diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 18 | ||||
| -rw-r--r-- | src/algebra/boolean.spad.pamphlet | 46 | ||||
| -rw-r--r-- | src/algebra/strap/DFLOAT.lsp | 8 | ||||
| -rw-r--r-- | src/interp/bits.lisp | 12 | ||||
| -rw-r--r-- | src/interp/g-opt.boot | 21 | ||||
| -rw-r--r-- | src/interp/g-util.boot | 52 | ||||
| -rw-r--r-- | src/interp/types.boot | 6 | ||||
| -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 | 1352 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9128 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31124 |
12 files changed, 22034 insertions, 21943 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 6d9c399b..d35a3d4a 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,23 @@ 2011-01-02 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/g-util.boot: Expand new bit vector operators. + * interp/g-opt.boot (opt2bit): New. + (opt2bool): Likewise. + * interp/bits.lisp (BVEC-SIZE): Remove. + (BVEC-COPY): Likewise. + (BVEC-CONCAT): Likewise. + (BVEC-EQUAL): Likewise. + (BVEC-AND): Likewise. + (BVEC-OR): Likewise. + (BVEC-XOR): Likewise. + (BVEC-NAND): Likewise. + (BVEC-NOR): Likewise. + (BVEC-NOT): Likewise. + * algebra/boolean.spad.pamphlet (IndexedBits): Remove uses of + Lisp-level functions. + +2011-01-02 Gabriel Dos Reis <gdr@cs.tamu.edu> + * interp/nrunfast.boot (evalSlotDomain): Expand to VM forms before value argument evaluation. (lazyMatch): Check for %llength too. diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet index d2b7ffa5..9a14a146 100644 --- a/src/algebra/boolean.spad.pamphlet +++ b/src/algebra/boolean.spad.pamphlet @@ -546,13 +546,24 @@ IndexedBits(mn:Integer): BitAggregate() with ++ And(n,m) returns the bit-by-bit logical {\em And} of ++ n and m. == add - - range: (%, Integer) -> Integer - --++ range(j,i) returnes the range i of the boolean j. + import %2bool: NonNegativeInteger -> Boolean from Foreign Builtin + import %2bit: Boolean -> NonNegativeInteger from Foreign Builtin + import %bitveccopy: % -> % from Foreign Builtin + import %bitveclength: % -> NonNegativeInteger from Foreign Builtin + import %bitvecref: (%,Integer) -> NonNegativeInteger + from Foreign Builtin + import %bitveceq: (%,%) -> Boolean from Foreign Builtin + import %bitvecnot: % -> % from Foreign Builtin + import %bitvecand: (%,%) -> % from Foreign Builtin + import %bitvecor: (%,%) -> % from Foreign Builtin + import %bitvecxor: (%,%) -> % from Foreign Builtin + import %makebitvec: (NonNegativeInteger,NonNegativeInteger) -> % + from Foreign Builtin minIndex u == mn - range(v, i) == + -- range check index of `i' into `v'. + range(v: %, i: Integer): Integer == i >= 0 and i < #v => i error "Index out of range" @@ -564,24 +575,23 @@ IndexedBits(mn:Integer): BitAggregate() with s.i := if v.j then t else f s::OutputForm - new(n, b) == BVEC_-MAKE_-FULL(n, %2bit(b)$Foreign(Builtin))$Lisp - empty() == BVEC_-MAKE_-FULL(0,0)$Lisp - copy v == BVEC_-COPY(v)$Lisp - #v == BVEC_-SIZE(v)$Lisp - v = u == BVEC_-EQUAL(v, u)$Lisp + new(n, b) == %makebitvec(n, %2bit(b)$Foreign(Builtin)) + empty() == %makebitvec(0,0) + copy v == %bitveccopy v + #v == %bitveclength v + v = u == %bitveceq(v,u) v < u == BVEC_-GREATER(u, v)$Lisp - u and v == (#v=#u => BVEC_-AND(v,u)$Lisp; map("and",v,u)) - u or v == (#v=#u => BVEC_-OR(v, u)$Lisp; map("or", v,u)) - xor(v,u) == (#v=#u => BVEC_-XOR(v,u)$Lisp; map("xor",v,u)) + u and v == (#v=#u => %bitvecand(v,u); map("and",v,u)) + u or v == (#v=#u => %bitvecor(v,u); map("or", v,u)) + xor(v,u) == (#v=#u => %bitvecxor(v,u); map("xor",v,u)) setelt(v:%, i:Integer, f:Boolean) == - %2bool(BVEC_-SETELT(v, range(v, i-mn), - %2bit(f)$Foreign(Builtin))$Lisp)$Foreign(Builtin) + %2bool %store(%bitvecref(v,range(v,i-mn)),%2bit f)$Foreign(Builtin) elt(v:%, i:Integer) == - %2bool(BVEC_-ELT(v, range(v, i-mn))$Lisp)$Foreign(Builtin) + %2bool %bitvecref(v,range(v,i-mn)) - Not v == BVEC_-NOT(v)$Lisp - And(u, v) == (#v=#u => BVEC_-AND(v,u)$Lisp; map("and",v,u)) - Or(u, v) == (#v=#u => BVEC_-OR(v, u)$Lisp; map("or", v,u)) + Not v == %bitvecnot v + And(u, v) == (#v=#u => %bitvecand(v,u); map("and",v,u)) + Or(u, v) == (#v=#u => %bitvecor(v,u); map("or", v,u)) @ \section{domain BITS Bits} diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp index d62aab80..f84457bf 100644 --- a/src/algebra/strap/DFLOAT.lsp +++ b/src/algebra/strap/DFLOAT.lsp @@ -472,7 +472,7 @@ (DEFUN |DFLOAT;pi;$;17| ($) (DECLARE (IGNORE $)) - (COERCE PI 'DOUBLE-FLOAT)) + (COERCE PI '|%DoubleFloat|)) (DEFUN |DFLOAT;coerce;$Of;18| (|x| $) (SPADCALL |x| (|getShellEntry| $ 48))) @@ -626,15 +626,15 @@ (SEQ (COND ((ZEROP |x|) (COND - ((PLUSP |y|) (/ (COERCE PI 'DOUBLE-FLOAT) 2)) - ((MINUSP |y|) (- (/ (COERCE PI 'DOUBLE-FLOAT) 2))) + ((PLUSP |y|) (/ (COERCE PI '|%DoubleFloat|) 2)) + ((MINUSP |y|) (- (/ (COERCE PI '|%DoubleFloat|) 2))) (T 0.0))) (T (SEQ (LETT |theta| (ATAN (ABS (/ |y| |x|))) |DFLOAT;atan;3$;79|) (COND ((MINUSP |x|) (SETQ |theta| - (- (COERCE PI 'DOUBLE-FLOAT) |theta|)))) + (- (COERCE PI '|%DoubleFloat|) |theta|)))) (COND ((MINUSP |y|) (SETQ |theta| (- |theta|)))) (EXIT |theta|)))))))) diff --git a/src/interp/bits.lisp b/src/interp/bits.lisp index 4ae37adf..5b20b3e7 100644 --- a/src/interp/bits.lisp +++ b/src/interp/bits.lisp @@ -1,6 +1,6 @@ ;; Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ;; All rights reserved. -;; Copyright (C) 2007, Gabriel Dos Reis. +;; Copyright (C) 2007-2011, Gabriel Dos Reis. ;; All rights reserved. ;; ;; Redistribution and use in source and binary forms, with or without @@ -55,20 +55,10 @@ (defmacro bvec-elt (bv i) `(sbit ,bv ,i)) (defmacro bvec-setelt (bv i x) `(setf (sbit ,bv ,i) ,x)) -(defmacro bvec-size (bv) `(size ,bv)) -(defun bvec-copy (bv) (copy-seq bv)) -(defun bvec-concat (bv1 bv2) (concatenate '(vector bit) bv1 bv2)) -(defun bvec-equal (bv1 bv2) (equal bv1 bv2)) (defun bvec-greater (bv1 bv2) (let ((pos (mismatch bv1 bv2))) (cond ((or (null pos) (>= pos (length bv1))) nil) ((< pos (length bv2)) (> (bit bv1 pos) (bit bv2 pos))) ((find 1 bv1 :start pos) t) (t nil)))) -(defun bvec-and (bv1 bv2) (bit-and bv1 bv2)) -(defun bvec-or (bv1 bv2) (bit-ior bv1 bv2)) -(defun bvec-xor (bv1 bv2) (bit-xor bv1 bv2)) -(defun bvec-nand (bv1 bv2) (bit-nand bv1 bv2)) -(defun bvec-nor (bv1 bv2) (bit-nor bv1 bv2)) -(defun bvec-not (bv) (bit-not bv)) diff --git a/src/interp/g-opt.boot b/src/interp/g-opt.boot index 8bed62d1..827a750a 100644 --- a/src/interp/g-opt.boot +++ b/src/interp/g-opt.boot @@ -453,13 +453,16 @@ $VMsideEffectFreeOperators == %lreverse %lempty? %hash %ismall? %string? %f2s %ccst %ceq %clt %cle %cgt %cge %c2i %i2c %s2c %cup %cdown %sname %strlength %streq %i2s %schar %strlt %strconc %strcopy %strstc - %vref %vlength %before?) + %vref %vlength + %bitvecnot %bitvecand %bitvecnand %bivecor %bitvecnor %bitvecxor + %bitveccopy %bitvecconc %bitveclength %bitvecref %bitveceq + %before?) ++ List of simple VM operators $simpleVMoperators == append($VMsideEffectFreeOperators, ['CONS,'LIST,'VECTOR,'STRINGIMAGE,'FUNCALL,'%gensym, '%lreverse_!, - '%strstc,"MAKE-FULL-CVEC","BVEC-MAKE-FULL","COND"]) + '%strstc,'%makebitvec,"MAKE-FULL-CVEC","BVEC-MAKE-FULL","COND"]) ++ Return true if the `form' is semi-simple with respect to ++ to the list of operators `ops'. @@ -749,6 +752,18 @@ optIquo(x is ['%iquo,a,b]) == integer? a and integer? b => a quo b x +-- Boolean <-> bit conversion. +opt2bit(x is ['%2bit,a]) == + a is '%true => 1 + a is '%false => 0 + x + +opt2bool(x is ['%2bool,a]) == + integer? a => + a = 1 => '%true + '%false + x + --% --% optimizer hash table --% @@ -776,6 +791,8 @@ for x in '( (%call optCall) _ (%irem optIrem)_ (%iquo optIquo)_ (%imul optImul)_ + (%2bit opt2bit)_ + (%2bool opt2bool)_ (LIST optLIST)_ (QSMINUS optQSMINUS)_ (SPADCALL optSPADCALL)_ diff --git a/src/interp/g-util.boot b/src/interp/g-util.boot index fb98bc83..197da15a 100644 --- a/src/interp/g-util.boot +++ b/src/interp/g-util.boot @@ -366,6 +366,45 @@ expandStrlt ['%strlt,x,y] == expandStrstc ['%strstc,x,y,z] == expandToVMForm ['%store,['%schar,x,y],z] +-- bit vector operations +expandBitvecnot ['%bitvecnot,x] == + ['BIT_-NOT,expandToVMForm x] + +expandBitvecand ['%bitvecand,x,y] == + ['BIT_-AND,expandToVMForm x,expandToVMForm y] + +expandBitvecnand ['%bitvecnand,x,y] == + ['BIT_-NAND,expandToVMForm x,expandToVMForm y] + +expandBitvecor ['%bitvecor,x,y] == + ['BIT_-IOR,expandToVMForm x,expandToVMForm y] + +expandBitvecnor ['%bitvecnor,x,y] == + ['BIT_-NOR,expandToVMForm x,expandToVMForm y] + +expandBitvecxor ['%bitvecxor,x,y] == + ['BIT_-XOR,expandToVMForm x,expandToVMForm y] + +expandBitveclength ['%bitveclength,x] == + ['LENGTH,expandToVMForm x] + +expandBitveccopy ['%bitveccopy,x] == + ['COPY_-SEQ,expandToVMForm x] + +expandBitvecconc ['%bitvecconc,x,y] == + ['CONCATENATE, quoteForm '%BitVector,expandToVMForm x,expandToVMForm y] + +expandBitvecref ['%bitvecref,x,y] == + ['SBIT,expandToVMForm x,expandToVMForm y] + +expandBitveceq ['%bitveceq,x,y] == + ['EQUAL,expandToVMForm x,expandToVMForm y] + +expandMakebitvec ['%makebitvec,x,y] == + ['MAKE_-ARRAY,['LIST,expandToVMForm x], + KEYWORD::ELEMENT_-TYPE,quoteForm '%Bit, + KEYWORD::INITIAL_-ELEMENT,expandToVMForm y] + -- Local variable bindings expandBind ['%bind,inits,:body] == body := expandToVMForm body @@ -583,6 +622,19 @@ for x in [ ['%strlt, :function expandStrlt], ['%strstc, :function expandStrstc], + ['%bitvecnot, :function expandBitvecnot], + ['%bitvecand, :function expandBitvecand], + ['%bitvecnand, :function expandBitvecnand], + ['%bitvecor, :function expandBitvecor], + ['%bitvecxor, :function expandBitvecxor], + ['%bitvecnor, :function expandBitvecnor], + ['%bitveclength, :function expandBitveclength], + ['%bitveccopy, :function expandBitveccopy], + ['%bitvecconc, :function expandBitvecconc], + ['%bitveceq, :function expandBitveceq], + ['%bitvecref, :function expandBitvecref], + ['%makebitvec, :function expandMakebitvec], + ['%peq, :function expandPeq], ['%before?, :function expandBefore?], diff --git a/src/interp/types.boot b/src/interp/types.boot index 60139497..6022a5cb 100644 --- a/src/interp/types.boot +++ b/src/interp/types.boot @@ -52,6 +52,10 @@ namespace BOOT %Boolean <=> BOOLEAN +++ Type of a bit value. +%Bit <=> + BIT + ++ Type of 8-bit sized unsigned integer values. %Byte <=> UNSIGNED_-BYTE 8 @@ -115,6 +119,8 @@ namespace BOOT %Vector a <=> VECTOR a +%BitVector <=> %Vector %Bit + %Thing <=> true %Sequence <=> SEQUENCE diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 65f9fd0b..68367dbf 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2287550 . 3501779185) +(2287550 . 3502979432) (-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 -1683) +(-32 R -1725) ((|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| (LIST (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 -1683 UP UPUP -3601) +(-40 -1725 UP UPUP -1794) ((|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))) (-2196 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2196 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2196 (-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)))) (-2196 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2196 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-560)))) (-2196 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (LIST (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|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -1683) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2271 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2271 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2271 (-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)))) (-2271 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2271 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-560)))) (-2271 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (LIST (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|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -1725) ((|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| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (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)) -((-2196 (-12 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|))))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-871))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#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 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|))))))) +((-2271 (-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|))))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-871))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#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 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1683) +(-54 |Base| R -1725) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -4389) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -4404) ((|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 -4389) +(-62 -4404) ((|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 -4389) +(-63 -4404) ((|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 -4389) +(-64 -4404) ((|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 -4389) +(-65 -4404) ((|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 -4389) +(-66 -4404) ((|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 -4389) +(-67 -4404) ((|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 -4389) +(-68 -4404) ((|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 -4389) +(-69 -4404) ((|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 -4389) +(-70 -4404) ((|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 -4389) +(-71 -4404) ((|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 -4389) +(-72 -4404) ((|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 -4389) +(-73 -4404) ((|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 -4389) +(-74 -4404) ((|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 -4389) +(-75 -4404) ((|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 -4389) +(-78 -4404) ((|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 -4389) +(-79 -4404) ((|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 -4389) +(-80 -4404) ((|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 -4389) +(-81 -4404) ((|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 -4389) +(-82 -4404) ((|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 -4389) +(-83 -4404) ((|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 -4389) +(-84 -4404) ((|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 -4389) +(-85 -4404) ((|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 -4389) +(-86 -4404) ((|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 -4389) +(-87 -4404) ((|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 -4389) +(-88 -4404) ((|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 -4389) +(-89 -4404) ((|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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2196 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2271 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2271 (-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 -1683 UP) +(-117 -1725 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|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2196 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -118) (|devaluate| |#1|)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2271 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1182))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -118) (|devaluate| |#1|)) (LIST (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2271 (-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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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)) -((-2196 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (LIST (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (QUOTE -321) (QUOTE (-130)))))) (-2196 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2196 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (QUOTE -321) (QUOTE (-130)))))) +((-2271 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (LIST (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (QUOTE -321) (QUOTE (-130)))))) (-2271 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2271 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (LIST (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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4510 "*") . T)) NIL -(-137 |minix| -3662 R) +(-137 |minix| -2462 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| -3662 S T$) +(-138 |minix| -2462 S T$) ((|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)) -((-2196 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) +((-2271 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (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 -1683 UP UPUP) +(-150 -1725 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 -1683) +(-160 R -1725) ((|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| (LIST (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 -2196 (|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)) (-2917 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4501 -2271 (|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)) (-3030 . 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 -2196 (|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)) (-2917 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2196 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2196 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4507)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4501 -2271 (|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)) (-3030 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2271 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2271 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1233)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasAttribute| |#1| (QUOTE -4504)) (|HasAttribute| |#1| (QUOTE -4507)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-363))))) (-172 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|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| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -1683) +(-191 R -1725) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -1683 UP UPUP R) +(-219 -1725 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 -1683 FP) +(-220 -1725 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}."))) NIL NIL (-221) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2196 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2271 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -1683) +(-223 R -1725) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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 -1683) +(-228 R -1725) ((|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}."))) -((-2905 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-3025 . 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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (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 -3662 R) +(-244 S -2462 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 -3662 R) +(-245 -2462 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 -3662 R) +(-246 -2462 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. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4502 |has| |#2| (-1080)) (-4503 |has| |#2| (-1080)) (-4505 |has| |#2| (-6 -4505)) (-4508 . T)) -((-2196 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (LIST 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(|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1080)))) (-2196 (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-376))) 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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}."))) NIL NIL @@ -939,7 +939,7 @@ NIL (-252 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4509 . T) (-4508 . 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(|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -951,7 +951,7 @@ NIL (-255 |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 lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-256) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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(|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560)))))) (-2271 (-12 (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-871))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-560))))) (-2271 (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207)))))) (-2271 (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-2271 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1132)))) (-2271 (|HasAttribute| |#3| (QUOTE -4505)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (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 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#3| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#3| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-276 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. 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 -1683) +(-287 R -1725) ((|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 -1683) +(-288 R -1725) ((|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| -3836 -4167 |exactQuo|) +(-301 S R |Mod| -1995 -1971 |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 -2196 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) -((|HasCategory| |#1| (QUOTE (-376))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2196 (|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| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2196 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2196 (|HasCategory| |#1| (LIST (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)))) (-2196 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2196 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2196 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) +((-4505 -2271 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4502 |has| |#1| (-1080)) (-4503 |has| |#1| (-1080))) +((|HasCategory| |#1| (QUOTE (-376))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2271 (|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| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2271 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2271 (|HasCategory| |#1| (LIST (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)))) (-2271 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2271 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2271 (|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 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|)))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|)))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#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|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -1683 S) +(-311 -1725 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -1683) +(-312 E -1725) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -1683) +(-322 -1725) ((|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 . 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(-2271 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-842))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-871)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-1182))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-240))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -321) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (LIST (QUOTE -298) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1284) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1284 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| $ (QUOTE (-147)))) (-2271 (|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 -2196 (-12 (|has| |#1| (-571)) (-2196 (|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))) -((-2196 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-2196 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-1080))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))))) (-2196 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (-2196 (|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)))) (-2196 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2196 (|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)))) (-2196 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-2196 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))))) (-2196 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1143)))) (-2196 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))))) (-2196 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2196 (-12 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (QUOTE -1069) (QUOTE (-560))))) +((-4505 -2271 (-12 (|has| |#1| (-571)) (-2271 (|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))) +((-2271 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-571))) (-2271 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-21))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-1080))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))))) (-2271 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (-2271 (|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)))) (-2271 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2271 (|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)))) (-2271 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (-2271 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))))) (-2271 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1143)))) (-2271 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))))) (-2271 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2271 (-12 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| $ (QUOTE (-1080))) (|HasCategory| $ (LIST (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 -1683) +(-329 R -1725) ((|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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1683) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -1725) ((|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 -1683) +(-341 -1725) ((|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 -1683 UP UPUP R) +(-346 -1725 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 -1683 UP UPUP R) +(-348 S -1725 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 -1683 UP UPUP R) +(-349 -1725 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)) -((-2196 (|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 -1683 UP UPUP) +((-2271 (|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 -1725 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 -1683 UP UPUP) +(-355 -1725 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)) -((-2196 (|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)))) +((-2271 (|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)) -((-2196 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2271 (|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)) -((-2196 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2271 (|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 -1683) +(-364 R UP -1725) ((|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)) -((-2196 (|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)))) +((-2271 (|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)) -((-2196 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2271 (|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)) -((-2196 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2271 (|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)) -((-2196 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2271 (|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 -1683 GF) +(-370 -1725 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 -1683 FP FPP) +(-371 -1725 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)) -((-2196 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2271 (|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) (-2905 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-4491 . T) (-4499 . T) (-3025 . 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 -1683 UP UPUP R) +(-406 -1725 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 -4389 |returnType| -3285 |symbols|) +(-412 -4404 |returnType| -2617 |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 -1683 UP) +(-413 -1725 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\"."))) -((-2905 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-3025 . 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| (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1252))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1252)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-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 -1683 UP A) +(-427 R -1725 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 -1683 UP A |ibasis|) +(-429 R -1725 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| (LIST (QUOTE -1069) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (LIST (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| (LIST (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|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4505 -2196 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) +((-4505 -2271 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) ((-4510 "*") |has| |#1| (-571)) (-4501 |has| |#1| (-571)) (-4506 |has| |#1| (-571)) (-4500 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -1683) +(-442 R -1725) ((|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 -1683) +(-444 R -1725) ((|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 -1683) +(-445 R -1725) ((|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 -1683) +(-446 R -1725) ((|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 -1683) +(-447 R -1725) ((|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 -1683 UP) +(-449 R -1725 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| (LIST (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 -1683) +(-457 R UP -1725) ((|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))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (-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| -1683 R) +(-485 |lv| -1725 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.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-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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((-4509 . T)) -((-12 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|)))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|)))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132)))) (-490 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. 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 . T)) -((-12 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|)))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|)))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102)))) (-494) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. 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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(|HasAttribute| |#2| (QUOTE -4505)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-499 -1683 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-499 -1725 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) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2196 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2271 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2271 (-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 -1683 UP |AlExt| |AlPol|) +(-508 -1725 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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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 -1683) +(-513 R UP -1725) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -1683 |Expon| |VarSet| |DPoly|) +(-518 -1725 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-1207))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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)) -((-2196 (|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)))) +((-2271 (|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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (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 -1683 |Par|) +(-546 K -1725 |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 -1683 |Par|) +(-552 K -1725 |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 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|)))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102)))) -(-566 R -1683) +((-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|)))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102)))) +(-566 R -1725) ((|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 -1683 UP UPUP R) +(-567 R0 -1725 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."))) -((-2905 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-3025 . 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 -1683) +(-572 R -1725) ((|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 -1683 L) +(-575 R -1725 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| (LIST (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 -1683 UP UPUP R) +(-577 -1725 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 -1683 UP) +(-578 -1725 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 -1683 L) +(-580 R -1725 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| (LIST (QUOTE -680) (|devaluate| |#2|)))) -(-581 R -1683) +(-581 R -1725) ((|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| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -1683 UP) +(-582 -1725 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 -1683) +(-584 -1725) ((|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."))) -((-2905 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-3025 . 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 -1683) +(-587 R -1725) ((|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| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -1683 UP) +(-588 -1725 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 -1683) +(-589 R -1725) ((|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 -1683) +(-597 -1725) ((|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| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-1207))))) -(-598 E -1683) +(-598 E -1725) ((|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 -1683) +(-599 R -1725) ((|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)) -((-2196 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2196 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2196 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) +((-2271 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2271 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2271 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -3913) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -3871) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|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 -1683 FG) +(-614 R -1725 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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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 -2196 (-1404 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2196 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2271 (-1481 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2271 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (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 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -1683 UP) +(-634 -1725 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -1683) +(-641 R -1725) ((|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 -1683) +(-648 R -1725) ((|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| -1683) +(-650 |lv| -1725) ((|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 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -3067) (QUOTE (-51))))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 (-51))) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -1875) (QUOTE (-51))))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1189) (QUOTE (-871))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 (-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 -2196 (-1404 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) -((-2196 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) +((-4505 -2271 (-1481 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4503 . T) (-4502 . T)) +((-2271 (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (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 -((-1394 (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-376)))) +((-1470 (|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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (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 -1683 L) +(-675 R -1725 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 -3969) +(-676 A -4071) ((|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| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (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 -1683 UP) +(-681 -1725 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 -1683 |Row| |Col| M) +(-689 -1725 |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 -1683) +(-690 -1725) ((|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| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2196 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2271 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (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 -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4510 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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 -1683 FLAF FLAS) +(-714 S -1725 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)) (-2917 . T) (-4507 |has| (-721) (-6 -4507)) (-4504 |has| (-721) (-6 -4504)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2196 (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2196 (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207))))) (-2196 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (LIST (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (-2196 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-721) (QUOTE (-1051))) (|HasCategory| (-721) (QUOTE (-1233))) (-12 (|HasCategory| (-721) (QUOTE (-1033))) (|HasCategory| (-721) (QUOTE (-1233)))) (-2196 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (-2196 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-1233)))) (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939))) (-2196 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2196 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2196 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-571)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-571))) (|HasAttribute| (-721) (QUOTE -4507)) (|HasAttribute| (-721) (QUOTE -4504)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-363))))) +((-4501 . T) (-4506 |has| (-721) (-376)) (-4500 |has| (-721) (-376)) (-3030 . T) (-4507 |has| (-721) (-6 -4507)) (-4504 |has| (-721) (-6 -4504)) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2271 (|HasCategory| (-721) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2271 (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207))))) (-2271 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (LIST (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-721)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-721) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-721) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (-2271 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-721) (QUOTE (-1051))) (|HasCategory| (-721) (QUOTE (-1233))) (-12 (|HasCategory| (-721) (QUOTE (-1033))) (|HasCategory| (-721) (QUOTE (-1233)))) (-2271 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (-2271 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-1233)))) (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939))) (-2271 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2271 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2271 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-571)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-571))) (|HasAttribute| (-721) (QUOTE -4507)) (|HasAttribute| (-721) (QUOTE -4504)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (LIST (QUOTE -929) (QUOTE (-1207)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-363))))) (-717 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4509 . T)) @@ -2808,13 +2808,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-720 OV E -1683 PG) +(-720 OV E -1725 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-721) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-2905 . T) (-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) +((-3025 . 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.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-728 S -2111 I) +(-728 S -4045 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2860,14 +2860,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-733 R |Mod| -3836 -4167 |exactQuo|) +(-733 R |Mod| -1995 -1971 |exactQuo|) ((|constructor| (NIL "\\indented{1}{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{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL (-734 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4503 |has| |#1| (-175)) (-4502 |has| |#1| (-175)) (-4505 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -3836 -4167 |exactQuo|) +(-737 R |Mod| -1995 -1971 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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 -1683) +(-740 -1725) ((|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 -1683 UP) +(-749 -1725 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))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4506)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (-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 -1683) +(-787 -1725) ((|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 -1683) +(-788 P -1725) ((|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 -1683) +(-790 UP -1725) ((|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 -1683) +(-794 R -1725) ((|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 -1683 |ExtF| |SUEx| |ExtP| |n|) +(-799 -1725 |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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(-560))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-1470 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-560))))) (-1470 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-1207)))) (-1470 (|HasCategory| |#1| (LIST (QUOTE -1022) (QUOTE (-560))))))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-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| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4510 "*") |has| |#1| (-175)) (-4501 |has| |#1| (-571)) (-4504 |has| |#1| (-376)) (-4506 |has| |#1| (-6 -4506)) (-4503 . T) (-4502 . T) (-4505 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3211,8 +3211,8 @@ NIL (-820 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|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| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2196 (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2196 (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) -(-821 -2196 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2271 (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2271 (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) +(-821 -2271 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 -1683 L) +(-823 R -1725 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 -1683) +(-824 R -1725) ((|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 -1683) +(-826 R -1725) ((|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 -1683 UP UPUP R) +(-828 -1725 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 -1683 UP L LQ) +(-829 -1725 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 -1683 UP L LQ) +(-831 -1725 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 -1683 UP) +(-832 -1725 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 -1683 L UP A LO) +(-833 -1725 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 -1683 UP) +(-834 -1725 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 -1683 LO) +(-835 -1725 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 -1683 LODO) +(-836 -1725 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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(-560))))) (-12 (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-871))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207))))) (-2271 (|HasCategory| |#2| (QUOTE (-1080))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasAttribute| |#2| (QUOTE -4505)) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))))) (-838 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. 