diff options
Diffstat (limited to 'src/share/algebra/interp.daase')
| -rw-r--r-- | src/share/algebra/interp.daase | 1428 |
1 files changed, 714 insertions, 714 deletions
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index b7f0f4fb..ed7e2c16 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,53 +1,53 @@ -(2991528 . 3662084406) +(2636912 . 3662386291) ((|sorted?| ((#1=(|Boolean|) #2=(|Mapping| #1# |#2| |#2|) $) 86 T ELT) ((#1# $) NIL T ELT)) (|sort!| (($ #2# $) 18 T ELT) (#3=($ $) NIL T ELT)) (|setelt| #4=((|#2| $ #5=(|Integer|) |#2|) NIL T ELT) ((|#2| $ #6=(|UniversalSegment| #5#) |#2|) 44 T ELT)) (|reverse!| (#3# 80 T ELT)) (|reduce| ((|#2| #7=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| #7# $ |#2|) 50 T ELT) ((|#2| #7# $) 49 T ELT)) (|position| ((#5# #8=(|Mapping| #1# |#2|) $) 27 T ELT) ((#5# |#2| $) NIL T ELT) ((#5# |#2| $ #5#) 96 T ELT)) (|merge| (($ #2# $ $) 64 T ELT) (#9=($ $ $) NIL T ELT)) (|members| ((#10=(|List| |#2|) $) 13 T ELT)) (|map!| (#11=($ (|Mapping| |#2| |#2|) $) 37 T ELT)) (|map| (#11# NIL T ELT) (($ #7# $ $) 60 T ELT)) (|insert| (($ |#2| $ #5#) NIL T ELT) 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T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|Zero| #1=(*1 *1) #2=(|ofCategory| *1 (|AbelianMonoid|))) (|sample| #1# #2#) (|zero?| (*1 *2 *1) #3=(AND #2# (|isDomain| *2 (|Boolean|)))) (* (*1 *1 *2 *1) (AND #2# (|isDomain| *2 (|NonNegativeInteger|)))) (|opposite?| (*1 *2 *1 *1) #3#)) +(|Join| (|AbelianSemiGroup|) (CATEGORY |domain| (SIGNATURE |Zero| #1=($) |constant|) (SIGNATURE |sample| #1# |constant|) (SIGNATURE |zero?| (#2=(|Boolean|) $)) (SIGNATURE * ($ (|NonNegativeInteger|) $)) (SIGNATURE |opposite?| (#2# $ $)))) +(((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((* (($ (|PositiveInteger|) $) 10 T ELT))) (((|AbelianSemiGroup&| |#1|) (CATEGORY |package| (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianSemiGroup|)) (T |AbelianSemiGroup&|)) NIL ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT))) (((|AbelianSemiGroup|) (|Category|)) (T |AbelianSemiGroup|)) -((+ (*1 *1 *1 *1) (|ofCategory| *1 (|AbelianSemiGroup|))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|AbelianSemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) +((+ (*1 *1 *1 *1) #1=(|ofCategory| *1 (|AbelianSemiGroup|))) (* (*1 *1 *2 *1) (AND #1# (|isDomain| *2 (|PositiveInteger|))))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)) (SIGNATURE * ($ (|PositiveInteger|) $)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . 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#18#) 86 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zerosOf| (#3=(#4=(|List| $) #5=(|Polynomial| $)) 99 T ELT) (#6=(#4# #7=(|SparseUnivariatePolynomial| $)) 98 T ELT) (#8=(#4# #7# #9=(|Symbol|)) 97 T ELT)) (|zeroOf| (#10=($ #5#) 102 T ELT) (#11=($ #7#) 101 T ELT) (#12=($ #7# #9#) 100 T ELT)) (|zero?| (#13=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#14=($ $) 55 T ELT)) (|unit?| (#13# 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (#14# 92 T ELT)) (|squareFree| (#15=((|Factored| $) $) 91 T ELT)) (|sqrt| (#14# 111 T ELT)) (|sizeLess?| (#1# 76 T ELT)) (|sample| (#16=($) 23 T CONST)) (|rootsOf| (#3# 105 T ELT) (#6# 104 T ELT) (#8# 103 T ELT)) (|rootOf| (#10# 108 T ELT) (#11# 107 T ELT) (#12# 106 T ELT)) (|rem| (#17=($ $ $) 72 T ELT)) (|recip| ((#18=(|Union| $ #19="failed") $) 43 T ELT)) (|quo| (#17# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #4#) #20=(|:| |generator| $)) #4#) 67 T ELT)) (|prime?| (#13# 90 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#13# 45 T ELT)) (|nthRoot| (#21=($ $ #22=(|Integer|)) 110 T ELT)) (|multiEuclidean| (((|Union| #4# #19#) #4# $) 69 T ELT)) (|lcm| (#17# 61 T ELT) (#23=($ #4#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#14# 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7# #7# #7#) 59 T ELT)) (|gcd| (#17# 63 T ELT) (#23# 62 T ELT)) (|factor| (#15# 93 T ELT)) (|extendedEuclidean| (((|Record| #24=(|:| |coef1| $) #25=(|:| |coef2| $) #20#) $ $) 71 T ELT) (((|Union| (|Record| #24# #25#) #19#) $ $ $) 70 T ELT)) (|exquo| ((#18# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #4#) #4# $) 66 T ELT)) (|euclideanSize| ((#26=(|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #22#) 42 T ELT) (#14# 58 T ELT) (($ #27=(|Fraction| #22#)) 85 T ELT)) (|characteristic| ((#26#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#16# 24 T CONST)) (|One| (#16# 46 T CONST)) (= (#1# 8 T ELT)) (/ (#17# 84 T ELT)) (- (#14# 30 T ELT) (#17# 29 T ELT)) (+ (#17# 18 T ELT)) (** (($ $ #28=(|PositiveInteger|)) 36 T ELT) (($ $ #26#) 44 T ELT) (#21# 88 T ELT) (#29=($ $ #27#) 109 T ELT)) (* (($ #28# $) 17 T ELT) (($ #26# $) 21 T ELT) (($ #22# . #30=($)) 31 T ELT) (#17# 35 T ELT) (#29# 87 T ELT) (($ #27# . #30#) 86 T ELT))) (((|AlgebraicallyClosedField|) (|Category|)) (T |AlgebraicallyClosedField|)) -((|rootOf| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootOf| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|rootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|rootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|rootsOf| (*1 *2 *3 *4) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zeroOf| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zeroOf| (*1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zeroOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|AlgebraicallyClosedField|)))) (|zerosOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|AlgebraicallyClosedField|)) (|isDomain| *2 (|List| *1)))) (|zerosOf| (*1 *2 *3) (AND 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(|SparseUnivariatePolynomial| $))) (SIGNATURE |zerosOf| ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . 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T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| #7=(|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| #2#)) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Evalable| $) . T) ((|ExpressionSpace|) . T) ((|Field|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|FunctionSpace| |#1|) . T) ((|GcdDomain|) . T) ((|Group|) |has| |#1| (|Group|)) ((|InnerEvalable| #5# $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) |has| |#1| (|Ring|)) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #2#) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LeftModule| |#1|) |has| |#1| (|Ring|)) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #2#) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|Module| #1#) . T) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #6#) |has| |#1| (|Ring|)) ((|PartialDifferentialRing| #6#) |has| |#1| (|Ring|)) ((|PartialDifferentialSpace| #6#) |has| |#1| (|Ring|)) ((|PatternMatchable| #7#) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| #2#) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| #1#) OR (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|RetractableTo| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|RetractableTo| #3#) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #5#) . T) ((|RetractableTo| #4#) |has| |#1| (|Ring|)) ((|RetractableTo| #6#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((|yRange| #1=(((|Segment| #2=(|DoubleFloat|)) $) NIL T ELT)) (|xRange| #1#) (|refine| (($ $ #2#) 164 T ELT)) (|makeSketch| (($ (|Polynomial| #3=(|Integer|)) #4=(|Symbol|) #4# #5=(|Segment| (|Fraction| #3#)) #5#) 103 T ELT)) (|listBranches| (((|List| (|List| (|Point| #2#))) $) 181 T ELT)) (|coerce| (((|OutputForm|) $) 195 T ELT))) (((|PlaneAlgebraicCurvePlot|) (|Join| (|PlottablePlaneCurveCategory|) (CATEGORY |domain| (SIGNATURE |makeSketch| ($ (|Polynomial| #1=(|Integer|)) #2=(|Symbol|) #2# #3=(|Segment| (|Fraction| #1#)) #3#)) (SIGNATURE |refine| ($ $ (|DoubleFloat|)))))) (T |PlaneAlgebraicCurvePlot|)) ((|makeSketch| (*1 *1 *2 *3 *3 *4 *4) (AND (|isDomain| *2 (|Polynomial| #1=(|Integer|))) (|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|Segment| (|Fraction| #1#))) #2=(|isDomain| *1 (|PlaneAlgebraicCurvePlot|)))) (|refine| (*1 *1 *1 *2) (AND (|isDomain| *2 (|DoubleFloat|)) #2#))) @@ -60,28 +60,28 @@ NIL ((|sample| (($) 10 T CONST)) (|eq?| (((|Boolean|) $ $) 8 T ELT))) (((|Aggregate&| |#1|) (CATEGORY |package| (SIGNATURE |sample| (|#1|) |constant|) (SIGNATURE |eq?| ((|Boolean|) |#1| |#1|))) (|Aggregate|)) (T |Aggregate&|)) NIL -((|sample| (($) 6 T CONST)) (|eq?| (((|Boolean|) $ $) 10 T ELT)) (|empty?| (((|Boolean|) $) 7 T ELT)) (|empty| (($) 8 T ELT)) (|copy| (($ $) 9 T ELT))) +((|sample| (#1=($) 6 T CONST)) (|eq?| ((#2=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#1# 8 T ELT)) (|copy| (($ $) 9 T ELT))) (((|Aggregate|) (|Category|)) (T |Aggregate|)) -((|eq?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|Boolean|)))) (|copy| (*1 *1 *1) (|ofCategory| *1 (|Aggregate|))) (|empty| (*1 *1) (|ofCategory| *1 (|Aggregate|))) (|empty?| (*1 *2 *1) (AND (|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|Boolean|)))) (|sample| (*1 *1) (|ofCategory| *1 (|Aggregate|)))) -(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |eq?| ((|Boolean|) $ $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |empty| ($)) (SIGNATURE |empty?| ((|Boolean|) $)) (SIGNATURE |sample| ($) |constant|))) -(((|Join|) . T) ((|Type|) . T)) -((|atanh| (($ $) 11 T ELT)) (|asinh| (($ $) 10 T ELT)) (|asech| (($ $) 9 T ELT)) (|acsch| (($ $) 8 T ELT)) (|acoth| (($ $) 7 T ELT)) (|acosh| (($ $) 6 T ELT))) +((|eq?| (*1 *2 *1 *1) #1=(AND #2=(|ofCategory| *1 (|Aggregate|)) (|isDomain| *2 (|Boolean|)))) (|copy| (*1 *1 *1) #2#) (|empty| #3=(*1 *1) #2#) (|empty?| (*1 *2 *1) #1#) (|sample| #3# #2#)) +(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |eq?| (#1=(|Boolean|) $ $)) (SIGNATURE |copy| ($ $)) (SIGNATURE |empty| #2=($)) (SIGNATURE |empty?| (#1# $)) (SIGNATURE |sample| #2# |constant|))) +(((|Type|) . T)) +((|atanh| (#1=($ $) 11 T ELT)) (|asinh| (#1# 10 T ELT)) (|asech| (#1# 9 T ELT)) (|acsch| (#1# 8 T ELT)) (|acoth| (#1# 7 T ELT)) (|acosh| (#1# 6 T ELT))) (((|ArcHyperbolicFunctionCategory|) (|Category|)) (T |ArcHyperbolicFunctionCategory|)) -((|atanh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|asinh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|asech| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acsch| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acoth| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|))) (|acosh| (*1 *1 *1) (|ofCategory| *1 (|ArcHyperbolicFunctionCategory|)))) -(|Join| (CATEGORY |domain| (SIGNATURE |acosh| ($ $)) (SIGNATURE |acoth| ($ $)) (SIGNATURE |acsch| ($ $)) (SIGNATURE |asech| ($ $)) (SIGNATURE |asinh| ($ $)) (SIGNATURE |atanh| ($ $)))) -((~= (#1=((|Boolean|) $ $) 18 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2=((|BasicType|))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|value| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 136 T ELT)) (|third| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #3=($)) 159 T ELT)) (|tail| (#4=($ $) 157 T ELT)) (|table| (($) 95 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 94 T ELT)) (|swap!| ((#5=(|Void|) $ |#1| |#1|) 82 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) ((#5# $ #6=(|Integer|) #6#) 185 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|split!| (($ $ (|Integer|)) 170 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|sorted?| ((#7=(|Boolean|) (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 219 T ELT) ((#7# $) 213 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8=((|OrderedSet|))) ELT)) (|sort!| (($ (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #9=($)) 210 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (#10=($ $) 209 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT)) (|sort| (($ (|Mapping| #7# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #9#) 220 T ELT) (#10# 214 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) ELT)) (|size?| (#11=(#12=(|Boolean|) $ (|NonNegativeInteger|)) 202 T ELT)) (|setvalue!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 145 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setrest!| (#13=($ $ $) 166 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setlast!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 168 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setfirst!| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 164 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setelt| ((|#2| $ |#1| |#2|) 70 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #6# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 196 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #14=(|UniversalSegment| #6#) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 171 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #15="last" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 169 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ $ #16="rest" $) 167 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #17="first" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 165 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $ #18="value" (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 144 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|setchildren!| (($ $ #19=(|List| $)) 143 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|select!| (($ (|Mapping| #20=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #21=($)) 42 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #22=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #23=($)) 236 T ELT)) (|select| (($ (|Mapping| #24=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25=($)) 49 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #24# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25#) 183 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|second| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #3#) 158 T ELT)) (|search| (((|Union| |#2| . #26=("failed")) |#1| . #27=($)) 59 T ELT)) (|sample| (#28=($) 6 T CONST)) (|reverse!| (#10# 211 (|has| $ (|ShallowlyMutableAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|reverse| (#10# 221 T ELT)) (|rest| (#29=($ $ #30=(|NonNegativeInteger|)) 153 T ELT) (#4# 151 T ELT)) (|removeDuplicates!| (($ $) 234 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #31=((|BasicType|))) ELT)) (|removeDuplicates| (($ $) 51 (OR (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32=((|BasicType|))) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))))) ELT)) (|remove!| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 44 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Mapping| #20# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #21#) 43 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Union| |#2| . #26#) |#1| . #27#) 60 T ELT) (($ (|Mapping| #22# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #23#) 240 T ELT) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 235 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #31#) ELT)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #33=($)) 50 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT) (($ (|Mapping| #24# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25#) 48 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #33#) 184 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #32#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT) (($ (|Mapping| #24# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #25#) 182 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|reduce| (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 111 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34=((|BasicType|))) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 107 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #35=($)) 106 T ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) 232 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #34#) ELT) (((|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Mapping| (|Record| (|:| |key| |#1|) (|:| 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T) ((|BagAggregate| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| #1#) . T) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| #2=(|Integer|) #1#) . T) ((|Eltable| (|UniversalSegment| #2#) $) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| #2# #1#) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #1#) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|ExtensibleLinearAggregate| #1#) . T) ((|FiniteAggregate| #1#) . T) ((|FiniteLinearAggregate| #1#) . T) ((|Functorial| #1#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #1#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| #2# #1#) . T) ((|IndexedAggregate| |#1| |#2|) . 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|split| (#1=(#2=(|Factored| |#1|) |#1|) 41 T ELT)) (|factor| (#1# 30 T ELT) ((#2# |#1| (|List| (|AlgebraicNumber|))) 33 T ELT)) (|doublyTransitive?| (((|Boolean|) |#1|) 59 T ELT))) (((|AlgFactor| |#1|) (CATEGORY |package| (SIGNATURE |factor| (#1=(|Factored| |#1|) |#1| (|List| #2=(|AlgebraicNumber|)))) (SIGNATURE |factor| #3=(#1# |#1|)) (SIGNATURE |split| #3#) (SIGNATURE |doublyTransitive?| ((|Boolean|) |#1|))) (|UnivariatePolynomialCategory| #2#)) (T |AlgFactor|)) ((|doublyTransitive?| #1=(*1 *2 *3) (AND (|isDomain| *2 (|Boolean|)) #2=(|isDomain| *1 (|AlgFactor| *3)) #3=(|ofCategory| *3 (|UnivariatePolynomialCategory| #4=(|AlgebraicNumber|))))) (|split| #1# #5=(AND #6=(|isDomain| *2 (|Factored| *3)) #2# #3#)) (|factor| #1# #5#) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| #4#)) #6# #2# #3#))) @@ -106,11 +106,11 @@ NIL ((|monomial?| (((|Boolean|) $) 12 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 21 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #1=(|Integer|) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ #2=(|Fraction| #1#) $) 25 T ELT) (($ $ #2#) NIL T ELT))) (((|AbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE |monomial?| ((|Boolean|) |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|AbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |AbelianMonoidRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 76 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (($ $) 82 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial?| (((|Boolean|) $) 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (($ $) 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 72 (|has| |#1| . #3#) ELT)) (|degree| ((|#2| $) 85 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #6=(|Fraction| (|Integer|))) 79 (|has| |#1| . #7=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 71 (|has| |#1| . #3#) ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 75 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #8=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #8#) 89 T ELT) (($ #6# . #8#) 78 (|has| |#1| . #7#) ELT) (($ $ #6#) 77 (|has| |#1| . #7#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 #4=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#5=($ $) 74 #4# ELT)) (|unit?| (#3# 76 #4# ELT)) (|subtractIfCan| ((#6=(|Maybe| $) $ $) 26 T ELT)) (|sample| (#7=($) 23 T CONST)) (|reductum| (#5# 82 T ELT)) (|recip| ((#8=(|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|monomial?| (#3# 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#5# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#8# $ $) 72 #4# ELT)) (|degree| ((|#2| $) 85 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #9=(|Integer|)) 42 T ELT) (($ #10=(|Fraction| #9#)) 79 #11=(|has| |#1| (|Algebra| #10#)) ELT) (#5# 71 #4# ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| ((#6# $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#12=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 75 #4# ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#7# 24 T CONST)) (|One| (#7# 46 T CONST)) (= (#1# 8 T ELT)) (/ (#13=($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (#5# 30 T ELT) (#14=($ $ $) 29 T ELT)) (+ (#14# 18 T ELT)) (** (($ $ #15=(|PositiveInteger|)) 36 T ELT) (($ $ #12#) 44 T ELT)) (* (($ #15# $) 17 T ELT) (($ #12# $) 21 T ELT) (($ #9# . #16=($)) 31 T ELT) (#14# 35 T ELT) (#13# 90 T ELT) (($ |#1| . #16#) 89 T ELT) (($ #10# . #16#) 78 #11# ELT) (($ $ #10#) 77 #11# ELT))) (((|AbelianMonoidRing| |#1| |#2|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|)) (T |AbelianMonoidRing|)) -((|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (|leadingMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|monomial?| (*1 *2 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)))) (|monomial| (*1 *1 *2 *3) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)))) (|coefficient| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Ring|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|Field|))))) -(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|Functorial| |t#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingMonomial| ($ $)) (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |monomial| ($ |t#1| |t#2|)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ |t#2|)) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|))) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (ATTRIBUTE (|IntegralDomain|)) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (ATTRIBUTE (|Algebra| (|Fraction| (|Integer|)))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|leadingCoefficient| #1=(*1 *2 *1) #2=(AND #3=(|ofCategory| *1 (|AbelianMonoidRing| *2 *3)) #4=(|ofCategory| *3 #5=(|OrderedAbelianMonoid|)) #6=(|ofCategory| *2 #7=(|Ring|)))) (|leadingMonomial| #8=(*1 *1 *1) #9=(AND #3# #6# #4#)) (|degree| #1# (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *2)) #10=(|ofCategory| *3 #7#) (|ofCategory| *2 #5#))) (|monomial?| #1# (AND (|ofCategory| *1 (|AbelianMonoidRing| *3 *4)) #10# (|ofCategory| *4 #5#) (|isDomain| *2 (|Boolean|)))) (|monomial| (*1 *1 *2 *3) #9#) (|reductum| #8# #9#) (|coefficient| (*1 *2 *1 *3) #2#) (/ (*1 *1 *1 *2) (AND #3# #6# #4# (|ofCategory| *2 (|Field|))))) +(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|Functorial| |t#1|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingMonomial| #1=($ $)) (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |monomial?| ((|Boolean|) $)) (SIGNATURE |monomial| ($ |t#1| |t#2|)) (SIGNATURE |reductum| #1#) (SIGNATURE |coefficient| (|t#1| $ |t#2|)) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |%noBranch|) (IF (|has| |t#1| #2=(|CommutativeRing|)) (PROGN (ATTRIBUTE #2#) (ATTRIBUTE (|Algebra| |t#1|))) |%noBranch|) (IF (|has| |t#1| #3=(|CharacteristicZero|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |t#1| #4=(|CharacteristicNonZero|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |t#1| #5=(|IntegralDomain|)) (ATTRIBUTE #5#) |%noBranch|) (IF (|has| |t#1| #6=(|Algebra| (|Fraction| (|Integer|)))) (ATTRIBUTE #6#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zerosOf| #4=((#5=(|List| $) #6=(|SparseUnivariatePolynomial| $) #7=(|Symbol|)) NIL T ELT) #8=((#5# #6#) NIL T ELT) #9=((#5# #10=(|Polynomial| $)) NIL T ELT)) (|zeroOf| #11=(($ #6# #7#) NIL T ELT) #12=(($ #6#) NIL T ELT) #13=(($ #10#) NIL T ELT)) (|zero?| (#14=(#3# $) 9 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #15=(#16=($ $) NIL T ELT)) (|unit?| #17=(#14# NIL T ELT)) (|tower| #18=((#19=(|List| #20=(|Kernel| $)) $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|subst| #21=(($ $ #22=(|Equation| $)) NIL T ELT) #23=(($ $ (|List| #22#)) NIL T ELT) #24=(($ $ #19# #5#) NIL T ELT)) (|squareFreePart| #15#) (|squareFree| #25=(((|Factored| $) $) NIL T ELT)) (|sqrt| #15#) (|sizeLess?| #1#) (|sample| (#26=($) NIL T CONST)) (|rootsOf| #4# #8# #9#) (|rootOf| #11# #12# #13#) (|retractIfCan| #27=(((|Union| #20# . #28=(#29="failed")) . #30=($)) NIL T ELT) (((|Union| #31=(|Integer|) . #28#) . #30#) NIL T ELT) (((|Union| #32=(|Fraction| #31#) . #28#) . #30#) NIL T ELT)) (|retract| ((#20# . #33=($)) NIL T ELT) ((#31# . #33#) NIL T ELT) ((#32# . #33#) NIL T ELT)) (|rem| #34=(($ $ $) NIL T ELT)) (|reducedSystem| ((#35=(|Record| (|:| |mat| #36=(|Matrix| #31#)) (|:| |vec| (|Vector| #31#))) . #37=(#38=(|Matrix| $) #39=(|Vector| $))) NIL T ELT) ((#36# . #40=(#38#)) NIL T ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| #32#)) (|:| |vec| (|Vector| #32#))) . #37#) NIL T ELT) ((#42# . #40#) NIL T ELT)) (|reduce| #15#) (|recip| ((#43=(|Union| $ #29#) $) NIL T ELT)) (|quo| #34#) (|principalIdeal| (((|Record| (|:| |coef| #5#) #44=(|:| |generator| $)) #5#) NIL T ELT)) (|prime?| #17#) (|paren| #15# #45=(($ #5#) NIL T ELT)) (|opposite?| #1#) (|operators| ((#46=(|List| #47=(|BasicOperator|)) $) NIL T ELT)) (|operator| ((#47# #47#) NIL T ELT)) (|one?| (#14# 11 T ELT)) (|odd?| #48=(#14# NIL (|has| $ (|RetractableTo| #31#)) ELT)) (|numer| #49=((#50=(|SparseMultivariatePolynomial| #31# #20#) $) NIL T ELT)) (|nthRoot| #51=(($ $ #31#) NIL T ELT)) (|norm| ((#6# #6# #20#) NIL T ELT) ((#6# #6# #19#) NIL T ELT) (($ $ #20#) NIL T ELT) (($ $ #19#) NIL T ELT)) (|multiEuclidean| (((|Union| #5# #29#) #5# $) NIL T ELT)) (|minPoly| ((#6# #20#) NIL #52=(|has| $ (|Ring|)) ELT)) (|map| (($ #53=(|Mapping| $ $) #20#) NIL T ELT)) (|mainKernel| #27#) (|leftReducedSystem| ((#35# . #54=(#39# $)) NIL T ELT) ((#36# . #55=(#39#)) NIL T ELT) ((#41# . #54#) NIL T ELT) ((#42# . #55#) NIL T ELT)) (|lcm| #45# #34#) (|latex| (((|String|) $) NIL T ELT)) (|kernels| #18#) (|kernel| #56=(($ #47# $) NIL T ELT) #57=(($ #47# #5#) NIL T ELT)) (|is?| ((#3# $ #47#) NIL T ELT) #58=((#3# $ #7#) NIL T ELT)) (|inv| #15#) (|height| #59=((#60=(|NonNegativeInteger|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL T ELT)) (|gcd| #45# #34#) (|freeOf?| #1# #58#) (|factor| #25#) (|extendedEuclidean| (((|Union| (|Record| #61=(|:| |coef1| $) #62=(|:| |coef2| $)) #29#) $ $ $) NIL T ELT) (((|Record| #61# #62# #44#) $ $) NIL T ELT)) (|exquo| ((#43# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #5#) #5# $) NIL T ELT)) (|even?| #48#) (|eval| (($ $ #20# $) NIL T ELT) #24# #23# #21# (($ $ $ $) NIL T ELT) (($ $ #5# #5#) NIL T ELT) (($ $ #63=(|List| #7#) #64=(|List| #53#)) NIL T ELT) (($ $ #63# #65=(|List| #66=(|Mapping| $ #5#))) NIL T ELT) (($ $ #7# #66#) NIL T ELT) (($ $ #7# #53#) NIL T ELT) (($ $ #46# #64#) NIL T ELT) (($ $ #46# #65#) NIL T ELT) (($ $ #47# #66#) NIL T ELT) (($ $ #47# #53#) NIL T ELT)) (|euclideanSize| #59#) (|elt| #56# (($ #47# $ $) NIL T ELT) (($ #47# $ $ $) NIL T ELT) (($ #47# $ $ $ $) NIL T ELT) #57#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|distribute| #15# #34#) (|differentiate| #15# #67=(($ $ #60#) NIL T ELT)) (|denom| #49#) (|definingPolynomial| (#16# NIL #52# ELT)) (|convert| ((#68=(|Float|) . #69=($)) NIL T ELT) (((|DoubleFloat|) . #69#) NIL T ELT) (((|Complex| #68#) . #69#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #20#) NIL T ELT) (($ #32#) NIL T ELT) #15# (($ #31#) NIL T ELT) (($ #50#) NIL T ELT)) (|characteristic| ((#60#) NIL T CONST)) (|box| #15# #45#) (|belong?| ((#3# #47#) NIL T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#26# 6 T CONST)) (|One| (#26# 10 T CONST)) (D #15# #67#) (= (#2# 13 T ELT)) (/ #34#) (- #34# #15#) (+ #34#) (** #70=(($ $ #32#) NIL T ELT) #51# #67# (($ $ #71=(|PositiveInteger|)) NIL T ELT)) (* (($ #32# . #72=($)) NIL T ELT) #70# #34# (($ #31# . #72#) NIL T ELT) (($ #60# $) NIL T ELT) (($ #71# $) NIL T ELT))) (((|AlgebraicNumber|) (|Join| (|ExpressionSpace|) (|AlgebraicallyClosedField|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| #2=(|Fraction| #1#)) (|LinearlyExplicitRingOver| #1#) (|RealConstant|) (|LinearlyExplicitRingOver| #2#) (|CharacteristicZero|) (|ConvertibleTo| (|Complex| (|Float|))) (|DifferentialRing|) (|CoercibleFrom| #3=(|SparseMultivariatePolynomial| #1# #4=(|Kernel| $))) (CATEGORY |domain| (SIGNATURE |numer| #5=(#3# $)) (SIGNATURE |denom| #5#) (SIGNATURE |reduce| ($ $)) (SIGNATURE |norm| (#6=(|SparseUnivariatePolynomial| $) #6# #4#)) (SIGNATURE |norm| (#6# #6# #7=(|List| #4#))) (SIGNATURE |norm| ($ $ #4#)) (SIGNATURE |norm| ($ $ #7#))))) (T |AlgebraicNumber|)) ((|numer| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SparseMultivariatePolynomial| (|Integer|) #3=(|Kernel| #4=(|AlgebraicNumber|)))) #5=(|isDomain| *1 #4#))) (|denom| #1# #2#) (|reduce| (*1 *1 *1) #5#) (|norm| #6=(*1 *2 *2 *3) (AND #7=(|isDomain| *2 (|SparseUnivariatePolynomial| #4#)) (|isDomain| *3 #3#) #5#)) (|norm| #6# (AND #7# (|isDomain| *3 #8=(|List| #3#)) #5#)) (|norm| #9=(*1 *1 *1 *2) (AND (|isDomain| *2 #3#) #5#)) (|norm| #9# (AND (|isDomain| *2 #8#) #5#))) @@ -138,11 +138,11 @@ NIL ((|setRow!| (($ $ #1=(|Integer|) |#3|) 46 T ELT)) (|setColumn!| (($ $ #1# |#4|) 50 T ELT)) (|members| (((|List| |#2|) $) 41 T ELT)) (|member?| ((#2=(|Boolean|) |#2| $) 55 T ELT)) (|every?| (#3=(#2# #4=(|Mapping| #2# |#2|) $) 21 T ELT)) (|elt| ((|#2| $ #1# #1#) NIL T ELT) ((|#2| $ #1# #1# |#2|) 29 T ELT)) (|count| ((#5=(|NonNegativeInteger|) #4# $) 35 T ELT) ((#5# |#2| $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 63 T ELT)) (|any?| (#3# 20 T ELT)) (= ((#2# $ $) 54 T ELT)) (|#| ((#5# $) 26 T ELT))) (((|TwoDimensionalArrayCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |setColumn!| (|#1| |#1| #2=(|Integer|) |#4|)) (SIGNATURE |setRow!| (|#1| |#1| #2# |#3|)) (SIGNATURE |elt| (|#2| |#1| #2# #2# |#2|)) (SIGNATURE |elt| (|#2| |#1| #2# #2#)) (SIGNATURE |member?| (#1# |#2| |#1|)) (SIGNATURE |count| (#3=(|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |members| ((|List| |#2|) |#1|)) (SIGNATURE |count| (#3# #4=(|Mapping| #1# |#2|) |#1|)) (SIGNATURE |every?| #5=(#1# #4# |#1|)) (SIGNATURE |any?| #5#) (SIGNATURE |#| (#3# |#1|))) (|TwoDimensionalArrayCategory| |#2| |#3| |#4|) (|Type|) #6=(|FiniteLinearAggregate| |#2|) #6#) (T |TwoDimensionalArrayCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) 52 T ELT)) (|setRow!| (($ $ (|Integer|) |#2|) 50 T ELT)) (|setColumn!| (($ $ (|Integer|) |#3|) 49 T ELT)) (|sample| (#3=($) 6 T CONST)) (|row| ((|#2| $ (|Integer|)) 54 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 39 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 38 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 34 (|has| |#1| . #4=((|BasicType|))) ELT)) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) 51 T ELT)) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) 56 T ELT)) (|nrows| (((|NonNegativeInteger|) $) 59 T ELT)) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) 65 T ELT)) (|ncols| (((|NonNegativeInteger|) $) 58 T ELT)) (|minRowIndex| (((|Integer|) $) 63 T ELT)) (|minColIndex| (((|Integer|) $) 61 T ELT)) (|members| (((|List| |#1|) $) 40 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 35 (|has| |#1| . #4#) ELT)) (|maxRowIndex| (((|Integer|) $) 62 T ELT)) (|maxColIndex| (((|Integer|) $) 60 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 66 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 48 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) 47 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 37 T ELT)) (|fill!| (($ $ |#1|) 64 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #7=($)) 42 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#8=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#8# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|elt| ((|#1| $ (|Integer|) (|Integer|)) 57 T ELT) ((|#1| $ (|Integer|) (|Integer|) |#1|) 55 T ELT)) (|count| ((#9=(|NonNegativeInteger|) (|Mapping| #5# |#1|) $) 41 T ELT) ((#9# |#1| $) 36 (|has| |#1| . #4#) ELT)) (|copy| (($ $) 9 T ELT)) (|column| ((|#3| $ (|Integer|)) 53 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#5# (|Mapping| #5# |#1|) . #7#) 43 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#9# $) 44 T ELT))) -(((|TwoDimensionalArrayCategory| |#1| |#2| |#3|) (|Category|) (|Type|) (|FiniteLinearAggregate| |t#1|) (|FiniteLinearAggregate| |t#1|)) (T |TwoDimensionalArrayCategory|)) -((|new| (*1 *1 *2 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)))) (|fill!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *3 *4)) (|ofCategory| *2 (|Type|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|minRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|maxRowIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|minColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|maxColIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|Integer|)))) (|nrows| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|NonNegativeInteger|)))) (|ncols| (*1 *2 *1) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) (|ofCategory| *3 (|Type|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 (|FiniteLinearAggregate| *3)) (|isDomain| *2 (|NonNegativeInteger|)))) (|elt| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)) (|ofCategory| *5 (|FiniteLinearAggregate| *2)) (|ofCategory| *2 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(|Integer|) (|Integer|))) (SIGNATURE |elt| (|t#1| $ (|Integer|) (|Integer|) |t#1|)) (SIGNATURE |row| (|t#2| $ (|Integer|))) (SIGNATURE |column| (|t#3| $ (|Integer|))) (SIGNATURE |setelt| (|t#1| $ (|Integer|) (|Integer|) |t#1|)) (SIGNATURE |qsetelt!| (|t#1| $ (|Integer|) (|Integer|) |t#1|)) (SIGNATURE |setRow!| ($ $ (|Integer|) |t#2|)) (SIGNATURE |setColumn!| ($ $ (|Integer|) |t#3|)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $)) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $ |t#1|)))) -(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|setelt| (#4=(|#1| $ #5=(|Integer|) #5# |#1|) 52 T ELT)) (|setRow!| (($ $ #5# |#2|) 50 T ELT)) (|setColumn!| (($ $ #5# |#3|) 49 T ELT)) (|sample| (#6=($) 6 T CONST)) (|row| ((|#2| $ #5#) 54 T ELT)) (|reduce| ((|#1| #7=(|Mapping| |#1| |#1| |#1|) $) 39 T ELT) ((|#1| #7# $ |#1|) 38 T ELT) ((|#1| #7# $ |#1| |#1|) 34 #3# ELT)) (|qsetelt!| (#4# 51 T ELT)) (|qelt| (#8=(|#1| $ #5# #5#) 56 T ELT)) (|nrows| (#9=(#10=(|NonNegativeInteger|) $) 59 T ELT)) (|new| (($ #10# #10# |#1|) 65 T ELT)) (|ncols| (#9# 58 T ELT)) (|minRowIndex| (#11=(#5# $) 63 T ELT)) (|minColIndex| (#11# 61 T ELT)) (|members| ((#12=(|List| |#1|) $) 40 T ELT)) (|member?| ((#2# |#1| $) 35 #3# ELT)) (|maxRowIndex| (#11# 62 T ELT)) (|maxColIndex| (#11# 60 T ELT)) (|map!| (#13=($ (|Mapping| |#1| |#1|) $) 66 T ELT)) (|map| (#13# 26 T ELT) (($ #7# $ $) 48 T ELT) (($ #7# $ $ |#1|) 47 T ELT)) (|latex| (((|String|) $) 21 #14=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) 20 #14# ELT)) (|find| (((|Union| |#1| "failed") #15=(|Mapping| #2# |#1|) $) 37 T ELT)) (|fill!| (($ $ |#1|) 64 T ELT)) (|every?| (#16=(#2# #15# $) 42 T ELT)) (|eval| (($ $ (|List| #17=(|Equation| |#1|))) 25 #18=(AND (|has| |#1| (|Evalable| |#1|)) #14#) ELT) (($ $ #17#) 24 #18# ELT) (($ $ |#1| |#1|) 23 #18# ELT) (($ $ #12# #12#) 22 #18# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#6# 8 T ELT)) (|elt| (#8# 57 T ELT) (#4# 55 T ELT)) (|count| ((#10# #15# $) 41 T ELT) ((#10# |#1| $) 36 #3# ELT)) (|copy| (($ $) 9 T ELT)) (|column| ((|#3| $ #5#) 53 T ELT)) (|coerce| ((#19=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #19#)) ELT)) (|before?| (#1# 19 #3# ELT)) (|any?| (#16# 43 T ELT)) (= (#1# 17 #3# ELT)) (|#| (#9# 44 T ELT))) +(((|TwoDimensionalArrayCategory| |#1| |#2| |#3|) (|Category|) (|Type|) #1=(|FiniteLinearAggregate| |t#1|) #1#) (T |TwoDimensionalArrayCategory|)) +((|new| (*1 *1 *2 *2 *3) (AND #1=(|isDomain| *2 (|NonNegativeInteger|)) #2=(|ofCategory| *3 #3=(|Type|)) #4=(|ofCategory| *1 (|TwoDimensionalArrayCategory| *3 *4 *5)) #5=(|ofCategory| *4 #6=(|FiniteLinearAggregate| *3)) #7=(|ofCategory| *5 #6#))) (|fill!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *3 *4)) #8=(|ofCategory| *2 #3#) (|ofCategory| *3 #9=(|FiniteLinearAggregate| *2)) #10=(|ofCategory| *4 #9#))) (|minRowIndex| #11=(*1 *2 *1) #12=(AND #4# #2# #5# #7# #13=(|isDomain| *2 #14=(|Integer|)))) (|maxRowIndex| #11# #12#) (|minColIndex| #11# #12#) (|maxColIndex| #11# #12#) (|nrows| #11# #15=(AND #4# #2# #5# #7# #1#)) (|ncols| #11# #15#) (|elt| #16=(*1 *2 *1 *3 *3) #17=(AND #18=(|isDomain| *3 #14#) #19=(|ofCategory| *1 (|TwoDimensionalArrayCategory| *2 *4 *5)) #10# #20=(|ofCategory| *5 #9#) #8#)) (|qelt| #16# #17#) (|elt| #21=(*1 *2 *1 *3 *3 *2) #22=(AND #18# #19# #8# #10# #20#)) (|row| #23=(*1 *2 *1 *3) (AND #18# (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *2 *5)) #24=(|ofCategory| *4 #3#) #25=(|ofCategory| *5 #26=(|FiniteLinearAggregate| *4)) #27=(|ofCategory| *2 #26#))) (|column| #23# (AND #18# (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *5 *2)) #24# #25# #27#)) (|setelt| #21# #22#) (|qsetelt!| #21# #22#) (|setRow!| #28=(*1 *1 *1 *2 *3) (AND #13# (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *3 *5)) #24# #29=(|ofCategory| *3 #26#) #25#)) (|setColumn!| #28# (AND #13# (|ofCategory| *1 (|TwoDimensionalArrayCategory| *4 *5 *3)) #24# #25# #29#)) (|map| (*1 *1 *2 *1 *1) #30=(AND (|isDomain| *2 (|Mapping| *3 *3 *3)) #4# #2# #5# #7#)) (|map| (*1 *1 *2 *1 *1 *3) #30#)) +(|Join| (|FiniteAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |new| ($ #1=(|NonNegativeInteger|) #1# |t#1|)) (SIGNATURE |fill!| ($ $ |t#1|)) (SIGNATURE |minRowIndex| #2=(#3=(|Integer|) $)) (SIGNATURE |maxRowIndex| #2#) (SIGNATURE |minColIndex| #2#) (SIGNATURE |maxColIndex| #2#) (SIGNATURE |nrows| #4=(#1# $)) (SIGNATURE |ncols| #4#) (SIGNATURE |elt| #5=(|t#1| $ #3# #3#)) (SIGNATURE |qelt| #5#) (SIGNATURE |elt| #6=(|t#1| $ #3# #3# |t#1|)) (SIGNATURE |row| (|t#2| $ #3#)) (SIGNATURE |column| (|t#3| $ #3#)) (SIGNATURE |setelt| #6#) (SIGNATURE |qsetelt!| #6#) (SIGNATURE |setRow!| ($ $ #3# |t#2|)) (SIGNATURE |setColumn!| ($ $ #3# |t#3|)) (SIGNATURE |map| ($ #7=(|Mapping| |t#1| |t#1| |t#1|) $ $)) (SIGNATURE |map| ($ #7# $ $ |t#1|)))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #7=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#8=(#3# $) NIL #9=(|has| |#1| #10=(|OrderedSet|)) ELT)) (|sort!| (#11=($ #7# $) NIL #6# ELT) (#12=($ $) NIL (AND #6# #9#) ELT)) (|sort| (#11# NIL T ELT) (#12# NIL #9# ELT)) (|setelt| #13=(#14=(|#1| $ #5# |#1|) NIL #6# ELT) ((|#1| $ #15=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select| #16=(($ #17=(|Mapping| #3# |#1|) $) NIL #18=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#19=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| #20=(#12# NIL T ELT)) (|removeDuplicates| (#12# NIL #21=(AND #18# #4#) ELT)) (|remove| (#22=($ |#1| $) NIL #21# ELT) #16#) (|reduce| ((|#1| #23=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #23# $ |#1|) NIL T ELT) ((|#1| #23# $) NIL T ELT)) (|qsetelt!| #13#) (|qelt| #24=((|#1| $ #5#) NIL T ELT)) (|position| ((#5# #17# $) NIL T ELT) ((#5# |#1| $) NIL #4# ELT) ((#5# |#1| $ #5#) NIL #4# ELT)) (|oneDimensionalArray| (#25=($ #26=(|List| |#1|)) 11 T ELT) (#27=($ #28=(|NonNegativeInteger|) |#1|) 14 T ELT)) (|new| (#27# 13 T ELT)) (|minIndex| #29=((#5# $) NIL #30=(|has| #5# #10#) ELT)) (|min| #31=(#32=($ $ $) NIL #9# ELT)) (|merge| (($ #7# $ $) NIL T ELT) #31#) (|members| #33=((#26# $) NIL T ELT)) (|member?| (#34=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| #29#) (|max| #31#) (|map!| #35=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #35# (($ #23# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #36=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #5#) NIL T ELT) (#37=($ $ $ #5#) NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #36# ELT)) (|first| ((|#1| $) NIL #30# ELT)) (|find| (((|Union| |#1| "failed") #17# $) NIL T ELT)) (|fill!| (#38=($ $ |#1|) NIL #6# ELT)) (|every?| #39=((#3# #17# $) NIL T ELT)) (|eval| (($ $ (|List| #40=(|Equation| |#1|))) NIL #41=(AND (|has| |#1| (|Evalable| |#1|)) #36#) ELT) (($ $ #40#) NIL #41# ELT) (($ $ |#1| |#1|) NIL #41# ELT) (($ $ #26# #26#) NIL #41# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#34# NIL #21# ELT)) (|entries| #33#) (|empty?| (#8# NIL T ELT)) (|empty| (#19# NIL T ELT)) (|elt| (#14# NIL T ELT) #24# #42=(($ $ #15#) NIL T ELT)) (|delete| (($ $ #5#) NIL T ELT) #42#) (|count| ((#28# |#1| $) NIL #4# ELT) ((#28# #17# $) NIL T ELT)) (|copyInto!| (#37# NIL #6# ELT)) (|copy| #20#) (|convert| ((#43=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #43#)) ELT)) (|construct| (#25# 10 T ELT)) (|concat| (#38# NIL T ELT) (#22# NIL T ELT) (#32# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#44=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #44#)) ELT)) (|before?| #1#) (|any?| #39#) (>= #45=(#2# NIL #9# ELT)) (> #45#) (= #1#) (<= #45#) (< #45#) (|#| ((#28# $) NIL T ELT))) (((|OneDimensionalArray| |#1|) (|Join| (|OneDimensionalArrayAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |oneDimensionalArray| ($ (|List| |#1|))) (SIGNATURE |oneDimensionalArray| ($ (|NonNegativeInteger|) |#1|)))) (|Type|)) (T |OneDimensionalArray|)) ((|oneDimensionalArray| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Type|)) #2=(|isDomain| *1 (|OneDimensionalArray| *3)))) (|oneDimensionalArray| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) #2# #1#))) @@ -165,14 +165,14 @@ NIL (((|AbstractSyntaxCategory|) (|Category|)) (T |AbstractSyntaxCategory|)) NIL (|Join| (|SetCategory|) (|HomotopicTo| (|Syntax|))) -(((|BasicType|) . T) ((|CoercibleFrom| #1=(|Syntax|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleFrom| #1=(|Syntax|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|asec| (#1=($ $) 10 T ELT)) (|acsc| (#1# 12 T ELT))) (((|ArcTrigonometricFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |acsc| #1=(|#1| |#1|)) (SIGNATURE |asec| #1#)) (|ArcTrigonometricFunctionCategory|)) (T |ArcTrigonometricFunctionCategory&|)) NIL -((|atan| (($ $) 11 T ELT)) (|asin| (($ $) 10 T ELT)) (|asec| (($ $) 9 T ELT)) (|acsc| (($ $) 8 T ELT)) (|acot| (($ $) 7 T ELT)) (|acos| (($ $) 6 T ELT))) +((|atan| (#1=($ $) 11 T ELT)) (|asin| (#1# 10 T ELT)) (|asec| (#1# 9 T ELT)) (|acsc| (#1# 8 T ELT)) (|acot| (#1# 7 T ELT)) (|acos| (#1# 6 T ELT))) (((|ArcTrigonometricFunctionCategory|) (|Category|)) (T |ArcTrigonometricFunctionCategory|)) -((|atan| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asin| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asec| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acsc| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acot| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|acos| (*1 *1 *1) (|ofCategory| *1 (|ArcTrigonometricFunctionCategory|)))) -(|Join| (CATEGORY |domain| (SIGNATURE |acos| ($ $)) (SIGNATURE |acot| ($ $)) (SIGNATURE |acsc| ($ $)) (SIGNATURE |asec| ($ $)) (SIGNATURE |asin| ($ $)) (SIGNATURE |atan| ($ $)))) +((|atan| #1=(*1 *1 *1) #2=(|ofCategory| *1 (|ArcTrigonometricFunctionCategory|))) (|asin| #1# #2#) (|asec| #1# #2#) (|acsc| #1# #2#) (|acot| #1# #2#) (|acos| #1# #2#)) +(|Join| (CATEGORY |domain| (SIGNATURE |acos| #1=($ $)) (SIGNATURE |acot| #1#) (SIGNATURE |acsc| #1#) (SIGNATURE |asec| #1#) (SIGNATURE |asin| #1#) (SIGNATURE |atan| #1#))) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|name| (((|SpadAst|) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|AttributeAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |name| ((|SpadAst|) $))))) (T |AttributeAst|)) ((|name| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|AttributeAst|))))) @@ -193,7 +193,7 @@ NIL (((|BasicType|) (|Category|)) (T |BasicType|)) ((= #1=(*1 *2 *1 *1) #2=(AND (|ofCategory| *1 (|BasicType|)) (|isDomain| *2 (|Boolean|)))) (~= #1# #2#) (|before?