sortConstraints| |fibonacci| + |setAttributeButtonStep| |highCommonTerms| |cAtanh| |roman| |augment| + |infinityNorm| |multiplyCoefficients| |atanhIfCan| |s18acf| |mainForm| + |createPrimitiveElement| |fortranReal| |lineColorDefault| + |jvmDoubleConstantTag| |padecf| |neglist| |f02fjf| + |complementaryBasis| |ellipticCylindrical| |validExponential| |red| + |t| |continuedFraction| |extendedSubResultantGcd| |setMinPoints3D| + |currentSubProgram| |genericRightDiscriminant| |primitivePart| + |bubbleSort!| |lists| |complexZeros| |inverse| |lazy?| + |numberOfOperations| |forLoop| |f2df| |quasiComponent| + |reducedContinuedFraction| |primlimitedint| |jvmLongConstantTag| |in?| + |randnum| |subscript| |reverseLex| |laurentIfCan| |cAtan| + |roughBasicSet| |ScanRoman| |super| |linear?| |moreAlgebraic?| + |returnType!| |moduloP| |buildSyntax| |nonQsign| |f04axf| + |dihedralGroup| |nthFactor| |monicRightDivide| |intermediateResultsIF| + |superHeight| |viewZoomDefault| |elaboration| |functionIsOscillatory| + |factorList| |chebyshevU| |HenselLift| |rule| |weierstrass| + |decreasePrecision| |createMultiplicationMatrix| |univariateSolve| + |linearMatrix| |solveInField| |inrootof| |jvmInterface| + |rootOfIrreduciblePoly| |exponent| |d01asf| |overlabel| + |getProperties| |dflist| |cap| |stoseInvertible?sqfreg| + |trailingCoefficient| |symmetricDifference| |imports| |e02gaf| + |intersect| |cyclicCopy| |doublyTransitive?| |nsqfree| |simpleBounds?| + |iFTable| |wholePart| |rewriteIdealWithRemainder| ** + |leftAlternative?| |rightRegularRepresentation| |f04arf| + |subresultantVector| |double?| |currentScope| |convergents| |cyclic| + |show| |complex?| |minIndex| |reducedSystem| |powers| + |leftRankPolynomial| |patternVariable| |showFortranOutputStack| + |revert| |f02aaf| |rationalPower| |rootBound| |palgRDE| |gcdprim| + |inputOutputBinaryFile| |distance| + |solveLinearPolynomialEquationByRecursion| |simplifyPower| + |radicalEigenvector| |leftGcd| |medialSet| |surface| |e01sef| |trace| + |minRowIndex| RF2UTS |complexRoots| |conditionsForIdempotents| + |setMaxPoints3D| |getMultiplicationMatrix| |insertMatch| + |absolutelyIrreducible?| |startTable!| |outputMeasure| |sumSquares| + |moduleSum| |retract| |dim| |factorByRecursion| |cosIfCan| |generic?| + |setScreenResolution3D| |jacobian| |qPot| |ramifiedAtInfinity?| + |leftReducedSystem| |f01brf| |OMopenString| |remove!| |bfKeys| + |sdf2lst| |setRow!| |viewport3D| |upperCase?| |kmax| |f01rdf| + |leftExactQuotient| |preprocess| |clipWithRanges| |triangular?| + |d01ajf| |rationalPoints| |lazyEvaluate| |d01bbf| |drawStyle| + |plusInfinity| |corrPoly| |univariatePolynomials| |binarySearchTree| + |f04mcf| |overlap| |denominators| |zerosOf| |xCoord| + |oddInfiniteProduct| |e01sbf| |minusInfinity| |droot| |sechIfCan| + |stirling2| |cyclePartition| |inR?| |saturate| |tubeRadiusDefault| + |s17aff| |lowerBound| |rightLcm| |rightTraceMatrix| |s18def| |lintgcd| + |yCoord| |compdegd| |predicate| |explimitedint| |lex| + |reducedDiscriminant| |column| |besselK| |digit?| |complete| + |clearTheIFTable| |abelianGroup| |kind| |OMputFloat| + |initializeGroupForWordProblem| |nextNormalPrimitivePoly| + |checkPrecision| |outputFixed| |halfExtendedSubResultantGcd2| + |generateIrredPoly| |complexForm| |balancedBinaryTree| |elliptic?| + |implies| |innerSolve| |nil?| |d02bhf| |s17ahf| |transcendent?| + |pointColorPalette| |d01gaf| |leadingBasisTerm| |pushucoef| + |enterPointData| |homogeneous?| |wordInGenerators| + |internalZeroSetSplit| |type| |bindings| |write!| |constant| + |symmetricGroup| |OMputObject| |bivariatePolynomials| |normalElement| + |OMgetString| |stronglyReduce| |operation| |wordsForStrongGenerators| + |formfeed| |palgint| |branchIfCan| |extractClosed| |totalDifferential| + |optAttributes| |precision| |space| |useNagFunctions| |irDef| |f04maf| + |collect| |e04mbf| |ode| |notelem| |critpOrder| |setnext!| |showAll?| + |minPol| |coerce| |partialDenominators| |light| |leadingTerm| + |polyRicDE| |retractIfCan| |slex| |numberOfMonomials| + |useEisensteinCriterion| |f04adf| |dmp2rfi| |construct| |karatsuba| + |laurentRep| |oneDimensionalArray| |nextPartition| |size?| + |integralAtInfinity?| |assert| |unitsColorDefault| |jvmStatic| + |findBinding| |subNodeOf?| |basisOfCommutingElements| |blue| |next| + |leftTraceMatrix| |iteratedInitials| |power| |nextSubsetGray| + |unrankImproperPartitions1| |parameters| |redpps| |merge!| |variable| + |primeFrobenius| |second| |OMclose| |vspace| |unary?| |mapBivariate| + |screenResolution| |indicialEquations| |solveLinear| |iterators| + |LowTriBddDenomInv| UTS2UP |pdf2df| |third| |isobaric?| |row| + |cot2trig| |numericalIntegration| |linear| |mkPrim| |getBadValues| + |critB| |stiffnessAndStabilityFactor| |cAcot| |rightExtendedGcd| + |pade| |qqq| |generalizedEigenvector| |Si| |mainMonomial| |prindINFO| + |realRoots| |setTopPredicate| |fglmIfCan| |squareFreeLexTriangular| + |makeUnit| |changeNameToObjf| |polynomial| |withPredicates| |cfirst| + |palgint0| |semiResultantEuclideannaif| + |selectMultiDimensionalRoutines| |countable?| |omError| |tower| |is?| + |certainlySubVariety?| |radicalEigenvalues| |createThreeSpace| + |mpsode| |extractTop!| |symbolTableOf| |binomThmExpt| + |nthFractionalTerm| |var2Steps| |mapUnivariate| |writeLine!| + |principalAncestors| |cyclicEqual?| |sup| |minset| |tube| |entries| + |exQuo| |leftMult| |genericLeftDiscriminant| |choosemon| |radPoly| + |rational| |listOfMonoms| |getIdentifier| |minPoints3D| |s18dcf| + |rdHack1| |cPower| |e01saf| |mesh?| |endOfFile?| |bounds| |host| + |toseInvertible?| |isPlus| |invertibleSet| |any| |findConstructor| + |symmetricRemainder| |sincos| |fortranLogical| |makeSeries| |schema| + |createPrimitiveNormalPoly| |pdct| |leader| |iiatan| |e01bff| + |disjunction| |OMconnInDevice| |map| |numberOfFactors| |extension| + |subCase?| |c06frf| |radicalEigenvectors| |leftUnit| |initTable!| + |newline| |e02aef| |jvmPrivate| |iCompose| |removeSquaresIfCan| + |reset| |dioSolve| |resultantEuclideannaif| |constantLeft| + |OMconnectTCP| |pmComplexintegrate| |computePowers| |elaborateFile| + |gramschmidt| |low| |jvmInterfaceMethodConstantTag| |removeCosSq| + |s19acf| |accuracyIF| |e02bdf| |constantCoefficientRicDE| |lp| |unit| + |minimumExponent| |initiallyReduce| |write| |extendedEuclidean| + |limit| |over| |pquo| |getOperands| |region| |autoReduced?| + |shanksDiscLogAlgorithm| |save| |bright| |extractSplittingLeaf| + |makeViewport2D| |typeForm| |randomR| |basisOfRightNucleus| + |lieAdmissible?| |splitLinear| |euclideanSize| |quote| + |zeroSquareMatrix| |eulerPhi| |reduceByQuasiMonic| |extensionDegree| + |LyndonWordsList| |possiblyInfinite?| |linearPart| |triangSolve| + |degreeSubResultant| |primitive?| |s13acf| |logGamma| |algint| + |c05adf| |getGraph| |toroidal| |mulmod| |getPickedPoints| |iiperm| + |e04ucf| |primintegrate| |diagonals| |mirror| |expintfldpoly| + |denominator| |besselJ| |jvmNative| |setFieldInfo| |upperCase| + |c06fqf| |s20acf| |computeBasis| |car| |categoryFrame| |acothIfCan| + |leftScalarTimes!| |integral?| |factorOfDegree| |s17dgf| |isTimes| + |orbits| |numeric| |inGroundField?| |leftRemainder| |sign| + |OMgetInteger| |approximants| |toScale| |cycles| |less?| |romberg| + |radical| |basis| |representationType| |sumOfKthPowerDivisors| + |isList| |rk4a| |pushNewContour| |legendre| |discriminant| |addPoint| + |nextsubResultant2| |mergeDifference| |monomial?| + |noncommutativeJordanAlgebra?| |createNormalElement| |sqfree| + |cartesian| |universe| |exprToUPS| |sort| |splitSquarefree| + |linearAssociatedLog| |divisor| |thetaCoord| |irreducibleFactor| + |tableau| |inputBinaryFile| |internalDecompose| |ode1| + |integralLastSubResultant| |fTable| |stoseInvertibleSetreg| |Lazard2| + |radicalOfLeftTraceForm| |dimensionsOf| |plot| |interactiveEnv| + |hasTopPredicate?| |rightDivide| |random| |decomposeFunc| + |nextPrimitivePoly| |f07fdf| |byteBuffer| |bezoutDiscriminant| |lift| + |quadraticForm| |invmultisect| |clearTheFTable| |trigs2explogs| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 5de6e5cf..39a4be71 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5471 +1,5471 @@ -(3472733 . 3505945391) -((-1624 (((-114) (-1 (-114) |#2| |#2|) $) 86 T ELT) (((-114) $) NIL T ELT)) (-4204 (($ (-1 (-114) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-2721 ((|#2| $ (-560) |#2|) NIL T ELT) ((|#2| $ (-1264 (-560)) |#2|) 44 T ELT)) (-1828 (($ $) 80 T ELT)) (-3449 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3483 (((-560) (-1 (-114) |#2|) $) 27 T ELT) (((-560) |#2| $) NIL T ELT) (((-560) |#2| $ (-560)) 96 T ELT)) (-4088 (((-663 |#2|) $) 13 T ELT)) (-2026 (($ (-1 (-114) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-3181 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-2358 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-1830 (($ |#2| $ (-560)) NIL T ELT) (($ $ $ (-560)) 67 T ELT)) (-3511 (((-3 |#2| "failed") (-1 (-114) |#2|) $) 29 T ELT)) (-2245 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2157 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1233)) ((-95) |has| |#1| (-1233)) ((-102) . T) ((-111 #0# #0#) -2157 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2157 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2157 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-887)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1051)) ((-633 (-171 (-391))) |has| |#1| (-1051)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-633 #1=(-1201 |#1|)) . 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T) ((-236 $) -2157 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2157 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-668 (-560)) -2157 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2157 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1080)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-670 |#2|) -2157 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2157 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-660 |#2|) |has| |#2| (-1080)) ((-739 |#2|) -2157 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1080)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-871) -2157 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2157 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1207)) -2157 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-927 (-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) ((-929 #3#) -2157 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-1069 #0#) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-1069 (-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ((-1069 |#2|) |has| |#2| (-1132)) ((-1082 |#2|) -2157 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2157 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1088) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1132) -2157 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1247) . T) ((-1305 |#2|) |has| |#2| (-376))) -((-2264 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-4352 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-3246 (($ (-948)) 62 (|has| |#2| (-1080)) ELT)) (-1553 (((-1303) $ (-560) (-560)) NIL (|has| $ (-6 -4509)) ELT)) (-3976 (($ $ $) 68 (|has| |#2| (-815)) ELT)) (-1541 (((-3 $ "failed") $ $) 53 (|has| |#2| (-133)) ELT)) (-4434 (((-114) $ (-793)) NIL T ELT)) (-1966 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-2721 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4509)) ELT)) (-4143 (($) NIL T CONST)) (-3969 (((-3 (-560) "failed") $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-3 (-421 (-560)) "failed") $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1132)) ELT)) (-3665 (((-560) $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-421 (-560)) $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) ((|#2| $) 28 (|has| |#2| (-1132)) ELT)) 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T) ((-102) -2188 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2188 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2188 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-635 (-560)) -2188 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132)))) ((-635 |#2|) |has| |#2| (-1132)) ((-632 (-887)) -2188 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-887))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1297 |#2|)) . T) ((-236 $) -2188 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2188 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-668 (-560)) -2188 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2188 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1080)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-670 |#2|) -2188 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2188 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-660 |#2|) |has| |#2| (-1080)) ((-739 |#2|) -2188 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1080)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-871) -2188 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2188 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1207)) -2188 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-927 (-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080))) ((-929 #3#) -2188 (-12 (|has| |#2| (-929 (-1207))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) ((-1069 #0#) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-1069 (-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ((-1069 |#2|) |has| |#2| (-1132)) ((-1082 |#2|) -2188 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2188 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1088) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1132) -2188 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1247) . T) ((-1305 |#2|) |has| |#2| (-376))) +((-2177 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-1529 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-2510 (($ (-948)) 62 (|has| |#2| (-1080)) ELT)) (-3773 (((-1303) $ (-560) (-560)) NIL (|has| $ (-6 -4509)) ELT)) (-4297 (($ $ $) 68 (|has| |#2| (-815)) ELT)) (-3651 (((-3 $ "failed") $ $) 53 (|has| |#2| (-133)) ELT)) (-4218 (((-114) $ (-793)) NIL T ELT)) (-1706 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-2425 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4509)) ELT)) (-3282 (($) NIL T CONST)) (-4207 (((-3 (-560) "failed") $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-3 (-421 (-560)) "failed") $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1132)) ELT)) (-4080 (((-560) $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-421 (-560)) $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) ((|#2| $) 28 (|has| |#2| (-1132)) ELT)) 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T) ((-571) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2157 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2157 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1247) . T) ((-1252) |has| |#1| (-939))) -((-2264 (((-114) $ $) 20 (|has| |#1| (-102)) ELT)) (-2283 ((|#1| $) 55 T ELT)) (-3273 ((|#1| $) 45 T ELT)) (-4434 (((-114) $ (-793)) 8 T ELT)) (-4143 (($) 7 T CONST)) (-2977 (($ $) 61 T ELT)) (-1828 (($ $) 49 T ELT)) (-3578 ((|#1| |#1| $) 47 T ELT)) (-2405 ((|#1| $) 46 T ELT)) (-4088 (((-663 |#1|) $) 31 (|has| $ (-6 -4508)) ELT)) (-3802 (((-114) $ (-793)) 9 T ELT)) (-2813 (((-663 |#1|) $) 30 (|has| $ (-6 -4508)) ELT)) (-1473 (((-114) |#1| $) 28 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-3181 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4509)) ELT)) (-2358 (($ (-1 |#1| |#1|) $) 36 T ELT)) (-2591 (((-114) $ (-793)) 10 T ELT)) (-4170 (((-793) $) 62 T ELT)) (-2297 (((-1189) $) 23 (|has| |#1| (-1132)) ELT)) (-1905 ((|#1| $) 40 T ELT)) (-3611 ((|#1| |#1| $) 53 T ELT)) (-2514 ((|#1| |#1| $) 52 T ELT)) (-4156 (($ |#1| $) 41 T ELT)) (-4293 (((-793) $) 56 T ELT)) (-3302 (((-1151) $) 22 (|has| |#1| (-1132)) ELT)) (-1825 ((|#1| $) 63 T ELT)) (-3038 ((|#1| $) 51 T ELT)) (-3799 ((|#1| $) 50 T ELT)) (-3412 ((|#1| $) 42 T ELT)) (-2245 (((-114) (-1 (-114) |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-2815 (($ $ (-663 (-305 |#1|))) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 24 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-2315 (((-114) $ $) 14 T ELT)) (-3575 ((|#1| |#1| $) 59 T ELT)) (-2067 (((-114) $) 11 T ELT)) (-2856 (($) 12 T ELT)) (-3315 ((|#1| $) 60 T ELT)) (-3212 (($) 58 T ELT) (($ (-663 |#1|)) 57 T ELT)) (-2797 (((-793) $) 44 T ELT)) (-1463 (((-793) (-1 (-114) |#1|) $) 32 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 29 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2743 (($ $) 13 T ELT)) (-2556 (((-887) $) 18 (|has| |#1| (-632 (-887))) ELT)) (-2955 ((|#1| $) 54 T ELT)) (-1789 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2313 (($ (-663 |#1|)) 43 T ELT)) (-1447 ((|#1| $) 64 T ELT)) (-3338 (((-114) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT)) (-2299 (((-114) $ $) 19 (|has| |#1| (-102)) ELT)) (-2277 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) +((-1400 (*1 *2 *3) (-12 (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-2701 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 *4)))) (-1940 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-1940 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2433 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2330 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-2319 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2330 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-2319 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-4251 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-114)))) (-4330 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-815)) (-4 *2 (-277 *4)))) (-2832 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-3052 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-1400 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-979 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1069 |t#2|) (-10 -8 (-15 -1400 ((-1 $ (-793)) |t#2|)) (-15 -2701 ((-663 |t#2|) $)) (-15 -1940 ((-793) $ |t#2|)) (-15 -1940 ((-793) $)) (-15 -2433 ((-793) $ |t#2|)) (-15 -2330 ((-663 (-793)) $)) (-15 -2319 ((-793) $)) (-15 -2330 ((-663 (-793)) $ |t#2|)) (-15 -2319 ((-793) $ |t#2|)) (-15 -4251 ((-114) $)) (-15 -4330 (|t#3| $)) (-15 -2832 ($ $)) (-15 -3052 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -1400 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2188 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-887)) . T) ((-175) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-633 (-915 (-391)))) (|has| |#3| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-633 (-915 (-560)))) (|has| |#3| (-633 (-915 (-560))))) ((-236 $) -2188 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2188 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2188 (|has| |#1| (-939)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2188 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2188 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1247) . T) ((-1252) |has| |#1| (-939))) +((-2177 (((-114) $ $) 20 (|has| |#1| (-102)) ELT)) (-1356 ((|#1| $) 55 T ELT)) (-1725 ((|#1| $) 45 T ELT)) (-4218 (((-114) $ (-793)) 8 T ELT)) (-3282 (($) 7 T CONST)) (-1709 (($ $) 61 T ELT)) (-2400 (($ $) 49 T ELT)) (-2739 ((|#1| |#1| $) 47 T ELT)) (-3179 ((|#1| $) 46 T ELT)) (-3224 (((-663 |#1|) $) 31 (|has| $ (-6 -4508)) ELT)) (-3199 (((-114) $ (-793)) 9 T ELT)) (-2807 (((-663 |#1|) $) 30 (|has| $ (-6 -4508)) ELT)) (-3614 (((-114) |#1| $) 28 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2309 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4509)) ELT)) (-4335 (($ (-1 |#1| |#1|) $) 36 T ELT)) (-4437 (((-114) $ (-793)) 10 T ELT)) (-2648 (((-793) $) 62 T ELT)) (-1485 (((-1189) $) 23 (|has| |#1| (-1132)) ELT)) (-1949 ((|#1| $) 40 T ELT)) (-1808 ((|#1| |#1| $) 53 T ELT)) (-1763 ((|#1| |#1| $) 52 T ELT)) (-3422 (($ |#1| $) 41 T ELT)) (-3395 (((-793) $) 56 T ELT)) (-3012 (((-1151) $) 22 (|has| |#1| (-1132)) ELT)) (-2367 ((|#1| $) 63 T ELT)) (-4288 ((|#1| $) 51 T ELT)) (-3159 ((|#1| $) 50 T ELT)) (-3600 ((|#1| $) 42 T ELT)) (-2230 (((-114) (-1 (-114) |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-2704 (($ $ (-663 (-305 |#1|))) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 24 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-3609 (((-114) $ $) 14 T ELT)) (-2706 ((|#1| |#1| $) 59 T ELT)) (-2978 (((-114) $) 11 T ELT)) (-3113 (($) 12 T ELT)) (-1916 ((|#1| $) 60 T ELT)) (-3448 (($) 58 T ELT) (($ (-663 |#1|)) 57 T ELT)) (-2535 (((-793) $) 44 T ELT)) (-3024 (((-793) (-1 (-114) |#1|) $) 32 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 29 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-2448 (($ $) 13 T ELT)) (-4202 (((-887) $) 18 (|has| |#1| (-632 (-887))) ELT)) (-2777 ((|#1| $) 54 T ELT)) (-3289 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-1619 (($ (-663 |#1|)) 43 T ELT)) (-1450 ((|#1| $) 64 T ELT)) (-2123 (((-114) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT)) (-2324 (((-114) $ $) 19 (|has| |#1| (-102)) ELT)) (-2187 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) (((-263 |#1|) (-142) (-1247)) (T -263)) -((-3212 (*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3212 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1247)) (-4 *1 (-263 *3)))) (-4293 (*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1247)) (-5 *2 (-793)))) (-2283 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-2955 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3611 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-2514 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3038 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-3799 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1828 (*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247))))) -(-13 (-1152 |t#1|) (-1026 |t#1|) (-10 -8 (-15 -3212 ($)) (-15 -3212 ($ (-663 |t#1|))) (-15 -4293 ((-793) $)) (-15 -2283 (|t#1| $)) (-15 -2955 (|t#1| $)) (-15 -3611 (|t#1| |t#1| $)) (-15 -2514 (|t#1| |t#1| $)) (-15 -3038 (|t#1| $)) (-15 -3799 (|t#1| $)) (-15 -1828 ($ $)))) -(((-34) . 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T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1080)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-950) |has| |#1| (-571)) ((-1069 (-421 (-560))) -2157 (|has| |#1| (-1069 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1069 (-560))))) ((-1069 #1#) |has| |#1| (-571)) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 #3#) |has| |#1| (-1080)) ((-1069 #4#) . T) ((-1069 |#1|) . T) ((-1082 #0#) |has| |#1| (-571)) ((-1082 |#1|) |has| |#1| (-175)) ((-1082 $) |has| |#1| (-571)) ((-1087 #0#) |has| |#1| (-571)) ((-1087 |#1|) |has| |#1| (-175)) ((-1087 $) |has| |#1| (-571)) ((-1080) -2157 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1088) -2157 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1143) -2157 (|has| |#1| (-1143)) (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1132) . T) ((-1247) . 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T) ((-950) |has| |#1| (-571)) ((-1069 (-421 (-560))) -2188 (|has| |#1| (-1069 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1069 (-560))))) ((-1069 #1#) |has| |#1| (-571)) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 #3#) |has| |#1| (-1080)) ((-1069 #4#) . T) ((-1069 |#1|) . T) ((-1082 #0#) |has| |#1| (-571)) ((-1082 |#1|) |has| |#1| (-175)) ((-1082 $) |has| |#1| (-571)) ((-1087 #0#) |has| |#1| (-571)) ((-1087 |#1|) |has| |#1| (-175)) ((-1087 $) |has| |#1| (-571)) ((-1080) -2188 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1088) -2188 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1143) -2188 (|has| |#1| (-1143)) (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1132) . T) ((-1247) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2157 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2157 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1207)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1143)) ((-302) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1143)) ((-302) -2188 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1207) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1207) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2188 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . 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T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1207)))) ((-1069 |#2|) . T) ((-1082 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) -12 (|has| |#1| (-376)) (|has| |#2| (-1182))) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1259 |#1|) . T) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2157 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2157 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2157 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2157 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . 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$)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2188 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2188 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2188 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2188 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) -12 (|has| (-1113) (-911 (-391))) (|has| |#1| (-911 (-391)))) ((-911 (-560)) -12 (|has| (-1113) (-911 (-560))) (|has| |#1| (-911 (-560)))) ((-979 |#1| #0# #2#) . T) ((-939) |has| |#1| (-939)) ((-950) |has| |#1| (-376)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2188 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) |has| |#1| (-1182)) ((-1247) . 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T) ((-662 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1082 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2188 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2157 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 $ $) |has| (-421 (-560)) (-1143)) ((-302) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-376) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-571) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1207)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1207)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1069 |#2|) . T) ((-1082 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2157 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1252) |has| |#1| (-376)) ((-1276 |#1| #0#) . T) ((-1280 |#1|) . 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T) ((-1082 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2157 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1276 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2188 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2188 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . 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T) ((-1082 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2188 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1233) |has| |#1| (-38 (-421 (-560)))) ((-1236) |has| |#1| (-38 (-421 (-560)))) ((-1247) . T) ((-1276 |#1| #0#) . 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3472728 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472703 3472708 3472713 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472688 3472693 3472698 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472673 3472678 3472683 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471660 3472548 3472625 "ZMOD" 3472630 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3470696 3470878 3471101 "ZLINDEP" 3471492 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3459858 3461764 3463736 "ZDSOLVE" 3468826 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459092 3459245 3459434 "YSTREAM" 3459704 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458452 3458761 3458876 "YDIAGRAM" 3458999 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3455900 3457753 3457957 "XRPOLY" 3458295 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452167 3453771 3454346 "XPR" 3455372 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449498 3451174 3451229 "XPOLYC" 3451517 NIL XPOLYC (NIL T T) -9 NIL 3451630 NIL) (-1319 3446893 3448829 3449033 "XPOLY" 3449329 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3442839 3445410 3445798 "XPBWPOLY" 3446551 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3437731 3439310 3439365 "XFALG" 3441537 NIL XFALG (NIL T T) -9 NIL 3442326 NIL) (-1316 3433000 3435707 3435749 "XF" 3436370 NIL XF (NIL T) -9 NIL 3436770 NIL) (-1315 3432597 3432709 3432878 "XF-" 3432883 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3431712 3431834 3432039 "XEXPPKG" 3432489 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429453 3431562 3431658 "XDPOLY" 3431663 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428108 3428846 3428889 "XALG" 3428894 NIL XALG (NIL T) -9 NIL 3429005 NIL) (-1311 3421018 3426085 3426579 "WUTSET" 3427700 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419120 3420070 3420393 "WP" 3420829 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418668 3418942 3419012 "WHILEAST" 3419072 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418080 3418385 3418479 "WHEREAST" 3418596 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3416954 3417164 3417459 "WFFINTBS" 3417877 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3414822 3415285 3415747 "WEIER" 3416526 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3413746 3414304 3414346 "VSPACE" 3414482 NIL VSPACE (NIL T) -9 NIL 3414556 NIL) (-1304 3413578 3413611 3413702 "VSPACE-" 3413707 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413375 3413429 3413497 "VOID" 3413532 T VOID (NIL) -8 NIL NIL NIL) (-1302 3409643 3410438 3411175 "VIEWDEF" 3412660 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3398587 3401191 3403364 "VIEW3D" 3407492 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3390604 3392498 3394077 "VIEW2D" 3397030 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3388704 3389099 3389505 "VIEW" 3390220 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3387257 3387540 3387858 "VECTOR2" 3388434 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3382163 3387027 3387119 "VECTOR" 3387200 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3375117 3379867 3379910 "VECTCAT" 3380905 NIL VECTCAT (NIL T) -9 NIL 3381492 NIL) (-1295 3374059 3374385 3374775 "VECTCAT-" 3374780 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373465 3373710 3373830 "VARIABLE" 3373974 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373398 3373403 3373433 "UTYPE" 3373438 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372206 3372382 3372644 "UTSODETL" 3373224 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369598 3370106 3370630 "UTSODE" 3371747 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3359605 3365531 3365574 "UTSCAT" 3366686 NIL UTSCAT (NIL T) -9 NIL 3367444 NIL) (-1289 3356731 3357675 3358664 "UTSCAT-" 3358669 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3356352 3356401 3356534 "UTS2" 3356682 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3347662 3354113 3354593 "UTS" 3355930 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3341529 3344472 3344515 "URAGG" 3346585 NIL URAGG (NIL T) -9 NIL 3347308 NIL) (-1285 3338252 3339331 3340454 "URAGG-" 3340459 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333621 3336887 3337352 "UPXSSING" 3337916 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3326036 3333525 3333597 "UPXSCONS" 3333602 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3314784 3322238 3322300 "UPXSCCA" 3322874 NIL UPXSCCA (NIL T T) -9 NIL 3323107 NIL) (-1281 3314404 3314507 3314681 "UPXSCCA-" 3314686 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3303052 3310231 3310274 "UPXSCAT" 3310922 NIL UPXSCAT (NIL T) -9 NIL 3311531 NIL) (-1279 3302476 3302561 3302740 "UPXS2" 3302967 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3293954 3301858 3302122 "UPXS" 3302270 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3292590 3292861 3293212 "UPSQFREE" 3293697 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285418 3288856 3288911 "UPSCAT" 3289991 NIL UPSCAT (NIL T T) -9 NIL 3290757 NIL) (-1275 3284574 3284829 3285156 "UPSCAT-" 3285161 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3284195 3284244 3284377 "UPOLYC2" 3284525 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3268329 3277322 3277365 "UPOLYC" 3279466 NIL UPOLYC (NIL T) -9 NIL 3280687 NIL) (-1272 3259177 3262083 3265230 "UPOLYC-" 3265235 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3258498 3258623 3258787 "UPMP" 3259066 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3258045 3258132 3258271 "UPDIVP" 3258411 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3256583 3256862 3257178 "UPDECOMP" 3257794 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3255796 3255926 3256112 "UPCDEN" 3256467 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3255309 3255384 3255533 "UP2" 3255721 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3245884 3254992 3255121 "UP" 3255228 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3245089 3245226 3245431 "UNISEG2" 3245727 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3243442 3244293 3244570 "UNISEG" 3244847 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3242484 3242682 3242908 "UNIFACT" 3243258 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3229194 3242388 3242460 "ULSCONS" 3242465 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3208994 3222274 3222336 "ULSCCAT" 3222974 NIL ULSCCAT (NIL T T) -9 NIL 3223263 NIL) (-1260 3207990 3208289 3208677 "ULSCCAT-" 3208682 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3196435 3203536 3203579 "ULSCAT" 3204442 NIL ULSCAT (NIL T) -9 NIL 3205173 