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 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-840 (-1207)) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-839 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-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))) (-2196 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2196 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2271 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2271 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4505 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2196 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2196 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2271 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2271 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-865 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3396,7 +3396,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-867 -3662 S) +(-867 -2462 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| -3327) +(-878 R |sigma| -3866) ((|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| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-879 |x| R |sigma| -3327) +(-879 |x| R |sigma| -3866) ((|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| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (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|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2196 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -893) (|devaluate| |#1|)) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) +((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2271 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -528) (QUOTE (-1207)) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -321) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -298) (LIST (QUOTE -893) (|devaluate| |#1|)) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2271 (-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| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2196 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2271 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (-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)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (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 (-1394 (|HasCategory| |#2| (QUOTE (-1080)))) (-1394 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-1394 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207))))) +((-12 (-1470 (|HasCategory| |#2| (QUOTE (-1080)))) (-1470 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (-1470 (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (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 -2111) +(-916 R -4045) ((|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 -1683) +(-923 UP -1725) ((|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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4505 . T)) -((-2196 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) +((-2271 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (-932 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 -1683 UP UPUP R) +(-940 R0 -1725 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 -1683) +(-947 -1725) ((|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| -1683) +(-951 |xx| -1725) ((|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 -1683 P) +(-952 -1725 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 -1683) +(-959 R -1725) ((|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 -1683) +(-961 S R -1725) ((|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| (LIST (QUOTE -911) (|devaluate| |#1|)))) -(-966 -2111) +(-966 -4045) ((|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 -1683 -2111) +(-967 R -1725 -4045) ((|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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1207) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-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 -1683) +(-980 E V R P -1725) ((|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 -1683) +(-982 E V R P -1725) ((|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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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 -1683) +(-990 -1725) ((|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)))) -((-2196 (-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)))) (-2196 (-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)))) (-2196 (-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)))) (-2196 (-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)))) (-2196 (-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))))) +((-2271 (-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)))) (-2271 (-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)))) (-2271 (-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)))) (-2271 (-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)))) (-2271 (-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 -1683) +(-1016 K R UP -1725) ((|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| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2196 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2271 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -528) (QUOTE (-1207)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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 -1683 UP UPUP |radicnd| |n|) +(-1034 -1725 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 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2196 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2196 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2196 (-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)))) (-2196 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2196 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-560)))) (-2196 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (LIST (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|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2271 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2271 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2271 (-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)))) (-2271 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2271 (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -660) (QUOTE (-560)))) (-2271 (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (LIST (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|) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (-1035 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|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) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2196 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2271 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1182))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| (-560) (LIST (QUOTE -528) (QUOTE (-1207)) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (LIST (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (LIST (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2271 (-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 -1683) +(-1044 R -1725) ((|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 -1683) +(-1045 R -1725) ((|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 -1683 UP) +(-1046 -1725 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 -1683 UP) +(-1047 -1725 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)) -((-2196 (|HasCategory| (-421 (-560)) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (LIST (QUOTE -1069) (QUOTE (-560))))) -(-1056 -1683 L) +((-2271 (|HasCategory| (-421 (-560)) (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (LIST (QUOTE -1069) (QUOTE (-560))))) +(-1056 -1725 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 -1683 |Expon| |VarSet| |FPol| |LFPol|) +(-1065 -1725 |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 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -3067) (QUOTE (-51))))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -1875) (QUOTE (-51))))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-102)))) (-1067) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4252,7 +4252,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4505 . T)) NIL -(-1081 |xx| -1683) +(-1081 |xx| -1725) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4271,7 +4271,7 @@ NIL (-1085 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|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))) (-2196 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|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| (LIST (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-887))))) +((|HasCategory| |#3| (QUOTE (-175))) (-2271 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|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| (LIST (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (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 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -3067) (QUOTE (-51))))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (QUOTE (-1207))) (LIST (QUOTE |:|) (QUOTE -1875) (QUOTE (-51))))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (LIST (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-1132))) (|HasCategory| (-1207) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1207)) (|:| -1875 (-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 -1683) +(-1106 |Base| R -1725) ((|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 -1683) +(-1108 |Base| R -1725) ((|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 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))))) (-1111 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|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))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1119 (-1207)) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1119 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential 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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-4502 |has| |#3| (-1080)) (-4503 |has| |#3| (-1080)) (-4505 |has| |#3| (-6 -4505)) (-4508 . 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(QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-871))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -929) (QUOTE (-1207))))) (-2271 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1132)))) (|HasAttribute| |#3| (QUOTE -4505)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (LIST (QUOTE -927) (QUOTE (-1207))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (LIST (QUOTE -321) (|devaluate| |#3|))))) (-1145 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|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 -1683) +(-1148 R -1725) ((|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))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4506)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2271 (-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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2271 (|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 -1683) +(-1159 UP -1725) ((|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|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2196 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2196 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2271 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2271 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (LIST (QUOTE -321) (LIST (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (LIST (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| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2196 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2271 (|HasAttribute| |#2| (QUOTE (-4510 "*"))) (|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (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 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|)))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|)))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#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| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (LIST (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)) -((-2196 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2196 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2196 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) +((-2271 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (-2271 (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2271 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (LIST (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 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#1|)))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 (-1189)) (|:| -3067 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (QUOTE (-1189))) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#1|)))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1189) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#1|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 (-1189)) (|:| -1875 |#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.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) (((-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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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 . T) (-4503 . T) (-4505 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -3913) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2196 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -4424) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -4162) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -3871) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2271 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -1743) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2973) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) (-1205 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\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}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{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.")) (|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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -3913) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2196 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -4424) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -4162) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -3871) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2271 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -1743) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2973) (LIST (LIST (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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2196 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2271 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (LIST (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 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1438) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3067) (|devaluate| |#2|)))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2196 (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -321) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1462) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1875) (|devaluate| |#2|)))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887))))) (-2271 (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -1462 |#1|) (|:| -1875 |#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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4509 . T) (-4508 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2196 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2271 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1235 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4876,7 +4876,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1237 R -1683) +(-1237 R -1725) ((|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 -1683) +(-1239 R -1725) ((|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| (LIST (QUOTE -633) (LIST (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2271 (|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| (LIST (QUOTE -632) (QUOTE (-887))))) -(-1246 -1683) +(-1246 -1725) ((|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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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 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2196 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2196 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2196 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (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)))) (-2196 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (LIST (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -633) (LIST (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (LIST (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (QUOTE (-560)))) (-2271 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (-2271 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2271 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (LIST (QUOTE -929) (QUOTE (-1207)))) (|HasCategory| |#2| (LIST (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)))) (-2271 (-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| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3913) (LIST (|devaluate| |#2|) (QUOTE (-1207)))))) +((|HasCategory| |#2| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3871) (LIST (|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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -3913) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2196 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -4424) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -4162) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -3871) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2271 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -1743) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2973) (LIST (LIST (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))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2196 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -3913) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2196 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -4424) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -4162) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2271 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (LIST (QUOTE -3871) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -421) (QUOTE (-560)))))) (-2271 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -1743) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2973) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (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|) (LIST (QUOTE -38) (LIST (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))) (-2196 (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (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|) (LIST (QUOTE -38) (LIST (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))) (-2271 (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (QUOTE -1069) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1278 |#2| |#3| |#4|) (LIST (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| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2196 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -3913) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2196 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -4424) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -4162) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2271 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (LIST (QUOTE -927) (QUOTE (-1207)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (LIST (QUOTE -3871) (LIST (|devaluate| |#1|) (QUOTE (-1207)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2271 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1233))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (LIST (QUOTE -1743) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1207))))) (|HasSignature| |#1| (LIST (QUOTE -2973) (LIST (LIST (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| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (LIST (QUOTE -4162) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4424) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1233))) (|HasSignature| |#2| (LIST (QUOTE -2973) (LIST (LIST (QUOTE -663) (QUOTE (-1207))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1743) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1207))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (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 -1683 UP L UTS) +(-1292 -1725 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)) -((-2196 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2196 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2196 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2196 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) +((-2271 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|))))) (-2271 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (LIST (QUOTE -633) (QUOTE (-549)))) (-2271 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2271 (|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| (LIST (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (LIST (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 -1683) +(-1307 K R UP -1725) ((|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 -1683) +(-1315 S -1725) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1316 -1683) +(-1316 -1725) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4500 . T) (-4506 . T) (-4501 . T) ((-4510 "*") . T) (-4502 . T) (-4503 . T) (-4505 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 27cdaaa6..41cf2f48 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205732 . 3501779190) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) #0#) |has| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (-321 (-2 (|:| -1438 |#1|) (|:| -3067 |#2|))))) -((((-560)) . T) (($) -2196 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2196 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +(205732 . 3502979437) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) #0#) |has| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (-321 (-2 (|:| -1462 |#1|) (|:| -1875 |#2|))))) +((((-560)) . T) (($) -2271 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2271 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-560)) . T)) -((($ $) -2196 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) +((($ $) -2271 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560))))) ((($) . T)) (((|#1|) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T)) -((($) -2196 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2271 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-939)) ((((-887)) . T)) ((((-887)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1189)) . T) (((-229)) . T) (((-391)) . T) (((-915 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-887)) . T)) -(-2196 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2196 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2271 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2271 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2196 (|has| |#1| (-21)) (|has| |#1| (-870))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2196 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) -(-2196 (|has| |#1| (-842)) (|has| |#1| (-871))) +(-2271 (|has| |#1| (-21)) (|has| |#1| (-870))) +((($ $) . T) ((#0=(-421 (-560)) #0#) -2271 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . T)) +(-2271 (|has| |#1| (-842)) (|has| |#1| (-871))) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-326 |#1|)) . T) (((-560)) . T) (($) . T)) (((|#1| |#2| |#3|) . T)) ((((-560)) . T) (((-893 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((($) . T) (((-421 (-560))) -2196 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-421 (-560))) -2271 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . 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))))) -(-2196 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2196 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(((|#2| (-496 (-2256 |#1|) (-793))) . T)) -((((-1207)) -2196 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +(-2271 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2271 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(((|#2| (-496 (-2375 |#1|) (-793))) . T)) +((((-1207)) -2271 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) (((|#1| (-545 (-1207))) . T)) ((((-1189)) . T) (((-987 (-130))) . T) (((-887)) . T)) ((((-887)) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) (((#0=(-893 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -2196 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2196 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -1591 |#1|) (|:| -2030 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -2271 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2271 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -1643 |#1|) (|:| -4039 |#2|))) . T)) ((($) . T)) ((((-887)) |has| |#1| (-632 (-887))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-560)) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1207)) . T)) +((((-887)) -2271 (|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) (($ $) -2196 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2271 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (|has| |#1| (-1132)) (((|#1|) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2196 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((($) -2196 (|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)) (($) -2271 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((($) -2271 (|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)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2196 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2271 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2196 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2196 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2271 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2271 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) ((($ $) . T)) ((($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) @@ -132,30 +132,30 @@ (|has| |#1| (-381)) (((|#1|) . T)) ((((-887)) . T)) -((((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) -(((|#1|) . T) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) +(((|#1|) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (($) . T)) -(-2196 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2271 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) ((((-560)) . T)) ((((-887)) . T)) (((|#1| |#2|) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1264 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -2196 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2271 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . 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) (($ $) -2196 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -((($ $) -2196 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T)) @@ -349,15 +349,15 @@ (|has| |#1| (-1132)) ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T)) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-887)) . T) (((-1212)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2196 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2271 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((((-1212)) . 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T)) (((|#1| (-1002)) . T)) ((((-560)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1182)) -((((-2 (|:| -1438 (-1189)) (|:| -3067 |#1|))) . T)) +((((-2 (|:| -1462 (-1189)) (|:| -1875 |#1|))) . T)) (|has| (-1284 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1284 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) -((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-840 (-1207))) . T) (($) -2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-840 (-1207))) . T) (($) -2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . 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T)) -((($) -2196 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2271 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-887)) . T)) ((((-887)) . T)) (|has| (-1278 |#2| |#3| |#4|) (-149)) @@ -415,18 +415,18 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2196 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2271 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) (((|#1|) . T)) ((($) . T)) ((((-560) |#1|) . T)) (((|#2|) |has| |#2| (-175))) (((|#1|) . 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T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1207)) . T)) (|has| |#1| (-571)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2256 |#1|) (-793)) (-888 |#1|)) . T)) +(((|#2| (-246 (-2375 |#1|) (-793)) (-888 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2271 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) ((((-887)) . T)) ((((-935 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-870)) -((($) -2196 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2196 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . 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T)) -((((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2196 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2196 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1287 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2271 (|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)) -(-2196 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(((|#2| (-496 (-2256 |#1|) (-793)) (-888 |#1|)) . T)) +(-2271 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(((|#2| (-496 (-2375 |#1|) (-793)) (-888 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1207)) (-1207)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1438 (-1189)) (|:| -3067 |#1|))) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -1462 (-1189)) (|:| -1875 |#1|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1438 (-1207)) (|:| -3067 (-51)))) . T)) +((((-2 (|:| -1462 (-1207)) (|:| -1875 (-51)))) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) ((((-1207) (-51)) . 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T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#3|) -2196 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-2196 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) -((($) -2196 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . 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T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1|) . T)) -(-2196 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2271 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-870)) (|has| |#1| (-870)) (|has| |#1| (-870)) @@ -1860,14 +1860,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) ((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T)) (((|#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 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) (|has| |#1| (-813)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2196 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -((($) -2196 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-2271 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +((($) -2271 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2383,7 +2383,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-887)) . T)) (((|#2|) . T) (((-887)) . T)) -((($ (-1207)) -2196 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +((($ (-1207)) -2271 (|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 (|:| -1438 (-1189)) (|:| -3067 |#1|))) . T)) +((((-2 (|:| -1462 (-1189)) (|:| -1875 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) |has| (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)) (-321 (-2 (|:| -1438 |#1|) (|:| -3067 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) |has| (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)) (-321 (-2 (|:| -1462 |#1|) (|:| -1875 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) (((|#2|) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,13 +2460,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1278 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2196 (|has| |#2| (-842)) (|has| |#2| (-871))) +(-2271 (|has| |#2| (-842)) (|has| |#2| (-871))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2196 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2271 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1207)) -2196 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2271 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T)) -(((|#2|) -2196 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)))) -(((|#2|) -2196 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) -((($ (-1207)) -2196 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) +(((|#2|) -2271 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)))) +(((|#2|) -2271 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) +((($ (-1207)) -2271 (-12 (|has| |#3| (-927 (-1207))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1207))) (|has| |#3| (-1080))))) ((($ $) . T) ((#0=(-1278 |#2| |#3| |#4|) #0#) . T) ((#1=(-421 (-560)) #1#) |has| #0# (-38 (-421 (-560))))) ((((-935 |#1|)) . T)) (-12 (|has| |#1| (-376)) (|has| |#2| (-842))) @@ -2787,14 +2787,14 @@ ((((-887)) . T)) ((($) . T) (((-560)) . T)) ((($) . T)) -(-2196 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-376)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1278 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560))))) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -(-2196 (-12 (|has| |#1| (-319)) (|has| |#1| (-939))) (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2196 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) +(-2271 (-12 (|has| |#1| (-319)) (|has| |#1| (-939))) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2271 (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080))) ((((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-887)) . T)) @@ -2832,7 +2832,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . T)) -((($ (-1207)) -2196 (-12 (|has| |#1| (-376)) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-929 (-1207)))))) +((($ (-1207)) -2271 (-12 (|has| |#1| (-376)) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-929 (-1207)))))) ((((-887)) . T)) (((|#1| (-545 (-1207))) . T)) ((($ $) . T)) @@ -2842,29 +2842,29 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) (((|#2|) . T)) -(((|#2|) -2196 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) -(-2196 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(((|#2|) -2271 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) +(-2271 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (|has| |#2| (-939)) (|has| |#1| (-939)) -((($) -2196 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) +((($) -2271 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) (((|#2|) |has| |#2| (-175))) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) ((((-1287 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-887)) . T)) ((((-887)) . T)) ((((-549)) . T) (((-560)) . T) (((-915 (-560))) . T) (((-391)) . T) (((-229)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) -((((-2 (|:| -1438 (-1189)) (|:| -3067 (-51)))) . T)) +((((-2 (|:| -1462 (-1189)) (|:| -1875 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-2196 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2271 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-870)) @@ -2880,7 +2880,7 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-186)) . T) (((-887)) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#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 (|:| -1438 (-1189)) (|:| -3067 |#1|))) . T)) -((($) -2196 (-12 (|has| (-1205 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1205 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) +((((-2 (|:| -1462 (-1189)) (|:| -1875 |#1|))) . T)) +((($) -2271 (-12 (|has| (-1205 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1205 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) ((((-887)) . T)) (((|#2|) |has| |#2| (-376))) ((((-887)) . T)) @@ -2913,19 +2913,19 @@ (|has| |#3| (-1080)) (|has| |#1| (-1132)) ((((-1207) (-51)) . T)) -(-2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2937,12 +2937,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (|has| |#1| (-842)) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-870)) -((((-1234 |#1|)) . T) (((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-1234 |#1|)) . T) (((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1080)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080)))) @@ -2961,36 +2961,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . 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T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-363))) (((#0=(-421 (-560)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-376))) ((((-887)) . T)) (|has| |#1| (-1132)) (((|#1|) . T)) -(((|#1|) -2196 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) -(((|#1|) -2196 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2271 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2271 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) (((|#2|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-593)) . T)) (((|#3| |#3|) . T)) -((($ (-1207)) -2196 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((($ (-1207)) -2271 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (|has| |#1| (-871)) (|has| |#2| (-240)) ((((-888 |#1|)) . T)) @@ -3011,10 +3011,10 @@ (|has| |#1| (-1132)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2196 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2271 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-2196 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2271 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1051)) ((($) . T)) (|has| |#1| (-939)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-935 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . 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T)) -(((#0=(-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) #0#) |has| (-2 (|:| -1438 (-1207)) (|:| -3067 (-51))) (-321 (-2 (|:| -1438 (-1207)) (|:| -3067 (-51)))))) +(((#0=(-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) #0#) |has| (-2 (|:| -1462 (-1207)) (|:| -1875 (-51))) (-321 (-2 (|:| -1462 (-1207)) (|:| -1875 (-51)))))) ((((-1189)) . T)) (|has| |#1| (-939)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-2196 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2271 (|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)))) -(-2196 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2271 (|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)) -2196 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1207)))))) +((((-1207)) -2271 (-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) (($) . T)) @@ -3126,13 +3126,13 @@ ((((-560) |#1|) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) (((|#1|) . T)) -(-2196 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2271 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2196 (|has| |#4| (-815)) (|has| |#4| (-871))) -(-2196 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2271 (|has| |#4| (-815)) (|has| |#4| (-871))) +(-2271 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#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)))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3176,27 +3176,27 @@ (((|#3|) . T)) ((((-1189)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-2196 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2271 (|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 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) -((((-2 (|:| -1438 (-1189)) (|:| -3067 |#1|))) . T)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) +((((-2 (|:| -1462 (-1189)) (|:| -1875 |#1|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-2196 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2271 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2196 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2271 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2196 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2271 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . 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) (($ $) . T)) (((|#1|) . T)) -(-2196 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2271 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-887)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-1207)) -2196 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) -(-2196 (|has| |#1| (-102)) (|has| |#1| (-1132))) +((((-1207)) -2271 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207))))) +(-2271 (|has| |#1| (-102)) (|has| |#1| (-1132))) (|has| |#1| (-813)) (|has| |#1| (-813)) ((((-887)) . T)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-887)) . T)) ((((-887)) . T)) -(-2196 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(-2271 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-887)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1207)) -2196 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +((((-1207)) -2271 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) ((((-887)) . T)) ((((-560)) . T)) -(-2196 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2271 (|has| |#2| (-815)) (|has| |#2| (-871))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-887)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-2196 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) +(-2271 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1207))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) (|has| |#1| (-1182)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-2196 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2271 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-887)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-887)) . T)) -((((-1207)) -2196 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2271 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1207) |#1|) . T)) -(((|#1|) -2196 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2271 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1207)) . T)) -(((|#1|) -2196 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) +(((|#1|) -2271 (|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) (($) . T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1132)) ((((-802 |#1| (-888 |#2|))) |has| (-802 |#1| (-888 |#2|)) (-321 (-802 |#1| (-888 |#2|))))) -(-2196 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2271 (|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)))) . T)) -((($) -2196 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) +((($) -2271 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) ((((-595 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) -((((-2 (|:| -1438 (-1189)) (|:| -3067 (-51)))) . T)) +((((-2 (|:| -1462 (-1189)) (|:| -1875 (-51)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-560)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (|has| |#2| (-376)) ((((-887)) . T)) ((((-887)) . T)) -(-2196 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2271 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-887)) . T)) ((((-1151)) . T) (((-887)) . T)) ((((-549)) . T) (((-887)) . T)) @@ -3353,14 +3353,14 @@ ((((-560)) . T)) (((|#3|) . T)) ((((-887)) . T)) -(-2196 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) -((((-560)) . 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T) (($) -2271 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) +((((-1156 |#1| |#2|)) . T) ((|#2|) . T) (($) -2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-560)) . T)) +((((-1201 |#1|)) . T) (((-560)) . T) (($) -2271 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1113)) . T) ((|#1|) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560)))))) +(-2271 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-571)) (|has| |#1| (-1080))) (((#0=(-595 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) -((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-1119 (-1207))) . T) (($) -2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) +((((-1156 |#1| (-1207))) . T) (((-560)) . T) (((-1119 (-1207))) . T) (($) -2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1207)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1297 |#1|) (-1297 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . 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) (($ $) -2196 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2271 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -2196 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2196 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2271 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2271 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-2196 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2196 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2271 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2271 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1207)) . T) ((|#1|) . T)) @@ -3419,15 +3419,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-2196 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) +(-2271 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (((|#1|) . T)) (((|#1|) . T)) -(-2196 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2271 (|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)) . T) (($) . T)) ((((-549)) . T)) ((((-887)) . T)) -((($) -2196 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080))))) +((($) -2271 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080))))) (|has| |#1| (-871)) ((((-887)) . T)) ((((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) @@ -3443,21 +3443,21 @@ ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) ((((-1207)) |has| |#1| (-927 (-1207)))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -((($) . T) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2196 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((($) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T) (((-560)) |has| |#2| (-1069 (-560))) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) ((((-1113)) . T) ((|#2|) . T) (((-560)) |has| |#2| (-1069 (-560))) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) (((|#1|) . T)) @@ -3477,11 +3477,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-842)) (|has| |#2| (-842)) -((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) ((($ (-1207)) |has| |#1| (-927 (-1207)))) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -((($) -2196 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) -(((|#1|) . T) (((-421 (-560))) -2196 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -2271 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -2271 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . 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|) -2196 (|has| |#2| (-6 (-4510 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2271 (|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|)) . T)) -(-2196 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) -(-2196 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-815)) (|has| |#3| (-1080))) +(-2271 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) +(-2271 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-815)) (|has| |#3| (-1080))) ((((-887)) . T)) (((|#1|) . T)) -(-2196 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2196 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2271 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2271 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) ((((-893 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-381)) @@ -3533,7 +3533,7 @@ (((|#1|) . T)) ((((-887)) . T)) ((($) . T) ((|#2|) . T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-2196 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2271 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-887)) . T)) (|has| |#2| (-939)) -((((-2 (|:| -1438 (-1207)) (|:| -3067 (-51)))) . T)) +((((-2 (|:| -1462 (-1207)) (|:| -1875 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560))))) ((((-887)) . T)) ((((-887)) . T)) @@ -3553,7 +3553,7 @@ ((((-1201 |#1|)) . T) (((-887)) . T)) ((((-887)) . T)) ((((-421 (-560))) |has| |#2| (-1069 (-421 (-560)))) (((-560)) |has| |#2| (-1069 (-560))) ((|#2|) . T) (((-888 |#1|)) . T)) -((((-1207)) -2196 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . T)) +((((-1207)) -2271 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (((-1113)) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T) (((-1207)) . T)) ((((-887)) . T)) @@ -3573,10 +3573,10 @@ ((((-663 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((($) . T) (((-560)) . T) (((-1284 |#1| |#2| |#3| |#4|)) . T) (((-421 (-560))) . 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T)) @@ -3591,16 +3591,16 @@ ((((-421 |#2|) |#3|) . T)) (((|#1|) . T)) ((((-887)) . T)) -(-2196 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(((|#2| (-496 (-2256 |#1|) (-793))) . T)) +(-2271 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(((|#2| (-496 (-2375 |#1|) (-793))) . T)) ((((-560) |#1|) . T)) ((((-1189)) . T) (((-887)) . T)) (((|#2| |#2|) . T)) (((|#1| (-545 (-1207))) . T)) -(-2196 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2271 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) ((((-560)) . T)) (((|#2|) . T)) -((($) -2196 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) +((($) -2271 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) (((|#2|) . T)) ((((-1207)) |has| |#1| (-927 (-1207))) (((-1113)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) @@ -3609,9 +3609,9 @@ ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . T)) -(-2196 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2271 (|has| |#1| (-871)) (|has| |#1| (-1132))) (((|#1|) . T)) -((($) -2196 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2271 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-887)) . T)) ((((-146)) . T)) (((|#1|) . T) (((-421 (-560))) . T)) @@ -3620,7 +3620,7 @@ ((((-887)) . T)) (((|#1|) . T)) (|has| |#1| (-1182)) -((($ (-1207)) -2196 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) +((($ (-1207)) -2271 (|has| (-421 |#2|) (-927 (-1207))) (|has| (-421 |#2|) (-929 (-1207))))) (((|#1|) . T)) (((|#1| (-545 (-888 |#2|)) (-888 |#2|) (-802 |#1| (-888 |#2|))) . 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T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-363))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-363))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-421 (-560)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-421 (-560))) . T) (($) . T)) @@ -3886,7 +3886,7 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2196 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2271 (|has| |#1| (-240)) (|has| |#1| (-239))) (((|#1|) . T) (((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) ((((-887)) . T)) @@ -3895,21 +3895,21 @@ ((((-657 |#2|)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| (-545 (-888 |#2|)) (-888 |#2|) (-802 |#1| (-888 |#2|))) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2196 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2271 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((($) . 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T)) -((($) -2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#2| (-939)) (((|#1| |#2| (-246 |#1| |#2|) (-246 |#1| |#2|)) . T)) ((((-887)) . T)) @@ -3925,9 +3925,9 @@ (((|#1| |#1|) |has| |#1| (-175))) ((((-721)) . T)) ((((-721)) . T)) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-1212)) . T)) -(-2196 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2271 (|has| |#2| (-815)) (|has| |#2| (-871))) (((|#1|) |has| |#1| (-175))) ((((-1212)) . T)) (((|#1| |#1|) . T)) @@ -3940,19 +3940,19 @@ (((|#1| (-560)) . T)) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . T) (($) . T)) -((($ (-1207)) -2196 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) +((($ (-1207)) -2271 (|has| |#1| (-927 (-1207))) (|has| |#1| (-929 (-1207)))) (($ (-1113)) . T)) (((|#1|) |has| |#1| (-175))) ((((-1212)) . T)) ((((-1212)) . T)) ((((-1212)) . T)) ((((-1212)) . T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1212)) . T)) ((((-1212)) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -(-2196 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-175)) (|has| |#1| (-571))) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1| (-793)) . T)) @@ -3960,24 +3960,24 @@ (((|#1| (-545 |#2|) |#2|) . T)) ((((-560) |#1|) . T)) ((((-560) |#1|) . 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T)) ((((-1207)) -12 (|has| |#2| (-927 (-1207))) (|has| |#2| (-1080)))) (|has| |#2| (-1080)) -(-2196 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-2271 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4010,7 +4010,7 @@ (((|#1| |#2|) . T)) ((((-560)) . T) ((|#2|) |has| |#2| (-175))) ((((-115)) . T) ((|#1|) . T) (((-560)) . T)) -(-2196 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2271 (|has| |#1| (-363)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) @@ -4019,11 +4019,11 @@ ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . 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)))) -(-2196 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2271 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2271 (|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)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2196 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2271 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#2|) . T)) -(-2196 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2271 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-887)) -2196 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) +((((-887)) -2271 (-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)) -(-2196 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2271 (|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)) -2196 (-12 (|has| (-1205 |#1| |#2| |#3|) (-927 (-1207))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1207)))))) +((((-1207)) -2271 (-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) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1171 |#1| |#2|)) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) -((((-2 (|:| -1438 (-1207)) (|:| -3067 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) +((((-2 (|:| -1462 (-1207)) (|:| -1875 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1051)) -(((|#2|) . T) (((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) ((($) . T)) ((((-887)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560)))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-391)) . #0=(|has| |#2| (-1051))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1207)) -2196 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) +((((-1207)) -2271 (|has| |#2| (-927 (-1207))) (|has| |#2| (-929 (-1207))))) ((((-887)) . T)) (((|#2|) . T)) ((((-887)) . T)) @@ -4106,15 +4106,15 @@ ((((-1205 |#1| |#2| |#3|)) . T)) ((((-1205 |#1| |#2| |#3|)) . T) (((-1198 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T)) ((((-1205 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2196 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) -(((|#2|) . T) ((|#3|) -2196 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2271 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) +(((|#2|) . T) ((|#3|) -2271 (|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)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T) (((-1264 (-560)) $) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-2196 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) +(-2271 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) ((($ (-1207)) |has| |#1| (-1080))) -(-2196 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2271 (|has| |#1| (-871)) (|has| |#1| (-1132))) ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -1438 (-1207)) (|:| -3067 (-51)))) . T)) +((((-2 (|:| -1462 (-1207)) (|:| -1875 (-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)) -(-2196 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2196 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2271 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2271 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((($) . T)) (((|#2| (-545 (-888 |#1|))) . T)) ((((-1212)) . T)) @@ -4174,7 +4174,7 @@ ((((-1212)) . T)) ((((-887)) . T) (((-1212)) . T)) ((((-1212)) . T)) -((((-887)) -2196 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2271 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1189) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -1438 |#1|) (|:| -3067 |#2|))) . T)) +((((-2 (|:| -1462 |#1|) (|:| -1875 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4192,14 +4192,14 @@ ((((-560)) . T) (($) . 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T) (($) -2271 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-1113)) . T) ((|#2|) . T) (((-421 (-560))) -2271 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560)))))) +((((-1027 |#1|)) . T) ((|#1|) . T) (((-560)) -2271 (|has| (-1027 |#1|) (-1069 (-560))) (|has| |#1| (-1069 (-560)))) (((-421 (-560))) -2271 (|has| (-1027 |#1|) (-1069 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560)))))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . 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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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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((-1257 . -1069) 192783) ((-1240 . -528) 192750) ((-529 . -635) 192734) ((-1219 . -633) NIL) ((-1219 . -632) 192716) ((-1173 . -1154) 192661) ((-495 . -939) 192640) ((-1118 . -739) 192489) ((-1093 . -670) 192461) ((-975 . -670) 192350) ((-840 . -874) T) ((-803 . -739) 192179) ((-611 . -504) 192160) ((-600 . -504) 192141) ((-611 . -632) 192107) ((-600 . -632) 192073) ((-549 . -632) 192055) ((-593 . -1247) T) ((-549 . -633) 192036) ((-802 . -739) 191885) ((-1108 . -102) T) ((-642 . -668) 191857) ((-395 . -25) T) ((-395 . -21) T) ((-495 . -670) 191746) ((-475 . -739) 191717) ((-468 . -739) 191566) ((-1017 . -102) T) ((-1077 . -1242) 191495) ((-930 . -321) 191433) ((-758 . -102) T) ((-659 . -635) 191410) ((-119 . -668) 191340) ((-900 . -93) T) ((-736 . -635) 191294) ((-703 . -93) T) ((-545 . -25) T) ((-698 . -93) T) ((-686 . -632) 191276) ((-667 . -504) 191257) ((-667 . -632) 191210) ((-143 . -102) T) ((-44 . -133) T) ((-610 . -1247) T) ((-609 . -1247) T) ((-357 . -1088) T) ((-301 . -1143) 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) ((-488 . -1087) 185086) ((-514 . -113) T) ((-357 . -1132) T) ((-325 . -1182) NIL) ((-301 . -133) T) ((-407 . -1132) T) ((-893 . -1088) T) ((-716 . -383) 185053) ((-353 . -668) 184983) ((-227 . -640) 184960) ((-339 . -298) 184912) ((-488 . -111) 184733) ((-1283 . -1080) T) ((-1262 . -1080) T) ((-838 . -390) 184717) ((-848 . -1247) T) ((-171 . -748) T) ((-1313 . -1247) T) ((-678 . -102) T) ((-1283 . -250) 184696) ((-1283 . -240) 184648) ((-1262 . -240) 184553) ((-1262 . -250) 184532) ((-1034 . -416) NIL) ((-692 . -660) 184480) ((-326 . -38) 184390) ((-325 . -38) 184319) ((-69 . -632) 184301) ((-331 . -507) 184267) ((-48 . -668) 184217) ((-1219 . -300) 184196) ((-1256 . -871) T) ((-1144 . -1143) 184174) ((-84 . -1247) T) ((-62 . -632) 184156) ((-888 . -874) T) ((-493 . -300) 184135) ((-1313 . -1069) 184112) ((-1195 . -1132) T) ((-1144 . -23) 183964) ((-838 . -927) 183900) ((-1266 . -748) T) ((-1128 . -1247) T) ((-488 . -635) 183726) ((-365 . -239) T) ((-1118 . -302) 183657) ((-995 . -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) ((-1262 . -819) 179015) ((-260 . -390) 178984) ((-259 . -390) 178953) ((-564 . -874) T) ((-678 . -38) 178923) ((-627 . -34) T) ((-496 . -1143) 178901) ((-489 . -34) T) ((-1144 . -133) 178772) ((-993 . -25) 178583) ((-935 . -635) 178533) ((-898 . -632) 178515) ((-218 . -866) T) ((-993 . -21) 178470) ((-837 . -25) 178303) ((-837 . -21) 178214) ((-1254 . -381) T) ((-642 . -1088) T) ((-1209 . -571) 178193) ((-1201 . -47) 178170) ((-368 . -1080) T) ((-366 . -1080) T) ((-496 . -23) 178022) ((-358 . -1080) T) ((-275 . -1080) T) ((-255 . -1080) T) ((-1156 . -47) 177994) ((-119 . -1088) T) ((-1065 . -670) 177968) ((-987 . -34) T) ((-368 . -240) 177947) ((-368 . -250) T) ((-366 . -240) 177926) ((-366 . -250) T) ((-358 . -240) 177905) ((-358 . -250) T) ((-275 . -338) 177877) ((-255 . -338) 177834) ((-275 . -240) 177813) ((-1185 . -153) 177797) ((-260 . -927) 177729) ((-259 . -927) 177661) ((-1173 . -921) 177582) ((-1113 . -871) T) ((-1264 . -1247) 177560) ((-429 . -1143) T) ((-1240 . -1033) 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) ((-850 . -748) T) ((-1147 . -1247) T) ((-663 . -1247) T) ((-1110 . -660) 175464) ((-1201 . -927) 175407) ((-1156 . -927) 175391) ((-837 . -236) 175282) ((-674 . -1087) 175266) ((-108 . -660) 175248) ((-496 . -133) 175119) ((-1209 . -1143) T) ((-841 . -1247) T) ((-975 . -47) 175088) ((-642 . -1132) T) ((-674 . -111) 175067) ((-505 . -632) 175033) ((-339 . -300) 175010) ((-400 . -1247) T) ((-336 . -1247) T) ((-495 . -47) 174967) ((-1209 . -23) T) ((-119 . -1132) T) ((-103 . -102) 174917) ((-1310 . -1143) T) ((-563 . -871) T) ((-229 . -1247) T) ((-1085 . -133) T) ((-1055 . -1088) T) ((-1310 . -23) T) ((-1227 . -632) 174899) ((-841 . -1069) 174883) ((-1151 . -843) T) ((-1034 . -746) 174855) ((-1136 . -1132) T) ((-721 . -739) 174820) ((-597 . -632) 174802) ((-400 . -1069) 174786) ((-353 . -1088) T) ((-394 . -133) T) ((-336 . -1069) 174770) ((-1110 . -21) T) ((-1110 . -25) T) ((-1035 . -842) T) ((-229 . -911) 174752) ((-1035 . -950) T) ((-91 . -34) T) ((-1027 . -321) 174717) ((-943 . -950) 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) ((-1027 . -38) 171848) ((-626 . -1132) T) ((-621 . -1132) T) ((-595 . -632) 171830) ((-495 . -390) 171814) ((-595 . -633) 171796) ((-532 . -632) 171778) ((-935 . -1316) 171765) ((-895 . -1247) T) ((-723 . -466) T) ((-509 . -528) 171731) ((-1309 . -1247) T) ((-1308 . -1247) T) ((-501 . -376) T) ((-368 . -381) 171710) ((-366 . -381) 171689) ((-358 . -381) 171668) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1321 . -1312) 171652) ((-895 . -909) 171629) ((-895 . -911) NIL) ((-993 . -871) 171528) ((-837 . -871) 171479) ((-1255 . -102) T) ((-678 . -680) 171463) ((-1234 . -34) T) ((-174 . -632) 171445) ((-1144 . -25) 171278) ((-1144 . -21) 171189) ((-895 . -1069) 171166) ((-975 . -927) 171147) ((-1266 . -47) 171124) ((-935 . -381) T) ((-607 . -874) T) ((-58 . -673) 171108) ((-530 . -673) 171092) ((-495 . -927) 171069) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171053) ((-58 . -385) 171037) ((-642 . -175) T) ((-530 . -385) 171021) ((-510 . -385) 171005) ((-561 . -1247) T) ((-850 . -730) 170989) ((-1201 . -319) 170968) ((-1209 . -133) T) ((-1173 . -1082) 170952) ((-119 . -175) T) ((-1173 . -662) 170884) ((-1177 . -321) 170822) ((-171 . -1247) T) ((-1310 . -133) T) ((-1278 . -950) 170801) ((-1262 . -939) 170754) ((-1257 . -950) 170733) ((-890 . -1082) 170703) ((-652 . -766) 170687) ((-620 . -766) 170671) ((-1257 . -842) NIL) ((-1055 . -1132) T) ((-931 . -1143) T) ((-890 . -662) 170641) ((-716 . -739) 170591) ((-925 . -1247) T) ((-895 . -390) 170568) ((-895 . -351) 170545) ((-863 . -1247) T) ((-830 . -1247) T) ((-171 . -909) 170529) ((-171 . -911) 170454) ((-791 . -1247) T) ((-699 . -1247) T) ((-1297 . -528) 170387) ((-1283 . -670) 170284) ((-1110 . -236) 170157) ((-501 . -1143) T) ((-353 . -1132) T) ((-221 . -1143) T) ((-77 . -455) T) ((-77 . -410) T) ((-171 . -1069) 170053) ((-305 . -921) 170010) ((-331 . -871) T) ((-1262 . -670) 169818) ((-896 . -816) 169797) ((-896 . -813) 169776) ((-896 . -748) T) ((-501 . -23) T) ((-372 . -236) 169749) ((-367 . -236) 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) ((-1234 . -1041) 162696) ((-1212 . -632) 162663) ((-1219 . -34) T) ((-983 . -632) 162629) ((-948 . -632) 162611) ((-1144 . -871) 162562) ((-793 . -632) 162544) ((-694 . -632) 162526) ((-531 . -1247) T) ((-1266 . -319) 162505) ((-1185 . -321) 162443) ((-1172 . -34) T) ((-493 . -34) T) ((-1123 . -1247) T) ((-491 . -466) T) ((-1065 . -1247) T) ((-1118 . -1080) T) ((-50 . -635) 162412) ((-803 . -1080) T) ((-802 . -1080) T) ((-669 . -242) 162396) ((-651 . -242) 162342) ((-1209 . -21) T) ((-595 . -635) 162292) ((-532 . -635) 162222) ((-496 . -236) 162113) ((-1209 . -25) T) ((-1118 . -338) 162074) ((-468 . -1080) T) ((-1118 . -240) 162053) ((-803 . -338) 162030) ((-803 . -240) T) ((-802 . -338) 162002) ((-753 . -1252) 161981) ((-533 . -34) T) ((-339 . -673) 161965) ((-530 . -34) T) ((-58 . -34) T) ((-511 . -34) T) ((-510 . -34) T) ((-468 . -338) 161944) ((-339 . -385) 161928) ((-374 . -1247) T) ((-334 . -1247) T) ((-1034 . -1182) NIL) ((-753 . -571) 161859) ((-652 . -102) T) ((-620 . -102) T) ((-368 . -748) T) ((-366 . -748) T) ((-358 . -748) T) ((-275 . -748) T) ((-255 . -748) T) ((-391 . -1247) T) ((-1310 . -21) T) ((-1077 . -321) 161767) ((-1310 . -25) T) ((-930 . -1132) 161745) ((-840 . -236) 161732) ((-50 . -1080) T) ((-1205 . -571) 161711) ((-1204 . -1252) 161690) ((-1204 . -571) 161641) ((-1198 . -1252) 161620) ((-1198 . -571) 161571) ((-1055 . -302) T) ((-595 . -1080) T) ((-532 . -1080) T) ((-1034 . -38) 161516) ((-374 . -1069) 161500) ((-334 . -1069) 161484) ((-1027 . -668) 161407) ((-391 . -911) 161389) ((-856 . -1247) T) ((-850 . -1247) T) ((-847 . -1247) T) ((-820 . -1143) T) ((-935 . -748) T) ((-595 . -250) T) ((-595 . -240) T) ((-532 . -240) T) ((-532 . -250) T) ((-1157 . -571) 161368) ((-353 . -302) T) ((-669 . -717) 161352) ((-391 . -1069) 161312) ((-305 . -1082) 161233) ((-352 . -921) 161212) ((-1151 . -1088) T) ((-103 . -127) 161196) ((-305 . -662) 161138) ((-820 . -23) T) ((-1319 . -1317) 161114) ((-1318 . -1317) 161093) ((-1297 . -298) 161045) ((-1284 . -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 . -929) 159421) ((-221 . -660) 159403) ((-229 . -418) T) ((-674 . -670) 159387) ((-55 . -632) 159369) ((-1201 . -950) 159348) ((-753 . -1143) T) ((-657 . -102) T) ((-529 . -1247) T) ((-525 . -1247) T) ((-522 . -1247) T) ((-365 . -102) T) ((-1248 . -1114) T) ((-1151 . -866) T) ((-840 . -871) T) ((-753 . -23) T) ((-357 . -1087) 159293) ((-1178 . -107) 159277) ((-1300 . -632) 159259) ((-1205 . -23) T) ((-1205 . -1143) T) ((-1204 . -1143) T) ((-659 . -1247) T) ((-1204 . -23) T) ((-1198 . -1143) T) ((-1198 . -23) T) ((-1173 . -274) 159243) ((-529 . -1069) 159227) ((-1173 . -234) 159211) ((-1157 . -1143) T) ((-357 . -111) 159140) ((-1035 . -1252) T) ((-128 . -1247) T) ((-943 . -1252) T) ((-1157 . -23) T) ((-1107 . -1132) T) ((-716 . -298) NIL) ((-736 . -1247) T) ((-1035 . -571) T) ((-943 . -571) T) ((-837 . -239) 159037) ((-625 . -684) T) ((-624 . -684) T) ((-257 . -1247) T) ((-186 . -1247) T) ((-163 . -1247) T) ((-159 . -1247) T) ((-256 . -632) 159019) ((-622 . -684) T) ((-820 . -133) T) 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156900) ((-391 . -1051) T) ((-108 . -149) T) ((-108 . -147) NIL) ((-45 . -242) 156850) ((-678 . -1132) T) ((-627 . -107) 156797) ((-499 . -133) T) ((-489 . -107) 156747) ((-246 . -1143) 156725) ((-31 . -1247) T) ((-896 . -390) 156709) ((-896 . -351) 156693) ((-246 . -23) 156545) ((-40 . -635) 156475) ((-1311 . -528) 156408) ((-1093 . -950) T) ((-1093 . -842) T) ((-595 . -381) T) ((-532 . -381) T) ((-1287 . -571) 156387) ((-1283 . -1247) T) ((-1278 . -1252) 156366) ((-1278 . -571) 156317) ((-1262 . -1247) T) ((-365 . -1182) T) ((-339 . -34) T) ((-44 . -432) 156301) ((-1212 . -635) 156237) ((-897 . -1247) T) ((-404 . -766) 156221) ((-1262 . -911) 156094) ((-1262 . -909) 156064) ((-1173 . -668) 156023) ((-753 . -133) T) ((-694 . -635) 156007) ((-1257 . -1252) 155986) ((-1257 . -571) 155937) ((-1205 . -133) T) ((-1204 . -133) T) ((-1198 . -133) T) ((-1157 . -133) T) ((-324 . -1114) T) ((-1055 . -1033) T) ((-758 . -528) 155870) ((-1035 . -23) T) ((-1035 . -1143) T) ((-918 . -1132) T) ((-146 . -866) T) ((-1034 . -363) NIL) ((-713 . -632) 155852) ((-972 . -874) 155831) ((-537 . -321) 155769) ((-1002 . -23) T) ((-143 . -528) NIL) ((-890 . -668) 155714) ((-943 . -1143) T) ((-943 . -23) T) ((-896 . -927) 155673) ((-365 . -38) 155638) ((-893 . -1087) 155625) ((-343 . -874) T) ((-83 . -632) 155607) ((-40 . -1080) T) ((-893 . -111) 155592) ((-740 . -1247) T) ((-723 . -102) T) ((-716 . -632) 155574) ((-616 . -1247) T) ((-610 . -571) 155553) ((-443 . -1143) T) ((-352 . -1082) 155537) ((-216 . -1132) T) ((-177 . -1082) 155469) ((-488 . -47) 155439) ((-40 . -240) 155411) ((-40 . -250) T) ((-136 . -102) T) ((-118 . -102) T) ((-609 . -571) 155390) ((-352 . -662) 155374) ((-716 . -633) 155282) ((-326 . -528) 155248) ((-177 . -662) 155180) ((-325 . -528) 155072) ((-501 . -236) 155059) ((-1283 . -1069) 155043) ((-1262 . -1069) 154829) ((-1027 . -426) 154813) ((-221 . -236) 154800) ((-443 . -23) T) ((-1151 . -175) T) ((-626 . -504) 154767) ((-621 . -504) 154749) ((-626 . -632) 154701) 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. -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 . 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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) 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-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 . 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100184) ((-73 . -1247) T) ((-105 . -632) 100166) ((-918 . -1247) T) ((-1322 . -632) 100148) ((-395 . -632) 100130) ((-352 . -635) 100082) ((-177 . -635) 99999) ((-1248 . -504) 99980) ((-753 . -38) 99829) ((-585 . -1236) T) ((-585 . -1233) T) ((-545 . -632) 99811) ((-534 . -321) 99749) ((-514 . -632) 99731) ((-514 . -633) 99713) ((-1248 . -632) 99679) ((-1198 . -1182) NIL) ((-216 . -1247) T) ((-1058 . -1102) 99648) ((-1058 . -1132) T) ((-1035 . -102) T) ((-1002 . -102) T) ((-943 . -102) T) ((-918 . -1069) 99625) ((-1173 . -748) T) ((-1034 . -670) 99532) ((-490 . -1132) T) ((-477 . -1132) T) ((-597 . -23) T) ((-585 . -35) T) ((-585 . -95) T) ((-443 . -102) T) ((-1094 . -233) 99478) ((-1205 . -38) 99375) ((-1204 . -38) 99216) ((-948 . -874) T) ((-890 . -748) T) ((-793 . -874) T) ((-716 . -950) T) ((-694 . -874) T) ((-526 . -25) T) ((-521 . -21) T) ((-521 . -25) T) ((-1198 . -38) 99012) ((-352 . -1080) T) ((-146 . -1247) T) ((-1110 . -175) T) ((-177 . -1080) T) ((-1157 . -38) 98909) ((-734 . -47) 98886) ((-372 . -175) T) ((-367 . -175) T) ((-533 . -57) 98860) ((-511 . -57) 98810) ((-365 . -1316) 98787) ((-229 . -466) T) ((-331 . -302) 98738) ((-359 . -175) T) ((-177 . -250) T) ((-1262 . -871) 98637) ((-108 . -175) T) ((-896 . -1022) 98621) ((-676 . -1143) T) ((-595 . -376) T) ((-595 . -341) 98608) ((-532 . -341) 98585) ((-532 . -376) T) ((-326 . -319) 98564) ((-325 . -319) T) ((-616 . -871) 98543) ((-1144 . -739) 98485) ((-623 . -1247) T) ((-534 . -294) 98469) ((-676 . -23) T) ((-419 . -234) 98453) ((-419 . -274) 98437) ((-325 . -1051) NIL) ((-346 . -23) T) ((-103 . -1041) 98421) ((-657 . -381) T) ((-45 . -36) 98400) ((-630 . -1132) T) ((-365 . -381) T) ((-538 . -102) T) ((-509 . -27) T) ((-246 . -321) 98338) ((-1118 . -1143) T) ((-1321 . -670) 98312) ((-803 . -1143) T) ((-802 . -1143) T) ((-1209 . -426) 98296) ((-468 . -1143) T) ((-1093 . -466) T) ((-1183 . -1132) T) ((-975 . -466) 98247) ((-1147 . -1114) T) ((-110 . -1132) T) ((-1118 . -23) T) ((-1190 . -528) 98030) 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-979) 94641) ((-44 . -298) 94618) ((-130 . -632) 94585) ((-51 . -632) 94567) ((-218 . -874) T) ((-677 . -426) 94551) ((-1257 . -102) T) ((-1189 . -528) NIL) ((-674 . -25) T) ((-638 . -1087) 94535) ((-674 . -21) T) ((-985 . -668) 94445) ((-757 . -668) 94390) ((-737 . -668) 94362) ((-404 . -111) 94341) ((-226 . -263) 94325) ((-1085 . -1084) 94265) ((-1085 . -1132) T) ((-1035 . -1182) T) ((-840 . -1132) T) ((-467 . -668) 94180) ((-652 . -670) 94164) ((-638 . -111) 94143) ((-620 . -670) 94127) ((-610 . -102) T) ((-357 . -1252) T) ((-324 . -504) 94108) ((-597 . -133) T) ((-609 . -102) T) ((-429 . -1132) T) ((-394 . -1132) T) ((-324 . -632) 94074) ((-231 . -1132) 94052) ((-669 . -528) 93985) ((-651 . -528) 93829) ((-854 . -1080) 93808) ((-663 . -153) 93792) ((-357 . -571) T) ((-734 . -927) 93735) ((-565 . -233) 93685) ((-1287 . -296) 93651) ((-1278 . -296) 93617) ((-1110 . -302) 93568) ((-560 . -874) T) ((-501 . -870) T) ((-227 . -1143) T) ((-1257 . -296) 93534) ((-1240 . -507) 93500) 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90854) ((-1190 . -503) 90788) ((-1313 . -1082) 90772) ((-395 . -1087) 90756) ((-1313 . -662) 90726) ((-838 . -102) T) ((-491 . -250) T) ((-736 . -149) 90705) ((-736 . -147) 90684) ((-119 . -874) NIL) ((-498 . -503) 90668) ((-499 . -349) 90637) ((-524 . -1132) 90588) ((-1322 . -111) 90567) ((-1027 . -390) 90551) ((-427 . -102) T) ((-395 . -111) 90530) ((-1027 . -351) 90514) ((-290 . -1014) 90498) ((-289 . -1014) 90482) ((-1035 . -929) NIL) ((-1319 . -632) 90464) ((-1318 . -632) 90446) ((-110 . -528) NIL) ((-1201 . -1273) 90430) ((-878 . -876) 90414) ((-1209 . -1132) T) ((-103 . -1247) T) ((-975 . -979) 90375) ((-839 . -739) 90317) ((-1257 . -1182) NIL) ((-495 . -979) 90262) ((-1093 . -145) T) ((-60 . -102) 90212) ((-44 . -632) 90194) ((-75 . -632) 90176) ((-365 . -670) 90121) ((-625 . -1132) T) ((-624 . -1132) T) ((-622 . -1132) T) ((-1310 . -1132) T) ((-526 . -871) T) ((-301 . -298) 90100) ((-357 . -1143) T) ((-307 . -1132) T) ((-1027 . -927) 90059) ((-307 . -629) 90038) ((-1322 . -635) 89987) ((-1287 . -38) 89884) ((-1278 . -38) 89725) ((-1257 . -38) 89521) ((-501 . -1088) T) ((-395 . -635) 89505) ((-221 . -1088) T) ((-357 . -23) T) ((-154 . -632) 89487) ((-854 . -819) 89466) ((-854 . -814) 89445) ((-1248 . -635) 89426) ((-610 . -38) 89399) ((-609 . -38) 89296) ((-893 . -571) T) ((-227 . -133) T) ((-331 . -1033) 89262) ((-79 . -632) 89244) ((-734 . -319) 89223) ((-305 . -748) 89125) ((-848 . -102) T) ((-888 . -866) T) ((-305 . -487) 89104) ((-1313 . -102) T) ((-40 . -376) T) ((-896 . -149) 89083) ((-499 . -668) 89065) ((-896 . -147) 89044) ((-1189 . -503) 89026) ((-1322 . -1080) T) ((-496 . -528) 88959) ((-661 . -133) T) ((-1177 . -1247) T) ((-993 . -632) 88941) ((-669 . -503) 88925) ((-651 . -503) 88856) ((-837 . -632) 88549) ((-48 . -27) T) ((-1209 . -739) 88446) ((-975 . -921) 88425) ((-677 . -1132) T) ((-886 . -885) T) ((-451 . -378) 88399) ((-753 . -668) 88309) ((-495 . -921) 88284) ((-1128 . -102) T) ((-1001 . -1132) T) ((-888 . -1132) T) ((-838 . -321) 88271) ((-547 . -541) T) ((-547 . -590) T) ((-1318 . -397) 88243) ((-716 . -874) T) ((-1085 . -528) 88176) ((-1190 . -298) 88152) ((-246 . -274) 88121) ((-246 . -234) 88090) ((-260 . -1082) 87991) ((-259 . -1082) 87892) ((-1310 . -739) 87862) ((-1197 . -93) T) ((-1025 . -93) T) ((-839 . -175) 87841) ((-260 . -662) 87763) ((-259 . -662) 87685) ((-1245 . -504) 87662) ((-592 . -1247) T) ((-231 . -528) 87595) ((-638 . -819) 87574) ((-638 . -814) 87553) ((-1245 . -632) 87465) ((-226 . -1247) T) ((-697 . -632) 87397) ((-1205 . -668) 87307) ((-1185 . -1041) 87291) ((-972 . -102) 87221) ((-365 . -748) T) ((-886 . -632) 87203) ((-1204 . -668) 87085) ((-1198 . -668) 86922) ((-1157 . -668) 86832) ((-1257 . -414) 86784) ((-1144 . -503) 86768) ((-60 . -321) 86706) ((-343 . -102) T) ((-1240 . -21) T) ((-1240 . -25) T) ((-40 . -1143) T) ((-733 . -21) T) ((-646 . -632) 86688) ((-529 . -335) 86667) ((-733 . -25) T) ((-453 . -102) T) ((-108 . -298) NIL) ((-948 . -1143) T) ((-40 . -23) T) ((-793 . -1143) T) ((-560 . -1252) T) ((-509 . -1252) T) ((-1035 . -274) 86649) ((-331 . -632) 86631) ((-1035 . -234) 86613) ((-171 . -168) 86597) ((-594 . -571) T) ((-560 . -571) T) ((-509 . -571) T) ((-793 . -23) T) ((-1283 . -149) 86576) ((-1283 . -147) 86555) ((-1190 . -618) 86531) ((-1262 . -147) 86456) ((-1058 . -503) 86440) ((-1255 . -1247) T) ((-1262 . -149) 86365) ((-1313 . -1320) 86344) ((-895 . -921) NIL) ((-490 . -503) 86328) ((-477 . -503) 86312) ((-537 . -34) T) ((-677 . -739) 86282) ((-1287 . -929) 86195) ((-1278 . -929) 86101) ((-1257 . -929) 85862) ((-114 . -998) T) ((-1209 . -175) 85813) ((-674 . -871) 85792) ((-377 . -102) T) ((-609 . -929) 85705) ((-246 . -245) 85684) ((-260 . -102) T) ((-259 . -102) T) ((-1266 . -979) 85653) ((-252 . -871) 85632) ((-1055 . -874) T) ((-838 . -38) 85481) ((-45 . -528) 85273) ((-1189 . -298) 85223) ((-217 . -1132) T) ((-1181 . -1132) T) ((-896 . -239) 85174) ((-1181 . -629) 85153) ((-597 . -25) T) ((-597 . -21) T) ((-1128 . -321) 85091) ((-985 . -426) 85075) ((-721 . -1252) T) ((-651 . -298) 85028) ((-1118 . -660) 84976) ((-931 . -1132) T) ((-803 . -660) 84924) ((-802 . -660) 84872) ((-357 . -133) T) ((-301 . -632) 84854) ((-893 . -1143) T) ((-721 . -571) T) ((-130 . -635) 84836) ((-468 . -660) 84784) ((-171 . -921) 84705) ((-931 . -933) 84689) ((-391 . -466) T) ((-501 . -1132) T) ((-972 . -321) 84627) ((-723 . -670) 84599) ((-564 . -866) T) ((-221 . -1132) T) ((-326 . -950) 84578) ((-325 . -950) T) ((-325 . -842) NIL) ((-404 . -742) T) ((-893 . -23) T) ((-118 . -670) 84565) ((-488 . -147) 84544) ((-419 . -426) 84528) ((-488 . -149) 84507) ((-110 . -503) 84489) ((-324 . -635) 84470) ((-2 . -632) 84452) ((-190 . -102) T) ((-1189 . -19) 84434) ((-1189 . -618) 84409) ((-676 . -21) T) ((-676 . -25) T) ((-607 . -1175) T) ((-1144 . -298) 84386) ((-346 . -25) T) ((-346 . -21) T) ((-913 . -1247) T) ((-910 . -1247) T) ((-1319 . -1087) 84370) ((-246 . -668) 84149) ((-509 . -376) T) ((-1318 . -1087) 84133) ((-1313 . -38) 84103) ((-1283 . -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) 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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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. -950) T) ((-723 . -842) T) ((-443 . -632) 39859) ((-1151 . -21) T) ((-1151 . -25) T) ((-692 . -390) 39843) ((-118 . -950) T) ((-896 . -274) 39827) ((-896 . -234) 39811) ((-44 . -1247) T) ((-75 . -1247) T) ((-128 . -127) 39795) ((-1085 . -34) T) ((-1319 . -1069) 39769) ((-1318 . -1069) 39726) ((-1266 . -1088) T) ((-879 . -1088) T) ((-368 . -1182) 39705) ((-366 . -1182) 39684) ((-358 . -1182) 39663) ((-496 . -816) 39642) ((-496 . -815) 39621) ((-231 . -34) T) ((-496 . -748) 39599) ((-820 . -635) 39445) ((-674 . -1082) 39429) ((-60 . -503) 39413) ((-585 . -1088) T) ((-1201 . -175) 39304) ((-674 . -662) 39288) ((-488 . -929) 39194) ((-154 . -1247) T) ((-1156 . -175) 39105) ((-1093 . -1132) T) ((-1118 . -979) 39050) ((-975 . -1132) T) ((-839 . -670) 39001) ((-803 . -979) 38970) ((-735 . -1132) T) ((-802 . -979) 38937) ((-530 . -294) 38921) ((-692 . -927) 38880) ((-495 . -1132) T) ((-468 . -979) 38847) ((-79 . -1247) T) ((-368 . -38) 38812) ((-366 . -38) 38777) ((-358 . -38) 38742) ((-275 . -38) 38591) ((-255 . -38) 38440) ((-935 . -1182) T) ((-538 . -504) 38421) ((-642 . -149) 38400) ((-642 . -147) 38379) ((-538 . -632) 38345) ((-119 . -149) T) ((-119 . -147) NIL) ((-429 . -748) T) ((-820 . -1080) T) ((-560 . -239) T) ((-509 . -239) T) ((-357 . -466) T) ((-1287 . -1033) 38311) ((-1278 . -1033) 38277) ((-1257 . -1033) 38243) ((-935 . -38) 38208) ((-229 . -739) 38173) ((-1027 . -133) T) ((-659 . -668) 38142) ((-331 . -47) 38112) ((-40 . -424) 38084) ((-142 . -632) 38066) ((-993 . -1247) T) ((-837 . -1247) T) ((-177 . -950) T) ((-564 . -381) T) ((-736 . -668) 38011) ((-619 . -635) 37992) ((-357 . -416) T) ((-693 . -635) 37973) ((-325 . -236) NIL) ((-183 . -635) 37954) ((-164 . -635) 37935) ((-158 . -635) 37916) ((-156 . -635) 37897) ((-534 . -300) 37874) ((-1262 . -234) 37844) ((-1262 . -274) 37814) ((-1245 . -1247) 37792) ((-1209 . -670) 37717) ((-900 . -102) T) ((-837 . -1069) 37544) ((-45 . -34) T) ((-703 . -102) T) ((-698 . -102) T) ((-678 . -21) T) ((-674 . -102) T) 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. -1132) T) ((-975 . -175) 33211) ((-803 . -1273) 33195) ((-663 . -528) 33128) ((-78 . -632) 33110) ((-753 . -338) 33075) ((-1209 . -748) T) ((-585 . -1132) T) ((-495 . -175) 32986) ((-252 . -321) 32924) ((-1173 . -1143) T) ((-70 . -632) 32906) ((-1310 . -748) T) ((-1205 . -1080) T) ((-1204 . -1080) T) ((-1198 . -1080) T) ((-339 . -102) 32836) ((-1173 . -23) T) ((-2 . -1247) T) ((-1157 . -1080) T) ((-91 . -1152) 32820) ((-890 . -1143) T) ((-1205 . -240) 32779) ((-1204 . -250) 32758) ((-1204 . -240) 32710) ((-1198 . -240) 32597) ((-1198 . -250) 32576) ((-331 . -927) 32482) ((-890 . -23) T) ((-171 . -739) 32310) ((-421 . -1252) T) ((-1133 . -381) T) ((-1034 . -376) T) ((-893 . -466) T) ((-1055 . -149) T) ((-972 . -298) 32262) ((-325 . -871) NIL) ((-1283 . -668) 32144) ((-898 . -102) T) ((-1262 . -668) 31999) ((-734 . -25) T) ((-421 . -571) T) ((-734 . -21) T) ((-539 . -635) 31980) ((-353 . -149) 31962) ((-353 . -147) T) ((-1178 . -1132) 31940) ((-467 . -742) T) ((-76 . -632) 31922) 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-1132) 21069) ((-108 . -1051) T) ((-560 . -145) T) ((-1297 . -153) 21053) ((-496 . -1069) 20880) ((-1284 . -147) 20841) ((-1284 . -149) 20802) ((-1085 . -1247) T) ((-1309 . -93) T) ((-1024 . -632) 20784) ((-840 . -1247) T) ((-887 . -632) 20766) ((-838 . -1087) 20609) ((-1308 . -93) T) ((-1201 . -633) NIL) ((-1127 . -1132) T) ((-1122 . -1132) T) ((-1118 . -321) 20596) ((-429 . -1247) T) ((-394 . -1247) T) ((-1104 . -1132) T) ((-231 . -1247) T) ((-1097 . -1132) T) ((-1067 . -1132) T) ((-1050 . -1132) T) ((-803 . -321) 20583) ((-802 . -321) 20570) ((-1201 . -632) 20552) ((-838 . -111) 20381) ((-1156 . -632) 20363) ((-645 . -1132) T) ((-591 . -176) T) ((-543 . -176) T) ((-468 . -321) 20350) ((-497 . -1132) T) ((-1156 . -633) 20098) ((-1065 . -175) T) ((-972 . -300) 20075) ((-222 . -1132) T) ((-878 . -632) 20057) ((-627 . -528) 19840) ((-81 . -635) 19781) ((-840 . -1069) 19765) ((-489 . -528) 19557) ((-854 . -874) 19536) ((-985 . -748) T) ((-757 . -748) T) ((-737 . -748) T) ((-365 . -1143) T) ((-1210 . -632) 19518) ((-227 . -102) T) ((-496 . -390) 19487) ((-529 . -1132) T) ((-525 . -1132) T) ((-522 . -1132) T) ((-820 . -670) 19461) ((-1055 . -466) T) ((-987 . -528) 19394) ((-365 . -23) T) ((-652 . -133) T) ((-620 . -133) T) ((-353 . -466) T) ((-246 . -381) 19373) ((-391 . -175) T) ((-1283 . -1088) T) ((-1262 . -1088) T) ((-229 . -1033) T) ((-838 . -635) 19110) ((-721 . -401) T) ((-419 . -748) T) ((-723 . -1252) T) ((-1173 . -660) 19058) ((-659 . -1132) T) ((-661 . -102) T) ((-594 . -894) 19042) ((-1313 . -1087) 19026) ((-1190 . -1224) 19002) ((-723 . -571) T) ((-128 . -1132) 18980) ((-736 . -1132) T) ((-676 . -38) 18950) ((-496 . -927) 18882) ((-257 . -1132) T) ((-186 . -1132) T) ((-353 . -416) T) ((-326 . -149) 18861) ((-326 . -147) 18840) ((-118 . -571) T) ((-131 . -528) NIL) ((-325 . -149) 18796) ((-325 . -147) 18752) ((-48 . -466) T) ((-163 . -1132) T) ((-159 . -1132) T) ((-1190 . -107) 18699) ((-803 . -1182) 18677) ((-1313 . -111) 18656) ((-711 . -34) T) ((-606 . 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17263) ((-400 . -632) 17245) ((-345 . -102) T) ((-336 . -632) 17227) ((-171 . -298) 17185) ((-1256 . -874) T) ((-64 . -1247) T) ((-114 . -102) T) ((-896 . -1132) T) ((-524 . -1247) T) ((-177 . -571) T) ((-736 . -739) 17155) ((-305 . -133) 17038) ((-229 . -632) 17020) ((-229 . -633) 16950) ((-1034 . -660) 16889) ((-1313 . -1080) T) ((-1209 . -1247) T) ((-1151 . -149) T) ((-651 . -1224) 16864) ((-753 . -939) 16843) ((-607 . -34) T) ((-669 . -107) 16827) ((-651 . -107) 16773) ((-625 . -1247) T) ((-624 . -1247) T) ((-622 . -1247) T) ((-1310 . -1247) T) ((-642 . -921) 16694) ((-1266 . -298) 16621) ((-753 . -670) 16510) ((-307 . -1247) T) ((-1209 . -1069) 16406) ((-972 . -637) 16383) ((-591 . -590) T) ((-591 . -541) T) ((-543 . -541) T) ((-119 . -921) NIL) ((-1198 . -939) NIL) ((-1093 . -633) 16298) ((-1093 . -632) 16280) ((-975 . -632) 16262) ((-735 . -504) 16212) ((-357 . -102) T) ((-260 . -1087) 16133) ((-259 . -1087) 16054) ((-407 . -102) T) ((-31 . -1132) T) ((-975 . -633) 15915) ((-735 . -632) 15850) ((-1311 . -1242) 15819) ((-495 . -632) 15801) ((-495 . -633) 15662) ((-275 . -426) 15646) ((-255 . -426) 15630) ((-325 . -239) NIL) ((-260 . -111) 15546) ((-259 . -111) 15462) ((-1255 . -684) T) ((-1205 . -670) 15387) ((-1204 . -670) 15284) ((-1198 . -670) 15136) ((-1157 . -670) 15061) ((-365 . -133) T) ((-83 . -455) T) ((-83 . -410) T) ((-1034 . -25) T) ((-1034 . -21) T) ((-897 . -1132) 15012) ((-40 . -1082) 14957) ((-896 . -739) 14909) ((-40 . -662) 14854) ((-391 . -302) T) ((-171 . -1033) 14805) ((-1118 . -929) 14704) ((-716 . -401) T) ((-1027 . -1029) 14688) ((-723 . -1143) T) ((-716 . -168) 14670) ((-803 . -929) 14577) ((-802 . -929) 14561) ((-1283 . -1132) T) ((-1262 . -1132) T) ((-1195 . -102) T) ((-326 . -1233) 14540) ((-326 . -1236) 14519) ((-468 . -929) 14496) ((-326 . -989) 14475) ((-136 . -1143) T) ((-118 . -1143) T) ((-1001 . -1247) T) ((-888 . -1247) T) ((-723 . -23) T) ((-677 . -1247) T) ((-616 . -1296) 14459) ((-616 . -1132) 14409) ((-545 . -874) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index fd1c1ff7..6dd8f214 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3501779183) +(30 . 3502979431) (4511 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -488,679 +488,677 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |blankSeparate| |low| - |voidMode| |lifting1| |makeCrit| |squareFreePrim| |subPolSet?| - |numerators| |deepestTail| |arbitrary| |fortranReal| |f01mcf| |e02daf| - |dimensions| |f01bsf| |t| |build| |totalfract| |OMconnectTCP| |center| - |rst| |d01fcf| |distdfact| |readUInt8!| |flatten| |e04jaf| |imagJ| - |OMgetEndApp| |clearTheSymbolTable| |iprint| |trivialIdeal?| |cos2sec| - |leftCharacteristicPolynomial| |firstSubsetGray| |universe| - |leftUnits| |times| |addmod| |OMsupportsCD?| |OMgetSymbol| - |zeroSetSplit| |bottom!| |groebnerFactorize| - |stiffnessAndStabilityOfODEIF| |lllp| |monicCompleteDecompose| - |charClass| |baseRDE| |removeConstantTerm| |parametric?| |mkPrim| - |entries| |rightDivide| |null| |OMputEndBVar| |completeEchelonBasis| - |rightExactQuotient| |rubiksGroup| |extractIndex| |chineseRemainder| - |internalAugment| |traverse| |not| |pushNewContour| - |localIntegralBasis| |matrixDimensions| |bat| |optpair| - |makeGraphImage| |plusInfinity| |eyeDistance| |OMgetType| |and| - |monom| |iicot| |lepol| |invertIfCan| |f02awf| |dioSolve| |laplacian| - |minusInfinity| |completeHermite| |radicalEigenvectors| |or| - |combineFeatureCompatibility| |bounds| |polyRicDE| |testModulus| - |hasPredicate?| |color| |magnitude| |xor| |printCode| |hostByteOrder| - |explicitEntries?| |cotIfCan| |e04ucf| |common| |value| |OMopenFile| - |stoseInvertible?sqfreg| |representationType| |nothing| |s14baf| - |case| |removeRoughlyRedundantFactorsInPols| |key| |expt| |removeZero| - |plenaryPower| |predicate| |contractSolve| |currentSubProgram| - |algint| |Zero| |leadingSupport| |rdHack1| - |inverseIntegralMatrixAtInfinity| |idealSimplify| |outerProduct| - |rewriteIdealWithQuasiMonicGenerators| |setprevious!| - |multiEuclideanTree| |createMultiplicationMatrix| |One| |filename| - |diag| |wreath| |order| |basisOfNucleus| |testDim| |uniform| - |errorKind| |terms| |e01sef| |d02bhf| |changeMeasure| |kovacic| - |getOperands| |minimalPolynomial| |trigs2explogs| |getMatch| - |cycleEntry| |maxRowIndex| |complexIntegrate| |closeComponent| - |limitPlus| |parse| |sayLength| |romberg| |exprHasAlgebraicWeight| - |e01sff| |mathieu23| |leaf?| |removeCoshSq| |dmpToHdmp| - |beauzamyBound| |xn| |next| EQ |e04naf| |indicialEquation| |untab| - |ffactor| |modularFactor| |cAsech| |quasiRegular?| |block| - |createLowComplexityTable| |f04axf| |imaginary| |invertible?| - 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|realEigenvectors| |algebraicDecompose| |monomRDE| |scalarMatrix| - |lfunc| |iflist2Result| |rational?| |purelyAlgebraic?| - |defineProperty| |abelianGroup| |hostPlatform| |expPot| |writeBytes!| - |OMwrite| |plot| |removeSuperfluousCases| |palgLODE0| |range| - |compound?| |mainContent| |indiceSubResultant| |normalizeIfCan| - |RittWuCompare| |index| |setEmpty!| |sumSquares| |leftLcm| - |var2StepsDefault| |lexGroebner| |alternative?| |routines| - |dualSignature| |nthFlag| |associatorDependence| |swapRows!| |c05pbf| - |rank| |bitCoef| |closedCurve?| |makeSketch| |function| - |startTableInvSet!| |rarrow| |inR?| |BasicMethod| |leftQuotient| |in?| - |e01baf| |resultantReduit| |pol| |permutations| |OMgetEndBind| - |numberOfOperations| |squareFreePart| |exprToXXP| Y |monicLeftDivide| - |separateDegrees| |split| |saturate| |symmetricSquare| - |argumentListOf| |pair| |toseSquareFreePart| |mpsode| |ip4Address| - |less?| |outputFloating| |maxint| |presub| |e02bef| |cothIfCan| - |tanintegrate| |e01bef| |hypergeometric0F1| |limitedint| - |linearAssociatedLog| |Vectorise| |patternMatch| |createGenericMatrix| - |removeIrreducibleRedundantFactors| |innerSolve1| |integers| |sup| - |solve| |LowTriBddDenomInv| |number?| |lazyPquo| - |functionIsFracPolynomial?| |ranges| |quadratic?| |janko2| - |padicFraction| |createPrimitiveNormalPoly| |hasSolution?| |setref| - |dominantTerm| |colorFunction| |cCos| |redpps| |overset?| |isTimes| - |stopTableInvSet!| |iidprod| |genericRightTrace| |monomial?| |mapmult| - |stFunc1| |normFactors| |shiftLeft| |setStatus| |c06gcf| |rotatex| - |sinIfCan| |prime| F |primlimintfrac| |OMputAtp| |headReduce| |write!| - |lexTriangular| |rightRank| |basicSet| |rightTraceMatrix| - |palginfieldint| |ramifiedAtInfinity?| |enterPointData| |has?| |deriv| - |fprindINFO| |PollardSmallFactor| |getOperator| |normDeriv2| - |harmonic| |lastSubResultantElseSplit| |perfectSqrt| |factorial| - |OMgetFloat| |particularSolution| |OMputString| |rightFactorCandidate| - |interReduce| |option| |upDateBranches| |primintfldpoly| - |generalInfiniteProduct| |conjugate| |notelem| |drawComplex| - |midpoint| |basisOfRightNucleus| |totalLex| |tubePointsDefault| - |double| |stronglyReduce| |rootBound| |univcase| |tubePlot| |leader| - |cAcos| |rationalApproximation| |getPickedPoints| |s19abf| |closed?| - |useSingleFactorBound| |changeName| |c06eaf| |e02ddf| |eq?| - |headReduced?| |iiasec| |qinterval| |paren| |pr2dmp| - |semiSubResultantGcdEuclidean1| |jokerMode| |scaleRoots| - |computePowers| |constantOperator| |outputArgs| |d02raf| |adaptive?| - |cCot| |parent| |mainSquareFreePart| |reciprocalPolynomial| - |algebraicOf| |setOrder| |rightUnits| |OMencodingXML| |central?| - |numberOfNormalPoly| |extendedEuclidean| |lex| |setScreenResolution| - |OMReadError?| |leastAffineMultiple| |rightLcm| |s19aaf| |lift| - |continuedFraction| |rischNormalize| |mappingMode| |bfKeys| - |consnewpol| |accuracyIF| |constantToUnaryFunction| |antisymmetric?| - |shiftRight| |associator| |reduce| |subscript| |ptFunc| |f02bjf| - |times!| |isList| |intcompBasis| |idealiserMatrix| |shift| |sort| - |leftNorm| |zeroDimensional?| |lastSubResultant| |dilog| |green| - |tRange| |lastSubResultantEuclidean| |coefChoose| |makeResult| - |vectorise| |declare!| |s18aef| |s17dlf| |isAnd| - |extendedSubResultantGcd| |bringDown| |mapUnivariate| |components| - |sin| |f04qaf| |oddlambert| |OMputSymbol| |createIrreduciblePoly| - |tube| |random| |fortran| |iibinom| |measure2Result| |mvar| |zeroDim?| - |d02gaf| |d02kef| |cos| |laplace| |stoseInvertibleSetsqfreg| - |inverseIntegralMatrix| |iCompose| |rightMinimalPolynomial| - |tubeRadius| |isMult| |leftRankPolynomial| |functionIsOscillatory| - |unparse| |contains?| |tan| |jvmClassConstantTag| |e04mbf| |close!| - |unitsColorDefault| |closed| |shuffle| |pushdown| |qroot| |applyRules| - |showArrayValues| |pdct| |cot| |curry| |cosh2sech| |writeInt8!| - |OMgetEndAttr| |vconcat| |colorDef| |shallowExpand| |exprex| |nlde| - |extractIfCan| |back| |sec| |badValues| |implies| |eulerE| |pattern| - |lcm| |OMUnknownSymbol?| |partialNumerators| |select!| |mathieu24| - |product| |intensity| |resetBadValues| |sign| |csc| |mat| - |splitNodeOf!| |fractRadix| |hue| |ipow| |infieldIntegrate| |sdf2lst| - |inspect| |binaryTournament| |leadingIdeal| |iterationVar| |asin| - |solid| |makeFR| |OMbindTCP| |segment| |algintegrate| |OMputEndError| - |cCsc| |identification| |critpOrder| |s18def| |lazyPseudoDivide| - |satisfy?| |acos| |makeSin| |cSech| |genericRightDiscriminant| - |bumptab1| |ksec| |definingInequation| |bits| |prefix| |df2ef| |seed| - |inverse| |atan| |setelt!| |getExplanations| |s17akf| |append| - |univariatePolynomials| |createZechTable| |denomLODE| - |showScalarValues| |att2Result| |setIntersection| |one?| - |userOrdered?