| #1# #2#)) (|Join| (|Type|) (CATEGORY |domain| (SIGNATURE = #1=((|Boolean|) $ $)) (SIGNATURE ~= #1#) (SIGNATURE |before?| #1#))) -(((|Join|) . T) ((|Type|) . T)) +(((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) NIL T ELT)) (|setvalue!| ((|#1| $ |#1|) 24 #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| #6=(($ $ $) NIL #5# ELT)) (|setleft!| #6#) (|setleaves!| (($ $ #7=(|List| |#1|)) 30 T ELT)) (|setelt| ((|#1| $ #8="value" |#1|) NIL #5# ELT) (($ $ #9="left" $) NIL #5# ELT) (($ $ #10="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #11=(|List| $)) NIL #5# ELT)) (|sample| (#12=($) NIL T CONST)) (|right| (#13=($ $) 12 T ELT)) (|reduce| ((|#1| #14=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #14# $ |#1|) NIL T ELT) ((|#1| #14# $) NIL T ELT)) (|nodes| #15=((#11# $) NIL T ELT)) (|node?| #1#) (|node| (($ $ |#1| $) 32 T ELT)) (|members| #16=((#7# $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|mapUp!| ((|#1| $ #14#) 40 T ELT) (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) 45 T ELT)) (|mapDown!| (($ $ |#1| #14#) 46 T ELT) (($ $ |#1| (|Mapping| #7# |#1| |#1| |#1|)) 49 T ELT)) (|map!| #17=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #17#) (|left| (#13# 11 T ELT)) (|leaves| #16#) (|leaf?| (#18=(#3# $) 13 T ELT)) (|latex| (((|String|) $) NIL #19=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #19# ELT)) (|find| (((|Union| |#1| "failed") #20=(|Mapping| #3# |#1|) $) NIL T ELT)) (|every?| #21=((#3# #20# $) NIL T ELT)) (|eval| (($ $ (|List| #22=(|Equation| |#1|))) NIL #23=(AND (|has| |#1| (|Evalable| |#1|)) #19#) ELT) (($ $ #22#) NIL #23# ELT) (($ $ |#1| |#1|) NIL #23# ELT) (($ $ #7# #7#) NIL #23# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#18# 9 T ELT)) (|empty| (#12# 31 T ELT)) (|elt| ((|#1| $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT) (($ $ #10#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| (#18# NIL T ELT)) (|count| ((#24=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#24# #20# $) NIL T ELT)) (|copy| (#13# NIL T ELT)) (|coerce| ((#25=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #25#)) ELT)) (|children| #15#) (|child?| #1#) (|before?| #1#) (|balancedBinaryTree| (($ #24# |#1|) 33 T ELT)) (|any?| #21#) (= #1#) (|#| ((#24# $) NIL T ELT))) (((|BalancedBinaryTree| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |balancedBinaryTree| ($ (|NonNegativeInteger|) |#1|)) (SIGNATURE |setleaves!| ($ $ #1=(|List| |#1|))) (SIGNATURE |mapUp!| (|#1| $ #2=(|Mapping| |#1| |#1| |#1|))) (SIGNATURE |mapUp!| ($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|))) (SIGNATURE |mapDown!| ($ $ |#1| #2#)) (SIGNATURE |mapDown!| ($ $ |#1| (|Mapping| #1# |#1| |#1| |#1|))))) (|SetCategory|)) (T |BalancedBinaryTree|)) ((|balancedBinaryTree| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) #1=(|isDomain| *1 (|BalancedBinaryTree| *3)) #2=(|ofCategory| *3 #3=(|SetCategory|)))) (|setleaves!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #2# #1#)) (|mapUp!| (*1 *2 *1 *3) (AND #4=(|isDomain| *3 (|Mapping| *2 *2 *2)) #5=(|isDomain| *1 (|BalancedBinaryTree| *2)) #6=(|ofCategory| *2 #3#))) (|mapUp!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 *3 *3 *3)) #2# #1#)) (|mapDown!| #7=(*1 *1 *1 *2 *3) (AND #4# #6# #5#)) (|mapDown!| #7# (AND (|isDomain| *3 (|Mapping| (|List| *2) *2 *2 *2)) #6# #5#))) @@ -203,11 +203,11 @@ NIL ((|bag| (($ (|List| |#2|)) 11 T ELT))) (((|BagAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bag| (|#1| (|List| |#2|)))) (|BagAggregate| |#2|) (|Type|)) (T |BagAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|inspect| ((|#1| $) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|extract!| ((|#1| $) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|sample| (#4=($) 6 T CONST)) (|map!| (#5=($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (#5# 26 T ELT)) (|latex| (((|String|) $) 21 #6=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#7=(|#1| $) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 #6# ELT)) (|extract!| (#7# 37 T ELT)) (|eval| (($ $ (|List| #8=(|Equation| |#1|))) 25 #9=(AND (|has| |#1| (|Evalable| |#1|)) #6#) ELT) (($ $ #8#) 24 #9# ELT) (($ $ |#1| |#1|) 23 #9# ELT) (($ $ #10=(|List| |#1|) #10#) 22 #9# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#4# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| ((#11=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #11#)) ELT)) (|before?| (#1# 19 #3# ELT)) (|bag| (($ #10#) 38 T ELT)) (= (#1# 17 #3# ELT))) (((|BagAggregate| |#1|) (|Category|) (|Type|)) (T |BagAggregate|)) -((|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|BagAggregate| *3)))) (|extract!| (*1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert!| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|inspect| (*1 *2 *1) (AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 (|Type|))))) -(|Join| (|HomogeneousAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |bag| ($ (|List| |t#1|))) (SIGNATURE |extract!| (|t#1| $)) (SIGNATURE |insert!| ($ |t#1| $)) (SIGNATURE |inspect| (|t#1| $)))) -(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((|bag| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 #1=(|Type|)) (|ofCategory| *1 (|BagAggregate| *3)))) (|extract!| #2=(*1 *2 *1) #3=(AND (|ofCategory| *1 (|BagAggregate| *2)) (|ofCategory| *2 #1#))) (|insert!| (*1 *1 *2 *1) #3#) (|inspect| #2# #3#)) +(|Join| (|HomogeneousAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |bag| ($ (|List| |t#1|))) (SIGNATURE |extract!| #1=(|t#1| $)) (SIGNATURE |insert!| ($ |t#1| $)) (SIGNATURE |inspect| #1#))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|Integer|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| ((#11=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #12=(((|Factored| #13=(|SparseUnivariatePolynomial| $)) #13#) NIL #14=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #15=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #16=(|List| #13#) #17="failed") #16# #13#) NIL #14# ELT)) (|sizeLess?| #1#) (|sign| (#6# NIL #18=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (#21=((|Union| #7# . #22=(#17#)) . #23=($)) NIL T ELT) (((|Union| #24=(|Symbol|) . #22#) . #23#) NIL #25=(|has| #7# (|RetractableTo| #24#)) ELT) (((|Union| #26=(|Fraction| #7#) . #22#) . #23#) NIL #27=(|has| #7# (|RetractableTo| #7#)) ELT) (#21# NIL #27# ELT)) (|retract| #28=(#6# NIL T ELT) ((#24# $) NIL #25# ELT) (#29=(#26# $) NIL #27# ELT) (#6# NIL #27# ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|reducedSystem| (#32=(#33=(|Matrix| #7#) #34=(|Matrix| $)) NIL #35=(|has| #7# (|LinearlyExplicitRingOver| #7#)) ELT) (#36=(#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #7#))) #34# #38=(|Vector| $)) NIL #35# ELT) (#36# NIL T ELT) (#32# NIL T ELT)) (|recip| ((#39=(|Union| $ #17#) $) NIL T ELT)) (|random| (#20# NIL #40=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #41=(|List| $)) #42=(|:| |generator| $)) #41#) NIL T ELT)) (|prime?| #4#) (|positive?| #43=(#5# NIL #18# ELT)) (|patternMatch| ((#44=(|PatternMatchResult| #7# . #45=($)) $ #46=(|Pattern| #7#) #44#) NIL (|has| #7# (|PatternMatchable| #7#)) ELT) ((#47=(|PatternMatchResult| #48=(|Float|) . #45#) $ #49=(|Pattern| #48#) #47#) NIL (|has| #7# (|PatternMatchable| #48#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #28#) (|nextItem| (#50=(#11# $) NIL #51=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #43#) (|multiEuclidean| (((|Union| #41# #17#) #41# $) NIL T ELT)) (|min| #52=(#31# NIL #53=(|has| #7# (|OrderedSet|)) ELT)) (|max| #52#) (|map| (($ #54=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| (#55=(#33# #38#) NIL #35# ELT) (#56=(#37# #38# $) NIL #35# ELT) (#56# NIL T ELT) (#55# NIL T ELT)) (|lcm| #30# #57=(($ #41#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#20# NIL #51# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13# #13# #13#) NIL T ELT)) (|gcd| #30# #57#) (|fractionPart| (#10# NIL #8# ELT) #58=(#29# NIL T ELT)) (|floor| #59=(#6# NIL #40# ELT)) (|factorSquareFreePolynomial| #12#) (|factorPolynomial| #12#) (|factor| #15#) (|extendedEuclidean| (((|Record| #60=(|:| |coef1| $) #61=(|:| |coef2| $) #42#) $ $) NIL T ELT) (((|Union| (|Record| #60# #61#) #17#) $ $ $) NIL T ELT)) (|exquo| ((#39# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #41#) #41# $) NIL T ELT)) (|eval| (($ $ #62=(|List| #7#) #62#) NIL #63=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #63# ELT) (($ $ #64=(|Equation| #7#)) NIL #63# ELT) (($ $ (|List| #64#)) NIL #63# ELT) (($ $ #65=(|List| #24#) #62#) NIL #66=(|has| #7# (|InnerEvalable| #24# #7#)) ELT) (($ $ #24# #7#) NIL #66# ELT)) (|euclideanSize| ((#67=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#68=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #69=(($ $ #54#) NIL T ELT) #70=(($ $ #54# #67#) NIL T ELT) #71=(($ $ #24#) NIL #72=(|has| #7# (|PartialDifferentialSpace| #24#)) ELT) #73=(($ $ #65#) NIL #72# ELT) #74=(($ $ #24# #67#) NIL #72# ELT) #75=(($ $ #65# (|List| #67#)) NIL #72# ELT) #76=(#10# NIL #77=(|has| #7# (|DifferentialSpace|)) ELT) #78=(#79=($ $ #67#) NIL #77# ELT)) (|denominator| #9#) (|denom| #28#) (|convert| ((#46# . #80=($)) NIL (|has| #7# (|ConvertibleTo| #46#)) ELT) ((#49# . #80#) NIL (|has| #7# (|ConvertibleTo| #49#)) ELT) ((#81=(|InputForm|) . #80#) NIL (|has| #7# (|ConvertibleTo| #81#)) ELT) ((#48# . #80#) NIL #82=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #80#) NIL #82# ELT)) (|conditionP| (((|Union| #38# #17#) #34#) NIL #83=(AND (|has| $ #84=(|CharacteristicNonZero|)) #14#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) #85=(($ #7#) NIL T ELT) #9# (#86=($ #26#) 8 T ELT) #85# (($ #24#) NIL #25# ELT) #58# (((|RadixExpansion| 2) $) 10 T ELT)) (|charthRoot| (#50# NIL (OR #83# (|has| #7# #84#)) ELT)) (|characteristic| ((#67#) NIL T CONST)) (|ceiling| #59#) (|binary| (#86# 9 T ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#10# NIL #18# ELT)) (|Zero| #19#) (|One| #19#) (D #69# #70# #71# #73# #74# #75# #76# #78#) (>= #87=(#2# NIL #53# ELT)) (> #87#) (= #1#) (<= #87#) (< #87#) (/ #30# (($ #7# #7#) NIL T ELT)) (- #9# #30#) (+ #30#) (** (($ $ #88=(|PositiveInteger|)) NIL T ELT) (#79# NIL T ELT) #89=(#68# NIL T ELT)) (* (($ #88# $) NIL T ELT) (($ #67# $) NIL T ELT) #90=(($ #7# . #91=($)) NIL T ELT) #30# (($ $ #26#) NIL T ELT) (($ #26# . #91#) NIL T ELT) #90# #89#)) (((|BinaryExpansion|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) (|CoercibleTo| #2=(|Fraction| #1#)) (|CoercibleTo| (|RadixExpansion| 2)) (CATEGORY |domain| (SIGNATURE |fractionPart| (#2# $)) (SIGNATURE |binary| ($ #2#))))) (T |BinaryExpansion|)) ((|fractionPart| (*1 *2 *1) #1=(AND (|isDomain| *2 (|Fraction| (|Integer|))) (|isDomain| *1 (|BinaryExpansion|)))) (|binary| (*1 *1 *2) #1#)) @@ -221,23 +221,23 @@ NIL (((|BinaryOperatorCategory| |#1|) (|Category|) (|Type|)) (T |BinaryOperatorCategory|)) NIL (|Join| (|MappingCategory| |t#1| |t#1| |t#1|)) -(((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) +(((|MappingCategory| |#1| |#1| |#1|) . T)) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (~ #3=(#4=($ $) NIL T ELT)) (|xor| #5=(#6=($ $ $) NIL T ELT)) (|swap!| (((|Void|) $ #7=(|Integer|) #7#) NIL #8=(|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|sorted?| (#9=(#2# $) NIL #10=(|has| #2# #11=(|OrderedSet|)) ELT) #12=((#2# #13=(|Mapping| #2# #2# #2#) $) NIL T ELT)) (|sort!| (#4# NIL (AND #8# #10#) ELT) (#14=($ #13# $) NIL #8# ELT)) (|sort| (#4# NIL #10# ELT) (#14# NIL T ELT)) (|setelt| ((#2# $ #15=(|UniversalSegment| #7#) #2#) NIL #8# ELT) #16=(#17=(#2# $ #7# #2#) NIL #8# ELT)) (|select| #18=(#19=($ #20=(|Mapping| #2# #2#) $) NIL #21=(|has| $ (|FiniteAggregate| #2#)) ELT)) (|sample| (#22=($) NIL T CONST)) (|reverse!| (#4# NIL #8# ELT)) (|reverse| #3#) (|removeDuplicates| (#4# NIL #23=(AND #21# #24=(|has| #2# (|BasicType|))) ELT)) (|remove| #18# (#25=($ #2# $) NIL #23# ELT)) (|reduce| #12# ((#2# #13# $ #2#) NIL T ELT) ((#2# #13# $ #2# #2#) NIL #24# ELT)) (|qsetelt!| #16#) (|qelt| #26=((#2# $ #7#) NIL T ELT)) (|position| ((#7# #2# $ #7#) NIL #24# ELT) ((#7# #2# $) NIL #24# ELT) ((#7# #20# $) NIL T ELT)) (|or| #5#) (|not| #3#) (|nor| #5#) (|new| (#27=($ #28=(|NonNegativeInteger|) #2#) 10 T ELT)) (|nand| #5#) (|minIndex| #29=((#7# $) NIL #30=(|has| #7# #11#) ELT)) (|min| #5#) (|merge| (#6# NIL #10# ELT) #31=(($ #13# $ $) NIL T ELT)) (|members| #32=((#33=(|List| #2#) $) NIL T ELT)) (|member?| (#34=(#2# #2# $) NIL #24# ELT)) (|maxIndex| #29#) (|max| #5#) (|map!| #35=(#19# NIL T ELT)) (|map| #31# #35#) (|latex| (((|String|) $) NIL T ELT)) (|insert| (#36=($ $ $ #7#) NIL T ELT) (($ #2# $ #7#) NIL T ELT)) (|indices| (((|List| #7#) $) NIL T ELT)) (|index?| ((#2# #7# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#9# NIL #30# ELT)) (|find| (((|Union| #2# "failed") #20# $) NIL T ELT)) (|fill!| (#37=($ $ #2#) NIL #8# ELT)) (|every?| #38=((#2# #20# $) NIL T ELT)) (|eval| (($ $ #33# #33#) NIL #39=(AND (|has| #2# (|Evalable| #2#)) (|has| #2# (|SetCategory|))) ELT) (($ $ #2# #2#) NIL #39# ELT) (($ $ #40=(|Equation| #2#)) NIL #39# ELT) (($ $ (|List| #40#)) NIL #39# ELT)) (|eq?| #1#) (|entry?| (#34# NIL #23# ELT)) (|entries| #32#) (|empty?| (#9# NIL T ELT)) (|empty| (#22# NIL T ELT)) (|elt| #41=(($ $ #15#) NIL T ELT) #26# (#17# NIL T ELT)) (|delete| #41# (($ $ #7#) NIL T ELT)) (|count| ((#28# #20# $) NIL T ELT) ((#28# #2# $) NIL #24# ELT)) (|copyInto!| (#36# NIL #8# ELT)) (|copy| #3#) (|convert| ((#42=(|InputForm|) $) NIL (|has| #2# (|ConvertibleTo| #42#)) ELT)) (|construct| (($ #33#) NIL T ELT)) (|concat| (($ (|List| $)) NIL T ELT) #5# (#25# NIL T ELT) (#37# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bits| (#27# 11 T ELT)) (|before?| #1#) (|any?| #38#) (|and| #5#) (|\\/| #5#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #5#) (|#| ((#28# $) NIL T ELT))) (((|Bits|) (|Join| (|BitAggregate|) (CATEGORY |domain| (SIGNATURE |bits| ($ (|NonNegativeInteger|) (|Boolean|)))))) (T |Bits|)) ((|bits| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Boolean|)) (|isDomain| *1 (|Bits|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#2|) 38 T ELT))) -(((|BiModule| |#1| |#2|) (|Category|) (|Ring|) (|Ring|)) (T |BiModule|)) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#4=($ $ $) 29 T ELT)) (+ (#4# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 31 T ELT) (($ |#1| . #5#) 34 T ELT) (($ $ |#2|) 38 T ELT))) +(((|BiModule| |#1| |#2|) (|Category|) #1=(|Ring|) #1#) (T |BiModule|)) NIL (|Join| (|LeftModule| |t#1|) (|RightModule| |t#2|)) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|or| (#1=($ $ $) 12 T ELT)) (|not| (($ $) 8 T ELT)) (|and| (#1# 10 T ELT))) (((|BooleanLogic&| |#1|) (CATEGORY |package| (SIGNATURE |or| #1=(|#1| |#1| |#1|)) (SIGNATURE |and| #1#) (SIGNATURE |not| (|#1| |#1|))) (|BooleanLogic|)) (T |BooleanLogic&|)) NIL -((~ (($ $) 8 T ELT)) (|or| (($ $ $) 9 T ELT)) (|not| (($ $) 11 T ELT)) (|and| (($ $ $) 10 T ELT)) (|\\/| (#1=($ $ $) 6 T ELT)) (|/\\| (#1# 7 T ELT))) +((~ (#1=($ $) 8 T ELT)) (|or| (#2=($ $ $) 9 T ELT)) (|not| (#1# 11 T ELT)) (|and| (#2# 10 T ELT)) (|\\/| (#2# 6 T ELT)) (|/\\| (#2# 7 T ELT))) (((|BooleanLogic|) (|Category|)) (T |BooleanLogic|)) -((|not| (*1 *1 *1) (|ofCategory| *1 (|BooleanLogic|))) (|and| (*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|))) (|or| (*1 *1 *1 *1) (|ofCategory| *1 (|BooleanLogic|)))) -(|Join| (|Logic|) (CATEGORY |domain| (SIGNATURE |not| ($ $)) (SIGNATURE |and| ($ $ $)) (SIGNATURE |or| ($ $ $)))) -(((|Join|) . T) ((|Logic|) . T) ((|Type|) . T)) +((|not| (*1 *1 *1) #1=(|ofCategory| *1 (|BooleanLogic|))) (|and| #2=(*1 *1 *1 *1) #1#) (|or| #2# #1#)) +(|Join| (|Logic|) (CATEGORY |domain| (SIGNATURE |not| ($ $)) (SIGNATURE |and| #1=($ $ $)) (SIGNATURE |or| #1#))) +(((|Logic|) . T) ((|Type|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (~ (#3=($ $) 9 T ELT)) (|xor| (#4=($ $ $) 14 T ELT)) (|true| (#5=($) 6 T CONST)) (|size| (((|NonNegativeInteger|)) 23 T ELT)) (|random| (#5# 32 T ELT)) (|or| (#4# 12 T ELT)) (|not| (#3# 8 T ELT)) (|nor| (#4# 15 T ELT)) (|nand| (#4# 16 T ELT)) (|min| #6=(#4# NIL T ELT) #7=(#5# NIL T CONST)) (|max| #6# #7#) (|lookup| ((#8=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #8#) 27 T ELT)) (|implies| (#4# 19 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|false| (#5# 7 T CONST)) (|equiv| (#4# 20 T ELT)) (|convert| (((|InputForm|) $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 36 T ELT)) (|before?| #1#) (|and| (#4# 10 T ELT)) (|\\/| (#4# 13 T ELT)) (>= #1#) (> #1#) (= (#2# 18 T ELT)) (<= #1#) (< (#2# 21 T ELT)) (|/\\| (#4# 11 T ELT))) (((|Boolean|) (|Join| (|OrderedFinite|) (|PropositionalLogic|) (|ConvertibleTo| (|InputForm|)) (CATEGORY |domain| (SIGNATURE |xor| #1=($ $ $)) (SIGNATURE |nand| #1#) (SIGNATURE |nor| #1#)))) (T |Boolean|)) ((|xor| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|Boolean|))) (|nand| #1# #2#) (|nor| #1# #2#)) @@ -259,11 +259,11 @@ NIL ((|setelt| ((|#2| $ #1="value" |#2|) NIL T ELT) (($ $ #2="left" $) 59 T ELT) (($ $ #3="right" $) 61 T ELT)) (|nodes| (#4=((|List| $) $) 31 T ELT)) (|node?| (#5=(#6=(|Boolean|) $ $) 36 T ELT)) (|leaves| (((|List| |#2|) $) 25 T ELT)) (|leaf?| (#7=(#6# $) 18 T ELT)) (|elt| ((|#2| $ #1#) NIL T ELT) (($ $ #2#) 10 T ELT) (($ $ #3#) 13 T ELT)) (|cyclic?| (#7# 55 T ELT)) (|coerce| (((|OutputForm|) $) 46 T ELT)) (|children| (#4# 32 T ELT)) (= (#5# 38 T ELT))) (((|BinaryRecursiveAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |setelt| (|#1| |#1| #3="right" |#1|)) (SIGNATURE |setelt| (|#1| |#1| #4="left" |#1|)) (SIGNATURE |elt| (|#1| |#1| #3#)) (SIGNATURE |elt| (|#1| |#1| #4#)) (SIGNATURE |setelt| (|#2| |#1| #5="value" |#2|)) (SIGNATURE |node?| #1#) (SIGNATURE |leaves| ((|List| |#2|) |#1|)) (SIGNATURE |cyclic?| #6=(#2# |#1|)) (SIGNATURE |elt| (|#2| |#1| #5#)) (SIGNATURE |leaf?| #6#) (SIGNATURE |nodes| #7=((|List| |#1|) |#1|)) (SIGNATURE |children| #7#)) (|BinaryRecursiveAggregate| |#2|) (|Type|)) (T |BinaryRecursiveAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (($ $ $) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setleft!| (($ $ $) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ "left" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ "right" $) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #4=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sample| (#5=($) 6 T CONST)) (|right| (($ $) 54 T ELT)) (|nodes| (#6=(#4# $) 45 T ELT)) (|node?| (#7=(#8=(|Boolean|) $ $) 37 (|has| |#1| . #9=((|BasicType|))) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|left| (($ $) 56 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#10=(#8# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #11=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #11#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT)) (|eq?| ((#12=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#12# $) 7 T ELT)) (|empty| (#5# 8 T ELT)) (|elt| ((|#1| $ #3#) 42 T ELT) (($ $ "left") 55 T ELT) (($ $ "right") 53 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#10# 41 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#6# 46 T ELT)) (|child?| (#7# 38 (|has| |#1| . #9#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 #4=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#5=($ $ $) 49 #4# ELT)) (|setleft!| (#5# 51 #4# ELT)) (|setelt| ((|#1| $ #6="value" |#1|) 35 #4# ELT) (($ $ #7="left" $) 52 #4# ELT) (($ $ #8="right" $) 50 #4# ELT)) (|setchildren!| (($ $ #9=(|List| $)) 36 #4# ELT)) (|sample| (#10=($) 6 T CONST)) (|right| (#11=($ $) 54 T ELT)) (|nodes| (#12=(#9# $) 45 T ELT)) (|node?| (#1# 37 #3# ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|left| (#11# 56 T ELT)) (|leaves| ((#13=(|List| |#1|) $) 40 T ELT)) (|leaf?| (#14=(#2# $) 44 T ELT)) (|latex| (((|String|) $) 21 #15=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) 20 #15# ELT)) (|eval| (($ $ (|List| #16=(|Equation| |#1|))) 25 #17=(AND (|has| |#1| (|Evalable| |#1|)) #15#) ELT) (($ $ #16#) 24 #17# ELT) (($ $ |#1| |#1|) 23 #17# ELT) (($ $ #13# #13#) 22 #17# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| (#14# 7 T ELT)) (|empty| (#10# 8 T ELT)) (|elt| ((|#1| $ #6#) 42 T ELT) (($ $ #7#) 55 T ELT) (($ $ #8#) 53 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#14# 41 T ELT)) (|copy| (#11# 9 T ELT)) (|coerce| ((#18=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #18#)) ELT)) (|children| (#12# 46 T ELT)) (|child?| (#1# 38 #3# ELT)) (|before?| (#1# 19 #3# ELT)) (= (#1# 17 #3# ELT))) (((|BinaryRecursiveAggregate| |#1|) (|Category|) (|Type|)) (T |BinaryRecursiveAggregate|)) -((|left| (*1 *1 *1) (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "left") (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|right| (*1 *1 *1) (AND (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|elt| (*1 *1 *1 *2) (AND (|isDomain| *2 "right") (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "left") (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setleft!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|setelt| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 "right") (|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setright!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) (|ofCategory| *2 (|Type|))))) -(|Join| (|RecursiveAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |left| ($ $)) (SIGNATURE |elt| ($ $ "left")) (SIGNATURE |right| ($ $)) (SIGNATURE |elt| ($ $ "right")) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (PROGN (SIGNATURE |setelt| ($ $ "left" $)) (SIGNATURE |setleft!| ($ $ $)) (SIGNATURE |setelt| ($ $ "right" $)) (SIGNATURE |setright!| ($ $ $))) |%noBranch|))) -(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) +((|left| #1=(*1 *1 *1) #2=(AND #3=(|ofCategory| *1 (|BinaryRecursiveAggregate| *2)) #4=(|ofCategory| *2 #5=(|Type|)))) (|elt| #6=(*1 *1 *1 *2) (AND #7=(|isDomain| *2 "left") #8=(|ofCategory| *1 (|BinaryRecursiveAggregate| *3)) #9=(|ofCategory| *3 #5#))) (|right| #1# #2#) (|elt| #6# (AND #10=(|isDomain| *2 "right") #8# #9#)) (|setelt| #11=(*1 *1 *1 *2 *1) (AND #7# #12=(|ofCategory| *1 (|ShallowlyMutableAggregate| *3)) #8# #9#)) (|setleft!| #13=(*1 *1 *1 *1) #14=(AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) #3# #4#)) (|setelt| #11# (AND #10# #12# #8# #9#)) (|setright!| #13# #14#)) +(|Join| (|RecursiveAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |left| #1=($ $)) (SIGNATURE |elt| ($ $ #2="left")) (SIGNATURE |right| #1#) (SIGNATURE |elt| ($ $ #3="right")) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (PROGN (SIGNATURE |setelt| ($ $ #2# $)) (SIGNATURE |setleft!| #4=($ $ $)) (SIGNATURE |setelt| ($ $ #3# $)) (SIGNATURE |setright!| #4#)) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) ((|noLinearFactor?| (#1=(#2=(|Boolean|) |#1|) 29 T ELT)) (|brillhartTrials| ((#3=(|NonNegativeInteger|) #3#) 28 T ELT) ((#3#) 27 T ELT)) (|brillhartIrreducible?| ((#2# |#1| #2#) 30 T ELT) (#1# 31 T ELT))) (((|BrillhartTests| |#1|) (CATEGORY |package| (SIGNATURE |brillhartIrreducible?| #1=(#2=(|Boolean|) |#1|)) (SIGNATURE |brillhartIrreducible?| (#2# |#1| #2#)) (SIGNATURE |brillhartTrials| (#3=(|NonNegativeInteger|))) (SIGNATURE |brillhartTrials| (#3# #3#)) (SIGNATURE |noLinearFactor?| #1#)) (|UnivariatePolynomialCategory| (|Integer|))) (T |BrillhartTests|)) ((|noLinearFactor?| #1=(*1 *2 *3) #2=(AND (|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 (|BrillhartTests| *3)) #4=(|ofCategory| *3 (|UnivariatePolynomialCategory| (|Integer|))))) (|brillhartTrials| (*1 *2 *2) #5=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4#)) (|brillhartTrials| (*1 *2) #5#) (|brillhartIrreducible?| (*1 *2 *3 *2) #2#) (|brillhartIrreducible?| #1# #2#)) @@ -273,19 +273,19 @@ NIL ((~ (#1=($ $) 13 T ELT)) (|not| (#1# 11 T ELT)) (|nor| (#2=($ $ $) 23 T ELT)) (|nand| (#2# 21 T ELT)) (|\\/| (#2# 19 T ELT)) (|/\\| (#2# 17 T ELT))) (((|BitAggregate&| |#1|) (CATEGORY |package| (SIGNATURE |nor| #1=(|#1| |#1| |#1|)) (SIGNATURE |nand| #1#) (SIGNATURE ~ #2=(|#1| |#1|)) (SIGNATURE |/\\| #1#) (SIGNATURE |\\/| #1#) (SIGNATURE |not| #2#)) (|BitAggregate|)) (T |BitAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (~ (($ $) 105 T ELT)) (|xor| (($ $ $) 34 T ELT)) (|swap!| (((|Void|) $ #2=(|Integer|) #2#) 60 (|has| $ (|ShallowlyMutableAggregate| #3=(|Boolean|))) ELT)) (|sorted?| ((#4=(|Boolean|) $) 99 (|has| #3# . #5=((|OrderedSet|))) ELT) ((#4# (|Mapping| #4# #3# #3#) $) 93 T ELT)) (|sort!| (#6=($ $) 103 (AND (|has| #3# . #5#) (|has| $ (|ShallowlyMutableAggregate| #3#))) ELT) (($ (|Mapping| #4# #3# #3#) . #7=($)) 102 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|sort| (#6# 98 (|has| #3# . #5#) ELT) (($ (|Mapping| #4# #3# #3#) . #7#) 92 T ELT)) (|setelt| ((#3# $ #8=(|UniversalSegment| #2#) #3#) 78 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT) ((#3# $ #2# #3#) 48 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|select| (($ (|Mapping| #9=(|Boolean|) #3#) . #10=($)) 64 (|has| $ (|FiniteAggregate| #3#)) ELT)) (|sample| (#11=($) 41 T CONST)) (|reverse!| (#6# 101 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|reverse| (#6# 91 T ELT)) (|removeDuplicates| (($ $) 62 (AND (|has| #3# . #12=((|BasicType|))) (|has| $ (|FiniteAggregate| #3#))) ELT)) (|remove| (($ (|Mapping| #9# #3#) . #10#) 65 (|has| $ (|FiniteAggregate| #3#)) ELT) (($ #3# $) 63 (AND (|has| #3# . #12#) (|has| $ (|FiniteAggregate| #3#))) ELT)) (|reduce| ((#3# (|Mapping| #3# #3# #3#) $) 84 T ELT) ((#3# (|Mapping| #3# #3# #3#) $ #3#) 83 T ELT) ((#3# (|Mapping| #3# #3# #3#) $ #3# #3#) 79 (|has| #3# . #13=((|BasicType|))) ELT)) (|qsetelt!| ((#3# $ #2# #3#) 47 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|qelt| ((#3# $ #2#) 49 T ELT)) (|position| ((#14=(|Integer|) #3# $ #14#) 96 (|has| #3# . #15=((|BasicType|))) ELT) ((#14# #3# $) 95 (|has| #3# . #15#) ELT) ((#14# (|Mapping| #4# #3#) $) 94 T ELT)) (|or| (#16=($ $ $) 110 T ELT)) (|not| (($ $) 108 T ELT)) (|nor| (($ $ $) 35 T ELT)) (|new| (($ (|NonNegativeInteger|) #3#) 68 T ELT)) (|nand| (($ $ $) 36 T ELT)) (|minIndex| ((#2# . #17=($)) 57 (|has| #2# . #18=((|OrderedSet|))) ELT)) (|min| (#19=($ $ $) 23 T ELT)) (|merge| (($ $ $) 97 (|has| #3# . #5#) ELT) (($ (|Mapping| #4# #3# #3#) $ $) 90 T ELT)) (|members| (((|List| #3#) $) 85 T ELT)) (|member?| ((#20=(|Boolean|) #3# $) 80 (|has| #3# . #13#) ELT)) (|maxIndex| ((#2# . #17#) 56 (|has| #2# . #18#) ELT)) (|max| (#19# 22 T ELT)) (|map!| (($ (|Mapping| #3# #3#) $) 104 T ELT)) (|map| (($ (|Mapping| #3# #3# #3#) $ $) 73 T ELT) (($ (|Mapping| #3# #3#) $) 42 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|insert| (($ $ $ #2#) 77 T ELT) (($ #3# $ #2#) 76 T ELT)) (|indices| (((|List| #2#) $) 54 T ELT)) (|index?| ((#21=(|Boolean|) #2# $) 53 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| ((#3# $) 58 (|has| #2# . #18#) ELT)) (|find| (((|Union| #3# "failed") (|Mapping| #20# #3#) $) 82 T ELT)) (|fill!| (($ $ #3#) 59 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|every?| ((#20# (|Mapping| #20# #3#) . #22=($)) 87 T ELT)) (|eval| (($ $ (|List| #3#) (|List| #3#)) 46 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23=((|SetCategory|)))) ELT) (($ $ #3# #3#) 45 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23#)) ELT) (($ $ (|Equation| #3#)) 44 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23#)) ELT) (($ $ (|List| (|Equation| #3#))) 43 (AND (|has| #3# (|Evalable| #3#)) (|has| #3# . #23#)) ELT)) (|eq?| ((#24=(|Boolean|) $ $) 37 T ELT)) (|entry?| ((#21# #3# $) 55 (AND (|has| $ (|FiniteAggregate| #3#)) (|has| #3# (|BasicType|))) ELT)) (|entries| (((|List| #3#) $) 52 T ELT)) (|empty?| ((#24# $) 40 T ELT)) (|empty| (#11# 39 T ELT)) (|elt| (($ $ #8#) 67 T ELT) ((#3# $ #2#) 51 T ELT) ((#3# $ #2# #3#) 50 T ELT)) (|delete| (($ $ #8#) 75 T ELT) (($ $ #2#) 74 T ELT)) (|count| ((#25=(|NonNegativeInteger|) (|Mapping| #20# #3#) $) 86 T ELT) ((#25# #3# $) 81 (|has| #3# . #13#) ELT)) (|copyInto!| (($ $ $ #14#) 100 (|has| $ (|ShallowlyMutableAggregate| #3#)) ELT)) (|copy| (($ $) 38 T ELT)) (|convert| ((#26=(|InputForm|) $) 61 (|has| #3# (|ConvertibleTo| #26#)) ELT)) (|construct| (($ (|List| #3#)) 66 T ELT)) (|concat| (($ (|List| $)) 72 T ELT) (($ $ $) 71 T ELT) (($ #3# $) 70 T ELT) (($ $ #3#) 69 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#20# (|Mapping| #20# #3#) . #22#) 88 T ELT)) (|and| (#16# 109 T ELT)) (|\\/| (#27=($ $ $) 107 T ELT)) (>= (#28=((|Boolean|) $ $) 21 T ELT)) (> (#28# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#28# 20 T ELT)) (< (#28# 18 T ELT)) (|/\\| (#27# 106 T ELT)) (|#| ((#25# $) 89 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (~ (#3=($ $) 105 T ELT)) (|xor| (#4=($ $ $) 34 T ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) 60 #6=(|has| $ (|ShallowlyMutableAggregate| #2#)) ELT)) (|sorted?| (#7=(#2# $) 99 #8=(|has| #2# #9=(|OrderedSet|)) ELT) (#10=(#2# #11=(|Mapping| #2# #2# #2#) $) 93 T ELT)) (|sort!| (#3# 103 (AND #8# #6#) ELT) (#12=($ #11# $) 102 #6# ELT)) (|sort| (#3# 98 #8# ELT) (#12# 92 T ELT)) (|setelt| ((#2# $ #13=(|UniversalSegment| #5#) #2#) 78 #6# ELT) (#14=(#2# $ #5# #2#) 48 #6# ELT)) (|select| (#15=($ #16=(|Mapping| #2# #2#) $) 64 #17=(|has| $ (|FiniteAggregate| #2#)) ELT)) (|sample| (#18=($) 41 T CONST)) (|reverse!| (#3# 101 #6# ELT)) (|reverse| (#3# 91 T ELT)) (|removeDuplicates| (#3# 62 #19=(AND #20=(|has| #2# (|BasicType|)) #17#) ELT)) (|remove| (#15# 65 #17# ELT) (#21=($ #2# $) 63 #19# ELT)) (|reduce| (#10# 84 T ELT) ((#2# #11# $ #2#) 83 T ELT) ((#2# #11# $ #2# #2#) 79 #20# ELT)) (|qsetelt!| (#14# 47 #6# ELT)) (|qelt| (#22=(#2# $ #5#) 49 T ELT)) (|position| ((#5# #2# $ #5#) 96 #20# ELT) ((#5# #2# $) 95 #20# ELT) ((#5# #16# $) 94 T ELT)) (|or| (#4# 110 T ELT)) (|not| (#3# 108 T ELT)) (|nor| (#4# 35 T ELT)) (|new| (($ #23=(|NonNegativeInteger|) #2#) 68 T ELT)) (|nand| (#4# 36 T ELT)) (|minIndex| (#24=(#5# $) 57 #25=(|has| #5# #9#) ELT)) (|min| (#4# 23 T ELT)) (|merge| (#4# 97 #8# ELT) (#26=($ #11# $ $) 90 T ELT)) (|members| (#27=(#28=(|List| #2#) $) 85 T ELT)) (|member?| (#29=(#2# #2# $) 80 #20# ELT)) (|maxIndex| (#24# 56 #25# ELT)) (|max| (#4# 22 T ELT)) (|map!| (#15# 104 T ELT)) (|map| (#26# 73 T ELT) (#15# 42 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|insert| (#30=($ $ $ #5#) 77 T ELT) (($ #2# $ #5#) 76 T ELT)) (|indices| (((|List| #5#) $) 54 T ELT)) (|index?| ((#2# #5# $) 53 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (#7# 58 #25# ELT)) (|find| (((|Union| #2# "failed") #16# $) 82 T ELT)) (|fill!| (#31=($ $ #2#) 59 #6# ELT)) (|every?| (#32=(#2# #16# $) 87 T ELT)) (|eval| (($ $ #28# #28#) 46 #33=(AND (|has| #2# (|Evalable| #2#)) (|has| #2# (|SetCategory|))) ELT) (($ $ #2# #2#) 45 #33# ELT) (($ $ #34=(|Equation| #2#)) 44 #33# ELT) (($ $ (|List| #34#)) 43 #33# ELT)) (|eq?| (#1# 37 T ELT)) (|entry?| (#29# 55 (AND #17# #20#) ELT)) (|entries| (#27# 52 T ELT)) (|empty?| (#7# 40 T ELT)) (|empty| (#18# 39 T ELT)) (|elt| (#35=($ $ #13#) 67 T ELT) (#22# 51 T ELT) (#14# 50 T ELT)) (|delete| (#35# 75 T ELT) (($ $ #5#) 74 T ELT)) (|count| ((#23# #16# $) 86 T ELT) ((#23# #2# $) 81 #20# ELT)) (|copyInto!| (#30# 100 #6# ELT)) (|copy| (#3# 38 T ELT)) (|convert| ((#36=(|InputForm|) $) 61 (|has| #2# (|ConvertibleTo| #36#)) ELT)) (|construct| (($ #28#) 66 T ELT)) (|concat| (($ (|List| $)) 72 T ELT) (#4# 71 T ELT) (#21# 70 T ELT) (#31# 69 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| (#32# 88 T ELT)) (|and| (#4# 109 T ELT)) (|\\/| (#4# 107 T ELT)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT)) (|/\\| (#4# 106 T ELT)) (|#| ((#23# $) 89 T ELT))) (((|BitAggregate|) (|Category|)) (T |BitAggregate|)) -((|nand| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|nor| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|))) (|xor| (*1 *1 *1 *1) (|ofCategory| *1 (|BitAggregate|)))) -(|Join| (|OrderedSet|) (|BooleanLogic|) (|Logic|) (|OneDimensionalArrayAggregate| (|Boolean|)) (CATEGORY |domain| (SIGNATURE |nand| ($ $ $)) (SIGNATURE |nor| ($ $ $)) (SIGNATURE |xor| ($ $ $)))) -(((|Aggregate|) . T) ((|BasicType|) . T) ((|BooleanLogic|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| #1=(|Boolean|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Boolean|) (|ConvertibleTo| (|InputForm|))) ((|Eltable| #2=(|Integer|) #1#) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #2# #1#) . T) ((|Evalable| #1#) AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))) ((|FiniteAggregate| #1#) . T) ((|FiniteLinearAggregate| #1#) . T) ((|Functorial| #1#) . T) ((|HomogeneousAggregate| #1#) . T) ((|IndexedAggregate| #2# #1#) . T) ((|InnerEvalable| #1# #1#) AND (|has| (|Boolean|) (|Evalable| (|Boolean|))) (|has| (|Boolean|) (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| #1#) . T) ((|Logic|) . T) ((|OneDimensionalArrayAggregate| #1#) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| #1#) . T) ((|Type|) . T)) +((|nand| #1=(*1 *1 *1 *1) #2=(|ofCategory| *1 (|BitAggregate|))) (|nor| #1# #2#) (|xor| #1# #2#)) +(|Join| (|OrderedSet|) (|BooleanLogic|) (|Logic|) (|OneDimensionalArrayAggregate| (|Boolean|)) (CATEGORY |domain| (SIGNATURE |nand| #1=($ $ $)) (SIGNATURE |nor| #1#) (SIGNATURE |xor| #1#))) +(((|Aggregate|) . T) ((|BasicType|) . T) ((|BooleanLogic|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| #1=(|Boolean|)) . T) ((|ConvertibleTo| (|InputForm|)) . T) ((|Eltable| #2=(|Integer|) #1#) . T) ((|Eltable| (|UniversalSegment| #2#) $) . T) ((|EltableAggregate| #2# #1#) . T) ((|FiniteAggregate| #1#) . T) ((|FiniteLinearAggregate| #1#) . T) ((|Functorial| #1#) . T) ((|HomogeneousAggregate| #1#) . T) ((|IndexedAggregate| #2# #1#) . T) ((|LinearAggregate| #1#) . T) ((|Logic|) . T) ((|OneDimensionalArrayAggregate| #1#) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| #1#) . T) ((|Type|) . T)) ((|map!| (($ (|Mapping| |#2| |#2|) $) 22 T ELT)) (|copy| (($ $) 16 T ELT)) (|#| (((|NonNegativeInteger|) $) 25 T ELT))) (((|BinaryTreeCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map!| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |#| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |copy| (|#1| |#1|))) (|BinaryTreeCategory| |#2|) (|SetCategory|)) (T |BinaryTreeCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#3=($ $ $) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setleft!| (#3# 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #4="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #5="left" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #6="right" $) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #7=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sample| (#8=($) 6 T CONST)) (|right| (#9=($ $) 54 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 (|has| |#1| . #10=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 67 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 66 T ELT)) (|nodes| (#11=(#7# $) 45 T ELT)) (|node?| (#12=(#13=(|Boolean|) $ $) 37 (|has| |#1| . #14=((|BasicType|))) ELT)) (|node| (($ $ |#1| $) 59 T ELT)) (|members| (((|List| |#1|) $) 65 T ELT)) (|member?| ((#15=(|Boolean|) |#1| $) 70 (|has| |#1| . #10#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 60 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|left| (#9# 56 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (#16=(#13# $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #17=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #17#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #15# |#1|) $) 68 T ELT)) (|every?| ((#15# (|Mapping| #15# |#1|) . #18=($)) 63 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT)) (|eq?| ((#19=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#19# $) 7 T ELT)) (|empty| (#8# 8 T ELT)) (|elt| ((|#1| $ #4#) 42 T ELT) (($ $ #5#) 55 T ELT) (($ $ #6#) 53 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#16# 41 T ELT)) (|count| ((#20=(|NonNegativeInteger|) |#1| $) 69 (|has| |#1| . #10#) ELT) ((#20# (|Mapping| #15# |#1|) $) 64 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (#11# 46 T ELT)) (|child?| (#12# 38 (|has| |#1| . #14#) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#15# (|Mapping| #15# |#1|) . #18#) 62 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#20# $) 61 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 #4=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#5=($ $ $) 49 #4# ELT)) (|setleft!| (#5# 51 #4# ELT)) (|setelt| ((|#1| $ #6="value" |#1|) 35 #4# ELT) (($ $ #7="left" $) 52 #4# ELT) (($ $ #8="right" $) 50 #4# ELT)) (|setchildren!| (($ $ #9=(|List| $)) 36 #4# ELT)) (|sample| (#10=($) 6 T CONST)) (|right| (#11=($ $) 54 T ELT)) (|reduce| ((|#1| #12=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 71 #3# ELT) ((|#1| #12# $ |#1|) 67 T ELT) ((|#1| #12# $) 66 T ELT)) (|nodes| (#13=(#9# $) 45 T ELT)) (|node?| (#1# 37 #3# ELT)) (|node| (($ $ |#1| $) 59 T ELT)) (|members| (#14=(#15=(|List| |#1|) $) 65 T ELT)) (|member?| ((#2# |#1| $) 70 #3# ELT)) (|map!| (#16=($ (|Mapping| |#1| |#1|) $) 60 T ELT)) (|map| (#16# 26 T ELT)) (|left| (#11# 56 T ELT)) (|leaves| (#14# 40 T ELT)) (|leaf?| (#17=(#2# $) 44 T ELT)) (|latex| (((|String|) $) 21 #18=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) 20 #18# ELT)) (|find| (((|Union| |#1| "failed") #19=(|Mapping| #2# |#1|) $) 68 T ELT)) (|every?| (#20=(#2# #19# $) 63 T ELT)) (|eval| (($ $ (|List| #21=(|Equation| |#1|))) 25 #22=(AND (|has| |#1| (|Evalable| |#1|)) #18#) ELT) (($ $ #21#) 24 #22# ELT) (($ $ |#1| |#1|) 23 #22# ELT) (($ $ #15# #15#) 22 #22# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| (#17# 7 T ELT)) (|empty| (#10# 8 T ELT)) (|elt| ((|#1| $ #6#) 42 T ELT) (($ $ #7#) 55 T ELT) (($ $ #8#) 53 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (#17# 41 T ELT)) (|count| ((#23=(|NonNegativeInteger|) |#1| $) 69 #3# ELT) ((#23# #19# $) 64 T ELT)) (|copy| (#11# 9 T ELT)) (|coerce| ((#24=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #24#)) ELT)) (|children| (#13# 46 T ELT)) (|child?| (#1# 38 #3# ELT)) (|before?| (#1# 19 #3# ELT)) (|any?| (#20# 62 T ELT)) (= (#1# 17 #3# ELT)) (|#| ((#23# $) 61 T ELT))) (((|BinaryTreeCategory| |#1|) (|Category|) (|SetCategory|)) (T |BinaryTreeCategory|)) ((|node| (*1 *1 *1 *2 *1) (AND (|ofCategory| *1 (|BinaryTreeCategory| *2)) (|ofCategory| *2 (|SetCategory|))))) (|Join| (|BinaryRecursiveAggregate| |t#1|) (|FiniteAggregate| |t#1|) (|ShallowlyMutableAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |node| ($ $ |t#1| $)))) -(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|BinaryRecursiveAggregate| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|BinaryRecursiveAggregate| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 18 T ELT)) (|setvalue!| ((|#1| $ |#1|) 22 #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| (#6=($ $ $) 23 #5# ELT)) (|setleft!| (#6# 21 #5# ELT)) (|setelt| ((|#1| $ #7="value" |#1|) NIL #5# ELT) (($ $ #8="left" $) NIL #5# ELT) (($ $ #9="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #10=(|List| $)) NIL #5# ELT)) (|sample| (#11=($) NIL T CONST)) (|right| (#12=($ $) 24 T ELT)) (|reduce| ((|#1| #13=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #13# $ |#1|) NIL T ELT) ((|#1| #13# $) NIL T ELT)) (|nodes| #14=((#10# $) NIL T ELT)) (|node?| #1#) (|node| (($ $ |#1| $) NIL T ELT)) (|members| #15=((#16=(|List| |#1|) $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| #17=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #17#) (|left| (#12# NIL T ELT)) (|leaves| #15#) (|leaf?| #18=(#19=(#3# $) NIL T ELT)) (|latex| (((|String|) $) NIL #20=(|has| |#1| (|SetCategory|)) ELT)) (|insert!| (($ |#1| $) 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL #20# ELT)) (|find| (((|Union| |#1| "failed") #21=(|Mapping| #3# |#1|) $) NIL T ELT)) (|every?| #22=((#3# #21# $) NIL T ELT)) (|eval| (($ $ (|List| #23=(|Equation| |#1|))) NIL #24=(AND (|has| |#1| (|Evalable| |#1|)) #20#) ELT) (($ $ #23#) NIL #24# ELT) (($ $ |#1| |#1|) NIL #24# ELT) (($ $ #16# #16#) NIL #24# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#19# 17 T ELT)) (|empty| (#11# 11 T ELT)) (|elt| ((|#1| $ #7#) NIL T ELT) (($ $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| #18#) (|count| ((#25=(|NonNegativeInteger|) |#1| $) NIL #4# ELT) ((#25# #21# $) NIL T ELT)) (|copy| (#12# 20 T ELT)) (|coerce| ((#26=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #26#)) ELT)) (|children| #14#) (|child?| #1#) (|binaryTournament| (($ #16#) 16 T ELT)) (|before?| #1#) (|any?| #22#) (= #1#) (|#| ((#25# $) NIL T ELT))) (((|BinaryTournament| |#1|) (|Join| (|BinaryTreeCategory| |#1|) (CATEGORY |domain| (SIGNATURE |binaryTournament| ($ (|List| |#1|))) (SIGNATURE |insert!| ($ |#1| $)))) (|OrderedSet|)) (T |BinaryTournament|)) ((|binaryTournament| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 #1=(|OrderedSet|)) (|isDomain| *1 (|BinaryTournament| *3)))) (|insert!| (*1 *1 *2 *1) (AND (|isDomain| *1 (|BinaryTournament| *2)) (|ofCategory| *2 #1#)))) @@ -302,16 +302,16 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|unknownEndian| (#3=($) 6 T CONST)) (|littleEndian| (#3# 7 T CONST)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 14 T ELT)) (|bigEndian| (#3# 8 T CONST)) (|before?| #1#) (= (#2# 10 T ELT))) (((|ByteOrder|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |littleEndian| #1=($) |constant|) (SIGNATURE |bigEndian| #1# |constant|) (SIGNATURE |unknownEndian| #1# |constant|)))) (T |ByteOrder|)) ((|littleEndian| #1=(*1 *1) #2=(|isDomain| *1 (|ByteOrder|))) (|bigEndian| #1# #2#) (|unknownEndian| #1# #2#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) (((|CancellationAbelianMonoid|) (|Category|)) (T |CancellationAbelianMonoid|)) ((|subtractIfCan| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CancellationAbelianMonoid|))))) (|Join| (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |subtractIfCan| ((|Maybe| $) $ $)))) -(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) 17 T ELT)) (|position| (((|NonNegativeInteger|) $) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) +(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|setPosition| (((|Void|) $ #2=(|NonNegativeInteger|)) 17 T ELT)) (|position| ((#2# $) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) (((|CachableSet|) (|Category|)) (T |CachableSet|)) -((|position| (*1 *2 *1) (AND (|ofCategory| *1 (|CachableSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|setPosition| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|CachableSet|)) (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Void|))))) -(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |position| ((|NonNegativeInteger|) $)) (SIGNATURE |setPosition| ((|Void|) $ (|NonNegativeInteger|))))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|position| (*1 *2 *1) (AND #1=(|ofCategory| *1 (|CachableSet|)) (|isDomain| *2 #2=(|NonNegativeInteger|)))) (|setPosition| (*1 *2 *1 *3) (AND #1# (|isDomain| *3 #2#) (|isDomain| *2 (|Void|))))) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |position| (#1=(|NonNegativeInteger|) $)) (SIGNATURE |setPosition| ((|Void|) $ #1#)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|List| (|SpadAst|)) $) 12 T ELT)) (|before?