NIL) (-1258 3195859 3195944 3196123 "ULS2" 3196350 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3177669 3195171 3195413 "ULS" 3195675 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3176588 3177288 3177402 "UINT8" 3177513 T UINT8 (NIL) -8 NIL NIL 3177605) (-1255 3175506 3176206 3176320 "UINT64" 3176431 T UINT64 (NIL) -8 NIL NIL 3176523) (-1254 3174424 3175124 3175238 "UINT32" 3175349 T UINT32 (NIL) -8 NIL NIL 3175441) (-1253 3173342 3174042 3174156 "UINT16" 3174267 T UINT16 (NIL) -8 NIL NIL 3174359) (-1252 3171421 3172588 3172618 "UFD" 3172830 T UFD (NIL) -9 NIL 3172944 NIL) (-1251 3171203 3171261 3171356 "UFD-" 3171361 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170261 3170468 3170684 "UDVO" 3171009 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168027 3168486 3168957 "UDPO" 3169825 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167739 3167982 3168013 "TYPEAST" 3168018 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3167672 3167677 3167707 "TYPE" 3167712 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166625 3166845 3167085 "TWOFACT" 3167466 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165600 3166034 3166269 "TUPLE" 3166425 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163237 3163810 3164349 "TUBETOOL" 3165083 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162043 3162284 3162526 "TUBE" 3163030 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3150185 3154800 3154897 "TSETCAT" 3160166 NIL TSETCAT (NIL T T T T) -9 NIL 3161698 NIL) (-1241 3144653 3146517 3148408 "TSETCAT-" 3148413 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3138832 3143625 3143908 "TS" 3144405 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3133305 3134318 3135247 "TRMANIP" 3137968 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3132734 3132809 3132972 "TRIMAT" 3133237 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130546 3130837 3131194 "TRIGMNIP" 3132483 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130030 3130179 3130209 "TRIGCAT" 3130422 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129675 3129778 3129919 "TRIGCAT-" 3129924 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126289 3128533 3128814 "TREE" 3129429 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125395 3126091 3126121 "TRANFUN" 3126156 T TRANFUN (NIL) -9 NIL 3126222 NIL) (-1232 3124614 3124865 3125145 "TRANFUN-" 3125150 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124412 3124450 3124511 "TOPSP" 3124575 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3123742 3123875 3124029 "TOOLSIGN" 3124293 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122256 3122919 3123158 "TEXTFILE" 3123525 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3122031 3122068 3122140 "TEX1" 3122219 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3119835 3120484 3120913 "TEX" 3121624 T TEX (NIL) -8 NIL NIL NIL) (-1226 3119471 3119546 3119636 "TEMUTL" 3119767 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117565 3117905 3118230 "TBCMPPK" 3119194 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108892 3115651 3115707 "TBAGG" 3116107 NIL TBAGG (NIL T T) -9 NIL 3116318 NIL) (-1223 3103776 3105450 3107204 "TBAGG-" 3107209 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103142 3103267 3103412 "TANEXP" 3103665 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102593 3102917 3103007 "TALGOP" 3103087 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3101987 3102104 3102242 "TABLEAU" 3102490 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095001 3101844 3101937 "TABLE" 3101942 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089531 3090829 3092077 "TABLBUMP" 3093787 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3088741 3088900 3089081 "SYSTEM" 3089372 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085146 3085899 3086682 "SYSSOLP" 3087992 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084908 3085101 3085132 "SYSPTR" 3085137 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3083747 3084439 3084565 "SYSNNI" 3084751 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084843) (-1213 3082954 3083509 3083588 "SYSINT" 3083648 NIL SYSINT (NIL NIL) -8 NIL NIL 3083693) (-1212 3079052 3080232 3080942 "SYNTAX" 3082266 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076132 3076812 3077444 "SYMTAB" 3078442 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071231 3072283 3073266 "SYMS" 3075171 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068130 3070682 3070915 "SYMPOLY" 3071033 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067635 3067722 3067845 "SYMFUNC" 3068042 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063433 3064947 3065760 "SYMBOL" 3066844 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056906 3058661 3060381 "SWITCH" 3061735 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049660 3055862 3056156 "SUTS" 3056670 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041138 3049042 3049306 "SUPXS" 3049454 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040285 3040424 3040641 "SUPFRACF" 3041006 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3039900 3039965 3040078 "SUP2" 3040220 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030423 3039518 3039644 "SUP" 3039809 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3028847 3029145 3029501 "SUMRF" 3030122 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028170 3028248 3028440 "SUMFS" 3028768 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010015 3027482 3027724 "SULS" 3027986 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009563 3009837 3009907 "SUCHTAST" 3009967 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3008804 3009088 3009228 "SUCH" 3009471 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002443 3003710 3004669 "SUBSPACE" 3007892 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001863 3001963 3002127 "SUBRESP" 3002331 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2995874 2997156 2998303 "STTFNC" 3000763 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989068 2990539 2991850 "STTF" 2994610 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980185 2982250 2984044 "STTAYLOR" 2987309 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972939 2980049 2980132 "STRTBL" 2980137 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967336 2972648 2972747 "STRING" 2972862 T STRING (NIL) -8 NIL NIL NIL) (-1188 2966840 2966923 2967067 "STREAM3" 2967253 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2965804 2966005 2966240 "STREAM2" 2966653 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965486 2965544 2965637 "STREAM1" 2965746 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957600 2963105 2963716 "STREAM" 2964910 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956592 2956797 2957028 "STINPROD" 2957416 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955707 2956081 2956229 "STEPAST" 2956466 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955203 2955455 2955485 "STEP" 2955565 T STEP (NIL) -9 NIL 2955643 NIL) (-1181 2948259 2955102 2955179 "STBL" 2955184 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2942817 2947422 2947465 "STAGG" 2947618 NIL STAGG (NIL T) -9 NIL 2947707 NIL) (-1179 2940369 2941121 2941993 "STAGG-" 2941998 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938341 2940139 2940231 "STACK" 2940312 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930348 2936482 2936938 "SREGSET" 2937971 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922695 2924142 2925655 "SRDCMPK" 2928954 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915004 2920054 2920084 "SRAGG" 2921387 T SRAGG (NIL) -9 NIL 2921995 NIL) (-1174 2913955 2914276 2914655 "SRAGG-" 2914660 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907539 2912902 2913323 "SQMATRIX" 2913581 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900951 2904257 2904984 "SPLTREE" 2906884 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896776 2897607 2898253 "SPLNODE" 2900377 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895751 2896056 2896086 "SPFCAT" 2896530 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894446 2894698 2894962 "SPECOUT" 2895509 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885092 2887410 2887440 "SPADXPT" 2892118 T SPADXPT (NIL) -9 NIL 2894284 NIL) (-1167 2884847 2884893 2884962 "SPADPRSR" 2885045 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882450 2884802 2884833 "SPADAST" 2884838 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874051 2876154 2876197 "SPACEC" 2880570 NIL SPACEC (NIL T) -9 NIL 2882386 NIL) (-1164 2871851 2873983 2874032 "SPACE3" 2874037 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870583 2870774 2871065 "SORTPAK" 2871656 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868645 2868978 2869390 "SOLVETRA" 2870247 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867683 2867917 2868178 "SOLVESER" 2868418 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862915 2863875 2864870 "SOLVERAD" 2866735 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858640 2859339 2860068 "SOLVEFOR" 2862282 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852251 2857988 2858085 "SNTSCAT" 2858090 NIL SNTSCAT (NIL T T T T) -9 NIL 2858160 NIL) (-1157 2845795 2850574 2850965 "SMTS" 2851941 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839510 2845683 2845760 "SMP" 2845765 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837639 2837970 2838368 "SMITH" 2839207 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829171 2834218 2834321 "SMATCAT" 2835672 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836222 NIL) (-1153 2825943 2826934 2828112 "SMATCAT-" 2828117 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823412 2825151 2825194 "SKAGG" 2825455 NIL SKAGG (NIL T) -9 NIL 2825590 NIL) (-1151 2818902 2822881 2823065 "SINT" 2823217 T SINT (NIL) -8 NIL NIL 2823379) (-1150 2818668 2818712 2818778 "SIMPAN" 2818858 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817488 2817727 2818002 "SIGNRF" 2818427 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816303 2816472 2816756 "SIGNEF" 2817317 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815543 2815886 2816010 "SIGAST" 2816201 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814768 2815078 2815218 "SIG" 2815425 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812420 2812912 2813418 "SHP" 2814309 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805793 2812321 2812397 "SHDP" 2812402 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805304 2805544 2805574 "SGROUP" 2805667 T SGROUP (NIL) -9 NIL 2805729 NIL) (-1142 2805156 2805188 2805261 "SGROUP-" 2805266 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801875 2802645 2803368 "SGCF" 2804455 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795584 2801321 2801418 "SFRTCAT" 2801423 NIL SFRTCAT (NIL T T T T) -9 NIL 2801462 NIL) (-1139 2788903 2790023 2791159 "SFRGCD" 2794567 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781921 2783102 2784288 "SFQCMPK" 2787836 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781523 2781630 2781741 "SFORT" 2781862 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780449 2781363 2781484 "SEXOF" 2781489 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776038 2776945 2777040 "SEXCAT" 2779662 NIL SEXCAT (NIL T T T T T) -9 NIL 2780222 NIL) (-1134 2774953 2775919 2775987 "SEX" 2775992 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773075 2773666 2773971 "SETMN" 2774694 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772605 2772793 2772823 "SETCAT" 2772940 T SETCAT (NIL) -9 NIL 2773025 NIL) (-1131 2772373 2772437 2772536 "SETCAT-" 2772541 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768476 2770834 2770877 "SETAGG" 2771747 NIL SETAGG (NIL T) -9 NIL 2772087 NIL) (-1129 2767898 2768050 2768287 "SETAGG-" 2768292 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764707 2767832 2767880 "SET" 2767885 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764090 2764403 2764504 "SEQAST" 2764628 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763217 2763583 2763644 "SEGXCAT" 2763930 NIL SEGXCAT (NIL T T) -9 NIL 2764050 NIL) (-1125 2762142 2762410 2762453 "SEGCAT" 2762975 NIL SEGCAT (NIL T) -9 NIL 2763196 NIL) (-1124 2761757 2761822 2761935 "SEGBIND2" 2762077 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760647 2761120 2761328 "SEGBIND" 2761584 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760166 2760448 2760525 "SEGAST" 2760592 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759375 2759511 2759715 "SEG2" 2760010 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758291 2759041 2759223 "SEG" 2759228 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757524 2758226 2758273 "SDVAR" 2758278 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748875 2757294 2757424 "SDPOL" 2757429 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747444 2747734 2748053 "SCPKG" 2748590 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746566 2746780 2746972 "SCOPE" 2747274 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745762 2745920 2746099 "SCACHE" 2746421 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745346 2745580 2745610 "SASTCAT" 2745615 T SASTCAT (NIL) -9 NIL 2745628 NIL) (-1113 2744749 2745181 2745257 "SAOS" 2745292 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744308 2744349 2744522 "SAERFFC" 2744708 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2743895 2743936 2744095 "SAEFACT" 2744267 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2736922 2743792 2743872 "SAE" 2743877 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735225 2735557 2735958 "RURPK" 2736588 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733802 2734168 2734473 "RULESET" 2735059 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733372 2733596 2733679 "RULECOLD" 2733754 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730487 2731125 2731583 "RULE" 2733053 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730271 2730305 2730376 "RTVALUE" 2730438 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729682 2729988 2730082 "RSTRCAST" 2730199 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724452 2725325 2726245 "RSETGCD" 2728881 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713023 2718760 2718857 "RSETCAT" 2722976 NIL RSETCAT (NIL T T T T) -9 NIL 2724073 NIL) (-1101 2710842 2711489 2712313 "RSETCAT-" 2712318 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703150 2704604 2706124 "RSDCMPK" 2709441 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701019 2701582 2701656 "RRCC" 2702742 NIL RRCC (NIL T T) -9 NIL 2703086 NIL) (-1098 2700340 2700544 2700823 "RRCC-" 2700828 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699723 2700036 2700137 "RPTAST" 2700261 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672109 2682835 2682902 "RPOLCAT" 2693568 NIL RPOLCAT (NIL T T T) -9 NIL 2696728 NIL) (-1095 2663079 2665947 2669069 "RPOLCAT-" 2669074 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653532 2661290 2661772 "ROUTINE" 2662619 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649581 2653158 2653298 "ROMAN" 2653414 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647693 2648441 2648701 "ROIRC" 2649386 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643411 2646182 2646212 "RNS" 2646516 T RNS (NIL) -9 NIL 2646790 NIL) (-1090 2641818 2642303 2642837 "RNS-" 2642912 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640779 2641183 2641385 "RNGBIND" 2641669 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640072 2640576 2640606 "RNG" 2640611 T RNG (NIL) -9 NIL 2640632 NIL) (-1087 2639367 2639845 2639888 "RMODULE" 2639893 NIL RMODULE (NIL T) -9 NIL 2639920 NIL) (-1086 2638191 2638297 2638633 "RMCAT2" 2639268 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634693 2637537 2637834 "RMATRIX" 2637953 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627192 2629780 2629895 "RMATCAT" 2633254 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634236 NIL) (-1083 2626531 2626714 2627021 "RMATCAT-" 2627026 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626104 2626318 2626361 "RLINSET" 2626423 NIL RLINSET (NIL T) -9 NIL 2626467 NIL) (-1081 2625665 2625746 2625874 "RINTERP" 2626023 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624589 2625263 2625293 "RING" 2625349 T RING (NIL) -9 NIL 2625441 NIL) (-1079 2624369 2624425 2624522 "RING-" 2624527 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623180 2623447 2623705 "RIDIST" 2624133 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613805 2622648 2622854 "RGCHAIN" 2623028 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613063 2613547 2613588 "RGBCSPC" 2613646 NIL RGBCSPC (NIL T) -9 NIL 2613698 NIL) (-1075 2612129 2612588 2612629 "RGBCMDL" 2612861 NIL RGBCMDL (NIL T) -9 NIL 2612975 NIL) (-1074 2611769 2611838 2611941 "RFFACTOR" 2612060 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611488 2611529 2611626 "RFFACT" 2611728 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609539 2609969 2610351 "RFDIST" 2611128 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606479 2607147 2607817 "RF" 2608903 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2605926 2606024 2606187 "RETSOL" 2606381 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605544 2605642 2605685 "RETRACT" 2605818 NIL RETRACT (NIL T) -9 NIL 2605905 NIL) (-1068 2605387 2605418 2605505 "RETRACT-" 2605510 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604935 2605209 2605279 "RETAST" 2605339 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597285 2604588 2604715 "RESULT" 2604830 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595720 2596554 2596753 "RESRING" 2597188 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595344 2595405 2595503 "RESLATC" 2595657 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595043 2595084 2595191 "REPSQ" 2595303 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594734 2594775 2594886 "REPDB" 2595002 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588566 2590023 2591246 "REP2" 2593546 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2584869 2585624 2586432 "REP1" 2587793 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582249 2582871 2583473 "REP" 2584289 T REP (NIL) -7 NIL NIL NIL) (-1058 2574257 2580390 2580846 "REGSET" 2581879 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572966 2573405 2573655 "REF" 2574042 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572331 2572446 2572613 "REDORDER" 2572850 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567695 2571544 2571771 "RECLOS" 2572159 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566729 2566928 2567143 "REALSOLV" 2567502 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563176 2564014 2564898 "REAL0Q" 2565894 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558729 2559765 2560826 "REAL0" 2562157 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558563 2558616 2558646 "REAL" 2558651 T REAL (NIL) -9 NIL 2558686 NIL) (-1050 2557974 2558280 2558374 "RDUCEAST" 2558491 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557373 2557451 2557658 "RDIV" 2557896 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556423 2556615 2556828 "RDIST" 2557195 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555008 2555307 2555679 "RDETRS" 2556131 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552802 2553274 2553812 "RDETR" 2554550 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551421 2551705 2552102 "RDEEFS" 2552518 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549924 2550236 2550661 "RDEEF" 2551109 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543401 2546878 2546908 "RCFIELD" 2548203 T RCFIELD (NIL) -9 NIL 2548934 NIL) (-1042 2541357 2541969 2542665 "RCFIELD-" 2542740 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537409 2539430 2539473 "RCAGG" 2540557 NIL RCAGG (NIL T) -9 NIL 2541022 NIL) (-1040 2537019 2537131 2537294 "RCAGG-" 2537299 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536336 2536466 2536631 "RATRET" 2536903 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535877 2535956 2536077 "RATFACT" 2536264 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535155 2535305 2535457 "RANDSRC" 2535747 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534883 2534933 2535006 "RADUTIL" 2535104 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527007 2533714 2534025 "RADIX" 2534606 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516601 2526849 2526979 "RADFF" 2526984 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516230 2516323 2516353 "RADCAT" 2516513 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516000 2516060 2516160 "RADCAT-" 2516165 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513911 2515770 2515862 "QUEUE" 2515943 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513536 2513585 2513716 "QUATCT2" 2513862 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2505912 2509959 2510001 "QUATCAT" 2510792 NIL QUATCAT (NIL T) -9 NIL 2511558 NIL) (-1028 2501793 2503088 2504478 "QUATCAT-" 2504574 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497632 2501726 2501774 "QUAT" 2501779 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2494888 2496680 2496723 "QUAGG" 2497104 NIL QUAGG (NIL T) -9 NIL 2497279 NIL) (-1025 2494436 2494710 2494780 "QQUTAST" 2494840 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493347 2493949 2494114 "QFORM" 2494317 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2492972 2493021 2493152 "QFCAT2" 2493298 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482648 2488819 2488861 "QFCAT" 2489529 NIL QFCAT (NIL T) -9 NIL 2490530 NIL) (-1021 2477963 2479416 2481010 "QFCAT-" 2481106 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477394 2477528 2477660 "QEQUAT" 2477853 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470412 2471593 2472779 "QCMPACK" 2476327 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469641 2469823 2470059 "QALGSET2" 2470230 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467091 2467627 2468057 "QALGSET" 2469296 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465758 2466000 2466319 "PWFFINTB" 2466864 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463903 2464101 2464457 "PUSHVAR" 2465572 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459630 2460846 2460889 "PTRANFN" 2462800 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457967 2458312 2458636 "PTPACK" 2459341 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457590 2457653 2457764 "PTFUNC2" 2457904 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451515 2456379 2456422 "PTCAT" 2456722 NIL PTCAT (NIL T) -9 NIL 2456875 NIL) (-1010 2451164 2451205 2451331 "PSQFR" 2451474 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449736 2450052 2450388 "PSEUDLIN" 2450862 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436256 2438831 2441157 "PSETPK" 2447496 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428964 2431992 2432090 "PSETCAT" 2435131 NIL PSETCAT (NIL T T T T) -9 NIL 2435945 NIL) (-1006 2426689 2427431 2428255 "PSETCAT-" 2428260 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426002 2426197 2426227 "PSCURVE" 2426499 T PSCURVE (NIL) -9 NIL 2426666 NIL) (-1004 2421718 2423492 2423559 "PSCAT" 2424411 NIL PSCAT (NIL T T T) -9 NIL 2424651 NIL) (-1003 2420712 2420994 2421397 "PSCAT-" 2421402 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418911 2419771 2420036 "PRTITION" 2420469 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418322 2418628 2418722 "PRTDAST" 2418839 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407166 2409588 2411778 "PRS" 2416184 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404786 2406488 2406528 "PRQAGG" 2406711 NIL PRQAGG (NIL T) -9 NIL 2406813 NIL) (-998 2403965 2404414 2404442 "PROPLOG" 2404581 T PROPLOG (NIL) -9 NIL 2404696 NIL) (-997 2403563 2403626 2403749 "PROPFUN2" 2403888 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402860 2402999 2403171 "PROPFUN1" 2403424 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400839 2401607 2401904 "PROPFRML" 2402596 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400284 2400415 2400543 "PROPERTY" 2400731 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394172 2398450 2399270 "PRODUCT" 2399510 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2393962 2394000 2394059 "PRINT" 2394133 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393278 2393419 2393571 "PRIMES" 2393842 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391325 2391744 2392210 "PRIMELT" 2392857 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391042 2391103 2391131 "PRIMCAT" 2391255 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390031 2390227 2390455 "PRIMARR2" 2390860 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385753 2389969 2390014 "PRIMARR" 2390019 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385390 2385452 2385563 "PREASSOC" 2385691 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382348 2384848 2385082 "PR" 2385201 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381799 2381956 2381984 "PPCURVE" 2382189 T PPCURVE (NIL) -9 NIL 2382325 NIL) (-983 2381346 2381594 2381677 "PORTNUM" 2381736 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378683 2379104 2379696 "POLYROOT" 2380927 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378060 2378124 2378358 "POLYLIFT" 2378619 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374281 2374784 2375413 "POLYCATQ" 2377605 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2359929 2366028 2366093 "POLYCAT" 2369607 NIL POLYCAT (NIL T T T) -9 NIL 2371485 NIL) (-978 2353048 2355240 2357624 "POLYCAT-" 2357629 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352629 2352703 2352823 "POLY2UP" 2352974 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352255 2352318 2352427 "POLY2" 2352566 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345463 2351859 2352019 "POLY" 2352128 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344124 2344387 2344663 "POLUTIL" 2345237 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342443 2342756 2343087 "POLTOPOL" 2343846 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337439 2342377 2342424 "POINT" 2342429 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335572 2335983 2336358 "PNTHEORY" 2337084 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334018 2334327 2334726 "PMTOOLS" 2335270 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333605 2333689 2333806 "PMSYM" 2333934 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333107 2333182 2333357 "PMQFCAT" 2333530 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332488 2332586 2332748 "PMPREDFS" 2333008 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2331831 2331953 2332109 "PMPRED" 2332365 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330485 2330703 2331081 "PMPLCAT" 2331593 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330011 2330096 2330248 "PMLSAGG" 2330400 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329478 2329560 2329742 "PMKERNEL" 2329929 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329089 2329170 2329283 "PMINS" 2329397 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328525 2328600 2328809 "PMFS" 2329014 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327741 2327871 2328076 "PMDOWN" 2328402 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326990 2327124 2327287 "PMASSFS" 2327628 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326133 2326315 2326496 "PMASS" 2326829 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325782 2325856 2325950 "PLOTTOOL" 2326059 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321434 2322628 2323550 "PLOT3D" 2324880 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320322 2320523 2320758 "PLOT1" 2321238 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314743 2316133 2317281 "PLOT" 2319194 T PLOT (NIL) -8 NIL NIL NIL) (-953 2289918 2294809 2299660 "PLEQN" 2310009 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289605 2289658 2289761 "PINTERPA" 2289865 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2288911 2289045 2289225 "PINTERP" 2289470 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2286996 2288169 2288197 "PID" 2288379 T PID (NIL) -9 NIL 2288513 NIL) (-949 2286741 2286784 2286859 "PICOERCE" 2286953 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2285837 2286505 2286592 "PI" 2286632 T PI (NIL) -8 NIL NIL 2286699) (-947 2285145 2285296 2285472 "PGROEB" 2285693 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280584 2281543 2282449 "PGE" 2284259 T PGE (NIL) -7 NIL NIL NIL) (-945 2278665 2278954 2279320 "PGCD" 2280301 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277991 2278106 2278267 "PFRPAC" 2278549 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274242 2276539 2276892 "PFR" 2277670 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272595 2272875 2273200 "PFOTOOLS" 2273989 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271110 2271367 2271718 "PFOQ" 2272352 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269593 2269823 2270179 "PFO" 2270894 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266671 2268184 2268212 "PFECAT" 2268797 T PFECAT (NIL) -9 NIL 2269181 NIL) (-938 2266098 2266270 2266484 "PFECAT-" 2266489 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264671 2264953 2265254 "PFBRU" 2265847 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262501 2262889 2263321 "PFBR" 2264322 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258426 2262390 2262459 "PF" 2262464 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253480 2254633 2255503 "PERMGRP" 2257589 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251392 2252504 2252545 "PERMCAT" 2252945 NIL PERMCAT (NIL T) -9 NIL 2253243 NIL) (-932 2251039 2251086 2251210 "PERMAN" 2251345 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2246841 2248548 2249196 "PERM" 2250424 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244082 2246506 2246628 "PENDTREE" 2246752 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242963 2243226 2243267 "PDSPC" 2243800 NIL PDSPC (NIL T) -9 NIL 2244045 NIL) (-928 2242018 2242284 2242646 "PDSPC-" 2242651 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240732 2241668 2241709 "PDRING" 2241714 NIL PDRING (NIL T) -9 NIL 2241742 NIL) (-926 2239475 2240237 2240291 "PDMOD" 2240296 NIL PDMOD (NIL T T) -9 NIL 2240400 NIL) (-925 2236642 2237468 2238136 "PDEPROB" 2238827 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234151 2234691 2235246 "PDEPACK" 2236107 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233039 2233253 2233504 "PDECOMP" 2233950 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230556 2231447 2231475 "PDECAT" 2232262 T PDECAT (NIL) -9 NIL 2232975 NIL) (-921 2230173 2230240 2230294 "PDDOM" 2230459 NIL PDDOM (NIL T T) -9 NIL 2230539 NIL) (-920 2229986 2230022 2230129 "PDDOM-" 2230134 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229731 2229770 2229860 "PCOMP" 2229947 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227771 2228532 2228829 "PBWLB" 2229460 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227397 2227460 2227569 "PATTERN2" 2227708 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225106 2225542 2225999 "PATTERN1" 2226986 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217285 2219179 2220517 "PATTERN" 2223789 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2216843 2216916 2217048 "PATRES2" 2217212 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214109 2214792 2215273 "PATRES" 2216408 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2211962 2212397 2212804 "PATMATCH" 2213776 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211416 2211667 2211708 "PATMAB" 2211815 NIL PATMAB (NIL T) -9 NIL 2211898 NIL) (-910 2209862 2210270 2210528 "PATLRES" 2211221 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209400 2209531 2209572 "PATAB" 2209577 NIL PATAB (NIL T) -9 NIL 2209749 NIL) (-908 2207540 2207977 2208400 "PARTPERM" 2208997 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207149 2207224 2207326 "PARSURF" 2207471 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206775 2206838 2206947 "PARSU2" 2207086 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206533 2206579 2206646 "PARSER" 2206728 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206142 2206217 2206319 "PARSCURV" 2206464 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205768 2205831 2205940 "PARSC2" 2206079 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205395 2205465 2205562 "PARPCURV" 2205704 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205021 2205084 2205193 "PARPC2" 2205332 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204010 2204394 2204576 "PARAMAST" 2204859 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203518 2203616 2203735 "PAN2EXPR" 2203911 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202211 2202639 2202867 "PALETTE" 2203310 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200556 2201216 2201576 "PAIR" 2201897 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193468 2199813 2200008 "PADICRC" 2200410 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185704 2192812 2192997 "PADICRAT" 2193315 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182494 2184364 2184404 "PADICCT" 2184985 NIL PADICCT (NIL NIL) -9 NIL 2185267 NIL) (-893 2180503 2182431 2182476 "PADIC" 2182481 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179448 2179660 2179928 "PADEPAC" 