| |acot| |level| |viewDefaults| |trapezoidal| |close| - |symmetricDifference| |recur| |nullSpace| |aromberg| - |leviCivitaSymbol| |coHeight| |diagonalProduct| |asec| |toroidal| - |subResultantGcdEuclidean| |definingEquations| |OMputApp| - |monomialIntegrate| |gcd| |bezoutMatrix| |selectODEIVPRoutines| - |strongGenerators| |jvmLongConstantTag| |showTheRoutinesTable| - 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|setMaxPoints3D| |acscIfCan| |debug| |readInt32!| |nodes| - |permutationRepresentation| |normal01| |jordanAdmissible?| |iomode| - |quasiMonicPolynomials| |fortranComplex| D |getGoodPrime| - |reduceByQuasiMonic| |ruleset| |quasiComponent| |double?| |setPoly| - |symFunc| |doubleRank| |string?| |open?| |generalSqFr| - |matrixConcat3D| |showFortranOutputStack| |fractRagits| - |leftMinimalPolynomial| BY |complexZeros| |repSq| |coth2tanh| |type| - |elements| |finiteBasis| |f01ref| |bivariatePolynomials| - |OMgetEndObject| |rightAlternative?| |jacobi| |approxNthRoot| - |writeLine!| |suchThat| |trapezoidalo| |fortranLiteralLine| |digamma| - |parabolicCylindrical| |laguerreL| |groebgen| |coerceListOfPairs| - |any?| |node?| |pop!| |sorted?| |useNagFunctions| |evaluate| |pack!| - |rischDE| |ScanFloatIgnoreSpacesIfCan| |setLength!| |critT| - |bombieriNorm| |char| |FormatRoman| |sts2stst| |rCoord| |trunc| - |solid?| |printInfo| |lfintegrate| |d01akf| |noKaratsuba| - |clipParametric| |OMencodingBinary| |setPosition| |zoom| - 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|LyndonBasis| |writeUInt8!| |definingPolynomial| |verticalTab| - |credPol| |nsqfree| |compBound| |reify| |nthCoef| |updatD| |subSet| - |algebraicCoefficients?| |nextNormalPrimitivePoly| - |jvmIntegerConstantTag| |youngDiagram| |attributeData| |interpret| - |lookupFunction| |processTemplate| |removeSinSq| |getProperties| - |heapSort| |bothWays| |initials| + |bitLength| |discriminantEuclidean| - |cyclicEntries| |oblateSpheroidal| |cycleRagits| |leftFactorIfCan| - |c06gsf| |pushup| |collect| |eq| |iiacoth| - |minPoints3D| - |rewriteSetByReducingWithParticularGenerators| |symmetricPower| - |critMonD1| |clearTheFTable| |youngGroup| |safeFloor| |roughBase?| - |disjunction| |iter| |birth| / |getMultiplicationTable| - |antisymmetricTensors| |quasiMonic?| |bfEntry| |code| |s21bdf| |trim| - |jvmSuper| |psolve| |mindegTerm| |factorAndSplit| |eigenvector| - |exprToGenUPS| |listBranches| |sqfrFactor| |limit| |weakBiRank| - |s18acf| |listConjugateBases| |numer| |makeViewport2D| - |rightExtendedGcd| |generalTwoFactor| |adaptive| |generic?| - 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|constantOpIfCan| |floor| |pile| |isExpt| |fullDisplay| |vector| - |sort!| |SturmHabicht| |laurentIfCan| |getMeasure| |integerIfCan| - |removeCosSq| |zeroOf| |polarCoordinates| |regularRepresentation| - |differentiate| |forLoop| |cLog| |rule| |solveInField| |nextSublist| - |generalizedEigenvector| |airyBi| |decrease| |maxrow| - |noLinearFactor?| |top| |identity| |palglimint0| - |purelyTranscendental?| |useEisensteinCriterion?| |normalDeriv| - |zeroDimPrimary?| |generalPosition| |s19adf| |continue| - |complementaryBasis| |limitedIntegrate| |bag| |makeEq| - |nextLatticePermutation| |heap| |OMputEndAtp| |prindINFO| - |stopTableGcd!| |primitiveElement| |complexLimit| |drawToScale| - |numFunEvals3D| |tab| |comp| |pointColorDefault| |var2Steps| - |cardinality| |lflimitedint| |cAtanh| |symmetric?| |randnum| |merge!| - |iitan| |maximumExponent| |coshIfCan| |zeroDimPrime?| |e02adf| - |minus!| |fractionPart| |compdegd| |nullity| |nextPrimitivePoly| - |addMatchRestricted| |signature| |viewWriteAvailable| |SFunction| - 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|leadingBasisTerm| |lazyGintegrate| |acoshIfCan| |cycleSplit!| - |index?| |f02abf| |determinant| |eisensteinIrreducible?| |resize| - |makeTerm| |ptree| |ratDsolve| |sinhIfCan| |cAcsch| |Lazard| |f02aaf| - |status| |irreducibleFactor| |external?| |c02aff| |f02adf| |simplify| - |pseudoQuotient| |lowerCase!| |outputForm| |littleEndian| |initTable!| - |sumOfKthPowerDivisors| |approximants| |enqueue!| |doubleResultant| - |writable?| |addPoint| |viewSizeDefault| |ratDenom| |returns| - |mainVariables| |li| |upperCase| |rightRankPolynomial| |alphabetic?| - |sizeLess?| |OMgetVariable| |divisorCascade| |adaptive3D?| |kind| - |nextPrimitiveNormalPoly| |legendreP| |dequeue!| |match?| |zag| - |clearDenominator| |simpson| |yCoordinates| |degreeSubResultant| - |numerator| |Ei| |bernoulli| |thenBranch| |op| |carriageReturn| - |linearPart| |LyndonWordsList1| |f04adf| |getIdentifier| |fTable| - |fixedDivisor| |f07fdf| |iteratedInitials| |brillhartTrials| - |wordInGenerators| |numberOfFactors| |upperCase!| |ODESolve| - |ricDsolve| |s14abf| |quoted?| |yCoord| |rdregime| |outlineRender| - |makeSeries| |e02bbf| |reorder| |se2rfi| |innerint| |leastMonomial| - |f02aef| |dn| |overlap| |physicalLength| |sample| |lfextendedint| - |endOfFile?| |ran| |cot2trig| |rootPoly| |headRemainder| - |jvmFieldrefConstantTag| |rootOfIrreduciblePoly| - |topFortranOutputStack| |cartesian| |perfectNthPower?| |thetaCoord| - |integralBasis| |integralMatrix| |fibonacci| |erf| |reducedForm| - |dimensionsOf| |isNot| |d02bbf| |s13adf| |removeRedundantFactors| - |f02ajf| |setMaxPoints| |semiResultantReduitEuclidean| |matrix| - |HermiteIntegrate| |mesh| |argscript| |cyclicParents| - |makeFloatFunction| |newReduc| |child| |putProperty| - |sylvesterSequence| |deleteProperty!| |ode2| |e02zaf| |setClipValue| - |rightOne| |sylvesterMatrix| |df2st| |inf| |createPrimitiveElement| - |setDifference| |aCubic| |normal?| |exactQuotient!| |union| - |direction| |f07aef| |jordanAlgebra?| |fortranDoubleComplex| |step| - |iitanh| |positiveSolve| |LyndonWordsList| |generator| F2FG |hermite| - |s21baf| |multiple?| |s19acf| |quasiAlgebraicSet| |tanhIfCan| - |sortConstraints| |elaboration| |resetVariableOrder| - |jvmInterfaceMethodConstantTag| |showRegion| |showIntensityFunctions| - |pushucoef| |wronskianMatrix| |pastel| |sin2csc| |modulus| |minrank| - |upperBound| |rootPower| |e02ajf| |child?| |associatedEquations| - |nonSingularModel| |inverseColeman| |getlo| |increasePrecision| - |newTypeLists| |fortranDouble| |jvmFloatConstantTag| |functorData| - |algebraicVariables| |clipPointsDefault| |outputList| |aQuartic| - |permanent| |algebraic?| |ceiling| |selectFiniteRoutines| |viewport3D| - |OMputInteger| |htrigs| |balancedBinaryTree| - |univariatePolynomialsGcds| |hexDigit?| |pushuconst| |bezoutResultant| - |dark| |divideIfCan!| |derivationCoordinates| |identityMatrix| - |generalizedContinuumHypothesisAssumed?| |c06fuf| |superscript| - |delete!| |chainSubResultants| |pascalTriangle| |leastPower| |say| - |fullPartialFraction| |selectfirst| |prinshINFO| |f02xef| - |relationsIdeal| |retract| |extendedint| |d03faf| |leftZero| |part?| - |setvalue!| |wholePart| |critBonD| |randomR| |removeDuplicates| - |maxdeg| |sec2cos| |totalDifferential| |dim| |selectOrPolynomials| - |constantIfCan| |removeZeroes| |pdf2ef| |elliptic| |mainForm| - |aLinear| |subresultantSequence| |mesh?| |roughSubIdeal?| |iilog| - |gradient| |rotate!| |evenlambert| |clearFortranOutputStack| |cfirst| - |fortranCarriageReturn| |semicolonSeparate| |rightUnit| |subspace| - |cylindrical| |iicosh| |stFuncN| |intPatternMatch| |leftExactQuotient| - |read!| |composites| |factorSquareFreePolynomial| - |mainDefiningPolynomial| |copy!| |just| |localAbs| |incr| - |resetAttributeButtons| |cAcosh| |float?| |mapSolve| - |semiDegreeSubResultantEuclidean| |real?| |mainKernel| |mapGen| - |probablyZeroDim?| |removeRoughlyRedundantFactorsInContents| |s01eaf| - |hi| |e02bcf| |isImplies| |fortranInteger| |asinhIfCan| |moebiusMu| - |OMputEndApp| |readInt16!| |ddFact| |inverseLaplace| |curve?| - |OMParseError?| |charpol| |lazyVariations| |endSubProgram| |mr| - |mirror| |f01maf| |hasHi| |doubleDisc| |deref| |arrayStack| |odd?| - 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|whileLoop| |directSum| |gderiv| |rootProduct| |getProperty| - |children| |solveLinearlyOverQ| |mergeDifference| |showTheIFTable| - |airyAi| |shape| |hermiteH| |expint| |unexpand| |addMatch| |cycle| - |lyndon| |selectPolynomials| |basis| |enterInCache| |derivative| - |sumOfDivisors| |variationOfParameters| |height| |hasTopPredicate?| - |univariateSolve| |pointPlot| |ReduceOrder| |irreducible?| - |collectQuasiMonic| |iipow| |mainVariable| |reduction| |pToDmp| - |monic?| |second| |Lazard2| |updateStatus!| |socf2socdf| - |possiblyInfinite?| |stirling1| |cAcoth| |expenseOfEvaluation| - |quickSort| |rootSplit| |isPlus| |useSingleFactorBound?| |nary?| - |generate| |third| |OMgetInteger| |outputBinaryFile| |overlabel| - |completeHensel| |appendPoint| |tower| |eigenvalues| |BumInSepFFE| - |constantRight| |semiResultantEuclidean2| |truncate| |parents| - |polynomialZeros| |extendIfCan| |nextsousResultant2| |loopPoints| - |iicos| |pureLex| |jvmFinal| |hspace| |OMserve| |imagK| - |dihedralGroup| |incrementBy| |noValueMode| |subResultantsChain| - |completeEval| |mainMonomial| |trace2PowMod| |graphImage| |display| - |factorPolynomial| |multiplyExponents| |splitSquarefree| |insert!| - |reducedDiscriminant| |expand| |hex| |subMatrix| |front| |branchIfCan| - |subset?| |controlPanel| |asechIfCan| |squareFree| |B1solve| |degree| - |generateIrredPoly| |filterWhile| |cup| |bernoulliB| |flexible?| - |showAllElements| |selectSumOfSquaresRoutines| |slex| |plotPolar| - |subCase?| |radicalEigenvector| |filterUntil| |coerce| - |subscriptedVariables| |useEisensteinCriterion| |specialTrigs| - |linearDependenceOverZ| |capacity| |charthRoot| |iiasin| - |modularGcdPrimitive| |const| |select| |construct| |before?| - |diagonalMatrix| |myDegree| |getBadValues| |retractIfCan| - |complexNumeric| |symmetricProduct| |decomposeFunc| |swapColumns!| - |nextColeman| |semiDiscriminantEuclidean| |schwerpunkt| - |realElementary| |f04atf| |crest| |input| |sub| |row| - |extractProperty| |systemCommand| |jvmSynchronized| |rootOf| - |randomLC| |componentUpperBound| |kernels| |library| |palgextint0| - |torsionIfCan| |elaborateFile| |bat1| |nthFractionalTerm| - |knownInfBasis| |escape| |palgextint| |postfix| |true| - |principalAncestors| |belong?| |operator| |zerosOf| |dmp2rfi| - |nextSubsetGray| |normal| |setProperties| |diff| - |radicalOfLeftTraceForm| |sequence| |lifting| |changeVar| - |partialQuotients| |modifyPoint| |drawComplexVectorField| |palgRDE0| - |minimumExponent| |iicsc| |tab1| |univariate| |GospersMethod| - |normalize| |pushdterm| |makeRecord| |orbit| |allRootsOf| |toScale| - |euclideanSize| |tail| |LyndonCoordinates| |startStats!| |copyInto!| - |queue| |viewDeltaYDefault| |setImagSteps| |cCsch| |commaSeparate| - |sqfree| |figureUnits| |f01qcf| |certainlySubVariety?| - |mainExpression| |taylorIfCan| |factorsOfDegree| |splitConstant| - |gramschmidt| |basisOfLeftAnnihilator| |conjugates| |dAndcExp| - |typeLists| |factor| |changeWeightLevel| |safetyMargin| - |reducedQPowers| |internalSubPolSet?| |primitive?| |topPredicate| - |entry?| |f02fjf| |sqrt| |binary| |makingStats?| |setErrorBound| - 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|jvmDoubleConstantTag| |oddintegers| |cyclotomic| |interpolate| - |primeFactor| |characteristic| |maxPoints| |qualifier| - |oneDimensionalArray| |ef2edf| |comment| |henselFact| |substitute| - |aQuadratic| |bigEndian| |rightPower| |infinite?| - |setLegalFortranSourceExtensions| |rightTrim| - |stiffnessAndStabilityFactor| |dequeue| |returnTypeOf| |realRoots| - |antiCommutator| |createPrimitivePoly| |light| |quotedOperators| - |antiAssociative?| |leftTrim| |linearlyDependent?| |reopen!| |d03edf| - |genericRightMinimalPolynomial| |divideIfCan| |iFTable| - |unprotectedRemoveRedundantFactors| |critM| |midpoints| |setTex!| - |UnVectorise| |coordinates| |high| |s13aaf| |optional| - |integralLastSubResultant| |curve| |symmetricGroup| |normalise| - |e01bhf| |showSummary| |table| |hMonic| |monicModulo| |primitivePart| - |createThreeSpace| |option?| |OMgetError| |makeMulti| - |SturmHabichtCoefficients| |comparison| |new| |expintfldpoly| - |findCycle| |iiatan| |minPoly| |rightScalarTimes!| |addPoint2| - |pointColor| |separate| |conical| |showAttributes| |minPol| |dot| - |iiabs| |coth2trigh| |complex?| |readUInt16!| |maxIndex| |normalized?| - |stack| |root| |repeatUntilLoop| |tanSum| |bipolar| - |explicitlyFinite?| |getOrder| |viewpoint| |OMcloseConn| |simplifyExp| - |mapCoef| |increase| |buildSyntax| |leftTrace| |whatInfinity| |goto| - |cscIfCan| |lazyEvaluate| |weierstrass| |companionBlocks| |ignore?| - |tanQ| |biRank| |integral| |jacobiIdentity?| |rightFactorIfCan| - |doubleComplex?| |property| |subResultantGcd| |leftRecip| - |pseudoRemainder| |linear?| |prefixRagits| |iiacsch| - |diophantineSystem| |quartic| |initiallyReduced?| |rightZero| - |triangulate| |fixedPointExquo| |jvmAbstract| |sturmSequence| - |radicalSolve| |rquo| |integerBound| |screenResolution3D| |infieldint| - |numeric| |jvmInterface| |OMmakeConn| |mappingAst| - |isAbsolutelyIrreducible?| |formfeed| |operators| |extractClosed| - |pointSizeDefault| |radical| |e04gcf| |apply| |computeBasis| |keys| - |algebraicSort| |branchPoint?| |primaryDecomp| |removeDuplicates!| - |leftDivide| |perfectNthRoot| |cubic| |selectNonFiniteRoutines| - |first| |left| |fixedPoint| |sequences| |freeOf?| - |inputOutputBinaryFile| |decimal| |pToHdmp| |irForm| |outputAsTex| - |makeprod| |rest| |right| |ord| |rk4| |intermediateResultsIF| - |connectTo| |factorials| |prevPrime| |froot| |lazyIrreducibleFactors| - |createLowComplexityNormalBasis| |varList| |countable?| |polar| - |invmod| |d01gbf| |associates?| |gcdPolynomial| |basisOfCentroid| - |binding| |expandTrigProducts| |unitCanonical| |split!| |singular?| - |typeList| |iisqrt2| |signatureAst| |jvmNative| |s17acf| |reverse| - |power| |kroneckerDelta| |setFormula!| |ratpart| |max| |nullary| - |asimpson| |principalIdeal| |binaryTree| |factorList| |sPol| - |insertTop!| |exprToUPS| |po| |name| |newSubProgram| |ramified?| - |poisson| |supersub| |tubePoints| |frobenius| |ParCondList| |hcrf| - |llprop| |lowerCase| |body| |push!| |lowerPolynomial| |HenselLift| - |c02agf| |bipolarCylindrical| |countRealRoots| |acschIfCan| - |changeNameToObjf| |btwFact| |constantKernel| |nativeModuleExtension| - |rationalPoints| |viewZoomDefault| |leftRegularRepresentation| - |monicDivide| |prinb| |stirling2| |inHallBasis?| |plus!| |numFunEvals| - |unary?| |tracePowMod| |hconcat| |integrate| |OMsend| - |jvmStringConstantTag| |unrankImproperPartitions0| |iiacosh| - |reverseLex| |exponents| |OMputAttr| |lSpaceBasis| |OMgetBind| - |invmultisect| |listexp| |drawCurves| |linkToFortran| |maxrank| |hclf| - |tablePow| |setAdaptive3D| |prem| |replace| |OMencodingUnknown| - |modifyPointData| |alternating| |polyRDE| |unitNormalize| - |primintegrate| |vspace| |triangularSystems| |super| |iifact| |symbol| - |divide| |rename!| |f01brf| |extractSplittingLeaf| |insertRoot!| - |lieAdmissible?| |rroot| |findBinding| |semiSubResultantGcdEuclidean2| - |sizePascalTriangle| |expression| |graphCurves| |axes| |dictionary| - |xCoord| |negative?| |viewDeltaXDefault| |elem?| |point?| - |numberOfChildren| |zeroVector| |ideal| |integer| |readBytes!| - |e01sbf| |port| |stosePrepareSubResAlgo| |f02akf| |tanh2coth| - |polyred| |rewriteIdealWithHeadRemainder| |basisOfCommutingElements| - |plus| |hitherPlane| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
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|optAttributes| |kernels| |indicialEquations| + |returnTypeOf| |collect| |sample| |ParCondList| |safeCeiling| + |genericRightTraceForm| |any?| |optional?| |rewriteIdealWithRemainder| + |controlPanel| |thetaCoord| |operator| |generalLambert| + |quadraticNorm| |dilog| |elaborate| |OMreceive| |htrigs| |generator| + |acoshIfCan| |raisePolynomial| |sts2stst| |logGamma| |readUInt32!| + |Beta| |sin| |previous| |conical| |tracePowMod| + |irreducibleRepresentation| |semiResultantEuclidean2| |doubleRank| + |factorsOfCyclicGroupSize| |module| |matrix| |univariate| |graphs| + |c05nbf| |brillhartIrreducible?| |outputArgs| |modTree| + |ScanFloatIgnoreSpaces| |noValueMode| |entries| |cycle| + |permutationGroup| |degreePartition| |range| |interactiveEnv| + |nothing| |df2st| |lazyPrem| |pastel| |generalInfiniteProduct| + |irreducible?| |roman| |inverse| |LyndonWordsList1| + |sturmVariationsOf| |digit| |rightMinimalPolynomial| |LyndonWordsList| + |coerceS| |badValues| |triangularSystems| |factor| |hcrf| |s17aef| + |getBadValues| |encodingDirectory| |s18acf| |isPower| + |radicalEigenvectors| |janko2| |sqrt| |graphCurves| |shiftRoots| + |beauzamyBound| |linearPolynomials| |failed| + |halfExtendedSubResultantGcd1| |lp| |tree| |expandTrigProducts| + |qualifier| |push| |vedf2vef| |realRoots| |UnVectorise| |heapSort| + |real| |expextendedint| |cfirst| |prindINFO| |cCsc| + |createMultiplicationTable| |basicSet| |lfextendedint| |cPower| + |f01rdf| |numericIfCan| |tRange| |imag| |swapRows!| |sturmSequence| + |indiceSubResultantEuclidean| |fintegrate| |halfExtendedResultant1| + |node?| |directProduct| |d02cjf| |denomRicDE| |ridHack1| |iiacoth| + |patternMatchTimes| |quotientByP| |balancedBinaryTree| |scalarTypeOf| + |incr| |truncate| |cycleSplit!| |any| |subResultantsChain| |epilogue| + |mathieu11| |integralBasis| |quoByVar| |dom| |minimize| + |realEigenvalues| |parametersOf| |hi| |region| |singleFactorBound| + |f01qef| |rCoord| |orthonormalBasis| |brace| |e01saf| |minPol| + |hconcat| |cyclic| |exprHasLogarithmicWeights| |pseudoDivide| |lyndon| + |asechIfCan| |root?| |elColumn2!| |destruct| |setelt!| |d02raf| + |lazyPseudoRemainder| |compound?| |tubeRadius| GF2FG + |viewDeltaYDefault| |s17def| |acosIfCan| |rectangularMatrix| |polCase| + |label| |conditionP| |listConjugateBases| |makeUnit| |scopes| + |decimal| |iifact| |string?| |minimumDegree| |f04adf| |more?| |inf| + |realZeros| |trigs2explogs| |padicFraction| |collectQuasiMonic| + |diagonal?| |oneDimensionalArray| |unitCanonical| |symmetricProduct| + |OMputObject| |red| |log| |title| |clipParametric| |monomial| + |roughEqualIdeals?| |axes| |llprop| |radPoly| |rightTraceMatrix| + |tensorProduct| |wordsForStrongGenerators| |multivariate| |polygon| + |c05pbf| |sdf2lst| |headReduced?| |index?| |pop!| |iisinh| + |lastSubResultantEuclidean| |variables| |stripCommentsAndBlanks| + |evenInfiniteProduct| |readInt8!| |bivariate?| |string| |extract!| + |isQuotient| |e| |argumentList!| |topPredicate| |integralMatrix| + |octon| |nil?| |nextIrreduciblePoly| |clearDenominator| + |polynomialZeros| |d01bbf| |writeInt8!| |s20adf| |quote| + |algebraicVariables| |nil| |exprHasWeightCosWXorSinWX| + |identitySquareMatrix| |mainValue| |rightLcm| |powers| + |getExplanations| |comparison| |zeroDimPrimary?| |isMult| + |symbolIfCan| |constructor| |updatD| |tanhIfCan| |level| |subscript| + |simplifyLog| |exQuo| |defineProperty| |createPrimitiveElement| + |rightMult| |generate| |queue| |cycleTail| |makeSeries| |qqq| + |bitCoef| |findConstructor| |arity| |height| |approximate| |getMatch| + |bothWays| |augment| |lowerCase| |complex| |setValue!| |empty?| + |primitivePart!| |Frobenius| |incrementBy| |pToHdmp| |zeroDimPrime?| + |endOfFile?| |blankSeparate| |e01sef| |screenResolution| |newReduc| + |binaryFunction| |expand| |reindex| |middle| |buildSyntax| + |horizontalTab| |stack| |viewZoomDefault| |linearDependenceOverZ| + |jvmSuper| |lazyVariations| |filterWhile| |makeVariable| |distribute| + |length| |clikeUniv| |inspect| |iiasec| |mkIntegral| + |lazyIrreducibleFactors| |filterUntil| |jordanAdmissible?| |scripts| + |OMencodingBinary| |parts| |children| |swap!| |iiacsc| + |stoseSquareFreePart| |logical?| |c06gcf| |select| |sortConstraints| + |hasoln| |lllp| |isExpt| |clipPointsDefault| |chineseRemainder| + |approxNthRoot| |isOp| |OMgetEndAttr| |setAdaptive3D| |bat1| + |integralCoordinates| |simpson| |asecIfCan| |nary?| |listLoops| + |transpose| |ptFunc| |e02bbf| |divisors| |expintfldpoly| |whitePoint| + |e01bgf| |doubleFloatFormat| |sequence| |remove| + |genericLeftTraceForm| |e02dcf| |s19aaf| |insertTop!| |convergents| + |generalPosition| |basisOfCommutingElements| |ellipticCylindrical| + |coHeight| |irForm| |ran| |subSet| |upDateBranches| |leftPower| + |abelianGroup| |measure2Result| |radicalEigenvalues| + |setVariableOrder| |last| |cycleEntry| |simpleBounds?| |initials| + |startTableGcd!| |assoc| |find| |setsubMatrix!| |apply| + |rangePascalTriangle| |characteristicSerie| |constantIfCan| + |makeRecord| |numberOfCycles| |leftTrace| |checkRur| |outputForm| + |removeRoughlyRedundantFactorsInPol| |order| |first| |psolve| + |endSubProgram| |tanNa| |setPosition| |iomode| |linearDependence| + |exprHasAlgebraicWeight| |capacity| |leftRegularRepresentation| |rest| + |createLowComplexityNormalBasis| |child| |property| |mr| |Is| |e02adf| + |stoseInternalLastSubResultant| |closedCurve| |rotatex| |commutative?| + |d02bhf| |unit| |varList| |outputGeneral| |OMconnectTCP| + |expenseOfEvaluationIF| |ref| |nthFractionalTerm| |solveLinearlyOverQ| + |fullDisplay| |tail| |reverse| |binaryTournament| |qinterval| + |rangeIsFinite| |iiexp| |leftDiscriminant| |monicLeftDivide| |insert!| + |reseed| |monicCompleteDecompose| |cyclicCopy| |fixedPointExquo| + |categoryFrame| |leftTraceMatrix| |selectAndPolynomials| |writeLine!| + |mapUnivariateIfCan| |ode1| |dioSolve| |f02bjf| |prem| |iisin| + |leftCharacteristicPolynomial| |yCoordinates| |character?| |imagE| + |OMgetInteger| |curryRight| |elaboration| |reorder| |normInvertible?| + |multMonom| |antiCommutative?| |aQuartic| |nthFactor| + |standardBasisOfCyclicSubmodule| |lifting| |vconcat| |bitLength| + |continuedFraction| |exprToUPS| |internalAugment| |findCycle| + |selectPDERoutines| |hitherPlane| |fi2df| |viewPhiDefault| + |algebraicCoefficients?| |cot2trig| |littleEndian| |basisOfNucleus| + |e02gaf| |pquo| LODO2FUN |lieAlgebra?| |cyclePartition| |npcoef| + |whatInfinity| |solveLinearPolynomialEquationByFractions| |s19adf| + |hostPlatform| |mvar| |mirror| |diagonalProduct| |outputAsTex| + |pomopo!| |minus!| |e01sff| |binarySearchTree| |submod| |meshFun2Var| + |countable?| |putProperty| |removeZeroes| |multinomial| + |quasiMonicPolynomials| |expr| |cons| |resultant| |prologue| + |primeFrobenius| |int| |hessian| |contours| |sinIfCan| |mindegTerm| + |subResultantGcd| |s14aaf| |exponentialOrder| |cTan| |sort!| + |represents| |charthRoot| |changeMeasure| |linefeed| + |leadingCoefficientRicDE| |separateDegrees| |zoom| |times!| + |mergeDifference| |rightRecip| |plus| |startTable!| |monicDivide| + |trapezoidalo| |showTheSymbolTable| |universe| |rst| |f04jgf| + |rootPoly| |replace| |dihedral| |leadingIdeal| |qPot| |paren| + |subHeight| |polygon?| |cothIfCan| |subspace| |rischNormalize| + |reducedDiscriminant| |discriminantEuclidean| |variable| + |commutativeEquality| |ldf2lst| |gcdPrimitive| |degreeSubResultant| + |fortranCharacter| |pmintegrate| |factorset| |screenResolution3D| + |goto| |nextNormalPrimitivePoly| |palgLODE| |iterators| |source| |po| + |aspFilename| |permanent| |returnType!| |times| |outputBinaryFile| + |limitedint| |changeVar| |laplacian| |derivative| |se2rfi| |leftLcm| + |update| |iiGamma| |rename| |zeroDim?| |f01maf| |toroidal| |refine| + |fortranComplex| |infRittWu?| |callForm?| |iiatan| |traverse| + |generators| |scan| |lyndon?| |clipWithRanges| |colorDef| |zCoord| + |target| |symmetricRemainder| |category| |integralDerivationMatrix| + |complementaryBasis| |polar| |factorAndSplit| |pdf2ef| + |resetVariableOrder| |fractionPart| |radicalRoots| |fortranLiteral| + |initTable!| |OMreadFile| |domain| |expPot| |e02ahf| |prime| + |sylvesterSequence| |monom| |quotient| |makeprod| |fill!| |OMgetBVar| + |positiveRemainder| |mathieu23| |pushdterm| |package| |testDim| + |alternatingGroup| |underscore| |jvmDoubleConstantTag| |jvmTransient| + |duplicates| |showTheIFTable| |isList| |basisOfRightAnnihilator| + |normalElement| |goodnessOfFit| |sum| |fortranLiteralLine| |mantissa| + |rowEchelon| |column| |primextendedint| |wholeRagits| |leftRecip| + |genericLeftTrace| |OMencodingUnknown| |headRemainder| |SturmHabicht| + |iiasin| |common| |prinb| |internalSubQuasiComponent?| + |prepareDecompose| |outputAsScript| |d01fcf| |mightHaveRoots| |result| + |expressIdealMember| |mappingMode| |cyclicEntries| |clipBoolean| + |iicoth| |c06gbf| |pr2dmp| |perfectSquare?| |overlabel| |toScale| + |split| |hex| |innerint| |cscIfCan| |stopMusserTrials| |inRadical?| + |minPoints| |numericalOptimization| |cosIfCan| |weights| + |multiEuclidean| |ParCond| |sumOfDivisors| |jvmIntegerConstantTag| + |newSubProgram| |numerator| |iterationVar| |moebius| |d02gaf| + |seriesSolve| |iicsch| |leftReducedSystem| |getGoodPrime| + |var2StepsDefault| |linearMatrix| |shallowCopy| |besselI| |hasHi| + |partialQuotients| |shallowExpand| |rightDiscriminant| |cyclicGroup| + |sumOfKthPowerDivisors| |rank| |limitedIntegrate| |algebraic?| + |deleteProperty!| |invmod| |factorSFBRlcUnit| |bitTruth| |compdegd| + |preprocess| |e02akf| |eigenvector| |minPoly| |putGraph| + |primlimintfrac| |transform| |obj| |subResultantGcdEuclidean| + |jvmInterfaceMethodConstantTag| |oblateSpheroidal| |hdmpToDmp| + |superHeight| |powerSum| |cExp| |writeBytes!| |oddintegers| + |showTheRoutinesTable| |elliptic| |intcompBasis| |completeHermite| + |hash| |airyAi| |associative?| |showTheFTable| |listOfMonoms| + |fixedPoints| |eigenMatrix| |expandLog| |musserTrials| |count| + |createRandomElement| |smith| |modifyPointData| + |resultantEuclideannaif| |stirling2| |OMputVariable| |digamma| + |infLex?| |pseudoRemainder| |sparsityIF| |jvmFieldrefConstantTag| + |leastMonomial| |laurentIfCan| |modularGcdPrimitive| + |semiSubResultantGcdEuclidean1| |elliptic?| |completeHensel| + |distdfact| |lhs| |jvmPrivate| |lazyEvaluate| |youngDiagram| |c06ecf| + |leadingIndex| |numberOfVariables| |fracPart| |hdmpToP| |saturate| + |rhs| |s20acf| |maxRowIndex| |ramified?| |lists| |solid| |parabolic| + |Ei| |interpret| |e04fdf| |discreteLog| |OMsetEncoding| |mapUp!| + |variationOfParameters| |match?| |lexGroebner| |typeForm| |principal?| + |univariatePolynomial| |exprToGenUPS| |doubleDisc| |width| |digits| + |dAndcExp| |d02ejf| |wholeRadix| |newline| |bag| |leftFactor| |d01gbf| + |d02kef| |modifyPoint| |f02bbf| |partition| |nullity| |approximants| + |macroExpand| |OMputAtp| |ode2| |kind| |definingEquations| |pushdown| + |reduceByQuasiMonic| |shape| |csch2sinh| |palglimint| + |jvmNameAndTypeConstantTag| |calcRanges| |cyclotomic| |op| |quatern| + |diagonal| |alternating| |idealiserMatrix| |domainTemplate| |support| + |countRealRootsMultiple| |mkcomm| |parabolicCylindrical| |mainForm| + |real?| |number?| |restorePrecision| |cSin| |plotPolar| |closed?| + |gbasis| |vertConcat| |depth| |subNode?| |cubic| |poisson| + |divisorCascade| |OMunhandledSymbol| |appendPoint| |initiallyReduce| + |linear?| |cycles| |delete!| |ricDsolve| |alternative?| |reverse!| + |splitNodeOf!| |lcm| |d03eef| |numericalIntegration| |readUInt8!| + |optional| |typeLists| |numberOfMonomials| |deepestInitial| + |leadingTerm| |hyperelliptic| |increasePrecision| |laplace| + |mathieu22| |symmetricSquare| |OMread| |leftOne| |explicitlyFinite?| + |enqueue!| |noLinearFactor?| |dimensionOfIrreducibleRepresentation| + |nextNormalPoly| |qroot| |separant| |exists?| |leftMult| |power!| + |createThreeSpace| |cAcoth| |f01rcf| |s15adf| |union| |mainKernel| + |quadraticForm| |symmetric?| |definingInequation| |LiePoly| + |scalarMatrix| |e01sbf| |expIfCan| |drawComplexVectorField| |lookup| + |leadingSupport| |jvmSynchronized| |scripted?| |cTanh| |round| + |completeSmith| |f04qaf| |debug3D| |OMputApp| + |selectNonFiniteRoutines| |s17dgf| |composite| |step| + |transcendentalDecompose| |acschIfCan| |extensionDegree| |coefficient| + |OMreadStr| |autoReduced?| |sinh2csch| |explicitEntries?| |consnewpol| + |infieldint| |nullary| |useSingleFactorBound| |HermiteIntegrate| + |monomialIntPoly| |viewThetaDefault| |evenlambert| |cap| + |compactFraction| |listexp| |list?| |PDESolve| + |removeRoughlyRedundantFactorsInPols| |center| |adaptive3D?| + |subCase?| |skewSFunction| |antisymmetricTensors| |aLinear| |trunc| + |extendedEuclidean| |seriesToOutputForm| |factorial| |fractRadix| + |distance| |ddFact| |OMputBVar| |changeWeightLevel| |credPol| + |chainSubResultants| |external?| |d01asf| |toseInvertibleSet| + |intermediateResultsIF| |weight| |pol| |applyRules| |s14abf| + |getOrder| |OMclose| |identity| |modularGcd| |polyPart| |mapmult| + |f01mcf| |categories| |internalInfRittWu?| |areEquivalent?| |besselJ| + |pmComplexintegrate| |jacobian| |newTypeLists| |contract| |f01ref| + |leftAlternative?| |localUnquote| |randnum| |viewWriteDefault| + |indicialEquation| |option?| |fglmIfCan| |expenseOfEvaluation| + |tanh2trigh| |coefficients| |mapGen| |rootOf| |sech2cosh| |df2mf| + |conjunction| |edf2fi| |d01apf| |d02gbf| |stosePrepareSubResAlgo| + |dmp2rfi| |script| |fixedPoint| |whileLoop| |recip| |nthRootIfCan| + |nthRoot| |readLine!| |changeNameToObjf| |lfunc| |presub| + |initializeGroupForWordProblem| |wrregime| |removeDuplicates| |df2fi| + |accuracyIF| |s17dcf| |Nul| |startStats!| |changeName| + |branchPointAtInfinity?| |meatAxe| |commonDenominator| |oddlambert| + |symmetricDifference| |solid?| |cotIfCan| UP2UTS |bumptab| + |localReal?| |generalizedEigenvectors| |factor1| |orbit| |quasiMonic?| + |tex| |points| |revert| |pascalTriangle| |drawCurves| |asimpson| + |nextPrimitiveNormalPoly| |radicalEigenvector| |inverseLaplace| |mesh| + |setprevious!| |safetyMargin| |wordInStrongGenerators| |lex| |expt| + |operation| |showAll?| |removeZero| |connectTo| |simpsono| + |subNodeOf?| |showArrayValues| |nsqfree| |viewpoint| |OMgetFloat| + |numer| |palglimint0| |normalizedAssociate| |quickSort| |stFunc1| + |biRank| |pointData| |randomLC| |quoted?| |c02aff| |denom| + |rightRemainder| |hue| |rootsOf| |qfactor| |e02daf| + |removeSquaresIfCan| |toseLastSubResultant| |scale| |search| |lquo| + |fortranDouble| |toseInvertible?| |packageCall| |bivariatePolynomials| + |permutations| |setImagSteps| |probablyZeroDim?| |setRealSteps| + |reduceLODE| |squareMatrix| |pi| |tanIfCan| |setStatus!| |f04arf| + |lllip| |tan2cot| |curveColorPalette| |sequences| + |constantToUnaryFunction| |merge!| |genericRightNorm| |infinity| + |btwFact| |OMgetError| |f02akf| |uniform| |viewPosDefault| |presuper| + |leastPower| |directSum| |primPartElseUnitCanonical!| + |subscriptedVariables| |c06eaf| |balancedFactorisation| |OMputSymbol| + |nextSubsetGray| |euclideanNormalForm| |normalizedDivide| + |relativeApprox| |sin?| |iflist2Result| |c05adf| |moduleSum| + |acothIfCan| |multiEuclideanTree| |predicate| |lfintegrate| + |linkToFortran| |OMcloseConn| |kernel| |s21bbf| |legendreP| + |primPartElseUnitCanonical| |bfEntry| |upperCase?| |linearElement| + |reducedQPowers| |readInt32!| |setScreenResolution| |principalIdeal| + |list| |delta| |curve?| |isOpen?| |addPointLast| |argscript| |coerce| + |recur| |prinpolINFO| |close| |compBound| |viewWriteAvailable| |draw| + |particularSolution| |factorials| |lazy?| |is?| |size| + |lazyPremWithDefault| |construct| |showClipRegion| |pdct| |yCoord| + |componentUpperBound| |iiasech| |plenaryPower| |purelyTranscendental?| + |normFactors| |OMgetEndObject| |maxdeg| |freeOf?| |display| + |createNormalPrimitivePoly| |ode| |f02adf| |ipow| |powmod| + |predicates| |chebyshevT| |integral| |curveColor| |iitan| + |antisymmetric?| |relerror| |mainVariable?| |currentCategoryFrame| + |rootSplit| |minColIndex| |OMgetEndBind| |doublyTransitive?| |comment| + |remove!| |printInfo!| |constantOpIfCan| |makeObject| |lfextlimint| + |constantKernel| |integral?| |factorGroebnerBasis| |dimensions| + |d01akf| |fullPartialFraction| |roughUnitIdeal?| |binaryTree| |coef| + |jvmFloatConstantTag| |e02ddf| |numberOfComputedEntries| |tanh2coth| + |elseBranch| |internalSubPolSet?| |gderiv| |sincos| |lepol| |lambda| + |makeMulti| |dequeue!| |errorKind| |eyeDistance| |totalDegree| + |parameters| |true| |input| |curry| |maxrank| |simplifyExp| + |bandedHessian| |summation| |createIrreduciblePoly| + |tubeRadiusDefault| |fillPascalTriangle| |nrows| |setProperties| + |library| |rightGcd| |SFunction| |OMReadError?| |OMputEndAttr| + |anfactor| |varselect| |rational?| |ncols| |OMParseError?| + |resultantReduitEuclidean| |s19acf| |reify| |nodes| + |selectMultiDimensionalRoutines| |node| |useEisensteinCriterion?| + |useEisensteinCriterion| |s21bdf| |assign| |nullSpace| + |squareFreePolynomial| |palgextint0| |rdregime| |OMputString| ** + |bandedJacobian| |quadratic| |totalGroebner| |cyclicParents| |getCode| + |inputOutputBinaryFile| |squareTop| |interpretString| |simplify| + |iicosh| |f02wef| |contractSolve| |lowerCase?| |pushNewContour| + |sec2cos| |radicalSolve| |properties| |tableForDiscreteLogarithm| + |maximumExponent| |shiftRight| |graphStates| |cCoth| + |subQuasiComponent?| |linearlyDependentOverZ?| |rightAlternative?| + |prevPrime| |jacobiIdentity?| |leftUnits| |internalIntegrate0| + |translate| |OMgetEndBVar| |constant?| |infinityNorm| |jvmInterface| + |infieldIntegrate| |nativeModuleExtension| |host| |shiftLeft| + |numberOfOperations| |tanintegrate| |noKaratsuba| |rootProduct| + |complexRoots| |digit?| |double| |eq?| |leader| |withPredicates| + |debug| |headAst| |constantLeft| |f01bsf| |primitive?| |dflist| + |selectfirst| |exponent| |basisOfCenter| |functorData| |log10| + |jvmAbstract| |trailingCoefficient| D |isPlus| |setelt| + |numberOfDivisors| |condition| |factorFraction| |mapCoef| |hclf| + |floor| |e02bef| |complexEigenvectors| |zag| |polyred| + |monicRightFactorIfCan| |asinIfCan| |bitand| |cosh2sech| |setright!| + |leastAffineMultiple| |invertIfCan| |linGenPos| |binomial| |OMgetType| + |SturmHabichtCoefficients| |copy| |terms| |diff| |bitior| |cAsin| + |nthCoef| |permutationRepresentation| |getDatabase| |normalDeriv| + |purelyAlgebraic?| |Aleph| |polygamma| |aromberg| |quasiAlgebraicSet| + |zeroSquareMatrix| |outlineRender| |linearAssociatedLog| |factorList| + |reducedContinuedFraction| |primlimitedint| |charpol| |tube| + |moreAlgebraic?| |torsionIfCan| |isEquiv| |rightFactorCandidate| + |torsion?| |generalizedContinuumHypothesisAssumed| |boundOfCauchy| + |makeFloatFunction| |commutator| |totalDifferential| |cos| + |taylorIfCan| |stiffnessAndStabilityOfODEIF| |show| |separateFactors| + |symbol?| |declare!| |csc2sin| |specialTrigs| |linearForm| |options| + |unitNormal| |trim| |cschIfCan| |cyclotomicDecomposition| |tan| + |zeroMatrix| |associator| |unknown| |pseudoQuotient| |rationalPoints| + |pow| |redmat| |equation| |autoCoerce| |localIntegralBasis| + |rightFactorIfCan| |generalizedInverse| |cot| |trace| |increase| + |coshIfCan| |medialSet| |jacobi| |froot| |build| |regime| |sec| + |getProperty| |normal01| |f02awf| |d03edf| |symmetricGroup| |print| + |logIfCan| |setStatus| |squareFreePart| |outputSpacing| |csc| + |retractable?| |diagonals| |leftExtendedGcd| |basisOfLeftNucleus| + |stoseInvertible?| |resolve| |basisOfRightNucloid| |f01qdf| + |readable?| |localAbs| |asin| |elaborateFile| |tablePow| + |evaluateInverse| |forLoop| |OMlistCDs| |useSingleFactorBound?| + |f02aff| |partialFraction| |OMopenFile| |acos| |pile| |rootBound| + |slash| |gcdcofact| |rewriteIdealWithHeadRemainder| + |radicalOfLeftTraceForm| |algebraicSort| |atan| |lift| + |brillhartTrials| |mapdiv| |segment| |transcendent?| |returns| + |bernoulliB| |leviCivitaSymbol| |startPolynomial| |iicot| + |alphanumeric| |id| |acot| |reduce| |makeSin| |algebraicOf| |sPol| + |rightTrim| |showSummary| |map| |c06gqf| |cot2tan| |iibinom| + |matrixDimensions| |nthr| |lo| |jvmStrict| |asec| |computeCycleLength| + |dimension| |interReduce| |leftTrim| |genericRightMinimalPolynomial| + |f07fef| |compile| |leftGcd| |cdr| |diophantineSystem| |acsc| + |divideIfCan!| |coordinate| |lowerCase!| |showAttributes| |cCosh| + |cLog| |product| |semicolonSeparate| |Lazard2| |factorsOfDegree| + |selectOrPolynomials| |OMgetEndApp| |sinh| |cAcsc| |setPredicates| + |karatsubaOnce| |addBadValue| |collectUpper| |coercePreimagesImages| + |lagrange| |rquo| |resetAttributeButtons| |doubleComplex?| |cosh| + |mpsode| |maxIndex| |pointColorDefault| |alphabetic| |backspace| + |genericLeftDiscriminant| |child?| |e01bef| |point?| |dfRange| + |exprToXXP| |listOfLists| |coord| |tanh| |sumSquares| + |internalIntegrate| |gcdcofactprim| |normalise| |finiteBound| + |safeFloor| |getStream| |totalfract| |minset| |member?| |coth| + |makeop| |infiniteProduct| |PollardSmallFactor| |univcase| |rk4f| + |fortranCompilerName| |isAnd| |iicsc| |readByte!| |normalize| + |branchPoint?| |sech| |exponents| |complexElementary| |sinhIfCan| + |iiasinh| |mainVariables| |isImplies| |delay| + |zeroSetSplitIntoTriangularSystems| |selectODEIVPRoutines| + |numberOfComposites| |csch| |getButtonValue| |setOrder| |bumprow| |Si| + |create3Space| |s13adf| |rubiksGroup| |signAround| |asinh| |setClosed| + |realElementary| |wordInGenerators| |graphState| |flexible?| + |divideIfCan| |positive?| |findBinding| |escape| |palgint| + |stoseInvertible?sqfreg| |acosh| |cSech| |euler| |elementary| + |mergeFactors| |solveInField| |overset?| |nodeOf?| |att2Result| + |cache| |roughSubIdeal?| |atanh| |multiplyCoefficients| + |complexIntegrate| |head| |OMsupportsSymbol?| |omError| |untab| + |chiSquare| |oddInfiniteProduct| |dual| |f02axf| |quartic| |acoth| + |derivationCoordinates| |currentScope| |measure| |complexZeros| + |cRationalPower| |karatsubaDivide| |constant| |f04mcf| + |stoseInvertibleSet| |leftZero| |byte| |ip4Address| + |stoseInvertible?reg| |asech| |e01daf| |rightDivide| |makeViewport3D| + |sayLength| |convert| |OMgetEndError| |intensity| |categoryMode| + |firstNumer| |setchildren!| |splitConstant| |clearTheSymbolTable| + |computeInt| |normalized?| |shift| |power| |associatedEquations| + |tubePlot| |entry?| |LyndonCoordinates| |invertibleElseSplit?| |units| + |BasicMethod| |setAttributeButtonStep| |s21bcf| |multiple| |graeffe| + |var2Steps| |getOperator| |iisec| |internalLastSubResultant| + |nullary?| |updateStatus!| |countRealRoots| |initial| |applyQuote| + |divergence| |content| |integralBasisAtInfinity| |coerceImages| + |cAcsch| |e01bhf| |upperCase| |iiacot| |numberOfChildren| |subPolSet?| + |tab1| |viewport2D| |rotatez| |imagI| |supDimElseRittWu?| + |linearAssociatedOrder| |iFTable| |numberOfHues| |resultantnaif| + |writeByte!| |name| |cAcosh| |OMputFloat| |f04atf| |OMputAttr| + |stoseInvertibleSetreg| |space| |rowEchelonLocal| |fortranInteger| + |e02def| |solveRetract| |representationType| |body| |OMgetApp| + |ruleset| |genericRightDiscriminant| |rightUnits| |critB| |code| + |nextSublist| |cross| |extendedSubResultantGcd| |extractIndex| + |palgextint| |primaryDecomp| |strongGenerators| |numberOfFactors| + |c06frf| |unit?| |flexibleArray| |ScanArabic| + |semiSubResultantGcdEuclidean2| |roughBase?| |setIntersection| + |rational| |iilog| |log2| |LyndonBasis| |identityMatrix| |twist| |rur| + |showAllElements| |isTimes| |removeRedundantFactors| |laguerre| + |isobaric?| |suchThat| |Hausdorff| |key?| |s17ajf| |constDsolve| + |iroot| |ffactor| |iisech| |bytes| |minRowIndex| |imagk| + |initiallyReduced?| |root| |closeComponent| |kroneckerDelta| + |algSplitSimple| |cAcos| |rowEch| |primes| |part?| |iprint| + |gramschmidt| |OMputEndBVar| |OMgetString| |normDeriv2| + |rightRankPolynomial| |resetBadValues| |setColumn!| |f02fjf| + |numerators| |jvmPublic| |less?| |cardinality| |scanOneDimSubspaces| + |Lazard| |generalizedEigenvector| |nonSingularModel| |repSq| |romberg| + |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2196 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2196 (|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#) -2196 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2196 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2196 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2196 (|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) ((-921 $ #3=(-1207)) -2196 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #3#) -2196 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-911 (-391)) |has| |#1| (-911 (-391))) ((-911 (-560)) |has| |#1| (-911 (-560))) ((-909 |#1|) . T) ((-939) -12 (|has| |#1| (-319)) (|has| |#1| (-939))) ((-950) -2196 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1033) -12 (|has| |#1| (-1033)) (|has| |#1| (-1233))) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1082 #0#) -2196 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1082 |#1|) . T) ((-1082 $) . T) ((-1087 #0#) -2196 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1087 |#1|) . T) ((-1087 $) . T) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1182) |has| |#1| (-363)) ((-1233) |has| |#1| (-1233)) ((-1236) |has| |#1| (-1233)) ((-1247) . 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T) ((-236 $) -2196 (-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) -2196 (-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|) . 