| #1#) (= #1#)) (((|CapsuleAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |body| ((|List| (|SpadAst|)) $))))) (T |CapsuleAst|)) ((|body| (*1 *2 *1) (AND (|isDomain| *2 (|List| (|SpadAst|))) (|isDomain| *1 (|CapsuleAst|))))) @@ -342,26 +342,26 @@ NIL ((|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) 17 T ELT)) (|commonDenominator| ((|#1| |#3|) 9 T ELT)) (|clearDenominator| ((|#3| |#3|) 15 T ELT))) (((|CommonDenominator| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| |#3|)) (SIGNATURE |clearDenominator| (|#3| |#3|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|) (|FiniteLinearAggregate| |#2|)) (T |CommonDenominator|)) ((|splitDenominator| #1=(*1 *2 *3) (AND (|ofCategory| *4 #2=(|IntegralDomain|)) (|ofCategory| *5 (|QuotientFieldCategory| *4)) (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *4))) (|isDomain| *1 (|CommonDenominator| *4 *5 *3)) (|ofCategory| *3 (|FiniteLinearAggregate| *5)))) (|clearDenominator| (*1 *2 *2) (AND (|ofCategory| *3 #2#) (|ofCategory| *4 (|QuotientFieldCategory| *3)) (|isDomain| *1 (|CommonDenominator| *3 *4 *2)) (|ofCategory| *2 #3=(|FiniteLinearAggregate| *4)))) (|commonDenominator| #1# (AND (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|CommonDenominator| *2 *4 *3)) (|ofCategory| *3 #3#)))) -((|permutation| (($ $ $) 8 T ELT)) (|factorial| (($ $) 7 T ELT)) (|binomial| (($ $ $) 6 T ELT))) +((|permutation| (#1=($ $ $) 8 T ELT)) (|factorial| (($ $) 7 T ELT)) (|binomial| (#1# 6 T ELT))) (((|CombinatorialFunctionCategory|) (|Category|)) (T |CombinatorialFunctionCategory|)) -((|permutation| (*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|))) (|factorial| (*1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|))) (|binomial| (*1 *1 *1 *1) (|ofCategory| *1 (|CombinatorialFunctionCategory|)))) -(|Join| (CATEGORY |domain| (SIGNATURE |binomial| ($ $ $)) (SIGNATURE |factorial| ($ $)) (SIGNATURE |permutation| ($ $ $)))) +((|permutation| #1=(*1 *1 *1 *1) #2=(|ofCategory| *1 (|CombinatorialFunctionCategory|))) (|factorial| (*1 *1 *1) #2#) (|binomial| #1# #2#)) +(|Join| (CATEGORY |domain| (SIGNATURE |binomial| #1=($ $ $)) (SIGNATURE |factorial| ($ $)) (SIGNATURE |permutation| #1#))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|verticalTab| (#4=($) 30 T CONST)) (|upperCase?| (#5=(#3# $) 42 T ELT)) (|upperCase| (#6=($ $) 52 T ELT)) (|underscore| (#4# 23 T CONST)) (|space| (#4# 21 T CONST)) (|size| ((#7=(|NonNegativeInteger|)) 13 T ELT)) (|random| (#4# 20 T ELT)) (|quote| (#4# 22 T CONST)) (|ord| ((#7# $) 17 T ELT)) (|newline| (#4# 24 T CONST)) (|min| #8=(($ $ $) NIL T ELT) #9=(#4# NIL T CONST)) (|max| #8# #9#) (|lowerCase?| (#5# 44 T ELT)) (|lowerCase| (#6# 53 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 18 T ELT)) (|linefeed| (#4# 26 T CONST)) (|latex| ((#11=(|String|) $) 50 T ELT)) (|index| (($ #10#) 16 T ELT)) (|horizontalTab| (#4# 29 T CONST)) (|hexDigit?| (#5# 40 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|formfeed| (#4# 27 T CONST)) (|escape| (#4# 31 T CONST)) (|digit?| (#5# 38 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT)) (|char| (($ #7#) 14 T ELT) (($ #11#) 51 T ELT)) (|carriageReturn| (#4# 25 T CONST)) (|before?| #1#) (|backspace| (#4# 28 T CONST)) (|alphanumeric?| (#5# 48 T ELT)) (|alphabetic?| (#5# 46 T ELT)) (>= (#2# 11 T ELT)) (> (#2# 9 T ELT)) (= (#2# 7 T ELT)) (<= (#2# 10 T ELT)) (< (#2# 8 T ELT))) (((|Character|) (|Join| (|OrderedFinite|) (CATEGORY |domain| (SIGNATURE |ord| (#1=(|NonNegativeInteger|) $)) (SIGNATURE |char| ($ #1#)) (SIGNATURE |char| ($ (|String|))) (SIGNATURE |space| #2=($) |constant|) (SIGNATURE |quote| #2# |constant|) (SIGNATURE |underscore| #2# |constant|) (SIGNATURE |newline| #2# |constant|) (SIGNATURE |carriageReturn| #2# |constant|) (SIGNATURE |linefeed| #2# |constant|) (SIGNATURE |formfeed| #2# |constant|) (SIGNATURE |backspace| #2# |constant|) (SIGNATURE |horizontalTab| #2# |constant|) (SIGNATURE |verticalTab| #2# |constant|) (SIGNATURE |escape| #2# |constant|) (SIGNATURE |upperCase| #3=($ $)) (SIGNATURE |lowerCase| #3#) (SIGNATURE |digit?| #4=((|Boolean|) $)) (SIGNATURE |hexDigit?| #4#) (SIGNATURE |alphabetic?| #4#) (SIGNATURE |upperCase?| #4#) (SIGNATURE |lowerCase?| #4#) (SIGNATURE |alphanumeric?| #4#)))) (T |Character|)) ((|ord| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3=(|isDomain| *1 (|Character|)))) (|char| #4=(*1 *1 *2) #2#) (|char| #4# (AND (|isDomain| *2 (|String|)) #3#)) (|space| #5=(*1 *1) #3#) (|quote| #5# #3#) (|underscore| #5# #3#) (|newline| #5# #3#) (|carriageReturn| #5# #3#) (|linefeed| #5# #3#) (|formfeed| #5# #3#) (|backspace| #5# #3#) (|horizontalTab| #5# #3#) (|verticalTab| #5# #3#) (|escape| #5# #3#) (|upperCase| #6=(*1 *1 *1) #3#) (|lowerCase| #6# #3#) (|digit?| #1# #7=(AND (|isDomain| *2 (|Boolean|)) #3#)) (|hexDigit?| #1# #7#) (|alphabetic?| #1# #7#) (|upperCase?| #1# #7#) (|lowerCase?| #1# #7#) (|alphanumeric?| #1# #7#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|charthRoot| (((|Maybe| $) $) 48 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| ((#4=(|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #6=(|Integer|)) 42 T ELT)) (|charthRoot| ((#4# $) 48 T ELT)) (|characteristic| ((#7=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (#5# 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#8=($ $ $) 29 T ELT)) (+ (#8# 18 T ELT)) (** (($ $ #9=(|PositiveInteger|)) 36 T ELT) (($ $ #7#) 44 T ELT)) (* (($ #9# $) 17 T ELT) (($ #7# $) 21 T ELT) (($ #6# $) 31 T ELT) (#8# 35 T ELT))) (((|CharacteristicNonZero|) (|Category|)) (T |CharacteristicNonZero|)) ((|charthRoot| (*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CharacteristicNonZero|))))) (|Join| (|Ring|) (CATEGORY |domain| (SIGNATURE |charthRoot| ((|Maybe| $) $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) 19 T ELT))) (((|CharacteristicPolynomialPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (|#1| (|Matrix| |#1|) |#1|))) (|CommutativeRing|)) (T |CharacteristicPolynomialPackage|)) ((|characteristicPolynomial| (*1 *2 *3 *2) (AND (|isDomain| *3 (|Matrix| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|isDomain| *1 (|CharacteristicPolynomialPackage| *2))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #5=(|Integer|)) 42 T ELT)) (|characteristic| ((#6=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#7=($ $ $) 29 T ELT)) (+ (#7# 18 T ELT)) (** (($ $ #8=(|PositiveInteger|)) 36 T ELT) (($ $ #6#) 44 T ELT)) (* (($ #8# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #5# $) 31 T ELT) (#7# 35 T ELT))) (((|CharacteristicZero|) (|Category|)) (T |CharacteristicZero|)) NIL (|Join| (|Ring|)) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|rootPoly| (((|Record| (|:| |exponent| #1=(|NonNegativeInteger|)) #2=(|:| |coef| #3=(|Fraction| |#2|)) (|:| |radicand| |#2|)) #3# #1#) 76 T ELT)) (|radPoly| (((|Union| (|Record| (|:| |radicand| #3#) #4=(|:| |deg| #1#)) "failed") |#3|) 56 T ELT)) (|mkIntegral| (((|Record| #2# #5=(|:| |poly| |#3|)) |#3|) 41 T ELT)) (|goodPoint| ((|#1| |#3| |#3|) 44 T ELT)) (|eval| ((|#3| |#3| #3# #3#) 20 T ELT)) (|chvar| (((|Record| (|:| |func| |#3|) #5# (|:| |c1| #3#) (|:| |c2| #3#) #4#) |#3| |#3|) 53 T ELT))) (((|ChangeOfVariable| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |mkIntegral| ((|Record| #1=(|:| |coef| #2=(|Fraction| |#2|)) #3=(|:| |poly| |#3|)) |#3|)) (SIGNATURE |radPoly| ((|Union| (|Record| (|:| |radicand| #2#) #4=(|:| |deg| #5=(|NonNegativeInteger|))) "failed") |#3|)) (SIGNATURE |rootPoly| ((|Record| (|:| |exponent| #5#) #1# (|:| |radicand| |#2|)) #2# #5#)) (SIGNATURE |goodPoint| (|#1| |#3| |#3|)) (SIGNATURE |eval| (|#3| |#3| #2# #2#)) (SIGNATURE |chvar| ((|Record| (|:| |func| |#3|) #3# (|:| |c1| #2#) (|:| |c2| #2#) #4#) |#3| |#3|))) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| #2#)) (T |ChangeOfVariable|)) ((|chvar| #1=(*1 *2 *3 *3) (AND #2=(|ofCategory| *4 #3=(|UniqueFactorizationDomain|)) #4=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |func| *3) #5=(|:| |poly| *3) (|:| |c1| #6=(|Fraction| *5)) (|:| |c2| #6#) #7=(|:| |deg| #8=(|NonNegativeInteger|)))) #9=(|isDomain| *1 (|ChangeOfVariable| *4 *5 *3)) #10=(|ofCategory| *3 (|UnivariatePolynomialCategory| #6#)))) (|eval| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 #6#) #2# #4# (|isDomain| *1 (|ChangeOfVariable| *4 *5 *2)) (|ofCategory| *2 #11=(|UnivariatePolynomialCategory| *3)))) (|goodPoint| #1# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #3#) (|isDomain| *1 (|ChangeOfVariable| *2 *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|rootPoly| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| *6)) (|ofCategory| *5 #3#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |exponent| #8#) (|:| |coef| *3) (|:| |radicand| *6))) (|isDomain| *1 (|ChangeOfVariable| *5 *6 *7)) (|isDomain| *4 #8#) (|ofCategory| *7 #11#))) (|radPoly| #12=(*1 *2 *3) (|partial| AND #2# #4# (|isDomain| *2 (|Record| (|:| |radicand| #6#) #7#)) #9# #10#)) (|mkIntegral| #12# (AND #2# #4# (|isDomain| *2 (|Record| (|:| |coef| #6#) #5#)) #9# #10#))) @@ -371,11 +371,11 @@ NIL ((|select| (#1=($ (|Mapping| (|Boolean|) |#2|) $) 16 T ELT)) (|removeDuplicates| (($ $) 21 T ELT)) (|remove| (#1# 14 T ELT) (($ |#2| $) 19 T ELT))) (((|Collection&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |removeDuplicates| (|#1| |#1|)) (SIGNATURE |remove| (|#1| |#2| |#1|)) (SIGNATURE |select| #1=(|#1| (|Mapping| (|Boolean|) |#2|) |#1|)) (SIGNATURE |remove| #1#)) (|Collection| |#2|) (|Type|)) (T |Collection&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) 38 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#3=($) 6 T CONST)) (|removeDuplicates| (($ $) 36 (AND (|has| |#1| (|BasicType|)) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) 39 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ |#1| $) 37 (AND (|has| |#1| (|BasicType|)) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| (((|InputForm|) $) 35 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|construct| (($ (|List| |#1|)) 40 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|select| (#4=($ (|Mapping| #2# |#1|) $) 38 #5=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#6=($) 6 T CONST)) (|removeDuplicates| (#7=($ $) 36 #8=(AND #3# #5#) ELT)) (|remove| (#4# 39 #5# ELT) (($ |#1| $) 37 #8# ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 #9=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) 20 #9# ELT)) (|eval| (($ $ (|List| #10=(|Equation| |#1|))) 25 #11=(AND (|has| |#1| (|Evalable| |#1|)) #9#) ELT) (($ $ #10#) 24 #11# ELT) (($ $ |#1| |#1|) 23 #11# ELT) (($ $ #12=(|List| |#1|) #12#) 22 #11# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#6# 8 T ELT)) (|copy| (#7# 9 T ELT)) (|convert| ((#13=(|InputForm|) $) 35 (|has| |#1| (|ConvertibleTo| #13#)) ELT)) (|construct| (($ #12#) 40 T ELT)) (|coerce| ((#14=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #14#)) ELT)) (|before?| (#1# 19 #3# ELT)) (= (#1# 17 #3# ELT))) (((|Collection| |#1|) (|Category|) (|Type|)) (T |Collection|)) -((|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|Collection| *3)))) (|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|remove| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|)))) (|removeDuplicates| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|))))) -(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ (|List| |t#1|))) (IF (|has| $ (|FiniteAggregate| |t#1|)) (PROGN (SIGNATURE |remove| ($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select| ($ (|Mapping| (|Boolean|) |t#1|) $)) (IF (|has| |t#1| (|BasicType|)) (PROGN (SIGNATURE |remove| ($ |t#1| $)) (SIGNATURE |removeDuplicates| ($ $))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|))) -(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) +((|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 #2=(|Type|)) #3=(|ofCategory| *1 (|Collection| *3)))) (|remove| #4=(*1 *1 *2 *1) #5=(AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) #3# #1#)) (|select| #4# #5#) (|remove| #4# #6=(AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 #2#) (|ofCategory| *2 (|BasicType|)))) (|removeDuplicates| (*1 *1 *1) #6#)) +(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ (|List| |t#1|))) (IF (|has| $ (|FiniteAggregate| |t#1|)) (PROGN (SIGNATURE |remove| #1=($ (|Mapping| (|Boolean|) |t#1|) $)) (SIGNATURE |select| #1#) (IF (|has| |t#1| (|BasicType|)) (PROGN (SIGNATURE |remove| ($ |t#1| $)) (SIGNATURE |removeDuplicates| ($ $))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| #2=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #2#) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) 113 T ELT)) (|opposite?| #1#) (|one?| #4#) (|monomial| (($ |#2| #6=(|List| #7=(|PositiveInteger|))) 72 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|e| (($ #7#) 58 T ELT)) (|dimension| (((|CardinalNumber|)) 23 T ELT)) (|coerce| (((|OutputForm|) $) 88 T ELT) (($ #8=(|Integer|)) 54 T ELT) (($ |#2|) 55 T ELT)) (|coefficient| ((|#2| $ #6#) 75 T ELT)) (|characteristic| ((#9=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#5# 48 T CONST)) (|One| (#5# 52 T CONST)) (= (#2# 34 T ELT)) (/ #10=(($ $ |#2|) NIL T ELT)) (- (($ $) 43 T ELT) (#11=($ $ $) 41 T ELT)) (+ (#11# 39 T ELT)) (** (($ $ #7#) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #7# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #8# $) 45 T ELT) (#11# 64 T ELT) (($ |#2| $) 47 T ELT) #10#)) (((|CliffordAlgebra| |#1| |#2| |#3|) (|Join| (|Ring|) (|Algebra| |#2|) (|VectorSpace| |#2|) (CATEGORY |domain| (SIGNATURE |e| ($ #1=(|PositiveInteger|))) (SIGNATURE |monomial| ($ |#2| #2=(|List| #1#))) (SIGNATURE |coefficient| (|#2| $ #2#)))) #1# (|Field|) (|QuadraticForm| |#1| |#2|)) (T |CliffordAlgebra|)) ((|e| (*1 *1 *2) (AND (|isDomain| *2 #1=(|PositiveInteger|)) (|isDomain| *1 (|CliffordAlgebra| *3 *4 *5)) (|ofType| *3 *2) (|ofCategory| *4 #2=(|Field|)) (|ofType| *5 (|QuadraticForm| *3 *4)))) (|monomial| (*1 *1 *2 *3) (AND #3=(|isDomain| *3 (|List| #1#)) #4=(|isDomain| *1 (|CliffordAlgebra| *4 *2 *5)) #5=(|ofType| *4 #1#) #6=(|ofCategory| *2 #2#) #7=(|ofType| *5 (|QuadraticForm| *4 *2)))) (|coefficient| (*1 *2 *1 *3) (AND #3# #6# #4# #5# #7#))) @@ -400,10 +400,10 @@ NIL ((|stirling2| (#1=(|#1| |#1| |#1|) 66 T ELT)) (|stirling1| (#1# 63 T ELT)) (|permutation| (#1# 57 T ELT)) (|partition| (#2=(|#1| |#1|) 43 T ELT)) (|multinomial| ((|#1| |#1| (|List| |#1|)) 55 T ELT)) (|factorial| (#2# 47 T ELT)) (|binomial| (#1# 51 T ELT))) (((|IntegerCombinatoricFunctions| |#1|) (CATEGORY |package| (SIGNATURE |binomial| #1=(|#1| |#1| |#1|)) (SIGNATURE |factorial| #2=(|#1| |#1|)) (SIGNATURE |multinomial| (|#1| |#1| (|List| |#1|))) (SIGNATURE |partition| #2#) (SIGNATURE |permutation| #1#) (SIGNATURE |stirling1| #1#) (SIGNATURE |stirling2| #1#)) (|IntegerNumberSystem|)) (T |IntegerCombinatoricFunctions|)) ((|stirling2| #1=(*1 *2 *2 *2) #2=(AND #3=(|isDomain| *1 (|IntegerCombinatoricFunctions| *2)) #4=(|ofCategory| *2 (|IntegerNumberSystem|)))) (|stirling1| #1# #2#) (|permutation| #1# #2#) (|partition| #5=(*1 *2 *2) #2#) (|multinomial| (*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) #4# #3#)) (|factorial| #5# #2#) (|binomial| #1# #2#)) -((|summation| (($ $ (|Symbol|)) 12 T ELT) (($ $ (|SegmentBinding| $)) 11 T ELT)) (|product| (($ $ (|Symbol|)) 10 T ELT) (($ $ (|SegmentBinding| $)) 9 T ELT)) (|permutation| (#1=($ $ $) 8 T ELT)) (|factorials| (($ $) 14 T ELT) (($ $ (|Symbol|)) 13 T ELT)) (|factorial| (($ $) 7 T ELT)) (|binomial| (#1# 6 T ELT))) +((|summation| (#1=($ $ (|Symbol|)) 12 T ELT) (#2=($ $ (|SegmentBinding| $)) 11 T ELT)) (|product| (#1# 10 T ELT) (#2# 9 T ELT)) (|permutation| (#3=($ $ $) 8 T ELT)) (|factorials| (#4=($ $) 14 T ELT) (#1# 13 T ELT)) (|factorial| (#4# 7 T ELT)) (|binomial| (#3# 6 T ELT))) (((|CombinatorialOpsCategory|) (|Category|)) (T |CombinatorialOpsCategory|)) -((|factorials| (*1 *1 *1) (|ofCategory| *1 (|CombinatorialOpsCategory|))) (|factorials| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|summation| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|summation| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|CombinatorialOpsCategory|)))) (|product| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|CombinatorialOpsCategory|)) (|isDomain| *2 (|Symbol|)))) (|product| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|CombinatorialOpsCategory|))))) -(|Join| (|CombinatorialFunctionCategory|) (CATEGORY |domain| (SIGNATURE |factorials| ($ $)) (SIGNATURE |factorials| ($ $ (|Symbol|))) (SIGNATURE |summation| ($ $ (|Symbol|))) (SIGNATURE |summation| ($ $ (|SegmentBinding| $))) (SIGNATURE |product| ($ $ (|Symbol|))) (SIGNATURE |product| ($ $ (|SegmentBinding| $))))) +((|factorials| (*1 *1 *1) #1=(|ofCategory| *1 (|CombinatorialOpsCategory|))) (|factorials| #2=(*1 *1 *1 *2) #3=(AND #1# (|isDomain| *2 (|Symbol|)))) (|summation| #2# #3#) (|summation| #2# #4=(AND (|isDomain| *2 (|SegmentBinding| *1)) #1#)) (|product| #2# #3#) (|product| #2# #4#)) +(|Join| (|CombinatorialFunctionCategory|) (CATEGORY |domain| (SIGNATURE |factorials| ($ $)) (SIGNATURE |factorials| #1=($ $ (|Symbol|))) (SIGNATURE |summation| #1#) (SIGNATURE |summation| #2=($ $ (|SegmentBinding| $))) (SIGNATURE |product| #1#) (SIGNATURE |product| #2#))) (((|CombinatorialFunctionCategory|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|mkcomm| (($ (|Integer|)) 15 T ELT) (($ $ $) 16 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT)) (|before?| #1#) (= (#2# 11 T ELT))) (((|Commutator|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |mkcomm| ($ (|Integer|))) (SIGNATURE |mkcomm| ($ $ $))))) (T |Commutator|)) @@ -424,15 +424,15 @@ NIL (((|CommutativeOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |CommutativeOperatorCategory|)) NIL (|Join| (|BinaryOperatorCategory| |t#1|) (CATEGORY |domain| (ATTRIBUTE (|%Rule| |commutativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|) (|:| |y| |t#1|)) (= (|f| |x| |y|) (|f| |y| |x|))))))) -(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) +(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T)) ((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 222 T ELT)) (|trace| (#1=(|#2| $) 102 T ELT)) (|tanh| (#2=($ $) 255 T ELT)) (|tan| (#2# 249 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #3=(|List| #4=(|SparseUnivariatePolynomial| $)) #5="failed") #3# #4#) 47 T ELT)) (|sinh| (#2# 253 T ELT)) (|sin| (#2# 247 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) #5#) $) NIL T ELT) (#7=((|Union| #8=(|Fraction| #6#) #5#) $) NIL T ELT) (((|Union| |#2| #5#) $) 146 T ELT)) (|retract| ((#6# $) NIL T ELT) (#9=(#8# $) NIL T ELT) (#1# 144 T ELT)) (|rem| (#10=($ $ $) 228 T ELT)) (|reducedSystem| ((#11=(|Matrix| #6#) #12=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #11#) (|:| |vec| (|Vector| #6#))) #12# #13=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #14=(|Matrix| |#2|)) (|:| |vec| #15=(|Vector| |#2|))) #12# #13#) 160 T ELT) ((#14# #12#) 154 T ELT)) (|reduce| (#16=($ #17=(|SparseUnivariatePolynomial| |#2|)) 125 T ELT) ((#18=(|Union| $ #5#) (|Fraction| #17#)) NIL T ELT)) (|recip| ((#18# $) 213 T ELT)) (|rationalIfCan| (#7# 203 T ELT)) (|rational?| ((#19=(|Boolean|) $) 198 T ELT)) (|rational| (#9# 201 T ELT)) (|rank| ((#20=(|PositiveInteger|)) 96 T ELT)) (|quo| (#10# 230 T ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) 267 T ELT)) (|pi| (#21=($) 244 T ELT)) (|patternMatch| ((#22=(|PatternMatchResult| #6# $) $ #23=(|Pattern| #6#) #22#) 192 T ELT) ((#24=(|PatternMatchResult| #25=(|Float|) $) $ #26=(|Pattern| #25#) #24#) 197 T ELT)) (|norm| (#1# 100 T ELT)) (|minimalPolynomial| (#27=(#17# $) 127 T ELT)) (|map| (($ #28=(|Mapping| |#2| |#2|) $) 108 T ELT)) (|log| (#2# 246 T ELT)) (|lift| (#27# 126 T ELT)) (|inv| (#2# 206 T ELT)) (|imaginary| (#21# 103 T ELT)) (|factorSquareFreePolynomial| (#29=((|Factored| #4#) #4#) 95 T ELT)) (|factorPolynomial| (#29# 64 T ELT)) (|exquo| ((#18# $ |#2|) 208 T ELT) ((#18# $ $) 211 T ELT)) (|exp| (#2# 245 T ELT)) (|euclideanSize| ((#30=(|NonNegativeInteger|) $) 225 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 234 T ELT)) (|discriminant| ((|#2| #13#) NIL T ELT) ((|#2|) 98 T ELT)) (|differentiate| (($ $ #28#) 119 T ELT) (($ $ #28# #30#) NIL T ELT) #31=(($ $ #30#) NIL T ELT) #32=(#2# NIL T ELT) (($ $ #33=(|List| #34=(|Symbol|)) (|List| #30#)) NIL T ELT) (($ $ #34# #30#) NIL T ELT) (($ $ #33#) NIL T ELT) (($ $ #34#) NIL T ELT)) (|definingPolynomial| ((#17#) 120 T ELT)) (|cosh| (#2# 254 T ELT)) (|cos| (#2# 248 T ELT)) (|coordinates| ((#15# $ #13#) 136 T ELT) ((#14# #13# #13#) NIL T ELT) (#35=(#15# $) 116 T ELT) ((#14# #13#) NIL T ELT)) (|convert| (#35# NIL T ELT) (($ #15#) NIL T ELT) (#27# NIL T ELT) (#16# NIL T ELT) ((#23# $) 183 T ELT) ((#26# $) 187 T ELT) (((|Complex| #25#) $) 172 T ELT) (((|Complex| (|DoubleFloat|)) $) 167 T ELT) (((|InputForm|) $) 179 T ELT)) (|conjugate| (#2# 104 T ELT)) (|coerce| (((|OutputForm|) $) 143 T ELT) (($ #6#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #8#) NIL T ELT) #32#) (|characteristicPolynomial| (#27# 32 T ELT)) (|characteristic| ((#30#) 106 T CONST)) (|before?| (#36=(#19# $ $) 13 T ELT)) (|atanh| (#2# 258 T ELT)) (|atan| (#2# 252 T ELT)) (|asinh| (#2# 256 T ELT)) (|asin| (#2# 250 T ELT)) (|argument| (#1# 241 T ELT)) (|acosh| (#2# 257 T ELT)) (|acos| (#2# 251 T ELT)) (|abs| (#2# 162 T ELT)) (= (#36# 110 T ELT)) (- (#2# 112 T ELT) #37=(#10# NIL T ELT)) (+ (#10# 111 T ELT)) (** (($ $ #20#) NIL T ELT) #31# (#38=($ $ #8#) 274 T ELT) #37# (($ $ #6#) NIL T ELT)) (* (($ #20# $) NIL T ELT) (($ #30# $) NIL T ELT) (($ #6# $) 118 T ELT) (#10# 147 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 114 T ELT) (($ #8# $) NIL T ELT) (#38# NIL T ELT))) (((|ComplexCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |differentiate| (|#1| |#1| #1=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #2=(|List| #1#))) (SIGNATURE |differentiate| (|#1| |#1| #1# #3=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #2# (|List| #3#))) (SIGNATURE |differentiate| #4=(|#1| |#1|)) (SIGNATURE |differentiate| #5=(|#1| |#1| #3#)) (SIGNATURE |coerce| #4#) (SIGNATURE |exquo| (#6=(|Union| |#1| #7="failed") |#1| |#1|)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |euclideanSize| (#3# |#1|)) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |quo| #8=(|#1| |#1| |#1|)) (SIGNATURE |rem| #8#) (SIGNATURE |inv| #4#) (SIGNATURE ** (|#1| |#1| #9=(|Integer|))) (SIGNATURE * #10=(|#1| |#1| #11=(|Fraction| #9#))) (SIGNATURE * (|#1| #11# |#1|)) (SIGNATURE |coerce| (|#1| #11#)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Complex| (|DoubleFloat|)) |#1|)) (SIGNATURE |convert| ((|Complex| #12=(|Float|)) |#1|)) (SIGNATURE |tan| #4#) (SIGNATURE |sin| #4#) (SIGNATURE |cos| #4#) (SIGNATURE |acos| #4#) (SIGNATURE |asin| #4#) (SIGNATURE |atan| #4#) (SIGNATURE |cosh| #4#) (SIGNATURE |sinh| #4#) (SIGNATURE |tanh| #4#) (SIGNATURE |acosh| #4#) (SIGNATURE |asinh| #4#) (SIGNATURE |atanh| #4#) (SIGNATURE |log| #4#) (SIGNATURE |exp| #4#) (SIGNATURE ** #8#) (SIGNATURE |pi| #13=(|#1|)) (SIGNATURE ** #10#) (SIGNATURE |factorPolynomial| #14=((|Factored| #15=(|SparseUnivariatePolynomial| |#1|)) #15#)) (SIGNATURE |factorSquareFreePolynomial| #14#) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #16=(|List| #15#) #7#) #16# #15#)) (SIGNATURE |rationalIfCan| #17=((|Union| #11# #7#) |#1|)) (SIGNATURE |rational| #18=(#11# |#1|)) (SIGNATURE |rational?| (#19=(|Boolean|) |#1|)) (SIGNATURE |polarCoordinates| ((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) |#1|)) (SIGNATURE |argument| #20=(|#2| |#1|)) (SIGNATURE |abs| #4#) (SIGNATURE |exquo| (#6# |#1| |#2|)) (SIGNATURE |conjugate| #4#) (SIGNATURE |imaginary| #13#) (SIGNATURE |convert| (#21=(|Pattern| #12#) |#1|)) (SIGNATURE |convert| (#22=(|Pattern| #9#) |#1|)) (SIGNATURE |patternMatch| (#23=(|PatternMatchResult| #12# |#1|) |#1| #21# #23#)) (SIGNATURE |patternMatch| (#24=(|PatternMatchResult| #9# |#1|) |#1| #22# #24#)) (SIGNATURE |map| (|#1| #25=(|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #25# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #25#)) (SIGNATURE |reduce| (#6# (|Fraction| #26=(|SparseUnivariatePolynomial| |#2|)))) (SIGNATURE |lift| #27=(#26# |#1|)) (SIGNATURE |convert| #28=(|#1| #26#)) (SIGNATURE |reduce| #28#) (SIGNATURE |definingPolynomial| (#26#)) (SIGNATURE |reducedSystem| (#29=(|Matrix| |#2|) #30=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #29#) (|:| |vec| #31=(|Vector| |#2|))) #30# #32=(|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #33=(|Matrix| #9#)) (|:| |vec| (|Vector| #9#))) #30# #32#)) (SIGNATURE |reducedSystem| (#33# #30#)) (SIGNATURE |retractIfCan| ((|Union| |#2| #7#) |#1|)) (SIGNATURE |retract| #20#) (SIGNATURE |retract| #18#) (SIGNATURE |retractIfCan| #17#) (SIGNATURE |retract| (#9# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #9# #7#) |#1|)) (SIGNATURE |convert| #27#) (SIGNATURE |discriminant| (|#2|)) (SIGNATURE |convert| (|#1| #31#)) (SIGNATURE |convert| #34=(#31# |#1|)) (SIGNATURE |coordinates| (#29# #32#)) (SIGNATURE |coordinates| #34#) (SIGNATURE |minimalPolynomial| #27#) (SIGNATURE |characteristicPolynomial| #27#) (SIGNATURE |discriminant| (|#2| #32#)) (SIGNATURE |coordinates| (#29# #32# #32#)) (SIGNATURE |coordinates| (#31# |#1| #32#)) (SIGNATURE |norm| #20#) (SIGNATURE |trace| #20#) (SIGNATURE |rank| (#35=(|PositiveInteger|))) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |characteristic| (#3#) |constant|) (SIGNATURE |coerce| (|#1| #9#)) (SIGNATURE |recip| (#6# |#1|)) (SIGNATURE ** #5#) (SIGNATURE * #8#) (SIGNATURE ** (|#1| |#1| #35#)) (SIGNATURE - #8#) (SIGNATURE - #4#) (SIGNATURE * (|#1| #9# |#1|)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE * (|#1| #35# |#1|)) (SIGNATURE + #8#) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |before?| #36=(#19# |#1| |#1|)) (SIGNATURE = #36#)) 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#20=(|SparseUnivariatePolynomial| $)) #20#) 264 #6# ELT)) (|squareFreePart| (#8# 134 #21=(OR #6# #22=(|has| |#1| (|Field|))) ELT)) (|squareFree| (#23=((|Factored| $) $) 135 #21# ELT)) (|sqrt| (#8# 263 #24=(AND (|has| |#1| (|RadicalCategory|)) #13#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #25=(|List| #20#) #26="failed") #25# #20#) 267 #6# ELT)) (|sizeLess?| (#1# 125 #7# ELT)) (|size| (#27=(#15#) 108 #28=(|has| |#1| (|Finite|)) ELT)) (|sinh| (#8# 249 #13# ELT)) (|sin| (#8# 234 #13# ELT)) (|sech| (#8# 248 #13# ELT)) (|sec| (#8# 235 #13# ELT)) (|sample| (#29=($) 23 T CONST)) (|retractIfCan| (((|Union| #16# . #30=(#26#)) . #31=($)) 194 #32=(|has| |#1| (|RetractableTo| #16#)) ELT) (#33=((|Union| #34=(|Fraction| #16#) #26#) $) 192 #35=(|has| |#1| (|RetractableTo| #34#)) ELT) (((|Union| |#1| . #30#) . #31#) 189 T ELT)) (|retract| ((#16# $) 193 #32# ELT) (#36=(#34# $) 191 #35# ELT) (#12# 190 T ELT)) (|represents| (($ #37=(|Vector| |#1|) #11#) 64 T ELT) (#38=($ #37#) 80 T ELT)) 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$)) #51#) 123 #7# ELT)) (|primitiveElement| (#29# 169 #17# ELT)) (|primitive?| (#3# 170 #17# ELT)) (|primeFrobenius| (#53=($ $ #15#) 161 #17# ELT) (#8# 160 #17# ELT)) (|prime?| (#3# 136 #21# ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) 271 (AND #54=(|has| |#1| (|RealNumberSystem|)) #13#) ELT)) (|pi| (#29# 260 #13# ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #16# . #56=($)) $ #57=(|Pattern| #16#) #55#) 283 (|has| |#1| (|PatternMatchable| #16#)) ELT) ((#58=(|PatternMatchResult| #59=(|Float|) . #56#) $ #60=(|Pattern| #59#) #58#) 282 (|has| |#1| (|PatternMatchable| #59#)) ELT)) (|order| (#61=(#14# $) 172 #17# ELT) (((|OnePointCompletion| #14#) $) 158 #17# ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|nthRoot| (#62=($ $ #16#) 262 #24# ELT)) (|norm| (#12# 67 T ELT)) (|nextItem| (#63=(#18# $) 162 #17# ELT)) (|multiEuclidean| (((|Union| #51# #26#) #51# $) 132 #7# ELT)) (|minimalPolynomial| (#64=(#48# $) 60 #22# ELT)) (|map| (($ #65=(|Mapping| |#1| |#1|) $) 284 T ELT)) (|lookup| (#61# 110 #28# ELT)) (|log| (#8# 257 #13# ELT)) (|lift| (#64# 176 T ELT)) (|leftReducedSystem| ((#40# #11#) 188 #43# ELT) ((#44# . #66=(#11# $)) 187 #43# ELT) ((#46# . #66#) 182 T ELT) (#9# 181 T ELT)) (|lcm| (#67=($ #51#) 121 #68=(OR #7# #6#) ELT) (#39# 120 #68# ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#8# 137 #22# ELT)) (|init| (#29# 163 #17# CONST)) (|index| (($ #14#) 109 #28# ELT)) (|imaginary| (#29# 279 T ELT)) (|imag| (#12# 276 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (#29# 180 T ELT)) (|gcdPolynomial| ((#20# #20# #20#) 122 #68# ELT)) (|gcd| (#67# 119 #68# ELT) (#39# 118 #68# ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) 166 #17# ELT)) (|factorSquareFreePolynomial| (#19# 266 #6# ELT)) (|factorPolynomial| (#19# 265 #6# ELT)) (|factor| (#23# 133 #21# ELT)) (|extendedEuclidean| (((|Union| (|Record| #69=(|:| |coef1| $) #70=(|:| |coef2| $)) #26#) $ $ $) 131 #7# ELT) (((|Record| #69# #70# #52#) $ $) 130 #7# ELT)) (|exquo| ((#49# $ |#1|) 274 #5# ELT) ((#49# $ $) 113 #4# ELT)) (|expressIdealMember| (((|Maybe| #51#) #51# $) 124 #7# ELT)) (|exp| (#8# 258 #13# ELT)) (|eval| (($ $ #71=(|List| |#1|) #71#) 290 #72=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 289 #72# ELT) (($ $ #73=(|Equation| |#1|)) 288 #72# ELT) (($ $ (|List| #73#)) 287 #72# ELT) (($ $ #74=(|List| #75=(|Symbol|)) #71#) 286 #76=(|has| |#1| (|InnerEvalable| #75# |#1|)) ELT) (($ $ #75# |#1|) 285 #76# ELT)) (|euclideanSize| (#77=(#15# $) 126 #7# ELT)) (|elt| (#78=($ $ |#1|) 291 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 127 #7# ELT)) (|discriminant| ((|#1| #11#) 63 T ELT) ((|#1|) 76 T ELT)) (|discreteLog| (#77# 171 #17# ELT) (((|Union| #15# #26#) $ $) 159 #17# ELT)) (|differentiate| (#79=($ $ #65#) 145 T ELT) (#80=($ $ #65# #15#) 144 T ELT) (#53# 156 #81=(OR (|and| #22# #82=(|has| |#1| (|DifferentialSpace|))) (|and| #22# (|has| |#1| (|DifferentialRing|))) #82# (|and| #82# #22#)) ELT) (#8# 154 #81# ELT) (#83=($ $ #74# (|List| #15#)) 150 #84=(OR (|and| #22# #85=(|has| |#1| (|PartialDifferentialSpace| #75#))) (|and| #22# (|has| |#1| (|PartialDifferentialRing| #75#))) #85#) ELT) (#86=($ $ #75# #15#) 149 #84# ELT) (#87=($ $ #74#) 148 #84# ELT) (#88=($ $ #75#) 146 #84# ELT)) (|derivationCoordinates| ((#10# #11# #65#) 174 #22# ELT)) (|definingPolynomial| ((#48#) 179 T ELT)) (|csch| (#8# 247 #13# ELT)) (|csc| (#8# 236 #13# ELT)) (|createPrimitiveElement| (#29# 168 #17# ELT)) (|coth| (#8# 246 #13# ELT)) (|cot| (#8# 237 #13# ELT)) (|cosh| (#8# 245 #13# ELT)) (|cos| (#8# 238 #13# ELT)) (|coordinates| ((#37# $ #11#) 66 T ELT) ((#10# #11# #11#) 65 T ELT) (#89=(#37# $) 82 T ELT) (#9# 81 T ELT)) (|convert| (#89# 79 T ELT) (#38# 78 T ELT) (#64# 195 T ELT) (#47# 177 T ELT) ((#57# . #90=($)) 281 (|has| |#1| (|ConvertibleTo| #57#)) ELT) ((#60# . #90#) 280 (|has| |#1| (|ConvertibleTo| #60#)) ELT) (((|Complex| #59#) . #90#) 232 #91=(|has| |#1| (|RealConstant|)) ELT) (((|Complex| (|DoubleFloat|)) . #90#) 231 #91# ELT) ((#92=(|InputForm|) . #90#) 230 (|has| |#1| (|ConvertibleTo| #92#)) ELT)) (|conjugate| (#8# 278 T ELT)) (|conditionP| (((|Union| #11# #26#) #42#) 165 (OR #93=(|and| (|has| $ #94=(|CharacteristicNonZero|)) #6#) #17#) ELT)) (|complex| (($ |#1| |#1|) 277 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #16#) 42 T ELT) (($ |#1|) 53 T ELT) (($ #34#) 107 (OR #22# #35#) ELT) (#8# 112 #4# ELT)) (|charthRoot| (#8# 164 #17# ELT) (#63# 59 (OR #93# (|has| |#1| #94#)) ELT)) (|characteristicPolynomial| (#64# 61 T ELT)) (|characteristic| (#27# 41 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| ((#11#) 83 T ELT)) (|atanh| (#8# 256 #13# ELT)) (|atan| (#8# 244 #13# ELT)) (|associates?| (#1# 116 #4# ELT)) (|asinh| (#8# 255 #13# ELT)) (|asin| (#8# 243 #13# ELT)) (|asech| (#8# 254 #13# ELT)) (|asec| (#8# 242 #13# ELT)) (|argument| (#12# 272 #13# ELT)) (|annihilate?| (#1# 34 T ELT)) (|acsch| (#8# 253 #13# 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*1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|RealNumberSystem|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|isDomain| *2 (|Record| (|:| |r| *3) (|:| |phi| *3))))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|ComplexCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) -(|Join| (|MonogenicAlgebra| |t#1| (|SparseUnivariatePolynomial| |t#1|)) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyPatternMatchable| |t#1|) (|Patternable| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (|CommutativeRing|) (CATEGORY |domain| (ATTRIBUTE |complex|) (SIGNATURE |imaginary| ($)) (SIGNATURE |conjugate| ($ $)) (SIGNATURE |complex| ($ |t#1| |t#1|)) (SIGNATURE |imag| (|t#1| $)) (SIGNATURE |real| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|IntegralDomain|)) (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|))) |%noBranch|) (IF (|has| |t#1| (|EuclideanDomain|)) (ATTRIBUTE (|EuclideanDomain|)) |%noBranch|) (IF (|has| |t#1| (ATTRIBUTE |multiplicativeValuation|)) (ATTRIBUTE |multiplicativeValuation|) |%noBranch|) (IF (|has| |t#1| (ATTRIBUTE |additiveValuation|)) (ATTRIBUTE |additiveValuation|) |%noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|Field|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|) (IF (|has| |t#1| (|RealConstant|)) (PROGN (ATTRIBUTE (|ConvertibleTo| (|Complex| (|DoubleFloat|)))) (ATTRIBUTE (|ConvertibleTo| (|Complex| (|Float|))))) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| ($ $)) |%noBranch|) (IF (|has| |t#1| (|TranscendentalFunctionCategory|)) (PROGN (ATTRIBUTE (|TranscendentalFunctionCategory|)) (SIGNATURE |argument| (|t#1| $)) (IF (|has| |t#1| (|RadicalCategory|)) (ATTRIBUTE (|RadicalCategory|)) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |polarCoordinates| ((|Record| (|:| |r| |t#1|) (|:| |phi| |t#1|)) $)) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |%noBranch|) (IF (|has| |t#1| (|PolynomialFactorizationExplicit|)) (IF (|has| |t#1| (|EuclideanDomain|)) (ATTRIBUTE (|PolynomialFactorizationExplicit|)) |%noBranch|) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Algebra| |#1|) . T) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|Complex| (|DoubleFloat|))) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|Complex| (|Float|))) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|ConvertibleTo| #2=(|SparseUnivariatePolynomial| |#1|)) . T) ((|DifferentialDomain| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpace|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|DivisionRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|ElementaryFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|EuclideanDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Field|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|FieldOfPrimeCharacteristic|) |has| |#1| (|FiniteFieldCategory|)) ((|Finite|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Finite|))) ((|FiniteFieldCategory|) |has| |#1| (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| |#1| #2#) . T) ((|FramedAlgebra| |#1| #2#) . T) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|HyperbolicFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|Join|) . T) ((|LeftLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftModule| #3=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LinearSet| |#1|) . T) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|LinearlyExplicitRingOver| #3#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Module| |#1|) . T) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|MonogenicAlgebra| |#1| #2#) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PolynomialFactorizationExplicit|) AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) ((|PrincipalIdealDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (|has| |#1| (|EuclideanDomain|))) ((|RadicalCategory|) AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|TranscendentalFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|TrigonometricFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)) (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))))) +((|norm| #1=(*1 *2 *1) #2=(AND #3=(|ofCategory| *1 (|ComplexCategory| *2)) #4=(|ofCategory| *2 #5=(|CommutativeRing|)))) (|imaginary| (*1 *1) #2#) (|conjugate| #6=(*1 *1 *1) #2#) (|complex| (*1 *1 *2 *2) #2#) (|imag| #1# #2#) (|real| #1# #2#) (|exquo| (*1 *1 *1 *2) (|partial| AND #3# #4# (|ofCategory| *2 (|IntegralDomain|)))) (|abs| #6# (AND #3# #4# (|ofCategory| *2 #7=(|RealNumberSystem|)))) (|argument| #1# (AND #3# #4# (|ofCategory| *2 #8=(|TranscendentalFunctionCategory|)))) (|polarCoordinates| #1# (AND #9=(|ofCategory| *1 (|ComplexCategory| *3)) #10=(|ofCategory| *3 #5#) (|ofCategory| *3 #7#) (|ofCategory| *3 #8#) (|isDomain| *2 (|Record| (|:| |r| *3) (|:| |phi| *3))))) (|rational?| #1# (AND #9# #10# #11=(|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| #1# (AND #9# #10# #11# #12=(|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| #1# (|partial| AND #9# #10# #11# #12#))) +(|Join| (|MonogenicAlgebra| |t#1| (|SparseUnivariatePolynomial| |t#1|)) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyPatternMatchable| |t#1|) (|Patternable| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (|CommutativeRing|) (CATEGORY |domain| (ATTRIBUTE |complex|) (SIGNATURE |imaginary| ($)) (SIGNATURE |conjugate| #1=($ $)) (SIGNATURE |complex| ($ |t#1| |t#1|)) (SIGNATURE |imag| #2=(|t#1| $)) (SIGNATURE |real| #2#) (SIGNATURE |norm| #2#) (IF (|has| |t#1| #3=(|IntegralDomain|)) (PROGN (ATTRIBUTE #3#) (SIGNATURE |exquo| ((|Union| $ #4="failed") $ |t#1|))) |%noBranch|) (IF #5=(|has| |t#1| #6=(|EuclideanDomain|)) (ATTRIBUTE #6#) |%noBranch|) (IF (|has| |t#1| #7=(ATTRIBUTE |multiplicativeValuation|)) #7# |%noBranch|) (IF (|has| |t#1| #8=(ATTRIBUTE |additiveValuation|)) #8# |%noBranch|) (IF (|has| |t#1| #9=(|Field|)) (ATTRIBUTE #9#) |%noBranch|) (IF (|has| |t#1| #10=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #10#) |%noBranch|) (IF (|has| |t#1| #11=(|CharacteristicZero|)) (ATTRIBUTE #11#) |%noBranch|) (IF (|has| |t#1| #12=(|CharacteristicNonZero|)) (ATTRIBUTE #12#) |%noBranch|) (IF (|has| |t#1| (|RealConstant|)) (PROGN (ATTRIBUTE (|ConvertibleTo| (|Complex| (|DoubleFloat|)))) (ATTRIBUTE (|ConvertibleTo| (|Complex| (|Float|))))) |%noBranch|) (IF #13=(|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| #1#) |%noBranch|) (IF (|has| |t#1| #14=(|TranscendentalFunctionCategory|)) (PROGN (ATTRIBUTE #14#) (SIGNATURE |argument| #2#) (IF (|has| |t#1| #15=(|RadicalCategory|)) (ATTRIBUTE #15#) |%noBranch|) (IF #13# (SIGNATURE |polarCoordinates| ((|Record| (|:| |r| |t#1|) (|:| |phi| |t#1|)) $)) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| (#16=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #16# #4#) $))) |%noBranch|) (IF (|has| |t#1| #17=(|PolynomialFactorizationExplicit|)) (IF #5# (ATTRIBUTE #17#) |%noBranch|) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Field|)) ((|Algebra| |#1|) . T) ((|Algebra| $) OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Field|)) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|Complex| (|DoubleFloat|))) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|Complex| #3=(|Float|))) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| #3#)) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| #2#)) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|ConvertibleTo| #4=(|SparseUnivariatePolynomial| |#1|)) . T) ((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpaceExtension| |#1|) . T) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|EuclideanDomain|) |has| |#1| (|EuclideanDomain|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Field|) |has| |#1| (|Field|)) ((|FieldOfPrimeCharacteristic|) |has| |#1| (|FiniteFieldCategory|)) ((|Finite|) |has| |#1| (|Finite|)) ((|FiniteFieldCategory|) |has| |#1| (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| |#1| #4#) . T) ((|FramedAlgebra| |#1| #4#) . T) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|EuclideanDomain|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|InnerEvalable| #5=(|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|IntegralDomain|) OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|LeftLinearSet| #1#) |has| |#1| (|Field|)) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Field|)) ((|LeftModule| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Field|)) ((|LinearSet| |#1|) . T) ((|LinearSet| $) OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Field|)) ((|Module| |#1|) . T) ((|Module| $) OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|MonogenicAlgebra| |#1| #4#) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #5#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialRing| #5#) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #5#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PatternMatchable| #3#) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| #2#) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PolynomialFactorizationExplicit|) AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) ((|PrincipalIdealDomain|) |has| |#1| (|EuclideanDomain|)) ((|RadicalCategory|) AND (|has| |#1| (|RadicalCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Field|)) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) |has| |#1| (|Field|)) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|TranscendentalFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|TrigonometricFunctionCategory|) |has| |#1| (|TranscendentalFunctionCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (AND (|has| |#1| (|EuclideanDomain|)) (|has| |#1| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|Field|)))) ((|factor| (((|Factored| |#2|) |#2|) 67 T ELT))) (((|ComplexFactorization| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#2|) |#2|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| (|Complex| |#1|))) (T |ComplexFactorization|)) ((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|ComplexFactorization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| (|Complex| *4)))))) @@ -451,11 +451,11 @@ NIL ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|solid?