2180290 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178648 2178793 2178999 "PADE" 2179310 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176881 2177856 2178136 "OWP" 2178452 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176326 2176587 2176684 "OVERSET" 2176804 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175246 2175931 2176103 "OVAR" 2176194 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2163482 2166355 2168555 "OUTFORM" 2173066 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2162764 2163079 2163206 "OUTBFILE" 2163375 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2162041 2162236 2162264 "OUTBCON" 2162582 T OUTBCON (NIL) -9 NIL 2162748 NIL) (-884 2161624 2161754 2161911 "OUTBCON-" 2161916 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2160864 2161009 2161170 "OUT" 2161483 T OUT (NIL) -7 NIL NIL NIL) (-882 2160160 2160593 2160682 "OSI" 2160795 T OSI (NIL) -8 NIL NIL NIL) (-881 2159579 2160001 2160029 "OSGROUP" 2160034 T OSGROUP (NIL) -9 NIL 2160056 NIL) (-880 2158290 2158551 2158836 "ORTHPOL" 2159326 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155541 2158125 2158246 "OREUP" 2158251 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152644 2155232 2155359 "ORESUP" 2155483 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150144 2150672 2151233 "OREPCTO" 2152133 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143522 2146017 2146058 "OREPCAT" 2148406 NIL OREPCAT (NIL T) -9 NIL 2149510 NIL) (-875 2140495 2141451 2142509 "OREPCAT-" 2142514 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139688 2139965 2139993 "ORDTYPE" 2140302 T ORDTYPE (NIL) -9 NIL 2140465 NIL) (-873 2138989 2139205 2139460 "ORDTYPE-" 2139465 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138345 2138728 2138886 "ORDSTRCT" 2138891 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137843 2138213 2138241 "ORDSET" 2138246 T ORDSET (NIL) -9 NIL 2138268 NIL) (-870 2136201 2137172 2137200 "ORDRING" 2137402 T ORDRING (NIL) -9 NIL 2137527 NIL) (-869 2135822 2135940 2136084 "ORDRING-" 2136089 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135073 2135638 2135666 "ORDMON" 2135671 T ORDMON (NIL) -9 NIL 2135692 NIL) (-867 2134217 2134382 2134577 "ORDFUNS" 2134922 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133432 2133947 2133975 "ORDFIN" 2134040 T ORDFIN (NIL) -9 NIL 2134114 NIL) (-865 2132686 2132825 2133011 "ORDCOMP2" 2133292 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2129033 2131272 2131681 "ORDCOMP" 2132310 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2125554 2126524 2127338 "OPTPROB" 2128239 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122296 2122995 2123699 "OPTPACK" 2124870 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119909 2120735 2120763 "OPTCAT" 2121582 T OPTCAT (NIL) -9 NIL 2122232 NIL) (-860 2119227 2119586 2119691 "OPSIG" 2119824 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118989 2119034 2119100 "OPQUERY" 2119181 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2118295 2118575 2118616 "OPERCAT" 2118828 NIL OPERCAT (NIL T) -9 NIL 2118925 NIL) (-857 2118038 2118106 2118223 "OPERCAT-" 2118228 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2114947 2116349 2116853 "OP" 2117567 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114240 2114367 2114541 "ONECOMP2" 2114819 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2110853 2113037 2113406 "ONECOMP" 2113904 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110254 2110378 2110508 "OMSERVER" 2110743 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106768 2109694 2109734 "OMSAGG" 2109795 NIL OMSAGG (NIL T) -9 NIL 2109859 NIL) (-851 2105343 2105654 2105936 "OMPKG" 2106506 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103690 2104892 2105061 "OMLO" 2105224 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102626 2102797 2103017 "OMEXPR" 2103516 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101711 2102047 2102207 "OMERRK" 2102486 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2100948 2101257 2101393 "OMERR" 2101595 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100339 2100625 2100733 "OMENC" 2100860 T OMENC (NIL) -8 NIL NIL NIL) (-845 2093976 2095419 2096590 "OMDEV" 2099188 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2093009 2093216 2093410 "OMCONN" 2093802 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2092415 2092542 2092570 "OM" 2092869 T OM (NIL) -9 NIL NIL NIL) (-842 2090693 2091885 2091913 "OINTDOM" 2091918 T OINTDOM (NIL) -9 NIL 2091939 NIL) (-841 2087767 2089381 2089718 "OFMONOID" 2090388 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2087001 2087704 2087749 "ODVAR" 2087754 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084138 2086746 2086901 "ODR" 2086906 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075543 2083914 2084040 "ODPOL" 2084045 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068886 2075415 2075520 "ODP" 2075525 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067628 2067867 2068142 "ODETOOLS" 2068660 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064571 2065253 2065969 "ODESYS" 2066961 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059401 2060361 2061386 "ODERTRIC" 2063646 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2058821 2058909 2059103 "ODERED" 2059313 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055673 2056257 2056934 "ODERAT" 2058244 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052590 2053097 2053694 "ODEPRRIC" 2055202 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050485 2051129 2051615 "ODEPROB" 2052124 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046951 2047490 2048137 "ODEPRIM" 2049964 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046194 2046302 2046562 "ODEPAL" 2046843 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042296 2043147 2044011 "ODEPACK" 2045350 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041339 2041464 2041686 "ODEINT" 2042185 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035404 2036865 2038312 "ODEIFTBL" 2039912 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030754 2031588 2032540 "ODEEF" 2034563 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030097 2030192 2030415 "ODECONST" 2030659 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028160 2028869 2028897 "ODECAT" 2029502 T ODECAT (NIL) -9 NIL 2030033 NIL) (-821 2027792 2027841 2027968 "OCTCT2" 2028111 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024285 2027497 2027619 "OCT" 2027702 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023508 2024078 2024106 "OCAMON" 2024111 T OCAMON (NIL) -9 NIL 2024132 NIL) (-818 2017777 2020551 2020591 "OC" 2021688 NIL OC (NIL T) -9 NIL 2022546 NIL) (-817 2014812 2015752 2016742 "OC-" 2016836 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014232 2014657 2014685 "OASGP" 2014690 T OASGP (NIL) -9 NIL 2014710 NIL) (-815 2013358 2013955 2013983 "OAMONS" 2014023 T OAMONS (NIL) -9 NIL 2014066 NIL) (-814 2012649 2013178 2013206 "OAMON" 2013211 T OAMON (NIL) -9 NIL 2013231 NIL) (-813 2011760 2012398 2012426 "OAGROUP" 2012431 T OAGROUP (NIL) -9 NIL 2012451 NIL) (-812 2011442 2011498 2011587 "NUMTUBE" 2011704 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004961 2006533 2008069 "NUMQUAD" 2009926 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000641 2001675 2002710 "NUMODE" 2003946 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997922 1998862 1998890 "NUMINT" 1999813 T NUMINT (NIL) -9 NIL 2000577 NIL) (-808 1996834 1997067 1997285 "NUMFMT" 1997724 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983017 1986138 1988670 "NUMERIC" 1994341 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976728 1982465 1982560 "NTSCAT" 1982565 NIL NTSCAT (NIL T T T T) -9 NIL 1982604 NIL) (-805 1975908 1976087 1976280 "NTPOLFN" 1976567 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975534 1975597 1975706 "NSUP2" 1975845 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962295 1972359 1973171 "NSUP" 1974755 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951131 1962069 1962202 "NSMP" 1962207 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949539 1949864 1950221 "NREP" 1950819 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948118 1948382 1948740 "NPCOEF" 1949282 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947166 1947299 1947515 "NORMRETR" 1947999 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945177 1945497 1945906 "NORMPK" 1946874 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944856 1944890 1945014 "NORMMA" 1945143 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944639 1944674 1944743 "NONE1" 1944820 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944403 1944596 1944625 "NONE" 1944630 T NONE (NIL) -8 NIL NIL NIL) (-794 1943894 1943962 1944141 "NODE1" 1944335 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941986 1943017 1943272 "NNI" 1943619 T NNI (NIL) -8 NIL NIL 1943854) (-792 1940382 1940719 1941083 "NLINSOL" 1941654 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936563 1937618 1938517 "NIPROB" 1939503 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935302 1935554 1935856 "NFINTBAS" 1936325 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934386 1934952 1934993 "NETCLT" 1935165 NIL NETCLT (NIL T) -9 NIL 1935247 NIL) (-788 1933058 1933325 1933606 "NCODIV" 1934154 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932814 1932857 1932932 "NCNTFRAC" 1933015 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930970 1931358 1931778 "NCEP" 1932439 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929633 1930580 1930608 "NASRING" 1930718 T NASRING (NIL) -9 NIL 1930798 NIL) (-784 1929416 1929472 1929566 "NASRING-" 1929571 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928383 1929034 1929062 "NARNG" 1929179 T NARNG (NIL) -9 NIL 1929270 NIL) (-782 1928057 1928142 1928276 "NARNG-" 1928281 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926894 1927143 1927378 "NAGSP" 1927842 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917938 1919850 1921523 "NAGS" 1925241 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916462 1916794 1917125 "NAGF07" 1917627 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910934 1912291 1913598 "NAGF04" 1915175 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903806 1905516 1907149 "NAGF02" 1909321 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898970 1900130 1901247 "NAGF01" 1902709 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892550 1894164 1895749 "NAGE04" 1897405 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883611 1885840 1887970 "NAGE02" 1890440 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879504 1880511 1881475 "NAGE01" 1882667 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877281 1877833 1878391 "NAGD03" 1878966 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868977 1870959 1872913 "NAGD02" 1875347 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862716 1864213 1865653 "NAGD01" 1867557 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858853 1859747 1860584 "NAGC06" 1861899 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857300 1857650 1858006 "NAGC05" 1858517 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856664 1856795 1856939 "NAGC02" 1857176 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855465 1856192 1856232 "NAALG" 1856311 NIL NAALG (NIL T) -9 NIL 1856372 NIL) (-765 1855294 1855329 1855419 "NAALG-" 1855424 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849166 1850352 1851539 "MULTSQFR" 1854190 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848473 1848560 1848744 "MULTFACT" 1849078 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840618 1845056 1845109 "MTSCAT" 1846179 NIL MTSCAT (NIL T T) -9 NIL 1846695 NIL) (-761 1840324 1840384 1840476 "MTHING" 1840558 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840110 1840149 1840209 "MSYSCMD" 1840284 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836855 1839671 1839712 "MSETAGG" 1839717 NIL MSETAGG (NIL T) -9 NIL 1839751 NIL) (-758 1832569 1835610 1835930 "MSET" 1836568 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828161 1829948 1830693 "MRING" 1831869 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827721 1827794 1827925 "MRF2" 1828088 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827333 1827374 1827518 "MRATFAC" 1827680 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824903 1825240 1825671 "MPRFF" 1827038 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818230 1824757 1824854 "MPOLY" 1824859 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817714 1817755 1817963 "MPCPF" 1818189 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817222 1817271 1817455 "MPC3" 1817665 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816405 1816498 1816719 "MPC2" 1817137 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814682 1815043 1815433 "MONOTOOL" 1816065 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813827 1814210 1814238 "MONOID" 1814457 T MONOID (NIL) -9 NIL 1814604 NIL) (-747 1813343 1813492 1813673 "MONOID-" 1813678 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802297 1809163 1809222 "MONOGEN" 1809896 NIL MONOGEN (NIL T T) -9 NIL 1810352 NIL) (-745 1799347 1800250 1801250 "MONOGEN-" 1801369 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798064 1798612 1798640 "MONADWU" 1799032 T MONADWU (NIL) -9 NIL 1799270 NIL) (-743 1797394 1797595 1797843 "MONADWU-" 1797848 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796679 1796983 1797011 "MONAD" 1797218 T MONAD (NIL) -9 NIL 1797330 NIL) (-741 1796346 1796442 1796574 "MONAD-" 1796579 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794485 1795259 1795538 "MOEBIUS" 1796099 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793653 1794153 1794193 "MODULE" 1794198 NIL MODULE (NIL T) -9 NIL 1794237 NIL) (-738 1793191 1793317 1793507 "MODULE-" 1793512 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790721 1791555 1791882 "MODRING" 1793015 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787443 1788826 1789347 "MODOP" 1790250 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785929 1786510 1786787 "MODMONOM" 1787306 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774669 1784220 1784634 "MODMON" 1785566 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771495 1773513 1773789 "MODFIELD" 1774544 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770406 1770776 1770966 "MMLFORM" 1771325 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769926 1769975 1770154 "MMAP" 1770357 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767819 1768758 1768799 "MLO" 1769222 NIL MLO (NIL T) -9 NIL 1769464 NIL) (-729 1765167 1765701 1766303 "MLIFT" 1767300 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764546 1764642 1764796 "MKUCFUNC" 1765078 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764139 1764215 1764338 "MKRECORD" 1764469 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763162 1763348 1763576 "MKFUNC" 1763950 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762538 1762654 1762810 "MKFLCFN" 1763045 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761803 1761917 1762102 "MKBCFUNC" 1762431 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757786 1761357 1761493 "MINT" 1761687 T MINT (NIL) -8 NIL NIL NIL) (-722 1756568 1756841 1757118 "MHROWRED" 1757541 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751312 1755103 1755508 "MFLOAT" 1756183 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750657 1750745 1750916 "MFINFACT" 1751224 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746936 1747820 1748704 "MESH" 1749793 T MESH (NIL) -7 NIL NIL NIL) (-718 1745290 1745638 1745991 "MDDFACT" 1746623 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741826 1744421 1744462 "MDAGG" 1744717 NIL MDAGG (NIL T) -9 NIL 1744860 NIL) (-716 1729528 1741119 1741326 "MCMPLX" 1741639 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728647 1728811 1729012 "MCDEN" 1729377 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726495 1726807 1727187 "MCALCFN" 1728377 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725372 1725660 1725893 "MAYBE" 1726301 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722930 1723507 1724069 "MATSTOR" 1724843 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718352 1722302 1722550 "MATRIX" 1722715 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714052 1714825 1715561 "MATLIN" 1717709 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712628 1712799 1713132 "MATCAT2" 1713887 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701974 1705685 1705762 "MATCAT" 1710794 NIL MATCAT (NIL T T T) -9 NIL 1712266 NIL) (-707 1697927 1699237 1700650 "MATCAT-" 1700655 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696003 1696363 1696747 "MAPPKG3" 1697602 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694960 1695157 1695379 "MAPPKG2" 1695827 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693417 1693743 1694070 "MAPPKG1" 1694666 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692418 1692823 1693000 "MAPPAST" 1693260 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692023 1692087 1692210 "MAPHACK3" 1692354 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691603 1691676 1691790 "MAPHACK2" 1691955 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691029 1691144 1691286 "MAPHACK1" 1691494 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688952 1689729 1690033 "MAGMA" 1690757 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688371 1688676 1688767 "MACROAST" 1688881 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684614 1686610 1687071 "M3D" 1687943 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678094 1682925 1682966 "LZSTAGG" 1683748 NIL LZSTAGG (NIL T) -9 NIL 1684043 NIL) (-695 1673776 1675225 1676682 "LZSTAGG-" 1676687 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670689 1671667 1672154 "LWORD" 1673321 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670211 1670493 1670568 "LSTAST" 1670634 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662139 1669982 1670116 "LSQM" 1670121 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661357 1661502 1661730 "LSPP" 1661994 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658094 1658810 1659540 "LSMP1" 1660659 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655876 1656207 1656663 "LSMP" 1657783 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649012 1654966 1655007 "LSAGG" 1655069 NIL LSAGG (NIL T) -9 NIL 1655147 NIL) (-687 1645521 1646631 1647844 "LSAGG-" 1647849 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642816 1644665 1644914 "LPOLY" 1645316 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642392 1642483 1642606 "LPEFRAC" 1642725 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642075 1642154 1642182 "LOGIC" 1642293 T LOGIC (NIL) -9 NIL 1642375 NIL) (-683 1641931 1641960 1642031 "LOGIC-" 1642036 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641106 1641264 1641457 "LODOOPS" 1641787 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639630 1639879 1640232 "LODOF" 1640853 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635506 1638265 1638306 "LODOCAT" 1638744 NIL LODOCAT (NIL T) -9 NIL 1638955 NIL) (-679 1635221 1635297 1635424 "LODOCAT-" 1635429 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632207 1635062 1635180 "LODO2" 1635185 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629314 1632144 1632189 "LODO1" 1632194 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626409 1629230 1629296 "LODO" 1629301 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625278 1625455 1625760 "LODEEF" 1626232 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623455 1624372 1624625 "LO" 1625110 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618427 1621621 1621662 "LNAGG" 1622524 NIL LNAGG (NIL T) -9 NIL 1622959 NIL) (-672 1617520 1617788 1618130 "LNAGG-" 1618135 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613500 1614445 1615084 "LMOPS" 1616935 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612799 1613277 1613318 "LMODULE" 1613323 NIL LMODULE (NIL T) -9 NIL 1613349 NIL) (-669 1609754 1612444 1612567 "LMDICT" 1612709 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609330 1609544 1609585 "LLINSET" 1609646 NIL LLINSET (NIL T) -9 NIL 1609690 NIL) (-667 1608975 1609238 1609298 "LITERAL" 1609303 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608494 1608574 1608713 "LIST3" 1608895 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606592 1606940 1607339 "LIST2MAP" 1608141 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605581 1605777 1606005 "LIST2" 1606410 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598035 1604515 1604819 "LIST" 1605310 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597618 1597854 1597895 "LINSET" 1597900 NIL LINSET (NIL T) -9 NIL 1597934 NIL) (-661 1596432 1597126 1597293 "LINFORM" 1597503 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594731 1595459 1595500 "LINEXP" 1595990 NIL LINEXP (NIL T) -9 NIL 1596263 NIL) (-659 1593307 1594211 1594392 "LINELT" 1594602 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591864 1592144 1592455 "LINDEP" 1593059 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591000 1591596 1591706 "LINBASIS" 1591794 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587737 1588486 1589263 "LIMITRF" 1590255 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586022 1586336 1586745 "LIMITPS" 1587432 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584850 1585425 1585465 "LIECAT" 1585605 NIL LIECAT (NIL T) -9 NIL 1585756 NIL) (-653 1584685 1584718 1584806 "LIECAT-" 1584811 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578705 1584196 1584424 "LIE" 1584506 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570890 1578245 1578401 "LIB" 1578569 T LIB (NIL) -8 NIL NIL NIL) (-650 1566459 1567408 1568343 "LGROBP" 1570007 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565083 1565991 1566019 "LFCAT" 1566226 T LFCAT (NIL) -9 NIL 1566365 NIL) (-648 1563021 1563355 1563705 "LF" 1564804 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559881 1560553 1561241 "LEXTRIPK" 1562385 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556469 1557451 1557954 "LEXP" 1559461 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555885 1556190 1556282 "LETAST" 1556397 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554271 1554596 1554997 "LEADCDET" 1555567 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553449 1553535 1553764 "LAZM3PK" 1554192 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547960 1551526 1552064 "LAUPOL" 1552961 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547533 1547583 1547744 "LAPLACE" 1547910 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546381 1547097 1547138 "LALG" 1547200 NIL LALG (NIL T) -9 NIL 1547259 NIL) (-639 1546077 1546154 1546290 "LALG-" 1546295 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543814 1545178 1545429 "LA" 1545910 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543643 1543673 1543714 "KVTFROM" 1543776 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542400 1543010 1543195 "KTVLOGIC" 1543478 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542229 1542259 1542300 "KRCFROM" 1542362 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541121 1541320 1541619 "KOVACIC" 1542029 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540950 1540980 1541021 "KONVERT" 1541083 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540779 1540809 1540850 "KOERCE" 1540912 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540263 1540356 1540488 "KERNEL2" 1540693 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537950 1538856 1539233 "KERNEL" 1539919 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531421 1536427 1536481 "KDAGG" 1536858 NIL KDAGG (NIL T T) -9 NIL 1537064 NIL) (-628 1530932 1531074 1531279 "KDAGG-" 1531284 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523632 1530593 1530748 "KAFILE" 1530810 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523236 1523521 1523584 "JVMOP" 1523589 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521972 1522476 1522725 "JVMMDACC" 1523007 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520908 1521362 1521567 "JVMFDACC" 1521787 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519489 1519984 1520284 "JVMCSTTG" 1520628 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518625 1519029 1519190 "JVMCFACC" 1519348 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518303 1518542 1518591 "JVMBCODE" 1518596 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512322 1517814 1518042 "JORDAN" 1518124 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511635 1511971 1512092 "JOINAST" 1512221 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507670 1509812 1509866 "IXAGG" 1510795 NIL IXAGG (NIL T T) -9 NIL 1511254 NIL) (-617 1506523 1506895 1507314 "IXAGG-" 1507319 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501612 1506445 1506504 "IVECTOR" 1506509 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500336 1500615 1500881 "ITUPLE" 1501379 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498808 1499015 1499310 "ITRIGMNP" 1500158 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497535 1497757 1498040 "ITFUN3" 1498584 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497161 1497224 1497333 "ITFUN2" 1497472 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1496266 1496641 1496815 "ITFORM" 1497007 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494035 1495286 1495564 "ITAYLOR" 1496021 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482432 1488172 1489335 "ISUPS" 1492905 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481524 1481676 1481912 "ISUMP" 1482279 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476374 1481469 1481510 "ISTRING" 1481515 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475790 1476095 1476187 "ISAST" 1476302 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474987 1475081 1475297 "IRURPK" 1475704 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473899 1474124 1474364 "IRSN" 1474767 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471944 1472325 1472754 "IRRF2F" 1473537 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471685 1471729 1471805 "IRREDFFX" 1471900 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470258 1470559 1470858 "IROOT" 1471418 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469397 1469751 1469902 "IRFORM" 1470127 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468479 1468610 1468824 "IR2F" 1469280 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466068 1466587 1467153 "IR2" 1467957 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462508 1463752 1464444 "IR" 1465408 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462293 1462333 1462393 "IPRNTPK" 1462468 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458246 1462182 1462251 "IPF" 1462256 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456267 1458171 1458228 "IPADIC" 1458233 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455525 1455827 1455957 "IP4ADDR" 1456157 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454863 1455154 1455286 "IOMODE" 1455413 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453834 1454460 1454587 "IOBFILE" 1454756 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453244 1453738 1453766 "IOBCON" 1453771 T IOBCON (NIL) -9 NIL 1453792 NIL) (-589 1452749 1452813 1452996 "INVLAPLA" 1453180 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442319 1444751 1447137 "INTTR" 1450413 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438612 1439396 1440261 "INTTOOLS" 1441504 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438192 1438289 1438406 "INTSLPE" 1438515 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435659 1438115 1438174 "INTRVL" 1438179 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433237 1433773 1434348 "INTRF" 1435144 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432630 1432745 1432887 "INTRET" 1433135 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430603 1431016 1431486 "INTRAT" 1432238 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427848 1428449 1429068 "INTPM" 1430088 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424565 1425192 1425930 "INTPAF" 1427234 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419666 1420706 1421757 "INTPACK" 1423534 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418912 1419070 1419278 "INTHERTR" 1419508 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418345 1418431 1418619 "INTHERAL" 1418826 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416113 1416634 1417091 "INTHEORY" 1417908 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407445 1409140 1410912 "INTG0" 1414465 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387970 1392808 1397618 "INTFTBL" 1402655 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387195 1387357 1387530 "INTFACT" 1387829 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384592 1385068 1385625 "INTEF" 1386749 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382789 1383684 1383712 "INTDOM" 1384013 T INTDOM (NIL) -9 NIL 1384220 NIL) (-570 1382128 1382332 1382574 "INTDOM-" 1382579 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378002 1380417 1380471 "INTCAT" 1381270 NIL INTCAT (NIL T) -9 NIL 1381591 NIL) (-568 1377456 1377577 1377705 "INTBIT" 1377894 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376137 1376309 1376616 "INTALG" 1377301 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375614 1375710 1375867 "INTAF" 1376041 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368581 1375424 1375564 "INTABL" 1375569 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367822 1368384 1368449 "INT8" 1368483 T INT8 (NIL) -8 NIL NIL 1368528) (-563 1367062 1367624 1367689 "INT64" 1367723 T INT64 (NIL) -8 NIL NIL 1367768) (-562 1366302 1366864 1366929 "INT32" 1366963 T INT32 (NIL) -8 NIL NIL 1367008) (-561 1365542 1366104 1366169 "INT16" 1366203 T INT16 (NIL) -8 NIL NIL 1366248) (-560 1361730 1365339 1365448 "INT" 1365453 T INT (NIL) -8 NIL NIL NIL) (-559 1355831 1359278 1359306 "INS" 1360240 T INS (NIL) -9 NIL 1360905 NIL) (-558 1352885 1353842 1354816 "INS-" 1354889 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351642 1351887 1352185 "INPSIGN" 1352638 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350736 1350877 1351074 "INPRODPF" 1351522 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349606 1349747 1349984 "INPRODFF" 1350616 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348594 1348758 1349018 "INNMFACT" 1349442 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347773 1347888 1348076 "INMODGCD" 1348493 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346257 1346526 1346850 "INFSP" 1347518 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345417 1345558 1345741 "INFPROD0" 1346137 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1345015 1345087 1345185 "INFORM1" 1345352 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341582 1343080 1343595 "INFORM" 1344508 T INFORM (NIL) -8 NIL NIL NIL) (-548 1341087 1341194 1341308 "INFINITY" 1341488 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340161 1340807 1340908 "INETCLTS" 1341006 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338759 1339027 1339348 "INEP" 1339909 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337820 1338656 1338721 "INDE" 1338726 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337372 1337452 1337569 "INCRMAPS" 1337747 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336094 1336641 1336847 "INBFILE" 1337186 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331273 1332330 1333274 "INBFF" 1335182 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330127 1330450 1330478 "INBCON" 1330991 T INBCON (NIL) -9 NIL 1331257 NIL) (-540 1329337 1329602 1329878 "INBCON-" 1329883 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328756 1329061 1329152 "INAST" 1329266 T INAST (NIL) -8 NIL NIL NIL) (-538 1328123 1328435 1328541 "IMPTAST" 1328670 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324044 1327967 1328071 "IMATRIX" 1328076 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322736 1322875 1323191 "IMATQF" 1323900 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320916 1321183 1321520 "IMATLIN" 1322492 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314831 1320840 1320898 "ILIST" 1320903 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312497 1314691 1314804 "IIARRAY2" 1314809 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307297 1312408 1312472 "IFF" 1312477 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306578 1306914 1307030 "IFAST" 1307201 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301090 1305870 1306058 "IFARRAY" 1306435 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300128 1300994 1301067 "IFAMON" 1301072 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299700 1299777 1299831 "IEVALAB" 1300038 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299363 1299443 1299603 "IEVALAB-" 1299608 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298427 1299252 1299327 "IDPOAMS" 1299332 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297560 1298316 1298391 "IDPOAM" 1298396 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296941 1297475 1297537 "IDPO" 1297542 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295421 1295948 1296000 "IDPC" 1296512 NIL IDPC (NIL T T) -9 NIL 1296793 NIL) (-522 