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T) ((-102) -2271 (|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|) -2271 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2271 (|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)) -2271 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132)))) ((-635 |#2|) |has| |#2| (-1132)) ((-632 (-887)) -2271 (|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 $) -2271 (-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) -2271 (-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)) -2271 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2271 (|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|) -2271 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2271 (|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|) -2271 (|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) -2271 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2271 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1207)) -2271 (-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#) -2271 (-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|) -2271 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2271 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1088) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1132) -2271 (|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))) +((-2363 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-1805 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-2019 (($ (-948)) 62 (|has| |#2| (-1080)) ELT)) (-3069 (((-1303) $ (-560) (-560)) NIL (|has| $ (-6 -4509)) ELT)) (-1909 (($ $ $) 68 (|has| |#2| (-815)) ELT)) (-2699 (((-3 $ "failed") $ $) 53 (|has| |#2| (-133)) ELT)) (-1730 (((-114) $ (-793)) NIL T ELT)) (-3882 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-4047 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4509)) ELT)) (-2773 (($) NIL T CONST)) (-2751 (((-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)) (-2474 (((-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) -2196 (|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 $) -2196 (|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 $) -2196 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2196 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2196 (|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 $) -2196 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2196 (|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))) -((-2243 (((-114) $ $) 20 (|has| |#1| (-102)) ELT)) (-2763 ((|#1| $) 55 T ELT)) (-3172 ((|#1| $) 45 T ELT)) (-3045 (((-114) $ (-793)) 8 T ELT)) (-3525 (($) 7 T CONST)) (-3675 (($ $) 61 T ELT)) (-2372 (($ $) 49 T ELT)) (-4401 ((|#1| |#1| $) 47 T ELT)) (-2151 ((|#1| $) 46 T ELT)) (-3737 (((-663 |#1|) $) 31 (|has| $ (-6 -4508)) ELT)) (-3332 (((-114) $ (-793)) 9 T ELT)) (-3243 (((-663 |#1|) $) 30 (|has| $ (-6 -4508)) ELT)) (-3091 (((-114) |#1| $) 28 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-3324 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4509)) ELT)) (-2260 (($ (-1 |#1| |#1|) $) 36 T ELT)) (-1634 (((-114) $ (-793)) 10 T ELT)) (-2946 (((-793) $) 62 T ELT)) (-3358 (((-1189) $) 23 (|has| |#1| (-1132)) ELT)) (-1878 ((|#1| $) 40 T ELT)) (-4386 ((|#1| |#1| $) 53 T ELT)) (-2759 ((|#1| |#1| $) 52 T ELT)) (-3888 (($ |#1| $) 41 T ELT)) (-3827 (((-793) $) 56 T ELT)) (-3376 (((-1151) $) 22 (|has| |#1| (-1132)) ELT)) (-3893 ((|#1| $) 63 T ELT)) (-2599 ((|#1| $) 51 T ELT)) (-4169 ((|#1| $) 50 T ELT)) (-2796 ((|#1| $) 42 T ELT)) (-2086 (((-114) (-1 (-114) |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-2371 (($ $ (-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)) (-1736 (((-114) $ $) 14 T ELT)) (-3464 ((|#1| |#1| $) 59 T ELT)) (-2706 (((-114) $) 11 T ELT)) (-2832 (($) 12 T ELT)) (-3483 ((|#1| $) 60 T ELT)) (-4206 (($) 58 T ELT) (($ (-663 |#1|)) 57 T ELT)) (-3063 (((-793) $) 44 T ELT)) (-3384 (((-793) (-1 (-114) |#1|) $) 32 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 29 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-4107 (($ $) 13 T ELT)) (-3913 (((-887) $) 18 (|has| |#1| (-632 (-887))) ELT)) (-1373 ((|#1| $) 54 T ELT)) (-3925 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-3184 (($ (-663 |#1|)) 43 T ELT)) (-1855 ((|#1| $) 64 T ELT)) (-2149 (((-114) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT)) (-2340 (((-114) $ $) 19 (|has| |#1| (-102)) ELT)) (-2256 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) +((-3055 (*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)))) (-1500 (*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)))) (-3137 (*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)))) (-3137 (*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)))) (-2005 (*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)))) (-3415 (*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))))) (-3686 (*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)))) (-3415 (*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))))) (-3686 (*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)))) (-4449 (*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)))) (-4030 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-815)) (-4 *2 (-277 *4)))) (-4382 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-3611 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-3055 (*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 -3055 ((-1 $ (-793)) |t#2|)) (-15 -1500 ((-663 |t#2|) $)) (-15 -3137 ((-793) $ |t#2|)) (-15 -3137 ((-793) $)) (-15 -2005 ((-793) $ |t#2|)) (-15 -3415 ((-663 (-793)) $)) (-15 -3686 ((-793) $)) (-15 -3415 ((-663 (-793)) $ |t#2|)) (-15 -3686 ((-793) $ |t#2|)) (-15 -4449 ((-114) $)) (-15 -4030 (|t#3| $)) (-15 -4382 ($ $)) (-15 -3611 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -3055 ((-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 $) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2271 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-887)) . T) ((-175) -2271 (|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 $) -2271 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2271 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2271 (|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) -2271 (|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 $) -2271 (|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 $) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1207)) -2271 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-921 $ |#3|) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-927 |#3|) . T) ((-929 #2#) -2271 (|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 $) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2271 (|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))) +((-2363 (((-114) $ $) 20 (|has| |#1| (-102)) ELT)) (-1882 ((|#1| $) 55 T ELT)) (-1987 ((|#1| $) 45 T ELT)) (-1730 (((-114) $ (-793)) 8 T ELT)) (-2773 (($) 7 T CONST)) (-2196 (($ $) 61 T ELT)) (-3587 (($ $) 49 T ELT)) (-1897 ((|#1| |#1| $) 47 T ELT)) (-2970 ((|#1| $) 46 T ELT)) (-3067 (((-663 |#1|) $) 31 (|has| $ (-6 -4508)) ELT)) (-2941 (((-114) $ (-793)) 9 T ELT)) (-1341 (((-663 |#1|) $) 30 (|has| $ (-6 -4508)) ELT)) (-4265 (((-114) |#1| $) 28 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-1418 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4509)) ELT)) (-4198 (($ (-1 |#1| |#1|) $) 36 T ELT)) (-4481 (((-114) $ (-793)) 10 T ELT)) (-3057 (((-793) $) 62 T ELT)) (-1486 (((-1189) $) 23 (|has| |#1| (-1132)) ELT)) (-3059 ((|#1| $) 40 T ELT)) (-3104 ((|#1| |#1| $) 53 T ELT)) (-2730 ((|#1| |#1| $) 52 T ELT)) (-3177 (($ |#1| $) 41 T ELT)) (-3024 (((-793) $) 56 T ELT)) (-3468 (((-1151) $) 22 (|has| |#1| (-1132)) ELT)) (-2408 ((|#1| $) 63 T ELT)) (-1566 ((|#1| $) 51 T ELT)) (-2086 ((|#1| $) 50 T ELT)) (-2979 ((|#1| $) 42 T ELT)) (-1477 (((-114) (-1 (-114) |#1|) $) 33 (|has| $ (-6 -4508)) ELT)) (-2448 (($ $ (-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)) (-4029 (((-114) $ $) 14 T ELT)) (-3606 ((|#1| |#1| $) 59 T ELT)) (-3032 (((-114) $) 11 T ELT)) (-2120 (($) 12 T ELT)) (-3941 ((|#1| $) 60 T ELT)) (-2671 (($) 58 T ELT) (($ (-663 |#1|)) 57 T ELT)) (-3574 (((-793) $) 44 T ELT)) (-3477 (((-793) (-1 (-114) |#1|) $) 32 (|has| $ (-6 -4508)) ELT) (((-793) |#1| $) 29 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4508))) ELT)) (-4069 (($ $) 13 T ELT)) (-3871 (((-887) $) 18 (|has| |#1| (-632 (-887))) ELT)) (-2259 ((|#1| $) 54 T ELT)) (-2493 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-3533 (($ (-663 |#1|)) 43 T ELT)) (-2708 ((|#1| $) 64 T ELT)) (-2777 (((-114) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4508)) ELT)) (-2405 (((-114) $ $) 19 (|has| |#1| (-102)) ELT)) (-2375 (((-793) $) 6 (|has| $ (-6 -4508)) ELT))) (((-263 |#1|) (-142) (-1247)) (T -263)) -((-4206 (*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-4206 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1247)) (-4 *1 (-263 *3)))) (-3827 (*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1247)) (-5 *2 (-793)))) (-2763 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-1373 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-4386 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-2759 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-2599 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-4169 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247)))) (-2372 (*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1247))))) -(-13 (-1152 |t#1|) (-1026 |t#1|) (-10 -8 (-15 -4206 ($)) (-15 -4206 ($ (-663 |t#1|))) (-15 -3827 ((-793) $)) (-15 -2763 (|t#1| $)) (-15 -1373 (|t#1| $)) (-15 -4386 (|t#1| |t#1| $)) (-15 -2759 (|t#1| |t#1| $)) (-15 -2599 (|t#1| $)) (-15 -4169 (|t#1| $)) (-15 -2372 ($ $)))) -(((-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))) -2196 (|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) -2196 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1088) -2196 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1143) -2196 (|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))) -2271 (|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) -2271 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1088) -2271 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1143) -2271 (|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) ((-102) -2196 (|has| |#1| (-1132)) (|has| |#1| (-871)) (|has| |#1| (-102))) ((-632 (-887)) -2196 (|has| |#1| (-1132)) (|has| |#1| (-871)) (|has| |#1| (-632 (-887)))) ((-153 |#1|) . T) ((-637 (-663 |#1|)) . T) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-298 #0=(-560) |#1|) . T) ((-298 (-1264 (-560)) $) . T) ((-300 #0# |#1|) . T) ((-321 |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-385 |#1|) . T) ((-503 |#1|) . T) ((-618 #0# |#1|) . T) ((-528 |#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ((-673 |#1|) . T) ((-19 |#1|) . T) ((-871) |has| |#1| (-871)) ((-874) |has| |#1| (-871)) ((-1132) -2196 (|has| |#1| (-1132)) (|has| |#1| (-871))) ((-1247) . T) ((-1296 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2196 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2196 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2196 (|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) -2196 (|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) -2196 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2196 (|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#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2196 (|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) -2271 (|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) -2271 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2271 (|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#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2271 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2271 (|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#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2271 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2271 (|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 $) -2196 (|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 $ $) -2196 (|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#) -2196 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2196 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2196 (|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) -2196 (|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) -2196 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2196 (|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 $) -2196 (|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 $) -2196 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2196 (|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 $) -2271 (|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 $ $) -2271 (|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#) -2271 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2271 (|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) -2271 (|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) -2271 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2271 (|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 $) -2271 (|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 $) -2271 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1207)) -2271 (|has| |#1| (-929 (-1207))) (|has| |#1| (-927 (-1207)))) ((-927 #2#) . T) ((-927 (-1207)) |has| |#1| (-927 (-1207))) ((-929 #2#) . T) ((-929 #4#) -2271 (|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 $) -2271 (|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 $) -2271 (|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#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2271 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2271 (|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#) -2271 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2271 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2271 (|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))) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2196 (|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) -2196 (|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) -2196 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2196 (|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#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2196 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2196 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 $) -2196 (|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 $) -2196 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2196 (|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 $ $) -2271 (|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) -2271 (|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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3472764 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472739 3472744 3472749 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472724 3472729 3472734 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472709 3472714 3472719 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471696 3472584 3472661 "ZMOD" 3472666 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3470732 3470914 3471137 "ZLINDEP" 3471528 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3459894 3461800 3463772 "ZDSOLVE" 3468862 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459128 3459281 3459470 "YSTREAM" 3459740 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458488 3458797 3458912 "YDIAGRAM" 3459035 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3455936 3457789 3457993 "XRPOLY" 3458331 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452203 3453807 3454382 "XPR" 3455408 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449534 3451210 3451265 "XPOLYC" 3451553 NIL XPOLYC (NIL T T) -9 NIL 3451666 NIL) (-1319 3446929 3448865 3449069 "XPOLY" 3449365 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3442875 3445446 3445834 "XPBWPOLY" 3446587 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3437767 3439346 3439401 "XFALG" 3441573 NIL XFALG (NIL T T) -9 NIL 3442362 NIL) (-1316 3433036 3435743 3435785 "XF" 3436406 NIL XF (NIL T) -9 NIL 3436806 NIL) (-1315 3432633 3432745 3432914 "XF-" 3432919 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3431748 3431870 3432075 "XEXPPKG" 3432525 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429489 3431598 3431694 "XDPOLY" 3431699 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428144 3428882 3428925 "XALG" 3428930 NIL XALG (NIL T) -9 NIL 3429041 NIL) (-1311 3421054 3426121 3426615 "WUTSET" 3427736 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419156 3420106 3420429 "WP" 3420865 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418704 3418978 3419048 "WHILEAST" 3419108 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418116 3418421 3418515 "WHEREAST" 3418632 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3416990 3417200 3417495 "WFFINTBS" 3417913 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3414858 3415321 3415783 "WEIER" 3416562 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3413782 3414340 3414382 "VSPACE" 3414518 NIL VSPACE (NIL T) -9 NIL 3414592 NIL) (-1304 3413614 3413647 3413738 "VSPACE-" 3413743 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413411 3413465 3413533 "VOID" 3413568 T VOID (NIL) -8 NIL NIL NIL) (-1302 3409679 3410474 3411211 "VIEWDEF" 3412696 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3398623 3401227 3403400 "VIEW3D" 3407528 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3390640 3392534 3394113 "VIEW2D" 3397066 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3388740 3389135 3389541 "VIEW" 3390256 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3387293 3387576 3387894 "VECTOR2" 3388470 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3382199 3387063 3387155 "VECTOR" 3387236 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3375153 3379903 3379946 "VECTCAT" 3380941 NIL VECTCAT (NIL T) -9 NIL 3381528 NIL) (-1295 3374095 3374421 3374811 "VECTCAT-" 3374816 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373501 3373746 3373866 "VARIABLE" 3374010 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373434 3373439 3373469 "UTYPE" 3373474 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372242 3372418 3372680 "UTSODETL" 3373260 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369634 3370142 3370666 "UTSODE" 3371783 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3359641 3365567 3365610 "UTSCAT" 3366722 NIL UTSCAT (NIL T) -9 NIL 3367480 NIL) (-1289 3356767 3357711 3358700 "UTSCAT-" 3358705 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3356388 3356437 3356570 "UTS2" 3356718 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3347698 3354149 3354629 "UTS" 3355966 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3341565 3344508 3344551 "URAGG" 3346621 NIL URAGG (NIL T) -9 NIL 3347344 NIL) (-1285 3338288 3339367 3340490 "URAGG-" 3340495 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333657 3336923 3337388 "UPXSSING" 3337952 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3326072 3333561 3333633 "UPXSCONS" 3333638 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3314820 3322274 3322336 "UPXSCCA" 3322910 NIL UPXSCCA (NIL T T) -9 NIL 3323143 NIL) (-1281 3314440 3314543 3314717 "UPXSCCA-" 3314722 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3303088 3310267 3310310 "UPXSCAT" 3310958 NIL UPXSCAT (NIL T) -9 NIL 3311567 NIL) (-1279 3302512 3302597 3302776 "UPXS2" 3303003 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3293990 3301894 3302158 "UPXS" 3302306 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3292626 3292897 3293248 "UPSQFREE" 3293733 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285454 3288892 3288947 "UPSCAT" 3290027 NIL UPSCAT (NIL T T) -9 NIL 3290793 NIL) (-1275 3284610 3284865 3285192 "UPSCAT-" 3285197 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3284231 3284280 3284413 "UPOLYC2" 3284561 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3268365 3277358 3277401 "UPOLYC" 3279502 NIL UPOLYC (NIL T) -9 NIL 3280723 NIL) (-1272 3259213 3262119 3265266 "UPOLYC-" 3265271 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3258534 3258659 3258823 "UPMP" 3259102 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3258081 3258168 3258307 "UPDIVP" 3258447 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3256619 3256898 3257214 "UPDECOMP" 3257830 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3255832 3255962 3256148 "UPCDEN" 3256503 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3255345 3255420 3255569 "UP2" 3255757 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3245920 3255028 3255157 "UP" 3255264 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3245125 3245262 3245467 "UNISEG2" 3245763 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3243478 3244329 3244606 "UNISEG" 3244883 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3242520 3242718 3242944 "UNIFACT" 3243294 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3229230 3242424 3242496 "ULSCONS" 3242501 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3209030 3222310 3222372 "ULSCCAT" 3223010 NIL ULSCCAT (NIL T T) -9 NIL 3223299 NIL) (-1260 3208026 3208325 3208713 "ULSCCAT-" 3208718 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3196471 3203572 3203615 "ULSCAT" 3204478 NIL ULSCAT (NIL T) -9 NIL 3205209 NIL) (-1258 3195895 3195980 3196159 "ULS2" 3196386 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3177705 3195207 3195449 "ULS" 3195711 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3176620 3177320 3177434 "UINT8" 3177545 T UINT8 (NIL) -8 NIL NIL 3177637) (-1255 3175534 3176234 3176348 "UINT64" 3176459 T UINT64 (NIL) -8 NIL NIL 3176551) (-1254 3174448 3175148 3175262 "UINT32" 3175373 T UINT32 (NIL) -8 NIL NIL 3175465) (-1253 3173362 3174062 3174176 "UINT16" 3174287 T UINT16 (NIL) -8 NIL NIL 3174379) (-1252 3171441 3172608 3172638 "UFD" 3172850 T UFD (NIL) -9 NIL 3172964 NIL) (-1251 3171223 3171281 3171376 "UFD-" 3171381 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170281 3170488 3170704 "UDVO" 3171029 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168047 3168506 3168977 "UDPO" 3169845 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167759 3168002 3168033 "TYPEAST" 3168038 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3167692 3167697 3167727 "TYPE" 3167732 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166645 3166865 3167105 "TWOFACT" 3167486 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165620 3166054 3166289 "TUPLE" 3166445 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163257 3163830 3164369 "TUBETOOL" 3165103 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162063 3162304 3162546 "TUBE" 3163050 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3150205 3154820 3154917 "TSETCAT" 3160186 NIL TSETCAT (NIL T T T T) -9 NIL 3161718 NIL) (-1241 3144673 3146537 3148428 "TSETCAT-" 3148433 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3138852 3143645 3143928 "TS" 3144425 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3133325 3134338 3135267 "TRMANIP" 3137988 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3132754 3132829 3132992 "TRIMAT" 3133257 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130566 3130857 3131214 "TRIGMNIP" 3132503 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130050 3130199 3130229 "TRIGCAT" 3130442 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129695 3129798 3129939 "TRIGCAT-" 3129944 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126309 3128553 3128834 "TREE" 3129449 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125415 3126111 3126141 "TRANFUN" 3126176 T TRANFUN (NIL) -9 NIL 3126242 NIL) (-1232 3124634 3124885 3125165 "TRANFUN-" 3125170 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124432 3124470 3124531 "TOPSP" 3124595 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3123762 3123895 3124049 "TOOLSIGN" 3124313 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122276 3122939 3123178 "TEXTFILE" 3123545 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3122051 3122088 3122160 "TEX1" 3122239 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3119855 3120504 3120933 "TEX" 3121644 T TEX (NIL) -8 NIL NIL NIL) (-1226 3119491 3119566 3119656 "TEMUTL" 3119787 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117585 3117925 3118250 "TBCMPPK" 3119214 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108912 3115671 3115727 "TBAGG" 3116127 NIL TBAGG (NIL T T) -9 NIL 3116338 NIL) (-1223 3103796 3105470 3107224 "TBAGG-" 3107229 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103162 3103287 3103432 "TANEXP" 3103685 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102613 3102937 3103027 "TALGOP" 3103107 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3102007 3102124 3102262 "TABLEAU" 3102510 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095021 3101864 3101957 "TABLE" 3101962 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089551 3090849 3092097 "TABLBUMP" 3093807 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3088761 3088920 3089101 "SYSTEM" 3089392 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085166 3085919 3086702 "SYSSOLP" 3088012 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084928 3085121 3085152 "SYSPTR" 3085157 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3083763 3084455 3084581 "SYSNNI" 3084767 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084859) (-1213 3082966 3083521 3083600 "SYSINT" 3083660 NIL SYSINT (NIL NIL) -8 NIL NIL 3083705) (-1212 3079064 3080244 3080954 "SYNTAX" 3082278 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076144 3076824 3077456 "SYMTAB" 3078454 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071243 3072295 3073278 "SYMS" 3075183 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068142 3070694 3070927 "SYMPOLY" 3071045 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067647 3067734 3067857 "SYMFUNC" 3068054 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063445 3064959 3065772 "SYMBOL" 3066856 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056918 3058673 3060393 "SWITCH" 3061747 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049672 3055874 3056168 "SUTS" 3056682 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041150 3049054 3049318 "SUPXS" 3049466 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040297 3040436 3040653 "SUPFRACF" 3041018 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3039912 3039977 3040090 "SUP2" 3040232 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030435 3039530 3039656 "SUP" 3039821 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3028859 3029157 3029513 "SUMRF" 3030134 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028182 3028260 3028452 "SUMFS" 3028780 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010027 3027494 3027736 "SULS" 3027998 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009575 3009849 3009919 "SUCHTAST" 3009979 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3008816 3009100 3009240 "SUCH" 3009483 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002455 3003722 3004681 "SUBSPACE" 3007904 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001875 3001975 3002139 "SUBRESP" 3002343 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2995886 2997168 2998315 "STTFNC" 3000775 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989080 2990551 2991862 "STTF" 2994622 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980197 2982262 2984056 "STTAYLOR" 2987321 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972951 2980061 2980144 "STRTBL" 2980149 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967348 2972660 2972759 "STRING" 2972874 T STRING (NIL) -8 NIL NIL NIL) (-1188 2966852 2966935 2967079 "STREAM3" 2967265 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2965816 2966017 2966252 "STREAM2" 2966665 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965498 2965556 2965649 "STREAM1" 2965758 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957608 2963117 2963728 "STREAM" 2964922 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956600 2956805 2957036 "STINPROD" 2957424 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955715 2956089 2956237 "STEPAST" 2956474 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955211 2955463 2955493 "STEP" 2955573 T STEP (NIL) -9 NIL 2955651 NIL) (-1181 2948267 2955110 2955187 "STBL" 2955192 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2942825 2947430 2947473 "STAGG" 2947626 NIL STAGG (NIL T) -9 NIL 2947715 NIL) (-1179 2940377 2941129 2942001 "STAGG-" 2942006 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938349 2940147 2940239 "STACK" 2940320 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930356 2936490 2936946 "SREGSET" 2937979 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922703 2924150 2925663 "SRDCMPK" 2928962 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915012 2920062 2920092 "SRAGG" 2921395 T SRAGG (NIL) -9 NIL 2922003 NIL) (-1174 2913963 2914284 2914663 "SRAGG-" 2914668 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907547 2912910 2913331 "SQMATRIX" 2913589 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900959 2904265 2904992 "SPLTREE" 2906892 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896784 2897615 2898261 "SPLNODE" 2900385 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895759 2896064 2896094 "SPFCAT" 2896538 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894454 2894706 2894970 "SPECOUT" 2895517 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885100 2887418 2887448 "SPADXPT" 2892126 T SPADXPT (NIL) -9 NIL 2894292 NIL) (-1167 2884855 2884901 2884970 "SPADPRSR" 2885053 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882458 2884810 2884841 "SPADAST" 2884846 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874059 2876162 2876205 "SPACEC" 2880578 NIL SPACEC (NIL T) -9 NIL 2882394 NIL) (-1164 2871859 2873991 2874040 "SPACE3" 2874045 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870591 2870782 2871073 "SORTPAK" 2871664 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868653 2868986 2869398 "SOLVETRA" 2870255 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867691 2867925 2868186 "SOLVESER" 2868426 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862923 2863883 2864878 "SOLVERAD" 2866743 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858648 2859347 2860076 "SOLVEFOR" 2862290 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852259 2857996 2858093 "SNTSCAT" 2858098 NIL SNTSCAT (NIL T T T T) -9 NIL 2858168 NIL) (-1157 2845803 2850582 2850973 "SMTS" 2851949 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839518 2845691 2845768 "SMP" 2845773 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837647 2837978 2838376 "SMITH" 2839215 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829179 2834226 2834329 "SMATCAT" 2835680 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836230 NIL) (-1153 2825951 2826942 2828120 "SMATCAT-" 2828125 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823420 2825159 2825202 "SKAGG" 2825463 NIL SKAGG (NIL T) -9 NIL 2825598 NIL) (-1151 2818914 2822893 2823077 "SINT" 2823229 T SINT (NIL) -8 NIL NIL 2823391) (-1150 2818680 2818724 2818790 "SIMPAN" 2818870 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817500 2817739 2818014 "SIGNRF" 2818439 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816315 2816484 2816768 "SIGNEF" 2817329 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815555 2815898 2816022 "SIGAST" 2816213 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814780 2815090 2815230 "SIG" 2815437 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812432 2812924 2813430 "SHP" 2814321 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805805 2812333 2812409 "SHDP" 2812414 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805316 2805556 2805586 "SGROUP" 2805679 T SGROUP (NIL) -9 NIL 2805741 NIL) (-1142 2805168 2805200 2805273 "SGROUP-" 2805278 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801887 2802657 2803380 "SGCF" 2804467 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795596 2801333 2801430 "SFRTCAT" 2801435 NIL SFRTCAT (NIL T T T T) -9 NIL 2801474 NIL) (-1139 2788915 2790035 2791171 "SFRGCD" 2794579 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781933 2783114 2784300 "SFQCMPK" 2787848 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781535 2781642 2781753 "SFORT" 2781874 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780461 2781375 2781496 "SEXOF" 2781501 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776050 2776957 2777052 "SEXCAT" 2779674 NIL SEXCAT (NIL T T T T T) -9 NIL 2780234 NIL) (-1134 2774965 2775931 2775999 "SEX" 2776004 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773087 2773678 2773983 "SETMN" 2774706 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772617 2772805 2772835 "SETCAT" 2772952 T SETCAT (NIL) -9 NIL 2773037 NIL) (-1131 2772385 2772449 2772548 "SETCAT-" 2772553 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768488 2770846 2770889 "SETAGG" 2771759 NIL SETAGG (NIL T) -9 NIL 2772099 NIL) (-1129 2767910 2768062 2768299 "SETAGG-" 2768304 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764719 2767844 2767892 "SET" 2767897 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764102 2764415 2764516 "SEQAST" 2764640 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763229 2763595 2763656 "SEGXCAT" 2763942 NIL SEGXCAT (NIL T T) -9 NIL 2764062 NIL) (-1125 2762154 2762422 2762465 "SEGCAT" 2762987 NIL SEGCAT (NIL T) -9 NIL 2763208 NIL) (-1124 2761769 2761834 2761947 "SEGBIND2" 2762089 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760659 2761132 2761340 "SEGBIND" 2761596 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760178 2760460 2760537 "SEGAST" 2760604 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759387 2759523 2759727 "SEG2" 2760022 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758303 2759053 2759235 "SEG" 2759240 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757536 2758238 2758285 "SDVAR" 2758290 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748887 2757306 2757436 "SDPOL" 2757441 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747456 2747746 2748065 "SCPKG" 2748602 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746578 2746792 2746984 "SCOPE" 2747286 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745774 2745932 2746111 "SCACHE" 2746433 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745358 2745592 2745622 "SASTCAT" 2745627 T SASTCAT (NIL) -9 NIL 2745640 NIL) (-1113 2744761 2745193 2745269 "SAOS" 2745304 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744320 2744361 2744534 "SAERFFC" 2744720 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2743907 2743948 2744107 "SAEFACT" 2744279 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2736934 2743804 2743884 "SAE" 2743889 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735237 2735569 2735970 "RURPK" 2736600 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733814 2734180 2734485 "RULESET" 2735071 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733384 2733608 2733691 "RULECOLD" 2733766 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730499 2731137 2731595 "RULE" 2733065 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730283 2730317 2730388 "RTVALUE" 2730450 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729694 2730000 2730094 "RSTRCAST" 2730211 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724464 2725337 2726257 "RSETGCD" 2728893 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713035 2718772 2718869 "RSETCAT" 2722988 NIL RSETCAT (NIL T T T T) -9 NIL 2724085 NIL) (-1101 2710854 2711501 2712325 "RSETCAT-" 2712330 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703162 2704616 2706136 "RSDCMPK" 2709453 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701031 2701594 2701668 "RRCC" 2702754 NIL RRCC (NIL T T) -9 NIL 2703098 NIL) (-1098 2700352 2700556 2700835 "RRCC-" 2700840 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699735 2700048 2700149 "RPTAST" 2700273 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672121 2682847 2682914 "RPOLCAT" 2693580 NIL RPOLCAT (NIL T T T) -9 NIL 2696740 NIL) (-1095 2663091 2665959 2669081 "RPOLCAT-" 2669086 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653544 2661302 2661784 "ROUTINE" 2662631 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649593 2653170 2653310 "ROMAN" 2653426 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647705 2648453 2648713 "ROIRC" 2649398 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643423 2646194 2646224 "RNS" 2646528 T RNS (NIL) -9 NIL 2646802 NIL) (-1090 2641830 2642315 2642849 "RNS-" 2642924 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640791 2641195 2641397 "RNGBIND" 2641681 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640084 2640588 2640618 "RNG" 2640623 T RNG (NIL) -9 NIL 2640644 NIL) (-1087 2639379 2639857 2639900 "RMODULE" 2639905 NIL RMODULE (NIL T) -9 NIL 2639932 NIL) (-1086 2638203 2638309 2638645 "RMCAT2" 2639280 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634705 2637549 2637846 "RMATRIX" 2637965 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627204 2629792 2629907 "RMATCAT" 2633266 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634248 NIL) (-1083 2626543 2626726 2627033 "RMATCAT-" 2627038 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626116 2626330 2626373 "RLINSET" 2626435 NIL RLINSET (NIL T) -9 NIL 2626479 NIL) (-1081 2625677 2625758 2625886 "RINTERP" 2626035 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624601 2625275 2625305 "RING" 2625361 T RING (NIL) -9 NIL 2625453 NIL) (-1079 2624381 2624437 2624534 "RING-" 2624539 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623192 2623459 2623717 "RIDIST" 2624145 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613817 2622660 2622866 "RGCHAIN" 2623040 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613075 2613559 2613600 "RGBCSPC" 2613658 NIL RGBCSPC (NIL T) -9 NIL 2613710 NIL) (-1075 2612141 2612600 2612641 "RGBCMDL" 2612873 NIL RGBCMDL (NIL T) -9 NIL 2612987 NIL) (-1074 2611781 2611850 2611953 "RFFACTOR" 2612072 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611500 2611541 2611638 "RFFACT" 2611740 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609551 2609981 2610363 "RFDIST" 2611140 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606491 2607159 2607829 "RF" 2608915 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2605938 2606036 2606199 "RETSOL" 2606393 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605556 2605654 2605697 "RETRACT" 2605830 NIL RETRACT (NIL T) -9 NIL 2605917 NIL) (-1068 2605399 2605430 2605517 "RETRACT-" 2605522 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604947 2605221 2605291 "RETAST" 2605351 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597297 2604600 2604727 "RESULT" 2604842 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595732 2596566 2596765 "RESRING" 2597200 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595356 2595417 2595515 "RESLATC" 2595669 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595055 2595096 2595203 "REPSQ" 2595315 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594746 2594787 2594898 "REPDB" 2595014 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588578 2590035 2591258 "REP2" 2593558 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2584881 2585636 2586444 "REP1" 2587805 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582261 2582883 2583485 "REP" 2584301 T REP (NIL) -7 NIL NIL NIL) (-1058 2574269 2580402 2580858 "REGSET" 2581891 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572978 2573417 2573667 "REF" 2574054 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572343 2572458 2572625 "REDORDER" 2572862 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567707 2571556 2571783 "RECLOS" 2572171 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566741 2566940 2567155 "REALSOLV" 2567514 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563188 2564026 2564910 "REAL0Q" 2565906 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558741 2559777 2560838 "REAL0" 2562169 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558575 2558628 2558658 "REAL" 2558663 T REAL (NIL) -9 NIL 2558698 NIL) (-1050 2557986 2558292 2558386 "RDUCEAST" 2558503 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557385 2557463 2557670 "RDIV" 2557908 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556435 2556627 2556840 "RDIST" 2557207 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555020 2555319 2555691 "RDETRS" 2556143 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552814 2553286 2553824 "RDETR" 2554562 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551433 2551717 2552114 "RDEEFS" 2552530 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549936 2550248 2550673 "RDEEF" 2551121 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543413 2546890 2546920 "RCFIELD" 2548215 T RCFIELD (NIL) -9 NIL 2548946 NIL) (-1042 2541369 2541981 2542677 "RCFIELD-" 2542752 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537421 2539442 2539485 "RCAGG" 2540569 NIL RCAGG (NIL T) -9 NIL 2541034 NIL) (-1040 2537031 2537143 2537306 "RCAGG-" 2537311 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536348 2536478 2536643 "RATRET" 2536915 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535889 2535968 2536089 "RATFACT" 2536276 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535167 2535317 2535469 "RANDSRC" 2535759 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534895 2534945 2535018 "RADUTIL" 2535116 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527019 2533726 2534037 "RADIX" 2534618 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516613 2526861 2526991 "RADFF" 2526996 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516242 2516335 2516365 "RADCAT" 2516525 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516012 2516072 2516172 "RADCAT-" 2516177 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513923 2515782 2515874 "QUEUE" 2515955 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513548 2513597 2513728 "QUATCT2" 2513874 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2505924 2509971 2510013 "QUATCAT" 2510804 NIL QUATCAT (NIL T) -9 NIL 2511570 NIL) (-1028 2501805 2503100 2504490 "QUATCAT-" 2504586 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497644 2501738 2501786 "QUAT" 2501791 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2494900 2496692 2496735 "QUAGG" 2497116 NIL QUAGG (NIL T) -9 NIL 2497291 NIL) (-1025 2494448 2494722 2494792 "QQUTAST" 2494852 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493359 2493961 2494126 "QFORM" 2494329 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2492984 2493033 2493164 "QFCAT2" 2493310 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482660 2488831 2488873 "QFCAT" 2489541 NIL QFCAT (NIL T) -9 NIL 2490542 NIL) (-1021 2477975 2479428 2481022 "QFCAT-" 2481118 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477406 2477540 2477672 "QEQUAT" 2477865 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470424 2471605 2472791 "QCMPACK" 2476339 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469653 2469835 2470071 "QALGSET2" 2470242 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467103 2467639 2468069 "QALGSET" 2469308 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465770 2466012 2466331 "PWFFINTB" 2466876 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463915 2464113 2464469 "PUSHVAR" 2465584 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459642 2460858 2460901 "PTRANFN" 2462812 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457979 2458324 2458648 "PTPACK" 2459353 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457602 2457665 2457776 "PTFUNC2" 2457916 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451527 2456391 2456434 "PTCAT" 2456734 NIL PTCAT (NIL T) -9 NIL 2456887 NIL) (-1010 2451176 2451217 2451343 "PSQFR" 2451486 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449748 2450064 2450400 "PSEUDLIN" 2450874 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436268 2438843 2441169 "PSETPK" 2447508 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428976 2432004 2432102 "PSETCAT" 2435143 NIL PSETCAT (NIL T T T T) -9 NIL 2435957 NIL) (-1006 2426701 2427443 2428267 "PSETCAT-" 2428272 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426014 2426209 2426239 "PSCURVE" 2426511 T PSCURVE (NIL) -9 NIL 2426678 NIL) (-1004 2421730 2423504 2423571 "PSCAT" 2424423 NIL PSCAT (NIL T T T) -9 NIL 2424663 NIL) (-1003 2420724 2421006 2421409 "PSCAT-" 2421414 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418923 2419783 2420048 "PRTITION" 2420481 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418334 2418640 2418734 "PRTDAST" 2418851 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407178 2409600 2411790 "PRS" 2416196 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404798 2406500 2406540 "PRQAGG" 2406723 NIL PRQAGG (NIL T) -9 NIL 2406825 NIL) (-998 2403977 2404426 2404454 "PROPLOG" 2404593 T PROPLOG (NIL) -9 NIL 2404708 NIL) (-997 2403575 2403638 2403761 "PROPFUN2" 2403900 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402872 2403011 2403183 "PROPFUN1" 2403436 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400851 2401619 2401916 "PROPFRML" 2402608 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400296 2400427 2400555 "PROPERTY" 2400743 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394184 2398462 2399282 "PRODUCT" 2399522 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2393974 2394012 2394071 "PRINT" 2394145 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393290 2393431 2393583 "PRIMES" 2393854 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391337 2391756 2392222 "PRIMELT" 2392869 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391054 2391115 2391143 "PRIMCAT" 2391267 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390043 2390239 2390467 "PRIMARR2" 2390872 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385765 2389981 2390026 "PRIMARR" 2390031 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385402 2385464 2385575 "PREASSOC" 2385703 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382360 2384860 2385094 "PR" 2385213 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381811 2381968 2381996 "PPCURVE" 2382201 T PPCURVE (NIL) -9 NIL 2382337 NIL) (-983 2381358 2381606 2381689 "PORTNUM" 2381748 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378695 2379116 2379708 "POLYROOT" 2380939 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378072 2378136 2378370 "POLYLIFT" 2378631 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374293 2374796 2375425 "POLYCATQ" 2377617 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2359941 2366040 2366105 "POLYCAT" 2369619 NIL POLYCAT (NIL T T T) -9 NIL 2371497 NIL) (-978 2353060 2355252 2357636 "POLYCAT-" 2357641 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352641 2352715 2352835 "POLY2UP" 2352986 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352267 2352330 2352439 "POLY2" 2352578 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345475 2351871 2352031 "POLY" 2352140 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344136 2344399 2344675 "POLUTIL" 2345249 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342455 2342768 2343099 "POLTOPOL" 2343858 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337451 2342389 2342436 "POINT" 2342441 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335584 2335995 2336370 "PNTHEORY" 2337096 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334030 2334339 2334738 "PMTOOLS" 2335282 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333617 2333701 2333818 "PMSYM" 2333946 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333119 2333194 2333369 "PMQFCAT" 2333542 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332500 2332598 2332760 "PMPREDFS" 2333020 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2331843 2331965 2332121 "PMPRED" 2332377 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330497 2330715 2331093 "PMPLCAT" 2331605 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330023 2330108 2330260 "PMLSAGG" 2330412 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329490 2329572 2329754 "PMKERNEL" 2329941 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329101 2329182 2329295 "PMINS" 2329409 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328537 2328612 2328821 "PMFS" 2329026 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327753 2327883 2328088 "PMDOWN" 2328414 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2327002 2327136 2327299 "PMASSFS" 2327640 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326145 2326327 2326508 "PMASS" 2326841 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325794 2325868 2325962 "PLOTTOOL" 2326071 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321446 2322640 2323562 "PLOT3D" 2324892 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320334 2320535 2320770 "PLOT1" 2321250 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314755 2316145 2317293 "PLOT" 2319206 T PLOT (NIL) -8 NIL NIL NIL) (-953 2289930 2294821 2299672 "PLEQN" 2310021 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289617 2289670 2289773 "PINTERPA" 2289877 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2288923 2289057 2289237 "PINTERP" 2289482 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2287008 2288181 2288209 "PID" 2288391 T PID (NIL) -9 NIL 2288525 NIL) (-949 2286753 2286796 2286871 "PICOERCE" 2286965 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2285849 2286517 2286604 "PI" 2286644 T PI (NIL) -8 NIL NIL 2286711) (-947 2285157 2285308 2285484 "PGROEB" 2285705 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280596 2281555 2282461 "PGE" 2284271 T PGE (NIL) -7 NIL NIL NIL) (-945 2278677 2278966 2279332 "PGCD" 2280313 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2278003 2278118 2278279 "PFRPAC" 2278561 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274253 2276551 2276904 "PFR" 2277682 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272606 2272886 2273211 "PFOTOOLS" 2274000 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271121 2271378 2271729 "PFOQ" 2272363 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269604 2269834 2270190 "PFO" 2270905 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266682 2268195 2268223 "PFECAT" 2268808 T PFECAT (NIL) -9 NIL 2269192 NIL) (-938 2266109 2266281 2266495 "PFECAT-" 2266500 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264682 2264964 2265265 "PFBRU" 2265858 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262512 2262900 2263332 "PFBR" 2264333 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258437 2262401 2262470 "PF" 2262475 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253491 2254644 2255514 "PERMGRP" 