| (#3=(#2# $) 9 T ELT)) (|solid| (#4=(#2# $ #2#) 11 T ELT)) (|new| (($) 13 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|copy| (($ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|closed?| (#3# 8 T ELT)) (|close| (#4# 10 T ELT)) (|before?| #1#) (= #1#)) (((|SubSpaceComponentProperty|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |new| ($)) (SIGNATURE |closed?| #1=(#2=(|Boolean|) $)) (SIGNATURE |solid?| #1#) (SIGNATURE |close| #3=(#2# $ #2#)) (SIGNATURE |solid| #3#) (SIGNATURE |copy| ($ $))))) (T |SubSpaceComponentProperty|)) ((|new| (*1 *1) #1=(|isDomain| *1 (|SubSpaceComponentProperty|))) (|closed?| #2=(*1 *2 *1) #3=(AND (|isDomain| *2 (|Boolean|)) #1#)) (|solid?| #2# #3#) (|close| #4=(*1 *2 *1 *2) #3#) (|solid| #4# #3#) (|copy| (*1 *1 *1) #1#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #5=(|Integer|)) 42 T ELT)) (|characteristic| ((#6=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#7=($ $ $) 29 T ELT)) (+ (#7# 18 T ELT)) (** (($ $ #8=(|PositiveInteger|)) 36 T ELT) (($ $ #6#) 44 T ELT)) (* (($ #8# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #5# $) 31 T ELT) (#7# 35 T ELT))) (((|CommutativeRing|) (|Category|)) (T |CommutativeRing|)) NIL (|Join| (|Ring|) (|BiModule| $ $) (CATEGORY |package| (ATTRIBUTE (|commutative| "*")))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|close!| (($ $) 6 T ELT))) (((|Conduit|) (|Category|)) (T |Conduit|)) ((|close!| (*1 *1 *1) (|ofCategory| *1 (|Conduit|)))) @@ -496,11 +496,11 @@ NIL ((|operations| (((|List| (|OverloadSet|)) $) 16 T ELT)) (|kind| (((|ConstructorKind|) $) 8 T ELT)) (|dualSignature| (((|List| (|Boolean|)) $) 13 T ELT)) (|arity| (((|Arity|) $) 10 T ELT))) (((|ConstructorCategory&| |#1|) (CATEGORY |package| (SIGNATURE |operations| ((|List| (|OverloadSet|)) |#1|)) (SIGNATURE |dualSignature| ((|List| (|Boolean|)) |#1|)) (SIGNATURE |kind| ((|ConstructorKind|) |#1|)) (SIGNATURE |arity| ((|Arity|) |#1|))) (|ConstructorCategory|)) (T |ConstructorCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|operations| (((|List| (|OverloadSet|)) $) 22 T ELT)) (|name| ((#2=(|Identifier|) $) 19 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|kind| (((|ConstructorKind|) $) 24 T ELT)) (|is?| (((|Boolean|) $ #2#) 17 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dualSignature| (((|List| (|Boolean|)) $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|arity| (((|Arity|) $) 18 T ELT)) (= (#1# 8 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|operations| (((|List| (|OverloadSet|)) $) 22 T ELT)) (|name| ((#3=(|Identifier|) $) 19 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|kind| (((|ConstructorKind|) $) 24 T ELT)) (|is?| ((#2# $ #3#) 17 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dualSignature| (((|List| #2#) $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|arity| (((|Arity|) $) 18 T ELT)) (= (#1# 8 T ELT))) (((|ConstructorCategory|) (|Category|)) (T |ConstructorCategory|)) -((|kind| (*1 *2 *1) (AND (|ofCategory| *1 (|ConstructorCategory|)) (|isDomain| *2 (|ConstructorKind|)))) (|dualSignature| (*1 *2 *1) (AND (|ofCategory| *1 (|ConstructorCategory|)) (|isDomain| *2 (|List| (|Boolean|))))) (|operations| (*1 *2 *1) (AND (|ofCategory| *1 (|ConstructorCategory|)) (|isDomain| *2 (|List| (|OverloadSet|)))))) +((|kind| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|ConstructorCategory|)) (|isDomain| *2 (|ConstructorKind|)))) (|dualSignature| #1# (AND #2# (|isDomain| *2 (|List| (|Boolean|))))) (|operations| #1# (AND #2# (|isDomain| *2 (|List| (|OverloadSet|)))))) (|Join| (|OperatorCategory| (|Identifier|)) (CATEGORY |domain| (SIGNATURE |kind| ((|ConstructorKind|) $)) (SIGNATURE |dualSignature| ((|List| (|Boolean|)) $)) (SIGNATURE |operations| ((|List| (|OverloadSet|)) $)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OperatorCategory| (|Identifier|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OperatorCategory| (|Identifier|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|package| (#3=($) 8 T CONST)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|domain| (#3# 7 T CONST)) (|coerce| (((|OutputForm|) $) 12 T ELT)) (|category| (#3# 6 T CONST)) (|before?| #1#) (= (#2# 10 T ELT))) (((|ConstructorKind|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |category| #1=($) |constant|) (SIGNATURE |domain| #1# |constant|) (SIGNATURE |package| #1# |constant|)))) (T |ConstructorKind|)) ((|category| #1=(*1 *1) #2=(|isDomain| *1 (|ConstructorKind|))) (|domain| #1# #2#) (|package| #1# #2#)) @@ -567,66 +567,66 @@ NIL ((|select!| (#1=($ (|Mapping| #2=(|Boolean|) |#2|) $) 16 T ELT)) (|remove!| (($ |#2| $) NIL T ELT) (#1# 28 T ELT)) (|dictionary| (($) NIL T ELT) (($ (|List| |#2|)) 11 T ELT)) (= ((#2# $ $) 26 T ELT))) (((|Dictionary&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |select!| #2=(|#1| (|Mapping| #1# |#2|) |#1|)) (SIGNATURE |remove!| #2#) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |dictionary| (|#1| (|List| |#2|))) (SIGNATURE |dictionary| (|#1|))) (|Dictionary| |#2|) (|SetCategory|)) (T |Dictionary&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|select!| (($ (|Mapping| #3=(|Boolean|) |#1|) . #4=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #3# |#1|) . #4#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #8#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #5# |#1|) . #6#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #9=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #10=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #9#) ELT)) (|extract!| ((|#1| . #10#) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT)) (|eq?| ((#11=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#11# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#12=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #12#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|select!| (#4=($ (|Mapping| #2# |#1|) $) 42 #5=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (#4# 49 #5# ELT)) (|sample| (#6=($) 6 T CONST)) (|removeDuplicates| (#7=($ $) 51 #8=(AND #3# #5#) ELT)) (|remove!| (#9=($ |#1| $) 44 #5# ELT) (#4# 43 #5# ELT)) (|remove| (#9# 50 #8# ELT) (#4# 48 #5# ELT)) (|map!| (#10=($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (#10# 26 T ELT)) (|latex| (((|String|) $) 21 #11=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#12=(|#1| $) 35 T ELT)) (|insert!| (#9# 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 #11# ELT)) (|extract!| (#12# 37 T ELT)) (|eval| (($ $ (|List| #13=(|Equation| |#1|))) 25 #14=(AND (|has| |#1| (|Evalable| |#1|)) #11#) ELT) (($ $ #13#) 24 #14# ELT) (($ $ |#1| |#1|) 23 #14# ELT) (($ $ #15=(|List| |#1|) #15#) 22 #14# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#6# 8 T ELT)) (|dictionary| (#6# 46 T ELT) (#16=($ #15#) 45 T ELT)) (|copy| (#7# 9 T ELT)) (|convert| ((#17=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #17#)) ELT)) (|construct| (#16# 47 T ELT)) (|coerce| ((#18=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #18#)) ELT)) (|before?| (#1# 19 #3# ELT)) (|bag| (#16# 38 T ELT)) (= (#1# 17 #3# ELT))) (((|Dictionary| |#1|) (|Category|) (|SetCategory|)) (T |Dictionary|)) NIL (|Join| (|DictionaryOperations| |t#1|)) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|Mapping| |#1| |#1|) . #4=((|NonNegativeInteger|))) 66 T ELT) (($ $ (|Mapping| |#1| |#1|)) 65 T ELT) (($ $ #5=(|Symbol|)) 64 (|has| |#1| . #6=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ (|List| #5#)) 62 (|has| |#1| . #6#) ELT) (($ $ #5# . #7=(#8=(|NonNegativeInteger|))) 61 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9=((|List| #8#))) 60 (|has| |#1| . #6#) ELT) (($ . #10=($)) 56 (|has| |#1| . #11=((|DifferentialSpace|))) ELT) (#12=($ $ (|NonNegativeInteger|)) 54 (|has| |#1| . #11#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|Mapping| |#1| |#1|) . #4#) 68 T ELT) (($ $ (|Mapping| |#1| |#1|)) 67 T ELT) (($ $ #5#) 63 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#)) 59 (|has| |#1| . #6#) ELT) (($ $ #5# . #7#) 58 (|has| |#1| . #6#) ELT) (($ $ (|List| #5#) . #9#) 57 (|has| |#1| . #6#) ELT) (($ . #10#) 55 (|has| |#1| . #11#) ELT) (#12# 53 (|has| |#1| . #11#) ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#5=($ $ #6=(|Mapping| |#1| |#1|) #7=(|NonNegativeInteger|)) 66 T ELT) (#8=($ $ #6#) 65 T ELT) (#9=($ $ #10=(|Symbol|)) 64 #11=(|has| |#1| (|PartialDifferentialSpace| #10#)) ELT) (#12=($ $ #13=(|List| #10#)) 62 #11# ELT) (#14=($ $ #10# #7#) 61 #11# ELT) (#15=($ $ #13# (|List| #7#)) 60 #11# ELT) (#16=($ $) 56 #17=(|has| |#1| (|DifferentialSpace|)) ELT) (#18=($ $ #7#) 54 #17# ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #19=(|Integer|)) 42 T ELT)) (|characteristic| ((#7#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (D (#5# 68 T ELT) (#8# 67 T ELT) (#9# 63 #11# ELT) (#12# 59 #11# ELT) (#14# 58 #11# ELT) (#15# 57 #11# ELT) (#16# 55 #17# ELT) (#18# 53 #17# ELT)) (= (#1# 8 T ELT)) (- (#16# 30 T ELT) (#20=($ $ $) 29 T ELT)) (+ (#20# 18 T ELT)) (** (($ $ #21=(|PositiveInteger|)) 36 T ELT) (#18# 44 T ELT)) (* (($ #21# $) 17 T ELT) (($ #7# $) 21 T ELT) (($ #19# $) 31 T ELT) (#20# 35 T ELT))) (((|DifferentialExtension| |#1|) (|Category|) (|Ring|)) (T |DifferentialExtension|)) NIL -(|Join| (|Ring|) (|DifferentialSpaceExtension| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|DifferentialRing|)) (ATTRIBUTE (|DifferentialRing|)) |%noBranch|) (IF (|has| |t#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #1#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|Ring|) . 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. #25#)) ELT) (($ $ (|List| #42=(|Symbol|)) . #43=((|List| #44=(|NonNegativeInteger|)))) 97 (|and| (|has| |#2| . #45=((|PartialDifferentialSpace| (|Symbol|)))) (|has| |#2| . #25#)) ELT) (($ $ #42# . #46=(#44#)) 96 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|List| #42#)) 95 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ #42#) 93 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|Mapping| |#2| |#2|)) 92 (|has| |#2| . #25#) ELT) (($ $ (|Mapping| |#2| |#2|) . #47=((|NonNegativeInteger|))) 91 (|has| |#2| . #25#) ELT)) (|count| ((#48=(|NonNegativeInteger|) |#2| $) 139 (|has| |#2| . #24#) ELT) ((#48# (|Mapping| #30# |#2|) $) 134 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|Vector| |#2|) . #49=($)) 130 T ELT) (($ #9#) 68 (OR (|and| (|has| |#2| . #12#) (|has| |#2| . #13#)) (|has| |#2| . #25#)) ELT) (($ #14#) 65 (|and| (|has| |#2| . #15#) (|has| |#2| . #13#)) ELT) (($ |#2|) 60 (|has| |#2| . #13#) ELT) (((|OutputForm|) . #49#) 16 (|has| |#2| (|CoercibleTo| (|OutputForm|))) ELT)) (|characteristic| (((|NonNegativeInteger|)) 88 (|has| |#2| . #25#) CONST)) (|before?| (#1# 19 (|has| |#2| . #2#) ELT)) (|any?| ((#30# (|Mapping| #30# |#2|) . #36#) 132 T ELT)) (|annihilate?| (((|Boolean|) $ $) 83 (|has| |#2| . #25#) ELT)) (|Zero| (($) 71 (|has| |#2| . #4#) CONST)) (|One| (($) 84 (|has| |#2| . #25#) CONST)) (D (#39# 104 (|and| (|has| |#2| . #40#) (|has| |#2| . #25#)) ELT) (($ . #41#) 102 (|and| (|has| |#2| . #40#) (|has| |#2| . #25#)) ELT) (($ $ (|List| #42#) . #43#) 100 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ #42# . #46#) 99 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|List| #42#)) 98 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ #42#) 94 (|and| (|has| |#2| . #45#) (|has| |#2| . #25#)) ELT) (($ $ (|Mapping| |#2| |#2|)) 90 (|has| |#2| . #25#) ELT) (($ $ (|Mapping| |#2| |#2|) . #47#) 89 (|has| |#2| . #25#) ELT)) (>= (#50=((|Boolean|) $ $) 119 (|has| |#2| . #29#) ELT)) (> (#50# 121 (|has| |#2| . #29#) ELT)) (= (#1# 17 (|has| |#2| . #2#) ELT)) (<= (#50# 120 (|has| |#2| . #29#) ELT)) (< (#50# 122 (|has| |#2| . #29#) ELT)) (/ (($ $ |#2|) 125 (|has| |#2| . #38#) ELT)) (- (($ $ $) 78 (|has| |#2| . #51=((|AbelianGroup|))) ELT) (($ $) 77 (|has| |#2| . #51#) ELT)) (+ (($ $ $) 69 (|has| |#2| . #52=((|AbelianSemiGroup|))) ELT)) (** (($ $ (|NonNegativeInteger|)) 86 (|has| |#2| . #25#) ELT) (($ $ (|PositiveInteger|)) 81 (|has| |#2| . #25#) ELT)) (* (($ $ $) 82 (|has| |#2| . #25#) ELT) (($ $ |#2|) 80 (|has| |#2| . #53=((|Monoid|))) ELT) (($ |#2| . #54=($)) 79 (|has| |#2| . #53#) ELT) (($ (|Integer|) . #54#) 76 (|has| |#2| . #51#) ELT) (($ (|NonNegativeInteger|) $) 73 (|has| |#2| . #4#) ELT) (($ (|PositiveInteger|) $) 70 (|has| |#2| . #52#) ELT)) (|#| ((#48# $) 131 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#4=(#2# $) 72 #5=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#6=($ #7=(|PositiveInteger|)) 128 #8=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #9=(|Integer|) #9#) 35 #10=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#11=($ $ $) 124 #12=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 75 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#13=(#14=(|NonNegativeInteger|)) 113 #15=(|has| |#2| (|Finite|)) ELT)) (|setelt| (#16=(|#2| $ #9# |#2|) 47 #10# ELT)) (|sample| (#17=($) 6 T CONST)) (|retractIfCan| (((|Union| #9# . #18=(#19="failed")) . #20=($)) 67 #21=(|and| (|has| |#2| (|RetractableTo| #9#)) #22=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #23=(|Fraction| #9#) . #18#) . #20#) 64 #24=(|and| (|has| |#2| (|RetractableTo| #23#)) #22#) ELT) ((#25=(|Union| |#2| . #18#) . #20#) 61 #22# ELT)) (|retract| (#26=(#9# . #27=($)) 66 #21# ELT) ((#23# . #27#) 63 #24# ELT) (#28=(|#2| . #27#) 62 #22# ELT)) (|reducedSystem| ((#29=(|Matrix| #9#) . #30=(#31=(|Matrix| $))) 110 #32=(|and| (|has| |#2| (|LinearlyExplicitRingOver| #9#)) #8#) ELT) ((#33=(|Record| (|:| |mat| #29#) (|:| |vec| (|Vector| #9#))) . #34=(#31# #35=(|Vector| $))) 109 #32# ELT) ((#36=(|Record| (|:| |mat| #37=(|Matrix| |#2|)) (|:| |vec| #38=(|Vector| |#2|))) . #34#) 108 #8# ELT) ((#37# . #30#) 107 #8# ELT)) (|reduce| ((|#2| #39=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 141 #3# ELT) ((|#2| #39# $ |#2|) 137 T ELT) ((|#2| #39# $) 136 T ELT)) (|recip| (((|Union| $ #19#) $) 87 #8# ELT)) (|random| (#17# 116 #15# ELT)) (|qsetelt!| (#16# 48 #10# ELT)) (|qelt| (#40=(|#2| $ #9#) 46 T ELT)) (|positive?| (#4# 123 #12# ELT)) (|opposite?| (#1# 74 #5# ELT)) (|one?| (#4# 85 #8# ELT)) (|minIndex| (#26# 38 #41=(|has| #9# #42=(|OrderedSet|)) ELT)) (|min| (#11# 117 #43=(|has| |#2| #42#) ELT)) (|members| (#44=(#45=(|List| |#2|) $) 135 T ELT)) (|member?| (#46=(#2# |#2| $) 140 #3# ELT)) (|maxIndex| (#26# 39 #41# ELT)) (|max| (#11# 118 #43# ELT)) (|map| (($ #47=(|Mapping| |#2| |#2|) $) 26 T ELT)) (|lookup| ((#7# $) 115 #15# ELT)) (|leftReducedSystem| ((#29# . #48=(#35#)) 112 #32# ELT) ((#33# . #49=(#35# $)) 111 #32# ELT) ((#36# . #49#) 106 #8# ELT) ((#37# . #48#) 105 #8# ELT)) (|latex| (((|String|) $) 21 #22# ELT)) (|indices| (((|List| #9#) $) 41 T ELT)) (|index?| ((#2# #9# $) 42 T ELT)) (|index| (#6# 114 #15# ELT)) (|hash| (((|SingleInteger|) $) 20 #22# ELT)) (|first| (#28# 37 #41# ELT)) (|find| ((#25# #50=(|Mapping| #2# |#2|) $) 138 T ELT)) (|fill!| (#51=($ $ |#2|) 36 #10# ELT)) (|every?| (#52=(#2# #50# $) 133 T ELT)) (|eval| (($ $ (|List| #53=(|Equation| |#2|))) 25 #54=(AND (|has| |#2| (|Evalable| |#2|)) #22#) ELT) (($ $ #53#) 24 #54# ELT) (($ $ |#2| |#2|) 23 #54# ELT) (($ $ #45# #45#) 22 #54# ELT)) (|eq?| (#1# 10 T ELT)) (|entry?| (#46# 40 (AND (|has| $ (|FiniteAggregate| |#2|)) #3#) ELT)) (|entries| (#44# 43 T ELT)) (|empty?| (#4# 7 T ELT)) (|empty| (#17# 8 T ELT)) (|elt| (#16# 45 T ELT) (#40# 44 T ELT)) (|dot| ((|#2| $ $) 127 #8# ELT)) (|directProduct| (($ #38#) 129 T ELT)) (|dimension| (((|CardinalNumber|)) 126 #55=(|has| |#2| (|Field|)) ELT)) (|differentiate| (#56=($ $ #14#) 103 #57=(|and| (|has| |#2| (|DifferentialSpace|)) #8#) ELT) (#58=($ $) 101 #57# ELT) (#59=($ $ #60=(|List| #61=(|Symbol|)) (|List| #14#)) 97 #62=(|and| (|has| |#2| (|PartialDifferentialSpace| #61#)) #8#) ELT) (#63=($ $ #61# #14#) 96 #62# ELT) (#64=($ $ #60#) 95 #62# ELT) (#65=($ $ #61#) 93 #62# ELT) (#66=($ $ #47#) 92 #8# ELT) (#67=($ $ #47# #14#) 91 #8# ELT)) (|count| ((#14# |#2| $) 139 #3# ELT) ((#14# #50# $) 134 T ELT)) (|copy| (#58# 9 T ELT)) (|coerce| ((#38# . #68=($)) 130 T ELT) (($ #9#) 68 (OR #21# #8#) ELT) (($ #23#) 65 #24# ELT) (($ |#2|) 60 #22# ELT) ((#69=(|OutputForm|) . #68#) 16 (|has| |#2| (|CoercibleTo| #69#)) ELT)) (|characteristic| (#13# 88 #8# CONST)) (|before?| (#1# 19 #3# ELT)) (|any?| (#52# 132 T ELT)) (|annihilate?| (#1# 83 #8# ELT)) (|Zero| (#17# 71 #5# CONST)) (|One| (#17# 84 #8# CONST)) (D (#56# 104 #57# ELT) (#58# 102 #57# ELT) (#59# 100 #62# ELT) (#63# 99 #62# ELT) (#64# 98 #62# ELT) (#65# 94 #62# ELT) (#66# 90 #8# ELT) (#67# 89 #8# ELT)) (>= (#1# 119 #43# ELT)) (> (#1# 121 #43# ELT)) (= (#1# 17 #3# ELT)) (<= (#1# 120 #43# ELT)) (< (#1# 122 #43# ELT)) (/ (#51# 125 #55# ELT)) (- (#11# 78 #70=(|has| |#2| (|AbelianGroup|)) ELT) (#58# 77 #70# ELT)) (+ (#11# 69 #71=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#56# 86 #8# ELT) (($ $ #7#) 81 #8# ELT)) (* (#11# 82 #8# ELT) (#51# 80 #72=(|has| |#2| (|Monoid|)) ELT) (($ |#2| . #73=($)) 79 #72# ELT) (($ #9# . #73#) 76 #70# ELT) (($ #14# $) 73 #5# ELT) (($ #7# $) 70 #71# ELT)) (|#| ((#14# $) 131 T ELT))) (((|DirectProductCategory| |#1| |#2|) (|Category|) (|NonNegativeInteger|) (|Type|)) (T |DirectProductCategory|)) -((|directProduct| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|Type|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)))) (|unitVector| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|Type|)))) (|dot| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|))))) -(|Join| (|IndexedAggregate| (|Integer|) |t#2|) (|FiniteAggregate| |t#2|) (|CoercibleTo| (|Vector| |t#2|)) (CATEGORY |domain| (SIGNATURE |directProduct| ($ (|Vector| |t#2|))) (IF (|has| |t#2| (|SetCategory|)) (ATTRIBUTE (|FullyRetractableTo| |t#2|)) |%noBranch|) (IF (|has| |t#2| (|Ring|)) (PROGN (ATTRIBUTE (|BiModule| |t#2| |t#2|)) (ATTRIBUTE (|DifferentialExtension| |t#2|)) (ATTRIBUTE (|FullyLinearlyExplicitRingOver| |t#2|)) (SIGNATURE |unitVector| ($ (|PositiveInteger|))) (SIGNATURE |dot| (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (|AbelianSemiGroup|)) (ATTRIBUTE (|AbelianSemiGroup|)) |%noBranch|) (IF (|has| |t#2| (|CancellationAbelianMonoid|)) (ATTRIBUTE (|CancellationAbelianMonoid|)) |%noBranch|) (IF (|has| |t#2| (|AbelianMonoid|)) (ATTRIBUTE (|AbelianMonoid|)) |%noBranch|) (IF (|has| |t#2| (|AbelianGroup|)) (ATTRIBUTE (|AbelianGroup|)) |%noBranch|) (IF (|has| |t#2| (|Monoid|)) (ATTRIBUTE (|LinearSet| |t#2|)) |%noBranch|) (IF (|has| |t#2| (|Finite|)) (ATTRIBUTE (|Finite|)) |%noBranch|) (IF (|has| |t#2| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#2|)) |%noBranch|) (IF (|has| |t#2| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|) (IF (|has| |t#2| (|OrderedAbelianMonoidSup|)) (ATTRIBUTE (|OrderedAbelianMonoidSup|)) |%noBranch|) (IF (|has| |t#2| (|Field|)) (ATTRIBUTE (|VectorSpace| |t#2|)) |%noBranch|))) -(((|AbelianGroup|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|AbelianGroup|))) ((|AbelianMonoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|AbelianSemiGroup|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|Aggregate|) . T) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|BasicType|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|BiModule| |#2| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|CoercibleFrom| (|Integer|)) OR (|has| |#2| (|Ring|)) (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|)))) ((|CoercibleFrom| |#2|) |has| |#2| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|CoercibleTo| (|Vector| |#2|)) . T) ((|DifferentialDomain| $) OR (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) ((|DifferentialExtension| |#2|) |has| |#2| (|Ring|)) ((|DifferentialRing|) AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) ((|DifferentialSpace|) OR (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#2| (|Ring|)) ((|Eltable| #2=(|Integer|) |#2|) . T) ((|EltableAggregate| #2# |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Finite|) |has| |#2| (|Finite|)) ((|FiniteAggregate| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|FullyRetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| #2# |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|AbelianGroup|))) ((|LeftLinearSet| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LeftLinearSet| $) |has| |#2| (|Ring|)) ((|LeftModule| #3=(|Integer|)) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LeftModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LeftModule| $) |has| |#2| (|Ring|)) ((|LinearSet| |#2|) OR (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|LinearlyExplicitRingOver| #3#) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|Module| |#2|) OR (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|Monoid|) |has| |#2| (|Ring|)) ((|OrderedAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianMonoidSup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianSemiGroup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedCancellationAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedSet|) OR (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|OrderedType|) OR (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|))) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) ((|PartialDifferentialSpace| #4#) OR (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|RetractableTo| #1#) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| (|Integer|)) AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|RightLinearSet| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|RightModule| |#2|) OR (|has| |#2| (|Ring|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|))) ((|Ring|) |has| |#2| (|Ring|)) ((|Rng|) |has| |#2| (|Ring|)) ((|SemiGroup|) |has| |#2| (|Ring|)) ((|SemiRing|) |has| |#2| (|Ring|)) ((|SetCategory|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|Ring|)) (|has| |#2| (|OrderedSet|)) (|has| |#2| (|OrderedAbelianMonoidSup|)) (|has| |#2| (|Monoid|)) (|has| |#2| (|Finite|)) (|has| |#2| (|Field|)) (|has| |#2| (|CommutativeRing|)) (|has| |#2| (|CancellationAbelianMonoid|)) (|has| |#2| (|AbelianSemiGroup|)) (|has| |#2| (|AbelianMonoid|)) (|has| |#2| (|AbelianGroup|))) ((|Type|) . T) ((|VectorSpace| |#2|) |has| |#2| (|Field|))) +((|directProduct| #1=(*1 *1 *2) (AND (|isDomain| *2 (|Vector| *4)) #2=(|ofCategory| *4 #3=(|Type|)) #4=(|ofCategory| *1 (|DirectProductCategory| *3 *4)))) (|unitVector| #1# (AND (|isDomain| *2 (|PositiveInteger|)) #4# (|ofCategory| *4 #5=(|Ring|)) #2#)) (|dot| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 #3#) (|ofCategory| *2 #5#)))) +(|Join| (|IndexedAggregate| (|Integer|) |t#2|) (|FiniteAggregate| |t#2|) (|CoercibleTo| #1=(|Vector| |t#2|)) (CATEGORY |domain| (SIGNATURE |directProduct| ($ #1#)) (IF (|has| |t#2| (|SetCategory|)) (ATTRIBUTE (|FullyRetractableTo| |t#2|)) |%noBranch|) (IF (|has| |t#2| (|Ring|)) (PROGN (ATTRIBUTE (|BiModule| |t#2| |t#2|)) (ATTRIBUTE (|DifferentialExtension| |t#2|)) (ATTRIBUTE (|FullyLinearlyExplicitRingOver| |t#2|)) (SIGNATURE |unitVector| ($ (|PositiveInteger|))) (SIGNATURE |dot| (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| #2=(|AbelianSemiGroup|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |t#2| #3=(|CancellationAbelianMonoid|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |t#2| #4=(|AbelianMonoid|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |t#2| #5=(|AbelianGroup|)) (ATTRIBUTE #5#) |%noBranch|) (IF (|has| |t#2| (|Monoid|)) (ATTRIBUTE (|LinearSet| |t#2|)) |%noBranch|) (IF (|has| |t#2| #6=(|Finite|)) (ATTRIBUTE #6#) |%noBranch|) (IF (|has| |t#2| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#2|)) |%noBranch|) (IF (|has| |t#2| #7=(|OrderedSet|)) (ATTRIBUTE #7#) |%noBranch|) (IF (|has| |t#2| #8=(|OrderedAbelianMonoidSup|)) (ATTRIBUTE #8#) |%noBranch|) (IF (|has| |t#2| (|Field|)) (ATTRIBUTE (|VectorSpace| |t#2|)) |%noBranch|))) +(((|AbelianGroup|) |has| |#2| (|AbelianGroup|)) ((|AbelianMonoid|) |has| |#2| (|AbelianMonoid|)) ((|AbelianSemiGroup|) |has| |#2| (|AbelianSemiGroup|)) ((|Aggregate|) . T) ((|BasicType|) OR (|has| |#2| (|BasicType|)) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|BiModule| |#2| |#2|) |has| |#2| (|Ring|)) ((|CancellationAbelianMonoid|) |has| |#2| (|CancellationAbelianMonoid|)) ((|CoercibleFrom| #1=(|Fraction| #2=(|Integer|))) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|CoercibleFrom| #2#) OR (AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) (|has| |#2| (|Ring|))) ((|CoercibleFrom| |#2|) |has| |#2| (|SetCategory|)) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|CoercibleTo| (|OutputForm|))) (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|CoercibleTo| (|Vector| |#2|)) . T) ((|DifferentialDomain| $) OR (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|)))) ((|DifferentialExtension| |#2|) |has| |#2| (|Ring|)) ((|DifferentialRing|) AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) ((|DifferentialSpace|) OR (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|Ring|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#2| (|Ring|)) ((|Eltable| #2# |#2|) . T) ((|EltableAggregate| #2# |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Finite|) |has| |#2| (|Finite|)) ((|FiniteAggregate| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|FullyRetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| #2# |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|LeftLinearSet| #2#) |has| |#2| (|AbelianGroup|)) ((|LeftLinearSet| |#2|) |has| |#2| (|Monoid|)) ((|LeftLinearSet| $) |has| |#2| (|Ring|)) ((|LeftModule| #2#) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LeftModule| |#2|) |has| |#2| (|Ring|)) ((|LeftModule| $) |has| |#2| (|Ring|)) ((|LinearSet| |#2|) |has| |#2| (|Monoid|)) ((|LinearlyExplicitRingOver| #2#) AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) ((|LinearlyExplicitRingOver| |#2|) |has| |#2| (|Ring|)) ((|Module| |#2|) |has| |#2| (|CommutativeRing|)) ((|Monoid|) |has| |#2| (|Ring|)) ((|OrderedAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianMonoidSup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedAbelianSemiGroup|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedCancellationAbelianMonoid|) |has| |#2| (|OrderedAbelianMonoidSup|)) ((|OrderedSet|) |has| |#2| (|OrderedSet|)) ((|OrderedType|) |has| |#2| (|OrderedSet|)) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) OR (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) ((|PartialDifferentialSpace| #3#) OR (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#2| (|Ring|)))) ((|RetractableTo| #1#) AND (|has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| #2#) AND (|has| |#2| (|RetractableTo| (|Integer|))) (|has| |#2| (|SetCategory|))) ((|RetractableTo| |#2|) |has| |#2| (|SetCategory|)) ((|RightLinearSet| |#2|) |has| |#2| (|Monoid|)) ((|RightModule| |#2|) |has| |#2| (|Ring|)) ((|Ring|) |has| |#2| (|Ring|)) ((|Rng|) |has| |#2| (|Ring|)) ((|SemiGroup|) |has| |#2| (|Ring|)) ((|SemiRing|) |has| |#2| (|Ring|)) ((|SetCategory|) OR (AND (|has| |#2| (|DifferentialRing|)) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#2| (|Ring|))) (AND (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|Ring|))) (|has| |#2| (|SetCategory|))) ((|Type|) . T) ((|VectorSpace| |#2|) |has| |#2| (|Field|))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) 71 #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) 77 #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 61 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#14=(#15=(|NonNegativeInteger|)) NIL #16=(|has| |#2| (|Finite|)) ELT)) (|setelt| #17=(#18=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #20=(#21="failed")) . #22=($)) NIL #23=(AND (|has| |#2| (|RetractableTo| #10#)) #24=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #25=(|Fraction| #10#) . #20#) . #22#) NIL #26=(AND (|has| |#2| (|RetractableTo| #25#)) #24#) ELT) ((#27=(|Union| |#2| . #20#) $) 31 #24# ELT)) (|retract| (#28=(#10# . #29=($)) NIL #23# ELT) ((#25# . #29#) NIL #26# ELT) (#30=(|#2| $) 29 #24# ELT)) (|reducedSystem| ((#31=(|Matrix| #10#) . #32=(#33=(|Matrix| $))) NIL #34=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#35=(|Record| (|:| |mat| #31#) (|:| |vec| (|Vector| #10#))) . #36=(#33# #37=(|Vector| $))) NIL #34# ELT) ((#38=(|Record| (|:| |mat| #39=(|Matrix| |#2|)) (|:| |vec| #40=(|Vector| |#2|))) . #36#) NIL #9# ELT) ((#39# . #32#) NIL #9# ELT)) (|reduce| ((|#2| #41=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #41# $ |#2|) NIL T ELT) ((|#2| #41# $) NIL T ELT)) (|recip| (((|Union| $ #21#) $) 67 #9# ELT)) (|random| (#19# NIL #16# ELT)) (|qsetelt!| #17#) (|qelt| (#42=(|#2| $ #10#) 64 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| (#28# 20 #43=(|has| #10# #44=(|OrderedSet|)) ELT)) (|min| #45=(#12# NIL #46=(|has| |#2| #44#) ELT)) (|members| (#47=(#48=(|List| |#2|) $) 14 T ELT)) (|member?| (#49=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| (#28# NIL #43# ELT)) (|max| #45#) (|map| (($ #50=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #16# ELT)) (|leftReducedSystem| ((#31# . #51=(#37#)) NIL #34# ELT) ((#35# . #52=(#37# $)) NIL #34# ELT) ((#38# . #52#) NIL #9# ELT) ((#39# . #51#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #24# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #16# ELT)) (|hash| (((|SingleInteger|) $) NIL #24# ELT)) (|first| (#30# NIL #43# ELT)) (|find| ((#27# #53=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#54=($ $ |#2|) NIL #11# ELT)) (|every?| (#55=(#3# #53# $) 24 T ELT)) (|eval| (($ $ (|List| #56=(|Equation| |#2|))) NIL #57=(AND (|has| |#2| (|Evalable| |#2|)) #24#) ELT) (($ $ #56#) NIL #57# ELT) (($ $ |#2| |#2|) NIL #57# ELT) (($ $ #48# #48#) NIL #57# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#49# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| (#47# NIL T ELT)) (|empty?| (#5# NIL T ELT)) (|empty| (#19# NIL T ELT)) (|elt| (#18# NIL T ELT) (#42# 21 T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #40#) 18 T ELT)) (|dimension| (((|CardinalNumber|)) NIL #58=(|has| |#2| (|Field|)) ELT)) (|differentiate| #59=(#60=($ $ #15#) NIL #61=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #62=(#63=($ $) NIL #61# ELT) #64=(($ $ #65=(|List| #66=(|Symbol|)) (|List| #15#)) NIL #67=(AND (|has| |#2| (|PartialDifferentialSpace| #66#)) #9#) ELT) #68=(($ $ #66# #15#) NIL #67# ELT) #69=(($ $ #65#) NIL #67# ELT) #70=(($ $ #66#) NIL #67# ELT) #71=(($ $ #50#) NIL #9# ELT) #72=(($ $ #50# #15#) NIL #9# ELT)) (|count| ((#15# |#2| $) NIL #4# ELT) ((#15# #53# $) NIL T ELT)) (|copy| (#63# NIL T ELT)) (|coerce| ((#40# $) 9 T ELT) (($ #10#) NIL (OR #23# #9#) ELT) (($ #25#) NIL #26# ELT) (($ |#2|) 12 #24# ELT) ((#73=(|OutputForm|) $) NIL (|has| |#2| (|CoercibleTo| #73#)) ELT)) (|characteristic| (#14# NIL #9# CONST)) (|before?| #1#) (|any?| (#55# NIL T ELT)) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#19# 37 #6# CONST)) (|One| (#19# 41 #9# CONST)) (D #59# #62# #64# #68# #69# #70# #71# #72#) (>= #74=(#2# NIL #46# ELT)) (> #74#) (= (#2# 28 #4# ELT)) (<= #74#) (< (#2# 75 #46# ELT)) (/ (#54# NIL #58# ELT)) (- (#12# NIL #75=(|has| |#2| (|AbelianGroup|)) ELT) (#63# NIL #75# ELT)) (+ (#12# 35 #76=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#60# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# 47 #9# ELT) (#54# 45 #77=(|has| |#2| (|Monoid|)) ELT) (($ |#2| $) 46 #77# ELT) (($ #10# $) NIL #75# ELT) (($ #15# $) NIL #6# ELT) (($ #8# $) NIL #76# ELT)) (|#| ((#15# $) NIL T ELT))) (((|DirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|Type|)) (T |DirectProduct|)) NIL @@ -639,27 +639,27 @@ NIL ((** (($ $ #1=(|PositiveInteger|)) NIL T ELT) (($ $ #2=(|NonNegativeInteger|)) NIL T ELT) (($ $ #3=(|Integer|)) 18 T ELT)) (* (($ #1# $) NIL T ELT) (($ #2# $) NIL T ELT) (($ #3# $) NIL T ELT) (($ $ $) NIL T ELT) (($ #4=(|Fraction| #3#) $) 25 T ELT) (($ $ #4#) NIL T ELT))) (((|DivisionRing&| |#1|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| #1=(|Integer|))) (SIGNATURE * (|#1| |#1| #2=(|Fraction| #1#))) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE ** (|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE * (|#1| |#1| |#1|)) (SIGNATURE ** (|#1| |#1| #4=(|PositiveInteger|))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE * (|#1| #3# |#1|)) (SIGNATURE * (|#1| #4# |#1|))) (|DivisionRing|)) (T |DivisionRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 56 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #4=(|Fraction| (|Integer|))) 60 T ELT)) (|characteristic| 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(|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #30#) (|leftReducedSystem| ((#36# . #65=(#42#)) NIL #39# ELT) ((#40# . #66=(#42# $)) NIL #39# ELT) ((#43# . #66#) NIL T ELT) ((#44# . #65#) NIL T ELT)) (|leadingMonomial| #35#) (|leadingCoefficient| #31#) (|lcm| #67=(($ #49#) NIL #19# ELT) #68=(#69=($ $ $) NIL #19# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #22#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #22#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #31#) (|gcdPolynomial| ((#8# #8# #8#) NIL #19# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #16#) (|factorPolynomial| #16#) (|factor| (#20# NIL #17# ELT)) (|exquo| ((#45# $ |#2|) NIL #10# ELT) ((#45# $ $) NIL #10# ELT)) (|eval| (($ $ (|List| #71=(|Equation| $))) NIL T ELT) (($ $ #71#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #49# #49#) NIL T ELT) (($ $ #7# |#2|) NIL T ELT) (($ $ #6# #72=(|List| |#2|)) NIL T ELT) (($ $ #7# $) NIL T ELT) (($ $ #6# #49#) NIL T ELT)) (|discriminant| (#47# NIL #34# ELT)) (|differentiate| #60# #59# #73=(($ $ #6#) NIL T ELT) #74=(#47# NIL T ELT)) (|degree| #62# #63# #64#) (|convert| ((#54# . #75=($)) NIL (AND (|has| #7# #76=(|ConvertibleTo| #54#)) (|has| |#2| #76#)) ELT) ((#57# . #75#) NIL (AND (|has| #7# #77=(|ConvertibleTo| #57#)) (|has| |#2| #77#)) ELT) ((#78=(|InputForm|) . #75#) NIL (AND (|has| #7# #79=(|ConvertibleTo| #78#)) (|has| |#2| #79#)) ELT)) (|content| (#32# NIL #19# ELT) #46#) (|conditionP| (((|Union| #42# #22#) #38#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #17#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #27#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) (($ #26#) NIL (OR #82=(|has| |#2| (|Algebra| #26#)) #28#) ELT) #11#) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| ((#15# $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #34# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #23#) (|One| #23#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #35# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #27# . #86=($)) NIL T ELT) #84# (($ $ #26#) NIL #82# ELT) (($ #26# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Join| (|PolynomialCategory| |#2| (|DirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|)) (T |DistributedMultivariatePolynomial|)) ((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 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T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . 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T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#2|) . T) ((|RetractableTo| |#3|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . 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T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#4|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| #3=(|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| #2#)) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpaceExtension| |#1|) . T) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#4|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|GcdDomain|)) ((|InnerEvalable| |#2| |#1|) |has| |#1| (|DifferentialRing|)) ((|InnerEvalable| |#2| $) |has| |#1| (|DifferentialRing|)) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| #4#) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| #4#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialSpace| |#3|) . T) ((|PatternMatchable| #3#) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| #2#) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| |#4| |#3|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#2|) . T) ((|RetractableTo| |#3|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|top!| (#4=(|#1| $) 64 T ELT)) (|top| (#4# 42 T ELT)) (|sample| (#5=($) 6 T CONST)) (|rotate!| (#6=($ $) 70 T ELT)) (|reverse!| (#6# 58 T ELT)) (|reduce| ((|#1| #7=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 55 #3# ELT) ((|#1| #7# $ |#1|) 51 T ELT) ((|#1| #7# $) 50 T ELT)) (|push!| (#8=(|#1| |#1| $) 44 T ELT)) (|pop!| (#4# 43 T ELT)) (|members| ((#9=(|List| |#1|) $) 49 T ELT)) (|member?| ((#2# |#1| $) 54 #3# ELT)) (|map!| (#10=($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (#10# 26 T ELT)) (|length| (#11=(#12=(|NonNegativeInteger|) $) 71 T ELT)) (|latex| (((|String|) $) 21 #13=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#4# 35 T ELT)) (|insertTop!| (#8# 62 T ELT)) (|insertBottom!| (#8# 61 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|height| (#11# 65 T ELT)) (|hash| (((|SingleInteger|) $) 20 #13# ELT)) (|front| (#4# 72 T ELT)) (|find| (((|Union| |#1| "failed") #14=(|Mapping| #2# |#1|) $) 52 T ELT)) (|extractTop!| (#4# 60 T ELT)) (|extractBottom!| (#4# 59 T ELT)) (|extract!| (#4# 37 T ELT)) (|every?| (#15=(#2# #14# $) 47 T ELT)) (|eval| (($ $ (|List| #16=(|Equation| |#1|))) 25 #17=(AND (|has| |#1| (|Evalable| |#1|)) #13#) ELT) (($ $ #16#) 24 #17# ELT) (($ $ |#1| |#1|) 23 #17# ELT) (($ $ #9# #9#) 22 #17# ELT)) (|eq?| (#1# 10 T ELT)) (|enqueue!| (#8# 68 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#5# 8 T ELT)) (|dequeue!| (#4# 69 T ELT)) (|dequeue| (#5# 67 T ELT) (#18=($ #9#) 66 T ELT)) (|depth| (#11# 41 T ELT)) (|count| ((#12# |#1| $) 53 #3# ELT) ((#12# #14# $) 48 T ELT)) (|copy| (#6# 9 T ELT)) (|coerce| ((#19=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #19#)) ELT)) (|bottom!| (#4# 63 T ELT)) (|before?| (#1# 19 #3# ELT)) (|bag| (#18# 38 T ELT)) (|back| (#4# 73 T ELT)) (|any?| (#15# 46 T ELT)) (= (#1# 17 #3# ELT)) (|#| (#11# 45 T ELT))) (((|DequeueAggregate| |#1|) (|Category|) (|Type|)) (T |DequeueAggregate|)) -((|dequeue| (*1 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|dequeue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|DequeueAggregate| *3)))) (|height| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|top!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|bottom!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insertTop!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insertBottom!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|extractTop!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|extractBottom!| (*1 *2 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|reverse!| (*1 *1 *1) (AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 (|Type|))))) -(|Join| (|StackAggregate| |t#1|) (|QueueAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($)) (SIGNATURE |dequeue| ($ (|List| |t#1|))) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |top!| (|t#1| $)) (SIGNATURE |bottom!| (|t#1| $)) (SIGNATURE |insertTop!| (|t#1| |t#1| $)) (SIGNATURE |insertBottom!| (|t#1| |t#1| $)) (SIGNATURE |extractTop!| (|t#1| $)) (SIGNATURE |extractBottom!| (|t#1| $)) (SIGNATURE |reverse!| ($ $)))) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|QueueAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|StackAggregate| |#1|) . T) ((|Type|) . T)) +((|dequeue| (*1 *1) #1=(AND (|ofCategory| *1 (|DequeueAggregate| *2)) (|ofCategory| *2 #2=(|Type|)))) (|dequeue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #3=(|ofCategory| *3 #2#) #4=(|ofCategory| *1 (|DequeueAggregate| *3)))) (|height| #5=(*1 *2 *1) (AND #4# #3# (|isDomain| *2 (|NonNegativeInteger|)))) (|top!| #5# #1#) (|bottom!| #5# #1#) (|insertTop!| #6=(*1 *2 *2 *1) #1#) (|insertBottom!| #6# #1#) (|extractTop!| #5# #1#) (|extractBottom!| #5# #1#) (|reverse!| (*1 *1 *1) #1#)) +(|Join| (|StackAggregate| |t#1|) (|QueueAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |dequeue| ($)) (SIGNATURE |dequeue| ($ (|List| |t#1|))) (SIGNATURE |height| ((|NonNegativeInteger|) $)) (SIGNATURE |top!| #1=(|t#1| $)) (SIGNATURE |bottom!| #1#) (SIGNATURE |insertTop!| #2=(|t#1| |t#1| $)) (SIGNATURE |insertBottom!| #2#) (SIGNATURE |extractTop!| #1#) (SIGNATURE |extractBottom!| #1#) (SIGNATURE |reverse!