1294753 1295313 1295386 "IDPAM" 1295391 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293968 1294645 1294718 "IDPAG" 1294723 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293512 1293774 1293864 "IDENT" 1293898 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289731 1290615 1291510 "IDECOMP" 1292669 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282366 1283654 1284701 "IDEAL" 1288767 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281508 1281638 1281838 "ICDEN" 1282250 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280483 1280988 1281135 "ICARD" 1281381 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278513 1278856 1279261 "IBPTOOLS" 1280160 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273628 1278133 1278246 "IBITS" 1278432 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270303 1270927 1271622 "IBATOOL" 1273045 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268064 1268544 1269077 "IBACHIN" 1269838 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265654 1267910 1268013 "IARRAY2" 1268018 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261367 1265580 1265637 "IARRAY1" 1265642 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254377 1259779 1260260 "IAN" 1260906 T IAN (NIL) -8 NIL NIL NIL) (-508 1253882 1253945 1254118 "IALGFACT" 1254314 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253374 1253523 1253551 "HYPCAT" 1253758 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252876 1253029 1253215 "HYPCAT-" 1253220 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252423 1252671 1252754 "HOSTNAME" 1252813 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252256 1252305 1252346 "HOMOTOP" 1252351 NIL HOMOTOP (NIL T) -9 NIL 1252384 NIL) (-503 1248689 1250188 1250229 "HOAGG" 1251210 NIL HOAGG (NIL T) -9 NIL 1251939 NIL) (-502 1247205 1247682 1248208 "HOAGG-" 1248213 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240241 1246798 1246948 "HEXADEC" 1247075 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238953 1239211 1239474 "HEUGCD" 1240018 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237885 1238790 1238920 "HELLFDIV" 1238925 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235895 1237662 1237750 "HEAP" 1237829 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235092 1235447 1235581 "HEADAST" 1235781 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228479 1235007 1235069 "HDP" 1235074 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221491 1228114 1228266 "HDMP" 1228380 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220797 1220955 1221119 "HB" 1221347 T HB (NIL) -7 NIL NIL NIL) (-493 1213807 1220643 1220747 "HASHTBL" 1220752 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213223 1213528 1213620 "HASAST" 1213735 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210629 1212845 1213027 "HACKPI" 1213061 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205801 1210482 1210595 "GTSET" 1210600 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198840 1205679 1205777 "GSTBL" 1205782 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190589 1198005 1198261 "GSERIES" 1198640 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189620 1190133 1190161 "GROUP" 1190364 T GROUP (NIL) -9 NIL 1190498 NIL) (-486 1188944 1189145 1189396 "GROUP-" 1189401 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187293 1187632 1188019 "GROEBSOL" 1188621 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186121 1186481 1186532 "GRMOD" 1187061 NIL GRMOD (NIL T T) -9 NIL 1187229 NIL) (-483 1185877 1185925 1186053 "GRMOD-" 1186058 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181017 1182231 1183231 "GRIMAGE" 1184897 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179411 1179744 1180068 "GRDEF" 1180713 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178843 1178971 1179112 "GRAY" 1179290 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177920 1178422 1178473 "GRALG" 1178626 NIL GRALG (NIL T T) -9 NIL 1178719 NIL) (-478 1177557 1177654 1177817 "GRALG-" 1177822 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174038 1177140 1177319 "GPOLSET" 1177463 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173386 1173449 1173707 "GOSPER" 1173975 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168956 1169824 1170350 "GMODPOL" 1173085 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167943 1168145 1168383 "GHENSEL" 1168768 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162015 1162942 1163962 "GENUPS" 1167027 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161706 1161763 1161852 "GENUFACT" 1161958 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161106 1161195 1161360 "GENPGCD" 1161624 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160574 1160615 1160828 "GENMFACT" 1161065 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159110 1159397 1159704 "GENEEZ" 1160317 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152282 1158721 1158883 "GDMP" 1159033 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141020 1146053 1147159 "GCNAALG" 1151265 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139147 1140195 1140223 "GCDDOM" 1140478 T GCDDOM (NIL) -9 NIL 1140635 NIL) (-465 1138587 1138744 1138959 "GCDDOM-" 1138964 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1127059 1129533 1131925 "GBINTERN" 1136278 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124860 1125188 1125609 "GBF" 1126734 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123617 1123806 1124073 "GBEUCLID" 1124676 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1122267 1122474 1122778 "GB" 1123396 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121598 1121741 1121890 "GAUSSFAC" 1122138 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119919 1120267 1120581 "GALUTIL" 1121317 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118179 1118501 1118825 "GALPOLYU" 1119646 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115478 1115834 1116241 "GALFACTU" 1117876 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107092 1108783 1110391 "GALFACT" 1113910 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104378 1105138 1105166 "FVFUN" 1106322 T FVFUN (NIL) -9 NIL 1107042 NIL) (-454 1103608 1103826 1103854 "FVC" 1104145 T FVC (NIL) -9 NIL 1104328 NIL) (-453 1103209 1103433 1103501 "FUNDESC" 1103560 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102782 1103006 1103087 "FUNCTION" 1103161 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101459 1102083 1102286 "FTEM" 1102599 T FTEM (NIL) -8 NIL NIL NIL) (-450 1099089 1099781 1100247 "FT" 1101013 T FT (NIL) -8 NIL NIL NIL) (-449 1097358 1097669 1098066 "FSUPFACT" 1098780 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095677 1096044 1096376 "FST" 1097046 T FST (NIL) -8 NIL NIL NIL) (-447 1094858 1094982 1095170 "FSRED" 1095559 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093547 1093813 1094160 "FSPRMELT" 1094573 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090757 1091291 1091777 "FSPECF" 1093110 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1090279 1090339 1090509 "FSINT" 1090698 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088415 1089272 1089575 "FSERIES" 1090058 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087439 1087573 1087797 "FSCINT" 1088295 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086463 1086624 1086851 "FSAGG2" 1087292 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1082327 1085407 1085448 "FSAGG" 1085818 NIL FSAGG (NIL T) -9 NIL 1086077 NIL) (-439 1079927 1080690 1081486 "FSAGG-" 1081581 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077587 1077885 1078433 "FS2UPS" 1079645 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076453 1076636 1076938 "FS2EXPXP" 1077412 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1076081 1076130 1076259 "FS2" 1076404 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1056308 1065855 1065896 "FS" 1069780 NIL FS (NIL T) -9 NIL 1072069 NIL) (-434 1044369 1047944 1052001 "FS-" 1052301 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043783 1043910 1044062 "FRUTIL" 1044249 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1038301 1041472 1041512 "FRNAALG" 1042832 NIL FRNAALG (NIL T) -9 NIL 1043430 NIL) (-431 1033782 1035050 1036325 "FRNAALG-" 1037075 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033414 1033463 1033590 "FRNAAF2" 1033733 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031701 1032263 1032559 "FRMOD" 1033226 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030886 1030979 1031270 "FRIDEAL2" 1031608 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028491 1029261 1029579 "FRIDEAL" 1030677 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027582 1028038 1028079 "FRETRCT" 1028084 NIL FRETRCT (NIL T) -9 NIL 1028260 NIL) (-425 1026640 1026925 1027276 "FRETRCT-" 1027281 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023454 1024924 1024983 "FRAMALG" 1025865 NIL FRAMALG (NIL T T) -9 NIL 1026157 NIL) (-423 1021492 1022043 1022673 "FRAMALG-" 1022896 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1021122 1021185 1021292 "FRAC2" 1021429 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1014093 1020595 1020872 "FRAC" 1020877 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013723 1013786 1013893 "FR2" 1014030 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004640 1009218 1010576 "FR" 1012397 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998557 1002019 1002047 "FPS" 1003166 T FPS (NIL) -9 NIL 1003723 NIL) (-417 997982 998115 998279 "FPS-" 998425 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994934 996939 996967 "FPC" 997192 T FPC (NIL) -9 NIL 997334 NIL) (-415 994715 994767 994864 "FPC-" 994869 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993473 994203 994244 "FPATMAB" 994249 NIL FPATMAB (NIL T) -9 NIL 994401 NIL) (-413 991616 992215 992562 "FPARFRAC" 993189 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986908 987508 988190 "FORTRAN" 991048 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984482 985146 985174 "FORTFN" 986234 T FORTFN (NIL) -9 NIL 986858 NIL) (-410 984234 984296 984324 "FORTCAT" 984383 T FORTCAT (NIL) -9 NIL 984445 NIL) (-409 981920 982450 982989 "FORT" 983715 T FORT (NIL) -7 NIL NIL NIL) (-408 981702 981738 981807 "FORMULA1" 981884 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979706 980318 980708 "FORMULA" 981332 T FORMULA (NIL) -8 NIL NIL NIL) (-406 979223 979281 979454 "FORDER" 979648 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978283 978483 978676 "FOP" 979050 T FOP (NIL) -7 NIL NIL NIL) (-404 976696 977563 977737 "FNLA" 978165 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975315 975826 975854 "FNCAT" 976314 T FNCAT (NIL) -9 NIL 976574 NIL) (-402 974758 975274 975302 "FNAME" 975307 T FNAME (NIL) -8 NIL NIL NIL) (-401 973084 974257 974285 "FMTC" 974290 T FMTC (NIL) -9 NIL 974326 NIL) (-400 971632 973020 973066 "FMONOID" 973071 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968221 969587 969628 "FMONCAT" 970845 NIL FMONCAT (NIL T) -9 NIL 971450 NIL) (-398 965543 966291 966319 "FMFUN" 967463 T FMFUN (NIL) -9 NIL 968171 NIL) (-397 962416 963468 963522 "FMCAT" 964717 NIL FMCAT (NIL T T) -9 NIL 965212 NIL) (-396 961649 961866 961894 "FMC" 962184 T FMC (NIL) -9 NIL 962366 NIL) (-395 960317 961415 961515 "FM1" 961594 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959335 960059 960208 "FM" 960213 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 957073 957525 958019 "FLOATRP" 958886 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954475 955011 955589 "FLOATCP" 956540 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 947131 952204 952825 "FLOAT" 953874 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945649 946723 946764 "FLINEXP" 946769 NIL FLINEXP (NIL T) -9 NIL 946862 NIL) (-389 944779 945038 945366 "FLINEXP-" 945371 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943837 943999 944223 "FLASORT" 944631 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940755 941807 941859 "FLALG" 943086 NIL FLALG (NIL T T) -9 NIL 943553 NIL) (-386 939779 939940 940167 "FLAGG2" 940608 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 933043 937188 937229 "FLAGG" 938491 NIL FLAGG (NIL T) -9 NIL 939143 NIL) (-384 931697 932108 932598 "FLAGG-" 932603 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928328 929542 929601 "FINRALG" 930729 NIL FINRALG (NIL T T) -9 NIL 931237 NIL) (-382 927452 927717 928056 "FINRALG-" 928061 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926758 927057 927085 "FINITE" 927281 T FINITE (NIL) -9 NIL 927388 NIL) (-380 918709 921288 921328 "FINAALG" 924995 NIL FINAALG (NIL T) -9 NIL 926448 NIL) (-379 913825 915091 916235 "FINAALG-" 917614 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912385 912807 912861 "FILECAT" 913545 NIL FILECAT (NIL T T) -9 NIL 913761 NIL) (-377 911663 912140 912243 "FILE" 912315 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 909059 910893 910921 "FIELD" 910961 T FIELD (NIL) -9 NIL 911041 NIL) (-375 907601 908064 908575 "FIELD-" 908580 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905283 906236 906583 "FGROUP" 907287 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904355 904537 904757 "FGLMICPK" 905115 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899589 904280 904337 "FFX" 904342 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899184 899251 899386 "FFSLPE" 899522 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898682 898724 898933 "FFPOLY2" 899142 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894558 895454 896250 "FFPOLY" 897918 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889806 894477 894540 "FFP" 894545 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884316 889149 889339 "FFNBX" 889660 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878628 883451 883709 "FFNBP" 884170 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872645 877912 878123 "FFNB" 878461 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871465 871675 871990 "FFINTBAS" 872442 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 867041 869712 869740 "FFIELDC" 870360 T FFIELDC (NIL) -9 NIL 870736 NIL) (-362 865619 866074 866571 "FFIELDC-" 866576 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865176 865234 865358 "FFHOM" 865561 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862835 863358 863875 "FFF" 864691 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857849 862577 862678 "FFCGX" 862778 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852867 857581 857688 "FFCGP" 857792 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847446 852594 852702 "FFCG" 852803 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846851 846900 847135 "FFCAT2" 847397 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825514 836583 836669 "FFCAT" 841834 NIL FFCAT (NIL T T T) -9 NIL 843285 NIL) (-354 820525 821759 823073 "FFCAT-" 824303 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815325 820436 820500 "FF" 820505 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803978 808297 809517 "FEXPR" 814177 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802906 803375 803416 "FEVALAB" 803500 NIL FEVALAB (NIL T) -9 NIL 803761 NIL) (-350 802023 802275 802613 "FEVALAB-" 802618 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798885 799770 799885 "FDIVCAT" 801453 NIL FDIVCAT (NIL T T T T) -9 NIL 801890 NIL) (-348 798641 798674 798844 "FDIVCAT-" 798849 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797855 797948 798225 "FDIV2" 798548 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796265 797238 797441 "FDIV" 797754 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795173 795560 795762 "FCTRDATA" 796083 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793829 794118 794407 "FCPAK1" 794904 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792832 793329 793470 "FCOMP" 793720 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776146 779982 783520 "FC" 789314 T FC (NIL) -8 NIL NIL NIL) (-341 767841 772467 772507 "FAXF" 774309 NIL FAXF (NIL T) -9 NIL 775001 NIL) (-340 764962 765775 766600 "FAXF-" 767065 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759531 764338 764514 "FARRAY" 764819 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754095 756478 756531 "FAMR" 757554 NIL FAMR (NIL T T) -9 NIL 758014 NIL) (-337 752919 753287 753722 "FAMR-" 753727 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751946 752841 752894 "FAMONOID" 752899 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749576 750428 750481 "FAMONC" 751422 NIL FAMONC (NIL T T) -9 NIL 751808 NIL) (-334 748050 749330 749467 "FAGROUP" 749472 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745803 746164 746567 "FACUTIL" 747731 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744890 745087 745309 "FACTFUNC" 745613 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736648 744193 744392 "EXPUPXS" 744746 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734101 734671 735257 "EXPRTUBE" 736082 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730312 730964 731694 "EXPRODE" 733440 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724746 725453 726259 "EXPR2UPS" 729610 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724372 724435 724544 "EXPR2" 724683 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708666 723021 723450 "EXPR" 723976 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698983 707817 708108 "EXPEXPAN" 708502 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698403 698707 698798 "EXITAST" 698912 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698167 698360 698389 "EXIT" 698394 T EXIT (NIL) -8 NIL NIL NIL) (-322 697788 697856 697969 "EVALCYC" 698099 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697305 697447 697488 "EVALAB" 697658 NIL EVALAB (NIL T) -9 NIL 697762 NIL) (-320 696762 696908 697129 "EVALAB-" 697134 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693870 695418 695446 "EUCDOM" 696001 T EUCDOM (NIL) -9 NIL 696351 NIL) (-318 692209 692717 693307 "EUCDOM-" 693312 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691835 691898 692007 "ESTOOLS2" 692146 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691580 691628 691708 "ESTOOLS1" 691787 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678897 681878 684628 "ESTOOLS" 688850 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678636 678674 678756 "ESCONT1" 678859 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674944 675771 676551 "ESCONT" 677876 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674613 674669 674769 "ES2" 674888 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674237 674301 674410 "ES1" 674549 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667938 669868 669896 "ES" 672664 T ES (NIL) -9 NIL 674074 NIL) (-309 662615 664172 665989 "ES-" 666153 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661807 661960 662136 "ERROR" 662459 T ERROR (NIL) -7 NIL NIL NIL) (-307 654823 661666 661757 "EQTBL" 661762 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654449 654512 654621 "EQ2" 654760 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646708 649763 651212 "EQ" 653033 NIL -1495 (NIL T) -8 NIL NIL NIL) (-304 641951 643046 644139 "EP" 645647 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640491 640842 641148 "ENV" 641665 T ENV (NIL) -8 NIL NIL NIL) (-302 639451 640125 640153 "ENTIRER" 640158 T ENTIRER (NIL) -9 NIL 640204 NIL) (-301 635863 637633 637994 "EMR" 639259 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634967 635178 635232 "ELTAGG" 635612 NIL ELTAGG (NIL T T) -9 NIL 635823 NIL) (-299 634674 634748 634889 "ELTAGG-" 634894 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634432 634467 634521 "ELTAB" 634605 NIL ELTAB (NIL T T) -9 NIL 634657 NIL) (-297 633534 633704 633903 "ELFUTS" 634283 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633258 633332 633360 "ELEMFUN" 633465 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633122 633149 633217 "ELEMFUN-" 633222 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627539 631164 631205 "ELAGG" 632145 NIL ELAGG (NIL T) -9 NIL 632608 NIL) (-293 625716 626258 626921 "ELAGG-" 626926 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624998 625165 625321 "ELABOR" 625580 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623605 623938 624232 "ELABEXPR" 624724 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616117 618242 619071 "EFUPXS" 622880 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609243 611366 612177 "EFULS" 615392 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606680 607086 607558 "EFSTRUC" 608875 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596117 598037 599585 "EF" 605195 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595095 595602 595751 "EAB" 595988 T EAB (NIL) -8 NIL NIL NIL) (-285 594217 595054 595082 "E04UCFA" 595087 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593339 594176 594204 "E04NAFA" 594209 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592461 593298 593326 "E04MBFA" 593331 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591583 592420 592448 "E04JAFA" 592453 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590707 591542 591570 "E04GCFA" 591575 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589831 590666 590694 "E04FDFA" 590699 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588953 589790 589818 "E04DGFA" 589823 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583030 584478 585842 "E04AGNT" 587609 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581650 582331 582371 "DVARCAT" 582712 NIL DVARCAT (NIL T) -9 NIL 582875 NIL) (-276 580800 581066 581380 "DVARCAT-" 581385 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572761 580599 580728 "DSMP" 580733 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571112 571903 571944 "DSEXT" 572307 NIL DSEXT (NIL T) -9 NIL 572601 NIL) (-273 569301 569825 570491 "DSEXT-" 570496 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 568960 569025 569123 "DROPT1" 569236 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 563979 565201 566338 "DROPT0" 567843 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558562 559924 560992 "DROPT" 562931 T DROPT (NIL) -8 NIL NIL NIL) (-269 556871 557232 557618 "DRAWPT" 558196 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556498 556557 556675 "DRAWHACK" 556812 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555199 555498 555789 "DRAWCX" 556227 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554708 554783 554934 "DRAWCURV" 555125 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545026 547138 549253 "DRAWCFUN" 552613 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539517 540536 541615 "DRAW" 544000 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 535988 538182 538223 "DQAGG" 538852 NIL DQAGG (NIL T) -9 NIL 539126 NIL) (-262 522571 530199 530282 "DPOLCAT" 532134 NIL DPOLCAT (NIL T T T T) -9 NIL 532679 NIL) (-261 517090 518756 520714 "DPOLCAT-" 520719 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509947 516951 517049 "DPMO" 517054 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502701 509727 509894 "DPMM" 509899 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502223 502485 502574 "DOMTMPLT" 502632 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501572 502025 502105 "DOMCTOR" 502163 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500724 501052 501203 "DOMAIN" 501441 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493736 500359 500511 "DMP" 500625 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491513 492803 492844 "DMEXT" 492849 NIL DMEXT (NIL T) -9 NIL 493025 NIL) (-253 491107 491169 491313 "DLP" 491451 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484230 490434 490624 "DLIST" 490949 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480768 483055 483096 "DLAGG" 483646 NIL DLAGG (NIL T) -9 NIL 483876 NIL) (-250 479280 480094 480122 "DIVRING" 480214 T DIVRING (NIL) -9 NIL 480297 NIL) (-249 478463 478707 479007 "DIVRING-" 479012 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476505 476922 477328 "DISPLAY" 478077 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475335 475556 475821 "DIRPROD2" 476298 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468742 475249 475312 "DIRPROD" 475317 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456961 463453 463506 "DIRPCAT" 463764 NIL DIRPCAT (NIL NIL T) -9 NIL 464639 NIL) (-244 454161 454929 455810 "DIRPCAT-" 456147 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453442 453608 453794 "DIOSP" 453995 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449856 452326 452367 "DIOPS" 452801 NIL DIOPS (NIL T) -9 NIL 453030 NIL) (-241 449375 449519 449710 "DIOPS-" 449715 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448282 449054 449082 "DIFRING" 449087 T DIFRING (NIL) -9 NIL 449109 NIL) (-239 447930 448028 448056 "DIFFSPC" 448175 T DIFFSPC (NIL) -9 NIL 448250 NIL) (-238 447551 447653 447805 "DIFFSPC-" 447810 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446487 447085 447126 "DIFFMOD" 447131 NIL DIFFMOD (NIL T) -9 NIL 447229 NIL) (-236 446183 446240 446281 "DIFFDOM" 446402 NIL DIFFDOM (NIL T) -9 NIL 446470 NIL) (-235 446030 446060 446144 "DIFFDOM-" 446149 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443770 445234 445275 "DIFEXT" 445280 NIL DIFEXT (NIL T) -9 NIL 445433 NIL) (-233 440804 443274 443315 "DIAGG" 443320 NIL DIAGG (NIL T) -9 NIL 443340 NIL) (-232 440152 440345 440597 "DIAGG-" 440602 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 435002 439111 439388 "DHMATRIX" 439921 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430470 431523 432533 "DFSFUN" 434012 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424704 429401 429713 "DFLOAT" 430178 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422943 423248 423637 "DFINTTLS" 424412 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419762 420964 421364 "DERHAM" 422609 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417298 419537 419626 "DEQUEUE" 419706 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416540 416685 416868 "DEGRED" 417160 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412946 413715 414561 "DEFINTRF" 415768 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410483 410970 411562 "DEFINTEF" 412465 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409767 410103 410218 "DEFAST" 410388 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402803 409360 409510 "DECIMAL" 409637 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400261 400773 401279 "DDFACT" 402347 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399851 399900 400051 "DBLRESP" 400212 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 399052 399621 399712 "DBASIS" 399800 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396836 397282 397643 "DBASE" 398818 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 396024 396316 396462 "DATAARY" 396735 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395082 395983 396011 "D03FAFA" 396016 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394141 395041 395069 "D03EEFA" 395074 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 392067 392557 393046 "D03AGNT" 393672 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391308 392026 392054 "D02EJFA" 392059 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390549 391267 391295 "D02CJFA" 391300 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389790 390508 390536 "D02BHFA" 390541 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 389031 389749 389777 "D02BBFA" 389782 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382162 383817 385423 "D02AGNT" 387445 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379912 380453 380999 "D01WGTS" 381636 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378919 379871 379899 "D01TRNS" 379904 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377927 378878 378906 "D01GBFA" 378911 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376935 377886 377914 "D01FCFA" 377919 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375943 376894 376922 "D01ASFA" 376927 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374951 375902 375930 "D01AQFA" 375935 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373959 374910 374938 "D01APFA" 374943 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372967 373918 373946 "D01ANFA" 373951 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371975 372926 372954 "D01AMFA" 372959 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370983 371934 371962 "D01ALFA" 371967 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369991 370942 370970 "D01AKFA" 370975 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368999 369950 369978 "D01AJFA" 369983 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362222 363847 365408 "D01AGNT" 367458 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361541 361687 361839 "CYCLOTOM" 362090 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358196 358989 359716 "CYCLES" 360834 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357496 357642 357813 "CVMP" 358057 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355283 355595 355964 "CTRIGMNP" 357224 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354756 355014 355115 "CTORKIND" 355202 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353961 354349 354377 "CTORCAT" 354559 T CTORCAT (NIL) -9 NIL 354672 NIL) (-188 353535 353670 353829 "CTORCAT-" 353834 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352949 353209 353317 "CTORCALL" 353459 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352307 352743 352816 "CTOR" 352896 T CTOR (NIL) -8 NIL NIL NIL) (-185 351663 351780 351933 "CSTTOOLS" 352204 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347360 348119 348877 "CRFP" 350975 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346775 347081 347173 "CRCEAST" 347288 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345798 346007 346235 "CRAPACK" 346579 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345178 345283 345487 "CPMATCH" 345674 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344897 344931 345037 "CPIMA" 345144 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341155 341917 342636 "COORDSYS" 344232 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340543 340688 340830 "CONTOUR" 341033 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 336008 338546 339038 "CONTFRAC" 340083 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335882 335909 335937 "CONDUIT" 335974 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334836 335510 335538 "COMRING" 335543 T COMRING (NIL) -9 NIL 335595 NIL) (-174 333818 334194 334378 "COMPPROP" 334672 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333473 333514 333642 "COMPLPAT" 333777 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 333103 333166 333273 "COMPLEX2" 333410 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321486 332912 333021 "COMPLEX" 333026 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320807 320946 321106 "COMPILER" 321346 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320519 320560 320658 "COMPFACT" 320766 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301894 314223 314263 "COMPCAT" 315267 NIL COMPCAT (NIL T) -9 NIL 316615 NIL) (-167 290782 294333 297960 "COMPCAT-" 298316 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290505 290539 290642 "COMMUPC" 290748 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290293 290333 290392 "COMMONOP" 290466 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289815 290097 290172 "COMMAAST" 290238 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289323 289566 289653 "COMM" 289748 T COMM (NIL) -8 NIL NIL NIL) (-162 288518 288766 288794 "COMBOPC" 289132 T COMBOPC (NIL) -9 NIL 289307 NIL) (-161 287372 287624 287866 "COMBINAT" 288308 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283715 284403 285030 "COMBF" 286794 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282377 282831 283066 "COLOR" 283500 T COLOR (NIL) -8 NIL NIL NIL) (-158 281793 282098 282190 "COLONAST" 282305 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281427 281480 281605 "CMPLXRT" 281740 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280815 281127 281226 "CLLCTAST" 281348 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276275 277345 278425 "CLIP" 279755 T CLIP (NIL) -7 NIL NIL NIL) (-154 274448 275376 275616 "CLIF" 276102 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270430 272566 272607 "CLAGG" 273536 NIL CLAGG (NIL T) -9 NIL 274072 NIL) (-152 268774 269309 269892 "CLAGG-" 269897 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268312 268403 268543 "CINTSLPE" 268683 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265777 266284 266832 "CHVAR" 267840 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264817 265491 265519 "CHARZ" 265524 T CHARZ (NIL) -9 NIL 265539 NIL) (-148 264565 264611 264689 "CHARPOL" 264771 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263483 264196 264224 "CHARNZ" 264271 T CHARNZ (NIL) -9 NIL 264327 NIL) (-146 260427 261537 262066 "CHAR" 262974 T CHAR (NIL) -8 NIL NIL NIL) (-145 260135 260214 260242 "CFCAT" 260353 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259358 259487 259670 "CDEN" 260019 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254955 258511 258791 "CCLASS" 259098 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254176 254363 254540 "CATEGORY" 254798 T -10 (NIL) -8 NIL NIL NIL) (-141 253671 254095 254143 "CATCTOR" 254148 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253062 