2257600 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251403 2252515 2252556 "PERMCAT" 2252956 NIL PERMCAT (NIL T) -9 NIL 2253254 NIL) (-932 2251050 2251097 2251221 "PERMAN" 2251356 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2246852 2248559 2249207 "PERM" 2250435 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244093 2246517 2246639 "PENDTREE" 2246763 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242974 2243237 2243278 "PDSPC" 2243811 NIL PDSPC (NIL T) -9 NIL 2244056 NIL) (-928 2242029 2242295 2242657 "PDSPC-" 2242662 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240743 2241679 2241720 "PDRING" 2241725 NIL PDRING (NIL T) -9 NIL 2241753 NIL) (-926 2239486 2240248 2240302 "PDMOD" 2240307 NIL PDMOD (NIL T T) -9 NIL 2240411 NIL) (-925 2236653 2237479 2238147 "PDEPROB" 2238838 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234162 2234702 2235257 "PDEPACK" 2236118 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233050 2233264 2233515 "PDECOMP" 2233961 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230567 2231458 2231486 "PDECAT" 2232273 T PDECAT (NIL) -9 NIL 2232986 NIL) (-921 2230184 2230251 2230305 "PDDOM" 2230470 NIL PDDOM (NIL T T) -9 NIL 2230550 NIL) (-920 2229997 2230033 2230140 "PDDOM-" 2230145 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229742 2229781 2229871 "PCOMP" 2229958 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227782 2228543 2228840 "PBWLB" 2229471 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227408 2227471 2227580 "PATTERN2" 2227719 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225117 2225553 2226010 "PATTERN1" 2226997 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217296 2219190 2220528 "PATTERN" 2223800 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2216854 2216927 2217059 "PATRES2" 2217223 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214120 2214803 2215284 "PATRES" 2216419 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2211973 2212408 2212815 "PATMATCH" 2213787 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211427 2211678 2211719 "PATMAB" 2211826 NIL PATMAB (NIL T) -9 NIL 2211909 NIL) (-910 2209873 2210281 2210539 "PATLRES" 2211232 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209411 2209542 2209583 "PATAB" 2209588 NIL PATAB (NIL T) -9 NIL 2209760 NIL) (-908 2207551 2207988 2208411 "PARTPERM" 2209008 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207160 2207235 2207337 "PARSURF" 2207482 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206786 2206849 2206958 "PARSU2" 2207097 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206544 2206590 2206657 "PARSER" 2206739 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206153 2206228 2206330 "PARSCURV" 2206475 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205779 2205842 2205951 "PARSC2" 2206090 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205406 2205476 2205573 "PARPCURV" 2205715 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205032 2205095 2205204 "PARPC2" 2205343 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204021 2204405 2204587 "PARAMAST" 2204870 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203529 2203627 2203746 "PAN2EXPR" 2203922 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202222 2202650 2202878 "PALETTE" 2203321 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200567 2201227 2201587 "PAIR" 2201908 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193479 2199824 2200019 "PADICRC" 2200421 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185715 2192823 2193008 "PADICRAT" 2193326 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182505 2184375 2184415 "PADICCT" 2184996 NIL PADICCT (NIL NIL) -9 NIL 2185278 NIL) (-893 2180514 2182442 2182487 "PADIC" 2182492 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179459 2179671 2179939 "PADEPAC" 2180301 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178659 2178804 2179010 "PADE" 2179321 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176892 2177867 2178147 "OWP" 2178463 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176337 2176598 2176695 "OVERSET" 2176815 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175257 2175942 2176114 "OVAR" 2176205 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2163493 2166366 2168566 "OUTFORM" 2173077 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2162775 2163090 2163217 "OUTBFILE" 2163386 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2162052 2162247 2162275 "OUTBCON" 2162593 T OUTBCON (NIL) -9 NIL 2162759 NIL) (-884 2161635 2161765 2161922 "OUTBCON-" 2161927 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2160875 2161020 2161181 "OUT" 2161494 T OUT (NIL) -7 NIL NIL NIL) (-882 2160171 2160604 2160693 "OSI" 2160806 T OSI (NIL) -8 NIL NIL NIL) (-881 2159590 2160012 2160040 "OSGROUP" 2160045 T OSGROUP (NIL) -9 NIL 2160067 NIL) (-880 2158301 2158562 2158847 "ORTHPOL" 2159337 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155552 2158136 2158257 "OREUP" 2158262 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152655 2155243 2155370 "ORESUP" 2155494 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150155 2150683 2151244 "OREPCTO" 2152144 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143533 2146028 2146069 "OREPCAT" 2148417 NIL OREPCAT (NIL T) -9 NIL 2149521 NIL) (-875 2140506 2141462 2142520 "OREPCAT-" 2142525 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139699 2139976 2140004 "ORDTYPE" 2140313 T ORDTYPE (NIL) -9 NIL 2140476 NIL) (-873 2139000 2139216 2139471 "ORDTYPE-" 2139476 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138356 2138739 2138897 "ORDSTRCT" 2138902 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137854 2138224 2138252 "ORDSET" 2138257 T ORDSET (NIL) -9 NIL 2138279 NIL) (-870 2136212 2137183 2137211 "ORDRING" 2137413 T ORDRING (NIL) -9 NIL 2137538 NIL) (-869 2135833 2135951 2136095 "ORDRING-" 2136100 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135084 2135649 2135677 "ORDMON" 2135682 T ORDMON (NIL) -9 NIL 2135703 NIL) (-867 2134228 2134393 2134588 "ORDFUNS" 2134933 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133443 2133958 2133986 "ORDFIN" 2134051 T ORDFIN (NIL) -9 NIL 2134125 NIL) (-865 2132697 2132836 2133022 "ORDCOMP2" 2133303 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2129044 2131283 2131692 "ORDCOMP" 2132321 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2125565 2126535 2127349 "OPTPROB" 2128250 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122307 2123006 2123710 "OPTPACK" 2124881 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119920 2120746 2120774 "OPTCAT" 2121593 T OPTCAT (NIL) -9 NIL 2122243 NIL) (-860 2119238 2119597 2119702 "OPSIG" 2119835 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2119000 2119045 2119111 "OPQUERY" 2119192 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2118306 2118586 2118627 "OPERCAT" 2118839 NIL OPERCAT (NIL T) -9 NIL 2118936 NIL) (-857 2118049 2118117 2118234 "OPERCAT-" 2118239 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2114958 2116360 2116864 "OP" 2117578 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114251 2114378 2114552 "ONECOMP2" 2114830 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2110864 2113048 2113417 "ONECOMP" 2113915 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110265 2110389 2110519 "OMSERVER" 2110754 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106779 2109705 2109745 "OMSAGG" 2109806 NIL OMSAGG (NIL T) -9 NIL 2109870 NIL) (-851 2105354 2105665 2105947 "OMPKG" 2106517 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103701 2104903 2105072 "OMLO" 2105235 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102637 2102808 2103028 "OMEXPR" 2103527 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101722 2102058 2102218 "OMERRK" 2102497 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2100959 2101268 2101404 "OMERR" 2101606 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100350 2100636 2100744 "OMENC" 2100871 T OMENC (NIL) -8 NIL NIL NIL) (-845 2093987 2095430 2096601 "OMDEV" 2099199 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2093020 2093227 2093421 "OMCONN" 2093813 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2092426 2092553 2092581 "OM" 2092880 T OM (NIL) -9 NIL NIL NIL) (-842 2090704 2091896 2091924 "OINTDOM" 2091929 T OINTDOM (NIL) -9 NIL 2091950 NIL) (-841 2087778 2089392 2089729 "OFMONOID" 2090399 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2087012 2087715 2087760 "ODVAR" 2087765 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084149 2086757 2086912 "ODR" 2086917 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075554 2083925 2084051 "ODPOL" 2084056 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068897 2075426 2075531 "ODP" 2075536 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067639 2067878 2068153 "ODETOOLS" 2068671 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064582 2065264 2065980 "ODESYS" 2066972 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059412 2060372 2061397 "ODERTRIC" 2063657 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2058832 2058920 2059114 "ODERED" 2059324 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055684 2056268 2056945 "ODERAT" 2058255 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052601 2053108 2053705 "ODEPRRIC" 2055213 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050496 2051140 2051626 "ODEPROB" 2052135 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046962 2047501 2048148 "ODEPRIM" 2049975 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046205 2046313 2046573 "ODEPAL" 2046854 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042307 2043158 2044022 "ODEPACK" 2045361 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041350 2041475 2041697 "ODEINT" 2042196 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035415 2036876 2038323 "ODEIFTBL" 2039923 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030765 2031599 2032551 "ODEEF" 2034574 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030108 2030203 2030426 "ODECONST" 2030670 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028171 2028880 2028908 "ODECAT" 2029513 T ODECAT (NIL) -9 NIL 2030044 NIL) (-821 2027803 2027852 2027979 "OCTCT2" 2028122 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024296 2027508 2027630 "OCT" 2027713 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023519 2024089 2024117 "OCAMON" 2024122 T OCAMON (NIL) -9 NIL 2024143 NIL) (-818 2017788 2020562 2020602 "OC" 2021699 NIL OC (NIL T) -9 NIL 2022557 NIL) (-817 2014823 2015763 2016753 "OC-" 2016847 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014243 2014668 2014696 "OASGP" 2014701 T OASGP (NIL) -9 NIL 2014721 NIL) (-815 2013369 2013966 2013994 "OAMONS" 2014034 T OAMONS (NIL) -9 NIL 2014077 NIL) (-814 2012660 2013189 2013217 "OAMON" 2013222 T OAMON (NIL) -9 NIL 2013242 NIL) (-813 2011771 2012409 2012437 "OAGROUP" 2012442 T OAGROUP (NIL) -9 NIL 2012462 NIL) (-812 2011453 2011509 2011598 "NUMTUBE" 2011715 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004972 2006544 2008080 "NUMQUAD" 2009937 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000652 2001686 2002721 "NUMODE" 2003957 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997933 1998873 1998901 "NUMINT" 1999824 T NUMINT (NIL) -9 NIL 2000588 NIL) (-808 1996845 1997078 1997296 "NUMFMT" 1997735 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983028 1986149 1988681 "NUMERIC" 1994352 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976739 1982476 1982571 "NTSCAT" 1982576 NIL NTSCAT (NIL T T T T) -9 NIL 1982615 NIL) (-805 1975919 1976098 1976291 "NTPOLFN" 1976578 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975545 1975608 1975717 "NSUP2" 1975856 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962306 1972370 1973182 "NSUP" 1974766 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951142 1962080 1962213 "NSMP" 1962218 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949550 1949875 1950232 "NREP" 1950830 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948129 1948393 1948751 "NPCOEF" 1949293 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947177 1947310 1947526 "NORMRETR" 1948010 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945188 1945508 1945917 "NORMPK" 1946885 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944867 1944901 1945025 "NORMMA" 1945154 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944650 1944685 1944754 "NONE1" 1944831 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944414 1944607 1944636 "NONE" 1944641 T NONE (NIL) -8 NIL NIL NIL) (-794 1943905 1943973 1944152 "NODE1" 1944346 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941997 1943028 1943283 "NNI" 1943630 T NNI (NIL) -8 NIL NIL 1943865) (-792 1940393 1940730 1941094 "NLINSOL" 1941665 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936574 1937629 1938528 "NIPROB" 1939514 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935313 1935565 1935867 "NFINTBAS" 1936336 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934397 1934963 1935004 "NETCLT" 1935176 NIL NETCLT (NIL T) -9 NIL 1935258 NIL) (-788 1933069 1933336 1933617 "NCODIV" 1934165 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932825 1932868 1932943 "NCNTFRAC" 1933026 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930981 1931369 1931789 "NCEP" 1932450 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929644 1930591 1930619 "NASRING" 1930729 T NASRING (NIL) -9 NIL 1930809 NIL) (-784 1929427 1929483 1929577 "NASRING-" 1929582 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928394 1929045 1929073 "NARNG" 1929190 T NARNG (NIL) -9 NIL 1929281 NIL) (-782 1928068 1928153 1928287 "NARNG-" 1928292 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926905 1927154 1927389 "NAGSP" 1927853 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917949 1919861 1921534 "NAGS" 1925252 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916473 1916805 1917136 "NAGF07" 1917638 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910945 1912302 1913609 "NAGF04" 1915186 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903817 1905527 1907160 "NAGF02" 1909332 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898981 1900141 1901258 "NAGF01" 1902720 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892561 1894175 1895760 "NAGE04" 1897416 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883622 1885851 1887981 "NAGE02" 1890451 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879515 1880522 1881486 "NAGE01" 1882678 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877292 1877844 1878402 "NAGD03" 1878977 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868988 1870970 1872924 "NAGD02" 1875358 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862727 1864224 1865664 "NAGD01" 1867568 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858864 1859758 1860595 "NAGC06" 1861910 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857311 1857661 1858017 "NAGC05" 1858528 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856675 1856806 1856950 "NAGC02" 1857187 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855476 1856203 1856243 "NAALG" 1856322 NIL NAALG (NIL T) -9 NIL 1856383 NIL) (-765 1855305 1855340 1855430 "NAALG-" 1855435 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849177 1850363 1851550 "MULTSQFR" 1854201 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848484 1848571 1848755 "MULTFACT" 1849089 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840629 1845067 1845120 "MTSCAT" 1846190 NIL MTSCAT (NIL T T) -9 NIL 1846706 NIL) (-761 1840335 1840395 1840487 "MTHING" 1840569 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840121 1840160 1840220 "MSYSCMD" 1840295 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836866 1839682 1839723 "MSETAGG" 1839728 NIL MSETAGG (NIL T) -9 NIL 1839762 NIL) (-758 1832580 1835621 1835941 "MSET" 1836579 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828172 1829959 1830704 "MRING" 1831880 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827732 1827805 1827936 "MRF2" 1828099 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827344 1827385 1827529 "MRATFAC" 1827691 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824914 1825251 1825682 "MPRFF" 1827049 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818241 1824768 1824865 "MPOLY" 1824870 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817725 1817766 1817974 "MPCPF" 1818200 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817233 1817282 1817466 "MPC3" 1817676 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816416 1816509 1816730 "MPC2" 1817148 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814693 1815054 1815444 "MONOTOOL" 1816076 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813838 1814221 1814249 "MONOID" 1814468 T MONOID (NIL) -9 NIL 1814615 NIL) (-747 1813354 1813503 1813684 "MONOID-" 1813689 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802308 1809174 1809233 "MONOGEN" 1809907 NIL MONOGEN (NIL T T) -9 NIL 1810363 NIL) (-745 1799358 1800261 1801261 "MONOGEN-" 1801380 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798075 1798623 1798651 "MONADWU" 1799043 T MONADWU (NIL) -9 NIL 1799281 NIL) (-743 1797405 1797606 1797854 "MONADWU-" 1797859 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796690 1796994 1797022 "MONAD" 1797229 T MONAD (NIL) -9 NIL 1797341 NIL) (-741 1796357 1796453 1796585 "MONAD-" 1796590 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794496 1795270 1795549 "MOEBIUS" 1796110 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793664 1794164 1794204 "MODULE" 1794209 NIL MODULE (NIL T) -9 NIL 1794248 NIL) (-738 1793202 1793328 1793518 "MODULE-" 1793523 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790732 1791566 1791893 "MODRING" 1793026 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787454 1788837 1789358 "MODOP" 1790261 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785940 1786521 1786798 "MODMONOM" 1787317 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774680 1784231 1784645 "MODMON" 1785577 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771506 1773524 1773800 "MODFIELD" 1774555 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770417 1770787 1770977 "MMLFORM" 1771336 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769937 1769986 1770165 "MMAP" 1770368 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767830 1768769 1768810 "MLO" 1769233 NIL MLO (NIL T) -9 NIL 1769475 NIL) (-729 1765178 1765712 1766314 "MLIFT" 1767311 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764557 1764653 1764807 "MKUCFUNC" 1765089 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764150 1764226 1764349 "MKRECORD" 1764480 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763173 1763359 1763587 "MKFUNC" 1763961 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762549 1762665 1762821 "MKFLCFN" 1763056 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761814 1761928 1762113 "MKBCFUNC" 1762442 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757797 1761368 1761504 "MINT" 1761698 T MINT (NIL) -8 NIL NIL NIL) (-722 1756579 1756852 1757129 "MHROWRED" 1757552 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751323 1755114 1755519 "MFLOAT" 1756194 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750668 1750756 1750927 "MFINFACT" 1751235 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746947 1747831 1748715 "MESH" 1749804 T MESH (NIL) -7 NIL NIL NIL) (-718 1745301 1745649 1746002 "MDDFACT" 1746634 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741837 1744432 1744473 "MDAGG" 1744728 NIL MDAGG (NIL T) -9 NIL 1744871 NIL) (-716 1729539 1741130 1741337 "MCMPLX" 1741650 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728658 1728822 1729023 "MCDEN" 1729388 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726506 1726818 1727198 "MCALCFN" 1728388 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725383 1725671 1725904 "MAYBE" 1726312 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722941 1723518 1724080 "MATSTOR" 1724854 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718363 1722313 1722561 "MATRIX" 1722726 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714063 1714836 1715572 "MATLIN" 1717720 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712639 1712810 1713143 "MATCAT2" 1713898 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701985 1705696 1705773 "MATCAT" 1710805 NIL MATCAT (NIL T T T) -9 NIL 1712277 NIL) (-707 1697938 1699248 1700661 "MATCAT-" 1700666 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696014 1696374 1696758 "MAPPKG3" 1697613 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694971 1695168 1695390 "MAPPKG2" 1695838 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693428 1693754 1694081 "MAPPKG1" 1694677 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692429 1692834 1693011 "MAPPAST" 1693271 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692034 1692098 1692221 "MAPHACK3" 1692365 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691614 1691687 1691801 "MAPHACK2" 1691966 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691040 1691155 1691297 "MAPHACK1" 1691505 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688963 1689740 1690044 "MAGMA" 1690768 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688382 1688687 1688778 "MACROAST" 1688892 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684625 1686621 1687082 "M3D" 1687954 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678105 1682936 1682977 "LZSTAGG" 1683759 NIL LZSTAGG (NIL T) -9 NIL 1684054 NIL) (-695 1673787 1675236 1676693 "LZSTAGG-" 1676698 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670700 1671678 1672165 "LWORD" 1673332 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670222 1670504 1670579 "LSTAST" 1670645 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662150 1669993 1670127 "LSQM" 1670132 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661368 1661513 1661741 "LSPP" 1662005 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658105 1658821 1659551 "LSMP1" 1660670 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655887 1656218 1656674 "LSMP" 1657794 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649023 1654977 1655018 "LSAGG" 1655080 NIL LSAGG (NIL T) -9 NIL 1655158 NIL) (-687 1645532 1646642 1647855 "LSAGG-" 1647860 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642827 1644676 1644925 "LPOLY" 1645327 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642403 1642494 1642617 "LPEFRAC" 1642736 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642086 1642165 1642193 "LOGIC" 1642304 T LOGIC (NIL) -9 NIL 1642386 NIL) (-683 1641942 1641971 1642042 "LOGIC-" 1642047 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641117 1641275 1641468 "LODOOPS" 1641798 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639641 1639890 1640243 "LODOF" 1640864 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635517 1638276 1638317 "LODOCAT" 1638755 NIL LODOCAT (NIL T) -9 NIL 1638966 NIL) (-679 1635232 1635308 1635435 "LODOCAT-" 1635440 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632218 1635073 1635191 "LODO2" 1635196 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629325 1632155 1632200 "LODO1" 1632205 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626420 1629241 1629307 "LODO" 1629312 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625289 1625466 1625771 "LODEEF" 1626243 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623466 1624383 1624636 "LO" 1625121 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618438 1621632 1621673 "LNAGG" 1622535 NIL LNAGG (NIL T) -9 NIL 1622970 NIL) (-672 1617531 1617799 1618141 "LNAGG-" 1618146 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613511 1614456 1615095 "LMOPS" 1616946 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612810 1613288 1613329 "LMODULE" 1613334 NIL LMODULE (NIL T) -9 NIL 1613360 NIL) (-669 1609765 1612455 1612578 "LMDICT" 1612720 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609341 1609555 1609596 "LLINSET" 1609657 NIL LLINSET (NIL T) -9 NIL 1609701 NIL) (-667 1608986 1609249 1609309 "LITERAL" 1609314 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608505 1608585 1608724 "LIST3" 1608906 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606603 1606951 1607350 "LIST2MAP" 1608152 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605592 1605788 1606016 "LIST2" 1606421 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598046 1604526 1604830 "LIST" 1605321 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597629 1597865 1597906 "LINSET" 1597911 NIL LINSET (NIL T) -9 NIL 1597945 NIL) (-661 1596443 1597137 1597304 "LINFORM" 1597514 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594742 1595470 1595511 "LINEXP" 1596001 NIL LINEXP (NIL T) -9 NIL 1596274 NIL) (-659 1593318 1594222 1594403 "LINELT" 1594613 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591875 1592155 1592466 "LINDEP" 1593070 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591011 1591607 1591717 "LINBASIS" 1591805 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587748 1588497 1589274 "LIMITRF" 1590266 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586033 1586347 1586756 "LIMITPS" 1587443 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584861 1585436 1585476 "LIECAT" 1585616 NIL LIECAT (NIL T) -9 NIL 1585767 NIL) (-653 1584696 1584729 1584817 "LIECAT-" 1584822 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578716 1584207 1584435 "LIE" 1584517 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570903 1578256 1578412 "LIB" 1578580 T LIB (NIL) -8 NIL NIL NIL) (-650 1566472 1567421 1568356 "LGROBP" 1570020 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565096 1566004 1566032 "LFCAT" 1566239 T LFCAT (NIL) -9 NIL 1566378 NIL) (-648 1563034 1563368 1563718 "LF" 1564817 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559894 1560566 1561254 "LEXTRIPK" 1562398 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556482 1557464 1557967 "LEXP" 1559474 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555898 1556203 1556295 "LETAST" 1556410 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554284 1554609 1555010 "LEADCDET" 1555580 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553462 1553548 1553777 "LAZM3PK" 1554205 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547973 1551539 1552077 "LAUPOL" 1552974 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547546 1547596 1547757 "LAPLACE" 1547923 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546394 1547110 1547151 "LALG" 1547213 NIL LALG (NIL T) -9 NIL 1547272 NIL) (-639 1546090 1546167 1546303 "LALG-" 1546308 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543827 1545191 1545442 "LA" 1545923 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543656 1543686 1543727 "KVTFROM" 1543789 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542413 1543023 1543208 "KTVLOGIC" 1543491 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542242 1542272 1542313 "KRCFROM" 1542375 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541134 1541333 1541632 "KOVACIC" 1542042 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540963 1540993 1541034 "KONVERT" 1541096 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540792 1540822 1540863 "KOERCE" 1540925 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540276 1540369 1540501 "KERNEL2" 1540706 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537963 1538869 1539246 "KERNEL" 1539932 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531434 1536440 1536494 "KDAGG" 1536871 NIL KDAGG (NIL T T) -9 NIL 1537077 NIL) (-628 1530945 1531087 1531292 "KDAGG-" 1531297 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523645 1530606 1530761 "KAFILE" 1530823 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523249 1523534 1523597 "JVMOP" 1523602 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521985 1522489 1522738 "JVMMDACC" 1523020 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520921 1521375 1521580 "JVMFDACC" 1521800 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519502 1519997 1520297 "JVMCSTTG" 1520641 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518638 1519042 1519203 "JVMCFACC" 1519361 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518316 1518555 1518604 "JVMBCODE" 1518609 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512336 1517827 1518055 "JORDAN" 1518137 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511649 1511985 1512106 "JOINAST" 1512235 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507684 1509826 1509880 "IXAGG" 1510809 NIL IXAGG (NIL T T) -9 NIL 1511268 NIL) (-617 1506537 1506909 1507328 "IXAGG-" 1507333 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501626 1506459 1506518 "IVECTOR" 1506523 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500350 1500629 1500895 "ITUPLE" 1501393 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498822 1499029 1499324 "ITRIGMNP" 1500172 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497549 1497771 1498054 "ITFUN3" 1498598 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497175 1497238 1497347 "ITFUN2" 1497486 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1496280 1496655 1496829 "ITFORM" 1497021 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494049 1495300 1495578 "ITAYLOR" 1496035 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482446 1488186 1489349 "ISUPS" 1492919 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481538 1481690 1481926 "ISUMP" 1482293 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476388 1481483 1481524 "ISTRING" 1481529 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475804 1476109 1476201 "ISAST" 1476316 T ISAST (NIL) -8 NIL NIL NIL) (-605 1475001 1475095 1475311 "IRURPK" 1475718 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473913 1474138 1474378 "IRSN" 1474781 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471958 1472339 1472768 "IRRF2F" 1473551 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471699 1471743 1471819 "IRREDFFX" 1471914 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470272 1470573 1470872 "IROOT" 1471432 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469411 1469765 1469916 "IRFORM" 1470141 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468493 1468624 1468838 "IR2F" 1469294 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466082 1466601 1467167 "IR2" 1467971 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462522 1463766 1464458 "IR" 1465422 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462307 1462347 1462407 "IPRNTPK" 1462482 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458260 1462196 1462265 "IPF" 1462270 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456281 1458185 1458242 "IPADIC" 1458247 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455539 1455841 1455971 "IP4ADDR" 1456171 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454877 1455168 1455300 "IOMODE" 1455427 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453848 1454474 1454601 "IOBFILE" 1454770 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453258 1453752 1453780 "IOBCON" 1453785 T IOBCON (NIL) -9 NIL 1453806 NIL) (-589 1452763 1452827 1453010 "INVLAPLA" 1453194 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442333 1444765 1447151 "INTTR" 1450427 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438626 1439410 1440275 "INTTOOLS" 1441518 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438206 1438303 1438420 "INTSLPE" 1438529 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435673 1438129 1438188 "INTRVL" 1438193 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433251 1433787 1434362 "INTRF" 1435158 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432644 1432759 1432901 "INTRET" 1433149 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430617 1431030 1431500 "INTRAT" 1432252 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427862 1428463 1429082 "INTPM" 1430102 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424579 1425206 1425944 "INTPAF" 1427248 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419680 1420720 1421771 "INTPACK" 1423548 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418926 1419084 1419292 "INTHERTR" 1419522 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418359 1418445 1418633 "INTHERAL" 1418840 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416127 1416648 1417105 "INTHEORY" 1417922 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407459 1409154 1410926 "INTG0" 1414479 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387984 1392822 1397632 "INTFTBL" 1402669 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387209 1387371 1387544 "INTFACT" 1387843 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384606 1385082 1385639 "INTEF" 1386763 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382803 1383698 1383726 "INTDOM" 1384027 T INTDOM (NIL) -9 NIL 1384234 NIL) (-570 1382142 1382346 1382588 "INTDOM-" 1382593 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378016 1380431 1380485 "INTCAT" 1381284 NIL INTCAT (NIL T) -9 NIL 1381605 NIL) (-568 1377470 1377591 1377719 "INTBIT" 1377908 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376151 1376323 1376630 "INTALG" 1377315 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375628 1375724 1375881 "INTAF" 1376055 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368595 1375438 1375578 "INTABL" 1375583 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367832 1368394 1368459 "INT8" 1368493 T INT8 (NIL) -8 NIL NIL 1368538) (-563 1367068 1367630 1367695 "INT64" 1367729 T INT64 (NIL) -8 NIL NIL 1367774) (-562 1366304 1366866 1366931 "INT32" 1366965 T INT32 (NIL) -8 NIL NIL 1367010) (-561 1365540 1366102 1366167 "INT16" 1366201 T INT16 (NIL) -8 NIL NIL 1366246) (-560 1361728 1365337 1365446 "INT" 1365451 T INT (NIL) -8 NIL NIL NIL) (-559 1355829 1359276 1359304 "INS" 1360238 T INS (NIL) -9 NIL 1360903 NIL) (-558 1352883 1353840 1354814 "INS-" 1354887 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351640 1351885 1352183 "INPSIGN" 1352636 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350734 1350875 1351072 "INPRODPF" 1351520 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349604 1349745 1349982 "INPRODFF" 1350614 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348592 1348756 1349016 "INNMFACT" 1349440 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347771 1347886 1348074 "INMODGCD" 1348491 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1346255 1346524 1346848 "INFSP" 1347516 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345415 1345556 1345739 "INFPROD0" 1346135 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1345013 1345085 1345183 "INFORM1" 1345350 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341580 1343078 1343593 "INFORM" 1344506 T INFORM (NIL) -8 NIL NIL NIL) (-548 1341085 1341192 1341306 "INFINITY" 1341486 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1340159 1340805 1340906 "INETCLTS" 1341004 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338757 1339025 1339346 "INEP" 1339907 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337818 1338654 1338719 "INDE" 1338724 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1337370 1337450 1337567 "INCRMAPS" 1337745 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1336092 1336639 1336845 "INBFILE" 1337184 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1331271 1332328 1333272 "INBFF" 1335180 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1330125 1330448 1330476 "INBCON" 1330989 T INBCON (NIL) -9 NIL 1331255 NIL) (-540 1329335 1329600 1329876 "INBCON-" 1329881 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328754 1329059 1329150 "INAST" 1329264 T INAST (NIL) -8 NIL NIL NIL) (-538 1328121 1328433 1328539 "IMPTAST" 1328668 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1324042 1327965 1328069 "IMATRIX" 1328074 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322734 1322873 1323189 "IMATQF" 1323898 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320914 1321181 1321518 "IMATLIN" 1322490 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314829 1320838 1320896 "ILIST" 1320901 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312495 1314689 1314802 "IIARRAY2" 1314807 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1307295 1312406 1312470 "IFF" 1312475 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306576 1306912 1307028 "IFAST" 1307199 T IFAST (NIL) -8 NIL NIL NIL) (-530 1301088 1305868 1306056 "IFARRAY" 1306433 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1300126 1300992 1301065 "IFAMON" 1301070 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299698 1299775 1299829 "IEVALAB" 1300036 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1299361 1299441 1299601 "IEVALAB-" 1299606 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298425 1299250 1299325 "IDPOAMS" 1299330 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297558 1298314 1298389 "IDPOAM" 1298394 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296939 1297473 1297535 "IDPO" 1297540 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295419 1295946 1295998 "IDPC" 1296510 NIL IDPC (NIL T T) -9 NIL 1296791 NIL) (-522 1294751 1295311 1295384 "IDPAM" 1295389 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293966 1294643 1294716 "IDPAG" 1294721 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293510 1293772 1293862 "IDENT" 1293896 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289729 1290613 1291508 "IDECOMP" 1292667 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282364 1283652 1284699 "IDEAL" 1288765 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281506 1281636 1281836 "ICDEN" 1282248 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280481 1280986 1281133 "ICARD" 1281379 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278511 1278854 1279259 "IBPTOOLS" 1280158 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273626 1278131 1278244 "IBITS" 1278430 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1270301 1270925 1271620 "IBATOOL" 1273043 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1268062 1268542 1269075 "IBACHIN" 1269836 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265652 1267908 1268011 "IARRAY2" 1268016 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261365 1265578 1265635 "IARRAY1" 1265640 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254375 1259777 1260258 "IAN" 1260904 T IAN (NIL) -8 NIL NIL NIL) (-508 1253880 1253943 1254116 "IALGFACT" 1254312 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253372 1253521 1253549 "HYPCAT" 1253756 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252874 1253027 1253213 "HYPCAT-" 1253218 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252421 1252669 1252752 "HOSTNAME" 1252811 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1252254 1252303 1252344 "HOMOTOP" 1252349 NIL HOMOTOP (NIL T) -9 NIL 1252382 NIL) (-503 1248687 1250186 1250227 "HOAGG" 1251208 NIL HOAGG (NIL T) -9 NIL 1251937 NIL) (-502 1247203 1247680 1248206 "HOAGG-" 1248211 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1240239 1246796 1246946 "HEXADEC" 1247073 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238951 1239209 1239472 "HEUGCD" 1240016 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237883 1238788 1238918 "HELLFDIV" 1238923 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235893 1237660 1237748 "HEAP" 1237827 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1235090 1235445 1235579 "HEADAST" 1235779 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228477 1235005 1235067 "HDP" 1235072 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221489 1228112 1228264 "HDMP" 1228378 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220795 1220953 1221117 "HB" 1221345 T HB (NIL) -7 NIL NIL NIL) (-493 1213805 1220641 1220745 "HASHTBL" 1220750 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1213221 1213526 1213618 "HASAST" 1213733 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210627 1212843 1213025 "HACKPI" 1213059 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205799 1210480 1210593 "GTSET" 1210598 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198838 1205677 1205775 "GSTBL" 1205780 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190587 1198003 1198259 "GSERIES" 1198638 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189618 1190131 1190159 "GROUP" 1190362 T GROUP (NIL) -9 NIL 1190496 NIL) (-486 1188942 1189143 1189394 "GROUP-" 1189399 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1187291 1187630 1188017 "GROEBSOL" 1188619 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1186119 1186479 1186530 "GRMOD" 1187059 NIL GRMOD (NIL T T) -9 NIL 1187227 NIL) (-483 1185875 1185923 1186051 "GRMOD-" 1186056 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1181015 1182229 1183229 "GRIMAGE" 1184895 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179409 1179742 1180066 "GRDEF" 1180711 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178841 1178969 1179110 "GRAY" 1179288 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177918 1178420 1178471 "GRALG" 1178624 NIL GRALG (NIL T T) -9 NIL 1178717 NIL) (-478 1177555 1177652 1177815 "GRALG-" 1177820 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1174036 1177138 1177317 "GPOLSET" 1177461 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173384 1173447 1173705 "GOSPER" 1173973 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168954 1169822 1170348 "GMODPOL" 1173083 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167941 1168143 1168381 "GHENSEL" 1168766 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1162013 1162940 1163960 "GENUPS" 1167025 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161704 1161761 1161850 "GENUFACT" 1161956 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1161104 1161193 1161358 "GENPGCD" 1161622 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160572 1160613 1160826 "GENMFACT" 1161063 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1159108 1159395 1159702 "GENEEZ" 1160315 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1152280 1158719 1158881 "GDMP" 1159031 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1141019 1146051 1147157 "GCNAALG" 1151263 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1139146 1140194 1140222 "GCDDOM" 1140477 T GCDDOM (NIL) -9 NIL 1140634 NIL) (-465 1138586 1138743 1138958 "GCDDOM-" 1138963 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1127058 1129532 1131924 "GBINTERN" 1136277 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124859 1125187 1125608 "GBF" 1126733 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123616 1123805 1124072 "GBEUCLID" 1124675 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1122266 1122473 1122777 "GB" 1123395 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121597 1121740 1121889 "GAUSSFAC" 1122137 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119918 1120266 1120580 "GALUTIL" 1121316 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1118178 1118500 1118824 "GALPOLYU" 1119645 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115477 1115833 1116240 "GALFACTU" 1117875 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1107091 1108782 1110390 "GALFACT" 1113909 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104377 1105137 1105165 "FVFUN" 1106321 T FVFUN (NIL) -9 NIL 1107041 NIL) (-454 1103607 1103825 1103853 "FVC" 1104144 T FVC (NIL) -9 NIL 1104327 NIL) (-453 1103208 1103432 1103500 "FUNDESC" 1103559 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102781 1103005 1103086 "FUNCTION" 1103160 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101458 1102082 1102285 "FTEM" 1102598 T FTEM (NIL) -8 NIL NIL NIL) (-450 1099088 1099780 1100246 "FT" 1101012 T FT (NIL) -8 NIL NIL NIL) (-449 1097357 1097668 1098065 "FSUPFACT" 1098779 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095676 1096043 1096375 "FST" 1097045 T FST (NIL) -8 NIL NIL NIL) (-447 1094857 1094981 1095169 "FSRED" 1095558 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093546 1093812 1094159 "FSPRMELT" 1094572 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090756 1091290 1091776 "FSPECF" 1093109 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1090278 1090338 1090508 "FSINT" 1090697 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088414 1089271 1089574 "FSERIES" 1090057 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087438 1087572 1087796 "FSCINT" 1088294 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086462 1086623 1086850 "FSAGG2" 1087291 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1082326 1085406 1085447 "FSAGG" 1085817 NIL FSAGG (NIL T) -9 NIL 1086076 NIL) (-439 1079926 1080689 1081485 "FSAGG-" 1081580 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077586 1077884 1078432 "FS2UPS" 1079644 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076452 1076635 1076937 "FS2EXPXP" 1077411 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1076080 1076129 1076258 "FS2" 1076403 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1056307 1065854 1065895 "FS" 1069779 NIL FS (NIL T) -9 NIL 1072068 NIL) (-434 1044368 1047943 1052000 "FS-" 1052300 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043782 1043909 1044061 "FRUTIL" 1044248 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1038300 1041471 1041511 "FRNAALG" 1042831 NIL FRNAALG (NIL T) -9 NIL 1043429 NIL) (-431 1033781 1035049 1036324 "FRNAALG-" 1037074 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033413 