| ($ $)))) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|QueueAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|StackAggregate| |#1|) . T) ((|Type|) . T)) ((|makeObject| ((#1=(|ThreeSpace| (|DoubleFloat|)) #2=(|ParametricSurface| |#1|) #3=(|SegmentBinding| (|Float|)) #3#) 75 T ELT) ((#1# #2# #3# #3# #4=(|List| (|DrawOption|))) 74 T ELT) ((#1# |#1| #3# #3#) 65 T ELT) ((#1# |#1| #3# #3# #4#) 64 T ELT) ((#1# #5=(|ParametricSpaceCurve| |#1|) #3#) 56 T ELT) ((#1# #5# #3# #4#) 55 T ELT)) (|draw| ((#6=(|ThreeDimensionalViewport|) #2# #3# #3#) 78 T ELT) ((#6# #2# #3# #3# #4#) 77 T ELT) ((#6# |#1| #3# #3#) 68 T ELT) ((#6# |#1| #3# #3# #4#) 67 T ELT) ((#6# #5# #3#) 60 T ELT) ((#6# #5# #3# #4#) 59 T ELT) ((#7=(|TwoDimensionalViewport|) #8=(|ParametricPlaneCurve| |#1|) #3#) 47 T ELT) ((#7# #8# #3# #4#) 46 T ELT) ((#7# |#1| #3#) 38 T ELT) ((#7# |#1| #3# #4#) 36 T ELT))) (((|TopLevelDrawFunctions| |#1|) (CATEGORY |package| (SIGNATURE |draw| (#1=(|TwoDimensionalViewport|) |#1| #2=(|SegmentBinding| (|Float|)) #3=(|List| (|DrawOption|)))) (SIGNATURE |draw| (#1# |#1| #2#)) (SIGNATURE |draw| (#1# #4=(|ParametricPlaneCurve| |#1|) #2# #3#)) (SIGNATURE |draw| (#1# #4# #2#)) (SIGNATURE |draw| (#5=(|ThreeDimensionalViewport|) #6=(|ParametricSpaceCurve| |#1|) #2# #3#)) (SIGNATURE |draw| (#5# #6# #2#)) (SIGNATURE |makeObject| (#7=(|ThreeSpace| (|DoubleFloat|)) #6# #2# #3#)) (SIGNATURE |makeObject| (#7# #6# #2#)) (SIGNATURE |draw| (#5# |#1| #2# #2# #3#)) (SIGNATURE |draw| (#5# |#1| #2# #2#)) (SIGNATURE |makeObject| (#7# |#1| #2# #2# #3#)) (SIGNATURE |makeObject| (#7# |#1| #2# #2#)) (SIGNATURE |draw| (#5# #8=(|ParametricSurface| |#1|) #2# #2# #3#)) (SIGNATURE |draw| (#5# #8# #2# #2#)) (SIGNATURE |makeObject| (#7# #8# #2# #2# #3#)) (SIGNATURE |makeObject| (#7# #8# #2# #2#))) (|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|))) (T |TopLevelDrawFunctions|)) ((|makeObject| #1=(*1 *2 *3 *4 *4) (AND #2=(|isDomain| *3 (|ParametricSurface| *5)) #3=(|isDomain| *4 (|SegmentBinding| (|Float|))) #4=(|ofCategory| *5 #5=(|Join| (|ConvertibleTo| (|InputForm|)) (|SetCategory|))) #6=(|isDomain| *2 (|ThreeSpace| (|DoubleFloat|))) #7=(|isDomain| *1 (|TopLevelDrawFunctions| *5)))) (|makeObject| #8=(*1 *2 *3 *4 *4 *5) (AND #9=(|isDomain| *3 (|ParametricSurface| *6)) #3# #10=(|isDomain| *5 (|List| (|DrawOption|))) #11=(|ofCategory| *6 #5#) #6# #12=(|isDomain| *1 (|TopLevelDrawFunctions| *6)))) (|draw| #1# (AND #2# #3# #4# #13=(|isDomain| *2 (|ThreeDimensionalViewport|)) #7#)) (|draw| #8# (AND #9# #3# #10# #11# #13# #12#)) (|makeObject| #1# (AND #3# #6# #14=(|isDomain| *1 (|TopLevelDrawFunctions| *3)) #15=(|ofCategory| *3 #5#))) (|makeObject| #8# (AND #3# #10# #6# #14# #15#)) (|draw| #1# (AND #3# #13# #14# #15#)) (|draw| #8# (AND #3# #10# #13# #14# #15#)) (|makeObject| #16=(*1 *2 *3 *4) (AND #17=(|isDomain| *3 (|ParametricSpaceCurve| *5)) #3# #4# #6# #7#)) (|makeObject| #18=(*1 *2 *3 *4 *5) (AND #19=(|isDomain| *3 (|ParametricSpaceCurve| *6)) #3# #10# #11# #6# #12#)) (|draw| #16# (AND #17# #3# #4# #13# #7#)) (|draw| #18# (AND #19# #3# #10# #11# #13# #12#)) (|draw| #16# (AND (|isDomain| *3 (|ParametricPlaneCurve| *5)) #3# #4# #20=(|isDomain| *2 (|TwoDimensionalViewport|)) #7#)) (|draw| #18# (AND (|isDomain| *3 (|ParametricPlaneCurve| *6)) #3# #10# #11# #20# #12#)) (|draw| #16# (AND #3# #20# #14# #15#)) (|draw| #18# (AND #3# #10# #20# #14# #15#))) @@ -721,22 +721,22 @@ NIL ((|differentiate| (#1=($ $ #2=(|Mapping| |#2| |#2|)) NIL T ELT) (#3=($ $ #2# #4=(|NonNegativeInteger|)) 11 T ELT) #5=(($ $ #6=(|List| #7=(|Symbol|)) (|List| #4#)) NIL T ELT) #8=(($ $ #7# #4#) NIL T ELT) #9=(($ $ #6#) NIL T ELT) (#10=($ $ #7#) 19 T ELT) #11=(($ $ #4#) NIL T ELT) (#12=($ $) 16 T ELT)) (D (#1# 12 T ELT) (#3# 14 T ELT) #5# #8# #9# (#10# NIL T ELT) #11# (#12# NIL T ELT))) (((|DifferentialSpaceExtension&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |differentiate| #1=(|#1| |#1|)) (SIGNATURE D #1#) (SIGNATURE |differentiate| #2=(|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE D #2#) (SIGNATURE |differentiate| #4=(|#1| |#1| #5=(|Symbol|))) (SIGNATURE D #4#) (SIGNATURE |differentiate| #6=(|#1| |#1| #7=(|List| #5#))) (SIGNATURE |differentiate| #8=(|#1| |#1| #5# #3#)) (SIGNATURE |differentiate| #9=(|#1| |#1| #7# (|List| #3#))) (SIGNATURE D #6#) (SIGNATURE D #8#) (SIGNATURE D #9#) (SIGNATURE D #10=(|#1| |#1| #11=(|Mapping| |#2| |#2|) #3#)) (SIGNATURE D #12=(|#1| |#1| #11#)) (SIGNATURE |differentiate| #10#) (SIGNATURE |differentiate| #12#)) (|DifferentialSpaceExtension| |#2|) (|Type|)) (T |DifferentialSpaceExtension&|)) NIL -((|differentiate| (($ $ (|Mapping| |#1| |#1|)) 23 T ELT) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 22 T ELT) (($ $ (|List| #1=(|Symbol|)) . #2=((|List| #3=(|NonNegativeInteger|)))) 16 (|has| |#1| . #4=((|PartialDifferentialSpace| (|Symbol|)))) ELT) (($ $ #1# . #5=(#3#)) 15 (|has| |#1| . #4#) ELT) (($ $ (|List| #1#)) 14 (|has| |#1| . #4#) ELT) (($ $ #1#) 12 (|has| |#1| . #4#) ELT) (#6=($ $ (|NonNegativeInteger|)) 10 (|has| |#1| . #7=((|DifferentialSpace|))) ELT) (($ . #8=($)) 8 (|has| |#1| . #7#) ELT)) (D (($ $ (|Mapping| |#1| |#1|)) 21 T ELT) (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) 20 T ELT) (($ $ (|List| #1#) . #2#) 19 (|has| |#1| . #4#) ELT) (($ $ #1# . #5#) 18 (|has| |#1| . #4#) ELT) (($ $ (|List| #1#)) 17 (|has| |#1| . #4#) ELT) (($ $ #1#) 13 (|has| |#1| . #4#) ELT) (#6# 11 (|has| |#1| . #7#) ELT) (($ . #8#) 9 (|has| |#1| . #7#) ELT))) +((|differentiate| (#1=($ $ #2=(|Mapping| |#1| |#1|)) 23 T ELT) (#3=($ $ #2# #4=(|NonNegativeInteger|)) 22 T ELT) (#5=($ $ #6=(|List| #7=(|Symbol|)) (|List| #4#)) 16 #8=(|has| |#1| (|PartialDifferentialSpace| #7#)) ELT) (#9=($ $ #7# #4#) 15 #8# ELT) (#10=($ $ #6#) 14 #8# ELT) (#11=($ $ #7#) 12 #8# ELT) (#12=($ $ #4#) 10 #13=(|has| |#1| (|DifferentialSpace|)) ELT) (#14=($ $) 8 #13# ELT)) (D (#1# 21 T ELT) (#3# 20 T ELT) (#5# 19 #8# ELT) (#9# 18 #8# ELT) (#10# 17 #8# ELT) (#11# 13 #8# ELT) (#12# 11 #13# ELT) (#14# 9 #13# ELT))) (((|DifferentialSpaceExtension| |#1|) (|Category|) (|Type|)) (T |DifferentialSpaceExtension|)) -((|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialSpaceExtension| *3)) (|ofCategory| *3 (|Type|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialSpaceExtension| *4)) (|ofCategory| *4 (|Type|)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialSpaceExtension| *3)) (|ofCategory| *3 (|Type|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialSpaceExtension| *4)) (|ofCategory| *4 (|Type|))))) -(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|))) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|) (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|Mapping| |t#1| |t#1|))) (SIGNATURE D ($ $ (|Mapping| |t#1| |t#1|) (|NonNegativeInteger|))) (IF (|has| |t#1| (|DifferentialSpace|)) (ATTRIBUTE (|DifferentialSpace|)) |%noBranch|) (IF (|has| |t#1| (|PartialDifferentialSpace| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialSpace| (|Symbol|))) |%noBranch|))) -(((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|Join|) . T) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialSpace| #1#) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|Type|) . T)) +((|differentiate| #1=(*1 *1 *1 *2) #2=(AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|DifferentialSpaceExtension| *3)) (|ofCategory| *3 #3=(|Type|)))) (|differentiate| #4=(*1 *1 *1 *2 *3) #5=(AND (|isDomain| *2 (|Mapping| *4 *4)) (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialSpaceExtension| *4)) (|ofCategory| *4 #3#))) (D #1# #2#) (D #4# #5#)) +(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| #1=($ $ #2=(|Mapping| |t#1| |t#1|))) (SIGNATURE |differentiate| #3=($ $ #2# (|NonNegativeInteger|))) (SIGNATURE D #1#) (SIGNATURE D #3#) (IF (|has| |t#1| #4=(|DifferentialSpace|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |t#1| #5=(|PartialDifferentialSpace| (|Symbol|))) (ATTRIBUTE #5#) |%noBranch|))) +(((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|PartialDifferentialDomain| $ #1=(|Symbol|)) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|PartialDifferentialSpace| #1#) |has| |#1| (|PartialDifferentialSpace| (|Symbol|))) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|weights| ((#6=(|List| #7=(|NonNegativeInteger|)) $) NIL T ELT) ((#6# $ |#2|) NIL T ELT)) (|weight| #8=(#9=(#7# $) NIL T ELT) #10=((#7# $ |#2|) NIL T ELT)) (|variables| ((#11=(|List| |#3|) $) NIL T ELT)) (|univariate| ((#12=(|SparseUnivariatePolynomial| $) $ |#3|) NIL T ELT) ((#13=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#5# NIL #14# ELT)) (|totalDegree| #8# ((#7# $ #11#) NIL T ELT)) (|subtractIfCan| ((#17=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #12#) #12#) NIL #19=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#16# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #12#) #24="failed") #23# #12#) NIL #19# ELT)) (|separant| #25=(#16# NIL T ELT)) (|sample| #26=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #27=(#24#)) . #28=($)) NIL T ELT) (((|Union| #29=(|Fraction| #30=(|Integer|)) . #27#) . #28#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) (((|Union| #30# . #27#) . #28#) NIL #32=(|has| |#1| (|RetractableTo| #30#)) ELT) #33=(((|Union| |#3| . #27#) . #28#) NIL T ELT) (((|Union| |#2| . #27#) . #28#) NIL T ELT) (((|Union| #34=(|SparseMultivariatePolynomial| |#1| |#2|) . #27#) $) 23 T ELT)) (|retract| #35=(#36=(|#1| $) NIL T ELT) ((#29# . #37=($)) NIL #31# ELT) ((#30# . #37#) NIL #32# ELT) #38=((|#3| . #37#) NIL T ELT) ((|#2| . #37#) NIL T ELT) ((#34# . #37#) NIL T ELT)) (|resultant| (($ $ $ |#3|) NIL #39=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| #25#) (|reducedSystem| ((#40=(|Matrix| #30#) . #41=(#42=(|Matrix| $))) NIL #43=(|has| |#1| (|LinearlyExplicitRingOver| #30#)) ELT) ((#44=(|Record| (|:| |mat| #40#) (|:| |vec| (|Vector| #30#))) . #45=(#42# #46=(|Vector| $))) NIL #43# ELT) ((#47=(|Record| (|:| |mat| #48=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #45#) NIL T ELT) ((#48# . #41#) NIL T ELT)) (|recip| ((#49=(|Union| $ #24#) $) NIL T ELT)) (|primitivePart| #20# #50=(#51=($ $ |#3|) NIL #21# ELT)) (|primitiveMonomials| #52=((#53=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#1| #54=(|IndexedExponents| |#3|) $) NIL T ELT)) (|patternMatch| ((#55=(|PatternMatchResult| #56=(|Float|) . #57=($)) $ #58=(|Pattern| #56#) #55#) NIL (AND (|has| |#1| #59=(|PatternMatchable| #56#)) (|has| |#3| #59#)) ELT) ((#60=(|PatternMatchResult| #30# . #57#) $ #61=(|Pattern| #30#) #60#) NIL (AND (|has| |#1| #62=(|PatternMatchable| #30#)) (|has| |#3| #62#)) ELT)) (|order| #10# (#9# 10 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #8#) (|multivariate| (($ #13# |#3|) NIL T ELT) (($ #12# |#3|) NIL T ELT)) (|monomials| #52#) (|monomial?| #4#) (|monomial| (($ |#1| #54#) NIL T ELT) #63=(($ $ |#3| #7#) NIL T ELT) #64=(($ $ #11# #6#) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) NIL T ELT)) (|minimumDegree| #65=((#54# $) NIL T ELT) #66=((#7# $ |#3|) NIL T ELT) #67=((#6# $ #11#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #54# #54#) $) NIL T ELT)) (|map| (($ #68=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeVariable| ((#69=(|Mapping| $ #7#) |#2|) NIL T ELT) ((#69# $) NIL #70=(|has| |#1| (|DifferentialRing|)) ELT)) (|mainVariable| #33#) (|leftReducedSystem| ((#40# . #71=(#46#)) NIL #43# ELT) ((#44# . #72=(#46# $)) NIL #43# ELT) ((#47# . #72#) NIL T ELT) ((#48# . #71#) NIL T ELT)) (|leadingMonomial| #25#) (|leadingCoefficient| #35#) (|leader| #38#) (|lcm| #73=(($ #53#) NIL #21# ELT) #74=(#75=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #76=(((|Union| #53# #24#) $) NIL T ELT)) (|isPlus| #76#) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| #7#)) #24#) $) NIL T ELT)) (|initial| #25#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #35#) (|gcdPolynomial| ((#12# #12# #12#) NIL #21# ELT)) (|gcd| #73# #74#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#49# $ |#1|) NIL #14# ELT) ((#49# $ $) NIL #14# ELT)) (|eval| (($ $ (|List| #77=(|Equation| $))) NIL T ELT) (($ $ #77#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #53# #53#) NIL T ELT) (($ $ |#3| |#1|) NIL T ELT) (($ $ #11# #78=(|List| |#1|)) NIL T ELT) (($ $ |#3| $) NIL T ELT) (($ $ #11# #53#) NIL T ELT) (($ $ |#2| $) NIL #70# ELT) (($ $ #79=(|List| |#2|) #53#) NIL #70# ELT) (($ $ |#2| |#1|) NIL #70# ELT) (($ $ #79# #78#) NIL #70# ELT)) (|discriminant| (#51# NIL #39# ELT)) (|differentiate| #64# #63# #80=(($ $ #11#) NIL T ELT) #81=(#51# NIL T ELT) #82=(($ $ #68#) NIL T ELT) #83=(($ $ #68# #7#) NIL T ELT) #84=(($ $ #85=(|Symbol|)) NIL #86=(|has| |#1| (|PartialDifferentialSpace| #85#)) ELT) #87=(($ $ #88=(|List| #85#)) NIL #86# ELT) #89=(($ $ #85# #7#) NIL #86# ELT) #90=(($ $ #88# #6#) NIL #86# ELT) #91=(#16# NIL #92=(|has| |#1| (|DifferentialSpace|)) ELT) #93=(#94=($ $ #7#) NIL #92# ELT)) (|differentialVariables| ((#79# $) NIL T ELT)) (|degree| #65# #66# #67# #10#) (|convert| ((#58# . #95=($)) NIL (AND (|has| |#1| #96=(|ConvertibleTo| #58#)) (|has| |#3| #96#)) ELT) ((#61# . #95#) NIL (AND (|has| |#1| #97=(|ConvertibleTo| #61#)) (|has| |#3| #97#)) ELT) ((#98=(|InputForm|) . #95#) NIL (AND (|has| |#1| #99=(|ConvertibleTo| #98#)) (|has| |#3| #99#)) ELT)) (|content| (#36# NIL #21# ELT) #50#) (|conditionP| (((|Union| #46# #24#) #42#) NIL #100=(AND (|has| $ #101=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #30#) NIL T ELT) (($ |#1|) 26 T ELT) (($ |#3|) 25 T ELT) (($ |#2|) NIL T ELT) (($ #34#) 32 T ELT) (($ #29#) NIL (OR #102=(|has| |#1| (|Algebra| #29#)) #31#) ELT) #15#) (|coefficients| ((#78# $) NIL T ELT)) (|coefficient| ((|#1| $ #54#) NIL T ELT) #63# #64#) (|charthRoot| ((#17# $) NIL (OR #100# (|has| |#1| #101#)) ELT)) (|characteristic| ((#7#) NIL T CONST)) (|binomThmExpt| (($ $ $ #7#) NIL #39# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| #26#) (|One| #26#) (D #64# #63# #80# #81# #82# #83# #84# #87# #89# #90# #91# #93#) (= #1#) (/ (#103=($ $ |#1|) NIL (|has| |#1| (|Field|)) ELT)) (- #25# #104=(#75# NIL T ELT)) (+ #104#) (** (($ $ #105=(|PositiveInteger|)) NIL T ELT) (#94# NIL T ELT)) (* (($ #105# $) NIL T ELT) (($ #7# $) NIL T ELT) (($ #30# . #106=($)) NIL T ELT) #104# (($ $ #29#) NIL #102# ELT) (($ #29# . #106#) NIL #102# ELT) (($ |#1| . #106#) NIL T ELT) (#103# NIL T ELT))) (((|DifferentialSparseMultivariatePolynomial| |#1| |#2| |#3|) (|Join| (|DifferentialPolynomialCategory| |#1| |#2| |#3| (|IndexedExponents| |#3|)) (|RetractableTo| (|SparseMultivariatePolynomial| |#1| |#2|))) (|Ring|) (|OrderedSet|) (|DifferentialVariableCategory| |#2|)) (T |DifferentialSparseMultivariatePolynomial|)) NIL ((|weight| ((#1=(|NonNegativeInteger|) $) 37 T ELT)) (|retractIfCan| (((|Union| |#2| "failed") $) 22 T ELT)) (|retract| ((|#2| $) 33 T ELT)) (|differentiate| (($ $ #1#) 18 T ELT) (($ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ |#2|) 11 T ELT)) (= (#2=((|Boolean|) $ $) 26 T ELT)) (< (#2# 36 T ELT))) (((|DifferentialVariableCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |weight| (#1=(|NonNegativeInteger|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #1#)) (SIGNATURE < #2=((|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #2#)) (|DifferentialVariableCategory| |#2|) (|OrderedSet|)) (T |DifferentialVariableCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|weight| (((|NonNegativeInteger|) $) 26 T ELT)) (|variable| ((|#1| $) 27 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 31 T ELT)) (|retract| ((|#1| $) 32 T ELT)) (|order| (((|NonNegativeInteger|) $) 28 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) 29 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#3=($ $ (|NonNegativeInteger|)) 35 T ELT) (($ . #4=($)) 33 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 30 T ELT)) (|before?| (#1# 6 T ELT)) (D (#3# 36 T ELT) (($ . #4#) 34 T ELT)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|weight| (#2=(#3=(|NonNegativeInteger|) $) 26 T ELT)) (|variable| (#4=(|#1| $) 27 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 31 T ELT)) (|retract| (#4# 32 T ELT)) (|order| (#2# 28 T ELT)) (|min| (#5=($ $ $) 23 T ELT)) (|max| (#5# 22 T ELT)) (|makeVariable| (($ |#1| #3#) 29 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#6=($ $ #3#) 35 T ELT) (#7=($ $) 33 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 30 T ELT)) (|before?| (#1# 6 T ELT)) (D (#6# 36 T ELT) (#7# 34 T ELT)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT))) (((|DifferentialVariableCategory| |#1|) (|Category|) (|OrderedSet|)) (T |DifferentialVariableCategory|)) -((|makeVariable| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|variable| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|weight| (*1 *2 *1) (AND (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|))))) -(|Join| (|OrderedSet|) (|DifferentialSpace|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |makeVariable| ($ |t#1| (|NonNegativeInteger|))) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |variable| (|t#1| $)) (SIGNATURE |weight| ((|NonNegativeInteger|) $)))) -(((|BasicType|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialSpace|) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|makeVariable| (*1 *1 *2 *3) (AND (|isDomain| *3 #1=(|NonNegativeInteger|)) #2=(|ofCategory| *1 (|DifferentialVariableCategory| *2)) #3=(|ofCategory| *2 #4=(|OrderedSet|)))) (|order| #5=(*1 *2 *1) #6=(AND (|ofCategory| *1 (|DifferentialVariableCategory| *3)) (|ofCategory| *3 #4#) (|isDomain| *2 #1#))) (|variable| #5# (AND #2# #3#)) (|weight| #5# #6#)) +(|Join| (|OrderedSet|) (|DifferentialSpace|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |makeVariable| ($ |t#1| #1=(|NonNegativeInteger|))) (SIGNATURE |order| #2=(#1# $)) (SIGNATURE |variable| (|t#1| $)) (SIGNATURE |weight| #2#))) +(((|BasicType|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialSpace|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT)) (|max| #3#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exponents| ((#4=(|List| (|Integer|)) $) 28 T ELT)) (|degree| ((#5=(|NonNegativeInteger|) $) 26 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ #4#) 22 T ELT)) (|before?| #1#) (|Nul| (($ #5#) 29 T ELT)) (>= #1#) (> #1#) (= (#2# 11 T ELT)) (<= #1#) (< (#2# 18 T ELT))) (((|ExtAlgBasis|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|List| (|Integer|)))) (SIGNATURE |degree| (#2=(|NonNegativeInteger|) $)) (SIGNATURE |exponents| (#1# $)) (SIGNATURE |Nul| ($ #2#))))) (T |ExtAlgBasis|)) ((|coerce| #1=(*1 *1 *2) #2=(AND (|isDomain| *2 (|List| (|Integer|))) #3=(|isDomain| *1 (|ExtAlgBasis|)))) (|degree| #4=(*1 *2 *1) #5=(AND (|isDomain| *2 (|NonNegativeInteger|)) #3#)) (|exponents| #4# #2#) (|Nul| #1# #5#)) @@ -761,45 +761,45 @@ NIL ((|select| (#1=($ (|Mapping| #2=(|Boolean|) |#2|) $) 24 T ELT)) (|removeDuplicates| (($ $) 38 T ELT)) (|remove!| (#1# NIL T ELT) (#3=($ |#2| $) 36 T ELT)) (|remove| (#3# 34 T ELT) (#1# 18 T ELT)) (|merge!| (($ (|Mapping| #2# |#2| |#2|) $ $) NIL T ELT) (#4=($ $ $) 42 T ELT)) (|insert| (($ |#2| $ #5=(|Integer|)) 20 T ELT) (($ $ $ #5#) 22 T ELT)) (|delete| (($ $ #5#) 11 T ELT) (($ $ (|UniversalSegment| #5#)) 14 T ELT)) (|concat!| (#6=($ $ |#2|) 32 T ELT) (#4# NIL T ELT)) (|concat| (#6# 31 T ELT) (#3# NIL T ELT) (#4# 26 T ELT) (($ (|List| $)) NIL T ELT))) (((|ExtensibleLinearAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |merge!| #1=(|#1| |#1| |#1|)) (SIGNATURE |remove!| #2=(|#1| |#2| |#1|)) (SIGNATURE |merge!| (|#1| (|Mapping| #3=(|Boolean|) |#2| |#2|) |#1| |#1|)) (SIGNATURE |remove!| #4=(|#1| (|Mapping| #3# |#2|) |#1|)) (SIGNATURE |concat!| #1#) (SIGNATURE |concat!| #5=(|#1| |#1| |#2|)) (SIGNATURE |insert| (|#1| |#1| |#1| #6=(|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| #6#)) (SIGNATURE |delete| (|#1| |#1| (|UniversalSegment| #6#))) (SIGNATURE |delete| (|#1| |#1| #6#)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| #1#) (SIGNATURE |concat| #2#) (SIGNATURE |concat| #5#) (SIGNATURE |remove| #4#) (SIGNATURE |select| #4#) (SIGNATURE |remove| #2#) (SIGNATURE |removeDuplicates| (|#1| |#1|))) (|ExtensibleLinearAggregate| |#2|) (|Type|)) (T |ExtensibleLinearAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #4=(|UniversalSegment| #3#) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) 83 T ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates!| (($ $) 81 (|has| |#1| (|BasicType|)) ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) 87 T ELT) (($ |#1| $) 82 (|has| |#1| (|BasicType|)) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #8#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #5# |#1|) . #6#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #9=($)) 38 (|has| #3# . #10=((|OrderedSet|))) ELT)) (|merge!| (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) 84 T ELT) (($ $ $) 80 (|has| |#1| (|OrderedSet|)) ELT)) (|maxIndex| ((#3# . #9#) 39 (|has| #3# . #10#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 92 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #11=((|SetCategory|))) ELT)) (|insert!| (($ |#1| $ (|Integer|)) 86 T ELT) (($ $ $ (|Integer|)) 85 T ELT)) (|insert| (($ |#1| $ #3#) 57 T ELT) (($ $ $ #3#) 56 T ELT)) (|indices| (((|List| #3#) $) 41 T ELT)) (|index?| ((#12=(|Boolean|) #3# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #11#) ELT)) (|first| ((|#1| $) 37 (|has| #3# . #10#) ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #11#)) ELT)) (|eq?| ((#13=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#12# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#13# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ #4#) 66 T ELT)) (|delete!| (($ $ (|Integer|)) 89 T ELT) (($ $ (|UniversalSegment| (|Integer|))) 88 T ELT)) (|delete| (($ $ #3#) 59 T ELT) (($ $ #4#) 58 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#14=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #14#)) ELT)) (|construct| (($ (|List| |#1|)) 67 T ELT)) (|concat!| (($ $ |#1|) 91 T ELT) (($ $ $) 90 T ELT)) (|concat| (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #4=(|Integer|) #4#) 35 #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| (#6=(|#1| $ #4# |#1|) 47 #5# ELT) ((|#1| $ #7=(|UniversalSegment| #4#) |#1|) 55 #5# ELT)) (|select!| (#8=($ (|Mapping| #2# |#1|) $) 83 T ELT)) (|select| (#8# 69 #9=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#10=($) 6 T CONST)) (|removeDuplicates!| (#11=($ $) 81 #3# ELT)) (|removeDuplicates| (#11# 71 #12=(AND #3# #9#) ELT)) (|remove!| (#8# 87 T ELT) (#13=($ |#1| $) 82 #3# ELT)) (|remove| (#13# 70 #12# ELT) (#8# 68 #9# ELT)) (|qsetelt!| (#6# 48 #5# ELT)) (|qelt| (#14=(|#1| $ #4#) 46 T ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| (#15=(#4# $) 38 #16=(|has| #4# #17=(|OrderedSet|)) ELT)) (|merge!| (($ (|Mapping| #2# |#1| |#1|) $ $) 84 T ELT) (#18=($ $ $) 80 (|has| |#1| #17#) ELT)) (|maxIndex| (#15# 39 #16# ELT)) (|map!| (#19=($ (|Mapping| |#1| |#1|) $) 92 T ELT)) (|map| (#19# 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|latex| (((|String|) $) 21 #20=(|has| |#1| (|SetCategory|)) ELT)) (|insert!| (#21=($ |#1| $ #4#) 86 T ELT) (#22=($ $ $ #4#) 85 T ELT)) (|insert| (#21# 57 T ELT) (#22# 56 T ELT)) (|indices| (((|List| #4#) $) 41 T ELT)) (|index?| ((#2# #4# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 #20# ELT)) (|first| ((|#1| $) 37 #16# ELT)) (|fill!| (#23=($ $ |#1|) 36 #5# ELT)) (|eval| (($ $ (|List| #24=(|Equation| |#1|))) 25 #25=(AND (|has| |#1| (|Evalable| |#1|)) #20#) ELT) (($ $ #24#) 24 #25# ELT) (($ $ |#1| |#1|) 23 #25# ELT) (($ $ #26=(|List| |#1|) #26#) 22 #25# ELT)) (|eq?| (#1# 10 T ELT)) (|entry?| ((#2# |#1| $) 40 (AND #9# #3#) ELT)) (|entries| ((#26# $) 43 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#10# 8 T ELT)) (|elt| (#6# 45 T ELT) (#14# 44 T ELT) (#27=($ $ #7#) 66 T ELT)) (|delete!| (#28=($ $ #4#) 89 T ELT) (#27# 88 T ELT)) (|delete| (#28# 59 T ELT) (#27# 58 T ELT)) (|copy| (#11# 9 T ELT)) (|convert| ((#29=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #29#)) ELT)) (|construct| (($ #26#) 67 T ELT)) (|concat!| (#23# 91 T ELT) (#18# 90 T ELT)) (|concat| (#23# 64 T ELT) (#13# 63 T ELT) (#18# 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| ((#30=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #30#)) ELT)) (|before?| (#1# 19 #3# ELT)) (= (#1# 17 #3# ELT))) (((|ExtensibleLinearAggregate| |#1|) (|Category|) (|Type|)) (T |ExtensibleLinearAggregate|)) -((|concat!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|delete!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|remove!| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|insert!| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|ExtensibleLinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert!| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 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T)) +((|sizeLess?| #1=(*1 *2 *1 *1) (AND #2=(|ofCategory| *1 (|EuclideanDomain|)) (|isDomain| *2 (|Boolean|)))) (|euclideanSize| (*1 *2 *1) (AND #2# (|isDomain| *2 (|NonNegativeInteger|)))) (|divide| #1# (AND (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) #2#)) (|quo| #3=(*1 *1 *1 *1) #2#) (|rem| #3# #2#) (|extendedEuclidean| #1# (AND (|isDomain| *2 (|Record| #4=(|:| |coef1| *1) #5=(|:| |coef2| *1) (|:| |generator| *1))) #2#)) (|extendedEuclidean| (*1 *2 *1 *1 *1) (|partial| AND (|isDomain| *2 (|Record| #4# #5#)) #2#)) (|multiEuclidean| (*1 *2 *2 *1) (|partial| AND (|isDomain| *2 (|List| *1)) #2#))) +(|Join| (|PrincipalIdealDomain|) (CATEGORY |domain| (SIGNATURE |sizeLess?| ((|Boolean|) $ $)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) $)) (SIGNATURE |divide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |quo| #1=($ $ $)) (SIGNATURE |rem| #1#) (SIGNATURE |extendedEuclidean| ((|Record| #2=(|:| |coef1| $) #3=(|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |extendedEuclidean| ((|Union| (|Record| #2# #3#) #4="failed") $ $ $)) (SIGNATURE |multiEuclidean| ((|Union| #5=(|List| $) #4#) #5# $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|eval| (($ $ #1=(|List| |#2|) #1#) 14 T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ #2=(|Equation| |#2|)) 11 T ELT) (($ $ (|List| #2#)) NIL T ELT))) (((|Evalable&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |eval| (|#1| |#1| (|List| #1=(|Equation| |#2|)))) (SIGNATURE |eval| (|#1| |#1| #1#)) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| #2=(|List| |#2|) #2#))) (|Evalable| |#2|) (|SetCategory|)) (T |Evalable&|)) NIL -((|eval| (($ $ (|List| |#1|) (|List| |#1|)) 7 T ELT) (($ $ |#1| |#1|) 6 T ELT) (($ $ (|Equation| |#1|)) 13 T ELT) (($ $ (|List| (|Equation| |#1|))) 12 T ELT))) +((|eval| (($ $ #1=(|List| |#1|) #1#) 7 T ELT) (($ $ |#1| |#1|) 6 T ELT) (($ $ #2=(|Equation| |#1|)) 13 T ELT) (($ $ (|List| #2#)) 12 T ELT))) (((|Evalable| |#1|) (|Category|) (|SetCategory|)) (T |Evalable|)) -((|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Equation| *3)) (|ofCategory| *1 (|Evalable| *3)) (|ofCategory| *3 (|SetCategory|)))) (|eval| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Equation| *3))) (|ofCategory| *1 (|Evalable| *3)) (|ofCategory| *3 (|SetCategory|))))) -(|Join| (|InnerEvalable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |eval| ($ $ (|Equation| |t#1|))) (SIGNATURE |eval| ($ $ (|List| (|Equation| |t#1|)))))) +((|eval| #1=(*1 *1 *1 *2) (AND (|isDomain| *2 #2=(|Equation| *3)) #3=(|ofCategory| *1 (|Evalable| *3)) #4=(|ofCategory| *3 (|SetCategory|)))) (|eval| #1# (AND (|isDomain| *2 (|List| #2#)) #3# #4#))) +(|Join| (|InnerEvalable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |eval| ($ $ #1=(|Equation| |t#1|))) (SIGNATURE |eval| ($ $ (|List| #1#))))) (((|InnerEvalable| |#1| |#1|) . T)) ((|eval| ((|#1| (|Mapping| |#1| #1=(|Integer|)) (|SymmetricPolynomial| (|Fraction| #1#))) 26 T ELT))) (((|EvaluateCycleIndicators| |#1|) (CATEGORY |package| (SIGNATURE |eval| (|#1| (|Mapping| |#1| #1=(|Integer|)) (|SymmetricPolynomial| #2=(|Fraction| #1#))))) (|Algebra| #2#)) (T |EvaluateCycleIndicators|)) @@ -887,33 +887,33 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 19 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #4=(|Integer|)))) $) 21 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|size| ((#5=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| #6=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #4#) NIL T ELT)) (|nthCoef| ((#4# $ #4#) NIL T ELT)) (|min| #7=(#8=($ $ $) NIL #9=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #7#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #4# #4#) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#8# NIL (|has| #4# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#4# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #6#) (>= #10=(#2# NIL #9# ELT)) (> #10#) (= #1#) (<= #10#) (< (#2# 30 #9# ELT)) (- (($ $) 12 T ELT) (#8# 29 T ELT)) (+ (#8# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #5# $) NIL T ELT) (($ #4# $) NIL T ELT) (($ $ #4#) NIL T ELT) (($ #4# |#1|) 28 T ELT))) (((|FreeAbelianGroup| |#1|) (|Join| (|AbelianGroup|) (|Module| #1=(|Integer|)) (|FreeAbelianMonoidCategory| |#1| #1#) (CATEGORY |package| (IF (|has| |#1| #2=(|OrderedSet|)) (ATTRIBUTE #2#) |%noBranch|))) (|SetCategory|)) (T |FreeAbelianGroup|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 35 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|size| (((|NonNegativeInteger|) $) 36 T ELT)) (|sample| (#3=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 40 T ELT)) (|retract| ((|#1| $) 41 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nthFactor| ((|#1| $ (|Integer|)) 33 T ELT)) (|nthCoef| ((|#2| $ (|Integer|)) 34 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 30 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 31 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|highCommonTerms| (($ $ $) 29 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 39 T ELT)) (|coefficient| ((|#2| |#1| $) 32 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT) (($ |#1| $) 38 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ |#2| |#1|) 37 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 35 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|size| ((#3=(|NonNegativeInteger|) $) 36 T ELT)) (|sample| (#4=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 40 T ELT)) (|retract| ((|#1| $) 41 T ELT)) (|opposite?| (#1# 20 T ELT)) (|nthFactor| ((|#1| $ #5=(|Integer|)) 33 T ELT)) (|nthCoef| ((|#2| $ #5#) 34 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 30 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 31 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|highCommonTerms| (#6=($ $ $) 29 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 39 T ELT)) (|coefficient| ((|#2| |#1| $) 32 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#4# 24 T CONST)) (= (#1# 8 T ELT)) (+ (#6# 18 T ELT) (($ |#1| $) 38 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ #3# $) 21 T ELT) (($ |#2| |#1|) 37 T ELT))) (((|FreeAbelianMonoidCategory| |#1| |#2|) (|Category|) (|SetCategory|) (|CancellationAbelianMonoid|)) (T |FreeAbelianMonoidCategory|)) -((+ (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|CancellationAbelianMonoid|)))) (* (*1 *1 *2 *3) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|size| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|terms| (*1 *2 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))))) (|nthCoef| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *4 *2)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|nthFactor| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *4)) (|ofCategory| *4 (|CancellationAbelianMonoid|)) (|ofCategory| *2 (|SetCategory|)))) (|coefficient| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|CancellationAbelianMonoid|)))) (|mapCoef| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)))) (|mapGen| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|CancellationAbelianMonoid|)))) (|highCommonTerms| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|CancellationAbelianMonoid|)) (|ofCategory| *3 (|OrderedAbelianMonoid|))))) -(|Join| (|CancellationAbelianMonoid|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE + ($ |t#1| $)) (SIGNATURE * ($ |t#2| |t#1|)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |terms| ((|List| (|Record| (|:| |gen| |t#1|) (|:| |exp| |t#2|))) $)) (SIGNATURE |nthCoef| (|t#2| $ (|Integer|))) (SIGNATURE |nthFactor| (|t#1| $ (|Integer|))) (SIGNATURE |coefficient| (|t#2| |t#1| $)) (SIGNATURE |mapCoef| ($ (|Mapping| |t#2| |t#2|) $)) (SIGNATURE |mapGen| ($ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#2| (|OrderedAbelianMonoid|)) (SIGNATURE |highCommonTerms| ($ $ $)) |%noBranch|))) -(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((+ #1=(*1 *1 *2 *1) (AND #2=(|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *3)) #3=(|ofCategory| *2 #4=(|SetCategory|)) #5=(|ofCategory| *3 #6=(|CancellationAbelianMonoid|)))) (* (*1 *1 *2 *3) #7=(AND (|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *2)) #8=(|ofCategory| *3 #4#) #9=(|ofCategory| *2 #6#))) (|size| #10=(*1 *2 *1) (AND #11=(|ofCategory| *1 (|FreeAbelianMonoidCategory| *3 *4)) #8# #12=(|ofCategory| *4 #6#) (|isDomain| *2 (|NonNegativeInteger|)))) (|terms| #10# (AND #11# #8# #12# (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))))) (|nthCoef| #13=(*1 *2 *1 *3) (AND #14=(|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|FreeAbelianMonoidCategory| *4 *2)) (|ofCategory| *4 #4#) #9#)) (|nthFactor| #13# (AND #14# (|ofCategory| *1 (|FreeAbelianMonoidCategory| *2 *4)) #12# #3#)) (|coefficient| (*1 *2 *3 *1) #7#) (|mapCoef| #1# (AND (|isDomain| *2 (|Mapping| *4 *4)) #11# #8# #12#)) (|mapGen| #1# (AND (|isDomain| *2 (|Mapping| *3 *3)) #11# #8# #12#)) (|highCommonTerms| (*1 *1 *1 *1) (AND #2# #3# #5# (|ofCategory| *3 (|OrderedAbelianMonoid|))))) +(|Join| (|CancellationAbelianMonoid|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE + ($ |t#1| $)) (SIGNATURE * ($ |t#2| |t#1|)) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |terms| ((|List| (|Record| (|:| |gen| |t#1|) (|:| |exp| |t#2|))) $)) (SIGNATURE |nthCoef| (|t#2| $ #1=(|Integer|))) (SIGNATURE |nthFactor| (|t#1| $ #1#)) (SIGNATURE |coefficient| (|t#2| |t#1| $)) (SIGNATURE |mapCoef| ($ (|Mapping| |t#2| |t#2|) $)) (SIGNATURE |mapGen| ($ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#2| (|OrderedAbelianMonoid|)) (SIGNATURE |highCommonTerms| ($ $ $)) |%noBranch|))) +(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #3=(|NonNegativeInteger|)))) $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|size| ((#3# $) NIL T ELT)) (|sample| #4=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #5=(|Integer|)) NIL T ELT)) (|nthCoef| ((#3# $ #5#) NIL T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #3# #3#) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#6=($ $ $) NIL (|has| #3# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#3# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #4#) (= #1#) (+ (#6# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #3# $) NIL T ELT) (($ #3# |#1|) NIL T ELT))) (((|FreeAbelianMonoid| |#1|) (|FreeAbelianMonoidCategory| |#1| (|NonNegativeInteger|)) (|SetCategory|)) (T |FreeAbelianMonoid|)) NIL ((|primitivePart| (($ $) 72 T ELT)) (|pomopo!| (($ $ |#2| |#3| $) 14 T ELT)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) 51 T ELT)) (|ground?| (((|Boolean|) $) 42 T ELT)) (|ground| (#1=(|#2| $) 44 T ELT)) (|exquo| ((#2=(|Union| $ "failed") $ $) NIL T ELT) ((#2# $ |#2|) 64 T ELT)) (|content| (#1# 68 T ELT)) (|coefficients| (((|List| |#2|) $) 56 T ELT)) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) 37 T ELT)) (/ (($ $ |#2|) 60 T ELT))) (((|FiniteAbelianMonoidRing&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| #1=(|#2| |#1|)) (SIGNATURE |exquo| (#2=(|Union| |#1| "failed") |#1| |#2|)) (SIGNATURE |binomThmExpt| (|#1| |#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |pomopo!| (|#1| |#1| |#2| |#3| |#1|)) (SIGNATURE |mapExponents| (|#1| (|Mapping| |#3| |#3|) |#1|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |ground| #1#) (SIGNATURE |ground?| ((|Boolean|) |#1|)) (SIGNATURE |exquo| (#2# |#1| |#1|)) (SIGNATURE / (|#1| |#1| |#2|))) (|FiniteAbelianMonoidRing| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |FiniteAbelianMonoidRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 76 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=("failed")) . #8=($)) 110 (|has| |#1| . #9=((|RetractableTo| #6#))) ELT) (((|Union| #10=(|Fraction| #6#) . #7#) . #8#) 108 (|has| |#1| . #11=((|RetractableTo| #10#))) ELT) (((|Union| |#1| . #7#) . #8#) 105 T ELT)) (|retract| ((#6# . #12=($)) 109 (|has| |#1| . #9#) ELT) ((#10# . #12#) 107 (|has| 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30 T ELT) (#17# 29 T ELT)) (+ (#17# 18 T ELT)) (** (#8# 36 T ELT) (#21# 44 T ELT) (($ $ #11#) 88 T ELT)) (* (($ #9# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #11# . #37=($)) 31 T ELT) (#17# 35 T ELT) (($ $ #35#) 87 T ELT) (($ #35# . #37#) 86 T ELT) (#36# 118 T ELT) (($ |#1| . #37#) 117 T ELT))) (((|FiniteAlgebraicExtensionField| |#1|) (|Category|) (|Field|)) (T |FiniteAlgebraicExtensionField|)) -((|basis| (*1 *2) (AND (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)))) (|basis| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)))) (|minimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|definingPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|extensionDegree| (*1 *2) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|PositiveInteger|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Field|)))) (|trace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Field|)))) (|minimalPolynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *4 (|Finite|)) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)))) (|norm| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)))) (|trace| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)))) (|createNormalElement| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|normalElement| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|normal?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|Boolean|)))) (|generator| (*1 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|Field|)))) (|linearAssociatedExp| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|ofCategory| *3 (|Finite|)) (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)))) (|linearAssociatedOrder| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|linearAssociatedLog| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|linearAssociatedLog| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3))))) -(|Join| (|ExtensionField| |t#1|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |basis| ((|Vector| $) (|PositiveInteger|))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |definingPolynomial| ((|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |extensionDegree| ((|PositiveInteger|))) (SIGNATURE |degree| ((|PositiveInteger|) $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |trace| (|t#1| $)) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|FiniteFieldCategory|)) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|))) (SIGNATURE |norm| ($ $ (|PositiveInteger|))) (SIGNATURE |trace| ($ $ (|PositiveInteger|))) (SIGNATURE |createNormalElement| ($)) (SIGNATURE |normalElement| ($)) (SIGNATURE |normal?| ((|Boolean|) $)) (SIGNATURE |generator| ($)) (SIGNATURE |linearAssociatedExp| ($ $ (|SparseUnivariatePolynomial| |t#1|))) (SIGNATURE |linearAssociatedOrder| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |linearAssociatedLog| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |linearAssociatedLog| ((|Union| (|SparseUnivariatePolynomial| |t#1|) "failed") $ $))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialDomain| $) |has| |#1| (|Finite|)) ((|DifferentialRing|) |has| |#1| (|Finite|)) ((|DifferentialSpace|) |has| |#1| (|Finite|)) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|ExtensionField| |#1|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|Finite|) |has| |#1| (|Finite|)) ((|FiniteFieldCategory|) |has| |#1| (|Finite|)) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|Finite|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| |#1|) . T)) +((|basis| #1=(*1 *2) (AND #2=(|ofCategory| *3 #3=(|Field|)) #4=(|isDomain| *2 #5=(|Vector| *1)) #6=(|ofCategory| *1 (|FiniteAlgebraicExtensionField| *3)))) (|basis| #7=(*1 *2 *3) (AND #8=(|isDomain| *3 #9=(|PositiveInteger|)) #10=(|ofCategory| *4 #3#) #4# #11=(|ofCategory| *1 (|FiniteAlgebraicExtensionField| *4)))) (|coordinates| #12=(*1 *2 *1) (AND #6# #2# #13=(|isDomain| *2 (|Vector| *3)))) (|coordinates| #7# (AND (|isDomain| *3 #5#) #11# #10# (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2) (AND #13# #2# #6#)) (|minimalPolynomial| #12# #14=(AND #6# #2# #15=(|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|definingPolynomial| #1# #14#) (|extensionDegree| #1# #16=(AND #6# #2# #17=(|isDomain| *2 #9#))) (|degree| #12# #16#) (|norm| #12# #18=(AND #19=(|ofCategory| *1 (|FiniteAlgebraicExtensionField| *2)) #20=(|ofCategory| *2 #3#))) (|trace| #12# #18#) (|minimalPolynomial| (*1 *2 *1 *3) (AND #8# (|ofCategory| *4 #21=(|Finite|)) #10# (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) #11#)) (|norm| #22=(*1 *1 *1 *2) #23=(AND #17# #6# #2# #24=(|ofCategory| *3 #21#))) (|trace| #22# #23#) (|createNormalElement| #25=(*1 *1) #26=(AND #19# (|ofCategory| *2 #21#) #20#)) (|normalElement| #25# #26#) (|normal?| #12# (AND #6# #2# #24# (|isDomain| *2 (|Boolean|)))) (|generator| #25# #26#) (|linearAssociatedExp| #22# (AND #15# #24# #6# #2#)) (|linearAssociatedOrder| #12# #27=(AND #6# #2# #24# #15#)) (|linearAssociatedLog| #12# #27#) (|linearAssociatedLog| (*1 *2 *1 *1) (|partial| AND #6# #2# #24# #15#))) +(|Join| (|ExtensionField| |t#1|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |basis| (#1=(|Vector| $))) (SIGNATURE |basis| (#1# #2=(|PositiveInteger|))) (SIGNATURE |coordinates| (#3=(|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) #1#)) (SIGNATURE |represents| ($ #3#)) (SIGNATURE |minimalPolynomial| #4=(#5=(|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |definingPolynomial| (#5#)) (SIGNATURE |extensionDegree| (#2#)) (SIGNATURE |degree| (#2# $)) (SIGNATURE |norm| #6=(|t#1| $)) (SIGNATURE |trace| #6#) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|FiniteFieldCategory|)) (SIGNATURE |minimalPolynomial| ((|SparseUnivariatePolynomial| $) $ #2#)) (SIGNATURE |norm| #7=($ $ #2#)) (SIGNATURE |trace| #7#) (SIGNATURE |createNormalElement| #8=($)) (SIGNATURE |normalElement| #8#) (SIGNATURE |normal?| ((|Boolean|) $)) (SIGNATURE |generator| #8#) (SIGNATURE |linearAssociatedExp| ($ $ #5#)) (SIGNATURE |linearAssociatedOrder| #4#) (SIGNATURE |linearAssociatedLog| #4#) (SIGNATURE |linearAssociatedLog| ((|Union| #5# "failed") $ $))) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialDomain| $) |has| |#1| (|Finite|)) ((|DifferentialRing|) |has| |#1| (|Finite|)) ((|DifferentialSpace|) |has| |#1| (|Finite|)) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|ExtensionField| |#1|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))) ((|Finite|) |has| |#1| (|Finite|)) ((|FiniteFieldCategory|) |has| |#1| (|Finite|)) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|Finite|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T) ((|VectorSpace| |#1|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sin?| ((#3# $) 13 T ELT)) (|sin| (#4=($ |#1|) 10 T ELT)) (|min| #5=(($ $ $) NIL T ELT)) (|max| #5#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|cos| (#4# 12 T ELT)) (|coerce| (((|OutputForm|) $) 19 T ELT)) (|before?| #1#) (|argument| ((|#1| $) 14 T ELT)) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 21 T ELT))) (((|FourierComponent| |#1|) (|Join| #1=(|OrderedSet|) (CATEGORY |domain| (SIGNATURE |sin| #2=($ |#1|)) (SIGNATURE |cos| #2#) (SIGNATURE |sin?| ((|Boolean|) $)) (SIGNATURE |argument| (|#1| $)))) #1#) (T |FourierComponent|)) ((|sin| #1=(*1 *1 *2) #2=(AND (|isDomain| *1 (|FourierComponent| *2)) (|ofCategory| *2 #3=(|OrderedSet|)))) (|cos| #1# #2#) (|sin?| #4=(*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FourierComponent| *3)) (|ofCategory| *3 #3#))) (|argument| #4# #2#)) @@ -929,30 +929,30 @@ NIL ((|principal?| (((|Boolean|) $) 14 T ELT))) (((|FiniteDivisorCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |principal?| ((|Boolean|) |#1|))) (|FiniteDivisorCategory| |#2| |#3| |#4| |#5|) (|Field|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |FiniteDivisorCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reduce| (($ $) 36 T ELT)) (|principal?| (((|Boolean|) $) 35 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (((|Union| |#4| "failed") $) 34 T ELT)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 41 T ELT) (($ |#4|) 40 T ELT) (($ |#1| |#1|) 39 T ELT) (($ |#1| |#1| (|Integer|)) 38 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 33 T ELT)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 37 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|reduce| (#5=($ $) 36 T ELT)) (|principal?