253374 253472 "CATAST" 253593 T CATAST (NIL) -8 NIL NIL NIL) (-139 252478 252783 252875 "CASEAST" 252990 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251574 251734 251955 "CARTEN2" 252325 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246472 247731 248475 "CARTEN" 250886 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244602 245622 245879 "CARD" 246235 T CARD (NIL) -8 NIL NIL NIL) (-135 244124 244406 244481 "CAPSLAST" 244547 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243566 243822 243850 "CACHSET" 243982 T CACHSET (NIL) -9 NIL 244060 NIL) (-133 242956 243344 243372 "CABMON" 243422 T CABMON (NIL) -9 NIL 243478 NIL) (-132 242393 242660 242770 "BYTEORD" 242866 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237320 241898 242070 "BYTEBUF" 242241 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236078 236835 236984 "BYTE" 237147 T BYTE (NIL) -8 NIL NIL 237276) (-129 233340 235770 235877 "BTREE" 236004 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230542 232988 233110 "BTOURN" 233250 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227649 229984 230025 "BTCAT" 230093 NIL BTCAT (NIL T) -9 NIL 230170 NIL) (-126 227298 227396 227545 "BTCAT-" 227550 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222190 226544 226572 "BTAGG" 226686 T BTAGG (NIL) -9 NIL 226796 NIL) (-124 221644 221805 222011 "BTAGG-" 222016 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218380 220922 221137 "BSTREE" 221461 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217488 217644 217828 "BRILL" 218236 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213883 216186 216227 "BRAGG" 216876 NIL BRAGG (NIL T) -9 NIL 217134 NIL) (-120 212316 212818 213373 "BRAGG-" 213378 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204552 211660 211845 "BPADICRT" 212163 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202561 204489 204534 "BPADIC" 204539 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202253 202289 202403 "BOUNDZRO" 202525 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199980 200438 200913 "BOP1" 201811 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194962 196406 197318 "BOP" 199088 T BOP (NIL) -8 NIL NIL NIL) (-114 193627 194550 194692 "BOOLEAN" 194840 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193220 193377 193405 "BOOLE" 193516 T BOOLE (NIL) -9 NIL 193597 NIL) (-112 193088 193115 193181 "BOOLE-" 193186 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158914 159759 159901 "ASP80" 160043 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158641 158862 158901 "ASP8" 158906 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157487 158318 158436 "ASP78" 158554 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156348 157167 157284 "ASP77" 157401 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155152 155986 156117 "ASP74" 156248 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153944 154787 154919 "ASP73" 155051 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153579 153711 "ASP7" 153843 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP49" 149331 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147066 147929 148097 "ASP42" 148279 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145735 146599 146769 "ASP41" 146953 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145436 145546 "ASP4" 145656 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 141739 141778 "ASP30" 141783 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141237 141324 141400 "ASP29" 141475 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140966 141185 141224 "ASP28" 141229 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140695 140914 140953 "ASP27" 140958 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139671 140393 140504 "ASP24" 140615 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138640 139473 139585 "ASP20" 139590 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137475 138314 138433 "ASP19" 138552 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137194 137279 137355 "ASP12" 137430 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135938 136793 136937 "ASP10" 137081 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134918 135639 135749 "ASP1" 135859 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132530 134762 134853 "ARRAY2" 134858 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131544 131735 131956 "ARRAY12" 132353 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126904 131192 131306 "ARRAY1" 131461 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120949 123106 123181 "ARR2CAT" 125811 NIL ARR2CAT (NIL T T T) -9 NIL 126569 NIL) (-56 118239 119127 120081 "ARR2CAT-" 120086 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117490 117866 117991 "ARITY" 118132 T ARITY (NIL) -8 NIL NIL NIL) (-54 116248 116418 116717 "APPRULE" 117326 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115893 115947 116066 "APPLYORE" 116194 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115147 115294 115451 "ANY1" 115767 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114447 114740 114860 "ANY" 115045 T ANY (NIL) -8 NIL NIL NIL) (-50 111773 112884 113211 "ANTISYM" 114171 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111217 111480 111576 "ANON" 111695 T ANON (NIL) -8 NIL NIL NIL) (-48 104373 109756 110210 "AN" 110781 T AN (NIL) -8 NIL NIL NIL) (-47 100029 101645 101696 "AMR" 102444 NIL AMR (NIL T T) -9 NIL 103044 NIL) (-46 99081 99362 99725 "AMR-" 99730 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82550 98998 99059 "ALIST" 99064 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78847 82144 82313 "ALGSC" 82468 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75297 75957 76564 "ALGPKG" 78287 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74562 74675 74859 "ALGMFACT" 75183 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70545 71176 71770 "ALGMANIP" 74146 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59884 70171 70321 "ALGFF" 70478 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59056 59211 59390 "ALGFACT" 59742 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57845 58583 58621 "ALGEBRA" 58626 NIL ALGEBRA (NIL T) -9 NIL 58667 NIL) (-37 57545 57622 57754 "ALGEBRA-" 57759 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38506 55382 55434 "ALAGG" 55570 NIL ALAGG (NIL T T) -9 NIL 55731 NIL) (-35 38006 38155 38181 "AHYP" 38382 T AHYP (NIL) -9 NIL NIL NIL) (-34 36891 37185 37211 "AGG" 37710 T AGG (NIL) -9 NIL 37989 NIL) (-33 36289 36487 36701 "AGG-" 36706 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34049 34518 34923 "AF" 35931 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33469 33774 33864 "ADDAST" 33977 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32701 32996 33152 "ACPLOT" 33331 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20258 29633 29671 "ACFS" 30278 NIL ACFS (NIL T) -9 NIL 30517 NIL) (-28 18165 18775 19537 "ACFS-" 19542 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13873 16198 16224 "ACF" 17103 T ACF (NIL) -9 NIL 17516 NIL) (-26 12505 12911 13404 "ACF-" 13409 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12015 12258 12284 "ABELSG" 12376 T ABELSG (NIL) -9 NIL 12441 NIL) (-24 11876 11907 11973 "ABELSG-" 11978 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11145 11492 11518 "ABELMON" 11688 T ABELMON (NIL) -9 NIL 11800 NIL) (-22 10785 10893 11031 "ABELMON-" 11036 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10035 10491 10517 "ABELGRP" 10589 T ABELGRP (NIL) -9 NIL 10664 NIL) (-20 9462 9627 9843 "ABELGRP-" 9848 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8724 8763 "A1AGG" 8768 NIL A1AGG (NIL T) -9 NIL 8808 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3472718 3472723 3472728 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472703 3472708 3472713 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472688 3472693 3472698 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472673 3472678 3472683 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471660 3472548 3472625 "ZMOD" 3472630 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3470696 3470878 3471101 "ZLINDEP" 3471492 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3459858 3461764 3463736 "ZDSOLVE" 3468826 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459092 3459245 3459434 "YSTREAM" 3459704 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458452 3458761 3458876 "YDIAGRAM" 3458999 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3455900 3457753 3457957 "XRPOLY" 3458295 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452167 3453771 3454346 "XPR" 3455372 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449498 3451174 3451229 "XPOLYC" 3451517 NIL XPOLYC (NIL T T) -9 NIL 3451630 NIL) (-1319 3446893 3448829 3449033 "XPOLY" 3449329 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3442839 3445410 3445798 "XPBWPOLY" 3446551 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3437731 3439310 3439365 "XFALG" 3441537 NIL XFALG (NIL T T) -9 NIL 3442326 NIL) (-1316 3433000 3435707 3435749 "XF" 3436370 NIL XF (NIL T) -9 NIL 3436770 NIL) (-1315 3432597 3432709 3432878 "XF-" 3432883 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3431712 3431834 3432039 "XEXPPKG" 3432489 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429453 3431562 3431658 "XDPOLY" 3431663 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428108 3428846 3428889 "XALG" 3428894 NIL XALG (NIL T) -9 NIL 3429005 NIL) (-1311 3421018 3426085 3426579 "WUTSET" 3427700 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419120 3420070 3420393 "WP" 3420829 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418668 3418942 3419012 "WHILEAST" 3419072 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418080 3418385 3418479 "WHEREAST" 3418596 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3416954 3417164 3417459 "WFFINTBS" 3417877 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3414822 3415285 3415747 "WEIER" 3416526 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3413746 3414304 3414346 "VSPACE" 3414482 NIL VSPACE (NIL T) -9 NIL 3414556 NIL) (-1304 3413578 3413611 3413702 "VSPACE-" 3413707 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413375 3413429 3413497 "VOID" 3413532 T VOID (NIL) -8 NIL NIL NIL) (-1302 3409643 3410438 3411175 "VIEWDEF" 3412660 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3398587 3401191 3403364 "VIEW3D" 3407492 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3390604 3392498 3394077 "VIEW2D" 3397030 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3388704 3389099 3389505 "VIEW" 3390220 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3387257 3387540 3387858 "VECTOR2" 3388434 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3382163 3387027 3387119 "VECTOR" 3387200 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3375117 3379867 3379910 "VECTCAT" 3380905 NIL VECTCAT (NIL T) -9 NIL 3381492 NIL) (-1295 3374059 3374385 3374775 "VECTCAT-" 3374780 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373465 3373710 3373830 "VARIABLE" 3373974 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373398 3373403 3373433 "UTYPE" 3373438 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372206 3372382 3372644 "UTSODETL" 3373224 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369598 3370106 3370630 "UTSODE" 3371747 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3359605 3365531 3365574 "UTSCAT" 3366686 NIL UTSCAT (NIL T) -9 NIL 3367444 NIL) (-1289 3356731 3357675 3358664 "UTSCAT-" 3358669 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3356352 3356401 3356534 "UTS2" 3356682 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3347662 3354113 3354593 "UTS" 3355930 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3341529 3344472 3344515 "URAGG" 3346585 NIL URAGG (NIL T) -9 NIL 3347308 NIL) (-1285 3338252 3339331 3340454 "URAGG-" 3340459 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333621 3336887 3337352 "UPXSSING" 3337916 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3326036 3333525 3333597 "UPXSCONS" 3333602 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3314784 3322238 3322300 "UPXSCCA" 3322874 NIL UPXSCCA (NIL T T) -9 NIL 3323107 NIL) (-1281 3314404 3314507 3314681 "UPXSCCA-" 3314686 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3303052 3310231 3310274 "UPXSCAT" 3310922 NIL UPXSCAT (NIL T) -9 NIL 3311531 NIL) (-1279 3302476 3302561 3302740 "UPXS2" 3302967 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3293954 3301858 3302122 "UPXS" 3302270 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3292590 3292861 3293212 "UPSQFREE" 3293697 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285418 3288856 3288911 "UPSCAT" 3289991 NIL UPSCAT (NIL T T) -9 NIL 3290757 NIL) (-1275 3284574 3284829 3285156 "UPSCAT-" 3285161 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3284195 3284244 3284377 "UPOLYC2" 3284525 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3268329 3277322 3277365 "UPOLYC" 3279466 NIL UPOLYC (NIL T) -9 NIL 3280687 NIL) (-1272 3259177 3262083 3265230 "UPOLYC-" 3265235 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3258498 3258623 3258787 "UPMP" 3259066 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3258045 3258132 3258271 "UPDIVP" 3258411 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3256583 3256862 3257178 "UPDECOMP" 3257794 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3255796 3255926 3256112 "UPCDEN" 3256467 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3255309 3255384 3255533 "UP2" 3255721 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3245884 3254992 3255121 "UP" 3255228 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3245089 3245226 3245431 "UNISEG2" 3245727 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3243442 3244293 3244570 "UNISEG" 3244847 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3242484 3242682 3242908 "UNIFACT" 3243258 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3229194 3242388 3242460 "ULSCONS" 3242465 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3208994 3222274 3222336 "ULSCCAT" 3222974 NIL ULSCCAT (NIL T T) -9 NIL 3223263 NIL) (-1260 3207990 3208289 3208677 "ULSCCAT-" 3208682 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3196435 3203536 3203579 "ULSCAT" 3204442 NIL ULSCAT (NIL T) -9 NIL 3205173 NIL) (-1258 3195859 3195944 3196123 "ULS2" 3196350 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3177669 3195171 3195413 "ULS" 3195675 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3176588 3177288 3177402 "UINT8" 3177513 T UINT8 (NIL) -8 NIL NIL 3177605) (-1255 3175506 3176206 3176320 "UINT64" 3176431 T UINT64 (NIL) -8 NIL NIL 3176523) (-1254 3174424 3175124 3175238 "UINT32" 3175349 T UINT32 (NIL) -8 NIL NIL 3175441) (-1253 3173342 3174042 3174156 "UINT16" 3174267 T UINT16 (NIL) -8 NIL NIL 3174359) (-1252 3171421 3172588 3172618 "UFD" 3172830 T UFD (NIL) -9 NIL 3172944 NIL) (-1251 3171203 3171261 3171356 "UFD-" 3171361 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170261 3170468 3170684 "UDVO" 3171009 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168027 3168486 3168957 "UDPO" 3169825 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167739 3167982 3168013 "TYPEAST" 3168018 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3167672 3167677 3167707 "TYPE" 3167712 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166625 3166845 3167085 "TWOFACT" 3167466 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165600 3166034 3166269 "TUPLE" 3166425 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163237 3163810 3164349 "TUBETOOL" 3165083 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162043 3162284 3162526 "TUBE" 3163030 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3150185 3154800 3154897 "TSETCAT" 3160166 NIL TSETCAT (NIL T T T T) -9 NIL 3161698 NIL) (-1241 3144653 3146517 3148408 "TSETCAT-" 3148413 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3138832 3143625 3143908 "TS" 3144405 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3133305 3134318 3135247 "TRMANIP" 3137968 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3132734 3132809 3132972 "TRIMAT" 3133237 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130546 3130837 3131194 "TRIGMNIP" 3132483 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130030 3130179 3130209 "TRIGCAT" 3130422 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129675 3129778 3129919 "TRIGCAT-" 3129924 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126289 3128533 3128814 "TREE" 3129429 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125395 3126091 3126121 "TRANFUN" 3126156 T TRANFUN (NIL) -9 NIL 3126222 NIL) (-1232 3124614 3124865 3125145 "TRANFUN-" 3125150 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124412 3124450 3124511 "TOPSP" 3124575 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3123742 3123875 3124029 "TOOLSIGN" 3124293 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122256 3122919 3123158 "TEXTFILE" 3123525 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3122031 3122068 3122140 "TEX1" 3122219 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3119835 3120484 3120913 "TEX" 3121624 T TEX (NIL) -8 NIL NIL NIL) (-1226 3119471 3119546 3119636 "TEMUTL" 3119767 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117565 3117905 3118230 "TBCMPPK" 3119194 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108892 3115651 3115707 "TBAGG" 3116107 NIL TBAGG (NIL T T) -9 NIL 3116318 NIL) (-1223 3103776 3105450 3107204 "TBAGG-" 3107209 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103142 3103267 3103412 "TANEXP" 3103665 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102593 3102917 3103007 "TALGOP" 3103087 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3101987 3102104 3102242 "TABLEAU" 3102490 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095001 3101844 3101937 "TABLE" 3101942 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089531 3090829 3092077 "TABLBUMP" 3093787 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3088741 3088900 3089081 "SYSTEM" 3089372 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085146 3085899 3086682 "SYSSOLP" 3087992 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084908 3085101 3085132 "SYSPTR" 3085137 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3083747 3084439 3084565 "SYSNNI" 3084751 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084843) (-1213 3082954 3083509 3083588 "SYSINT" 3083648 NIL SYSINT (NIL NIL) -8 NIL NIL 3083693) (-1212 3079052 3080232 3080942 "SYNTAX" 3082266 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076132 3076812 3077444 "SYMTAB" 3078442 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071231 3072283 3073266 "SYMS" 3075171 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068130 3070682 3070915 "SYMPOLY" 3071033 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067635 3067722 3067845 "SYMFUNC" 3068042 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063433 3064947 3065760 "SYMBOL" 3066844 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056906 3058661 3060381 "SWITCH" 3061735 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049660 3055862 3056156 "SUTS" 3056670 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041138 3049042 3049306 "SUPXS" 3049454 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040285 3040424 3040641 "SUPFRACF" 3041006 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3039900 3039965 3040078 "SUP2" 3040220 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030423 3039518 3039644 "SUP" 3039809 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3028847 3029145 3029501 "SUMRF" 3030122 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028170 3028248 3028440 "SUMFS" 3028768 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010015 3027482 3027724 "SULS" 3027986 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009563 3009837 3009907 "SUCHTAST" 3009967 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3008804 3009088 3009228 "SUCH" 3009471 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002443 3003710 3004669 "SUBSPACE" 3007892 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001863 3001963 3002127 "SUBRESP" 3002331 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2995874 2997156 2998303 "STTFNC" 3000763 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989068 2990539 2991850 "STTF" 2994610 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980185 2982250 2984044 "STTAYLOR" 2987309 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972939 2980049 2980132 "STRTBL" 2980137 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967336 2972648 2972747 "STRING" 2972862 T STRING (NIL) -8 NIL NIL NIL) (-1188 2966840 2966923 2967067 "STREAM3" 2967253 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2965804 2966005 2966240 "STREAM2" 2966653 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965486 2965544 2965637 "STREAM1" 2965746 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957600 2963105 2963716 "STREAM" 2964910 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956592 2956797 2957028 "STINPROD" 2957416 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955707 2956081 2956229 "STEPAST" 2956466 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955203 2955455 2955485 "STEP" 2955565 T STEP (NIL) -9 NIL 2955643 NIL) (-1181 2948259 2955102 2955179 "STBL" 2955184 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2942817 2947422 2947465 "STAGG" 2947618 NIL STAGG (NIL T) -9 NIL 2947707 NIL) (-1179 2940369 2941121 2941993 "STAGG-" 2941998 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938341 2940139 2940231 "STACK" 2940312 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930348 2936482 2936938 "SREGSET" 2937971 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922695 2924142 2925655 "SRDCMPK" 2928954 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915004 2920054 2920084 "SRAGG" 2921387 T SRAGG (NIL) -9 NIL 2921995 NIL) (-1174 2913955 2914276 2914655 "SRAGG-" 2914660 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907539 2912902 2913323 "SQMATRIX" 2913581 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900951 2904257 2904984 "SPLTREE" 2906884 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896776 2897607 2898253 "SPLNODE" 2900377 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895751 2896056 2896086 "SPFCAT" 2896530 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894446 2894698 2894962 "SPECOUT" 2895509 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885092 2887410 2887440 "SPADXPT" 2892118 T SPADXPT (NIL) -9 NIL 2894284 NIL) (-1167 2884847 2884893 2884962 "SPADPRSR" 2885045 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882450 2884802 2884833 "SPADAST" 2884838 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874051 2876154 2876197 "SPACEC" 2880570 NIL SPACEC (NIL T) -9 NIL 2882386 NIL) (-1164 2871851 2873983 2874032 "SPACE3" 2874037 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870583 2870774 2871065 "SORTPAK" 2871656 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868645 2868978 2869390 "SOLVETRA" 2870247 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867683 2867917 2868178 "SOLVESER" 2868418 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862915 2863875 2864870 "SOLVERAD" 2866735 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858640 2859339 2860068 "SOLVEFOR" 2862282 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852251 2857988 2858085 "SNTSCAT" 2858090 NIL SNTSCAT (NIL T T T T) -9 NIL 2858160 NIL) (-1157 2845795 2850574 2850965 "SMTS" 2851941 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839510 2845683 2845760 "SMP" 2845765 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837639 2837970 2838368 "SMITH" 2839207 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829171 2834218 2834321 "SMATCAT" 2835672 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836222 NIL) (-1153 2825943 2826934 2828112 "SMATCAT-" 2828117 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823412 2825151 2825194 "SKAGG" 2825455 NIL SKAGG (NIL T) -9 NIL 2825590 NIL) (-1151 2818902 2822881 2823065 "SINT" 2823217 T SINT (NIL) -8 NIL NIL 2823379) (-1150 2818668 2818712 2818778 "SIMPAN" 2818858 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817488 2817727 2818002 "SIGNRF" 2818427 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816303 2816472 2816756 "SIGNEF" 2817317 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815543 2815886 2816010 "SIGAST" 2816201 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814768 2815078 2815218 "SIG" 2815425 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812420 2812912 2813418 "SHP" 2814309 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805793 2812321 2812397 "SHDP" 2812402 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805304 2805544 2805574 "SGROUP" 2805667 T SGROUP (NIL) -9 NIL 2805729 NIL) (-1142 2805156 2805188 2805261 "SGROUP-" 2805266 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801875 2802645 2803368 "SGCF" 2804455 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795584 2801321 2801418 "SFRTCAT" 2801423 NIL SFRTCAT (NIL T T T T) -9 NIL 2801462 NIL) (-1139 2788903 2790023 2791159 "SFRGCD" 2794567 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781921 2783102 2784288 "SFQCMPK" 2787836 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781523 2781630 2781741 "SFORT" 2781862 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780449 2781363 2781484 "SEXOF" 2781489 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776038 2776945 2777040 "SEXCAT" 2779662 NIL SEXCAT (NIL T T T T T) -9 NIL 2780222 NIL) (-1134 2774953 2775919 2775987 "SEX" 2775992 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773075 2773666 2773971 "SETMN" 2774694 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772605 2772793 2772823 "SETCAT" 2772940 T SETCAT (NIL) -9 NIL 2773025 NIL) (-1131 2772373 2772437 2772536 "SETCAT-" 2772541 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768476 2770834 2770877 "SETAGG" 2771747 NIL SETAGG (NIL T) -9 NIL 2772087 NIL) (-1129 2767898 2768050 2768287 "SETAGG-" 2768292 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764707 2767832 2767880 "SET" 2767885 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764090 2764403 2764504 "SEQAST" 2764628 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763217 2763583 2763644 "SEGXCAT" 2763930 NIL SEGXCAT (NIL T T) -9 NIL 2764050 NIL) (-1125 2762142 2762410 2762453 "SEGCAT" 2762975 NIL SEGCAT (NIL T) -9 NIL 2763196 NIL) (-1124 2761757 2761822 2761935 "SEGBIND2" 2762077 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760647 2761120 2761328 "SEGBIND" 2761584 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760166 2760448 2760525 "SEGAST" 2760592 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759375 2759511 2759715 "SEG2" 2760010 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758291 2759041 2759223 "SEG" 2759228 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757524 2758226 2758273 "SDVAR" 2758278 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748875 2757294 2757424 "SDPOL" 2757429 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747444 2747734 2748053 "SCPKG" 2748590 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746566 2746780 2746972 "SCOPE" 2747274 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745762 2745920 2746099 "SCACHE" 2746421 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745346 2745580 2745610 "SASTCAT" 2745615 T SASTCAT (NIL) -9 NIL 2745628 NIL) (-1113 2744749 2745181 2745257 "SAOS" 2745292 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744308 2744349 2744522 "SAERFFC" 2744708 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2743895 2743936 2744095 "SAEFACT" 2744267 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2736922 2743792 2743872 "SAE" 2743877 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735225 2735557 2735958 "RURPK" 2736588 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733802 2734168 2734473 "RULESET" 2735059 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733372 2733596 2733679 "RULECOLD" 2733754 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730487 2731125 2731583 "RULE" 2733053 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730271 2730305 2730376 "RTVALUE" 2730438 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729682 2729988 2730082 "RSTRCAST" 2730199 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724452 2725325 2726245 "RSETGCD" 2728881 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713023 2718760 2718857 "RSETCAT" 2722976 NIL RSETCAT (NIL T T T T) -9 NIL 2724073 NIL) (-1101 2710842 2711489 2712313 "RSETCAT-" 2712318 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703150 2704604 2706124 "RSDCMPK" 2709441 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701019 2701582 2701656 "RRCC" 2702742 NIL RRCC (NIL T T) -9 NIL 2703086 NIL) (-1098 2700340 2700544 2700823 "RRCC-" 2700828 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699723 2700036 2700137 "RPTAST" 2700261 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672109 2682835 2682902 "RPOLCAT" 2693568 NIL RPOLCAT (NIL T T T) -9 NIL 2696728 NIL) (-1095 2663079 2665947 2669069 "RPOLCAT-" 2669074 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653532 2661290 2661772 "ROUTINE" 2662619 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649581 2653158 2653298 "ROMAN" 2653414 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647693 2648441 2648701 "ROIRC" 2649386 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643411 2646182 2646212 "RNS" 2646516 T RNS (NIL) -9 NIL 2646790 NIL) (-1090 2641818 2642303 2642837 "RNS-" 2642912 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640779 2641183 2641385 "RNGBIND" 2641669 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640072 2640576 2640606 "RNG" 2640611 T RNG (NIL) -9 NIL 2640632 NIL) (-1087 2639367 2639845 2639888 "RMODULE" 2639893 NIL RMODULE (NIL T) -9 NIL 2639920 NIL) (-1086 2638191 2638297 2638633 "RMCAT2" 2639268 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634693 2637537 2637834 "RMATRIX" 2637953 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627192 2629780 2629895 "RMATCAT" 2633254 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634236 NIL) (-1083 2626531 2626714 2627021 "RMATCAT-" 2627026 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626104 2626318 2626361 "RLINSET" 2626423 NIL RLINSET (NIL T) -9 NIL 2626467 NIL) (-1081 2625665 2625746 2625874 "RINTERP" 2626023 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624589 2625263 2625293 "RING" 2625349 T RING (NIL) -9 NIL 2625441 NIL) (-1079 2624369 2624425 2624522 "RING-" 2624527 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623180 2623447 2623705 "RIDIST" 2624133 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613805 2622648 2622854 "RGCHAIN" 2623028 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613063 2613547 2613588 "RGBCSPC" 2613646 NIL RGBCSPC (NIL T) -9 NIL 2613698 NIL) (-1075 2612129 2612588 2612629 "RGBCMDL" 2612861 NIL RGBCMDL (NIL T) -9 NIL 2612975 NIL) (-1074 2611769 2611838 2611941 "RFFACTOR" 2612060 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611488 2611529 2611626 "RFFACT" 2611728 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609539 2609969 2610351 "RFDIST" 2611128 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606479 2607147 2607817 "RF" 2608903 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2605926 2606024 2606187 "RETSOL" 2606381 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605544 2605642 2605685 "RETRACT" 2605818 NIL RETRACT (NIL T) -9 NIL 2605905 NIL) (-1068 2605387 2605418 2605505 "RETRACT-" 2605510 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604935 2605209 2605279 "RETAST" 2605339 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597285 2604588 2604715 "RESULT" 2604830 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595720 2596554 2596753 "RESRING" 2597188 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595344 2595405 2595503 "RESLATC" 2595657 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595043 2595084 2595191 "REPSQ" 2595303 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594734 2594775 2594886 "REPDB" 2595002 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588566 2590023 2591246 "REP2" 2593546 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2584869 2585624 2586432 "REP1" 2587793 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582249 2582871 2583473 "REP" 2584289 T REP (NIL) -7 NIL NIL NIL) (-1058 2574257 2580390 2580846 "REGSET" 2581879 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572966 2573405 2573655 "REF" 2574042 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572331 2572446 2572613 "REDORDER" 2572850 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567695 2571544 2571771 "RECLOS" 2572159 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566729 2566928 2567143 "REALSOLV" 2567502 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563176 2564014 2564898 "REAL0Q" 2565894 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558729 2559765 2560826 "REAL0" 2562157 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558563 2558616 2558646 "REAL" 2558651 T REAL (NIL) -9 NIL 2558686 NIL) (-1050 2557974 2558280 2558374 "RDUCEAST" 2558491 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557373 2557451 2557658 "RDIV" 2557896 