1033462 1033589 "FRNAAF2" 1033732 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031700 1032262 1032558 "FRMOD" 1033225 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030885 1030978 1031269 "FRIDEAL2" 1031607 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028490 1029260 1029578 "FRIDEAL" 1030676 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027581 1028037 1028078 "FRETRCT" 1028083 NIL FRETRCT (NIL T) -9 NIL 1028259 NIL) (-425 1026639 1026924 1027275 "FRETRCT-" 1027280 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023453 1024923 1024982 "FRAMALG" 1025864 NIL FRAMALG (NIL T T) -9 NIL 1026156 NIL) (-423 1021491 1022042 1022672 "FRAMALG-" 1022895 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1021121 1021184 1021291 "FRAC2" 1021428 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1014092 1020594 1020871 "FRAC" 1020876 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013722 1013785 1013892 "FR2" 1014029 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004639 1009217 1010575 "FR" 1012396 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998556 1002018 1002046 "FPS" 1003165 T FPS (NIL) -9 NIL 1003722 NIL) (-417 997981 998114 998278 "FPS-" 998424 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994933 996938 996966 "FPC" 997191 T FPC (NIL) -9 NIL 997333 NIL) (-415 994714 994766 994863 "FPC-" 994868 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993472 994202 994243 "FPATMAB" 994248 NIL FPATMAB (NIL T) -9 NIL 994400 NIL) (-413 991615 992214 992561 "FPARFRAC" 993188 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986907 987507 988189 "FORTRAN" 991047 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984481 985145 985173 "FORTFN" 986233 T FORTFN (NIL) -9 NIL 986857 NIL) (-410 984233 984295 984323 "FORTCAT" 984382 T FORTCAT (NIL) -9 NIL 984444 NIL) (-409 981919 982449 982988 "FORT" 983714 T FORT (NIL) -7 NIL NIL NIL) (-408 981701 981737 981806 "FORMULA1" 981883 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979705 980317 980707 "FORMULA" 981331 T FORMULA (NIL) -8 NIL NIL NIL) (-406 979222 979280 979453 "FORDER" 979647 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 978282 978482 978675 "FOP" 979049 T FOP (NIL) -7 NIL NIL NIL) (-404 976695 977562 977736 "FNLA" 978164 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975314 975825 975853 "FNCAT" 976313 T FNCAT (NIL) -9 NIL 976573 NIL) (-402 974757 975273 975301 "FNAME" 975306 T FNAME (NIL) -8 NIL NIL NIL) (-401 973083 974256 974284 "FMTC" 974289 T FMTC (NIL) -9 NIL 974325 NIL) (-400 971631 973019 973065 "FMONOID" 973070 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 968220 969586 969627 "FMONCAT" 970844 NIL FMONCAT (NIL T) -9 NIL 971449 NIL) (-398 965542 966290 966318 "FMFUN" 967462 T FMFUN (NIL) -9 NIL 968170 NIL) (-397 962415 963467 963521 "FMCAT" 964716 NIL FMCAT (NIL T T) -9 NIL 965211 NIL) (-396 961648 961865 961893 "FMC" 962183 T FMC (NIL) -9 NIL 962365 NIL) (-395 960316 961414 961514 "FM1" 961593 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959334 960058 960207 "FM" 960212 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 957072 957524 958018 "FLOATRP" 958885 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954474 955010 955588 "FLOATCP" 956539 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 947130 952203 952824 "FLOAT" 953873 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945648 946722 946763 "FLINEXP" 946768 NIL FLINEXP (NIL T) -9 NIL 946861 NIL) (-389 944778 945037 945365 "FLINEXP-" 945370 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943836 943998 944222 "FLASORT" 944630 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940754 941806 941858 "FLALG" 943085 NIL FLALG (NIL T T) -9 NIL 943552 NIL) (-386 939778 939939 940166 "FLAGG2" 940607 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 933042 937187 937228 "FLAGG" 938490 NIL FLAGG (NIL T) -9 NIL 939142 NIL) (-384 931696 932107 932597 "FLAGG-" 932602 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928327 929541 929600 "FINRALG" 930728 NIL FINRALG (NIL T T) -9 NIL 931236 NIL) (-382 927451 927716 928055 "FINRALG-" 928060 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926757 927056 927084 "FINITE" 927280 T FINITE (NIL) -9 NIL 927387 NIL) (-380 918708 921287 921327 "FINAALG" 924994 NIL FINAALG (NIL T) -9 NIL 926447 NIL) (-379 913824 915090 916234 "FINAALG-" 917613 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912384 912806 912860 "FILECAT" 913544 NIL FILECAT (NIL T T) -9 NIL 913760 NIL) (-377 911662 912139 912242 "FILE" 912314 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 909058 910892 910920 "FIELD" 910960 T FIELD (NIL) -9 NIL 911040 NIL) (-375 907600 908063 908574 "FIELD-" 908579 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 905282 906235 906582 "FGROUP" 907286 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904354 904536 904756 "FGLMICPK" 905114 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899588 904279 904336 "FFX" 904341 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 899183 899250 899385 "FFSLPE" 899521 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898681 898723 898932 "FFPOLY2" 899141 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894557 895453 896249 "FFPOLY" 897917 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889805 894476 894539 "FFP" 894544 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884315 889148 889338 "FFNBX" 889659 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878627 883450 883708 "FFNBP" 884169 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872644 877911 878122 "FFNB" 878460 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871464 871674 871989 "FFINTBAS" 872441 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 867040 869711 869739 "FFIELDC" 870359 T FFIELDC (NIL) -9 NIL 870735 NIL) (-362 865618 866073 866570 "FFIELDC-" 866575 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 865175 865233 865357 "FFHOM" 865560 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862834 863357 863874 "FFF" 864690 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857848 862576 862677 "FFCGX" 862777 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852866 857580 857687 "FFCGP" 857791 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847445 852593 852701 "FFCG" 852802 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846850 846899 847134 "FFCAT2" 847396 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825513 836582 836668 "FFCAT" 841833 NIL FFCAT (NIL T T T) -9 NIL 843284 NIL) (-354 820524 821758 823072 "FFCAT-" 824302 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815324 820435 820499 "FF" 820504 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803977 808296 809516 "FEXPR" 814176 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802905 803374 803415 "FEVALAB" 803499 NIL FEVALAB (NIL T) -9 NIL 803760 NIL) (-350 802022 802274 802612 "FEVALAB-" 802617 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798884 799769 799884 "FDIVCAT" 801452 NIL FDIVCAT (NIL T T T T) -9 NIL 801889 NIL) (-348 798640 798673 798843 "FDIVCAT-" 798848 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797854 797947 798224 "FDIV2" 798547 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796264 797237 797440 "FDIV" 797753 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795172 795559 795761 "FCTRDATA" 796082 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793828 794117 794406 "FCPAK1" 794903 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792831 793328 793469 "FCOMP" 793719 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776146 779981 783519 "FC" 789313 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 -1491 (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 3472756 3472761 3472766 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472741 3472746 3472751 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472726 3472731 3472736 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472711 3472716 3472721 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1327 3471698 3472586 3472663 "ZMOD" 3472668 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1326 3470734 3470916 3471139 "ZLINDEP" 3471530 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1325 3459896 3461802 3463774 "ZDSOLVE" 3468864 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1324 3459130 3459283 3459472 "YSTREAM" 3459742 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1323 3458490 3458799 3458914 "YDIAGRAM" 3459037 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1322 3455938 3457791 3457995 "XRPOLY" 3458333 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1321 3452205 3453809 3454384 "XPR" 3455410 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1320 3449536 3451212 3451267 "XPOLYC" 3451555 NIL XPOLYC (NIL T T) -9 NIL 3451668 NIL) (-1319 3446931 3448867 3449071 "XPOLY" 3449367 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3442877 3445448 3445836 "XPBWPOLY" 3446589 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1317 3437769 3439348 3439403 "XFALG" 3441575 NIL XFALG (NIL T T) -9 NIL 3442364 NIL) (-1316 3433038 3435745 3435787 "XF" 3436408 NIL XF (NIL T) -9 NIL 3436808 NIL) (-1315 3432635 3432747 3432916 "XF-" 3432921 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3431750 3431872 3432077 "XEXPPKG" 3432527 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1313 3429491 3431600 3431696 "XDPOLY" 3431701 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1312 3428146 3428884 3428927 "XALG" 3428932 NIL XALG (NIL T) -9 NIL 3429043 NIL) (-1311 3421056 3426123 3426617 "WUTSET" 3427738 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1310 3419158 3420108 3420431 "WP" 3420867 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1309 3418706 3418980 3419050 "WHILEAST" 3419110 T WHILEAST (NIL) -8 NIL NIL NIL) (-1308 3418118 3418423 3418517 "WHEREAST" 3418634 T WHEREAST (NIL) -8 NIL NIL NIL) (-1307 3416992 3417202 3417497 "WFFINTBS" 3417915 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1306 3414860 3415323 3415785 "WEIER" 3416564 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1305 3413784 3414342 3414384 "VSPACE" 3414520 NIL VSPACE (NIL T) -9 NIL 3414594 NIL) (-1304 3413616 3413649 3413740 "VSPACE-" 3413745 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1303 3413413 3413467 3413535 "VOID" 3413570 T VOID (NIL) -8 NIL NIL NIL) (-1302 3409681 3410476 3411213 "VIEWDEF" 3412698 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1301 3398625 3401229 3403402 "VIEW3D" 3407530 T VIEW3D (NIL) -8 NIL NIL NIL) (-1300 3390642 3392536 3394115 "VIEW2D" 3397068 T VIEW2D (NIL) -8 NIL NIL NIL) (-1299 3388742 3389137 3389543 "VIEW" 3390258 T VIEW (NIL) -7 NIL NIL NIL) (-1298 3387295 3387578 3387896 "VECTOR2" 3388472 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1297 3382201 3387065 3387157 "VECTOR" 3387238 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3375155 3379905 3379948 "VECTCAT" 3380943 NIL VECTCAT (NIL T) -9 NIL 3381530 NIL) (-1295 3374097 3374423 3374813 "VECTCAT-" 3374818 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1294 3373503 3373748 3373868 "VARIABLE" 3374012 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1293 3373436 3373441 3373471 "UTYPE" 3373476 T UTYPE (NIL) -9 NIL NIL NIL) (-1292 3372244 3372420 3372682 "UTSODETL" 3373262 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1291 3369636 3370144 3370668 "UTSODE" 3371785 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1290 3359643 3365569 3365612 "UTSCAT" 3366724 NIL UTSCAT (NIL T) -9 NIL 3367482 NIL) (-1289 3356769 3357713 3358702 "UTSCAT-" 3358707 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1288 3356390 3356439 3356572 "UTS2" 3356720 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1287 3347700 3354151 3354631 "UTS" 3355968 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1286 3341567 3344510 3344553 "URAGG" 3346623 NIL URAGG (NIL T) -9 NIL 3347346 NIL) (-1285 3338290 3339369 3340492 "URAGG-" 3340497 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1284 3333659 3336925 3337390 "UPXSSING" 3337954 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1283 3326074 3333563 3333635 "UPXSCONS" 3333640 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1282 3314822 3322276 3322338 "UPXSCCA" 3322912 NIL UPXSCCA (NIL T T) -9 NIL 3323145 NIL) (-1281 3314442 3314545 3314719 "UPXSCCA-" 3314724 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1280 3303090 3310269 3310312 "UPXSCAT" 3310960 NIL UPXSCAT (NIL T) -9 NIL 3311569 NIL) (-1279 3302514 3302599 3302778 "UPXS2" 3303005 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1278 3293992 3301896 3302160 "UPXS" 3302308 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1277 3292628 3292899 3293250 "UPSQFREE" 3293735 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1276 3285456 3288894 3288949 "UPSCAT" 3290029 NIL UPSCAT (NIL T T) -9 NIL 3290795 NIL) (-1275 3284612 3284867 3285194 "UPSCAT-" 3285199 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1274 3284233 3284282 3284415 "UPOLYC2" 3284563 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3268367 3277360 3277403 "UPOLYC" 3279504 NIL UPOLYC (NIL T) -9 NIL 3280725 NIL) (-1272 3259215 3262121 3265268 "UPOLYC-" 3265273 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3258536 3258661 3258825 "UPMP" 3259104 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1270 3258083 3258170 3258309 "UPDIVP" 3258449 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1269 3256621 3256900 3257216 "UPDECOMP" 3257832 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1268 3255834 3255964 3256150 "UPCDEN" 3256505 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1267 3255347 3255422 3255571 "UP2" 3255759 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1266 3245922 3255030 3255159 "UP" 3255266 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1265 3245127 3245264 3245469 "UNISEG2" 3245765 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1264 3243480 3244331 3244608 "UNISEG" 3244885 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3242522 3242720 3242946 "UNIFACT" 3243296 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1262 3229232 3242426 3242498 "ULSCONS" 3242503 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1261 3209032 3222312 3222374 "ULSCCAT" 3223012 NIL ULSCCAT (NIL T T) -9 NIL 3223301 NIL) (-1260 3208028 3208327 3208715 "ULSCCAT-" 3208720 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1259 3196473 3203574 3203617 "ULSCAT" 3204480 NIL ULSCAT (NIL T) -9 NIL 3205211 NIL) (-1258 3195897 3195982 3196161 "ULS2" 3196388 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1257 3177707 3195209 3195451 "ULS" 3195713 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3176622 3177322 3177436 "UINT8" 3177547 T UINT8 (NIL) -8 NIL NIL 3177639) (-1255 3175536 3176236 3176350 "UINT64" 3176461 T UINT64 (NIL) -8 NIL NIL 3176553) (-1254 3174450 3175150 3175264 "UINT32" 3175375 T UINT32 (NIL) -8 NIL NIL 3175467) (-1253 3173364 3174064 3174178 "UINT16" 3174289 T UINT16 (NIL) -8 NIL NIL 3174381) (-1252 3171443 3172610 3172640 "UFD" 3172852 T UFD (NIL) -9 NIL 3172966 NIL) (-1251 3171225 3171283 3171378 "UFD-" 3171383 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1250 3170283 3170490 3170706 "UDVO" 3171031 T UDVO (NIL) -7 NIL NIL NIL) (-1249 3168049 3168508 3168979 "UDPO" 3169847 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1248 3167761 3168004 3168035 "TYPEAST" 3168040 T TYPEAST (NIL) -8 NIL NIL NIL) (-1247 3167694 3167699 3167729 "TYPE" 3167734 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166647 3166867 3167107 "TWOFACT" 3167488 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1245 3165622 3166056 3166291 "TUPLE" 3166447 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1244 3163259 3163832 3164371 "TUBETOOL" 3165105 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1243 3162065 3162306 3162548 "TUBE" 3163052 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1242 3150207 3154822 3154919 "TSETCAT" 3160188 NIL TSETCAT (NIL T T T T) -9 NIL 3161720 NIL) (-1241 3144675 3146539 3148430 "TSETCAT-" 3148435 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1240 3138854 3143647 3143930 "TS" 3144427 NIL TS (NIL T) -8 NIL NIL NIL) (-1239 3133327 3134340 3135269 "TRMANIP" 3137990 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1238 3132756 3132831 3132994 "TRIMAT" 3133259 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1237 3130568 3130859 3131216 "TRIGMNIP" 3132505 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1236 3130052 3130201 3130231 "TRIGCAT" 3130444 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1235 3129697 3129800 3129941 "TRIGCAT-" 3129946 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1234 3126311 3128555 3128836 "TREE" 3129451 NIL TREE (NIL T) -8 NIL NIL NIL) (-1233 3125417 3126113 3126143 "TRANFUN" 3126178 T TRANFUN (NIL) -9 NIL 3126244 NIL) (-1232 3124636 3124887 3125167 "TRANFUN-" 3125172 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1231 3124434 3124472 3124533 "TOPSP" 3124597 T TOPSP (NIL) -7 NIL NIL NIL) (-1230 3123764 3123897 3124051 "TOOLSIGN" 3124315 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1229 3122278 3122941 3123180 "TEXTFILE" 3123547 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1228 3122053 3122090 3122162 "TEX1" 3122241 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1227 3119857 3120506 3120935 "TEX" 3121646 T TEX (NIL) -8 NIL NIL NIL) (-1226 3119493 3119568 3119658 "TEMUTL" 3119789 T TEMUTL (NIL) -7 NIL NIL NIL) (-1225 3117587 3117927 3118252 "TBCMPPK" 3119216 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1224 3108914 3115673 3115729 "TBAGG" 3116129 NIL TBAGG (NIL T T) -9 NIL 3116340 NIL) (-1223 3103798 3105472 3107226 "TBAGG-" 3107231 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1222 3103164 3103289 3103434 "TANEXP" 3103687 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1221 3102615 3102939 3103029 "TALGOP" 3103109 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1220 3102009 3102126 3102264 "TABLEAU" 3102512 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1219 3095023 3101866 3101959 "TABLE" 3101964 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3089553 3090851 3092099 "TABLBUMP" 3093809 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1217 3088763 3088922 3089103 "SYSTEM" 3089394 T SYSTEM (NIL) -8 NIL NIL NIL) (-1216 3085168 3085921 3086704 "SYSSOLP" 3088014 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1215 3084930 3085123 3085154 "SYSPTR" 3085159 T SYSPTR (NIL) -8 NIL NIL NIL) (-1214 3083765 3084457 3084583 "SYSNNI" 3084769 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084861) (-1213 3082968 3083523 3083602 "SYSINT" 3083662 NIL SYSINT (NIL NIL) -8 NIL NIL 3083707) (-1212 3079066 3080246 3080956 "SYNTAX" 3082280 T SYNTAX (NIL) -8 NIL NIL NIL) (-1211 3076146 3076826 3077458 "SYMTAB" 3078456 T SYMTAB (NIL) -8 NIL NIL NIL) (-1210 3071245 3072297 3073280 "SYMS" 3075185 T SYMS (NIL) -8 NIL NIL NIL) (-1209 3068144 3070696 3070929 "SYMPOLY" 3071047 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1208 3067649 3067736 3067859 "SYMFUNC" 3068056 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1207 3063447 3064961 3065774 "SYMBOL" 3066858 T SYMBOL (NIL) -8 NIL NIL NIL) (-1206 3056920 3058675 3060395 "SWITCH" 3061749 T SWITCH (NIL) -8 NIL NIL NIL) (-1205 3049674 3055876 3056170 "SUTS" 3056684 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3041152 3049056 3049320 "SUPXS" 3049468 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3040299 3040438 3040655 "SUPFRACF" 3041020 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1202 3039914 3039979 3040092 "SUP2" 3040234 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1201 3030437 3039532 3039658 "SUP" 3039823 NIL SUP (NIL T) -8 NIL NIL NIL) (-1200 3028861 3029159 3029515 "SUMRF" 3030136 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1199 3028184 3028262 3028454 "SUMFS" 3028782 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1198 3010029 3027496 3027738 "SULS" 3028000 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1197 3009577 3009851 3009921 "SUCHTAST" 3009981 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1196 3008818 3009102 3009242 "SUCH" 3009485 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1195 3002457 3003724 3004683 "SUBSPACE" 3007906 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1194 3001877 3001977 3002141 "SUBRESP" 3002345 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1193 2995888 2997170 2998317 "STTFNC" 3000777 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1192 2989082 2990553 2991864 "STTF" 2994624 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2980199 2982264 2984058 "STTAYLOR" 2987323 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1190 2972953 2980063 2980146 "STRTBL" 2980151 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1189 2967350 2972662 2972761 "STRING" 2972876 T STRING (NIL) -8 NIL NIL NIL) (-1188 2966854 2966937 2967081 "STREAM3" 2967267 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1187 2965818 2966019 2966254 "STREAM2" 2966667 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1186 2965500 2965558 2965651 "STREAM1" 2965760 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1185 2957610 2963119 2963730 "STREAM" 2964924 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1184 2956602 2956807 2957038 "STINPROD" 2957426 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1183 2955717 2956091 2956239 "STEPAST" 2956476 T STEPAST (NIL) -8 NIL NIL NIL) (-1182 2955213 2955465 2955495 "STEP" 2955575 T STEP (NIL) -9 NIL 2955653 NIL) (-1181 2948269 2955112 2955189 "STBL" 2955194 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1180 2942827 2947432 2947475 "STAGG" 2947628 NIL STAGG (NIL T) -9 NIL 2947717 NIL) (-1179 2940379 2941131 2942003 "STAGG-" 2942008 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1178 2938351 2940149 2940241 "STACK" 2940322 NIL STACK (NIL T) -8 NIL NIL NIL) (-1177 2930358 2936492 2936948 "SREGSET" 2937981 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922705 2924152 2925665 "SRDCMPK" 2928964 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2915014 2920064 2920094 "SRAGG" 2921397 T SRAGG (NIL) -9 NIL 2922005 NIL) (-1174 2913965 2914286 2914665 "SRAGG-" 2914670 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2907549 2912912 2913333 "SQMATRIX" 2913591 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900961 2904267 2904994 "SPLTREE" 2906894 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896786 2897617 2898263 "SPLNODE" 2900387 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895761 2896066 2896096 "SPFCAT" 2896540 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2894456 2894708 2894972 "SPECOUT" 2895519 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2885102 2887420 2887450 "SPADXPT" 2892128 T SPADXPT (NIL) -9 NIL 2894294 NIL) (-1167 2884857 2884903 2884972 "SPADPRSR" 2885055 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2882460 2884812 2884843 "SPADAST" 2884848 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2874061 2876164 2876207 "SPACEC" 2880580 NIL SPACEC (NIL T) -9 NIL 2882396 NIL) (-1164 2871861 2873993 2874042 "SPACE3" 2874047 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2870593 2870784 2871075 "SORTPAK" 2871666 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868655 2868988 2869400 "SOLVETRA" 2870257 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867693 2867927 2868188 "SOLVESER" 2868428 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862925 2863885 2864880 "SOLVERAD" 2866745 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858650 2859349 2860078 "SOLVEFOR" 2862292 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2852261 2857998 2858095 "SNTSCAT" 2858100 NIL SNTSCAT (NIL T T T T) -9 NIL 2858170 NIL) (-1157 2845805 2850584 2850975 "SMTS" 2851951 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2839520 2845693 2845770 "SMP" 2845775 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837649 2837980 2838378 "SMITH" 2839217 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2829181 2834228 2834331 "SMATCAT" 2835682 NIL SMATCAT (NIL NIL T T T) -9 NIL 2836232 NIL) (-1153 2825953 2826944 2828122 "SMATCAT-" 2828127 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2823422 2825161 2825204 "SKAGG" 2825465 NIL SKAGG (NIL T) -9 NIL 2825600 NIL) (-1151 2818916 2822895 2823079 "SINT" 2823231 T SINT (NIL) -8 NIL NIL 2823393) (-1150 2818682 2818726 2818792 "SIMPAN" 2818872 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2817502 2817741 2818016 "SIGNRF" 2818441 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2816317 2816486 2816770 "SIGNEF" 2817331 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2815557 2815900 2816024 "SIGAST" 2816215 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814782 2815092 2815232 "SIG" 2815439 T SIG (NIL) -8 NIL NIL NIL) (-1145 2812434 2812926 2813432 "SHP" 2814323 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805807 2812335 2812411 "SHDP" 2812416 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2805318 2805558 2805588 "SGROUP" 2805681 T SGROUP (NIL) -9 NIL 2805743 NIL) (-1142 2805170 2805202 2805275 "SGROUP-" 2805280 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801889 2802659 2803382 "SGCF" 2804469 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2795598 2801335 2801432 "SFRTCAT" 2801437 NIL SFRTCAT (NIL T T T T) -9 NIL 2801476 NIL) (-1139 2788917 2790037 2791173 "SFRGCD" 2794581 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781935 2783116 2784302 "SFQCMPK" 2787850 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2781537 2781644 2781755 "SFORT" 2781876 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2780463 2781377 2781498 "SEXOF" 2781503 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2776052 2776959 2777054 "SEXCAT" 2779676 NIL SEXCAT (NIL T T T T T) -9 NIL 2780236 NIL) (-1134 2774967 2775933 2776001 "SEX" 2776006 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773089 2773680 2773985 "SETMN" 2774708 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772619 2772807 2772837 "SETCAT" 2772954 T SETCAT (NIL) -9 NIL 2773039 NIL) (-1131 2772387 2772451 2772550 "SETCAT-" 2772555 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2768490 2770848 2770891 "SETAGG" 2771761 NIL SETAGG (NIL T) -9 NIL 2772101 NIL) (-1129 2767912 2768064 2768301 "SETAGG-" 2768306 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764721 2767846 2767894 "SET" 2767899 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2764104 2764417 2764518 "SEQAST" 2764642 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2763231 2763597 2763658 "SEGXCAT" 2763944 NIL SEGXCAT (NIL T T) -9 NIL 2764064 NIL) (-1125 2762156 2762424 2762467 "SEGCAT" 2762989 NIL SEGCAT (NIL T) -9 NIL 2763210 NIL) (-1124 2761771 2761836 2761949 "SEGBIND2" 2762091 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760661 2761134 2761342 "SEGBIND" 2761598 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2760180 2760462 2760539 "SEGAST" 2760606 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2759389 2759525 2759729 "SEG2" 2760024 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2758305 2759055 2759237 "SEG" 2759242 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2757538 2758240 2758287 "SDVAR" 2758292 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748889 2757308 2757438 "SDPOL" 2757443 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2747458 2747748 2748067 "SCPKG" 2748604 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2746580 2746794 2746986 "SCOPE" 2747288 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745776 2745934 2746113 "SCACHE" 2746435 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2745360 2745594 2745624 "SASTCAT" 2745629 T SASTCAT (NIL) -9 NIL 2745642 NIL) (-1113 2744763 2745195 2745271 "SAOS" 2745306 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2744322 2744363 2744536 "SAERFFC" 2744722 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2743909 2743950 2744109 "SAEFACT" 2744281 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2736936 2743806 2743886 "SAE" 2743891 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735239 2735571 2735972 "RURPK" 2736602 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733816 2734182 2734487 "RULESET" 2735073 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2733386 2733610 2733693 "RULECOLD" 2733768 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2730501 2731139 2731597 "RULE" 2733067 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2730285 2730319 2730390 "RTVALUE" 2730452 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729696 2730002 2730096 "RSTRCAST" 2730213 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2724466 2725339 2726259 "RSETGCD" 2728895 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2713037 2718774 2718871 "RSETCAT" 2722990 NIL RSETCAT (NIL T T T T) -9 NIL 2724087 NIL) (-1101 2710856 2711503 2712327 "RSETCAT-" 2712332 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2703164 2704618 2706138 "RSDCMPK" 2709455 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2701033 2701596 2701670 "RRCC" 2702756 NIL RRCC (NIL T T) -9 NIL 2703100 NIL) (-1098 2700354 2700558 2700837 "RRCC-" 2700842 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699737 2700050 2700151 "RPTAST" 2700275 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2672123 2682849 2682916 "RPOLCAT" 2693582 NIL RPOLCAT (NIL T T T) -9 NIL 2696742 NIL) (-1095 2663093 2665961 2669083 "RPOLCAT-" 2669088 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2653546 2661304 2661786 "ROUTINE" 2662633 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649595 2653172 2653312 "ROMAN" 2653428 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647707 2648455 2648715 "ROIRC" 2649400 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2643425 2646196 2646226 "RNS" 2646530 T RNS (NIL) -9 NIL 2646804 NIL) (-1090 2641832 2642317 2642851 "RNS-" 2642926 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640793 2641197 2641399 "RNGBIND" 2641683 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2640086 2640590 2640620 "RNG" 2640625 T RNG (NIL) -9 NIL 2640646 NIL) (-1087 2639381 2639859 2639902 "RMODULE" 2639907 NIL RMODULE (NIL T) -9 NIL 2639934 NIL) (-1086 2638205 2638311 2638647 "RMCAT2" 2639282 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634707 2637551 2637848 "RMATRIX" 2637967 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2627206 2629794 2629909 "RMATCAT" 2633268 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2634250 NIL) (-1083 2626545 2626728 2627035 "RMATCAT-" 2627040 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2626118 2626332 2626375 "RLINSET" 2626437 NIL RLINSET (NIL T) -9 NIL 2626481 NIL) (-1081 2625679 2625760 2625888 "RINTERP" 2626037 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624603 2625277 2625307 "RING" 2625363 T RING (NIL) -9 NIL 2625455 NIL) (-1079 2624383 2624439 2624536 "RING-" 2624541 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2623194 2623461 2623719 "RIDIST" 2624147 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613819 2622662 2622868 "RGCHAIN" 2623042 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2613077 2613561 2613602 "RGBCSPC" 2613660 NIL RGBCSPC (NIL T) -9 NIL 2613712 NIL) (-1075 2612143 2612602 2612643 "RGBCMDL" 2612875 NIL RGBCMDL (NIL T) -9 NIL 2612989 NIL) (-1074 2611783 2611852 2611955 "RFFACTOR" 2612074 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2611502 2611543 2611640 "RFFACT" 2611742 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2609553 2609983 2610365 "RFDIST" 2611142 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2606493 2607161 2607831 "RF" 2608917 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2605940 2606038 2606201 "RETSOL" 2606395 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2605558 2605656 2605699 "RETRACT" 2605832 NIL RETRACT (NIL T) -9 NIL 2605919 NIL) (-1068 2605401 2605432 2605519 "RETRACT-" 2605524 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604949 2605223 2605293 "RETAST" 2605353 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2597299 2604602 2604729 "RESULT" 2604844 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595734 2596568 2596767 "RESRING" 2597202 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2595358 2595419 2595517 "RESLATC" 2595671 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2595057 2595098 2595205 "REPSQ" 2595317 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594748 2594789 2594900 "REPDB" 2595016 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2588580 2590037 2591260 "REP2" 2593560 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2584883 2585638 2586446 "REP1" 2587807 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2582263 2582885 2583487 "REP" 2584303 T REP (NIL) -7 NIL NIL NIL) (-1058 2574271 2580404 2580860 "REGSET" 2581893 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572980 2573419 2573669 "REF" 2574056 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2572345 2572460 2572627 "REDORDER" 2572864 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567709 2571558 2571785 "RECLOS" 2572173 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566743 2566942 2567157 "REALSOLV" 2567516 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2563190 2564028 2564912 "REAL0Q" 2565908 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558743 2559779 2560840 "REAL0" 2562171 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2558577 2558630 2558660 "REAL" 2558665 T REAL (NIL) -9 NIL 2558700 NIL) (-1050 2557988 2558294 2558388 "RDUCEAST" 2558505 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2557387 2557465 2557672 "RDIV" 2557910 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2556437 2556629 2556842 "RDIST" 2557209 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2555022 2555321 2555693 "RDETRS" 2556145 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552816 2553288 2553826 "RDETR" 2554564 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2551435 2551719 2552116 "RDEEFS" 2552532 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549938 2550250 2550675 "RDEEF" 2551123 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2543415 2546892 2546922 "RCFIELD" 2548217 T RCFIELD (NIL) -9 NIL 2548948 NIL) (-1042 2541371 2541983 2542679 "RCFIELD-" 2542754 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2537423 2539444 2539487 "RCAGG" 2540571 NIL RCAGG (NIL T) -9 NIL 2541036 NIL) (-1040 2537033 2537145 2537308 "RCAGG-" 2537313 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2536350 2536480 2536645 "RATRET" 2536917 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535891 2535970 2536091 "RATFACT" 2536278 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2535169 2535319 2535471 "RANDSRC" 2535761 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534897 2534947 2535020 "RADUTIL" 2535118 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2527021 2533728 2534039 "RADIX" 2534620 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516615 2526863 2526993 "RADFF" 2526998 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2516244 2516337 2516367 "RADCAT" 2516527 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2516014 2516074 2516174 "RADCAT-" 2516179 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513925 2515784 2515876 "QUEUE" 2515957 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2513550 2513599 2513730 "QUATCT2" 2513876 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2505926 2509973 2510015 "QUATCAT" 2510806 NIL QUATCAT (NIL T) -9 NIL 2511572 NIL) (-1028 2501807 2503102 2504492 "QUATCAT-" 2504588 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497646 2501740 2501788 "QUAT" 2501793 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2494902 2496694 2496737 "QUAGG" 2497118 NIL QUAGG (NIL T) -9 NIL 2497293 NIL) (-1025 2494450 2494724 2494794 "QQUTAST" 2494854 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2493361 2493963 2494128 "QFORM" 2494331 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2492986 2493035 2493166 "QFCAT2" 2493312 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482662 2488833 2488875 "QFCAT" 2489543 NIL QFCAT (NIL T) -9 NIL 2490544 NIL) (-1021 2477977 2479430 2481024 "QFCAT-" 2481120 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2477408 2477542 2477674 "QEQUAT" 2477867 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2470426 2471607 2472793 "QCMPACK" 2476341 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469655 2469837 2470073 "QALGSET2" 2470244 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2467105 2467641 2468071 "QALGSET" 2469310 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465772 2466014 2466333 "PWFFINTB" 2466878 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463917 2464115 2464471 "PUSHVAR" 2465586 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459644 2460860 2460903 "PTRANFN" 2462814 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457981 2458326 2458650 "PTPACK" 2459355 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457604 2457667 2457778 "PTFUNC2" 2457918 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2451529 2456393 2456436 "PTCAT" 2456736 NIL PTCAT (NIL T) -9 NIL 2456889 NIL) (-1010 2451178 2451219 2451345 "PSQFR" 2451488 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449750 2450066 2450402 "PSEUDLIN" 2450876 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2436270 2438845 2441171 "PSETPK" 2447510 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428978 2432006 2432104 "PSETCAT" 2435145 NIL PSETCAT (NIL T T T T) -9 NIL 2435959 NIL) (-1006 2426703 2427445 2428269 "PSETCAT-" 2428274 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2426016 2426211 2426241 "PSCURVE" 2426513 T PSCURVE (NIL) -9 NIL 2426680 NIL) (-1004 2421732 2423506 2423573 "PSCAT" 2424425 NIL PSCAT (NIL T T T) -9 NIL 2424665 NIL) (-1003 2420726 2421008 2421411 "PSCAT-" 2421416 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418925 2419785 2420050 "PRTITION" 2420483 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2418336 2418642 2418736 "PRTDAST" 2418853 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2407180 2409602 2411792 "PRS" 2416198 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404800 2406502 2406542 "PRQAGG" 2406725 NIL PRQAGG (NIL T) -9 NIL 2406827 NIL) (-998 2403979 2404428 2404456 "PROPLOG" 2404595 T PROPLOG (NIL) -9 NIL 2404710 NIL) (-997 2403577 2403640 2403763 "PROPFUN2" 2403902 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402874 2403013 2403185 "PROPFUN1" 2403438 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400853 2401621 2401918 "PROPFRML" 2402610 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2400298 2400429 2400557 "PROPERTY" 2400745 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2394186 2398464 2399284 "PRODUCT" 2399524 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2393976 2394014 2394073 "PRINT" 2394147 T PRINT (NIL) -7 NIL NIL NIL) (-991 2393292 2393433 2393585 "PRIMES" 2393856 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2391339 2391758 2392224 "PRIMELT" 2392871 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2391056 2391117 2391145 "PRIMCAT" 2391269 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2390045 2390241 2390469 "PRIMARR2" 2390874 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385767 2389983 2390028 "PRIMARR" 2390033 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2385404 2385466 2385577 "PREASSOC" 2385705 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2382362 2384862 2385096 "PR" 2385215 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381813 2381970 2381998 "PPCURVE" 2382203 T PPCURVE (NIL) -9 NIL 2382339 NIL) (-983 2381360 2381608 2381691 "PORTNUM" 2381750 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378697 2379118 2379710 "POLYROOT" 2380941 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2378074 2378138 2378372 "POLYLIFT" 2378633 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2374295 2374798 2375427 "POLYCATQ" 2377619 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2359943 2366042 2366107 "POLYCAT" 2369621 NIL POLYCAT (NIL T T T) -9 NIL 2371499 NIL) (-978 2353062 2355254 2357638 "POLYCAT-" 2357643 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2352643 2352717 2352837 "POLY2UP" 2352988 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2352269 2352332 2352441 "POLY2" 2352580 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2345477 2351873 2352033 "POLY" 2352142 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2344138 2344401 2344677 "POLUTIL" 2345251 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2342457 2342770 2343101 "POLTOPOL" 2343860 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2337453 2342391 2342438 "POINT" 2342443 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2335586 2335997 2336372 "PNTHEORY" 2337098 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2334032 2334341 2334740 "PMTOOLS" 2335284 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2333619 2333703 2333820 "PMSYM" 2333948 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2333121 2333196 2333371 "PMQFCAT" 2333544 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2332502 2332600 2332762 "PMPREDFS" 2333022 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2331845 2331967 2332123 "PMPRED" 2332379 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330499 2330717 2331095 "PMPLCAT" 2331607 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2330025 2330110 2330262 "PMLSAGG" 2330414 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2329492 2329574 2329756 "PMKERNEL" 2329943 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2329103 2329184 2329297 "PMINS" 2329411 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328539 2328614 2328823 "PMFS" 2329028 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327755 2327885 2328090 "PMDOWN" 2328416 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2327004 2327138 2327301 "PMASSFS" 2327642 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2326147 2326329 2326510 "PMASS" 2326843 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325796 2325870 2325964 "PLOTTOOL" 2326073 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2321448 2322642 2323564 "PLOT3D" 2324894 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2320336 2320537 2320772 "PLOT1" 2321252 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314757 2316147 2317295 "PLOT" 2319208 T PLOT (NIL) -8 NIL NIL NIL) (-953 2289932 2294823 2299674 "PLEQN" 2310023 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289619 2289672 2289775 "PINTERPA" 2289879 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2288925 2289059 2289239 "PINTERP" 2289484 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2287010 2288183 2288211 "PID" 2288393 T PID (NIL) -9 NIL 2288527 NIL) (-949 2286755 2286798 2286873 "PICOERCE" 2286967 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2285851 2286519 2286606 "PI" 2286646 T PI (NIL) -8 NIL NIL 2286713) (-947 2285159 2285310 2285486 "PGROEB" 2285707 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280598 2281557 2282463 "PGE" 2284273 T PGE (NIL) -7 NIL NIL NIL) (-945 2278679 2278968 2279334 "PGCD" 2280315 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2278005 2278120 2278281 "PFRPAC" 2278563 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2274255 2276553 2276906 "PFR" 2277684 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272608 2272888 2273213 "PFOTOOLS" 2274002 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2271123 2271380 2271731 "PFOQ" 2272365 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269606 2269836 2270192 "PFO" 2270907 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266684 2268197 2268225 "PFECAT" 2268810 T PFECAT (NIL) -9 NIL 2269194 NIL) (-938 2266111 2266283 2266497 "PFECAT-" 2266502 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264684 2264966 2265267 "PFBRU" 2265860 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2262514 2262902 2263334 "PFBR" 2264335 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2258439 2262403 2262472 "PF" 2262477 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2253493 2254646 2255516 "PERMGRP" 2257602 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2251405 2252517 2252558 "PERMCAT" 2252958 NIL PERMCAT (NIL T) -9 NIL 2253256 NIL) (-932 2251052 2251099 2251223 "PERMAN" 2251358 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2246854 2248561 2249209 "PERM" 2250437 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2244095 2246519 2246641 "PENDTREE" 2246765 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242976 2243239 2243280 "PDSPC" 2243813 NIL PDSPC (NIL T) -9 NIL 2244058 NIL) (-928 2242031 2242297 2242659 "PDSPC-" 2242664 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240745 2241681 2241722 "PDRING" 2241727 NIL PDRING (NIL T) -9 NIL 2241755 NIL) (-926 2239488 2240250 2240304 "PDMOD" 2240309 NIL PDMOD (NIL T T) -9 NIL 2240413 NIL) (-925 2236655 2237481 2238149 "PDEPROB" 2238840 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2234164 2234704 2235259 "PDEPACK" 2236120 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2233052 2233266 2233517 "PDECOMP" 2233963 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230569 2231460 2231488 "PDECAT" 2232275 T PDECAT (NIL) -9 NIL 2232988 NIL) (-921 2230186 2230253 2230307 "PDDOM" 2230472 NIL PDDOM (NIL T T) -9 NIL 2230552 NIL) (-920 2229999 2230035 2230142 "PDDOM-" 2230147 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229744 2229783 2229873 "PCOMP" 2229960 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2227784 