| (#3# 35 T ELT)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|ideal| ((#6=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (((|Union| |#4| "failed") $) 34 T ELT)) (|divisor| (($ #6#) 41 T ELT) (($ |#4|) 40 T ELT) (($ |#1| |#1|) 39 T ELT) (($ |#1| |#1| #7=(|Integer|)) 38 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 33 T ELT)) (|decompose| (((|Record| (|:| |id| #6#) (|:| |principalPart| |#4|)) $) 37 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#4# 24 T CONST)) (= (#1# 8 T ELT)) (- (#5# 30 T ELT) (#8=($ $ $) 29 T ELT)) (+ (#8# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ #7# $) 31 T ELT))) (((|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (|Category|) (|Field|) (|UnivariatePolynomialCategory| |t#1|) (|UnivariatePolynomialCategory| (|Fraction| |t#2|)) (|FunctionFieldCategory| |t#1| |t#2| |t#3|)) (T |FiniteDivisorCategory|)) -((|ideal| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|isDomain| *2 (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)))) (|divisor| (*1 *1 *2) (AND (|isDomain| *2 (|FractionalIdeal| 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|ideal| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)) #3=(|ofCategory| *3 #4=(|Field|)) #5=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) #6=(|ofCategory| *5 (|UnivariatePolynomialCategory| #7=(|Fraction| *4))) #8=(|ofCategory| *6 #9=(|FunctionFieldCategory| *3 *4 *5)) #10=(|isDomain| *2 #11=(|FractionalIdeal| *4 #7# *5 *6)))) (|divisor| #12=(*1 *1 *2) (AND #10# #5# #6# #8# #3# #2#)) (|divisor| #12# (AND #3# #5# #6# #13=(|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2)) #14=(|ofCategory| *2 #9#))) (|divisor| (*1 *1 *2 *2) (AND #15=(|ofCategory| *2 #4#) #16=(|ofCategory| *3 #17=(|UnivariatePolynomialCategory| *2)) #18=(|ofCategory| *4 #19=(|UnivariatePolynomialCategory| (|Fraction| *3))) #20=(|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5)) #21=(|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4)))) (|divisor| (*1 *1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) #15# (|ofCategory| *4 #17#) #6# (|ofCategory| *1 (|FiniteDivisorCategory| *2 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *2 *4 *5)))) (|decompose| #1# (AND #2# #3# #5# #6# #8# (|isDomain| *2 (|Record| (|:| |id| #11#) (|:| |principalPart| *6))))) (|reduce| (*1 *1 *1) (AND #20# #15# #16# #18# #21#)) (|principal?| #1# (AND #2# #3# #5# #6# #8# (|isDomain| *2 (|Boolean|)))) (|generator| #1# (|partial| AND #13# #3# #5# #6# #14#)) (|divisor| (*1 *1 *2 *3 *3 *3 *4) (AND (|ofCategory| *4 #4#) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 #19#) (|ofCategory| *1 (|FiniteDivisorCategory| *4 *3 *5 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *4 *3 *5))))) +(|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |ideal| (#1=(|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|) $)) (SIGNATURE |divisor| ($ #1#)) (SIGNATURE |divisor| ($ |t#4|)) (SIGNATURE |divisor| ($ |t#1| |t#1|)) (SIGNATURE |divisor| ($ |t#1| |t#1| (|Integer|))) (SIGNATURE |decompose| ((|Record| (|:| |id| #1#) (|:| |principalPart| |t#4|)) $)) (SIGNATURE |reduce| ($ $)) (SIGNATURE |principal?| ((|Boolean|) $)) (SIGNATURE |generator| ((|Union| |t#4| "failed") $)) (SIGNATURE |divisor| ($ |t#4| |t#2| |t#2| |t#2| |t#1|)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|eval| (($ $ #1=(|Symbol|) |#2|) NIL T ELT) (($ $ (|List| #1#) #2=(|List| |#2|)) 20 T ELT) (($ $ (|List| #3=(|Equation| |#2|))) 15 T ELT) (($ $ #3#) NIL T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ #2# #2#) NIL T ELT)) (|elt| (($ $ |#2|) 11 T ELT))) (((|FullyEvalableOver&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |elt| (|#1| |#1| |#2|)) (SIGNATURE |eval| (|#1| |#1| #1=(|List| |#2|) #1#)) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| #2=(|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| #2#))) (SIGNATURE |eval| (|#1| |#1| (|List| #3=(|Symbol|)) #1#)) (SIGNATURE |eval| (|#1| |#1| #3# |#2|))) (|FullyEvalableOver| |#2|) (|SetCategory|)) (T |FullyEvalableOver&|)) NIL -((|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|eval| (($ $ #1=(|Symbol|) |#1|) 17 (|has| |#1| (|InnerEvalable| #2=(|Symbol|) |#1|)) ELT) (($ $ (|List| #1#) (|List| |#1|)) 16 (|has| |#1| (|InnerEvalable| #2# |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 15 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 14 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 13 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 12 (|has| |#1| (|Evalable| |#1|)) ELT)) (|elt| (($ $ |#1|) 11 (|has| |#1| (|Eltable| |#1| |#1|)) ELT))) +((|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|eval| (($ $ #1=(|Symbol|) |#1|) 17 #2=(|has| |#1| (|InnerEvalable| #1# |#1|)) ELT) (($ $ (|List| #1#) #3=(|List| |#1|)) 16 #2# ELT) (($ $ (|List| #4=(|Equation| |#1|))) 15 #5=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ #4#) 14 #5# ELT) (($ $ |#1| |#1|) 13 #5# ELT) (($ $ #3# #3#) 12 #5# ELT)) (|elt| (($ $ |#1|) 11 (|has| |#1| (|Eltable| |#1| |#1|)) ELT))) (((|FullyEvalableOver| |#1|) (|Category|) (|SetCategory|)) (T |FullyEvalableOver|)) NIL -(|Join| (|Functorial| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|Eltable| |t#1| |t#1|)) (ATTRIBUTE (|Eltable| |t#1| $)) |%noBranch|) (IF (|has| |t#1| (|Evalable| |t#1|)) (ATTRIBUTE (|Evalable| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|InnerEvalable| (|Symbol|) |t#1|)) (ATTRIBUTE (|InnerEvalable| (|Symbol|) |t#1|)) |%noBranch|))) -(((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Join|) . T) ((|Type|) . T)) +(|Join| (|Functorial| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|Eltable| |t#1| |t#1|)) (ATTRIBUTE (|Eltable| |t#1| $)) |%noBranch|) (IF (|has| |t#1| #1=(|Evalable| |t#1|)) (ATTRIBUTE #1#) |%noBranch|) (IF (|has| |t#1| #2=(|InnerEvalable| (|Symbol|) |t#1|)) (ATTRIBUTE #2#) |%noBranch|))) +(((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Type|) . T)) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #3#) (|transcendent?| #3#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #9=((#10=(|PrimeField| |#1|) $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| #10# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #8#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| ((#16=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #18=(#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #20="failed") $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| 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ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 114 (|has| (|Fraction| |#2|) . #3=((|Field|))) ELT)) (|unitCanonical| (($ $) 115 (|has| (|Fraction| |#2|) . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 117 (|has| (|Fraction| |#2|) . #3#) ELT)) (|traceMatrix| (((|Matrix| (|Fraction| |#2|)) #5=(|Vector| $)) 62 T ELT) (((|Matrix| (|Fraction| |#2|))) 77 T ELT)) (|trace| (((|Fraction| |#2|) . #6=($)) 68 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #7=(|PositiveInteger|) #8=(|NonNegativeInteger|)) #9=(|Integer|)) 167 (|has| (|Fraction| |#2|) . #10=((|FiniteFieldCategory|))) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 134 (|has| (|Fraction| |#2|) . #3#) ELT)) (|squareFree| (#11=((|Factored| $) $) 135 (|has| (|Fraction| |#2|) . #3#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 125 (|has| (|Fraction| |#2|) . #3#) ELT)) (|size| (((|NonNegativeInteger|)) 108 (|has| (|Fraction| |#2|) . #12=((|Finite|))) ELT)) (|singularAtInfinity?| (((|Boolean|)) 242 T ELT)) (|singular?| (((|Boolean|) |#1|) 241 T ELT) (((|Boolean|) |#2|) 240 T ELT)) (|sample| (#13=($) 23 T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=("failed")) . #16=($)) 194 (|has| (|Fraction| |#2|) . #17=((|RetractableTo| #14#))) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) 192 (|has| (|Fraction| |#2|) . #19=((|RetractableTo| #18#))) ELT) (((|Union| (|Fraction| |#2|) . #15#) . #16#) 189 T ELT)) (|retract| ((#14# . #20=($)) 193 (|has| (|Fraction| |#2|) . #17#) ELT) ((#18# . #20#) 191 (|has| (|Fraction| |#2|) . #19#) ELT) (((|Fraction| |#2|) . #20#) 190 T ELT)) (|represents| (($ (|Vector| (|Fraction| |#2|)) #5#) 64 T ELT) (($ (|Vector| (|Fraction| |#2|))) 80 T ELT) (($ (|Vector| |#2|) |#2|) 224 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 173 (|has| (|Fraction| |#2|) . #10#) ELT)) (|rem| (#21=($ $ $) 129 (|has| (|Fraction| |#2|) . #3#) ELT)) (|regularRepresentation| (((|Matrix| (|Fraction| |#2|)) $ #5#) 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(((|Boolean|)) 239 T ELT)) (|ramified?| (((|Boolean|) |#1|) 238 T ELT) (((|Boolean|) |#2|) 237 T ELT)) (|quo| (#21# 128 (|has| (|Fraction| |#2|) . #3#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #28=(|List| $)) (|:| |generator| $)) #28#) 123 (|has| (|Fraction| |#2|) . #3#) ELT)) (|primitivePart| (($ $) 217 T ELT)) (|primitiveElement| (#29=($) 169 (|has| (|Fraction| |#2|) . #10#) ELT)) (|primitive?| (((|Boolean|) $) 170 (|has| (|Fraction| |#2|) . #10#) ELT)) (|primeFrobenius| (($ $ #30=(|NonNegativeInteger|)) 161 (|has| (|Fraction| |#2|) . #10#) ELT) (($ $) 160 (|has| (|Fraction| |#2|) . #10#) ELT)) (|prime?| (((|Boolean|) $) 136 (|has| (|Fraction| |#2|) . #3#) ELT)) (|order| ((#7# $) 172 (|has| (|Fraction| |#2|) . #10#) ELT) (((|OnePointCompletion| (|PositiveInteger|)) $) 158 (|has| (|Fraction| |#2|) . #10#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|numberOfComponents| (((|NonNegativeInteger|)) 249 T ELT)) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) 231 T ELT)) (|norm| (((|Fraction| |#2|) . #6#) 67 T ELT)) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) 212 (|has| |#1| (|Field|)) ELT)) (|nextItem| (((|Maybe| $) $) 162 (|has| (|Fraction| |#2|) . #10#) ELT)) (|multiEuclidean| (((|Union| #31=(|List| $) #32="failed") #31# $) 132 (|has| (|Fraction| |#2|) . #3#) ELT)) (|minimalPolynomial| ((|#3| . #33=($)) 60 (|has| (|Fraction| |#2|) (|Field|)) ELT)) (|lookup| ((#34=(|PositiveInteger|) $) 110 (|has| (|Fraction| |#2|) . #12#) ELT)) (|lift| ((|#3| $) 176 T ELT)) (|leftReducedSystem| (((|Matrix| #22#) . #35=(#27#)) 188 (|has| (|Fraction| |#2|) . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| #22#)) (|:| |vec| (|Vector| #22#))) . #36=(#27# $)) 187 (|has| (|Fraction| |#2|) . #25#) ELT) (((|Record| (|:| |mat| (|Matrix| (|Fraction| |#2|))) (|:| |vec| (|Vector| (|Fraction| |#2|)))) . #36#) 182 T ELT) (((|Matrix| (|Fraction| |#2|)) . #35#) 181 T ELT)) (|lcm| (#37=($ (|List| $)) 121 (|has| (|Fraction| |#2|) . #3#) ELT) (#38=($ $ $) 120 (|has| (|Fraction| |#2|) . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 226 T ELT)) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) 228 T ELT)) (|inv| (($ $) 137 (|has| (|Fraction| |#2|) . #3#) ELT)) (|integralRepresents| (($ (|Vector| |#2|) |#2|) 222 T ELT)) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) 227 T ELT)) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) 229 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) 221 T ELT)) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) 223 T ELT)) (|integralBasisAtInfinity| (((|Vector| $)) 235 T ELT)) (|integralBasis| (((|Vector| $)) 236 T ELT)) (|integralAtInfinity?| (((|Boolean|) $) 234 T ELT)) (|integral?| (((|Boolean|) $) 233 T ELT) (((|Boolean|) $ |#1|) 220 T ELT) (((|Boolean|) $ |#2|) 219 T ELT)) (|init| (($) 163 (|has| (|Fraction| |#2|) . #10#) CONST)) (|index| (($ #34#) 109 (|has| (|Fraction| |#2|) . #12#) ELT)) (|hyperelliptic| (((|Union| |#2| "failed")) 214 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|genus| (((|NonNegativeInteger|)) 248 T ELT)) (|generator| (($) 180 T ELT)) (|gcdPolynomial| ((#39=(|SparseUnivariatePolynomial| $) #39# #39#) 122 (|has| (|Fraction| |#2|) . #3#) ELT)) (|gcd| (#37# 119 (|has| (|Fraction| |#2|) . #3#) ELT) (#38# 118 (|has| (|Fraction| |#2|) . #3#) ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #9#) (|:| |exponent| #9#)))) 166 (|has| (|Fraction| |#2|) . #10#) ELT)) (|factor| (#11# 133 (|has| (|Fraction| |#2|) . #3#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $)) #32#) $ $ $) 131 (|has| (|Fraction| |#2|) . #3#) ELT) (((|Record| #40# #41# (|:| |generator| $)) $ $) 130 (|has| (|Fraction| |#2|) . #3#) ELT)) (|exquo| (((|Union| $ "failed") $ $) 113 (|has| (|Fraction| |#2|) . #3#) ELT)) 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#44=((|DifferentialSpace|)))) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #45=((|DifferentialRing|)))) (|and| (|has| (|Fraction| |#2|) . #44#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ . #46=($)) 154 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #44#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #45#)) (|and| (|has| (|Fraction| |#2|) . #44#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ $ (|List| #47=(|Symbol|)) . #48=((|List| #49=(|NonNegativeInteger|)))) 150 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50=((|PartialDifferentialSpace| #47#)))) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51=((|PartialDifferentialRing| (|Symbol|))))) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #47# . #52=(#49#)) 149 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ (|List| #47#)) 148 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #47#) 146 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT)) (|derivationCoordinates| (((|Matrix| (|Fraction| |#2|)) (|Vector| $) (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 174 (|has| (|Fraction| |#2|) . #3#) ELT)) (|definingPolynomial| ((|#3|) 179 T ELT)) (|createPrimitiveElement| (#29# 168 (|has| (|Fraction| |#2|) . #10#) ELT)) (|coordinates| (((|Vector| (|Fraction| |#2|)) $ #5#) 66 T ELT) (((|Matrix| (|Fraction| |#2|)) #5# #5#) 65 T ELT) (((|Vector| (|Fraction| |#2|)) . #53=($)) 82 T ELT) (((|Matrix| (|Fraction| |#2|)) #54=(|Vector| $)) 81 T ELT)) (|convert| (((|Vector| (|Fraction| |#2|)) . #53#) 79 T ELT) (($ (|Vector| (|Fraction| |#2|))) 78 T ELT) ((|#3| $) 195 T ELT) (($ |#3|) 177 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 165 (|has| (|Fraction| |#2|) . #10#) ELT)) (|complementaryBasis| (((|Vector| $) (|Vector| $)) 232 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ (|Fraction| |#2|)) 53 T ELT) (($ #55=(|Fraction| #56=(|Integer|))) 107 (OR (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #19#)) ELT) (($ $) 112 (|has| (|Fraction| |#2|) . #3#) ELT)) (|charthRoot| (($ $) 164 (|has| (|Fraction| |#2|) . #10#) ELT) (((|Maybe| $) $) 59 (|has| (|Fraction| |#2|) (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#3| . #33#) 61 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|branchPointAtInfinity?| (((|Boolean|)) 245 T ELT)) (|branchPoint?| (((|Boolean|) |#1|) 244 T ELT) (((|Boolean|) |#2|) 243 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| ((#54#) 83 T ELT)) (|associates?| ((#4# $ $) 116 (|has| (|Fraction| |#2|) . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) 213 T ELT)) (|absolutelyIrreducible?| (((|Boolean|)) 247 T ELT)) (|Zero| (#13# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 143 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) . #42#) 142 (|has| (|Fraction| |#2|) . #3#) ELT) (#43# 157 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #44#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #45#)) (|and| (|has| (|Fraction| |#2|) . #44#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ . #46#) 155 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #44#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #45#)) (|and| (|has| (|Fraction| |#2|) . #44#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ $ (|List| #47#) . #48#) 153 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #47# . #52#) 152 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ (|List| #47#)) 151 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #47#) 147 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51#)) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 141 (|has| (|Fraction| |#2|) . #3#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #56#) 138 (|has| (|Fraction| |#2|) . #3#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #57=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ (|Fraction| |#2|)) 55 T ELT) (($ (|Fraction| |#2|) . #57#) 54 T ELT) (($ #55# . #57#) 140 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ #55#) 139 (|has| (|Fraction| |#2|) . #3#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|yCoordinates| (#4=((|Record| (|:| |num| #5=(|Vector| |#2|)) #6=(|:| |den| |#2|)) $) 225 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 114 #7=(|has| #8=(|Fraction| |#2|) #9=(|Field|)) ELT)) (|unitCanonical| (#10=($ $) 115 #7# ELT)) (|unit?| (#3# 117 #7# ELT)) (|traceMatrix| (#11=(#12=(|Matrix| #8#) #13=(|Vector| $)) 62 T ELT) (#14=(#12#) 77 T ELT)) (|trace| (#15=(#8# $) 68 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #16=(|PositiveInteger|) #17=(|NonNegativeInteger|)) #18=(|Integer|)) 167 #19=(|has| #8# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| ((#20=(|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (#10# 134 #7# ELT)) (|squareFree| (#21=((|Factored| $) $) 135 #7# ELT)) (|sizeLess?| (#1# 125 #7# ELT)) (|size| (#22=(#17#) 108 #23=(|has| #8# #24=(|Finite|)) ELT)) (|singularAtInfinity?| (#25=(#2#) 242 T ELT)) (|singular?| (#26=(#2# |#1|) 241 T ELT) (#27=(#2# |#2|) 240 T ELT)) (|sample| (#28=($) 23 T CONST)) (|retractIfCan| (((|Union| #18# . #29=(#30="failed")) . #31=($)) 194 #32=(|has| #8# (|RetractableTo| #18#)) ELT) (((|Union| #33=(|Fraction| #18#) . #29#) . #31#) 192 #34=(|has| #8# (|RetractableTo| #33#)) ELT) (((|Union| #8# . #29#) . #31#) 189 T ELT)) (|retract| ((#18# . #35=($)) 193 #32# ELT) ((#33# . #35#) 191 #34# ELT) (#15# 190 T ELT)) (|represents| (($ #36=(|Vector| #8#) #13#) 64 T ELT) (#37=($ #36#) 80 T ELT) (#38=($ #5# |#2|) 224 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 173 #19# ELT)) (|rem| (#39=($ $ $) 129 #7# ELT)) (|regularRepresentation| ((#12# $ #13#) 69 T ELT) ((#12# $) 75 T ELT)) (|reducedSystem| ((#40=(|Matrix| #18#) . #41=(#42=(|Matrix| $))) 186 #43=(|has| #8# (|LinearlyExplicitRingOver| #18#)) ELT) ((#44=(|Record| (|:| |mat| #40#) (|:| |vec| (|Vector| #18#))) . #45=(#42# #13#)) 185 #43# ELT) ((#46=(|Record| (|:| |mat| #12#) (|:| |vec| #36#)) . #45#) 184 T ELT) ((#12# . #41#) 183 T ELT)) (|reduceBasisAtInfinity| (#47=(#13# #13#) 230 T ELT)) (|reduce| (#48=($ |#3|) 178 T ELT) ((#49=(|Union| $ #30#) (|Fraction| |#3|)) 175 #7# ELT)) (|recip| ((#49# $) 43 T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) 211 (|has| |#1| #24#) ELT)) (|rationalPoint?| ((#2# |#1| |#1|) 246 T ELT)) (|rank| ((#16#) 70 T ELT)) (|random| (#28# 111 #23# ELT)) (|ramifiedAtInfinity?| (#25# 239 T ELT)) (|ramified?| (#26# 238 T ELT) (#27# 237 T ELT)) (|quo| (#39# 128 #7# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #50=(|List| $)) #51=(|:| |generator| $)) #50#) 123 #7# ELT)) (|primitivePart| (#10# 217 T ELT)) (|primitiveElement| (#28# 169 #19# ELT)) (|primitive?| (#3# 170 #19# ELT)) (|primeFrobenius| (#52=($ $ #17#) 161 #19# ELT) (#10# 160 #19# ELT)) (|prime?| (#3# 136 #7# ELT)) (|order| (#53=(#16# $) 172 #19# ELT) (((|OnePointCompletion| #16#) $) 158 #19# ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|numberOfComponents| (#22# 249 T ELT)) (|normalizeAtInfinity| (#47# 231 T ELT)) (|norm| (#15# 67 T ELT)) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #54=(|Symbol|)) 212 (|has| |#1| #9#) ELT)) (|nextItem| (#55=(#20# $) 162 #19# ELT)) (|multiEuclidean| (((|Union| #50# #30#) #50# $) 132 #7# ELT)) (|minimalPolynomial| (#56=(|#3| $) 60 #7# ELT)) (|lookup| (#53# 110 #23# ELT)) (|lift| (#56# 176 T ELT)) (|leftReducedSystem| ((#40# #13#) 188 #43# ELT) ((#44# . #57=(#13# $)) 187 #43# ELT) ((#46# . #57#) 182 T ELT) (#11# 181 T ELT)) (|lcm| (#58=($ #50#) 121 #7# ELT) (#39# 120 #7# ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inverseIntegralMatrixAtInfinity| (#14# 226 T ELT)) (|inverseIntegralMatrix| (#14# 228 T ELT)) (|inv| (#10# 137 #7# ELT)) (|integralRepresents| (#38# 222 T ELT)) (|integralMatrixAtInfinity| (#14# 227 T ELT)) (|integralMatrix| (#14# 229 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #6#) #59=(|Mapping| |#2| |#2|)) 221 T ELT)) (|integralCoordinates| (#4# 223 T ELT)) (|integralBasisAtInfinity| (#60=(#13#) 235 T ELT)) (|integralBasis| (#60# 236 T ELT)) (|integralAtInfinity?| (#3# 234 T ELT)) (|integral?| (#3# 233 T ELT) ((#2# $ |#1|) 220 T ELT) ((#2# $ |#2|) 219 T ELT)) (|init| (#28# 163 #19# CONST)) (|index| (($ #16#) 109 #23# ELT)) (|hyperelliptic| (#61=((|Union| |#2| #30#)) 214 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|genus| (#22# 248 T ELT)) (|generator| (#28# 180 T ELT)) (|gcdPolynomial| ((#62=(|SparseUnivariatePolynomial| $) #62# #62#) 122 #7# ELT)) (|gcd| (#58# 119 #7# ELT) (#39# 118 #7# ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #18#) (|:| |exponent| #18#)))) 166 #19# ELT)) (|factor| (#21# 133 #7# ELT)) (|extendedEuclidean| (((|Union| (|Record| #63=(|:| |coef1| $) #64=(|:| |coef2| $)) #30#) $ $ $) 131 #7# ELT) (((|Record| #63# #64# #51#) $ $) 130 #7# ELT)) (|exquo| ((#49# $ $) 113 #7# ELT)) (|expressIdealMember| (((|Maybe| #50#) #50# $) 124 #7# ELT)) (|euclideanSize| (#65=(#17# $) 126 #7# ELT)) (|elt| ((|#1| $ |#1| |#1|) 216 T ELT)) (|elliptic| (#61# 215 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 127 #7# ELT)) (|discriminant| ((#8# #13#) 63 T ELT) ((#8#) 76 T ELT)) (|discreteLog| (#65# 171 #19# ELT) (((|Union| #17# #30#) $ $) 159 #19# ELT)) (|differentiate| (#66=($ $ #67=(|Mapping| #8# #8#)) 145 #7# ELT) (#68=($ $ #67# #17#) 144 #7# ELT) (($ $ #59#) 218 T ELT) (#52# 156 #69=(OR (|and| #7# #70=(|has| #8# (|DifferentialSpace|))) (|and| #7# (|has| #8# (|DifferentialRing|))) (|and| #70# #7#) #19#) ELT) (#10# 154 #69# ELT) (#71=($ $ #72=(|List| #54#) (|List| #17#)) 150 #73=(OR (|and| #7# #74=(|has| #8# (|PartialDifferentialSpace| #54#))) (|and| #7# (|has| #8# (|PartialDifferentialRing| #54#))) (|and| #74# #7#)) ELT) (#75=($ $ #54# #17#) 149 #73# ELT) (#76=($ $ #72#) 148 #73# ELT) (#77=($ $ #54#) 146 #73# ELT)) (|derivationCoordinates| ((#12# #13# #67#) 174 #7# ELT)) (|definingPolynomial| ((|#3|) 179 T ELT)) (|createPrimitiveElement| (#28# 168 #19# ELT)) (|coordinates| ((#36# $ #13#) 66 T ELT) ((#12# #13# #13#) 65 T ELT) (#78=(#36# $) 82 T ELT) (#11# 81 T ELT)) (|convert| (#78# 79 T ELT) (#37# 78 T ELT) (#56# 195 T ELT) (#48# 177 T ELT)) (|conditionP| (((|Union| #13# #30#) #42#) 165 #19# ELT)) (|complementaryBasis| (#47# 232 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #18#) 42 T ELT) (($ #8#) 53 T ELT) (($ #33#) 107 (OR #7# #34#) ELT) (#10# 112 #7# ELT)) (|charthRoot| (#10# 164 #19# ELT) (#55# 59 (|has| #8# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| (#56# 61 T ELT)) (|characteristic| (#22# 41 T CONST)) (|branchPointAtInfinity?| (#25# 245 T ELT)) (|branchPoint?| (#26# 244 T ELT) (#27# 243 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| (#60# 83 T ELT)) (|associates?| (#1# 116 #7# ELT)) (|annihilate?| (#1# 34 T ELT)) (|algSplitSimple| (((|Record| (|:| |num| $) #6# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #59#) 213 T ELT)) (|absolutelyIrreducible?| (#25# 247 T ELT)) (|Zero| (#28# 24 T CONST)) (|One| (#28# 46 T CONST)) (D (#66# 143 #7# ELT) (#68# 142 #7# ELT) (#52# 157 #69# ELT) (#10# 155 #69# ELT) (#71# 153 #73# ELT) (#75# 152 #73# ELT) (#76# 151 #73# ELT) (#77# 147 #73# ELT)) (= (#1# 8 T ELT)) (/ (#39# 141 #7# ELT)) (- (#10# 30 T ELT) (#39# 29 T ELT)) (+ (#39# 18 T ELT)) (** (($ $ #16#) 36 T ELT) (#52# 44 T ELT) (($ $ #18#) 138 #7# ELT)) (* (($ #16# $) 17 T ELT) (($ #17# $) 21 T ELT) (($ #18# . #79=($)) 31 T ELT) (#39# 35 T ELT) (($ $ #8#) 55 T ELT) (($ #8# . #79#) 54 T ELT) (($ #33# . #79#) 140 #7# ELT) (($ $ #33#) 139 #7# ELT))) (((|FunctionFieldCategory| |#1| |#2| |#3|) (|Category|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |t#1|) (|UnivariatePolynomialCategory| (|Fraction| |t#2|))) (T |FunctionFieldCategory|)) -((|numberOfComponents| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|NonNegativeInteger|)))) (|genus| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|NonNegativeInteger|)))) (|absolutelyIrreducible?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|rationalPoint?| (*1 *2 *3 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPointAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPoint?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|branchPoint?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|singularAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|singular?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|singular?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|ramifiedAtInfinity?| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|ramified?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|ramified?| (*1 *2 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|integralBasis| (*1 *2) (AND (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)))) (|integralBasisAtInfinity| (*1 *2) (AND (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)))) (|integralAtInfinity?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|integral?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Boolean|)))) (|complementaryBasis| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|normalizeAtInfinity| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|reduceBasisAtInfinity| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|integralMatrix| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| (|Fraction| *4))))) (|inverseIntegralMatrix| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Matrix| 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|integralBasisAtInfinity| ((|Vector| $))) (SIGNATURE |integralAtInfinity?| ((|Boolean|) $)) (SIGNATURE |integral?| ((|Boolean|) $)) (SIGNATURE |complementaryBasis| ((|Vector| $) (|Vector| $))) (SIGNATURE |normalizeAtInfinity| ((|Vector| $) (|Vector| $))) (SIGNATURE |reduceBasisAtInfinity| ((|Vector| $) (|Vector| $))) (SIGNATURE |integralMatrix| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |inverseIntegralMatrix| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |integralMatrixAtInfinity| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |inverseIntegralMatrixAtInfinity| ((|Matrix| (|Fraction| |t#2|)))) (SIGNATURE |yCoordinates| ((|Record| (|:| |num| (|Vector| |t#2|)) (|:| |den| |t#2|)) $)) (SIGNATURE |represents| ($ (|Vector| |t#2|) |t#2|)) (SIGNATURE |integralCoordinates| ((|Record| (|:| |num| (|Vector| |t#2|)) (|:| |den| |t#2|)) $)) (SIGNATURE |integralRepresents| ($ (|Vector| |t#2|) |t#2|)) (SIGNATURE |integralDerivationMatrix| ((|Record| (|:| |num| (|Matrix| |t#2|)) (|:| |den| |t#2|)) 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Algebra| #2=(|Fraction| |#2|)) . T) ((|Algebra| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|BasicType|) . T) ((|BiModule| #1# #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|BiModule| #2# #2#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| (|Fraction| |#2|) (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))) (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#3|) . T) ((|DifferentialDomain| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (AND (|has| (|Fraction| |#2|) (|DifferentialSpace|)) (|has| (|Fraction| |#2|) (|Field|))) (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|)))) ((|DifferentialExtension| #2#) |has| (|Fraction| |#2|) (|Field|)) ((|DifferentialRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|)))) ((|DifferentialSpace|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (AND (|has| (|Fraction| |#2|) (|DifferentialSpace|)) (|has| (|Fraction| |#2|) (|Field|))) (AND (|has| (|Fraction| |#2|) (|DifferentialRing|)) (|has| (|Fraction| |#2|) (|Field|)))) ((|DifferentialSpaceExtension| #2#) |has| (|Fraction| |#2|) (|Field|)) ((|DivisionRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|EntireRing|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|EuclideanDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Field|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|FieldOfPrimeCharacteristic|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|Finite|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Finite|))) ((|FiniteFieldCategory|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| #2# |#3|) . T) ((|FramedAlgebra| #2# |#3|) . T) ((|FullyLinearlyExplicitRingOver| #2#) . T) ((|FullyRetractableTo| #2#) . T) ((|GcdDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|IntegralDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LeftModule| #2#) . T) ((|LeftModule| #3=(|Integer|)) |has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| $) . T) ((|LinearSet| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LinearSet| #2#) . T) ((|LinearSet| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|LinearlyExplicitRingOver| #2#) . T) ((|LinearlyExplicitRingOver| #3#) |has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|))) ((|Module| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|Module| #2#) . T) ((|Module| $) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|MonogenicAlgebra| #2# |#3|) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialSpace| #4#) OR (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| (|Fraction| |#2|) (|Field|)) (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))))) ((|PrincipalIdealDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) . T) ((|RetractableTo| (|Integer|)) |has| (|Fraction| |#2|) (|RetractableTo| (|Integer|))) ((|RightLinearSet| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|RightLinearSet| #2#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|))) ((|RightModule| #2#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| (|Fraction| |#2|) (|FiniteFieldCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (|has| (|Fraction| |#2|) (|FiniteFieldCategory|)) (|has| (|Fraction| |#2|) (|Field|)))) +((|numberOfComponents| #1=(*1 *2) #2=(AND #3=(|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) #4=(|ofCategory| *3 #5=(|UniqueFactorizationDomain|)) #6=(|ofCategory| *4 #7=(|UnivariatePolynomialCategory| *3)) #8=(|ofCategory| *5 (|UnivariatePolynomialCategory| #9=(|Fraction| *4))) (|isDomain| *2 (|NonNegativeInteger|)))) (|genus| #1# #2#) (|absolutelyIrreducible?| #1# #10=(AND #3# #4# #6# #8# #11=(|isDomain| *2 (|Boolean|)))) (|rationalPoint?| (*1 *2 *3 *3) #10#) (|branchPointAtInfinity?| #1# #10#) (|branchPoint?| #12=(*1 *2 *3) #10#) (|branchPoint?| #12# #13=(AND #14=(|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) #15=(|ofCategory| *4 #5#) #16=(|ofCategory| *3 #17=(|UnivariatePolynomialCategory| *4)) #18=(|ofCategory| *5 #19=(|UnivariatePolynomialCategory| (|Fraction| *3))) #11#)) (|singularAtInfinity?| #1# #10#) (|singular?| #12# #10#) (|singular?| 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(|FunctionFieldCategory| *4 *5 *6)) #15# #31=(|ofCategory| *5 #17#) #32=(|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Record| (|:| |num| (|Matrix| *5)) #33=(|:| |den| *5))))) (|integral?| #34=(*1 *2 *1 *3) #10#) (|integral?| #34# #13#) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *4 *4)) #3# #4# #6# #8#)) (|primitivePart| (*1 *1 *1) #35=(AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4)) (|ofCategory| *2 #5#) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 #19#))) (|elt| (*1 *2 *1 *2 *2) #35#) (|elliptic| #1# #36=(|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4)) #4# (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 #7#))) (|hyperelliptic| #1# #36#) (|algSplitSimple| #34# (AND #29# #31# #15# #32# (|isDomain| *2 (|Record| (|:| |num| *1) #33# (|:| |derivden| *5) (|:| |gd| *5))) #30#)) (|nonSingularModel| #12# (AND (|isDomain| *3 (|Symbol|)) #30# #15# #31# #32# (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|rationalPoints| #1# (AND #3# #4# #6# #8# (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|List| (|List| *3)))))) +(|Join| (|MonogenicAlgebra| #1=(|Fraction| |t#2|) |t#3|) (CATEGORY |domain| (SIGNATURE |numberOfComponents| #2=((|NonNegativeInteger|))) (SIGNATURE |genus| #2#) (SIGNATURE |absolutelyIrreducible?| #3=(#4=(|Boolean|))) (SIGNATURE |rationalPoint?| (#4# |t#1| |t#1|)) (SIGNATURE |branchPointAtInfinity?| #3#) (SIGNATURE |branchPoint?| #5=(#4# |t#1|)) (SIGNATURE |branchPoint?| #6=(#4# |t#2|)) (SIGNATURE |singularAtInfinity?| #3#) (SIGNATURE |singular?| #5#) (SIGNATURE |singular?| #6#) (SIGNATURE |ramifiedAtInfinity?| #3#) (SIGNATURE |ramified?| #5#) (SIGNATURE |ramified?| #6#) (SIGNATURE |integralBasis| #7=(#8=(|Vector| $))) (SIGNATURE |integralBasisAtInfinity| #7#) (SIGNATURE |integralAtInfinity?| #9=(#4# $)) (SIGNATURE |integral?| #9#) (SIGNATURE |complementaryBasis| #10=(#8# #8#)) (SIGNATURE |normalizeAtInfinity| #10#) (SIGNATURE |reduceBasisAtInfinity| #10#) (SIGNATURE |integralMatrix| #11=((|Matrix| #1#))) (SIGNATURE |inverseIntegralMatrix| #11#) (SIGNATURE |integralMatrixAtInfinity| #11#) (SIGNATURE |inverseIntegralMatrixAtInfinity| #11#) (SIGNATURE |yCoordinates| #12=((|Record| (|:| |num| #13=(|Vector| |t#2|)) #14=(|:| |den| |t#2|)) $)) (SIGNATURE |represents| #15=($ #13# |t#2|)) (SIGNATURE |integralCoordinates| #12#) (SIGNATURE |integralRepresents| #15#) (SIGNATURE |integralDerivationMatrix| ((|Record| (|:| |num| (|Matrix| |t#2|)) #14#) #16=(|Mapping| |t#2| |t#2|))) (SIGNATURE |integral?| (#4# $ |t#1|)) (SIGNATURE |integral?| (#4# $ |t#2|)) (SIGNATURE |differentiate| ($ $ #16#)) (SIGNATURE |primitivePart| ($ $)) (SIGNATURE |elt| (|t#1| $ |t#1| |t#1|)) (SIGNATURE |elliptic| #17=((|Union| |t#2| "failed"))) (SIGNATURE |hyperelliptic| #17#) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| $) #14# (|:| |derivden| |t#2|) (|:| |gd| |t#2|)) $ #16#)) (IF (|has| |t#1| (|Field|)) (SIGNATURE |nonSingularModel| ((|List| (|Polynomial| |t#1|)) (|Symbol|))) |%noBranch|) (IF (|has| |t#1| (|Finite|)) (SIGNATURE |rationalPoints| ((|List| (|List| |t#1|)))) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| #3=(|Fraction| |#2|)) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| #3# #3#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| (|Fraction| |#2|) (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| (|Fraction| |#2|) (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #3#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#3|) . T) ((|DifferentialDomain| $) |has| (|Fraction| |#2|) (|DifferentialSpace|)) ((|DifferentialExtension| #3#) . T) ((|DifferentialRing|) |has| (|Fraction| |#2|) (|DifferentialRing|)) ((|DifferentialSpace|) |has| (|Fraction| |#2|) (|DifferentialSpace|)) ((|DifferentialSpaceExtension| #3#) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FiniteRankAlgebra| #3# |#3|) . T) ((|FramedAlgebra| #3# |#3|) . T) ((|FullyLinearlyExplicitRingOver| #3#) . T) ((|FullyRetractableTo| #3#) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #3#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #3#) . T) ((|LeftModule| #2#) |has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| #3#) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #3#) . T) ((|LinearlyExplicitRingOver| #2#) |has| (|Fraction| |#2|) (|LinearlyExplicitRingOver| (|Integer|))) ((|Module| #1#) . T) ((|Module| #3#) . T) ((|Module| $) . T) ((|MonogenicAlgebra| #3# |#3|) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialRing| #4#) |has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) OR (|has| (|Fraction| |#2|) (|PartialDifferentialRing| (|Symbol|))) (|has| (|Fraction| |#2|) (|PartialDifferentialSpace| (|Symbol|)))) ((|PrincipalIdealDomain|) . T) ((|RetractableTo| #1#) |has| (|Fraction| |#2|) (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #3#) . T) ((|RetractableTo| #2#) |has| (|Fraction| |#2|) (|RetractableTo| (|Integer|))) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| #3#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| #3#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) 19 T ELT))) (((|FunctionFieldCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|))) #1=(|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) #1# (|UnivariatePolynomialCategory| |#5|) (|UnivariatePolynomialCategory| (|Fraction| |#6|)) (|FunctionFieldCategory| |#5| |#6| |#7|)) (T |FunctionFieldCategoryFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *8 *5)) (|ofCategory| *5 #1=(|UniqueFactorizationDomain|)) (|ofCategory| *8 #1#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *9 (|UnivariatePolynomialCategory| *8)) (|ofCategory| *2 (|FunctionFieldCategory| *8 *9 *10)) (|isDomain| *1 (|FunctionFieldCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2)) (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *10 (|UnivariatePolynomialCategory| (|Fraction| *9)))))) @@ -974,11 +974,11 @@ NIL ((|primitive?| (((|Boolean|) $) 65 T ELT)) (|order| (((|OnePointCompletion| #1=(|PositiveInteger|)) $) 26 T ELT) ((#1# $) 69 T ELT)) (|nextItem| (#2=((|Maybe| $) $) 21 T ELT)) (|init| (#3=($) 9 T CONST)) (|gcdPolynomial| ((#4=(|SparseUnivariatePolynomial| $) #4# #4#) 120 T ELT)) (|discreteLog| (((|Union| #5=(|NonNegativeInteger|) #6="failed") $ $) 98 T ELT) ((#5# $) 84 T ELT)) (|differentiate| (#7=($ $) 8 T ELT) (($ $ #5#) NIL T ELT)) (|createPrimitiveElement| (#3# 58 T ELT)) (|conditionP| (((|Union| (|Vector| $) #6#) (|Matrix| $)) 41 T ELT)) (|charthRoot| (#2# 50 T ELT) (#7# 47 T ELT))) (((|FiniteFieldCategory&| |#1|) (CATEGORY |package| (SIGNATURE |order| (#1=(|PositiveInteger|) |#1|)) (SIGNATURE |discreteLog| (#2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |primitive?| ((|Boolean|) |#1|)) (SIGNATURE |createPrimitiveElement| #3=(|#1|)) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) #4="failed") (|Matrix| |#1|))) (SIGNATURE |charthRoot| #5=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2#)) (SIGNATURE |differentiate| #5#) (SIGNATURE |init| #3# |constant|) (SIGNATURE |nextItem| #6=((|Maybe| |#1|) |#1|)) (SIGNATURE |discreteLog| ((|Union| #2# #4#) |#1| |#1|)) (SIGNATURE |order| ((|OnePointCompletion| #1#) |#1|)) (SIGNATURE |charthRoot| #6#) (SIGNATURE |gcdPolynomial| (#7=(|SparseUnivariatePolynomial| |#1|) #7# #7#))) (|FiniteFieldCategory|)) (T |FiniteFieldCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 113 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|size| (((|NonNegativeInteger|)) 123 T ELT)) (|sample| (#5=($) 23 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 107 T ELT)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|random| (($) 126 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|primitiveElement| (($) 111 T ELT)) (|primitive?| (((|Boolean|) $) 110 T ELT)) (|primeFrobenius| (($ $) 98 T ELT) (($ $ #8=(|NonNegativeInteger|)) 97 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 100 T ELT) (((|PositiveInteger|) $) 108 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nextItem| (((|Maybe| $) $) 122 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 69 T ELT)) (|lookup| ((#11=(|PositiveInteger|) $) 125 T ELT)) (|lcm| (#12=($ $ $) 61 T ELT) (#13=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|init| (($) 121 T CONST)) (|index| (($ #11#) 124 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) 59 T ELT)) (|gcd| (#12# 63 T ELT) (#13# 62 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 114 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #15# #16#) #10#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 99 T ELT) (((|NonNegativeInteger|) $) 109 T ELT)) (|differentiate| (($ . #17=($)) 120 T ELT) (#18=($ $ (|NonNegativeInteger|)) 118 T ELT)) (|createPrimitiveElement| (($) 112 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 115 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #19=(|Fraction| #20=(|Integer|))) 85 T ELT)) (|charthRoot| (((|Maybe| $) $) 101 T ELT) (($ $) 116 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ . #17#) 119 T ELT) (#18# 117 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #20#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #21=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #19#) 87 T ELT) (($ #19# . #21#) 86 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #5=(|PositiveInteger|) #6=(|NonNegativeInteger|)) #7=(|Integer|)) 113 T ELT)) (|subtractIfCan| ((#8=(|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (#4# 92 T ELT)) (|squareFree| (#9=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (#1# 76 T ELT)) (|size| (#10=(#6#) 123 T ELT)) (|sample| (#11=($) 23 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 107 T ELT)) (|rem| (#12=($ $ $) 72 T ELT)) (|recip| ((#13=(|Union| $ #14="failed") $) 43 T ELT)) (|random| (#11# 126 T ELT)) (|quo| (#12# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) 67 T ELT)) (|primitiveElement| (#11# 111 T ELT)) (|primitive?| (#3# 110 T ELT)) (|primeFrobenius| (#4# 98 T ELT) (#17=($ $ #6#) 97 T ELT)) (|prime?| (#3# 90 T ELT)) (|order| (((|OnePointCompletion| #5#) $) 100 T ELT) (#18=(#5# $) 108 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|nextItem| (#19=(#8# $) 122 T ELT)) (|multiEuclidean| (((|Union| #15# #14#) #15# $) 69 T ELT)) (|lookup| (#18# 125 T ELT)) (|lcm| (#12# 61 T ELT) (#20=($ #15#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#4# 89 T ELT)) (|init| (#11# 121 T CONST)) (|index| (($ #5#) 124 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#21=(|SparseUnivariatePolynomial| $) #21# #21#) 59 T ELT)) (|gcd| (#12# 63 T ELT) (#20# 62 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #7#) (|:| |exponent| #7#)))) 114 T ELT)) (|factor| (#9# 93 T ELT)) (|extendedEuclidean| (((|Record| #22=(|:| |coef1| $) #23=(|:| |coef2| $) #16#) $ $) 71 T ELT) (((|Union| (|Record| #22# #23#) #14#) $ $ $) 70 T ELT)) (|exquo| ((#13# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #15#) #15# $) 66 T ELT)) (|euclideanSize| (#24=(#6# $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| #6# #14#) $ $) 99 T ELT) (#24# 109 T ELT)) (|differentiate| (#4# 120 T ELT) (#17# 118 T ELT)) (|createPrimitiveElement| (#11# 112 T ELT)) (|conditionP| (((|Union| (|Vector| $) #14#) (|Matrix| $)) 115 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #7#) 42 T ELT) (#4# 58 T ELT) (($ #25=(|Fraction| #7#)) 85 T ELT)) (|charthRoot| (#19# 101 T ELT) (#4# 116 T ELT)) (|characteristic| (#10# 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#11# 24 T CONST)) (|One| (#11# 46 T CONST)) (D (#4# 119 T ELT) (#17# 117 T ELT)) (= (#1# 8 T ELT)) (/ (#12# 84 T ELT)) (- (#4# 30 T ELT) (#12# 29 T ELT)) (+ (#12# 18 T ELT)) (** (($ $ #5#) 36 T ELT) (#17# 44 T ELT) (($ $ #7#) 88 T ELT)) (* (($ #5# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #7# . #26=($)) 31 T ELT) (#12# 35 T ELT) (($ $ #25#) 87 T ELT) (($ #25# . #26#) 86 T ELT))) (((|FiniteFieldCategory|) (|Category|)) (T |FiniteFieldCategory|)) -((|charthRoot| (*1 *1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|conditionP| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Vector| *1)))) (|factorsOfCyclicGroupSize| (*1 *2) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))))) (|tableForDiscreteLogarithm| (*1 *2 *3) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Table| (|PositiveInteger|) (|NonNegativeInteger|))))) (|createPrimitiveElement| (*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|primitiveElement| (*1 *1) (|ofCategory| *1 (|FiniteFieldCategory|))) (|primitive?| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Boolean|)))) (|discreteLog| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|PositiveInteger|)))) (|representationType| (*1 *2) (AND (|ofCategory| *1 (|FiniteFieldCategory|)) (|isDomain| *2 (|Union| "prime" "polynomial" "normal" "cyclic"))))) -(|Join| (|FieldOfPrimeCharacteristic|) (|Finite|) (|StepThrough|) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |charthRoot| ($ $)) (SIGNATURE |conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) (SIGNATURE |factorsOfCyclicGroupSize| ((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|)))))) (SIGNATURE |tableForDiscreteLogarithm| ((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|))) (SIGNATURE |createPrimitiveElement| ($)) (SIGNATURE |primitiveElement| ($)) (SIGNATURE |primitive?| ((|Boolean|) $)) (SIGNATURE |discreteLog| ((|NonNegativeInteger|) $)) (SIGNATURE |order| ((|PositiveInteger|) $)) (SIGNATURE |representationType| ((|Union| "prime" "polynomial" "normal" "cyclic"))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialDomain| $) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) . T) ((|Finite|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((|charthRoot| (*1 *1 *1) #1=(|ofCategory| *1 (|FiniteFieldCategory|))) (|conditionP| #2=(*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| *1)) #1# (|isDomain| *2 (|Vector| *1)))) (|factorsOfCyclicGroupSize| #3=(*1 *2) (AND #1# (|isDomain| *2 (|List| (|Record| (|:| |factor| #4=(|Integer|)) (|:| |exponent| #4#)))))) (|tableForDiscreteLogarithm| #2# (AND #1# (|isDomain| *3 #4#) (|isDomain| *2 (|Table| #5=(|PositiveInteger|) #6=(|NonNegativeInteger|))))) (|createPrimitiveElement| #7=(*1 *1) #1#) (|primitiveElement| #7# #1#) (|primitive?| #8=(*1 *2 *1) (AND #1# (|isDomain| *2 (|Boolean|)))) (|discreteLog| #8# (AND #1# (|isDomain| *2 #6#))) (|order| #8# (AND #1# (|isDomain| *2 #5#))) (|representationType| #3# (AND #1# (|isDomain| *2 (|Union| "prime" "polynomial" "normal" "cyclic"))))) +(|Join| (|FieldOfPrimeCharacteristic|) (|Finite|) (|StepThrough|) (|DifferentialRing|) (CATEGORY |domain| (SIGNATURE |charthRoot| ($ $)) (SIGNATURE |conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) (SIGNATURE |factorsOfCyclicGroupSize| ((|List| (|Record| (|:| |factor| #1=(|Integer|)) (|:| |exponent| #1#))))) (SIGNATURE |tableForDiscreteLogarithm| ((|Table| #2=(|PositiveInteger|) #3=(|NonNegativeInteger|)) #1#)) (SIGNATURE |createPrimitiveElement| #4=($)) (SIGNATURE |primitiveElement| #4#) (SIGNATURE |primitive?| ((|Boolean|) $)) (SIGNATURE |discreteLog| (#3# $)) (SIGNATURE |order| (#2# $)) (SIGNATURE |representationType| ((|Union| "prime" "polynomial" "normal" "cyclic"))))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DifferentialDomain| $) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) . T) ((|Finite|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((|localIntegralBasis| ((#1=(|Record| (|:| |basis| #2=(|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| #2#)) |#1|) 55 T ELT)) (|integralBasis| ((#1#) 53 T ELT))) (((|FunctionFieldIntegralBasis| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |integralBasis| (#1=(|Record| (|:| |basis| #2=(|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| #2#)))) (SIGNATURE |localIntegralBasis| (#1# |#1|))) (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $)))) (|UnivariatePolynomialCategory| |#1|) (|FramedAlgebra| |#1| |#2|)) (T |FunctionFieldIntegralBasis|)) ((|localIntegralBasis| (*1 *2 *3) #1=(AND (|ofCategory| *3 (|Join| (|EuclideanDomain|) (CATEGORY |domain| (SIGNATURE |squareFree| ((|Factored| $) $))))) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Record| (|:| |basis| #2=(|Matrix| *3)) (|:| |basisDen| *3) (|:| |basisInv| #2#))) (|isDomain| *1 (|FunctionFieldIntegralBasis| *3 *4 *5)) (|ofCategory| *5 (|FramedAlgebra| *3 *4)))) (|integralBasis| (*1 *2) #1#)) @@ -1015,78 +1015,78 @@ NIL ((|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 13 T ELT)) (|unitCanonical| (#1=($ $) 14 T ELT)) (|squareFree| (#2=((|Factored| $) $) 31 T ELT)) (|prime?| ((#3=(|Boolean|) $) 27 T ELT)) (|inv| (#1# 19 T ELT)) (|gcd| (#4=($ $ $) 22 T ELT) (($ (|List| $)) NIL T ELT)) (|factor| (#2# 32 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 21 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 25 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 36 T ELT)) (|associates?| ((#3# $ $) 16 T ELT)) (/ (#4# 34 T ELT))) (((|Field&| |#1|) (CATEGORY |package| (SIGNATURE / #1=(|#1| |#1| |#1|)) (SIGNATURE |inv| #2=(|#1| |#1|)) (SIGNATURE |prime?| (#3=(|Boolean|) |#1|)) (SIGNATURE |squareFree| #4=((|Factored| |#1|) |#1|)) (SIGNATURE |factor| #4#) (SIGNATURE |divide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |euclideanSize| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |gcd| (|#1| (|List| |#1|))) (SIGNATURE |gcd| #1#) (SIGNATURE |associates?| (#3# |#1| |#1|)) (SIGNATURE |unitCanonical| #2#) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| |#1|) (|:| |canonical| |#1|) (|:| |associate| |#1|)) |#1|)) (SIGNATURE |exquo| ((|Union| |#1| "failed") |#1| |#1|))) (|Field|)) (T |Field&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 69 T ELT)) (|lcm| (#10=($ $ $) 61 T ELT) (#11=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 59 T ELT)) (|gcd| (#10# 63 T ELT) (#11# 62 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 85 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #16#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #15#) 87 T ELT) (($ #15# . #17#) 86 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (#4# 92 T ELT)) (|squareFree| (#5=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (#1# 76 T ELT)) (|sample| (#6=($) 23 T CONST)) (|rem| (#7=($ $ $) 72 T ELT)) (|recip| ((#8=(|Union| $ #9="failed") $) 43 T ELT)) (|quo| (#7# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #10=(|List| $)) #11=(|:| |generator| $)) #10#) 67 T ELT)) (|prime?| (#3# 90 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|multiEuclidean| (((|Union| #10# #9#) #10# $) 69 T ELT)) (|lcm| (#7# 61 T ELT) (#12=($ #10#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#4# 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 59 T ELT)) (|gcd| (#7# 63 T ELT) (#12# 62 T ELT)) (|factor| (#5# 93 T ELT)) (|extendedEuclidean| (((|Record| #14=(|:| |coef1| $) #15=(|:| |coef2| $) #11#) $ $) 71 T ELT) (((|Union| (|Record| #14# #15#) #9#) $ $ $) 70 T ELT)) (|exquo| ((#8# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #10#) #10# $) 66 T ELT)) (|euclideanSize| ((#16=(|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #17=(|Integer|)) 42 T ELT) (#4# 58 T ELT) (($ #18=(|Fraction| #17#)) 85 T ELT)) (|characteristic| ((#16#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (#6# 46 T CONST)) (= (#1# 8 T ELT)) (/ (#7# 84 T ELT)) (- (#4# 30 T ELT) (#7# 29 T ELT)) (+ (#7# 18 T ELT)) (** (($ $ #19=(|PositiveInteger|)) 36 T ELT) (($ $ #16#) 44 T ELT) (($ $ #17#) 88 T ELT)) (* (($ #19# $) 17 T ELT) (($ #16# $) 21 T ELT) (($ #17# . #20=($)) 31 T ELT) (#7# 35 T ELT) (($ $ #18#) 87 T ELT) (($ #18# . #20#) 86 T ELT))) (((|Field|) (|Category|)) (T |Field|)) ((/ (*1 *1 *1 *1) (|ofCategory| *1 (|Field|)))) (|Join| (|EuclideanDomain|) (|UniqueFactorizationDomain|) (|DivisionRing|) (CATEGORY |domain| (SIGNATURE / ($ $ $)) (ATTRIBUTE |canonicalUnitNormal|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|write!| ((|#1| $ |#1|) 35 T ELT)) (|reopen!| (($ $ #3=(|String|)) 23 T ELT)) (|readIfCan!| (((|Union| |#1| "failed") $) 34 T ELT)) (|read!| ((|#1| $) 32 T ELT)) (|open| (($ #4=(|FileName|)) 22 T ELT) (($ #4# #3#) 21 T ELT)) (|name| ((#4# $) 25 T ELT)) (|latex| (#5=(#3# $) NIL T ELT)) (|iomode| (#5# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT)) (|close!| (($ $) 24 T ELT)) (|before?| #1#) (= (#2# 19 T ELT))) (((|File| |#1|) (|Join| (|FileCategory| (|FileName|) |#1|) (CATEGORY |domain| (SIGNATURE |readIfCan!| ((|Union| |#1| "failed") $)))) (|SetCategory|)) (T |File|)) ((|readIfCan!| (*1 *2 *1) (|partial| AND (|isDomain| *1 (|File| *2)) (|ofCategory| *2 (|SetCategory|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|write!| ((|#2| $ |#2|) 17 T ELT)) (|reopen!| (($ $ (|String|)) 22 T ELT)) (|read!| ((|#2| $) 18 T ELT)) (|open| (($ |#1|) 24 T ELT) (($ |#1| (|String|)) 23 T ELT)) (|name| ((|#1| $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|iomode| (((|String|) $) 19 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|close!| (($ $) 21 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) -(((|FileCategory| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |FileCategory|)) -((|open| (*1 *1 *2) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|open| (*1 *1 *2 *3) (AND (|isDomain| *3 (|String|)) (|ofCategory| *1 (|FileCategory| *2 *4)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|reopen!| (*1 *1 *1 *2) (AND (|isDomain| *2 (|String|)) (|ofCategory| *1 (|FileCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)))) (|close!| (*1 *1 *1) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|name| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *2 *3)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|iomode| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|String|)))) (|read!| (*1 *2 *1) (AND (|ofCategory| *1 (|FileCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|)))) (|write!| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|FileCategory| *3 *2)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *2 (|SetCategory|))))) -(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |open| ($ |t#1|)) (SIGNATURE |open| ($ |t#1| (|String|))) (SIGNATURE |reopen!| ($ $ (|String|))) (SIGNATURE |close!| ($ $)) (SIGNATURE |name| (|t#1| $)) (SIGNATURE |iomode| ((|String|) $)) (SIGNATURE |read!| (|t#2| $)) (SIGNATURE |write!| (|t#2| $ |t#2|)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|write!| ((|#2| $ |#2|) 17 T ELT)) (|reopen!| (($ $ #2=(|String|)) 22 T ELT)) (|read!| ((|#2| $) 18 T ELT)) (|open| (($ |#1|) 24 T ELT) (($ |#1| #2#) 23 T ELT)) (|name| ((|#1| $) 20 T ELT)) (|latex| (#3=(#2# $) 11 T ELT)) (|iomode| (#3# 19 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|close!| (($ $) 21 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) +(((|FileCategory| |#1| |#2|) (|Category|) #1=(|SetCategory|) #1#) (T |FileCategory|)) +((|open| (*1 *1 *2) #1=(AND #2=(|ofCategory| *1 (|FileCategory| *2 *3)) #3=(|ofCategory| *2 #4=(|SetCategory|)) #5=(|ofCategory| *3 #4#))) (|open| (*1 *1 *2 *3) (AND (|isDomain| *3 #6=(|String|)) (|ofCategory| *1 (|FileCategory| *2 *4)) #3# #7=(|ofCategory| *4 #4#))) (|reopen!| (*1 *1 *1 *2) (AND #8=(|isDomain| *2 #6#) #9=(|ofCategory| *1 (|FileCategory| *3 *4)) #5# #7#)) (|close!| (*1 *1 *1) #1#) (|name| #10=(*1 *2 *1) (AND #2# #5# #3#)) (|iomode| #10# (AND #9# #5# #7# #8#)) (|read!| #10# #11=(AND (|ofCategory| *1 (|FileCategory| *3 *2)) #5# #3#)) (|write!| (*1 *2 *1 *2) #11#)) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |open| ($ |t#1|)) (SIGNATURE |open| ($ |t#1| #1=(|String|))) (SIGNATURE |reopen!| ($ $ #1#)) (SIGNATURE |close!| ($ $)) (SIGNATURE |name| (|t#1| $)) (SIGNATURE |iomode| (#1# $)) (SIGNATURE |read!| (|t#2| $)) (SIGNATURE |write!| (|t#2| $ |t#2|)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|structuralConstants| (((|Vector| #1=(|Matrix| |#2|)) #2=(|Vector| $)) 67 T ELT)) (|rightTraceMatrix| (#3=(#1# #2#) 139 T ELT)) (|rightTrace| (#4=(|#2| $) 36 T ELT)) (|rightRegularRepresentation| (#5=(#1# $ #2#) 142 T ELT)) (|rightRecip| (#6=((|Union| $ "failed") $) 89 T ELT)) (|rightNorm| (#4# 39 T ELT)) (|rightMinimalPolynomial| (#7=((|SparseUnivariatePolynomial| |#2|) $) 98 T ELT)) (|rightDiscriminant| (#8=(|#2| #2#) 122 T ELT)) (|rightCharacteristicPolynomial| (#7# 32 T ELT)) (|rightAlternative?| (#9=((|Boolean|)) 116 T ELT)) (|represents| (($ #10=(|Vector| |#2|) #2#) 132 T ELT)) (|recip| (#6# 93 T ELT)) (|noncommutativeJordanAlgebra?| (#9# 111 T ELT)) (|lieAlgebra?| (#9# 106 T ELT)) (|lieAdmissible?| (#9# 58 T ELT)) (|leftTraceMatrix| (#3# 137 T ELT)) (|leftTrace| (#4# 35 T ELT)) (|leftRegularRepresentation| (#5# 141 T ELT)) (|leftRecip| (#6# 87 T ELT)) (|leftNorm| (#4# 38 T ELT)) (|leftMinimalPolynomial| (#7# 97 T ELT)) (|leftDiscriminant| (#8# 120 T ELT)) (|leftCharacteristicPolynomial| (#7# 30 T ELT)) (|leftAlternative?| (#9# 115 T ELT)) (|jordanAlgebra?| (#9# 108 T ELT)) (|jordanAdmissible?| (#9# 56 T ELT)) (|jacobiIdentity?| (#9# 103 T ELT)) (|flexible?| (#9# 117 T ELT)) (|coordinates| ((#10# $ #2#) NIL T ELT) ((#1# #2# #2#) 128 T ELT)) (|commutative?| (#9# 113 T ELT)) (|associatorDependence| (((|List| #10#)) 102 T ELT)) (|associative?| (#9# 114 T ELT)) (|antiCommutative?| (#9# 112 T ELT)) (|antiAssociative?| (#9# 51 T ELT)) (|alternative?| (#9# 118 T ELT))) (((|FiniteRankNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rightMinimalPolynomial| #1=((|SparseUnivariatePolynomial| |#2|) |#1|)) (SIGNATURE |leftMinimalPolynomial| #1#) (SIGNATURE |associatorDependence| ((|List| #2=(|Vector| |#2|)))) (SIGNATURE |rightRecip| #3=((|Union| |#1| "failed") |#1|)) (SIGNATURE |leftRecip| #3#) (SIGNATURE |recip| #3#) (SIGNATURE |lieAlgebra?| #4=((|Boolean|))) (SIGNATURE |jordanAlgebra?| #4#) (SIGNATURE |noncommutativeJordanAlgebra?| #4#) (SIGNATURE |jordanAdmissible?| #4#) (SIGNATURE |lieAdmissible?| #4#) (SIGNATURE |jacobiIdentity?| #4#) (SIGNATURE |alternative?| #4#) (SIGNATURE |flexible?| #4#) (SIGNATURE |rightAlternative?| #4#) (SIGNATURE |leftAlternative?| #4#) (SIGNATURE |antiAssociative?| #4#) (SIGNATURE |associative?| #4#) (SIGNATURE |antiCommutative?| #4#) (SIGNATURE |commutative?| #4#) (SIGNATURE |rightCharacteristicPolynomial| #1#) (SIGNATURE |leftCharacteristicPolynomial| #1#) (SIGNATURE |rightTraceMatrix| #5=(#6=(|Matrix| |#2|) #7=(|Vector| |#1|))) (SIGNATURE |leftTraceMatrix| #5#) (SIGNATURE |rightDiscriminant| #8=(|#2| #7#)) (SIGNATURE |leftDiscriminant| #8#) (SIGNATURE |represents| (|#1| #2# #7#)) (SIGNATURE |coordinates| (#6# #7# #7#)) (SIGNATURE |coordinates| (#2# |#1| #7#)) (SIGNATURE |rightNorm| #9=(|#2| |#1|)) (SIGNATURE |leftNorm| #9#) (SIGNATURE |rightTrace| #9#) (SIGNATURE |leftTrace| #9#) (SIGNATURE |rightRegularRepresentation| #10=(#6# |#1| #7#)) (SIGNATURE |leftRegularRepresentation| #10#) (SIGNATURE |structuralConstants| ((|Vector| #6#) #7#))) (|FiniteRankNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FiniteRankNonAssociativeAlgebra&|)) ((|commutative?| #1=(*1 *2) #2=(AND #3=(|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|FiniteRankNonAssociativeAlgebra&| *3 *4)) #5=(|ofCategory| *3 (|FiniteRankNonAssociativeAlgebra| *4)))) (|antiCommutative?| #1# #2#) (|associative?| #1# #2#) (|antiAssociative?| #1# #2#) (|leftAlternative?| #1# #2#) (|rightAlternative?| #1# #2#) (|flexible?| #1# #2#) (|alternative?| #1# #2#) (|jacobiIdentity?| #1# #2#) (|lieAdmissible?| #1# #2#) (|jordanAdmissible?| #1# #2#) (|noncommutativeJordanAlgebra?| #1# #2#) (|jordanAlgebra?| #1# #2#) (|lieAlgebra?| #1# #2#) (|associatorDependence| #1# (AND #3# (|isDomain| *2 (|List| (|Vector| *4))) #4# #5#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (((|Union| $ "failed")) 49 (|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) 90 T ELT)) (|someBasis| (((|Vector| $)) 93 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 52 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightUnit| (((|Union| $ "failed")) 50 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 77 T ELT)) (|rightTrace| ((|#1| $) 86 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 88 T ELT)) (|rightRecip| (((|Union| $ "failed") $) 57 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 38 T ELT)) (|rightNorm| ((|#1| $) 84 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 54 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightDiscriminant| ((|#1| (|Vector| $)) 79 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 75 T ELT)) (|rightAlternative?| (((|Boolean|)) 69 T ELT)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 59 (|has| |#1| (|IntegralDomain|)) ELT)) (|rank| (((|PositiveInteger|)) 92 T ELT)) (|powerAssociative?| (((|Boolean|)) 66 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 45 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 62 T ELT)) (|lieAlgebra?| (((|Boolean|)) 60 T ELT)) (|lieAdmissible?| (((|Boolean|)) 64 T ELT)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 53 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftUnit| (((|Union| $ "failed")) 51 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 78 T ELT)) (|leftTrace| ((|#1| $) 87 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 89 T ELT)) (|leftRecip| (((|Union| $ "failed") $) 58 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftPower| (#4# 39 T ELT)) (|leftNorm| ((|#1| $) 85 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 55 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftDiscriminant| ((|#1| (|Vector| $)) 80 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 76 T ELT)) (|leftAlternative?| (((|Boolean|)) 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (((|Boolean|)) 61 T ELT)) (|jordanAdmissible?| (((|Boolean|)) 63 T ELT)) (|jacobiIdentity?| (((|Boolean|)) 65 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (((|Boolean|)) 68 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 83 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 82 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) 91 T ELT)) (|commutator| (#5=($ $ $) 35 T ELT)) (|commutative?| (((|Boolean|)) 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 56 (|has| |#1| (|IntegralDomain|)) ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|associative?| (((|Boolean|)) 72 T ELT)) (|antiCommutator| (#5# 34 T ELT)) (|antiCommutative?| (((|Boolean|)) 73 T ELT)) (|antiAssociative?| (((|Boolean|)) 71 T ELT)) (|alternative?| (((|Boolean|)) 67 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 31 T ELT) (($ $ $) 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #6#) 46 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|unit| (#3=(#4=(|Union| $ #5="failed")) 49 #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|structuralConstants| (((|Vector| #7=(|Matrix| |#1|)) #8=(|Vector| $)) 90 T ELT)) (|someBasis| ((#8#) 93 T ELT)) (|sample| (#9=($) 23 T CONST)) (|rightUnits| (#10=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) 52 #6# ELT)) (|rightUnit| (#3# 50 #6# ELT)) (|rightTraceMatrix| (#11=(#7# #8#) 77 T ELT)) (|rightTrace| (#12=(|#1| $) 86 T ELT)) (|rightRegularRepresentation| (#13=(#7# $ #8#) 88 T ELT)) (|rightRecip| (#14=(#4# $) 57 #6# ELT)) (|rightPower| (#15=($ $ #16=(|PositiveInteger|)) 38 T ELT)) (|rightNorm| (#12# 84 T ELT)) (|rightMinimalPolynomial| (#17=((|SparseUnivariatePolynomial| |#1|) $) 54 #6# ELT)) (|rightDiscriminant| (#18=(|#1| #8#) 79 T ELT)) (|rightCharacteristicPolynomial| (#17# 75 T ELT)) (|rightAlternative?| (#19=(#2#) 69 T ELT)) (|represents| (($ #20=(|Vector| |#1|) #8#) 81 T ELT)) (|recip| (#14# 59 #6# ELT)) (|rank| ((#16#) 92 T ELT)) (|powerAssociative?| (#19# 66 T ELT)) (|plenaryPower| (#15# 45 T ELT)) (|opposite?| (#1# 20 T ELT)) (|noncommutativeJordanAlgebra?| (#19# 62 T ELT)) (|lieAlgebra?| (#19# 60 T ELT)) (|lieAdmissible?| (#19# 64 T ELT)) (|leftUnits| (#10# 53 #6# ELT)) (|leftUnit| (#3# 51 #6# ELT)) (|leftTraceMatrix| (#11# 78 T ELT)) (|leftTrace| (#12# 87 T ELT)) (|leftRegularRepresentation| (#13# 89 T ELT)) (|leftRecip| (#14# 58 #6# ELT)) (|leftPower| (#15# 39 T ELT)) (|leftNorm| (#12# 85 T ELT)) (|leftMinimalPolynomial| (#17# 55 #6# ELT)) (|leftDiscriminant| (#18# 80 T ELT)) (|leftCharacteristicPolynomial| (#17# 76 T ELT)) (|leftAlternative?| (#19# 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (#19# 61 T ELT)) (|jordanAdmissible?| (#19# 63 T ELT)) (|jacobiIdentity?| (#19# 65 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (#19# 68 T ELT)) (|coordinates| ((#20# $ #8#) 83 T ELT) ((#7# #8# #8#) 82 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) #8#) 91 T ELT)) (|commutator| (#21=($ $ $) 35 T ELT)) (|commutative?| (#19# 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associatorDependence| (((|List| #20#)) 56 #6# ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|associative?| (#19# 72 T ELT)) (|antiCommutator| (#21# 34 T ELT)) (|antiCommutative?| (#19# 73 T ELT)) (|antiAssociative?| (#19# 71 T ELT)) (|alternative?| (#19# 67 T ELT)) (|Zero| (#9# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#21# 29 T ELT)) (+ (#21# 18 T ELT)) (** (#15# 40 T ELT)) (* (($ #16# $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #22=($)) 31 T ELT) (#21# 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #22#) 46 T ELT))) (((|FiniteRankNonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |FiniteRankNonAssociativeAlgebra|)) -((|someBasis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|rank| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|PositiveInteger|)))) (|conditionsForIdempotents| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|structuralConstants| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| *4))))) (|leftRegularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|rightRegularRepresentation| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|leftTrace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightTrace| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftNorm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightNorm| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|coordinates| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *4)))) (|coordinates| (*1 *2 *3 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *4)) (|isDomain| *3 (|Vector| *1)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)))) (|leftDiscriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightDiscriminant| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftTraceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|rightTraceMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|leftCharacteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|rightCharacteristicPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|commutative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|antiCommutative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|associative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|antiAssociative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|leftAlternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|rightAlternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|flexible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|alternative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|powerAssociative?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jacobiIdentity?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|lieAdmissible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jordanAdmissible?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|noncommutativeJordanAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|jordanAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|lieAlgebra?| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Boolean|)))) (|recip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|leftRecip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|rightRecip| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|IntegralDomain|)))) (|associatorDependence| (*1 *2) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|List| (|Vector| *3))))) 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((|Boolean|))) (SIGNATURE |jacobiIdentity?| ((|Boolean|))) (SIGNATURE |lieAdmissible?| ((|Boolean|))) (SIGNATURE |jordanAdmissible?| ((|Boolean|))) (SIGNATURE |noncommutativeJordanAlgebra?| ((|Boolean|))) (SIGNATURE |jordanAlgebra?| ((|Boolean|))) (SIGNATURE |lieAlgebra?| ((|Boolean|))) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |recip| ((|Union| $ "failed") $)) (SIGNATURE |leftRecip| ((|Union| $ "failed") $)) (SIGNATURE |rightRecip| ((|Union| $ "failed") $)) (SIGNATURE |associatorDependence| ((|List| (|Vector| |t#1|)))) (SIGNATURE |leftMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightMinimalPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |leftUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |rightUnits| ((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |leftUnit| ((|Union| $ "failed"))) (SIGNATURE |rightUnit| ((|Union| $ "failed"))) (SIGNATURE |unit| ((|Union| $ "failed")))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|someBasis| #1=(*1 *2) (AND #2=(|ofCategory| *3 #3=(|CommutativeRing|)) (|isDomain| *2 #4=(|Vector| *1)) #5=(|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|rank| #1# (AND #5# #2# (|isDomain| *2 (|PositiveInteger|)))) (|conditionsForIdempotents| #6=(*1 *2 *3) (AND #7=(|isDomain| *3 #4#) #8=(|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *4)) #9=(|ofCategory| *4 #3#) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|structuralConstants| #6# (AND #7# #8# #9# (|isDomain| *2 (|Vector| #10=(|Matrix| *4))))) (|leftRegularRepresentation| #11=(*1 *2 *1 *3) #12=(AND #7# #8# #9# (|isDomain| *2 #10#))) (|rightRegularRepresentation| #11# #12#) (|leftTrace| #13=(*1 *2 *1) #14=(AND #15=(|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) #16=(|ofCategory| *2 #3#))) (|rightTrace| #13# #14#) (|leftNorm| #13# #14#) (|rightNorm| #13# #14#) (|coordinates| #11# (AND #7# #8# #9# #17=(|isDomain| *2 (|Vector| *4)))) (|coordinates| (*1 *2 *3 *3) #12#) (|represents| (*1 *1 *2 *3) (AND #17# #7# #9# #8#)) (|leftDiscriminant| #6# #18=(AND #7# #15# #16#)) (|rightDiscriminant| #6# #18#) (|leftTraceMatrix| #6# #12#) (|rightTraceMatrix| #6# #12#) (|leftCharacteristicPolynomial| #13# #19=(AND #5# #2# #20=(|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|rightCharacteristicPolynomial| #13# #19#) (|commutative?| #1# #21=(AND #5# #2# (|isDomain| *2 (|Boolean|)))) (|antiCommutative?| #1# #21#) (|associative?| #1# #21#) (|antiAssociative?| #1# #21#) (|leftAlternative?| #1# #21#) (|rightAlternative?| #1# #21#) (|flexible?| #1# #21#) (|alternative?| #1# #21#) (|powerAssociative?| #1# #21#) (|jacobiIdentity?| #1# #21#) (|lieAdmissible?| #1# #21#) (|jordanAdmissible?| #1# #21#) (|noncommutativeJordanAlgebra?| #1# #21#) (|jordanAlgebra?| #1# #21#) (|lieAlgebra?| #1# #21#) (|recip| #22=(*1 *1 *1) #23=(|partial| AND #15# #16# #24=(|ofCategory| *2 #25=(|IntegralDomain|)))) (|leftRecip| #22# #23#) (|rightRecip| #22# #23#) (|associatorDependence| #1# (AND #5# #2# #26=(|ofCategory| *3 #25#) (|isDomain| *2 (|List| (|Vector| *3))))) (|leftMinimalPolynomial| #13# #27=(AND #5# #2# #26# #20#)) (|rightMinimalPolynomial| #13# #27#) (|leftUnits| #1# #28=(|partial| AND #26# #2# (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1)))) #5#)) (|rightUnits| #1# #28#) (|leftUnit| #29=(*1 *1) #30=(|partial| AND #15# #24# #16#)) (|rightUnit| #29# #30#) (|unit| #29# #30#)) +(|Join| (|NonAssociativeAlgebra| |t#1|) (CATEGORY |domain| (SIGNATURE |someBasis| (#1=(|Vector| $))) (SIGNATURE |rank| ((|PositiveInteger|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)) #1#)) (SIGNATURE |structuralConstants| ((|Vector| #2=(|Matrix| |t#1|)) #1#)) (SIGNATURE |leftRegularRepresentation| #3=(#2# $ #1#)) (SIGNATURE |rightRegularRepresentation| #3#) (SIGNATURE |leftTrace| #4=(|t#1| $)) (SIGNATURE |rightTrace| #4#) (SIGNATURE |leftNorm| #4#) (SIGNATURE |rightNorm| #4#) (SIGNATURE |coordinates| (#5=(|Vector| |t#1|) $ #1#)) (SIGNATURE |coordinates| (#2# #1# #1#)) (SIGNATURE |represents| ($ #5# #1#)) (SIGNATURE |leftDiscriminant| #6=(|t#1| #1#)) (SIGNATURE |rightDiscriminant| #6#) (SIGNATURE |leftTraceMatrix| #7=(#2# #1#)) (SIGNATURE |rightTraceMatrix| #7#) (SIGNATURE |leftCharacteristicPolynomial| #8=((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightCharacteristicPolynomial| #8#) (SIGNATURE |commutative?| #9=((|Boolean|))) (SIGNATURE |antiCommutative?| #9#) (SIGNATURE |associative?| #9#) (SIGNATURE |antiAssociative?| #9#) (SIGNATURE |leftAlternative?| #9#) (SIGNATURE |rightAlternative?| #9#) (SIGNATURE |flexible?| #9#) (SIGNATURE |alternative?| #9#) (SIGNATURE |powerAssociative?| #9#) (SIGNATURE |jacobiIdentity?| #9#) (SIGNATURE |lieAdmissible?| #9#) (SIGNATURE |jordanAdmissible?| #9#) (SIGNATURE |noncommutativeJordanAlgebra?| #9#) (SIGNATURE |jordanAlgebra?| #9#) (SIGNATURE |lieAlgebra?| #9#) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |recip| #10=(#11=(|Union| $ #12="failed") $)) (SIGNATURE |leftRecip| #10#) (SIGNATURE |rightRecip| #10#) (SIGNATURE |associatorDependence| ((|List| #5#))) (SIGNATURE |leftMinimalPolynomial| #8#) (SIGNATURE |rightMinimalPolynomial| #8#) (SIGNATURE |leftUnits| #13=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #12#))) (SIGNATURE |rightUnits| #13#) (SIGNATURE |leftUnit| #14=(#11#)) (SIGNATURE |rightUnit| #14#) (SIGNATURE |unit| #14#)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|reduce| ((|#2| #1=(|Mapping| |#2| |#2| |#2|) $) NIL T ELT) ((|#2| #1# $ |#2|) NIL T ELT) ((|#2| #1# $ |#2| |#2|) 38 T ELT)) (|member?| ((#2=(|Boolean|) |#2| $) 35 T ELT)) (|find| (((|Union| |#2| "failed") #3=(|Mapping| #2# |#2|) $) 30 T ELT)) (|every?| (#4=(#2# #3# $) 24 T ELT)) (|empty?| ((#2# $) 13 T ELT)) (|count| ((#5=(|NonNegativeInteger|) #3# $) 27 T ELT) ((#5# |#2| $) 33 T ELT)) (|coerce| (((|OutputForm|) $) 46 T ELT)) (|any?| (#4# 21 T ELT)) (= ((#2# $ $) 40 T ELT)) (|#| ((#5# $) 17 T ELT))) (((|FiniteAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |reduce| (|#2| #2=(|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |member?| (#1# |#2| |#1|)) (SIGNATURE |count| (#3=(|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") #4=(|Mapping| #1# |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #2# |#1| |#2|)) (SIGNATURE |reduce| (|#2| #2# |#1|)) (SIGNATURE |count| (#3# #4# 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| (|XDistributedPolynomial| |#1| |#2|)) . T) ((|CoercibleTo| (|XRecursivePolynomial| |#1| |#2|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftModule| |#2|) . T) ((|LieAlgebra| |#2|) . T) ((|LinearSet| |#2|) . T) ((|Module| |#2|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|shellSort| (#1=(|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) 40 T ELT)) (|quickSort| (#1# 13 T ELT)) (|heapSort| (#1# 33 T ELT))) (((|FiniteLinearAggregateSort| |#1| |#2|) (CATEGORY |package| (SIGNATURE |quickSort| #1=(|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|)) (SIGNATURE |heapSort| #1#) (SIGNATURE |shellSort| #1#)) (|Type|) (|Join| (|FiniteLinearAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|))) (T |FiniteLinearAggregateSort|)) ((|shellSort| #1=(*1 *2 *3 *2) #2=(AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|Type|)) (|isDomain| *1 (|FiniteLinearAggregateSort| *4 *2)) (|ofCategory| *2 (|Join| (|FiniteLinearAggregate| *4) (|ShallowlyMutableAggregate| *4))))) (|heapSort| #1# #2#) (|quickSort| #1# #2#)) ((|reducedSystem| ((#1=(|Matrix| |#2|) #2=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #1#) (|:| |vec| (|Vector| |#2|))) #2# #3=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #4=(|Matrix| #5=(|Integer|))) (|:| |vec| (|Vector| #5#))) #2# #3#) 22 T ELT) ((#4# #2#) 14 T ELT))) (((|FullyLinearlyExplicitRingOver&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |reducedSystem| (#1=(|Matrix| #2=(|Integer|)) #3=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #1#) (|:| |vec| (|Vector| #2#))) #3# #4=(|Vector| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #5=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) #3# #4#)) (SIGNATURE |reducedSystem| (#5# #3#))) (|FullyLinearlyExplicitRingOver| |#2|) (|Ring|)) (T |FullyLinearlyExplicitRingOver&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| (((|Matrix| |#1|) . #4=(#5=(|Matrix| $))) 37 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #6=(#5# #7=(|Vector| $))) 36 T ELT) (((|Record| (|:| |mat| (|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) . #6#) 48 (|has| |#1| . #9=((|LinearlyExplicitRingOver| (|Integer|)))) ELT) (((|Matrix| #8#) . #4#) 47 (|has| |#1| . #9#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) . #10=(#7#)) 39 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #11=(#7# $)) 38 T ELT) (((|Record| (|:| |mat| (|Matrix| #8#)) (|:| |vec| (|Vector| #8#))) . #11#) 46 (|has| |#1| . #9#) ELT) (((|Matrix| #8#) . #10#) 45 (|has| |#1| . #9#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #12=($)) 31 T ELT) (($ |#1| . #12#) 34 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| ((#4=(|Matrix| |#1|) . #5=(#6=(|Matrix| $))) 37 T ELT) ((#7=(|Record| (|:| |mat| #4#) (|:| |vec| (|Vector| |#1|))) . #8=(#6# #9=(|Vector| $))) 36 T ELT) ((#10=(|Record| (|:| |mat| #11=(|Matrix| #12=(|Integer|))) (|:| |vec| (|Vector| #12#))) . #8#) 48 #13=(|has| |#1| (|LinearlyExplicitRingOver| #12#)) ELT) ((#11# . #5#) 47 #13# ELT)) (|opposite?| (#1# 20 T ELT)) (|leftReducedSystem| ((#4# . #14=(#9#)) 39 T ELT) ((#7# . #15=(#9# $)) 38 T ELT) ((#10# . #15#) 46 #13# ELT) ((#11# . #14#) 45 #13# ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#16=($ $ $) 29 T ELT)) (+ (#16# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ #12# . #17=($)) 31 T ELT) (($ |#1| . #17#) 34 T ELT))) (((|FullyLinearlyExplicitRingOver| |#1|) (|Category|) (|Ring|)) (T |FullyLinearlyExplicitRingOver|)) NIL -(|Join| (|LinearlyExplicitRingOver| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|LinearlyExplicitRingOver| (|Integer|))) (ATTRIBUTE (|LinearlyExplicitRingOver| (|Integer|))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| #1=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LinearlyExplicitRingOver| #1#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(|Join| (|LinearlyExplicitRingOver| |t#1|) (CATEGORY |package| (IF (|has| |t#1| #1=(|LinearlyExplicitRingOver| (|Integer|))) (ATTRIBUTE #1#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1=(|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| #1#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LinearlyExplicitRingOver| #1#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 16 T ELT)) (|wholePart| (#5=(#6=(|Integer|) $) 44 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|truncate| (#8# 120 T ELT)) (|tanh| (#8# 81 T ELT)) (|tan| (#8# 72 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #10=(((|Factored| $) $) NIL T ELT)) (|sqrt| (#8# 28 T ELT)) (|sizeLess?| #1#) (|sinh| (#8# 79 T ELT)) (|sin| (#8# 67 T ELT)) (|sign| (#5# 60 T ELT)) (|shift| (#11=($ $ #6#) 55 T ELT)) (|sech| #7#) (|sec| #7#) (|sample| (#12=($) NIL T CONST)) (|round| (#8# 122 T ELT)) (|retractIfCan| (((|Union| #6# . #13=(#14="failed")) $) 217 T ELT) (((|Union| #15=(|Fraction| #6#) . #13#) $) 213 T ELT)) (|retract| (#5# 215 T ELT) ((#15# $) 211 T ELT)) (|rem| #16=(#17=($ $ $) NIL T ELT)) (|relerror| ((#6# $ $) 110 T ELT)) (|recip| ((#18=(|Union| $ #14#) $) 125 T ELT)) (|rationalApproximation| ((#15# $ #19=(|NonNegativeInteger|)) 218 T ELT) ((#15# $ #19# #19#) 210 T ELT)) (|quo| #16#) (|principalIdeal| (((|Record| (|:| |coef| #20=(|List| $)) #21=(|:| |generator| $)) #20#) NIL T ELT)) (|prime?| #9#) (|precision| (#22=(#23=(|PositiveInteger|)) 106 T ELT) (#24=(#23# #23#) 107 #25=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (#4# 38 T ELT)) (|pi| (#12# 22 T ELT)) (|patternMatch| ((#26=(|PatternMatchResult| #27=(|Float|) $) $ #28=(|Pattern| #27#) #26#) NIL T ELT)) (|outputSpacing| (#29=(#30=(|Void|) #19#) 177 T ELT)) (|outputGeneral| (#31=(#30#) 182 T ELT) (#29# 183 T ELT)) (|outputFloating| (#31# 184 T ELT) (#29# 185 T ELT)) (|outputFixed| (#31# 180 T ELT) (#29# 181 T ELT)) (|order| (#5# 50 T ELT)) (|opposite?| #1#) (|one?| (#4# 21 T ELT)) (|nthRoot| (#11# NIL T ELT)) (|normalize| (#8# 32 T ELT)) (|norm| #7#) (|negative?| (#4# 18 T ELT)) (|multiEuclidean| (((|Union| #20# #14#) #20# $) NIL T ELT)) (|min| #16# #32=(#12# NIL (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| #25#)) ELT)) (|max| #16# #32#) (|mantissa| (#5# 112 T ELT)) (|log2| (#12# 90 T ELT) (#8# 97 T ELT)) (|log10| (#12# 96 T ELT) (#8# 98 T ELT)) (|log| (#8# 84 T ELT)) (|lcm| #16# #33=(($ #20#) NIL T ELT)) (|latex| (#34=((|String|) $) NIL T ELT)) (|inv| (#8# 127 T ELT)) (|increasePrecision| (#35=(#23# #6#) 27 #25# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#36=(|SparseUnivariatePolynomial| $) #36# #36#) NIL T ELT)) (|gcd| #16# #33#) (|fractionPart| (#8# 41 T ELT)) (|floor| (#8# 119 T ELT)) (|float| (($ #6# #6#) 115 T ELT) (($ #6# #6# #23#) 116 T ELT)) (|factor| #10#) (|extendedEuclidean| (((|Record| #37=(|:| |coef1| $) #38=(|:| |coef2| $) #21#) $ $) NIL T ELT) (((|Union| (|Record| #37# #38#) #14#) $ $ $) NIL T ELT)) (|exquo| ((#18# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #20#) #20# $) NIL T ELT)) (|exponent| (#5# 113 T ELT)) (|exp1| (#12# 99 T ELT)) (|exp| (#8# 78 T ELT)) (|euclideanSize| ((#19# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (#22# 108 T ELT) (#24# 109 #25# ELT)) (|differentiate| (#8# 126 T ELT) #39=(($ $ #19#) NIL T ELT)) (|decreasePrecision| (#35# 31 #25# ELT)) (|csch| #7#) (|csc| #7#) (|coth| #7#) (|cot| #7#) (|cosh| (#8# 80 T ELT)) (|cos| (#8# 71 T ELT)) (|convert| ((#27# $) 202 T ELT) (#40=(#41=(|DoubleFloat|) $) 204 T ELT) ((#28# $) NIL T ELT) (#34# 188 T ELT) (((|InputForm|) $) 200 T ELT) (($ #41#) 209 T ELT)) (|coerce| (((|OutputForm|) $) 192 T ELT) #42=(($ #6#) 214 T ELT) #7# #43=(($ #15#) NIL T ELT) #42# #43# (#40# 205 T ELT)) (|characteristic| ((#19#) NIL T CONST)) (|ceiling| (#8# 121 T ELT)) (|bits| (#22# 42 T ELT) (#24# 62 #25# ELT)) (|before?| #1#) (|base| (#22# 111 T ELT)) (|atanh| (#8# 87 T ELT)) (|atan| (#8# 30 T ELT) (#17# 40 T ELT)) (|associates?| #1#) (|asinh| (#8# 85 T ELT)) (|asin| (#8# 20 T ELT)) (|asech| #7#) (|asec| #7#) (|annihilate?| #1#) (|acsch| #7#) (|acsc| #7#) (|acoth| #7#) (|acot| #7#) (|acosh| (#8# 86 T ELT)) (|acos| (#8# 33 T ELT)) (|abs| (#8# 39 T ELT)) (|Zero| (#12# 17 T CONST)) (|One| (#12# 24 T CONST)) (D #7# #39#) (>= (#2# 189 T ELT)) (> (#2# 26 T ELT)) (= (#2# 37 T ELT)) (<= #1#) (< (#2# 43 T ELT)) (/ (#17# 29 T ELT) (#11# 23 T ELT)) (- (#8# 19 T ELT) (#17# 34 T ELT)) (+ (#17# 54 T ELT)) (** (($ $ #23#) 65 T ELT) #39# (#11# 91 T ELT) (#44=($ $ #15#) 137 T ELT) (#17# 129 T ELT)) (* (($ #23# $) 61 T ELT) (($ #19# $) NIL T ELT) (($ #6# $) 66 T ELT) (#17# 53 T ELT) (#44# NIL T ELT) (($ #15# $) NIL T ELT))) (((|Float|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|ConvertibleTo| (|String|)) (|CoercibleTo| #1=(|DoubleFloat|)) (|TranscendentalFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (|ConvertibleFrom| #1#) (CATEGORY |domain| (SIGNATURE / #2=($ $ #3=(|Integer|))) (SIGNATURE ** #4=($ $ $)) (SIGNATURE |normalize| #5=($ $)) (SIGNATURE |relerror| (#3# $ $)) (SIGNATURE |shift| #2#) (SIGNATURE |rationalApproximation| (#6=(|Fraction| #3#) $ #7=(|NonNegativeInteger|))) (SIGNATURE |rationalApproximation| (#6# $ #7# #7#)) (SIGNATURE |log2| #8=($)) (SIGNATURE |log10| #8#) (SIGNATURE |exp1| #8#) (SIGNATURE |atan| #4#) (SIGNATURE |log2| #5#) (SIGNATURE |log10| #5#) (SIGNATURE |outputFloating| #9=(#10=(|Void|))) (SIGNATURE |outputFloating| #11=(#10# #7#)) (SIGNATURE |outputFixed| #9#) (SIGNATURE |outputFixed| #11#) (SIGNATURE |outputGeneral| #9#) (SIGNATURE |outputGeneral| #11#) (SIGNATURE |outputSpacing| #11#) (ATTRIBUTE |arbitraryPrecision|) (ATTRIBUTE |arbitraryExponent|)))) (T |Float|)) ((** #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|Float|))) (/ #3=(*1 *1 *1 *2) #4=(AND (|isDomain| *2 #5=(|Integer|)) #2#)) (|normalize| #6=(*1 *1 *1) #2#) (|relerror| (*1 *2 *1 *1) #4#) (|shift| #3# #4#) (|rationalApproximation| (*1 *2 *1 *3) #7=(AND #8=(|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *2 (|Fraction| #5#)) #2#)) (|rationalApproximation| (*1 *2 *1 *3 *3) #7#) (|log2| #9=(*1 *1) #2#) (|log10| #9# #2#) (|exp1| #9# #2#) (|atan| #1# #2#) (|log2| #6# #2#) (|log10| #6# #2#) (|outputFloating| #10=(*1 *2) #11=(AND #12=(|isDomain| *2 (|Void|)) #2#)) (|outputFloating| #13=(*1 *2 *3) #14=(AND #8# #12# #2#)) (|outputFixed| #10# #11#) (|outputFixed| #13# #14#) (|outputGeneral| #10# #11#) (|outputGeneral| #13# #14#) (|outputSpacing| #13# #14#)) @@ -1105,27 +1105,27 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 15 T ELT)) (|right| (#4=($ $) 19 T ELT)) (|retractable?| ((#3# $) 20 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 23 T ELT)) (|retract| (#5=(|#1| $) 21 T ELT)) (|rest| (#4# 37 T ELT)) (|mirror| (#4# 25 T ELT)) (|min| #6=(#7=($ $ $) NIL T ELT)) (|max| #6#) (|lexico| (#2# 46 T ELT)) (|length| (((|PositiveInteger|) $) 40 T ELT)) (|left| (#4# 18 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#5# 36 T ELT)) (|coerce| (((|OutputForm|) $) 32 T ELT) (($ |#1|) 24 T ELT) (((|OrderedFreeMonoid| |#1|) $) 28 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 13 T ELT)) (<= #1#) (< (#2# 44 T ELT)) (* (#7# 35 T ELT))) (((|FreeMagma| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| |#1|) (|CoercibleTo| (|OrderedFreeMonoid| |#1|)) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |first| (|#1| $)) (SIGNATURE |left| #2=($ $)) (SIGNATURE |length| ((|PositiveInteger|) $)) (SIGNATURE |lexico| (#3=(|Boolean|) $ $)) (SIGNATURE |mirror| #2#) (SIGNATURE |rest| #2#) (SIGNATURE |retractable?| (#3# $)) (SIGNATURE |right| #2#) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |FreeMagma|)) ((* (*1 *1 *1 *1) #1=(AND (|isDomain| *1 (|FreeMagma| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|first| #3=(*1 *2 *1) #1#) (|left| #4=(*1 *1 *1) #1#) (|length| #3# (AND (|isDomain| *2 (|PositiveInteger|)) #5=(|isDomain| *1 (|FreeMagma| *3)) #6=(|ofCategory| *3 #2#))) (|lexico| (*1 *2 *1 *1) #7=(AND (|isDomain| *2 (|Boolean|)) #5# #6#)) (|mirror| #4# #1#) (|rest| #4# #1#) (|retractable?| #3# #7#) (|right| #4# #1#) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #5# #6#))) -((~= (#1=((|Boolean|) $ $) 31 T ELT)) (|zero?| ((#2=(|Boolean|) $) 40 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 43 T ELT)) (|sample| (#3=($) 39 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 28 T ELT)) (|retract| ((|#2| $) 29 T ELT)) (|reductum| (($ $) 15 T ELT)) (|opposite?