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556423 2556615 2556828 "RDIST" 2557195 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555008 2555307 2555679 "RDETRS" 2556131 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552802 2553274 2553812 "RDETR" 2554550 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551421 2551705 2552102 "RDEEFS" 2552518 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549924 2550236 2550661 "RDEEF" 2551109 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543401 2546878 2546908 "RCFIELD" 2548203 T RCFIELD (NIL) -9 NIL 2548934 NIL) (-1042 2541357 2541969 2542665 "RCFIELD-" 2542740 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537409 2539430 2539473 "RCAGG" 2540557 NIL RCAGG (NIL T) -9 NIL 2541022 NIL) (-1040 2537019 2537131 2537294 "RCAGG-" 2537299 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536336 2536466 2536631 "RATRET" 2536903 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535877 2535956 2536077 "RATFACT" 2536264 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535155 2535305 2535457 "RANDSRC" 2535747 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534883 2534933 2535006 "RADUTIL" 2535104 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527007 2533714 2534025 "RADIX" 2534606 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516601 2526849 2526979 "RADFF" 2526984 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516230 2516323 2516353 "RADCAT" 2516513 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516000 2516060 2516160 "RADCAT-" 2516165 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513911 2515770 2515862 "QUEUE" 2515943 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513536 2513585 2513716 "QUATCT2" 2513862 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2505912 2509959 2510001 "QUATCAT" 2510792 NIL QUATCAT (NIL T) -9 NIL 2511558 NIL) (-1028 2501793 2503088 2504478 "QUATCAT-" 2504574 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497632 2501726 2501774 "QUAT" 2501779 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2494888 2496680 2496723 "QUAGG" 2497104 NIL QUAGG (NIL T) -9 NIL 2497279 NIL) (-1025 2494436 2494710 2494780 "QQUTAST" 2494840 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493347 2493949 2494114 "QFORM" 2494317 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2492972 2493021 2493152 "QFCAT2" 2493298 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482648 2488819 2488861 "QFCAT" 2489529 NIL QFCAT (NIL T) -9 NIL 2490530 NIL) (-1021 2477963 2479416 2481010 "QFCAT-" 2481106 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477394 2477528 2477660 "QEQUAT" 2477853 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470412 2471593 2472779 "QCMPACK" 2476327 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469641 2469823 2470059 "QALGSET2" 2470230 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467091 2467627 2468057 "QALGSET" 2469296 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465758 2466000 2466319 "PWFFINTB" 2466864 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463903 2464101 2464457 "PUSHVAR" 2465572 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459630 2460846 2460889 "PTRANFN" 2462800 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457967 2458312 2458636 "PTPACK" 2459341 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457590 2457653 2457764 "PTFUNC2" 2457904 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451515 2456379 2456422 "PTCAT" 2456722 NIL PTCAT (NIL T) -9 NIL 2456875 NIL) (-1010 2451164 2451205 2451331 "PSQFR" 2451474 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449736 2450052 2450388 "PSEUDLIN" 2450862 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436256 2438831 2441157 "PSETPK" 2447496 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428964 2431992 2432090 "PSETCAT" 2435131 NIL PSETCAT (NIL T T T T) -9 NIL 2435945 NIL) (-1006 2426689 2427431 2428255 "PSETCAT-" 2428260 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426002 2426197 2426227 "PSCURVE" 2426499 T PSCURVE (NIL) -9 NIL 2426666 NIL) (-1004 2421718 2423492 2423559 "PSCAT" 2424411 NIL PSCAT (NIL T T T) -9 NIL 2424651 NIL) (-1003 2420712 2420994 2421397 "PSCAT-" 2421402 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418911 2419771 2420036 "PRTITION" 2420469 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418322 2418628 2418722 "PRTDAST" 2418839 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407166 2409588 2411778 "PRS" 2416184 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404786 2406488 2406528 "PRQAGG" 2406711 NIL PRQAGG (NIL T) -9 NIL 2406813 NIL) (-998 2403965 2404414 2404442 "PROPLOG" 2404581 T PROPLOG (NIL) -9 NIL 2404696 NIL) (-997 2403563 2403626 2403749 "PROPFUN2" 2403888 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402860 2402999 2403171 "PROPFUN1" 2403424 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400839 2401607 2401904 "PROPFRML" 2402596 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400284 2400415 2400543 "PROPERTY" 2400731 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394172 2398450 2399270 "PRODUCT" 2399510 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2393962 2394000 2394059 "PRINT" 2394133 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393278 2393419 2393571 "PRIMES" 2393842 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391325 2391744 2392210 "PRIMELT" 2392857 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391042 2391103 2391131 "PRIMCAT" 2391255 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390031 2390227 2390455 "PRIMARR2" 2390860 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385753 2389969 2390014 "PRIMARR" 2390019 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385390 2385452 2385563 "PREASSOC" 2385691 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382348 2384848 2385082 "PR" 2385201 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381799 2381956 2381984 "PPCURVE" 2382189 T PPCURVE (NIL) -9 NIL 2382325 NIL) (-983 2381346 2381594 2381677 "PORTNUM" 2381736 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378683 2379104 2379696 "POLYROOT" 2380927 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378060 2378124 2378358 "POLYLIFT" 2378619 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374281 2374784 2375413 "POLYCATQ" 2377605 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2359929 2366028 2366093 "POLYCAT" 2369607 NIL POLYCAT (NIL T T T) -9 NIL 2371485 NIL) (-978 2353048 2355240 2357624 "POLYCAT-" 2357629 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352629 2352703 2352823 "POLY2UP" 2352974 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352255 2352318 2352427 "POLY2" 2352566 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345463 2351859 2352019 "POLY" 2352128 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344124 2344387 2344663 "POLUTIL" 2345237 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342443 2342756 2343087 "POLTOPOL" 2343846 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337439 2342377 2342424 "POINT" 2342429 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335572 2335983 2336358 "PNTHEORY" 2337084 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334018 2334327 2334726 "PMTOOLS" 2335270 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333605 2333689 2333806 "PMSYM" 2333934 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333107 2333182 2333357 "PMQFCAT" 2333530 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332488 2332586 2332748 "PMPREDFS" 2333008 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2331831 2331953 2332109 "PMPRED" 2332365 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330485 2330703 2331081 "PMPLCAT" 2331593 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330011 2330096 2330248 "PMLSAGG" 2330400 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329478 2329560 2329742 "PMKERNEL" 2329929 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329089 2329170 2329283 "PMINS" 2329397 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328525 2328600 2328809 "PMFS" 2329014 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327741 2327871 2328076 "PMDOWN" 2328402 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326990 2327124 2327287 "PMASSFS" 2327628 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326133 2326315 2326496 "PMASS" 2326829 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325782 2325856 2325950 "PLOTTOOL" 2326059 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321434 2322628 2323550 "PLOT3D" 2324880 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320322 2320523 2320758 "PLOT1" 2321238 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314743 2316133 2317281 "PLOT" 2319194 T PLOT (NIL) -8 NIL NIL NIL) (-953 2289918 2294809 2299660 "PLEQN" 2310009 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289605 2289658 2289761 "PINTERPA" 2289865 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2288911 2289045 2289225 "PINTERP" 2289470 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2286996 2288169 2288197 "PID" 2288379 T PID (NIL) -9 NIL 2288513 NIL) (-949 2286741 2286784 2286859 "PICOERCE" 2286953 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2285837 2286505 2286592 "PI" 2286632 T PI (NIL) -8 NIL NIL 2286699) (-947 2285145 2285296 2285472 "PGROEB" 2285693 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280584 2281543 2282449 "PGE" 2284259 T PGE (NIL) -7 NIL NIL NIL) (-945 2278665 2278954 2279320 "PGCD" 2280301 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277991 2278106 2278267 "PFRPAC" 2278549 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274242 2276539 2276892 "PFR" 2277670 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272595 2272875 2273200 "PFOTOOLS" 2273989 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271110 2271367 2271718 "PFOQ" 2272352 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269593 2269823 2270179 "PFO" 2270894 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266671 2268184 2268212 "PFECAT" 2268797 T PFECAT (NIL) -9 NIL 2269181 NIL) (-938 2266098 2266270 2266484 "PFECAT-" 2266489 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264671 2264953 2265254 "PFBRU" 2265847 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262501 2262889 2263321 "PFBR" 2264322 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258426 2262390 2262459 "PF" 2262464 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253480 2254633 2255503 "PERMGRP" 2257589 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251392 2252504 2252545 "PERMCAT" 2252945 NIL PERMCAT (NIL T) -9 NIL 2253243 NIL) (-932 2251039 2251086 2251210 "PERMAN" 2251345 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2246841 2248548 2249196 "PERM" 2250424 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244082 2246506 2246628 "PENDTREE" 2246752 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242963 2243226 2243267 "PDSPC" 2243800 NIL PDSPC (NIL T) -9 NIL 2244045 NIL) (-928 2242018 2242284 2242646 "PDSPC-" 2242651 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240732 2241668 2241709 "PDRING" 2241714 NIL PDRING (NIL T) -9 NIL 2241742 NIL) (-926 2239475 2240237 2240291 "PDMOD" 2240296 NIL PDMOD (NIL T T) -9 NIL 2240400 NIL) (-925 2236642 2237468 2238136 "PDEPROB" 2238827 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234151 2234691 2235246 "PDEPACK" 2236107 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233039 2233253 2233504 "PDECOMP" 2233950 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230556 2231447 2231475 "PDECAT" 2232262 T PDECAT (NIL) -9 NIL 2232975 NIL) (-921 2230173 2230240 2230294 "PDDOM" 2230459 NIL PDDOM (NIL T T) -9 NIL 2230539 NIL) (-920 2229986 2230022 2230129 "PDDOM-" 2230134 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229731 2229770 2229860 "PCOMP" 2229947 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227771 2228532 2228829 "PBWLB" 2229460 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227397 2227460 2227569 "PATTERN2" 2227708 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225106 2225542 2225999 "PATTERN1" 2226986 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217285 2219179 2220517 "PATTERN" 2223789 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2216843 2216916 2217048 "PATRES2" 2217212 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214109 2214792 2215273 "PATRES" 2216408 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2211962 2212397 2212804 "PATMATCH" 2213776 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211416 2211667 2211708 "PATMAB" 2211815 NIL PATMAB (NIL T) -9 NIL 2211898 NIL) (-910 2209862 2210270 2210528 "PATLRES" 2211221 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209400 2209531 2209572 "PATAB" 2209577 NIL PATAB (NIL T) -9 NIL 2209749 NIL) (-908 2207540 2207977 2208400 "PARTPERM" 2208997 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207149 2207224 2207326 "PARSURF" 2207471 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206775 2206838 2206947 "PARSU2" 2207086 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206533 2206579 2206646 "PARSER" 2206728 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206142 2206217 2206319 "PARSCURV" 2206464 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205768 2205831 2205940 "PARSC2" 2206079 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205395 2205465 2205562 "PARPCURV" 2205704 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205021 2205084 2205193 "PARPC2" 2205332 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204010 2204394 2204576 "PARAMAST" 2204859 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203518 2203616 2203735 "PAN2EXPR" 2203911 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202211 2202639 2202867 "PALETTE" 2203310 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200556 2201216 2201576 "PAIR" 2201897 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193468 2199813 2200008 "PADICRC" 2200410 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185704 2192812 2192997 "PADICRAT" 2193315 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182494 2184364 2184404 "PADICCT" 2184985 NIL PADICCT (NIL NIL) -9 NIL 2185267 NIL) (-893 2180503 2182431 2182476 "PADIC" 2182481 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179448 2179660 2179928 "PADEPAC" 2180290 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178648 2178793 2178999 "PADE" 2179310 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176881 2177856 2178136 "OWP" 2178452 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176326 2176587 2176684 "OVERSET" 2176804 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175246 2175931 2176103 "OVAR" 2176194 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2163482 2166355 2168555 "OUTFORM" 2173066 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2162764 2163079 2163206 "OUTBFILE" 2163375 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2162041 2162236 2162264 "OUTBCON" 2162582 T OUTBCON (NIL) -9 NIL 2162748 NIL) (-884 2161624 2161754 2161911 "OUTBCON-" 2161916 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2160864 2161009 2161170 "OUT" 2161483 T OUT (NIL) -7 NIL NIL NIL) (-882 2160160 2160593 2160682 "OSI" 2160795 T OSI (NIL) -8 NIL NIL NIL) (-881 2159579 2160001 2160029 "OSGROUP" 2160034 T OSGROUP (NIL) -9 NIL 2160056 NIL) (-880 2158290 2158551 2158836 "ORTHPOL" 2159326 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155541 2158125 2158246 "OREUP" 2158251 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152644 2155232 2155359 "ORESUP" 2155483 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150144 2150672 2151233 "OREPCTO" 2152133 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143522 2146017 2146058 "OREPCAT" 2148406 NIL OREPCAT (NIL T) -9 NIL 2149510 NIL) (-875 2140495 2141451 2142509 "OREPCAT-" 2142514 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139688 2139965 2139993 "ORDTYPE" 2140302 T ORDTYPE (NIL) -9 NIL 2140465 NIL) (-873 2138989 2139205 2139460 "ORDTYPE-" 2139465 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138345 2138728 2138886 "ORDSTRCT" 2138891 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137843 2138213 2138241 "ORDSET" 2138246 T ORDSET (NIL) -9 NIL 2138268 NIL) (-870 2136201 2137172 2137200 "ORDRING" 2137402 T ORDRING (NIL) -9 NIL 2137527 NIL) (-869 2135822 2135940 2136084 "ORDRING-" 2136089 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135073 2135638 2135666 "ORDMON" 2135671 T ORDMON (NIL) -9 NIL 2135692 NIL) (-867 2134217 2134382 2134577 "ORDFUNS" 2134922 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133432 2133947 2133975 "ORDFIN" 2134040 T ORDFIN (NIL) -9 NIL 2134114 NIL) (-865 2132686 2132825 2133011 "ORDCOMP2" 2133292 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2129033 2131272 2131681 "ORDCOMP" 2132310 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2125554 2126524 2127338 "OPTPROB" 2128239 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122296 2122995 2123699 "OPTPACK" 2124870 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119909 2120735 2120763 "OPTCAT" 2121582 T OPTCAT (NIL) -9 NIL 2122232 NIL) (-860 2119227 2119586 2119691 "OPSIG" 2119824 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118989 2119034 2119100 "OPQUERY" 2119181 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2118295 2118575 2118616 "OPERCAT" 2118828 NIL OPERCAT (NIL T) -9 NIL 2118925 NIL) (-857 2118038 2118106 2118223 "OPERCAT-" 2118228 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2114947 2116349 2116853 "OP" 2117567 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114240 2114367 2114541 "ONECOMP2" 2114819 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2110853 2113037 2113406 "ONECOMP" 2113904 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110254 2110378 2110508 "OMSERVER" 2110743 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106768 2109694 2109734 "OMSAGG" 2109795 NIL OMSAGG (NIL T) -9 NIL 2109859 NIL) (-851 2105343 2105654 2105936 "OMPKG" 2106506 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103690 2104892 2105061 "OMLO" 2105224 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102626 2102797 2103017 "OMEXPR" 2103516 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101711 2102047 2102207 "OMERRK" 2102486 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2100948 2101257 2101393 "OMERR" 2101595 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100339 2100625 2100733 "OMENC" 2100860 T OMENC (NIL) -8 NIL NIL NIL) (-845 2093976 2095419 2096590 "OMDEV" 2099188 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2093009 2093216 2093410 "OMCONN" 2093802 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2092415 2092542 2092570 "OM" 2092869 T OM (NIL) -9 NIL NIL NIL) (-842 2090693 2091885 2091913 "OINTDOM" 2091918 T OINTDOM (NIL) -9 NIL 2091939 NIL) (-841 2087767 2089381 2089718 "OFMONOID" 2090388 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2087001 2087704 2087749 "ODVAR" 2087754 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084138 2086746 2086901 "ODR" 2086906 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075543 2083914 2084040 "ODPOL" 2084045 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068886 2075415 2075520 "ODP" 2075525 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067628 2067867 2068142 "ODETOOLS" 2068660 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064571 2065253 2065969 "ODESYS" 2066961 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059401 2060361 2061386 "ODERTRIC" 2063646 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2058821 2058909 2059103 "ODERED" 2059313 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055673 2056257 2056934 "ODERAT" 2058244 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052590 2053097 2053694 "ODEPRRIC" 2055202 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050485 2051129 2051615 "ODEPROB" 2052124 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046951 2047490 2048137 "ODEPRIM" 2049964 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046194 2046302 2046562 "ODEPAL" 2046843 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042296 2043147 2044011 "ODEPACK" 2045350 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041339 2041464 2041686 "ODEINT" 2042185 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035404 2036865 2038312 "ODEIFTBL" 2039912 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030754 2031588 2032540 "ODEEF" 2034563 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030097 2030192 2030415 "ODECONST" 2030659 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028160 2028869 2028897 "ODECAT" 2029502 T ODECAT (NIL) -9 NIL 2030033 NIL) (-821 2027792 2027841 2027968 "OCTCT2" 2028111 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024285 2027497 2027619 "OCT" 2027702 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023508 2024078 2024106 "OCAMON" 2024111 T OCAMON (NIL) -9 NIL 2024132 NIL) (-818 2017777 2020551 2020591 "OC" 2021688 NIL OC (NIL T) -9 NIL 2022546 NIL) (-817 2014812 2015752 2016742 "OC-" 2016836 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014232 2014657 2014685 "OASGP" 2014690 T OASGP (NIL) -9 NIL 2014710 NIL) (-815 2013358 2013955 2013983 "OAMONS" 2014023 T OAMONS (NIL) -9 NIL 2014066 NIL) (-814 2012649 2013178 2013206 "OAMON" 2013211 T OAMON (NIL) -9 NIL 2013231 NIL) (-813 2011760 2012398 2012426 "OAGROUP" 2012431 T OAGROUP (NIL) -9 NIL 2012451 NIL) (-812 2011442 2011498 2011587 "NUMTUBE" 2011704 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004961 2006533 2008069 "NUMQUAD" 2009926 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000641 2001675 2002710 "NUMODE" 2003946 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997922 1998862 1998890 "NUMINT" 1999813 T NUMINT (NIL) -9 NIL 2000577 NIL) (-808 1996834 1997067 1997285 "NUMFMT" 1997724 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983017 1986138 1988670 "NUMERIC" 1994341 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976728 1982465 1982560 "NTSCAT" 1982565 NIL NTSCAT (NIL T T T T) -9 NIL 1982604 NIL) (-805 1975908 1976087 1976280 "NTPOLFN" 1976567 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975534 1975597 1975706 "NSUP2" 1975845 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962295 1972359 1973171 "NSUP" 1974755 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951131 1962069 1962202 "NSMP" 1962207 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949539 1949864 1950221 "NREP" 1950819 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948118 1948382 1948740 "NPCOEF" 1949282 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947166 1947299 1947515 "NORMRETR" 1947999 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945177 1945497 1945906 "NORMPK" 1946874 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944856 1944890 1945014 "NORMMA" 1945143 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944639 1944674 1944743 "NONE1" 1944820 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944403 1944596 1944625 "NONE" 1944630 T NONE (NIL) -8 NIL NIL NIL) (-794 1943894 1943962 1944141 "NODE1" 1944335 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941986 1943017 1943272 "NNI" 1943619 T NNI (NIL) -8 NIL NIL 1943854) (-792 1940382 1940719 1941083 "NLINSOL" 1941654 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936563 1937618 1938517 "NIPROB" 1939503 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935302 1935554 1935856 "NFINTBAS" 1936325 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934386 1934952 1934993 "NETCLT" 1935165 NIL NETCLT (NIL T) -9 NIL 1935247 NIL) (-788 1933058 1933325 1933606 "NCODIV" 1934154 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932814 1932857 1932932 "NCNTFRAC" 1933015 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930970 1931358 1931778 "NCEP" 1932439 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929633 1930580 1930608 "NASRING" 1930718 T NASRING (NIL) -9 NIL 1930798 NIL) (-784 1929416 1929472 1929566 "NASRING-" 1929571 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928383 1929034 1929062 "NARNG" 1929179 T NARNG (NIL) -9 NIL 1929270 NIL) (-782 1928057 1928142 1928276 "NARNG-" 1928281 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926894 1927143 1927378 "NAGSP" 1927842 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917938 1919850 1921523 "NAGS" 1925241 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916462 1916794 1917125 "NAGF07" 1917627 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910934 1912291 1913598 "NAGF04" 1915175 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903806 1905516 1907149 "NAGF02" 1909321 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898970 1900130 1901247 "NAGF01" 1902709 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892550 1894164 1895749 "NAGE04" 1897405 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883611 1885840 1887970 "NAGE02" 1890440 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879504 1880511 1881475 "NAGE01" 1882667 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877281 1877833 1878391 "NAGD03" 1878966 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868977 1870959 1872913 "NAGD02" 1875347 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862716 1864213 1865653 "NAGD01" 1867557 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858853 1859747 1860584 "NAGC06" 1861899 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857300 1857650 1858006 "NAGC05" 1858517 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856664 1856795 1856939 "NAGC02" 1857176 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855465 1856192 1856232 "NAALG" 1856311 NIL NAALG (NIL T) -9 NIL 1856372 NIL) (-765 1855294 1855329 1855419 "NAALG-" 1855424 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849166 1850352 1851539 "MULTSQFR" 1854190 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848473 1848560 1848744 "MULTFACT" 1849078 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840618 1845056 1845109 "MTSCAT" 1846179 NIL MTSCAT (NIL T T) -9 NIL 1846695 NIL) (-761 1840324 1840384 1840476 "MTHING" 1840558 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840110 1840149 1840209 "MSYSCMD" 1840284 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836855 1839671 1839712 "MSETAGG" 1839717 NIL MSETAGG (NIL T) -9 NIL 1839751 NIL) (-758 1832569 1835610 1835930 "MSET" 1836568 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828161 1829948 1830693 "MRING" 1831869 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827721 1827794 1827925 "MRF2" 1828088 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827333 1827374 1827518 "MRATFAC" 1827680 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824903 1825240 1825671 "MPRFF" 1827038 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818230 1824757 1824854 "MPOLY" 1824859 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817714 1817755 1817963 "MPCPF" 1818189 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817222 1817271 1817455 "MPC3" 1817665 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816405 1816498 1816719 "MPC2" 1817137 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814682 1815043 1815433 "MONOTOOL" 1816065 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813827 1814210 1814238 "MONOID" 1814457 T MONOID (NIL) -9 NIL 1814604 NIL) (-747 1813343 1813492 1813673 "MONOID-" 1813678 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802297 1809163 1809222 "MONOGEN" 1809896 NIL MONOGEN (NIL T T) -9 NIL 1810352 NIL) (-745 1799347 1800250 1801250 "MONOGEN-" 1801369 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798064 1798612 1798640 "MONADWU" 1799032 T MONADWU (NIL) -9 NIL 1799270 NIL) (-743 1797394 1797595 1797843 "MONADWU-" 1797848 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796679 1796983 1797011 "MONAD" 1797218 T MONAD (NIL) -9 NIL 1797330 NIL) (-741 1796346 1796442 1796574 "MONAD-" 1796579 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794485 1795259 1795538 "MOEBIUS" 1796099 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793653 1794153 1794193 "MODULE" 1794198 NIL MODULE (NIL T) -9 NIL 1794237 NIL) (-738 1793191 1793317 1793507 "MODULE-" 1793512 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790721 1791555 1791882 "MODRING" 1793015 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787443 1788826 1789347 "MODOP" 1790250 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785929 1786510 1786787 "MODMONOM" 1787306 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774669 1784220 1784634 "MODMON" 1785566 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771495 1773513 1773789 "MODFIELD" 1774544 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770406 1770776 1770966 "MMLFORM" 1771325 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769926 1769975 1770154 "MMAP" 1770357 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767819 1768758 1768799 "MLO" 1769222 NIL MLO (NIL T) -9 NIL 1769464 NIL) (-729 1765167 1765701 1766303 "MLIFT" 1767300 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764546 1764642 1764796 "MKUCFUNC" 1765078 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764139 1764215 1764338 "MKRECORD" 1764469 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763162 1763348 1763576 "MKFUNC" 1763950 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762538 1762654 1762810 "MKFLCFN" 1763045 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761803 1761917 1762102 "MKBCFUNC" 1762431 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757786 1761357 1761493 "MINT" 1761687 T MINT (NIL) -8 NIL NIL NIL) (-722 1756568 1756841 1757118 "MHROWRED" 1757541 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751312 1755103 1755508 "MFLOAT" 1756183 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750657 1750745 1750916 "MFINFACT" 1751224 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746936 1747820 1748704 "MESH" 1749793 T MESH (NIL) -7 NIL NIL NIL) (-718 1745290 1745638 1745991 "MDDFACT" 1746623 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741826 1744421 1744462 "MDAGG" 1744717 NIL MDAGG (NIL T) -9 NIL 1744860 NIL) (-716 1729528 1741119 1741326 "MCMPLX" 1741639 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728647 1728811 1729012 "MCDEN" 1729377 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726495 1726807 1727187 "MCALCFN" 1728377 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725372 1725660 1725893 "MAYBE" 1726301 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722930 1723507 1724069 "MATSTOR" 1724843 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718352 1722302 1722550 "MATRIX" 1722715 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714052 1714825 1715561 "MATLIN" 1717709 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712628 1712799 1713132 "MATCAT2" 1713887 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701974 1705685 1705762 "MATCAT" 1710794 NIL MATCAT (NIL T T T) -9 NIL 1712266 NIL) (-707 1697927 1699237 1700650 "MATCAT-" 1700655 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696003 1696363 1696747 "MAPPKG3" 1697602 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694960 1695157 1695379 "MAPPKG2" 1695827 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693417 1693743 1694070 "MAPPKG1" 1694666 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692418 1692823 1693000 "MAPPAST" 1693260 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692023 1692087 1692210 "MAPHACK3" 1692354 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691603 1691676 1691790 "MAPHACK2" 1691955 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691029 1691144 1691286 "MAPHACK1" 1691494 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688952 1689729 1690033 "MAGMA" 1690757 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688371 1688676 1688767 "MACROAST" 1688881 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684614 1686610 1687071 "M3D" 1687943 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678094 1682925 1682966 "LZSTAGG" 1683748 NIL LZSTAGG (NIL T) -9 NIL 1684043 NIL) (-695 1673776 1675225 1676682 "LZSTAGG-" 1676687 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670689 1671667 1672154 "LWORD" 1673321 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670211 1670493 1670568 "LSTAST" 1670634 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662139 1669982 1670116 "LSQM" 1670121 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661357 1661502 1661730 "LSPP" 1661994 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658094 1658810 1659540 "LSMP1" 1660659 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655876 1656207 1656663 "LSMP" 1657783 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649012 1654966 1655007 "LSAGG" 1655069 NIL LSAGG (NIL T) -9 NIL 1655147 NIL) (-687 1645521 1646631 1647844 "LSAGG-" 1647849 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642816 1644665 1644914 "LPOLY" 1645316 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642392 1642483 1642606 "LPEFRAC" 1642725 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642075 1642154 1642182 "LOGIC" 1642293 T LOGIC (NIL) -9 NIL 1642375 NIL) (-683 1641931 1641960 1642031 "LOGIC-" 1642036 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641106 1641264 1641457 "LODOOPS" 1641787 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639630 1639879 1640232 "LODOF" 1640853 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635506 1638265 1638306 "LODOCAT" 