2228545 2228842 "PBWLB" 2229473 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2227410 2227473 2227582 "PATTERN2" 2227721 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2225119 2225555 2226012 "PATTERN1" 2226999 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2217298 2219192 2220530 "PATTERN" 2223802 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2216856 2216929 2217061 "PATRES2" 2217225 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2214122 2214805 2215286 "PATRES" 2216421 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2211975 2212410 2212817 "PATMATCH" 2213789 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2211429 2211680 2211721 "PATMAB" 2211828 NIL PATMAB (NIL T) -9 NIL 2211911 NIL) (-910 2209875 2210283 2210541 "PATLRES" 2211234 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2209413 2209544 2209585 "PATAB" 2209590 NIL PATAB (NIL T) -9 NIL 2209762 NIL) (-908 2207553 2207990 2208413 "PARTPERM" 2209010 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2207162 2207237 2207339 "PARSURF" 2207484 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2206788 2206851 2206960 "PARSU2" 2207099 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2206546 2206592 2206659 "PARSER" 2206741 T PARSER (NIL) -7 NIL NIL NIL) (-904 2206155 2206230 2206332 "PARSCURV" 2206477 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2205781 2205844 2205953 "PARSC2" 2206092 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2205408 2205478 2205575 "PARPCURV" 2205717 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2205034 2205097 2205206 "PARPC2" 2205345 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2204023 2204407 2204589 "PARAMAST" 2204872 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2203531 2203629 2203748 "PAN2EXPR" 2203924 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2202224 2202652 2202880 "PALETTE" 2203323 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2200569 2201229 2201589 "PAIR" 2201910 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2193481 2199826 2200021 "PADICRC" 2200423 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2185717 2192825 2193010 "PADICRAT" 2193328 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2182507 2184377 2184417 "PADICCT" 2184998 NIL PADICCT (NIL NIL) -9 NIL 2185280 NIL) (-893 2180516 2182444 2182489 "PADIC" 2182494 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179461 2179673 2179941 "PADEPAC" 2180303 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2178661 2178806 2179012 "PADE" 2179323 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176894 2177869 2178149 "OWP" 2178465 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2176339 2176600 2176697 "OVERSET" 2176817 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2175259 2175944 2176116 "OVAR" 2176207 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2163495 2166368 2168568 "OUTFORM" 2173079 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2162777 2163092 2163219 "OUTBFILE" 2163388 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2162054 2162249 2162277 "OUTBCON" 2162595 T OUTBCON (NIL) -9 NIL 2162761 NIL) (-884 2161637 2161767 2161924 "OUTBCON-" 2161929 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2160877 2161022 2161183 "OUT" 2161496 T OUT (NIL) -7 NIL NIL NIL) (-882 2160173 2160606 2160695 "OSI" 2160808 T OSI (NIL) -8 NIL NIL NIL) (-881 2159592 2160014 2160042 "OSGROUP" 2160047 T OSGROUP (NIL) -9 NIL 2160069 NIL) (-880 2158303 2158564 2158849 "ORTHPOL" 2159339 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2155554 2158138 2158259 "OREUP" 2158264 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2152657 2155245 2155372 "ORESUP" 2155496 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2150157 2150685 2151246 "OREPCTO" 2152146 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2143535 2146030 2146071 "OREPCAT" 2148419 NIL OREPCAT (NIL T) -9 NIL 2149523 NIL) (-875 2140508 2141464 2142522 "OREPCAT-" 2142527 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2139701 2139978 2140006 "ORDTYPE" 2140315 T ORDTYPE (NIL) -9 NIL 2140478 NIL) (-873 2139002 2139218 2139473 "ORDTYPE-" 2139478 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2138358 2138741 2138899 "ORDSTRCT" 2138904 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2137856 2138226 2138254 "ORDSET" 2138259 T ORDSET (NIL) -9 NIL 2138281 NIL) (-870 2136214 2137185 2137213 "ORDRING" 2137415 T ORDRING (NIL) -9 NIL 2137540 NIL) (-869 2135835 2135953 2136097 "ORDRING-" 2136102 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2135086 2135651 2135679 "ORDMON" 2135684 T ORDMON (NIL) -9 NIL 2135705 NIL) (-867 2134230 2134395 2134590 "ORDFUNS" 2134935 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2133445 2133960 2133988 "ORDFIN" 2134053 T ORDFIN (NIL) -9 NIL 2134127 NIL) (-865 2132699 2132838 2133024 "ORDCOMP2" 2133305 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2129046 2131285 2131694 "ORDCOMP" 2132323 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2125567 2126537 2127351 "OPTPROB" 2128252 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2122309 2123008 2123712 "OPTPACK" 2124883 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119922 2120748 2120776 "OPTCAT" 2121595 T OPTCAT (NIL) -9 NIL 2122245 NIL) (-860 2119240 2119599 2119704 "OPSIG" 2119837 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2119002 2119047 2119113 "OPQUERY" 2119194 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2118308 2118588 2118629 "OPERCAT" 2118841 NIL OPERCAT (NIL T) -9 NIL 2118938 NIL) (-857 2118051 2118119 2118236 "OPERCAT-" 2118241 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2114960 2116362 2116866 "OP" 2117580 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2114253 2114380 2114554 "ONECOMP2" 2114832 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2110866 2113050 2113419 "ONECOMP" 2113917 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2110267 2110391 2110521 "OMSERVER" 2110756 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2106781 2109707 2109747 "OMSAGG" 2109808 NIL OMSAGG (NIL T) -9 NIL 2109872 NIL) (-851 2105356 2105667 2105949 "OMPKG" 2106519 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2103703 2104905 2105074 "OMLO" 2105237 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2102639 2102810 2103030 "OMEXPR" 2103529 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2101724 2102060 2102220 "OMERRK" 2102499 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2100961 2101270 2101406 "OMERR" 2101608 T OMERR (NIL) -8 NIL NIL NIL) (-846 2100352 2100638 2100746 "OMENC" 2100873 T OMENC (NIL) -8 NIL NIL NIL) (-845 2093989 2095432 2096603 "OMDEV" 2099201 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2093022 2093229 2093423 "OMCONN" 2093815 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2092428 2092555 2092583 "OM" 2092882 T OM (NIL) -9 NIL NIL NIL) (-842 2090706 2091898 2091926 "OINTDOM" 2091931 T OINTDOM (NIL) -9 NIL 2091952 NIL) (-841 2087780 2089394 2089731 "OFMONOID" 2090401 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2087014 2087717 2087762 "ODVAR" 2087767 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2084151 2086759 2086914 "ODR" 2086919 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2075556 2083927 2084053 "ODPOL" 2084058 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068899 2075428 2075533 "ODP" 2075538 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2067641 2067880 2068155 "ODETOOLS" 2068673 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2064584 2065266 2065982 "ODESYS" 2066974 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2059414 2060374 2061399 "ODERTRIC" 2063659 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2058834 2058922 2059116 "ODERED" 2059326 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2055686 2056270 2056947 "ODERAT" 2058257 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2052603 2053110 2053707 "ODEPRRIC" 2055215 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2050498 2051142 2051628 "ODEPROB" 2052137 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046964 2047503 2048150 "ODEPRIM" 2049977 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2046207 2046315 2046575 "ODEPAL" 2046856 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2042309 2043160 2044024 "ODEPACK" 2045363 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2041352 2041477 2041699 "ODEINT" 2042198 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2035417 2036878 2038325 "ODEIFTBL" 2039925 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2030767 2031601 2032553 "ODEEF" 2034576 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2030110 2030205 2030428 "ODECONST" 2030672 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2028173 2028882 2028910 "ODECAT" 2029515 T ODECAT (NIL) -9 NIL 2030046 NIL) (-821 2027805 2027854 2027981 "OCTCT2" 2028124 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2024298 2027510 2027632 "OCT" 2027715 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023521 2024091 2024119 "OCAMON" 2024124 T OCAMON (NIL) -9 NIL 2024145 NIL) (-818 2017790 2020564 2020604 "OC" 2021701 NIL OC (NIL T) -9 NIL 2022559 NIL) (-817 2014825 2015765 2016755 "OC-" 2016849 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2014245 2014670 2014698 "OASGP" 2014703 T OASGP (NIL) -9 NIL 2014723 NIL) (-815 2013371 2013968 2013996 "OAMONS" 2014036 T OAMONS (NIL) -9 NIL 2014079 NIL) (-814 2012662 2013191 2013219 "OAMON" 2013224 T OAMON (NIL) -9 NIL 2013244 NIL) (-813 2011773 2012411 2012439 "OAGROUP" 2012444 T OAGROUP (NIL) -9 NIL 2012464 NIL) (-812 2011455 2011511 2011600 "NUMTUBE" 2011717 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004974 2006546 2008082 "NUMQUAD" 2009939 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000654 2001688 2002723 "NUMODE" 2003959 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997935 1998875 1998903 "NUMINT" 1999826 T NUMINT (NIL) -9 NIL 2000590 NIL) (-808 1996847 1997080 1997298 "NUMFMT" 1997737 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1983030 1986151 1988683 "NUMERIC" 1994354 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976741 1982478 1982573 "NTSCAT" 1982578 NIL NTSCAT (NIL T T T T) -9 NIL 1982617 NIL) (-805 1975921 1976100 1976293 "NTPOLFN" 1976580 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975547 1975610 1975719 "NSUP2" 1975858 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1962308 1972372 1973184 "NSUP" 1974768 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1951144 1962082 1962215 "NSMP" 1962220 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949552 1949877 1950234 "NREP" 1950832 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1948131 1948395 1948753 "NPCOEF" 1949295 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1947179 1947312 1947528 "NORMRETR" 1948012 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1945190 1945510 1945919 "NORMPK" 1946887 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944869 1944903 1945027 "NORMMA" 1945156 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944652 1944687 1944756 "NONE1" 1944833 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1944416 1944609 1944638 "NONE" 1944643 T NONE (NIL) -8 NIL NIL NIL) (-794 1943907 1943975 1944154 "NODE1" 1944348 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941999 1943030 1943285 "NNI" 1943632 T NNI (NIL) -8 NIL NIL 1943867) (-792 1940395 1940732 1941096 "NLINSOL" 1941667 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936576 1937631 1938530 "NIPROB" 1939516 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1935315 1935567 1935869 "NFINTBAS" 1936338 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1934399 1934965 1935006 "NETCLT" 1935178 NIL NETCLT (NIL T) -9 NIL 1935260 NIL) (-788 1933071 1933338 1933619 "NCODIV" 1934167 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932827 1932870 1932945 "NCNTFRAC" 1933028 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930983 1931371 1931791 "NCEP" 1932452 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929646 1930593 1930621 "NASRING" 1930731 T NASRING (NIL) -9 NIL 1930811 NIL) (-784 1929429 1929485 1929579 "NASRING-" 1929584 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1928396 1929047 1929075 "NARNG" 1929192 T NARNG (NIL) -9 NIL 1929283 NIL) (-782 1928070 1928155 1928289 "NARNG-" 1928294 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926907 1927156 1927391 "NAGSP" 1927855 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917951 1919863 1921536 "NAGS" 1925254 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916475 1916807 1917138 "NAGF07" 1917640 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910947 1912304 1913611 "NAGF04" 1915188 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903819 1905529 1907162 "NAGF02" 1909334 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898983 1900143 1901260 "NAGF01" 1902722 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892563 1894177 1895762 "NAGE04" 1897418 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883624 1885853 1887983 "NAGE02" 1890453 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879517 1880524 1881488 "NAGE01" 1882680 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1877294 1877846 1878404 "NAGD03" 1878979 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868990 1870972 1872926 "NAGD02" 1875360 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862729 1864226 1865666 "NAGD01" 1867570 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858866 1859760 1860597 "NAGC06" 1861912 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1857313 1857663 1858019 "NAGC05" 1858530 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856677 1856808 1856952 "NAGC02" 1857189 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855478 1856205 1856245 "NAALG" 1856324 NIL NAALG (NIL T) -9 NIL 1856385 NIL) (-765 1855307 1855342 1855432 "NAALG-" 1855437 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1849179 1850365 1851552 "MULTSQFR" 1854203 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848486 1848573 1848757 "MULTFACT" 1849091 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840631 1845069 1845122 "MTSCAT" 1846192 NIL MTSCAT (NIL T T) -9 NIL 1846708 NIL) (-761 1840337 1840397 1840489 "MTHING" 1840571 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1840123 1840162 1840222 "MSYSCMD" 1840297 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836868 1839684 1839725 "MSETAGG" 1839730 NIL MSETAGG (NIL T) -9 NIL 1839764 NIL) (-758 1832582 1835623 1835943 "MSET" 1836581 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1828174 1829961 1830706 "MRING" 1831882 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827734 1827807 1827938 "MRF2" 1828101 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1827346 1827387 1827531 "MRATFAC" 1827693 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824916 1825253 1825684 "MPRFF" 1827051 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1818243 1824770 1824867 "MPOLY" 1824872 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817727 1817768 1817976 "MPCPF" 1818202 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1817235 1817284 1817468 "MPC3" 1817678 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1816418 1816511 1816732 "MPC2" 1817150 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814695 1815056 1815446 "MONOTOOL" 1816078 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813840 1814223 1814251 "MONOID" 1814470 T MONOID (NIL) -9 NIL 1814617 NIL) (-747 1813356 1813505 1813686 "MONOID-" 1813691 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1802310 1809176 1809235 "MONOGEN" 1809909 NIL MONOGEN (NIL T T) -9 NIL 1810365 NIL) (-745 1799360 1800263 1801263 "MONOGEN-" 1801382 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1798077 1798625 1798653 "MONADWU" 1799045 T MONADWU (NIL) -9 NIL 1799283 NIL) (-743 1797407 1797608 1797856 "MONADWU-" 1797861 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796692 1796996 1797024 "MONAD" 1797231 T MONAD (NIL) -9 NIL 1797343 NIL) (-741 1796359 1796455 1796587 "MONAD-" 1796592 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794498 1795272 1795551 "MOEBIUS" 1796112 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793666 1794166 1794206 "MODULE" 1794211 NIL MODULE (NIL T) -9 NIL 1794250 NIL) (-738 1793204 1793330 1793520 "MODULE-" 1793525 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790734 1791568 1791895 "MODRING" 1793028 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1787456 1788839 1789360 "MODOP" 1790263 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785942 1786523 1786800 "MODMONOM" 1787319 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774682 1784233 1784647 "MODMON" 1785579 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771508 1773526 1773802 "MODFIELD" 1774557 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1770419 1770789 1770979 "MMLFORM" 1771338 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769939 1769988 1770167 "MMAP" 1770370 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767832 1768771 1768812 "MLO" 1769235 NIL MLO (NIL T) -9 NIL 1769477 NIL) (-729 1765180 1765714 1766316 "MLIFT" 1767313 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764559 1764655 1764809 "MKUCFUNC" 1765091 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1764152 1764228 1764351 "MKRECORD" 1764482 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1763175 1763361 1763589 "MKFUNC" 1763963 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762551 1762667 1762823 "MKFLCFN" 1763058 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761816 1761930 1762115 "MKBCFUNC" 1762444 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757799 1761370 1761506 "MINT" 1761700 T MINT (NIL) -8 NIL NIL NIL) (-722 1756581 1756854 1757131 "MHROWRED" 1757554 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1751325 1755116 1755521 "MFLOAT" 1756196 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750670 1750758 1750929 "MFINFACT" 1751237 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746949 1747833 1748717 "MESH" 1749806 T MESH (NIL) -7 NIL NIL NIL) (-718 1745303 1745651 1746004 "MDDFACT" 1746636 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741839 1744434 1744475 "MDAGG" 1744730 NIL MDAGG (NIL T) -9 NIL 1744873 NIL) (-716 1729541 1741132 1741339 "MCMPLX" 1741652 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728660 1728824 1729025 "MCDEN" 1729390 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726508 1726820 1727200 "MCALCFN" 1728390 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1725385 1725673 1725906 "MAYBE" 1726314 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722943 1723520 1724082 "MATSTOR" 1724856 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1718365 1722315 1722563 "MATRIX" 1722728 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1714065 1714838 1715574 "MATLIN" 1717722 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712641 1712812 1713145 "MATCAT2" 1713900 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701987 1705698 1705775 "MATCAT" 1710807 NIL MATCAT (NIL T T T) -9 NIL 1712279 NIL) (-707 1697940 1699250 1700663 "MATCAT-" 1700668 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696016 1696376 1696760 "MAPPKG3" 1697615 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694973 1695170 1695392 "MAPPKG2" 1695840 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693430 1693756 1694083 "MAPPKG1" 1694679 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692431 1692836 1693013 "MAPPAST" 1693273 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1692036 1692100 1692223 "MAPHACK3" 1692367 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691616 1691689 1691803 "MAPHACK2" 1691968 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1691042 1691157 1691299 "MAPHACK1" 1691507 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688965 1689742 1690046 "MAGMA" 1690770 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1688384 1688689 1688780 "MACROAST" 1688894 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684627 1686623 1687084 "M3D" 1687956 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1678107 1682938 1682979 "LZSTAGG" 1683761 NIL LZSTAGG (NIL T) -9 NIL 1684056 NIL) (-695 1673789 1675238 1676695 "LZSTAGG-" 1676700 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670702 1671680 1672167 "LWORD" 1673334 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1670224 1670506 1670581 "LSTAST" 1670647 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1662152 1669995 1670129 "LSQM" 1670134 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1661370 1661515 1661743 "LSPP" 1662007 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1658107 1658823 1659553 "LSMP1" 1660672 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655889 1656220 1656676 "LSMP" 1657796 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1649025 1654979 1655020 "LSAGG" 1655082 NIL LSAGG (NIL T) -9 NIL 1655160 NIL) (-687 1645534 1646644 1647857 "LSAGG-" 1647862 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642829 1644678 1644927 "LPOLY" 1645329 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1642405 1642496 1642619 "LPEFRAC" 1642738 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1642088 1642167 1642195 "LOGIC" 1642306 T LOGIC (NIL) -9 NIL 1642388 NIL) (-683 1641944 1641973 1642044 "LOGIC-" 1642049 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1641119 1641277 1641470 "LODOOPS" 1641800 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639643 1639892 1640245 "LODOF" 1640866 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635519 1638278 1638319 "LODOCAT" 1638757 NIL LODOCAT (NIL T) -9 NIL 1638968 NIL) (-679 1635234 1635310 1635437 "LODOCAT-" 1635442 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1632220 1635075 1635193 "LODO2" 1635198 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1629327 1632157 1632202 "LODO1" 1632207 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1626422 1629243 1629309 "LODO" 1629314 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1625291 1625468 1625773 "LODEEF" 1626245 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623468 1624385 1624638 "LO" 1625123 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618440 1621634 1621675 "LNAGG" 1622537 NIL LNAGG (NIL T) -9 NIL 1622972 NIL) (-672 1617533 1617801 1618143 "LNAGG-" 1618148 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613513 1614458 1615097 "LMOPS" 1616948 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612812 1613290 1613331 "LMODULE" 1613336 NIL LMODULE (NIL T) -9 NIL 1613362 NIL) (-669 1609767 1612457 1612580 "LMDICT" 1612722 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1609343 1609557 1609598 "LLINSET" 1609659 NIL LLINSET (NIL T) -9 NIL 1609703 NIL) (-667 1608988 1609251 1609311 "LITERAL" 1609316 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608507 1608587 1608726 "LIST3" 1608908 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606605 1606953 1607352 "LIST2MAP" 1608154 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605594 1605790 1606018 "LIST2" 1606423 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1598048 1604528 1604832 "LIST" 1605323 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597631 1597867 1597908 "LINSET" 1597913 NIL LINSET (NIL T) -9 NIL 1597947 NIL) (-661 1596445 1597139 1597306 "LINFORM" 1597516 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594744 1595472 1595513 "LINEXP" 1596003 NIL LINEXP (NIL T) -9 NIL 1596276 NIL) (-659 1593320 1594224 1594405 "LINELT" 1594615 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591877 1592157 1592468 "LINDEP" 1593072 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1591013 1591609 1591719 "LINBASIS" 1591807 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587750 1588499 1589276 "LIMITRF" 1590268 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1586035 1586349 1586758 "LIMITPS" 1587445 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584863 1585438 1585478 "LIECAT" 1585618 NIL LIECAT (NIL T) -9 NIL 1585769 NIL) (-653 1584698 1584731 1584819 "LIECAT-" 1584824 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578718 1584209 1584437 "LIE" 1584519 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570905 1578258 1578414 "LIB" 1578582 T LIB (NIL) -8 NIL NIL NIL) (-650 1566474 1567423 1568358 "LGROBP" 1570022 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1565098 1566006 1566034 "LFCAT" 1566241 T LFCAT (NIL) -9 NIL 1566380 NIL) (-648 1563036 1563370 1563720 "LF" 1564819 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559896 1560568 1561256 "LEXTRIPK" 1562400 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556484 1557466 1557969 "LEXP" 1559476 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555900 1556205 1556297 "LETAST" 1556412 T LETAST (NIL) -8 NIL NIL NIL) (-644 1554286 1554611 1555012 "LEADCDET" 1555582 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553464 1553550 1553779 "LAZM3PK" 1554207 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547975 1551541 1552079 "LAUPOL" 1552976 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547548 1547598 1547759 "LAPLACE" 1547925 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1546396 1547112 1547153 "LALG" 1547215 NIL LALG (NIL T) -9 NIL 1547274 NIL) (-639 1546092 1546169 1546305 "LALG-" 1546310 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543829 1545193 1545444 "LA" 1545925 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543658 1543688 1543729 "KVTFROM" 1543791 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1542415 1543025 1543210 "KTVLOGIC" 1543493 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1542244 1542274 1542315 "KRCFROM" 1542377 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1541136 1541335 1541634 "KOVACIC" 1542044 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540965 1540995 1541036 "KONVERT" 1541098 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540794 1540824 1540865 "KOERCE" 1540927 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1540278 1540371 1540503 "KERNEL2" 1540708 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537965 1538871 1539248 "KERNEL" 1539934 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531436 1536442 1536496 "KDAGG" 1536873 NIL KDAGG (NIL T T) -9 NIL 1537079 NIL) (-628 1530947 1531089 1531294 "KDAGG-" 1531299 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523647 1530608 1530763 "KAFILE" 1530825 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1523251 1523536 1523599 "JVMOP" 1523604 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521987 1522491 1522740 "JVMMDACC" 1523022 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520923 1521377 1521582 "JVMFDACC" 1521802 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519504 1519999 1520299 "JVMCSTTG" 1520643 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518640 1519044 1519205 "JVMCFACC" 1519363 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1518318 1518557 1518606 "JVMBCODE" 1518611 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1512338 1517829 1518057 "JORDAN" 1518139 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511651 1511987 1512108 "JOINAST" 1512237 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507686 1509828 1509882 "IXAGG" 1510811 NIL IXAGG (NIL T T) -9 NIL 1511270 NIL) (-617 1506539 1506911 1507330 "IXAGG-" 1507335 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501628 1506461 1506520 "IVECTOR" 1506525 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1500352 1500631 1500897 "ITUPLE" 1501395 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498824 1499031 1499326 "ITRIGMNP" 1500174 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497551 1497773 1498056 "ITFUN3" 1498600 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1497177 1497240 1497349 "ITFUN2" 1497488 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-611 1496282 1496657 1496831 "ITFORM" 1497023 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1494051 1495302 1495580 "ITAYLOR" 1496037 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1482448 1488188 1489351 "ISUPS" 1492921 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481540 1481692 1481928 "ISUMP" 1482295 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1476390 1481485 1481526 "ISTRING" 1481531 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475806 1476111 1476203 "ISAST" 1476318 T ISAST (NIL) -8 NIL NIL NIL) (-605 1475003 1475097 1475313 "IRURPK" 1475720 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473915 1474140 1474380 "IRSN" 1474783 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471960 1472341 1472770 "IRRF2F" 1473553 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471701 1471745 1471821 "IRREDFFX" 1471916 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1470274 1470575 1470874 "IROOT" 1471434 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1469413 1469767 1469918 "IRFORM" 1470143 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468495 1468626 1468840 "IR2F" 1469296 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1466084 1466603 1467169 "IR2" 1467973 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462524 1463768 1464460 "IR" 1465424 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1462309 1462349 1462409 "IPRNTPK" 1462484 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1458262 1462198 1462267 "IPF" 1462272 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1456283 1458187 1458244 "IPADIC" 1458249 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455541 1455843 1455973 "IP4ADDR" 1456173 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454879 1455170 1455302 "IOMODE" 1455429 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453850 1454476 1454603 "IOBFILE" 1454772 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1453260 1453754 1453782 "IOBCON" 1453787 T IOBCON (NIL) -9 NIL 1453808 NIL) (-589 1452765 1452829 1453012 "INVLAPLA" 1453196 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1442335 1444767 1447153 "INTTR" 1450429 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438628 1439412 1440277 "INTTOOLS" 1441520 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1438208 1438305 1438422 "INTSLPE" 1438531 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435675 1438131 1438190 "INTRVL" 1438195 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1433253 1433789 1434364 "INTRF" 1435160 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432646 1432761 1432903 "INTRET" 1433151 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430619 1431032 1431502 "INTRAT" 1432254 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427864 1428465 1429084 "INTPM" 1430104 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424581 1425208 1425946 "INTPAF" 1427250 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419682 1420722 1421773 "INTPACK" 1423550 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418928 1419086 1419294 "INTHERTR" 1419524 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1418361 1418447 1418635 "INTHERAL" 1418842 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1416129 1416650 1417107 "INTHEORY" 1417924 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407461 1409156 1410928 "INTG0" 1414481 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387986 1392824 1397634 "INTFTBL" 1402671 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1387211 1387373 1387546 "INTFACT" 1387845 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384608 1385084 1385641 "INTEF" 1386765 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382805 1383700 1383728 "INTDOM" 1384029 T INTDOM (NIL) -9 NIL 1384236 NIL) (-570 1382144 1382348 1382590 "INTDOM-" 1382595 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1378018 1380433 1380487 "INTCAT" 1381286 NIL INTCAT (NIL T) -9 NIL 1381607 NIL) (-568 1377472 1377593 1377721 "INTBIT" 1377910 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1376153 1376325 1376632 "INTALG" 1377317 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375630 1375726 1375883 "INTAF" 1376057 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368597 1375440 1375580 "INTABL" 1375585 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367834 1368396 1368461 "INT8" 1368495 T INT8 (NIL) -8 NIL NIL 1368540) (-563 1367070 1367632 1367697 "INT64" 1367731 T INT64 (NIL) -8 NIL NIL 1367776) (-562 1366306 1366868 1366933 "INT32" 1366967 T INT32 (NIL) -8 NIL NIL 1367012) (-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 -1529 (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 1f061129..a7640320 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,465 +1,387 @@ -(733360 . 3501779186) -(((*1 *2 *1 *3) (-12 (-5 *3 (-391)) (-5 *2 (-1303)) (-5 *1 (-1301))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1132)) (-4 *3 (-23)) - (-14 *4 *3))) - ((*1 *1 *2 *3 *1) - (-12 (-5 *1 (-671 *2 *3 *4)) (-4 *2 (-1132)) (-4 *3 (-23)) - (-14 *4 *3))) - ((*1 *1 *1 *1) - (-12 (-5 *1 (-697 *2)) (-4 *2 (-1080)) (-4 *2 (-1132))))) -(((*1 *2) - (-12 (-4 *3 (-571)) (-5 *2 (-663 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-432 *3))))) -(((*1 *2 *2 *1) - (-12 (-5 *2 (-663 *6)) (-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))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1273 (-421 (-560)))) (-5 *1 (-942 *3 *2)) - (-4 *2 (-1273 (-421 *3)))))) -(((*1 *2 *2) - (-12 (-4 *3 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(-13 (-870) (-376))) - (-4 *3 (-1273 *4)) (-5 *2 (-114))))) +(733360 . 3502979433) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5) + (-12 (-5 *3 (-1 (-391) (-391))) (-5 *4 (-391)) + (-5 *2 + (-2 (|:| -1492 *4) (|:| -2482 *4) (|:| |totalpts| (-560)) + (|:| |success| (-114)))) + (-5 *1 (-811)) (-5 *5 (-560))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1297 *4)) (-5 *3 (-793)) (-4 *4 (-363)) + (-5 *1 (-542 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-972 *2)) (-5 *1 (-1013 *2)) (-4 *2 (-1080))))) -(((*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1132)) (-4 *1 (-242 *3)))) - ((*1 *1) (-12 (-4 *1 (-242 *2)) (-4 *2 (-1132))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-948)) (-5 *4 (-898)) (-5 *2 (-1303)) (-5 *1 (-1300)))) - ((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-948)) (-5 *4 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1300)))) - ((*1 *2 *1 *3) (-12 (-5 *3 (-1189)) (-5 *2 (-1303)) (-5 *1 (-1301))))) -(((*1 *2 *3 *4 *4 *5 *6) - (-12 (-5 *3 (-663 (-663 (-972 (-229))))) (-5 *4 (-898)) - (-5 *5 (-948)) (-5 *6 (-663 (-270))) (-5 *2 (-482)) (-5 *1 (-1299)))) + (-12 (-5 *3 (-1207)) (-4 *5 (-1252)) (-4 *6 (-1273 *5)) + (-4 *7 (-1273 (-421 *6))) (-5 *2 (-663 (-975 *5))) + (-5 *1 (-354 *4 *5 *6 *7)) (-4 *4 (-355 *5 *6 *7)))) ((*1 *2 *3) - (-12 (-5 *3 (-663 (-663 (-972 (-229))))) (-5 *2 (-482)) - (-5 *1 (-1299)))) + (-12 (-5 *3 (-1207)) (-4 *1 (-355 *4 *5 *6)) (-4 *4 (-1252)) + (-4 *5 (-1273 *4)) (-4 *6 (-1273 (-421 *5))) (-4 *4 (-376)) + (-5 *2 (-663 (-975 *4)))))) +(((*1 *2 *3 *4 *5 *5) + (-12 (-5 *3 (-3 (-421 (-975 *6)) (-1196 (-1207) (-975 *6)))) + (-5 *5 (-793)) (-4 *6 (-466)) (-5 *2 (-663 (-711 (-421 (-975 *6))))) + (-5 *1 (-304 *6)) (-5 *4 (-711 (-421 (-975 *6)))))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-663 (-663 (-972 (-229))))) (-5 *4 (-663 (-270))) - (-5 *2 (-482)) (-5 *1 (-1299))))) -(((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-183)))) - ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-324)))) - ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-1001)))) - ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-1025)))) - ((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 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*1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1211)) (|:| -2458 (-663 (-342))))) + (-5 *2 (-2 (|:| |localSymbols| (-1211)) (|:| -4422 (-663 (-342))))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-1297 (-721))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1211)) (|:| -2458 (-663 (-342))))) + (-5 *2 (-2 (|:| |localSymbols| (-1211)) (|:| -4422 (-663 (-342))))) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-455)))) @@ -3579,7 +4309,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 (-2 (|:| -2625 *3) (|:| -1405 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -3929 *3) (|:| -3355 *4)))) (-4 *3 (-1080)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-785)))) ((*1 *1 *2) @@ -3588,25 +4318,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) - (|:| -1585 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| -2818 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -1585 (-663 (-1120 (-864 (-229))))) + (|:| -2818 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-229))) - (|:| -1585 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) + (|:| -2818 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) - (|:| -1585 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| -2818 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1247)))) @@ -3624,23 +4354,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -3239 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2426 (-663 (-229))) (|:| |lb| (-663 (-864 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-864 (-229)))))) (|:| |lsa| (-2 (|:| |lfn| (-663 (-326 (-229)))) - (|:| -3239 (-663 (-229))))))) + (|:| -2426 (-663 (-229))))))) (-5 *1 (-863)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -3239 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2426 (-663 (-229))))) (-5 *1 (-863)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-326 (-229))) (|:| -3239 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2426 (-663 (-229))) (|:| |lb| (-663 (-864 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-864 (-229)))))) (-5 *1 (-863)))) @@ -3741,1014 +4471,720 @@ ((*1 *1 *2) (-12 (-5 *2 (-686 *3 *4)) (-4 *3 (-871)) (-4 *4 (-175)) (-5 *1 (-1318 *3 *4))))) -(((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1247)) (-5 *1 (-615 *3)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-114) *3)) (-4 *3 (-1247)) 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(|:| |ineq| (-663 *9))))) + (-5 *1 (-1019 *6 *7 *8 *9 *10)) (-5 *3 (-663 *9)))) + ((*1 *2 *3 *4 *5 *5) + (-12 (-5 *4 (-663 *10)) (-5 *5 (-114)) (-4 *10 (-1102 *6 *7 *8 *9)) + (-4 *6 (-466)) (-4 *7 (-815)) (-4 *8 (-871)) + (-4 *9 (-1096 *6 *7 *8)) + (-5 *2 + (-663 + (-2 (|:| -1638 (-663 *9)) (|:| -2688 *10) (|:| |ineq| (-663 *9))))) + (-5 *1 (-1138 *6 *7 *8 *9 *10)) (-5 *3 (-663 *9))))) (((*1 *2 *3 *3) (|partial| -12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-114)) @@ -6693,163 +6618,188 @@ (|partial| -12 (-4 *4 (-466)) (-4 *5 (-815)) (-4 *6 (-871)) (-4 *7 (-1096 *4 *5 *6)) (-5 *2 (-114)) (-5 *1 (-1138 *4 *5 *6 *7 *3)) (-4 *3 (-1102 *4 *5 *6 *7))))) -(((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-887))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) - (|:| -1585 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) - (|:| |relerr| (-229)))) - (-5 *2 - (-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 (-195))))) -(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-448))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1014 *2)) (-4 *2 (-1233))))) -(((*1 *1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-505))))) -(((*1 *2 *1) - (-12 (-5 *2 (-663 (-51))) (-5 *1 (-915 *3)) (-4 *3 (-1132))))) -(((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-571) (-1069 (-560)))) (-4 *5 (-435 *4)) - (-5 *2 (-419 (-1201 (-421 (-560))))) (-5 *1 (-449 *4 *5 *3)) - (-4 *3 (-1273 *5))))) -(((*1 *2 *1) - (-12 (-4 *2 (-1273 *3)) (-5 *1 (-413 *3 *2)) - (-4 *3 (-13 (-376) (-149)))))) -(((*1 *2 *3 *4 *3 *5) - (-12 (-5 *3 (-1189)) (-5 *4 (-171 (-229))) (-5 *5 (-560)) - (-5 *2 (-1066)) (-5 *1 (-780))))) -(((*1 *2) (-12 (-5 *2 (-1189)) (-5 *1 (-248))))) -(((*1 *1 *1) (-12 (-4 *1 (-680 *2)) (-4 *2 (-1080)))) - ((*1 *2 *3) - (-12 (-4 *4 (-571)) (-4 *4 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(-4 *2 (-871)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-128 *2)) (-4 *2 (-871)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-560)) (-4 *1 (-294 *3)) (-4 *3 (-1247)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-560)) (-4 *1 (-294 *2)) (-4 *2 (-1247)))) ((*1 *1 *2) - (-12 (-5 *2 (-793)) (-4 *1 (-1296 *3)) (-4 *3 (-23)) (-4 *3 (-1247))))) + (-12 + (-5 *2 + (-2 + (|:| -1462 + (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) + (|:| -2818 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| |relerr| (-229)))) + (|:| -1875 + (-2 + (|:| |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"))) + (|:| -2818 + (-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 + (|:| -1462 + (-2 (|:| |xinit| (-229)) (|:| |xend| (-229)) + (|:| |fn| (-1297 (-326 (-229)))) (|:| |yinit| (-663 (-229))) + (|:| |intvals| (-663 (-229))) (|:| |g| (-326 (-229))) + (|:| |abserr| (-229)) (|:| |relerr| (-229)))) + (|:| -1875 + (-2 (|:| |stiffness| (-391)) (|:| |stability| (-391)) + (|:| |expense| (-391)) (|:| |accuracy| (-391)) + (|:| |intermediateResults| (-391)))))) + (-5 *1 (-825)))) + ((*1 *2 *3 *4) + (-12 (-5 *2 (-1303)) (-5 *1 (-1225 *3 *4)) (-4 *3 (-1132)) + (-4 *4 (-1132))))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-571)) (-4 *3 (-1080)) + (-5 *2 (-2 (|:| -3356 *1) (|:| -2698 *1))) (-4 *1 (-876 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-571)) (-4 *5 (-1080)) + (-5 *2 (-2 (|:| -3356 *3) (|:| -2698 *3))) (-5 *1 (-877 *5 *3)) + (-4 *3 (-876 *5))))) +(((*1 *2 *3) (-12 (-5 *3 (-1297 *1)) (-4 *1 (-380 *2)) (-4 *2 (-175)))) + ((*1 *2) (-12 (-4 *2 (-175)) (-5 *1 (-431 *3 *2)) (-4 *3 (-432 *2)))) + ((*1 *2) (-12 (-4 *1 (-432 *2)) (-4 *2 (-175))))) +(((*1 *2 *2) + (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) + (-4 *2 (-13 (-435 *3) (-1033)))))) (((*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1207)) (|:| |fn| (-326 (-229))) - (|:| -1585 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| -2818 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *2 - (-2 - (|:| |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"))) - (|:| -1585 - (-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 *2 *1) - (-12 (-4 *1 (-1135 *3 *4 *5 *6 *7)) (-4 *3 (-1132)) (-4 *4 (-1132)) - (-4 *5 (-1132)) (-4 *6 (-1132)) (-4 *7 (-1132)) (-5 *2 (-114))))) -(((*1 *2 *1) (-12 (-5 *2 (-1303)) (-5 *1 (-845))))) -(((*1 *2 *1 *2) - (-12 (-5 *2 (-114)) (-5 *1 (-1243 *3)) (-4 *3 (-1005))))) -(((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-915 *3)) (-4 *3 (-1132)))) - ((*1 *2 *1) (-12 (-4 *1 (-1152 *3)) (-4 *3 (-1247)) (-5 *2 (-793))))) -(((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814)))) - ((*1 *1 *1) - (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1080)) (-14 *3 (-663 (-1207))))) - ((*1 *1 *1) - (-12 (-5 *1 (-227 *2 *3)) (-4 *2 (-13 (-1080) (-871))) - (-14 *3 (-663 (-1207))))) - ((*1 *1 *1) - (-12 (-4 *1 (-397 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-1132)))) - ((*1 *1 *1) - (-12 (-14 *2 (-663 (-1207))) (-4 *3 (-175)) - (-4 *5 (-245 (-2256 *2) (-793))) - (-14 *6 - (-1 (-114) (-2 (|:| -1591 *4) (|:| -2030 *5)) - (-2 (|:| -1591 *4) (|:| -2030 *5)))) - (-5 *1 (-475 *2 *3 *4 *5 *6 *7)) (-4 *4 (-871)) - (-4 *7 (-979 *3 *5 (-888 *2))))) - ((*1 *1 *1) (-12 (-4 *1 (-523 *2 *3)) (-4 *2 (-102)) (-4 *3 (-874)))) - ((*1 *1 *1) - (-12 (-4 *2 (-571)) (-5 *1 (-642 *2 *3)) (-4 *3 (-1273 *2)))) - ((*1 *1 *1) (-12 (-4 *1 (-730 *2)) (-4 *2 (-1080)))) + (-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 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(-305 (-975 *4))))) (-5 *1 (-393 *4)) @@ -15668,7 +13818,7 @@ (|partial| -12 (-5 *5 (-1207)) (-4 *6 (-13 (-319) (-1069 (-560)) (-660 (-560)) (-149))) (-4 *4 (-13 (-29 *6) (-1233) (-989))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -3822 (-663 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -1832 (-663 *4)))) (-5 *1 (-675 *6 *4 *3)) (-4 *3 (-680 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1207)) (-5 *5 (-663 *2)) @@ -15679,41 +13829,41 @@ (-12 (-4 *5 (-376)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4509)))) (-4 *4 (-13 (-385 *5) (-10 -7 (-6 -4509)))) (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3822 (-663 *4)))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -1832 (-663 *4)))) (-5 *1 (-689 *5 *6 *4 *3)) (-4 *3 (-708 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-376)) (-4 *6 (-13 (-385 *5) (-10 -7 (-6 -4509)))) (-4 *7 (-13 (-385 *5) (-10 -7 (-6 -4509)))) (-5 *2 (-663 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -3822 (-663 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| 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*2 *3 *4) (-12 (-5 *3 (-663 (-975 *5))) (-5 *4 (-663 (-1207))) (-4 *5 (-571)) @@ -15730,7 +13880,7 @@ (-4 *7 (-13 (-29 *6) (-1233) (-989))) (-4 *6 (-13 (-319) (-1069 (-560)) (-660 (-560)) (-149))) (-5 *2 - (-2 (|:| |particular| (-1297 *7)) (|:| -3822 (-663 (-1297 *7))))) + (-2 (|:| |particular| (-1297 *7)) (|:| -1832 (-663 (-1297 *7))))) (-5 *1 (-824 *6 *7)) (-5 *4 (-1297 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-711 *6)) (-5 *4 (-1207)) @@ -15742,27 +13892,27 @@ (-5 *5 (-1207)) (-4 *7 (-13 (-29 *6) (-1233) (-989))) (-4 *6 (-13 (-319) (-1069 (-560)) (-660 (-560)) (-149))) (-5 *2 - (-2 (|:| |particular| (-1297 *7)) (|:| -3822 (-663 (-1297 *7))))) + (-2 (|:| |particular| (-1297 *7)) (|:| -1832 (-663 (-1297 *7))))) (-5 *1 (-824 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-663 *7)) (-5 *4 (-663 (-115))) (-5 *5 (-1207)) (-4 *7 (-13 (-29 *6) (-1233) (-989))) (-4 *6 (-13 (-319) (-1069 (-560)) (-660 (-560)) (-149))) (-5 *2 - (-2 (|:| |particular| (-1297 *7)) (|:| -3822 (-663 (-1297 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\ No newline at end of file |