1638744 NIL LODOCAT (NIL T) -9 NIL 1638955 NIL) (-679 1635221 1635297 1635424 "LODOCAT-" 1635429 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632207 1635062 1635180 "LODO2" 1635185 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629314 1632144 1632189 "LODO1" 1632194 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626409 1629230 1629296 "LODO" 1629301 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625278 1625455 1625760 "LODEEF" 1626232 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623455 1624372 1624625 "LO" 1625110 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618427 1621621 1621662 "LNAGG" 1622524 NIL LNAGG (NIL T) -9 NIL 1622959 NIL) (-672 1617520 1617788 1618130 "LNAGG-" 1618135 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613500 1614445 1615084 "LMOPS" 1616935 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612799 1613277 1613318 "LMODULE" 1613323 NIL LMODULE (NIL T) -9 NIL 1613349 NIL) (-669 1609754 1612444 1612567 "LMDICT" 1612709 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609330 1609544 1609585 "LLINSET" 1609646 NIL LLINSET (NIL T) -9 NIL 1609690 NIL) (-667 1608975 1609238 1609298 "LITERAL" 1609303 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608494 1608574 1608713 "LIST3" 1608895 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606592 1606940 1607339 "LIST2MAP" 1608141 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605581 1605777 1606005 "LIST2" 1606410 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598035 1604515 1604819 "LIST" 1605310 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597618 1597854 1597895 "LINSET" 1597900 NIL LINSET (NIL T) -9 NIL 1597934 NIL) (-661 1596432 1597126 1597293 "LINFORM" 1597503 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594731 1595459 1595500 "LINEXP" 1595990 NIL LINEXP (NIL T) -9 NIL 1596263 NIL) (-659 1593307 1594211 1594392 "LINELT" 1594602 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591864 1592144 1592455 "LINDEP" 1593059 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591000 1591596 1591706 "LINBASIS" 1591794 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587737 1588486 1589263 "LIMITRF" 1590255 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586022 1586336 1586745 "LIMITPS" 1587432 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584850 1585425 1585465 "LIECAT" 1585605 NIL LIECAT (NIL T) -9 NIL 1585756 NIL) (-653 1584685 1584718 1584806 "LIECAT-" 1584811 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578705 1584196 1584424 "LIE" 1584506 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570890 1578245 1578401 "LIB" 1578569 T LIB (NIL) -8 NIL NIL NIL) (-650 1566459 1567408 1568343 "LGROBP" 1570007 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565083 1565991 1566019 "LFCAT" 1566226 T LFCAT (NIL) -9 NIL 1566365 NIL) (-648 1563021 1563355 1563705 "LF" 1564804 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559881 1560553 1561241 "LEXTRIPK" 1562385 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556469 1557451 1557954 "LEXP" 1559461 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555885 1556190 1556282 "LETAST" 1556397 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554271 1554596 1554997 "LEADCDET" 1555567 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553449 1553535 1553764 "LAZM3PK" 1554192 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547960 1551526 1552064 "LAUPOL" 1552961 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547533 1547583 1547744 "LAPLACE" 1547910 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546381 1547097 1547138 "LALG" 1547200 NIL LALG (NIL T) -9 NIL 1547259 NIL) (-639 1546077 1546154 1546290 "LALG-" 1546295 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543814 1545178 1545429 "LA" 1545910 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543643 1543673 1543714 "KVTFROM" 1543776 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542400 1543010 1543195 "KTVLOGIC" 1543478 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542229 1542259 1542300 "KRCFROM" 1542362 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541121 1541320 1541619 "KOVACIC" 1542029 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540950 1540980 1541021 "KONVERT" 1541083 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540779 1540809 1540850 "KOERCE" 1540912 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540263 1540356 1540488 "KERNEL2" 1540693 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537950 1538856 1539233 "KERNEL" 1539919 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531421 1536427 1536481 "KDAGG" 1536858 NIL KDAGG (NIL T T) -9 NIL 1537064 NIL) (-628 1530932 1531074 1531279 "KDAGG-" 1531284 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523632 1530593 1530748 "KAFILE" 1530810 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523236 1523521 1523584 "JVMOP" 1523589 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521972 1522476 1522725 "JVMMDACC" 1523007 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520908 1521362 1521567 "JVMFDACC" 1521787 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519489 1519984 1520284 "JVMCSTTG" 1520628 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518625 1519029 1519190 "JVMCFACC" 1519348 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518303 1518542 1518591 "JVMBCODE" 1518596 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512322 1517814 1518042 "JORDAN" 1518124 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511635 1511971 1512092 "JOINAST" 1512221 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507670 1509812 1509866 "IXAGG" 1510795 NIL IXAGG (NIL T T) -9 NIL 1511254 NIL) (-617 1506523 1506895 1507314 "IXAGG-" 1507319 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501612 1506445 1506504 "IVECTOR" 1506509 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500336 1500615 1500881 "ITUPLE" 1501379 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498808 1499015 1499310 "ITRIGMNP" 1500158 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497535 1497757 1498040 "ITFUN3" 1498584 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497161 1497224 1497333 "ITFUN2" 1497472 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1496266 1496641 1496815 "ITFORM" 1497007 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494035 1495286 1495564 "ITAYLOR" 1496021 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482432 1488172 1489335 "ISUPS" 1492905 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481524 1481676 1481912 "ISUMP" 1482279 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476374 1481469 1481510 "ISTRING" 1481515 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475790 1476095 1476187 "ISAST" 1476302 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474987 1475081 1475297 "IRURPK" 1475704 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473899 1474124 1474364 "IRSN" 1474767 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471944 1472325 1472754 "IRRF2F" 1473537 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471685 1471729 1471805 "IRREDFFX" 1471900 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470258 1470559 1470858 "IROOT" 1471418 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469397 1469751 1469902 "IRFORM" 1470127 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468479 1468610 1468824 "IR2F" 1469280 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466068 1466587 1467153 "IR2" 1467957 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462508 1463752 1464444 "IR" 1465408 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462293 1462333 1462393 "IPRNTPK" 1462468 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458246 1462182 1462251 "IPF" 1462256 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456267 1458171 1458228 "IPADIC" 1458233 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455525 1455827 1455957 "IP4ADDR" 1456157 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454863 1455154 1455286 "IOMODE" 1455413 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453834 1454460 1454587 "IOBFILE" 1454756 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453244 1453738 1453766 "IOBCON" 1453771 T IOBCON (NIL) -9 NIL 1453792 NIL) (-589 1452749 1452813 1452996 "INVLAPLA" 1453180 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442319 1444751 1447137 "INTTR" 1450413 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438612 1439396 1440261 "INTTOOLS" 1441504 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438192 1438289 1438406 "INTSLPE" 1438515 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435659 1438115 1438174 "INTRVL" 1438179 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433237 1433773 1434348 "INTRF" 1435144 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432630 1432745 1432887 "INTRET" 1433135 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430603 1431016 1431486 "INTRAT" 1432238 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427848 1428449 1429068 "INTPM" 1430088 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424565 1425192 1425930 "INTPAF" 1427234 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419666 1420706 1421757 "INTPACK" 1423534 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418912 1419070 1419278 "INTHERTR" 1419508 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418345 1418431 1418619 "INTHERAL" 1418826 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416113 1416634 1417091 "INTHEORY" 1417908 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407445 1409140 1410912 "INTG0" 1414465 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387970 1392808 1397618 "INTFTBL" 1402655 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387195 1387357 1387530 "INTFACT" 1387829 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384592 1385068 1385625 "INTEF" 1386749 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382789 1383684 1383712 "INTDOM" 1384013 T INTDOM (NIL) -9 NIL 1384220 NIL) (-570 1382128 1382332 1382574 "INTDOM-" 1382579 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378002 1380417 1380471 "INTCAT" 1381270 NIL INTCAT (NIL T) -9 NIL 1381591 NIL) (-568 1377456 1377577 1377705 "INTBIT" 1377894 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376137 1376309 1376616 "INTALG" 1377301 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375614 1375710 1375867 "INTAF" 1376041 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368581 1375424 1375564 "INTABL" 1375569 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367822 1368384 1368449 "INT8" 1368483 T INT8 (NIL) -8 NIL NIL 1368528) (-563 1367062 1367624 1367689 "INT64" 1367723 T INT64 (NIL) -8 NIL NIL 1367768) (-562 1366302 1366864 1366929 "INT32" 1366963 T INT32 (NIL) -8 NIL NIL 1367008) (-561 1365542 1366104 1366169 "INT16" 1366203 T INT16 (NIL) -8 NIL NIL 1366248) (-560 1361730 1365339 1365448 "INT" 1365453 T INT (NIL) -8 NIL NIL NIL) (-559 1355831 1359278 1359306 "INS" 1360240 T INS (NIL) -9 NIL 1360905 NIL) (-558 1352885 1353842 1354816 "INS-" 1354889 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351642 1351887 1352185 "INPSIGN" 1352638 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350736 1350877 1351074 "INPRODPF" 1351522 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349606 1349747 1349984 "INPRODFF" 1350616 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348594 1348758 1349018 "INNMFACT" 1349442 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347773 1347888 1348076 "INMODGCD" 1348493 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346257 1346526 1346850 "INFSP" 1347518 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345417 1345558 1345741 "INFPROD0" 1346137 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1345015 1345087 1345185 "INFORM1" 1345352 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341582 1343080 1343595 "INFORM" 1344508 T INFORM (NIL) -8 NIL NIL NIL) (-548 1341087 1341194 1341308 "INFINITY" 1341488 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340161 1340807 1340908 "INETCLTS" 1341006 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338759 1339027 1339348 "INEP" 1339909 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337820 1338656 1338721 "INDE" 1338726 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337372 1337452 1337569 "INCRMAPS" 1337747 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336094 1336641 1336847 "INBFILE" 1337186 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331273 1332330 1333274 "INBFF" 1335182 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330127 1330450 1330478 "INBCON" 1330991 T INBCON (NIL) -9 NIL 1331257 NIL) (-540 1329337 1329602 1329878 "INBCON-" 1329883 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328756 1329061 1329152 "INAST" 1329266 T INAST (NIL) -8 NIL NIL NIL) (-538 1328123 1328435 1328541 "IMPTAST" 1328670 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324044 1327967 1328071 "IMATRIX" 1328076 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322736 1322875 1323191 "IMATQF" 1323900 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320916 1321183 1321520 "IMATLIN" 1322492 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314831 1320840 1320898 "ILIST" 1320903 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312497 1314691 1314804 "IIARRAY2" 1314809 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307297 1312408 1312472 "IFF" 1312477 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306578 1306914 1307030 "IFAST" 1307201 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301090 1305870 1306058 "IFARRAY" 1306435 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300128 1300994 1301067 "IFAMON" 1301072 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299700 1299777 1299831 "IEVALAB" 1300038 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299363 1299443 1299603 "IEVALAB-" 1299608 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298427 1299252 1299327 "IDPOAMS" 1299332 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297560 1298316 1298391 "IDPOAM" 1298396 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296941 1297475 1297537 "IDPO" 1297542 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295421 1295948 1296000 "IDPC" 1296512 NIL IDPC (NIL T T) -9 NIL 1296793 NIL) (-522 1294753 1295313 1295386 "IDPAM" 1295391 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293968 1294645 1294718 "IDPAG" 1294723 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293512 1293774 1293864 "IDENT" 1293898 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289731 1290615 1291510 "IDECOMP" 1292669 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282366 1283654 1284701 "IDEAL" 1288767 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281508 1281638 1281838 "ICDEN" 1282250 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280483 1280988 1281135 "ICARD" 1281381 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278513 1278856 1279261 "IBPTOOLS" 1280160 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273628 1278133 1278246 "IBITS" 1278432 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270303 1270927 1271622 "IBATOOL" 1273045 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268064 1268544 1269077 "IBACHIN" 1269838 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265654 1267910 1268013 "IARRAY2" 1268018 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261367 1265580 1265637 "IARRAY1" 1265642 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254377 1259779 1260260 "IAN" 1260906 T IAN (NIL) -8 NIL NIL NIL) (-508 1253882 1253945 1254118 "IALGFACT" 1254314 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253374 1253523 1253551 "HYPCAT" 1253758 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252876 1253029 1253215 "HYPCAT-" 1253220 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252423 1252671 1252754 "HOSTNAME" 1252813 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252256 1252305 1252346 "HOMOTOP" 1252351 NIL HOMOTOP (NIL T) -9 NIL 1252384 NIL) (-503 1248689 1250188 1250229 "HOAGG" 1251210 NIL HOAGG (NIL T) -9 NIL 1251939 NIL) (-502 1247205 1247682 1248208 "HOAGG-" 1248213 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240241 1246798 1246948 "HEXADEC" 1247075 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238953 1239211 1239474 "HEUGCD" 1240018 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237885 1238790 1238920 "HELLFDIV" 1238925 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235895 1237662 1237750 "HEAP" 1237829 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235092 1235447 1235581 "HEADAST" 1235781 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228479 1235007 1235069 "HDP" 1235074 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221491 1228114 1228266 "HDMP" 1228380 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220797 1220955 1221119 "HB" 1221347 T HB (NIL) -7 NIL NIL NIL) (-493 1213807 1220643 1220747 "HASHTBL" 1220752 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213223 1213528 1213620 "HASAST" 1213735 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210629 1212845 1213027 "HACKPI" 1213061 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205801 1210482 1210595 "GTSET" 1210600 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198840 1205679 1205777 "GSTBL" 1205782 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190589 1198005 1198261 "GSERIES" 1198640 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189620 1190133 1190161 "GROUP" 1190364 T GROUP (NIL) -9 NIL 1190498 NIL) (-486 1188944 1189145 1189396 "GROUP-" 1189401 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187293 1187632 1188019 "GROEBSOL" 1188621 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186121 1186481 1186532 "GRMOD" 1187061 NIL GRMOD (NIL T T) -9 NIL 1187229 NIL) (-483 1185877 1185925 1186053 "GRMOD-" 1186058 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181017 1182231 1183231 "GRIMAGE" 1184897 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179411 1179744 1180068 "GRDEF" 1180713 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178843 1178971 1179112 "GRAY" 1179290 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177920 1178422 1178473 "GRALG" 1178626 NIL GRALG (NIL T T) -9 NIL 1178719 NIL) (-478 1177557 1177654 1177817 "GRALG-" 1177822 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174038 1177140 1177319 "GPOLSET" 1177463 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173386 1173449 1173707 "GOSPER" 1173975 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168956 1169824 1170350 "GMODPOL" 1173085 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167943 1168145 1168383 "GHENSEL" 1168768 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162015 1162942 1163962 "GENUPS" 1167027 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161706 1161763 1161852 "GENUFACT" 1161958 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161106 1161195 1161360 "GENPGCD" 1161624 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160574 1160615 1160828 "GENMFACT" 1161065 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159110 1159397 1159704 "GENEEZ" 1160317 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152282 1158721 1158883 "GDMP" 1159033 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141020 1146053 1147159 "GCNAALG" 1151265 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139147 1140195 1140223 "GCDDOM" 1140478 T GCDDOM (NIL) -9 NIL 1140635 NIL) (-465 1138587 1138744 1138959 "GCDDOM-" 1138964 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1127059 1129533 1131925 "GBINTERN" 1136278 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124860 1125188 1125609 "GBF" 1126734 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123617 1123806 1124073 "GBEUCLID" 1124676 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1122267 1122474 1122778 "GB" 1123396 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121598 1121741 1121890 "GAUSSFAC" 1122138 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119919 1120267 1120581 "GALUTIL" 1121317 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118179 1118501 1118825 "GALPOLYU" 1119646 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115478 1115834 1116241 "GALFACTU" 1117876 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107092 1108783 1110391 "GALFACT" 1113910 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104378 1105138 1105166 "FVFUN" 1106322 T FVFUN (NIL) -9 NIL 1107042 NIL) (-454 1103608 1103826 1103854 "FVC" 1104145 T FVC (NIL) -9 NIL 1104328 NIL) (-453 1103209 1103433 1103501 "FUNDESC" 1103560 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102782 1103006 1103087 "FUNCTION" 1103161 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101459 1102083 1102286 "FTEM" 1102599 T FTEM (NIL) -8 NIL NIL NIL) (-450 1099089 1099781 1100247 "FT" 1101013 T FT (NIL) -8 NIL NIL NIL) (-449 1097358 1097669 1098066 "FSUPFACT" 1098780 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095677 1096044 1096376 "FST" 1097046 T FST (NIL) -8 NIL NIL NIL) (-447 1094858 1094982 1095170 "FSRED" 1095559 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093547 1093813 1094160 "FSPRMELT" 1094573 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090757 1091291 1091777 "FSPECF" 1093110 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1090279 1090339 1090509 "FSINT" 1090698 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088415 1089272 1089575 "FSERIES" 1090058 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087439 1087573 1087797 "FSCINT" 1088295 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086463 1086624 1086851 "FSAGG2" 1087292 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1082327 1085407 1085448 "FSAGG" 1085818 NIL FSAGG (NIL T) -9 NIL 1086077 NIL) (-439 1079927 1080690 1081486 "FSAGG-" 1081581 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077587 1077885 1078433 "FS2UPS" 1079645 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076453 1076636 1076938 "FS2EXPXP" 1077412 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1076081 1076130 1076259 "FS2" 1076404 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1056308 1065855 1065896 "FS" 1069780 NIL FS (NIL T) -9 NIL 1072069 NIL) (-434 1044369 1047944 1052001 "FS-" 1052301 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043783 1043910 1044062 "FRUTIL" 1044249 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1038301 1041472 1041512 "FRNAALG" 1042832 NIL FRNAALG (NIL T) -9 NIL 1043430 NIL) (-431 1033782 1035050 1036325 "FRNAALG-" 1037075 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033414 1033463 1033590 "FRNAAF2" 1033733 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031701 1032263 1032559 "FRMOD" 1033226 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030886 1030979 1031270 "FRIDEAL2" 1031608 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028491 1029261 1029579 "FRIDEAL" 1030677 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027582 1028038 1028079 "FRETRCT" 1028084 NIL FRETRCT (NIL T) -9 NIL 1028260 NIL) (-425 1026640 1026925 1027276 "FRETRCT-" 1027281 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023454 1024924 1024983 "FRAMALG" 1025865 NIL FRAMALG (NIL T T) -9 NIL 1026157 NIL) (-423 1021492 1022043 1022673 "FRAMALG-" 1022896 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1021122 1021185 1021292 "FRAC2" 1021429 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1014093 1020595 1020872 "FRAC" 1020877 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013723 1013786 1013893 "FR2" 1014030 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004640 1009218 1010576 "FR" 1012397 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998557 1002019 1002047 "FPS" 1003166 T FPS (NIL) -9 NIL 1003723 NIL) (-417 997982 998115 998279 "FPS-" 998425 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994934 996939 996967 "FPC" 997192 T FPC (NIL) -9 NIL 997334 NIL) (-415 994715 994767 994864 "FPC-" 994869 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993473 994203 994244 "FPATMAB" 994249 NIL FPATMAB (NIL T) -9 NIL 994401 NIL) (-413 991616 992215 992562 "FPARFRAC" 993189 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986908 987508 988190 "FORTRAN" 991048 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984482 985146 985174 "FORTFN" 986234 T FORTFN (NIL) -9 NIL 986858 NIL) (-410 984234 984296 984324 "FORTCAT" 984383 T FORTCAT (NIL) -9 NIL 984445 NIL) (-409 981920 982450 982989 "FORT" 983715 T FORT (NIL) -7 NIL NIL NIL) (-408 981702 981738 981807 "FORMULA1" 981884 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979706 980318 980708 "FORMULA" 981332 T FORMULA (NIL) -8 NIL NIL NIL) (-406 979223 979281 979454 "FORDER" 979648 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978283 978483 978676 "FOP" 979050 T FOP (NIL) -7 NIL NIL NIL) (-404 976696 977563 977737 "FNLA" 978165 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975315 975826 975854 "FNCAT" 976314 T FNCAT (NIL) -9 NIL 976574 NIL) (-402 974758 975274 975302 "FNAME" 975307 T FNAME (NIL) -8 NIL NIL NIL) (-401 973084 974257 974285 "FMTC" 974290 T FMTC (NIL) -9 NIL 974326 NIL) (-400 971632 973020 973066 "FMONOID" 973071 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968221 969587 969628 "FMONCAT" 970845 NIL FMONCAT (NIL T) -9 NIL 971450 NIL) (-398 965543 966291 966319 "FMFUN" 967463 T FMFUN (NIL) -9 NIL 968171 NIL) (-397 962416 963468 963522 "FMCAT" 964717 NIL FMCAT (NIL T T) -9 NIL 965212 NIL) (-396 961649 961866 961894 "FMC" 962184 T FMC (NIL) -9 NIL 962366 NIL) (-395 960317 961415 961515 "FM1" 961594 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959335 960059 960208 "FM" 960213 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 957073 957525 958019 "FLOATRP" 958886 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954475 955011 955589 "FLOATCP" 956540 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 947131 952204 952825 "FLOAT" 953874 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945649 946723 946764 "FLINEXP" 946769 NIL FLINEXP (NIL T) -9 NIL 946862 NIL) (-389 944779 945038 945366 "FLINEXP-" 945371 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943837 943999 944223 "FLASORT" 944631 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940755 941807 941859 "FLALG" 943086 NIL FLALG (NIL T T) -9 NIL 943553 NIL) (-386 939779 939940 940167 "FLAGG2" 940608 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 933043 937188 937229 "FLAGG" 938491 NIL FLAGG (NIL T) -9 NIL 939143 NIL) (-384 931697 932108 932598 "FLAGG-" 932603 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928328 929542 929601 "FINRALG" 930729 NIL FINRALG (NIL T T) -9 NIL 931237 NIL) (-382 927452 927717 928056 "FINRALG-" 928061 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926758 927057 927085 "FINITE" 927281 T FINITE (NIL) -9 NIL 927388 NIL) (-380 918709 921288 921328 "FINAALG" 924995 NIL FINAALG (NIL T) -9 NIL 926448 NIL) (-379 913825 915091 916235 "FINAALG-" 917614 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912385 912807 912861 "FILECAT" 913545 NIL FILECAT (NIL T T) -9 NIL 913761 NIL) (-377 911663 912140 912243 "FILE" 912315 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 909059 910893 910921 "FIELD" 910961 T FIELD (NIL) -9 NIL 911041 NIL) (-375 907601 908064 908575 "FIELD-" 908580 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905283 906236 906583 "FGROUP" 907287 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904355 904537 904757 "FGLMICPK" 905115 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899589 904280 904337 "FFX" 904342 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899184 899251 899386 "FFSLPE" 899522 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898682 898724 898933 "FFPOLY2" 899142 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894558 895454 896250 "FFPOLY" 897918 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889806 894477 894540 "FFP" 894545 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884316 889149 889339 "FFNBX" 889660 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878628 883451 883709 "FFNBP" 884170 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872645 877912 878123 "FFNB" 878461 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871465 871675 871990 "FFINTBAS" 872442 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 867041 869712 869740 "FFIELDC" 870360 T FFIELDC (NIL) -9 NIL 870736 NIL) (-362 865619 866074 866571 "FFIELDC-" 866576 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865176 865234 865358 "FFHOM" 865561 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862835 863358 863875 "FFF" 864691 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857849 862577 862678 "FFCGX" 862778 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852867 857581 857688 "FFCGP" 857792 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847446 852594 852702 "FFCG" 852803 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846851 846900 847135 "FFCAT2" 847397 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825514 836583 836669 "FFCAT" 841834 NIL FFCAT (NIL T T T) -9 NIL 843285 NIL) (-354 820525 821759 823073 "FFCAT-" 824303 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815325 820436 820500 "FF" 820505 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803978 808297 809517 "FEXPR" 814177 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802906 803375 803416 "FEVALAB" 803500 NIL FEVALAB (NIL T) -9 NIL 803761 NIL) (-350 802023 802275 802613 "FEVALAB-" 802618 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798885 799770 799885 "FDIVCAT" 801453 NIL FDIVCAT (NIL T T T T) -9 NIL 801890 NIL) (-348 798641 798674 798844 "FDIVCAT-" 798849 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797855 797948 798225 "FDIV2" 798548 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796265 797238 797441 "FDIV" 797754 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795173 795560 795762 "FCTRDATA" 796083 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793829 794118 794407 "FCPAK1" 794904 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792832 793329 793470 "FCOMP" 793720 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776146 779982 783520 "FC" 789314 T FC (NIL) -8 NIL NIL NIL) (-341 767841 772467 772507 "FAXF" 774309 NIL FAXF (NIL T) -9 NIL 775001 NIL) (-340 764962 765775 766600 "FAXF-" 767065 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759531 764338 764514 "FARRAY" 764819 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 754095 756478 756531 "FAMR" 757554 NIL FAMR (NIL T T) -9 NIL 758014 NIL) (-337 752919 753287 753722 "FAMR-" 753727 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751946 752841 752894 "FAMONOID" 752899 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749576 750428 750481 "FAMONC" 751422 NIL FAMONC (NIL T T) -9 NIL 751808 NIL) (-334 748050 749330 749467 "FAGROUP" 749472 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745803 746164 746567 "FACUTIL" 747731 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744890 745087 745309 "FACTFUNC" 745613 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736648 744193 744392 "EXPUPXS" 744746 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 734101 734671 735257 "EXPRTUBE" 736082 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730312 730964 731694 "EXPRODE" 733440 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724746 725453 726259 "EXPR2UPS" 729610 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724372 724435 724544 "EXPR2" 724683 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708666 723021 723450 "EXPR" 723976 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698983 707817 708108 "EXPEXPAN" 708502 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698403 698707 698798 "EXITAST" 698912 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698167 698360 698389 "EXIT" 698394 T EXIT (NIL) -8 NIL NIL NIL) (-322 697788 697856 697969 "EVALCYC" 698099 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697305 697447 697488 "EVALAB" 697658 NIL EVALAB (NIL T) -9 NIL 697762 NIL) (-320 696762 696908 697129 "EVALAB-" 697134 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693870 695418 695446 "EUCDOM" 696001 T EUCDOM (NIL) -9 NIL 696351 NIL) (-318 692209 692717 693307 "EUCDOM-" 693312 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691835 691898 692007 "ESTOOLS2" 692146 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691580 691628 691708 "ESTOOLS1" 691787 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678897 681878 684628 "ESTOOLS" 688850 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678636 678674 678756 "ESCONT1" 678859 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674944 675771 676551 "ESCONT" 677876 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674613 674669 674769 "ES2" 674888 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674237 674301 674410 "ES1" 674549 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667938 669868 669896 "ES" 672664 T ES (NIL) -9 NIL 674074 NIL) (-309 662615 664172 665989 "ES-" 666153 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661807 661960 662136 "ERROR" 662459 T ERROR (NIL) -7 NIL NIL NIL) (-307 654823 661666 661757 "EQTBL" 661762 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654449 654512 654621 "EQ2" 654760 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646708 649763 651212 "EQ" 653033 NIL -1493 (NIL T) -8 NIL NIL NIL) (-304 641951 643046 644139 "EP" 645647 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640491 640842 641148 "ENV" 641665 T ENV (NIL) -8 NIL NIL NIL) (-302 639451 640125 640153 "ENTIRER" 640158 T ENTIRER (NIL) -9 NIL 640204 NIL) (-301 635863 637633 637994 "EMR" 639259 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634967 635178 635232 "ELTAGG" 635612 NIL ELTAGG (NIL T T) -9 NIL 635823 NIL) (-299 634674 634748 634889 "ELTAGG-" 634894 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634432 634467 634521 "ELTAB" 634605 NIL ELTAB (NIL T T) -9 NIL 634657 NIL) (-297 633534 633704 633903 "ELFUTS" 634283 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633258 633332 633360 "ELEMFUN" 633465 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633122 633149 633217 "ELEMFUN-" 633222 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627539 631164 631205 "ELAGG" 632145 NIL ELAGG (NIL T) -9 NIL 632608 NIL) (-293 625716 626258 626921 "ELAGG-" 626926 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624998 625165 625321 "ELABOR" 625580 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623605 623938 624232 "ELABEXPR" 624724 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616117 618242 619071 "EFUPXS" 622880 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609243 611366 612177 "EFULS" 615392 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606680 607086 607558 "EFSTRUC" 608875 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596117 598037 599585 "EF" 605195 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595095 595602 595751 "EAB" 595988 T EAB (NIL) -8 NIL NIL NIL) (-285 594217 595054 595082 "E04UCFA" 595087 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593339 594176 594204 "E04NAFA" 594209 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592461 593298 593326 "E04MBFA" 593331 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591583 592420 592448 "E04JAFA" 592453 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590707 591542 591570 "E04GCFA" 591575 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589831 590666 590694 "E04FDFA" 590699 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588953 589790 589818 "E04DGFA" 589823 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 583030 584478 585842 "E04AGNT" 587609 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581650 582331 582371 "DVARCAT" 582712 NIL DVARCAT (NIL T) -9 NIL 582875 NIL) (-276 580800 581066 581380 "DVARCAT-" 581385 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572761 580599 580728 "DSMP" 580733 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571112 571903 571944 "DSEXT" 572307 NIL DSEXT (NIL T) -9 NIL 572601 NIL) (-273 569301 569825 570491 "DSEXT-" 570496 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 568960 569025 569123 "DROPT1" 569236 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 563979 565201 566338 "DROPT0" 567843 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558562 559924 560992 "DROPT" 562931 T DROPT (NIL) -8 NIL NIL NIL) (-269 556871 557232 557618 "DRAWPT" 558196 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556498 556557 556675 "DRAWHACK" 556812 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555199 555498 555789 "DRAWCX" 556227 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554708 554783 554934 "DRAWCURV" 555125 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 545026 547138 549253 "DRAWCFUN" 552613 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539517 540536 541615 "DRAW" 544000 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 535988 538182 538223 "DQAGG" 538852 NIL DQAGG (NIL T) -9 NIL 539126 NIL) (-262 522571 530199 530282 "DPOLCAT" 532134 NIL DPOLCAT (NIL T T T T) -9 NIL 532679 NIL) (-261 517090 518756 520714 "DPOLCAT-" 520719 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509947 516951 517049 "DPMO" 517054 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502701 509727 509894 "DPMM" 509899 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502223 502485 502574 "DOMTMPLT" 502632 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501572 502025 502105 "DOMCTOR" 502163 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500724 501052 501203 "DOMAIN" 501441 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493736 500359 500511 "DMP" 500625 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491513 492803 492844 "DMEXT" 492849 NIL DMEXT (NIL T) -9 NIL 493025 NIL) (-253 491107 491169 491313 "DLP" 491451 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484230 490434 490624 "DLIST" 490949 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480768 483055 483096 "DLAGG" 483646 NIL DLAGG (NIL T) -9 NIL 483876 NIL) (-250 479280 480094 480122 "DIVRING" 480214 T DIVRING (NIL) -9 NIL 480297 NIL) (-249 478463 478707 479007 "DIVRING-" 479012 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476505 476922 477328 "DISPLAY" 478077 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475335 475556 475821 "DIRPROD2" 476298 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468742 475249 475312 "DIRPROD" 475317 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456961 463453 463506 "DIRPCAT" 463764 NIL DIRPCAT (NIL NIL T) -9 NIL 464639 NIL) (-244 454161 454929 455810 "DIRPCAT-" 456147 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453442 453608 453794 "DIOSP" 453995 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449856 452326 452367 "DIOPS" 452801 NIL DIOPS (NIL T) -9 NIL 453030 NIL) (-241 449375 449519 449710 "DIOPS-" 449715 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448282 449054 449082 "DIFRING" 449087 T DIFRING (NIL) -9 NIL 449109 NIL) (-239 447930 448028 448056 "DIFFSPC" 448175 T DIFFSPC (NIL) -9 NIL 448250 NIL) (-238 447551 447653 447805 "DIFFSPC-" 447810 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446487 447085 447126 "DIFFMOD" 447131 NIL DIFFMOD (NIL T) -9 NIL 447229 NIL) (-236 446183 446240 446281 "DIFFDOM" 446402 NIL DIFFDOM (NIL T) -9 NIL 446470 NIL) (-235 446030 446060 446144 "DIFFDOM-" 446149 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443770 445234 445275 "DIFEXT" 445280 NIL DIFEXT (NIL T) -9 NIL 445433 NIL) (-233 440804 443274 443315 "DIAGG" 443320 NIL DIAGG (NIL T) -9 NIL 443340 NIL) (-232 440152 440345 440597 "DIAGG-" 440602 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 435002 439111 439388 "DHMATRIX" 439921 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430470 431523 432533 "DFSFUN" 434012 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424704 429401 429713 "DFLOAT" 430178 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422943 423248 423637 "DFINTTLS" 424412 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419762 420964 421364 "DERHAM" 422609 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417298 419537 419626 "DEQUEUE" 419706 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416540 416685 416868 "DEGRED" 417160 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412946 413715 414561 "DEFINTRF" 415768 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410483 410970 411562 "DEFINTEF" 412465 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409767 410103 410218 "DEFAST" 410388 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402803 409360 409510 "DECIMAL" 409637 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400261 400773 401279 "DDFACT" 402347 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399851 399900 400051 "DBLRESP" 400212 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 399052 399621 399712 "DBASIS" 399800 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396836 397282 397643 "DBASE" 398818 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 396024 396316 396462 "DATAARY" 396735 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395082 395983 396011 "D03FAFA" 396016 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394141 395041 395069 "D03EEFA" 395074 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 392067 392557 393046 "D03AGNT" 393672 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391308 392026 392054 "D02EJFA" 392059 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390549 391267 391295 "D02CJFA" 391300 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389790 390508 390536 "D02BHFA" 390541 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 389031 389749 389777 "D02BBFA" 389782 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382162 383817 385423 "D02AGNT" 387445 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379912 380453 380999 "D01WGTS" 381636 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378919 379871 379899 "D01TRNS" 379904 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377927 378878 378906 "D01GBFA" 378911 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376935 377886 377914 "D01FCFA" 377919 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375943 376894 376922 "D01ASFA" 376927 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374951 375902 375930 "D01AQFA" 375935 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373959 374910 374938 "D01APFA" 374943 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372967 373918 373946 "D01ANFA" 373951 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371975 372926 372954 "D01AMFA" 372959 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370983 371934 371962 "D01ALFA" 371967 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369991 370942 370970 "D01AKFA" 370975 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368999 369950 369978 "D01AJFA" 369983 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362222 363847 365408 "D01AGNT" 367458 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361541 361687 361839 "CYCLOTOM" 362090 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358196 358989 359716 "CYCLES" 360834 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357496 357642 357813 "CVMP" 358057 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355283 355595 355964 "CTRIGMNP" 357224 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354756 355014 355115 "CTORKIND" 355202 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353961 354349 354377 "CTORCAT" 354559 T CTORCAT (NIL) -9 NIL 354672 NIL) (-188 353535 353670 353829 "CTORCAT-" 353834 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352949 353209 353317 "CTORCALL" 353459 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352307 352743 352816 "CTOR" 352896 T CTOR (NIL) -8 NIL NIL NIL) (-185 351663 351780 351933 "CSTTOOLS" 352204 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347360 348119 348877 "CRFP" 350975 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346775 347081 347173 "CRCEAST" 347288 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345798 346007 346235 "CRAPACK" 346579 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345178 345283 345487 "CPMATCH" 345674 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344897 344931 345037 "CPIMA" 345144 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341155 341917 342636 "COORDSYS" 344232 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340543 340688 340830 "CONTOUR" 341033 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 336008 338546 339038 "CONTFRAC" 340083 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335882 335909 335937 "CONDUIT" 335974 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334836 335510 335538 "COMRING" 335543 T COMRING (NIL) -9 NIL 335595 NIL) (-174 333818 334194 334378 "COMPPROP" 334672 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333473 333514 333642 "COMPLPAT" 333777 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 333103 333166 333273 "COMPLEX2" 333410 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321486 332912 333021 "COMPLEX" 333026 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320807 320946 321106 "COMPILER" 321346 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320519 320560 320658 "COMPFACT" 320766 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301894 314223 314263 "COMPCAT" 315267 NIL COMPCAT (NIL T) -9 NIL 316615 NIL) (-167 290782 294333 297960 "COMPCAT-" 298316 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290505 290539 290642 "COMMUPC" 290748 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290293 290333 290392 "COMMONOP" 290466 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289815 290097 290172 "COMMAAST" 290238 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289323 289566 289653 "COMM" 289748 T COMM (NIL) -8 NIL NIL NIL) (-162 288518 288766 288794 "COMBOPC" 289132 T COMBOPC (NIL) -9 NIL 289307 NIL) (-161 287372 287624 287866 "COMBINAT" 288308 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283715 284403 285030 "COMBF" 286794 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282377 282831 283066 "COLOR" 283500 T COLOR (NIL) -8 NIL NIL NIL) (-158 281793 282098 282190 "COLONAST" 282305 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281427 281480 281605 "CMPLXRT" 281740 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280815 281127 281226 "CLLCTAST" 281348 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276275 277345 278425 "CLIP" 279755 T CLIP (NIL) -7 NIL NIL NIL) (-154 274448 275376 275616 "CLIF" 276102 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270430 272566 272607 "CLAGG" 273536 NIL CLAGG (NIL T) -9 NIL 274072 NIL) (-152 268774 269309 269892 "CLAGG-" 269897 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268312 268403 268543 "CINTSLPE" 268683 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265777 266284 266832 "CHVAR" 267840 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264817 265491 265519 "CHARZ" 265524 T CHARZ (NIL) -9 NIL 265539 NIL) (-148 264565 264611 264689 "CHARPOL" 264771 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263483 264196 264224 "CHARNZ" 264271 T CHARNZ (NIL) -9 NIL 264327 NIL) (-146 260427 261537 262066 "CHAR" 262974 T CHAR (NIL) -8 NIL NIL NIL) (-145 260135 260214 260242 "CFCAT" 260353 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259358 259487 259670 "CDEN" 260019 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254955 258511 258791 "CCLASS" 259098 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254176 254363 254540 "CATEGORY" 254798 T -10 (NIL) -8 NIL NIL NIL) (-141 253671 254095 254143 "CATCTOR" 254148 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253062 253374 253472 "CATAST" 253593 T CATAST (NIL) -8 NIL NIL NIL) (-139 252478 252783 252875 "CASEAST" 252990 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251574 251734 251955 "CARTEN2" 252325 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246472 247731 248475 "CARTEN" 250886 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244602 245622 245879 "CARD" 246235 T CARD (NIL) -8 NIL NIL NIL) (-135 244124 244406 244481 "CAPSLAST" 244547 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243566 243822 243850 "CACHSET" 243982 T CACHSET (NIL) -9 NIL 244060 NIL) (-133 242956 243344 243372 "CABMON" 243422 T CABMON (NIL) -9 NIL 243478 NIL) (-132 242393 242660 242770 "BYTEORD" 242866 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237320 241898 242070 "BYTEBUF" 242241 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236078 236835 236984 "BYTE" 237147 T BYTE (NIL) -8 NIL NIL 237276) (-129 233340 235770 235877 "BTREE" 236004 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230542 232988 233110 "BTOURN" 233250 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227649 229984 230025 "BTCAT" 230093 NIL BTCAT (NIL T) -9 NIL 230170 NIL) (-126 227298 227396 227545 "BTCAT-" 227550 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222190 226544 226572 "BTAGG" 226686 T BTAGG (NIL) -9 NIL 226796 NIL) (-124 221644 221805 222011 "BTAGG-" 222016 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218380 220922 221137 "BSTREE" 221461 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217488 217644 217828 "BRILL" 218236 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213883 216186 216227 "BRAGG" 216876 NIL BRAGG (NIL T) -9 NIL 217134 NIL) (-120 212316 212818 213373 "BRAGG-" 213378 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204552 211660 211845 "BPADICRT" 212163 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202561 204489 204534 "BPADIC" 204539 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202253 202289 202403 "BOUNDZRO" 202525 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199980 200438 200913 "BOP1" 201811 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194962 196406 197318 "BOP" 199088 T BOP (NIL) -8 NIL NIL NIL) (-114 193627 194550 194692 "BOOLEAN" 194840 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193220 193377 193405 "BOOLE" 193516 T BOOLE (NIL) -9 NIL 193597 NIL) (-112 193088 193115 193181 "BOOLE-" 193186 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158914 159759 159901 "ASP80" 160043 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158641 158862 158901 "ASP8" 158906 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157487 158318 158436 "ASP78" 158554 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156348 157167 157284 "ASP77" 157401 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155152 155986 156117 "ASP74" 156248 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153944 154787 154919 "ASP73" 155051 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153579 153711 "ASP7" 153843 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP49" 149331 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147066 147929 148097 "ASP42" 148279 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145735 146599 146769 "ASP41" 146953 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145436 145546 "ASP4" 145656 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 141739 141778 "ASP30" 141783 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141237 141324 141400 "ASP29" 141475 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140966 141185 141224 "ASP28" 141229 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140695 140914 140953 "ASP27" 140958 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139671 140393 140504 "ASP24" 140615 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138640 139473 139585 "ASP20" 139590 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137475 138314 138433 "ASP19" 138552 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137194 137279 137355 "ASP12" 137430 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135938 136793 136937 "ASP10" 137081 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134918 135639 135749 "ASP1" 135859 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132530 134762 134853 "ARRAY2" 134858 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131544 131735 131956 "ARRAY12" 132353 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126904 131192 131306 "ARRAY1" 131461 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120949 123106 123181 "ARR2CAT" 125811 NIL ARR2CAT (NIL T T T) -9 NIL 126569 NIL) (-56 118239 119127 120081 "ARR2CAT-" 120086 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117490 117866 117991 "ARITY" 118132 T ARITY (NIL) -8 NIL NIL NIL) (-54 116248 116418 116717 "APPRULE" 117326 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115893 115947 116066 "APPLYORE" 116194 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115147 115294 115451 "ANY1" 115767 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114447 114740 114860 "ANY" 115045 T ANY (NIL) -8 NIL NIL NIL) (-50 111773 112884 113211 "ANTISYM" 114171 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111217 111480 111576 "ANON" 111695 T ANON (NIL) -8 NIL NIL NIL) (-48 104373 109756 110210 "AN" 110781 T AN (NIL) -8 NIL NIL NIL) (-47 100029 101645 101696 "AMR" 102444 NIL AMR (NIL T T) -9 NIL 103044 NIL) (-46 99081 99362 99725 "AMR-" 99730 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82550 98998 99059 "ALIST" 99064 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78847 82144 82313 "ALGSC" 82468 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75297 75957 76564 "ALGPKG" 78287 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74562 74675 74859 "ALGMFACT" 75183 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70545 71176 71770 "ALGMANIP" 74146 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59884 70171 70321 "ALGFF" 70478 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59056 59211 59390 "ALGFACT" 59742 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57845 58583 58621 "ALGEBRA" 58626 NIL ALGEBRA (NIL T) -9 NIL 58667 NIL) (-37 57545 57622 57754 "ALGEBRA-" 57759 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38506 55382 55434 "ALAGG" 55570 NIL ALAGG (NIL T T) -9 NIL 55731 NIL) (-35 38006 38155 38181 "AHYP" 38382 T AHYP (NIL) -9 NIL NIL NIL) (-34 36891 37185 37211 "AGG" 37710 T AGG (NIL) -9 NIL 37989 NIL) (-33 36289 36487 36701 "AGG-" 36706 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34049 34518 34923 "AF" 35931 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33469 33774 33864 "ADDAST" 33977 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32701 32996 33152 "ACPLOT" 33331 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20258 29633 29671 "ACFS" 30278 NIL ACFS (NIL T) -9 NIL 30517 NIL) (-28 18165 18775 19537 "ACFS-" 19542 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13873 16198 16224 "ACF" 17103 T ACF (NIL) -9 NIL 17516 NIL) (-26 12505 12911 13404 "ACF-" 13409 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12015 12258 12284 "ABELSG" 12376 T ABELSG (NIL) -9 NIL 12441 NIL) (-24 11876 11907 11973 "ABELSG-" 11978 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11145 11492 11518 "ABELMON" 11688 T ABELMON (NIL) -9 NIL 11800 NIL) (-22 10785 10893 11031 "ABELMON-" 11036 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10035 10491 10517 "ABELGRP" 10589 T ABELGRP (NIL) -9 NIL 10664 NIL) (-20 9462 9627 9843 "ABELGRP-" 9848 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8724 8763 "A1AGG" 8768 NIL A1AGG (NIL T) -9 NIL 8808 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 167f96d0..3ce70da5 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,763 +1,298 @@ -(733360 . 3505945377) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-711 *8)) (-4 *8 (-979 *5 *7 *6)) - (-4 *5 (-13 (-319) (-149))) (-4 *6 (-13 (-871) (-633 (-1207)))) - (-4 *7 (-815)) - (-5 *2 - (-663 - (-2 (|:| -1983 (-793)) - (|:| |eqns| - (-663 - (-2 (|:| |det| *8) (|:| |rows| (-663 (-560))) - (|:| |cols| (-663 (-560)))))) - (|:| |fgb| (-663 *8))))) - (-5 *1 (-953 *5 *6 *7 *8)) (-5 *4 (-793))))) -(((*1 *2 *1) (-12 (-4 *1 (-1165 *3)) (-4 *3 (-1080)) (-5 *2 (-114))))) -(((*1 *1 *2) - (-12 (-5 *2 (-663 *3)) (-4 *3 (-1132)) (-5 *1 (-1031 *3))))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *5 (-630 *4)) (-5 *6 (-1207)) - (-4 *4 (-13 (-435 *7) (-27) (-1233))) - (-4 *7 (-13 (-466) (-1069 (-560)) (-149) (-660 (-560)))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) 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(-4 *4 (-363))))) + (-12 (-4 *4 (-939)) (-4 *5 (-815)) (-4 *6 (-871)) + (-4 *7 (-979 *4 *5 *6)) (-5 *2 (-419 (-1201 *7))) + (-5 *1 (-936 *4 *5 *6 *7)) (-5 *3 (-1201 *7)))) + ((*1 *2 *3) + (-12 (-4 *4 (-939)) (-4 *5 (-1273 *4)) (-5 *2 (-419 (-1201 *5))) + (-5 *1 (-937 *4 *5)) (-5 *3 (-1201 *5))))) +(((*1 *1 *2) (-12 (-5 *2 (-159)) (-5 *1 (-898))))) (((*1 *2 *3) (-12 (-5 *3 (-51)) (-5 *1 (-52 *2)) (-4 *2 (-1247)))) ((*1 *1 *2) (-12 (-5 *2 (-975 (-391))) (-5 *1 (-352 *3 *4 *5)) @@ -4400,11 +2868,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) - (|:| -2024 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| -3867 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -2024 (-663 (-1120 (-864 (-229))))) + (|:| -3867 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *2 *1) @@ -4420,13 +2888,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -3528 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -1984 (-663 (-229))) (|:| |lb| (-663 (-864 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-864 (-229)))))) (|:| |lsa| (-2 (|:| |lfn| (-663 (-326 (-229)))) - (|:| -3528 (-663 (-229))))))) + (|:| -1984 (-663 (-229))))))) (-5 *1 (-863)))) ((*1 *2 *1) (-12 @@ -4445,26 +2913,26 @@ (-4 *4 (-815)) (-4 *5 (-871)) (-4 *1 (-1007 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1069 *2)) (-4 *2 (-1247)))) ((*1 *1 *2) - (-2157 + (-2188 (-12 (-5 *2 (-975 *3)) - (-12 (-1452 (-4 *3 (-38 (-421 (-560))))) - (-1452 (-4 *3 (-38 (-560)))) (-4 *5 (-633 (-1207)))) + (-12 (-2553 (-4 *3 (-38 (-421 (-560))))) + (-2553 (-4 *3 (-38 (-560)))) (-4 *5 (-633 (-1207)))) (-4 *3 (-1080)) (-4 *1 (-1096 *3 *4 *5)) (-4 *4 (-815)) (-4 *5 (-871))) (-12 (-5 *2 (-975 *3)) - (-12 (-1452 (-4 *3 (-559))) (-1452 (-4 *3 (-38 (-421 (-560))))) + (-12 (-2553 (-4 *3 (-559))) (-2553 (-4 *3 (-38 (-421 (-560))))) (-4 *3 (-38 (-560))) (-4 *5 (-633 (-1207)))) (-4 *3 (-1080)) (-4 *1 (-1096 *3 *4 *5)) (-4 *4 (-815)) (-4 *5 (-871))) (-12 (-5 *2 (-975 *3)) - (-12 (-1452 (-4 *3 (-1022 (-560)))) (-4 *3 (-38 (-421 (-560)))) + (-12 (-2553 (-4 *3 (-1022 (-560)))) (-4 *3 (-38 (-421 (-560)))) (-4 *5 (-633 (-1207)))) (-4 *3 (-1080)) (-4 *1 (-1096 *3 *4 *5)) (-4 *4 (-815)) (-4 *5 (-871))))) ((*1 *1 *2) - (-2157 + (-2188 (-12 (-5 *2 (-975 (-560))) (-4 *1 (-1096 *3 *4 *5)) - (-12 (-1452 (-4 *3 (-38 (-421 (-560))))) (-4 *3 (-38 (-560))) + (-12 (-2553 (-4 *3 (-38 (-421 (-560))))) (-4 *3 (-38 (-560))) (-4 *5 (-633 (-1207)))) (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871))) (-12 (-5 *2 (-975 (-560))) (-4 *1 (-1096 *3 *4 *5)) @@ -4474,977 +2942,467 @@ (-12 (-5 *2 (-975 (-421 (-560)))) (-4 *1 (-1096 *3 *4 *5)) (-4 *3 (-38 (-421 (-560)))) (-4 *5 (-633 (-1207))) (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-391)))) - ((*1 *1 *1 *1) (-4 *1 (-559))) - ((*1 *1 *1 *2) (-12 (-5 *1 (-740 *2)) (-4 *2 (-376)))) - ((*1 *1 *2) (-12 (-5 *1 (-740 *2)) 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|lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1185 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3867 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-574)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-793)) (-4 *1 (-717 *2)) (-4 *2 (-1132)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -3699 + (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) + (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-663 (-229))) + (|:| |intvals| (-663 (-229))) (|:| |g| 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*1) + (-12 (-4 *1 (-1242 *3 *4 *5 *2)) (-4 *3 (-571)) (-4 *4 (-815)) + (-4 *5 (-871)) (-4 *2 (-1096 *3 *4 *5))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-972 (-229))) (-5 *2 (-1303)) (-5 *1 (-482))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1322 *4 *2)) (-4 *1 (-387 *4 *2)) (-4 *4 (-871)) (-4 *2 (-175)))) @@ -9272,54 +8609,41 @@ (-4 *2 (-1080)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1080)) (-5 *1 (-1321 *2 *3)) (-4 *3 (-868))))) -(((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-481)))) - ((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-481)))) - ((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-954))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)) (-5 *2 (-663 *1)) - (-4 *1 (-1096 *3 *4 *5))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-793)) (-5 *1 (-58 *3)) (-4 *3 (-1247)))) - ((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1247)) (-5 *1 (-58 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-871)) (-5 *2 (-663 (-663 *4))) (-5 *1 (-1218 *4)) - (-5 *3 (-663 *4))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *4 *5 *3 *3 *4 *3) - (-12 (-5 *3 (-560)) (-5 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(-421 (-560)))) (-5 *1 (-193)))) - ((*1 *1 *1) (-12 (-4 *1 (-696 *2)) (-4 *2 (-1247)))) - ((*1 *1 *1) (-4 *1 (-894 *2))) - ((*1 *1 *1) - (-12 (-4 *1 (-1004 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-814)) - (-4 *4 (-871))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 (-560))) (-5 *2 (-560)) (-5 *1 (-500 *4)) - (-4 *4 (-1273 *2))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1296 *2)) (-4 *2 (-1247)) (-4 *2 (-1033)) + (-4 *2 (-1080))))) +(((*1 *2 *2) (-12 (-5 *2 (-948)) (-5 *1 (-369 *3)) (-4 *3 (-363))))) +(((*1 *2 *2) + (-12 (-4 *3 (-466)) (-5 *1 (-1239 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1233)))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-1 *7 *7)) + (-5 *5 (-1 (-3 (-663 *6) "failed") (-560) *6 *6)) (-4 *6 (-376)) + (-4 *7 (-1273 *6)) + (-5 *2 (-2 (|:| |answer| (-597 (-421 *7))) (|:| |a0| *6))) + (-5 *1 (-588 *6 *7)) (-5 *3 (-421 *7))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-904 *6)) (-5 *4 (-1123 (-391))) (-5 *5 (-663 (-270))) (-4 *6 (-13 (-633 (-549)) (-1132))) (-5 *2 (-1164 (-229))) @@ -9373,262 +8697,165 @@ ((*1 *2 *3 *4 *4) (-12 (-5 *3 (-907 (-1 (-229) (-229) (-229)))) (-5 *4 (-1120 (-391))) (-5 *2 (-1164 (-229))) (-5 *1 (-265))))) -(((*1 *2 *2 *2) (-12 (-5 *1 (-161 *2)) (-4 *2 (-559))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-871)) (-5 *1 (-123 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1007 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-815)) - (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-571)) - (-5 *2 (-114))))) +(((*1 *2 *3 *1) (-12 (-5 *3 (-1207)) (-5 *2 (-450)) (-5 *1 (-1211))))) (((*1 *2 *3) - (-12 (-5 *3 (-1185 (-229))) (-5 *2 (-663 (-1189))) (-5 *1 (-195)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1185 (-229))) (-5 *2 (-663 (-1189))) (-5 *1 (-313)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1185 (-229))) (-5 *2 (-663 (-1189))) (-5 *1 (-315))))) -(((*1 *2 *2) (-12 (-5 *2 (-560)) (-5 *1 (-956))))) -(((*1 *2) - (-12 (-5 *2 (-711 (-935 *3))) (-5 *1 (-365 *3 *4)) (-14 *3 (-948)) - (-14 *4 (-948)))) - ((*1 *2) - (-12 (-5 *2 (-711 *3)) (-5 *1 (-366 *3 *4)) (-4 *3 (-363)) - (-14 *4 - (-3 (-1201 *3) - (-1297 (-663 (-2 (|:| -1617 *3) (|:| -4084 (-1151))))))))) + (|partial| -12 + (-5 *3 + (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) + (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-663 (-229))) + (|:| |intvals| (-663 (-229))) (|:| |g| (-326 (-229))) + (|:| |abserr| (-229)) (|:| |relerr| (-229)))) + (-5 *2 + (-2 (|:| |stiffness| (-391)) (|:| |stability| (-391)) + (|:| |expense| (-391)) (|:| |accuracy| (-391)) + (|:| |intermediateResults| (-391)))) + (-5 *1 (-825))))) +(((*1 *2 *1 *1 *3) (-12 (-4 *1 (-1175)) (-5 *3 (-560)) (-5 *2 (-114))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-466)) (-4 *6 (-815)) (-4 *7 (-871)) + (-4 *3 (-1096 *5 *6 *7)) (-5 *2 (-663 *4)) + (-5 *1 (-1139 *5 *6 *7 *3 *4)) (-4 *4 (-1102 *5 *6 *7 *3))))) +(((*1 *2 *1) + (-12 (-4 *3 (-175)) (-4 *2 (-23)) (-5 *1 (-301 *3 *4 *2 *5 *6 *7)) + (-4 *4 (-1273 *3)) (-14 *5 (-1 *4 *4 *2)) + (-14 *6 (-1 (-3 *2 "failed") *2 *2)) + (-14 *7 (-1 (-3 *4 "failed") *4 *4 *2)))) + ((*1 *2 *1) + (-12 (-4 *2 (-23)) (-5 *1 (-733 *3 *2 *4 *5 *6)) (-4 *3 (-175)) + (-14 *4 (-1 *3 *3 *2)) (-14 *5 (-1 (-3 *2 "failed") *2 *2)) + (-14 *6 (-1 (-3 *3 "failed") *3 *3 *2)))) ((*1 *2) - (-12 (-5 *2 (-711 *3)) (-5 *1 (-367 *3 *4)) (-4 *3 (-363)) - (-14 *4 (-948))))) -(((*1 *1 *1) (-12 (-4 *1 (-251 *2)) (-4 *2 (-1247))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-376)) (-5 *1 (-788 *2 *3)) (-4 *2 (-730 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-876 *2)) (-4 *2 (-1080)) (-4 *2 (-376))))) -(((*1 *2) (-12 (-5 *2 (-1178 (-1189))) (-5 *1 (-405))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-571)) (-5 *2 (-987 *3)) (-5 *1 (-1194 *4 *3)) - (-4 *3 (-1273 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-663 (-1248))) (-5 *1 (-538))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1201 *4)) (-4 *4 (-363)) - (-4 *2 - (-13 (-416) - (-10 -7 (-15 -2556 (*2 *4)) (-15 -1366 ((-948) *2)) - (-15 -1664 ((-1297 *2) (-948))) (-15 -3632 (*2 *2))))) - (-5 *1 (-370 *2 *4))))) + (-12 (-4 *2 (-1273 *3)) (-5 *1 (-734 *3 *2)) (-4 *3 (-1080)))) + ((*1 *2 *1) + (-12 (-4 *2 (-23)) (-5 *1 (-737 *3 *2 *4 *5 *6)) (-4 *3 (-175)) + (-14 *4 (-1 *3 *3 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(-4 *1 (-1096 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-815)) + (-4 *5 (-871)) (-5 *2 (-114)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1242 *3 *4 *5 *6)) (-4 *3 (-571)) (-4 *4 (-815)) + (-4 *5 (-871)) (-4 *6 (-1096 *3 *4 *5)) (-5 *2 (-114)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1242 *4 *5 *6 *3)) (-4 *4 (-571)) (-4 *5 (-815)) + (-4 *6 (-871)) (-4 *3 (-1096 *4 *5 *6)) (-5 *2 (-114))))) (((*1 *2 *3) (-12 (-5 *3 - (-663 - (-2 (|:| -1983 (-793)) - (|:| |eqns| - (-663 - (-2 (|:| |det| *7) (|:| |rows| (-663 (-560))) - (|:| |cols| (-663 (-560)))))) - (|:| |fgb| (-663 *7))))) - (-4 *7 (-979 *4 *6 *5)) (-4 *4 (-13 (-319) (-149))) - (-4 *5 (-13 (-871) (-633 (-1207)))) (-4 *6 (-815)) (-5 *2 (-793)) - (-5 *1 (-953 *4 *5 *6 *7))))) -(((*1 *2 *3 *3 *4 *4 *4 *4 *3 *3 *3 *3 *5 *3 *6) - (-12 (-5 *3 (-560)) (-5 *5 (-711 (-229))) - (-5 *6 (-3 (|:| |fn| (-402)) (|:| |fp| (-70 APROD)))) (-5 *4 (-229)) - (-5 *2 (-1066)) (-5 *1 (-778))))) -(((*1 *1 *2) - (-12 (-5 *2 (-1297 *3)) (-4 *3 (-1080)) (-5 *1 (-734 *3 *4)) - (-4 *4 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|endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1185 (-229))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3867 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1066)) (-5 *1 (-315))))) +(((*1 *2 *1) (-12 (-4 *1 (-34)) (-5 *2 (-114)))) + ((*1 *2 *1) + (-12 (-4 *3 (-466)) (-4 *4 (-871)) (-4 *5 (-815)) (-5 *2 (-114)) + (-5 *1 (-1017 *3 *4 *5 *6)) (-4 *6 (-979 *3 *5 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\ No newline at end of file |