| ((#2# $ $) 42 T ELT)) (|numberOfMonomials| (((|NonNegativeInteger|) $) 19 T ELT)) (|monomials| (((|List| $) $) 20 T ELT)) (|monomial?| (((|Boolean|) $) 23 T ELT)) (|monom| (($ |#2| |#1|) 24 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 16 T ELT)) (|leadingMonomial| ((|#2| $) 18 T ELT)) (|leadingCoefficient| ((|#1| $) 17 T ELT)) (|latex| (((|String|) $) 35 T ELT)) (|hash| (((|SingleInteger|) $) 34 T ELT)) (|coerce| (((|OutputForm|) $) 33 T ELT) (($ |#2|) 27 T ELT)) (|coefficients| (((|List| |#1|) $) 21 T ELT)) (|coefficient| ((|#1| $ |#2|) 25 T ELT)) (|before?| (#1# 32 T ELT)) (|Zero| (#3# 38 T CONST)) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 22 T ELT)) (= (#1# 30 T ELT)) (- (($ $ $) 46 T ELT) (($ $) 45 T ELT)) (+ (($ $ $) 36 T ELT)) (* (($ $ |#1|) 48 T ELT) (($ |#1| . #4=($)) 47 T ELT) (($ (|Integer|) . #4#) 44 T ELT) (($ (|NonNegativeInteger|) $) 41 T ELT) (($ (|PositiveInteger|) $) 37 T ELT) (($ |#1| |#2|) 26 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 31 T ELT)) (|zero?| (#3=(#2# $) 40 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 43 T ELT)) (|sample| (#4=($) 39 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 28 T ELT)) (|retract| (#5=(|#2| $) 29 T ELT)) (|reductum| (#6=($ $) 15 T ELT)) (|opposite?| (#1# 42 T ELT)) (|numberOfMonomials| ((#7=(|NonNegativeInteger|) $) 19 T ELT)) (|monomials| (((|List| $) $) 20 T ELT)) (|monomial?| (#3# 23 T ELT)) (|monom| (($ |#2| |#1|) 24 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 6 T ELT)) (|leadingTerm| ((#8=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 16 T ELT)) (|leadingMonomial| (#5# 18 T ELT)) 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T) ((|CoercibleFrom| #1=(|String|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|filename| #1=(*1 *1 *2 *2 *2) #2=(AND #3=(|isDomain| *2 (|String|)) #4=(|ofCategory| *1 (|FileNameCategory|)))) (|directory| #5=(*1 *2 *1) #6=(AND #4# #3#)) (|name| #5# #6#) (|extension| #5# #6#) (|exists?| #5# #7=(AND #4# (|isDomain| *2 (|Boolean|)))) (|readable?| #5# #7#) (|writable?| #5# #7#) (|new| #1# #2#)) +(|Join| (|SetCategory|) (|HomotopicTo| #1=(|String|)) (CATEGORY |domain| (SIGNATURE |filename| #2=($ #1# #1# #1#)) (SIGNATURE |directory| #3=(#1# $)) (SIGNATURE |name| #3#) (SIGNATURE |extension| #3#) (SIGNATURE |exists?| #4=((|Boolean|) $)) (SIGNATURE |readable?| #4#) (SIGNATURE |writable?| #4#) (SIGNATURE |new| #2#))) +(((|BasicType|) . T) ((|CoercibleFrom| #1=(|String|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|shallowExpand| (#4=((|OutputForm|) $) 64 T ELT)) (|sample| (#5=($) NIL T CONST)) (|rightPower| #6=(($ $ #7=(|PositiveInteger|)) NIL T ELT)) (|plenaryPower| #6#) (|opposite?| #1#) (|leftPower| #6#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (($ #8=(|NonNegativeInteger|)) 38 T ELT)) (|dimension| ((#8#) 18 T ELT)) (|deepExpand| (#4# 66 T ELT)) (|commutator| #9=(#10=($ $ $) NIL T ELT)) (|coerce| (#4# NIL T ELT)) (|before?| #1#) (|associator| (($ $ $ $) NIL T ELT)) (|antiCommutator| #9#) (|Zero| (#5# 24 T CONST)) (= (#2# 41 T ELT)) (- (($ $) 48 T ELT) (#10# 50 T ELT)) (+ (#10# 51 T ELT)) (** #6#) (* (($ #7# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ (|Integer|) . #11=($)) NIL T ELT) (#10# 52 T ELT) (($ $ |#3|) NIL T ELT) (($ |#3| . #11#) 47 T ELT))) (((|FreeNilpotentLie| |#1| |#2| |#3|) (|Join| (|NonAssociativeAlgebra| |#3|) (CATEGORY |domain| (SIGNATURE |dimension| (#1=(|NonNegativeInteger|))) (SIGNATURE |deepExpand| #2=((|OutputForm|) $)) (SIGNATURE |shallowExpand| #2#) (SIGNATURE |generator| ($ #1#)))) #1# #1# (|CommutativeRing|)) (T |FreeNilpotentLie|)) ((|dimension| (*1 *2) #1=(AND (|isDomain| *2 #2=(|NonNegativeInteger|)) #3=(|isDomain| *1 (|FreeNilpotentLie| *3 *4 *5)) (|ofType| *3 *2) (|ofType| *4 *2) #4=(|ofCategory| *5 (|CommutativeRing|)))) (|deepExpand| #5=(*1 *2 *1) #6=(AND (|isDomain| *2 (|OutputForm|)) #3# (|ofType| *3 #2#) (|ofType| *4 #2#) #4#)) (|shallowExpand| #5# #6#) (|generator| (*1 *1 *2) #1#)) @@ -1135,27 +1135,27 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|polyPart| ((|#2| $) 38 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fullPartialFraction| (($ #2=(|Fraction| |#2|)) 93 T ELT)) (|fracPart| ((#3=(|List| (|Record| (|:| |exponent| #4=(|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) 39 T 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(|fullPartialFraction| #5=(*1 *1 *2) (AND (|isDomain| *2 (|Fraction| *4)) #6=(|ofCategory| *4 #4#) #1# #7=(|isDomain| *1 (|FullPartialFractionExpansion| *3 *4)))) (|polyPart| #8=(*1 *2 *1) (AND #3# #2# #1#)) (|fracPart| #8# (AND #1# #9=(|isDomain| *2 (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| *4) (|:| |num| *4)))) #7# #6#)) (|construct| #5# (AND #9# #6# #1# #7#))) -((~= (#1=((|Boolean|) $ $) 10 (OR (|has| |#1| . #2=((|PatternMatchable| (|Integer|)))) (|has| |#1| . #3=((|PatternMatchable| (|Float|))))) ELT)) (|patternMatch| (((|PatternMatchResult| #4=(|Float|) . #5=($)) $ (|Pattern| #4#) (|PatternMatchResult| #4# . #5#)) 16 (|has| |#1| . #3#) ELT) (((|PatternMatchResult| #6=(|Integer|) . #5#) $ (|Pattern| #6#) (|PatternMatchResult| #6# . #5#)) 15 (|has| |#1| . #2#) ELT)) (|latex| (((|String|) $) 14 (OR (|has| |#1| . #2#) (|has| |#1| . #3#)) ELT)) (|hash| (((|SingleInteger|) $) 13 (OR (|has| |#1| . #2#) (|has| |#1| . #3#)) ELT)) (|coerce| (((|OutputForm|) $) 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(($ $ (|NonNegativeInteger|)) 97 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 100 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 69 T ELT)) (|lcm| (#10=($ $ $) 61 T ELT) (#11=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 59 T ELT)) (|gcd| (#10# 63 T ELT) (#11# 62 T ELT)) (|factor| (#4# 93 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 99 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 85 T ELT)) (|charthRoot| (((|Maybe| $) $) 101 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #16#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #15#) 87 T ELT) (($ #15# . #17#) 86 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| 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#17#) 59 T ELT)) (|gcd| (#8# 63 T ELT) (#16# 62 T ELT)) (|factor| (#6# 93 T ELT)) (|extendedEuclidean| (((|Record| #18=(|:| |coef1| $) #19=(|:| |coef2| $) #12#) $ $) 71 T ELT) (((|Union| (|Record| #18# #19#) #10#) $ $ $) 70 T ELT)) (|exquo| ((#9# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) 66 T ELT)) (|euclideanSize| ((#14# $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| #14# #10#) $ $) 99 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #20=(|Integer|)) 42 T ELT) (#4# 58 T ELT) (($ #21=(|Fraction| #20#)) 85 T ELT)) (|charthRoot| ((#5# $) 101 T ELT)) (|characteristic| ((#14#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#7# 24 T CONST)) (|One| (#7# 46 T CONST)) (= (#1# 8 T ELT)) (/ (#8# 84 T ELT)) (- (#4# 30 T ELT) (#8# 29 T ELT)) (+ (#8# 18 T ELT)) (** (($ $ #15#) 36 T ELT) (#13# 44 T ELT) (($ $ #20#) 88 T ELT)) (* (($ #15# $) 17 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((|order| (*1 *2 *1) (AND #1=(|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|discreteLog| (*1 *2 *1 *1) (|partial| AND #1# #2=(|isDomain| *2 (|NonNegativeInteger|)))) (|primeFrobenius| (*1 *1 *1) #1#) (|primeFrobenius| (*1 *1 *1 *2) (AND #1# #2#))) +(|Join| (|Field|) (|CharacteristicNonZero|) (CATEGORY |domain| (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) $)) (SIGNATURE |discreteLog| ((|Union| #1=(|NonNegativeInteger|) "failed") $ $)) (SIGNATURE |primeFrobenius| ($ $)) (SIGNATURE |primeFrobenius| ($ $ #1#)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((|float| (($ #1=(|Integer|) #1#) 11 T ELT) (($ #1# #1# #2=(|PositiveInteger|)) NIL T ELT)) (|digits| ((#2#) 19 T ELT) ((#2# #2#) NIL T ELT))) (((|FloatingPointSystem&| |#1|) (CATEGORY |package| (SIGNATURE |digits| (#1=(|PositiveInteger|) #1#)) (SIGNATURE |digits| (#1#)) (SIGNATURE |float| (|#1| #2=(|Integer|) #2# #1#)) (SIGNATURE |float| (|#1| #2# #2#))) (|FloatingPointSystem|)) (T |FloatingPointSystem&|)) ((|digits| (*1 *2) #1=(AND (|isDomain| *2 (|PositiveInteger|)) (|isDomain| *1 (|FloatingPointSystem&| *3)) (|ofCategory| *3 (|FloatingPointSystem|)))) (|digits| (*1 *2 *2) #1#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|wholePart| ((#3=(|Integer|) $) 109 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#4=(|Boolean|) $) 53 T ELT)) (|truncate| (#5=($ $) 107 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#6=((|Factored| $) $) 91 T ELT)) (|sqrt| (($ $) 117 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sign| (((|Integer|) $) 134 T ELT)) (|sample| (#7=($) 23 T CONST)) (|round| (#5# 106 T ELT)) (|retractIfCan| (((|Union| #3# . #8=("failed")) . #9=($)) 122 T ELT) (((|Union| #10=(|Fraction| #3#) . #8#) . #9#) 119 T ELT)) (|retract| ((#3# . #11=($)) 123 T ELT) ((#10# . #11#) 120 T ELT)) (|rem| (#12=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#12# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #13=(|List| $)) (|:| |generator| $)) #13#) 67 T ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|precision| (((|PositiveInteger|)) 150 T ELT) (((|PositiveInteger|) (|PositiveInteger|)) 147 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (((|Boolean|) $) 132 T ELT)) (|patternMatch| (((|PatternMatchResult| #14=(|Float|) . #15=($)) $ (|Pattern| #14#) (|PatternMatchResult| #14# . #15#)) 113 T ELT)) (|order| (((|Integer|) $) 156 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|nthRoot| (($ $ #16=(|Integer|)) 116 T ELT)) (|norm| (#5# 112 T ELT)) (|negative?| (((|Boolean|) $) 133 T ELT)) (|multiEuclidean| (((|Union| #17=(|List| $) #18="failed") #17# $) 69 T ELT)) (|min| (#19=($ $ $) 126 T ELT) (($) 144 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|max| (#19# 127 T ELT) (($) 143 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|mantissa| (((|Integer|) $) 153 T ELT)) (|lcm| (#20=($ $ $) 61 T ELT) (#21=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) 146 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#22=(|SparseUnivariatePolynomial| $) #22# #22#) 59 T ELT)) (|gcd| (#20# 63 T ELT) (#21# 62 T ELT)) 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114 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #26=(|Fraction| #27=(|Integer|))) 85 T ELT) (($ #3#) 121 T ELT) (($ #10#) 118 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|ceiling| (#5# 111 T ELT)) (|bits| (((|PositiveInteger|)) 152 T ELT) (((|PositiveInteger|) (|PositiveInteger|)) 149 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|before?| (#1# 6 T ELT)) (|base| (((|PositiveInteger|)) 155 T ELT)) (|associates?| ((#4# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| (($ $) 135 T ELT)) (|Zero| (#7# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#28=((|Boolean|) $ $) 128 T ELT)) (> (#28# 130 T ELT)) (= (#1# 8 T ELT)) (<= (#28# 129 T ELT)) (< (#28# 131 T ELT)) (/ (($ $ $) 84 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #27#) 88 T ELT) (($ $ (|Fraction| #16#)) 115 T ELT)) (* (($ 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$) 43 T ELT)) (|quo| (#13# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) 67 T ELT)) (|prime?| (#3# 90 T ELT)) (|precision| (#17=(#18=(|PositiveInteger|)) 150 T ELT) (#19=(#18# #18#) 147 #20=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (#3# 132 T ELT)) (|patternMatch| ((#21=(|PatternMatchResult| #22=(|Float|) $) $ #23=(|Pattern| #22#) #21#) 113 T ELT)) (|order| (#4# 156 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|nthRoot| (#24=($ $ #5#) 116 T ELT)) (|norm| (#6# 112 T ELT)) (|negative?| (#3# 133 T ELT)) (|multiEuclidean| (((|Union| #15# #10#) #15# $) 69 T ELT)) (|min| (#13# 126 T ELT) (#8# 144 #25=(AND (|not| #20#) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|max| (#13# 127 T ELT) (#8# 143 #25# ELT)) (|mantissa| (#4# 153 T ELT)) (|lcm| (#13# 61 T ELT) (#26=($ #15#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#6# 89 T ELT)) (|increasePrecision| (#27=(#18# #5#) 146 #20# ELT)) 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85 T ELT) (#33# 121 T ELT) (#34# 118 T ELT)) (|characteristic| ((#31#) 41 T CONST)) (|ceiling| (#6# 111 T ELT)) (|bits| (#17# 152 T ELT) (#19# 149 #20# ELT)) (|before?| (#1# 6 T ELT)) (|base| (#17# 155 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|abs| (#6# 135 T ELT)) (|Zero| (#8# 24 T CONST)) (|One| (#8# 46 T CONST)) (>= (#1# 128 T ELT)) (> (#1# 130 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 129 T ELT)) (< (#1# 131 T ELT)) (/ (#13# 84 T ELT)) (- (#6# 30 T ELT) (#13# 29 T ELT)) (+ (#13# 18 T ELT)) (** (($ $ #18#) 36 T ELT) (($ $ #31#) 44 T ELT) (#24# 88 T ELT) (#35=($ $ #12#) 115 T ELT)) (* (($ #18# $) 17 T ELT) (($ #31# $) 21 T ELT) (($ #5# . #36=($)) 31 T ELT) (#13# 35 T ELT) (#35# 87 T ELT) (($ #12# . #36#) 86 T ELT))) (((|FloatingPointSystem|) (|Category|)) (T |FloatingPointSystem|)) -((|float| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|float| (*1 *1 *2 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|)))) (|base| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|exponent| (*1 *2 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|)))) (|mantissa| (*1 *2 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|Integer|)))) (|bits| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|digits| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|precision| (*1 *2) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|bits| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|digits| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|precision| (*1 *2 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)))) (|increasePrecision| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|decreasePrecision| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|has| *1 (ATTRIBUTE |arbitraryPrecision|)) (|ofCategory| *1 (|FloatingPointSystem|)) (|isDomain| *2 (|PositiveInteger|)))) (|min| (*1 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|not| (|has| *1 (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| *1 (ATTRIBUTE |arbitraryExponent|))))) (|max| (*1 *1) (AND (|ofCategory| *1 (|FloatingPointSystem|)) (|not| (|has| *1 (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| *1 (ATTRIBUTE |arbitraryExponent|)))))) -(|Join| (|RealNumberSystem|) (CATEGORY |domain| (ATTRIBUTE |approximate|) (SIGNATURE |float| ($ (|Integer|) (|Integer|))) (SIGNATURE |float| ($ (|Integer|) (|Integer|) (|PositiveInteger|))) (SIGNATURE |order| ((|Integer|) $)) (SIGNATURE |base| ((|PositiveInteger|))) (SIGNATURE |exponent| ((|Integer|) $)) (SIGNATURE |mantissa| ((|Integer|) $)) (SIGNATURE |bits| ((|PositiveInteger|))) (SIGNATURE |digits| ((|PositiveInteger|))) (SIGNATURE |precision| ((|PositiveInteger|))) (IF (|has| $ (ATTRIBUTE |arbitraryPrecision|)) (PROGN (SIGNATURE |bits| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |digits| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |precision| ((|PositiveInteger|) (|PositiveInteger|))) (SIGNATURE |increasePrecision| ((|PositiveInteger|) (|Integer|))) (SIGNATURE |decreasePrecision| ((|PositiveInteger|) (|Integer|)))) |%noBranch|) (IF (|has| $ (ATTRIBUTE |arbitraryExponent|)) |%noBranch| (IF (|has| $ (ATTRIBUTE |arbitraryPrecision|)) |%noBranch| (PROGN (SIGNATURE |min| ($)) (SIGNATURE |max| ($))))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|Pattern| #2=(|Float|))) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #2#) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RealNumberSystem|) . T) ((|RetractableTo| (|Fraction| #3=(|Integer|))) . T) ((|RetractableTo| #3#) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((|float| (*1 *1 *2 *2) (AND #1=(|isDomain| *2 #2=(|Integer|)) #3=(|ofCategory| *1 (|FloatingPointSystem|)))) (|float| (*1 *1 *2 *2 *3) (AND #1# (|isDomain| *3 #4=(|PositiveInteger|)) #3#)) (|order| #5=(*1 *2 *1) #6=(AND #3# #1#)) (|base| #7=(*1 *2) #8=(AND #3# #9=(|isDomain| *2 #4#))) (|exponent| #5# #6#) (|mantissa| #5# #6#) (|bits| #7# #8#) (|digits| #7# #8#) (|precision| #7# #8#) (|bits| #10=(*1 *2 *2) #11=(AND #9# #12=(|has| *1 (ATTRIBUTE |arbitraryPrecision|)) #3#)) (|digits| #10# #11#) (|precision| #10# #11#) (|increasePrecision| #13=(*1 *2 *3) #14=(AND (|isDomain| *3 #2#) #12# #3# #9#)) (|decreasePrecision| #13# #14#) (|min| #15=(*1 *1) #16=(AND #3# (|not| #12#) (|not| (|has| *1 (ATTRIBUTE |arbitraryExponent|))))) (|max| #15# #16#)) +(|Join| (|RealNumberSystem|) (CATEGORY |domain| (ATTRIBUTE |approximate|) (SIGNATURE |float| ($ #1=(|Integer|) #1#)) (SIGNATURE |float| ($ #1# #1# #2=(|PositiveInteger|))) (SIGNATURE |order| #3=(#1# $)) (SIGNATURE |base| #4=(#2#)) (SIGNATURE |exponent| #3#) (SIGNATURE |mantissa| #3#) (SIGNATURE |bits| #4#) (SIGNATURE |digits| #4#) (SIGNATURE |precision| #4#) (IF #5=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) (PROGN (SIGNATURE |bits| #6=(#2# #2#)) (SIGNATURE |digits| #6#) (SIGNATURE |precision| #6#) (SIGNATURE |increasePrecision| #7=(#2# #1#)) (SIGNATURE |decreasePrecision| #7#)) |%noBranch|) (IF (|has| $ (ATTRIBUTE |arbitraryExponent|)) |%noBranch| (IF #5# |%noBranch| (PROGN (SIGNATURE |min| #8=($)) (SIGNATURE |max| #8#)))))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| #3=(|Float|)) . T) ((|ConvertibleTo| (|Pattern| #3#)) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #3#) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RealNumberSystem|) . T) ((|RetractableTo| #1#) . T) ((|RetractableTo| #2#) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 59 T ELT)) (|unitNormalize| (#5=($ $) 77 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 189 T ELT)) (|unitCanonical| #6=(#5# NIL T ELT)) (|unit?| (#4# 48 T ELT)) (|unit| (#7=(|#1| $) 16 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| (#5# NIL #8=(|has| |#1| (|UniqueFactorizationDomain|)) ELT)) (|squareFree| #9=(((|Factored| $) $) NIL #8# ELT)) (|sqfrFactor| (#10=($ |#1| #11=(|Integer|)) 42 T ELT)) (|sample| (#12=($) NIL T CONST)) (|retractIfCan| (((|Union| #11# . #13=(#14="failed")) $) NIL #15=(|has| |#1| (|RetractableTo| #11#)) ELT) (#16=((|Union| #17=(|Fraction| #11#) #14#) $) NIL #18=(|has| |#1| (|RetractableTo| #17#)) ELT) (((|Union| |#1| . #13#) $) 147 T ELT)) (|retract| (#19=(#11# $) NIL #15# ELT) (#20=(#17# $) NIL #18# ELT) (#7# 73 T ELT)) (|recip| ((#21=(|Union| $ #14#) $) 163 T ELT)) (|rationalIfCan| (#16# 84 #22=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# 80 #22# ELT)) (|rational| (#20# 82 #22# ELT)) (|primeFactor| (#10# 44 T ELT)) (|prime?| (#4# 209 #8# ELT)) (|opposite?| #1#) (|one?| (#4# 61 T ELT)) (|numberOfFactors| ((#23=(|NonNegativeInteger|) $) 51 T ELT)) (|nthFlag| ((#24=(|Union| "nil" "sqfr" "irred" "prime") $ #11#) 174 T ELT)) (|nthFactor| ((|#1| $ #11#) 173 T ELT)) (|nthExponent| ((#11# $ #11#) 172 T ELT)) (|nilFactor| (#10# 41 T ELT)) (|map| (($ #25=(|Mapping| |#1| |#1|) $) 182 T ELT)) (|makeFR| (($ |#1| #26=(|List| (|Record| (|:| |flg| #24#) (|:| |fctr| |#1|) (|:| |xpnt| #11#)))) 78 T ELT)) (|lcm| #27=(($ #28=(|List| $)) NIL #29=(|has| |#1| (|GcdDomain|)) ELT) (#30=($ $ $) NIL #29# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|irreducibleFactor| (#10# 43 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#31=(|SparseUnivariatePolynomial| $) #31# #31#) NIL #29# ELT)) (|gcd| #27# (#30# 190 #29# ELT)) (|flagFactor| (($ |#1| #11# #24#) 40 T ELT)) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| #11#))) $) 72 T ELT)) (|factorList| ((#26# $) 12 T ELT)) (|factor| #9#) (|exquo| ((#21# $ $) 175 T ELT)) (|exponent| (#19# 166 T ELT)) (|expand| (#7# 74 T ELT)) (|eval| (($ $ #32=(|List| |#1|) #32#) NIL #33=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #33# ELT) (($ $ #34=(|Equation| |#1|)) NIL #33# ELT) (($ $ (|List| #34#)) 99 #33# ELT) (($ $ #35=(|List| #36=(|Symbol|)) #32#) 105 #37=(|has| |#1| (|InnerEvalable| #36# |#1|)) ELT) (($ $ #36# |#1|) NIL #37# ELT) (($ $ #36# $) NIL #38=(|has| |#1| (|InnerEvalable| #36# $)) ELT) (($ $ #35# #28#) 106 #38# ELT) (($ $ (|List| #39=(|Equation| $))) 102 #40=(|has| |#1| (|Evalable| $)) ELT) (($ $ #39#) NIL #40# ELT) (($ $ $ $) NIL #40# ELT) (($ $ #28# #28#) NIL #40# ELT)) (|elt| (#41=($ $ |#1|) 91 (|has| |#1| (|Eltable| |#1| |#1|)) ELT) (#30# 92 (|has| |#1| (|Eltable| $ $)) ELT)) (|differentiate| (#42=($ $ #25#) 181 T ELT) #43=(($ $ #25# #23#) NIL T ELT) #44=(#5# NIL #45=(|has| |#1| (|DifferentialSpace|)) ELT) #46=(#47=($ $ #23#) NIL #45# ELT) #48=(($ $ #36#) NIL #49=(|has| |#1| (|PartialDifferentialSpace| #36#)) ELT) #50=(($ $ #35#) NIL #49# ELT) #51=(($ $ #36# #23#) NIL #49# ELT) #52=(($ $ #35# (|List| #23#)) NIL #49# ELT)) (|convert| ((#53=(|InputForm|) $) 39 (|has| |#1| (|ConvertibleTo| #53#)) ELT) (((|Float|) $) 112 #54=(|has| |#1| (|RealConstant|)) ELT) (((|DoubleFloat|) $) 118 #54# ELT)) (|coerce| (((|OutputForm|) $) 145 T ELT) (($ #11#) 64 T ELT) #6# (($ |#1|) 63 T ELT) (($ #17#) NIL #18# ELT)) (|characteristic| ((#23#) 66 T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#12# 53 T CONST)) (|One| (#12# 52 T CONST)) (D (#42# NIL T ELT) #43# #44# #46# #48# #50# #51# #52#) (= (#2# 158 T ELT)) (- (#5# 160 T ELT) (#30# NIL T ELT)) (+ (#30# 179 T ELT)) (** (($ $ #55=(|PositiveInteger|)) NIL T ELT) (#47# 124 T ELT)) (* (($ #55# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #11# $) 68 T ELT) (#30# 67 T ELT) (($ |#1| $) 69 T ELT) (#41# NIL T ELT))) (((|Factored| |#1|) (|Join| #1=(|IntegralDomain|) (|DifferentialExtension| |#1|) (|Algebra| |#1|) (|FullyEvalableOver| |#1|) (|FullyRetractableTo| |#1|) (|Functorial| |#1|) (CATEGORY |domain| (SIGNATURE |expand| #2=(|#1| $)) (SIGNATURE |exponent| (#3=(|Integer|) $)) (SIGNATURE |makeFR| ($ |#1| #4=(|List| (|Record| (|:| |flg| #5=(|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| #3#))))) (SIGNATURE |factorList| (#4# $)) (SIGNATURE |nilFactor| #6=($ |#1| #3#)) (SIGNATURE |factors| ((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| #3#))) $)) (SIGNATURE |irreducibleFactor| #6#) (SIGNATURE |nthExponent| (#3# $ #3#)) (SIGNATURE |nthFactor| (|#1| $ #3#)) (SIGNATURE |nthFlag| (#5# $ #3#)) (SIGNATURE |numberOfFactors| ((|NonNegativeInteger|) $)) (SIGNATURE |primeFactor| #6#) (SIGNATURE |sqfrFactor| #6#) (SIGNATURE |flagFactor| ($ |#1| #3# #5#)) (SIGNATURE |unit| #2#) (SIGNATURE |unitNormalize| ($ $)) (IF (|has| |#1| #7=(|GcdDomain|)) (ATTRIBUTE #7#) |%noBranch|) (IF (|has| |#1| #8=(|RealConstant|)) (ATTRIBUTE #8#) |%noBranch|) (IF (|has| |#1| #9=(|UniqueFactorizationDomain|)) (ATTRIBUTE #9#) |%noBranch|) (IF (|has| |#1| #10=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #10#) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| (#11=(|Fraction| #3#) $)) (SIGNATURE |rationalIfCan| ((|Union| #11# "failed") $))) |%noBranch|) (IF (|has| |#1| #12=(|Eltable| $ $)) (ATTRIBUTE #12#) |%noBranch|) (IF (|has| |#1| #13=(|Evalable| $)) (ATTRIBUTE #13#) |%noBranch|) (IF (|has| |#1| #14=(|InnerEvalable| (|Symbol|) $)) (ATTRIBUTE #14#) |%noBranch|))) #1#) (T |Factored|)) ((|expand| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *1 (|Factored| *2)) #4=(|ofCategory| *2 #5=(|IntegralDomain|)))) (|exponent| #1# #6=(AND (|isDomain| *2 #7=(|Integer|)) #8=(|isDomain| *1 (|Factored| *3)) #9=(|ofCategory| *3 #5#))) (|makeFR| #10=(*1 *1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| #11=(|:| |flg| #12=(|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *2) #13=(|:| |xpnt| #7#)))) #4# #3#)) (|factorList| #1# (AND (|isDomain| *2 (|List| (|Record| #11# (|:| |fctr| *3) #13#))) #8# #9#)) (|nilFactor| #10# #14=(AND #15=(|isDomain| *3 #7#) #3# #4#)) (|factors| #1# (AND (|isDomain| *2 (|List| (|Record| (|:| |factor| *3) (|:| |exponent| #7#)))) #8# #9#)) (|irreducibleFactor| #10# #14#) (|nthExponent| (*1 *2 *1 *2) #6#) (|nthFactor| #16=(*1 *2 *1 *3) #14#) (|nthFlag| #16# (AND #15# (|isDomain| *2 #12#) (|isDomain| *1 (|Factored| *4)) (|ofCategory| *4 #5#))) (|numberOfFactors| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #8# #9#)) (|primeFactor| #10# #14#) (|sqfrFactor| #10# #14#) (|flagFactor| (*1 *1 *2 *3 *4) (AND #15# (|isDomain| *4 #12#) #3# #4#)) (|unit| #1# #2#) (|unitNormalize| (*1 *1 *1) #2#) (|rational?| #1# (AND (|isDomain| *2 (|Boolean|)) #8# #17=(|ofCategory| *3 (|IntegerNumberSystem|)) #9#)) (|rational| #1# (AND #18=(|isDomain| *2 (|Fraction| #7#)) #8# #17# #9#)) (|rationalIfCan| #1# (|partial| AND #18# #8# #17# #9#))) @@ -1171,19 +1171,19 @@ NIL ((|traceMatrix| (#1=(#2=(|Matrix| |#2|) #3=(|Vector| $)) NIL T ELT) ((#2#) 18 T ELT)) (|represents| (($ #4=(|Vector| |#2|) #3#) NIL T ELT) (#5=($ #4#) 24 T ELT)) (|regularRepresentation| ((#2# $ #3#) NIL T ELT) ((#2# $) 40 T ELT)) (|minimalPolynomial| (#6=(|#3| $) 69 T ELT)) (|discriminant| ((|#2| #3#) NIL T ELT) ((|#2|) 20 T ELT)) (|coordinates| ((#4# $ #3#) NIL T ELT) ((#2# #3# #3#) NIL T ELT) (#7=(#4# $) 22 T ELT) (#1# 38 T ELT)) (|convert| (#7# 11 T ELT) (#5# 13 T ELT)) (|characteristicPolynomial| (#6# 55 T ELT))) (((|FramedAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |regularRepresentation| (#1=(|Matrix| |#2|) |#1|)) (SIGNATURE |discriminant| (|#2|)) (SIGNATURE |traceMatrix| (#1#)) (SIGNATURE |convert| #2=(|#1| #3=(|Vector| |#2|))) (SIGNATURE |convert| #4=(#3# |#1|)) (SIGNATURE |represents| #2#) (SIGNATURE |coordinates| #5=(#1# #6=(|Vector| |#1|))) (SIGNATURE |coordinates| #4#) (SIGNATURE |minimalPolynomial| #7=(|#3| |#1|)) (SIGNATURE |characteristicPolynomial| #7#) (SIGNATURE |traceMatrix| #5#) (SIGNATURE |discriminant| (|#2| #6#)) (SIGNATURE |represents| (|#1| #3# #6#)) (SIGNATURE |coordinates| (#1# #6# #6#)) (SIGNATURE |coordinates| (#3# |#1| #6#)) (SIGNATURE |regularRepresentation| (#1# |#1| #6#))) (|FramedAlgebra| |#2| |#3|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |#2|)) (T |FramedAlgebra&|)) ((|traceMatrix| #1=(*1 *2) (AND (|ofCategory| *4 #2=(|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)) (|isDomain| *1 (|FramedAlgebra&| *3 *4 *5)) (|ofCategory| *3 (|FramedAlgebra| *4 *5)))) (|discriminant| #1# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|FramedAlgebra&| *3 *2 *4)) (|ofCategory| *3 (|FramedAlgebra| *2 *4))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|traceMatrix| (((|Matrix| |#1|) #3=(|Vector| $)) 62 T ELT) (((|Matrix| |#1|)) 77 T ELT)) (|trace| ((|#1| . #4=($)) 68 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|represents| (($ (|Vector| |#1|) #3#) 64 T ELT) (($ (|Vector| |#1|)) 80 T ELT)) (|regularRepresentation| (((|Matrix| |#1|) $ #3#) 69 T ELT) (((|Matrix| |#1|) $) 75 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rank| (((|PositiveInteger|)) 70 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|norm| ((|#1| . #4#) 67 T ELT)) (|minimalPolynomial| ((|#2| . #6=($)) 60 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| #3#) 63 T ELT) ((|#1|) 76 T ELT)) (|coordinates| (((|Vector| |#1|) $ #3#) 66 T ELT) (((|Matrix| |#1|) #3# #3#) 65 T ELT) (((|Vector| |#1|) $) 82 T ELT) (((|Matrix| |#1|) (|Vector| $)) 81 T ELT)) (|convert| (((|Vector| |#1|) $) 79 T ELT) (($ (|Vector| |#1|)) 78 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT)) (|charthRoot| (((|Maybe| $) $) 59 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#2| . #6#) 61 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 83 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #7#) 54 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|traceMatrix| (#4=(#5=(|Matrix| |#1|) #6=(|Vector| $)) 62 T ELT) ((#5#) 77 T ELT)) (|trace| (#7=(|#1| $) 68 T ELT)) (|subtractIfCan| ((#8=(|Maybe| $) $ $) 26 T ELT)) (|sample| (#9=($) 23 T CONST)) (|represents| (($ #10=(|Vector| |#1|) #6#) 64 T ELT) (#11=($ #10#) 80 T ELT)) (|regularRepresentation| ((#5# $ #6#) 69 T ELT) ((#5# $) 75 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rank| ((#12=(|PositiveInteger|)) 70 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|norm| (#7# 67 T ELT)) (|minimalPolynomial| (#13=(|#2| $) 60 (|has| |#1| (|Field|)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|discriminant| ((|#1| #6#) 63 T ELT) ((|#1|) 76 T ELT)) (|coordinates| ((#10# $ #6#) 66 T ELT) ((#5# #6# #6#) 65 T ELT) (#14=(#10# $) 82 T ELT) (#4# 81 T ELT)) (|convert| (#14# 79 T ELT) (#11# 78 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #15=(|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT)) (|charthRoot| ((#8# $) 59 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| (#13# 61 T ELT)) (|characteristic| ((#16=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| ((#6#) 83 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#9# 24 T CONST)) (|One| (#9# 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#17=($ $ $) 29 T ELT)) (+ (#17# 18 T ELT)) (** (($ $ #12#) 36 T ELT) (($ $ #16#) 44 T ELT)) (* (($ #12# $) 17 T ELT) (($ #16# $) 21 T ELT) (($ #15# . #18=($)) 31 T ELT) (#17# 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #18#) 54 T ELT))) (((|FramedAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |FramedAlgebra|)) -((|basis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FramedAlgebra| *4 *5)) (|ofCategory| *4 (|CommutativeRing|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|convert| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Vector| *3)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|traceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Matrix| *3)))) (|discriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|regularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedAlgebra| *3 *4)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 (|Matrix| *3))))) -(|Join| (|FiniteRankAlgebra| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |convert| ((|Vector| |t#1|) $)) (SIGNATURE |convert| ($ (|Vector| |t#1|))) (SIGNATURE |traceMatrix| ((|Matrix| |t#1|))) (SIGNATURE |discriminant| (|t#1|)) (SIGNATURE |regularRepresentation| ((|Matrix| |t#1|) $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FiniteRankAlgebra| |#1| |#2|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|basis| #1=(*1 *2) (AND #2=(|ofCategory| *3 #3=(|CommutativeRing|)) #4=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|isDomain| *2 #5=(|Vector| *1)) #6=(|ofCategory| *1 (|FramedAlgebra| *3 *4)))) (|coordinates| #7=(*1 *2 *1) #8=(AND #6# #2# #4# #9=(|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 #5#) (|ofCategory| *1 (|FramedAlgebra| *4 *5)) (|ofCategory| *4 #3#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Matrix| *4)))) (|represents| #10=(*1 *1 *2) #11=(AND #9# #2# #6# #4#)) (|convert| #7# #8#) (|convert| #10# #11#) (|traceMatrix| #1# #12=(AND #6# #2# #4# (|isDomain| *2 (|Matrix| *3)))) (|discriminant| #1# (AND (|ofCategory| *1 (|FramedAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #3#))) (|regularRepresentation| #7# #12#)) +(|Join| (|FiniteRankAlgebra| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |basis| (#1=(|Vector| $))) (SIGNATURE |coordinates| #2=(#3=(|Vector| |t#1|) $)) (SIGNATURE |coordinates| (#4=(|Matrix| |t#1|) #1#)) (SIGNATURE |represents| #5=($ #3#)) (SIGNATURE |convert| #2#) (SIGNATURE |convert| #5#) (SIGNATURE |traceMatrix| (#4#)) (SIGNATURE |discriminant| (|t#1|)) (SIGNATURE |regularRepresentation| (#4# $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FiniteRankAlgebra| |#1| |#2|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|retractIfCan| (((|Union| |#2| #1="failed") $) NIL T ELT) (((|Union| #2=(|Fraction| #3=(|Integer|)) #1#) $) 27 T ELT) (((|Union| #3# #1#) $) 19 T ELT)) (|retract| ((|#2| $) NIL T ELT) ((#2# $) 24 T ELT) ((#3# $) 14 T ELT)) (|coerce| (($ |#2|) NIL T ELT) (($ #2#) 22 T ELT) (($ #3#) 11 T ELT))) (((|FullyRetractableTo&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| #1=(|Integer|))) (SIGNATURE |retractIfCan| ((|Union| #1# #2="failed") |#1|)) (SIGNATURE |retract| (#1# |#1|)) (SIGNATURE |coerce| (|#1| #3=(|Fraction| #1#))) (SIGNATURE |retractIfCan| ((|Union| #3# #2#) |#1|)) (SIGNATURE |retract| (#3# |#1|)) (SIGNATURE |retract| (|#2| |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #2#) |#1|)) (SIGNATURE |coerce| (|#1| |#2|))) (|FullyRetractableTo| |#2|) (|Type|)) (T |FullyRetractableTo&|)) NIL -((|retractIfCan| (((|Union| |#1| . #1=("failed")) . #2=($)) 9 T ELT) (((|Union| #3=(|Fraction| (|Integer|)) . #1#) . #2#) 16 (|has| |#1| . #4=((|RetractableTo| (|Fraction| (|Integer|))))) ELT) (((|Union| #5=(|Integer|) . #1#) . #2#) 13 (|has| |#1| . #6=((|RetractableTo| (|Integer|)))) ELT)) (|retract| ((|#1| . #7=($)) 8 T ELT) ((#3# . #7#) 17 (|has| |#1| . #4#) ELT) ((#5# . #7#) 14 (|has| |#1| . #6#) ELT)) (|coerce| (($ |#1|) 6 T ELT) (($ #3#) 15 (|has| |#1| . #4#) ELT) (($ #5#) 12 (|has| |#1| . #6#) ELT))) +((|retractIfCan| (((|Union| |#1| . #1=("failed")) . #2=($)) 9 T ELT) (((|Union| #3=(|Fraction| #4=(|Integer|)) . #1#) . #2#) 16 #5=(|has| |#1| (|RetractableTo| #3#)) ELT) (((|Union| #4# . #1#) . #2#) 13 #6=(|has| |#1| (|RetractableTo| #4#)) ELT)) (|retract| ((|#1| . #7=($)) 8 T ELT) ((#3# . #7#) 17 #5# ELT) ((#4# . #7#) 14 #6# ELT)) (|coerce| (($ |#1|) 6 T ELT) (($ #3#) 15 #5# ELT) (($ #4#) 12 #6# ELT))) (((|FullyRetractableTo| |#1|) (|Category|) (|Type|)) (T |FullyRetractableTo|)) NIL -(|Join| (|RetractableTo| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Integer|))) |%noBranch|) (IF (|has| |t#1| (|RetractableTo| (|Fraction| (|Integer|)))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|)))) |%noBranch|))) -(((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2=(|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|CoercibleFrom| |#1|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T)) +(|Join| (|RetractableTo| |t#1|) (CATEGORY |package| (IF (|has| |t#1| #1=(|RetractableTo| #2=(|Integer|))) (ATTRIBUTE #1#) |%noBranch|) (IF (|has| |t#1| #3=(|RetractableTo| (|Fraction| #2#))) (ATTRIBUTE #3#) |%noBranch|))) +(((|CoercibleFrom| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|CoercibleFrom| |#1|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|randomLC| ((|#4| #5=(|NonNegativeInteger|) #6=(|Vector| |#4|)) 55 T ELT)) (|one?| ((#3# $) NIL T ELT)) (|numer| (#7=(#6# $) 15 T ELT)) (|norm| ((|#2| $) 53 T ELT)) (|minimize| (#8=($ $) 155 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#8# 103 T ELT)) (|ideal| (($ #6#) 102 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#1| $) 16 T ELT)) (|conjugate| #9=(#10=($ $ $) NIL T ELT)) (|commutator| #9#) (|coerce| (((|OutputForm|) $) 147 T ELT)) (|before?| #1#) (|basis| (#7# 140 T ELT)) (|One| (#4# 11 T CONST)) (= (#2# 39 T ELT)) (/ #9#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #5#) NIL T ELT) (($ $ (|Integer|)) 133 T ELT)) (* (#10# 130 T ELT))) (((|FractionalIdeal| |#1| |#2| |#3| |#4|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |ideal| ($ #1=(|Vector| |#4|))) (SIGNATURE |basis| #2=(#1# $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |numer| #2#) (SIGNATURE |denom| (|#1| $)) (SIGNATURE |minimize| ($ $)) (SIGNATURE |randomLC| (|#4| (|NonNegativeInteger|) #1#)))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Join| (|FramedAlgebra| |#2| |#3|) (|RetractableTo| |#2|))) (T |FractionalIdeal|)) ((|ideal| (*1 *1 *2) (AND #1=(|isDomain| *2 (|Vector| *6)) #2=(|ofCategory| *6 (|Join| (|FramedAlgebra| *4 *5) (|RetractableTo| *4))) #3=(|ofCategory| *4 #4=(|QuotientFieldCategory| *3)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) #6=(|ofCategory| *3 #7=(|EuclideanDomain|)) #8=(|isDomain| *1 (|FractionalIdeal| *3 *4 *5 *6)))) (|basis| #9=(*1 *2 *1) #10=(AND #6# #3# #5# #1# #8# #2#)) (|norm| #9# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #4#) (|isDomain| *1 (|FractionalIdeal| *3 *2 *4 *5)) #6# (|ofCategory| *5 (|Join| (|FramedAlgebra| *2 *4) (|RetractableTo| *2))))) (|numer| #9# #10#) (|denom| #9# (AND #11=(|ofCategory| *3 (|QuotientFieldCategory| *2)) #12=(|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) #13=(|ofCategory| *2 #7#) #14=(|isDomain| *1 (|FractionalIdeal| *2 *3 *4 *5)) #15=(|ofCategory| *5 (|Join| (|FramedAlgebra| *3 *4) (|RetractableTo| *3))))) (|minimize| (*1 *1 *1) (AND #13# #11# #12# #14# #15#)) (|randomLC| (*1 *2 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Vector| *2)) (|ofCategory| *5 #7#) (|ofCategory| *6 (|QuotientFieldCategory| *5)) (|ofCategory| *2 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6))) (|isDomain| *1 (|FractionalIdeal| *5 *6 *7 *2)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6))))) @@ -1199,22 +1199,22 @@ NIL ((|unit| (#1=((|Union| $ #2="failed")) 99 T ELT)) (|structuralConstants| ((#3=(|Vector| #4=(|Matrix| |#2|)) #5=(|Vector| $)) NIL T ELT) ((#3#) 104 T ELT)) (|rightUnits| (#6=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #2#)) 97 T ELT)) (|rightUnit| (#1# 96 T ELT)) (|rightTraceMatrix| #7=(#8=(#4# #5#) NIL T ELT) (#9=(#4#) 115 T ELT)) (|rightRegularRepresentation| #10=((#4# $ #5#) NIL T ELT) (#11=(#4# $) 123 T ELT)) (|rightRankPolynomial| (#12=((|SparseUnivariatePolynomial| #13=(|Polynomial| |#2|))) 64 T ELT)) (|rightDiscriminant| #14=((|#2| #5#) NIL T ELT) (#15=(|#2|) 119 T ELT)) (|represents| (($ #16=(|Vector| |#2|) #5#) NIL T ELT) (#17=($ #16#) 125 T ELT)) (|leftUnits| (#6# 95 T ELT)) (|leftUnit| (#1# 87 T ELT)) (|leftTraceMatrix| #7# (#9# 113 T ELT)) (|leftRegularRepresentation| #10# (#11# 121 T ELT)) (|leftRankPolynomial| (#12# 63 T ELT)) (|leftDiscriminant| #14# (#15# 117 T ELT)) (|coordinates| ((#16# $ #5#) NIL T ELT) ((#4# #5# #5#) NIL T ELT) (#18=(#16# $) 124 T ELT) (#8# 133 T ELT)) (|convert| (#18# 109 T ELT) (#17# 111 T ELT)) (|conditionsForIdempotents| ((#19=(|List| #13#) #5#) NIL T ELT) ((#19#) 107 T ELT)) (|apply| (($ #4# $) 103 T ELT))) (((|FramedNonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |apply| (|#1| #1=(|Matrix| |#2|) |#1|)) (SIGNATURE |rightRankPolynomial| #2=((|SparseUnivariatePolynomial| #3=(|Polynomial| |#2|)))) (SIGNATURE |leftRankPolynomial| #2#) (SIGNATURE |rightRegularRepresentation| #4=(#1# |#1|)) (SIGNATURE |leftRegularRepresentation| #4#) (SIGNATURE |rightTraceMatrix| #5=(#1#)) (SIGNATURE |leftTraceMatrix| #5#) (SIGNATURE |rightDiscriminant| #6=(|#2|)) (SIGNATURE |leftDiscriminant| #6#) (SIGNATURE |convert| #7=(|#1| #8=(|Vector| |#2|))) (SIGNATURE |convert| #9=(#8# |#1|)) (SIGNATURE |represents| #7#) (SIGNATURE |conditionsForIdempotents| (#10=(|List| #3#))) (SIGNATURE |structuralConstants| (#11=(|Vector| #1#))) (SIGNATURE |coordinates| #12=(#1# #13=(|Vector| |#1|))) (SIGNATURE |coordinates| #9#) (SIGNATURE |unit| #14=((|Union| |#1| #15="failed"))) (SIGNATURE |rightUnit| #14#) (SIGNATURE |leftUnit| #14#) (SIGNATURE |rightUnits| #16=((|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) #15#))) (SIGNATURE |leftUnits| #16#) (SIGNATURE |rightTraceMatrix| #12#) (SIGNATURE |leftTraceMatrix| #12#) (SIGNATURE |rightDiscriminant| #17=(|#2| #13#)) (SIGNATURE |leftDiscriminant| #17#) (SIGNATURE |represents| (|#1| #8# #13#)) (SIGNATURE |coordinates| (#1# #13# #13#)) (SIGNATURE |coordinates| (#8# |#1| #13#)) (SIGNATURE |rightRegularRepresentation| #18=(#1# |#1| #13#)) (SIGNATURE |leftRegularRepresentation| #18#) (SIGNATURE |structuralConstants| (#11# #13#)) (SIGNATURE |conditionsForIdempotents| (#10# #13#))) (|FramedNonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra&|)) ((|structuralConstants| #1=(*1 *2) (AND #2=(|ofCategory| *4 #3=(|CommutativeRing|)) (|isDomain| *2 (|Vector| #4=(|Matrix| *4))) #5=(|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *4)) #6=(|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|conditionsForIdempotents| #1# (AND #2# (|isDomain| *2 (|List| #7=(|Polynomial| *4))) #5# #6#)) (|leftDiscriminant| #1# #8=(AND (|ofCategory| *2 #3#) (|isDomain| *1 (|FramedNonAssociativeAlgebra&| *3 *2)) (|ofCategory| *3 (|FramedNonAssociativeAlgebra| *2)))) (|rightDiscriminant| #1# #8#) (|leftTraceMatrix| #1# #9=(AND #2# (|isDomain| *2 #4#) #5# #6#)) (|rightTraceMatrix| #1# #9#) (|leftRankPolynomial| #1# #10=(AND #2# (|isDomain| *2 (|SparseUnivariatePolynomial| #7#)) #5# #6#)) (|rightRankPolynomial| #1# #10#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unit| (#3=(#4=(|Union| $ #5="failed")) 49 (|has| |#1| . #6=((|IntegralDomain|))) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) #7=(|Vector| $)) 90 T ELT) (((|Vector| (|Matrix| |#1|))) 116 T ELT)) (|someBasis| ((#7#) 93 T ELT)) (|sample| (#8=($) 23 T CONST)) (|rightUnits| (#9=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) 52 (|has| |#1| . #6#) ELT)) (|rightUnit| (#3# 50 (|has| |#1| . #6#) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) . #10=(#7#)) 77 T ELT) (((|Matrix| |#1|)) 108 T ELT)) (|rightTrace| ((|#1| . #11=($)) 86 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) . #12=($ #7#)) 88 T ELT) (((|Matrix| |#1|) $) 106 T ELT)) (|rightRecip| (#13=(#4# $) 57 (|has| |#1| . #6#) ELT)) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 104 (|has| |#1| (|Field|)) ELT)) (|rightPower| (#14=($ $ (|PositiveInteger|)) 38 T ELT)) (|rightNorm| ((|#1| . #11#) 84 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15=($)) 54 (|has| |#1| . #6#) ELT)) (|rightDiscriminant| ((|#1| . #16=(#7#)) 79 T ELT) ((|#1|) 110 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 75 T ELT)) (|rightAlternative?| (#17=((|Boolean|)) 69 T ELT)) (|represents| (($ (|Vector| |#1|) #7#) 81 T ELT) (($ (|Vector| |#1|)) 114 T ELT)) (|recip| (#13# 59 (|has| |#1| . #6#) ELT)) (|rank| (((|PositiveInteger|)) 92 T ELT)) (|powerAssociative?| (#17# 66 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 45 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (#17# 62 T ELT)) (|lieAlgebra?| (#17# 60 T ELT)) (|lieAdmissible?| (#17# 64 T ELT)) (|leftUnits| (#9# 53 (|has| |#1| . #6#) ELT)) (|leftUnit| (#3# 51 (|has| |#1| . #6#) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) . #10#) 78 T ELT) (((|Matrix| |#1|)) 109 T ELT)) (|leftTrace| ((|#1| . #11#) 87 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) . #12#) 89 T ELT) (((|Matrix| |#1|) $) 107 T ELT)) (|leftRecip| (#13# 58 (|has| |#1| . #6#) ELT)) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 105 (|has| |#1| (|Field|)) ELT)) (|leftPower| (#14# 39 T ELT)) (|leftNorm| ((|#1| . #11#) 85 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 55 (|has| |#1| . #6#) ELT)) (|leftDiscriminant| ((|#1| . #16#) 80 T ELT) ((|#1|) 111 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 76 T ELT)) (|leftAlternative?| (#17# 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (#17# 61 T ELT)) (|jordanAdmissible?| (#17# 63 T ELT)) (|jacobiIdentity?| (#17# 65 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (#17# 68 T ELT)) (|elt| ((|#1| $ (|Integer|)) 120 T ELT)) (|coordinates| (((|Vector| |#1|) $ #7#) 83 T ELT) (((|Matrix| |#1|) #7# #7#) 82 T ELT) (((|Vector| |#1|) $) 118 T ELT) (((|Matrix| |#1|) (|Vector| $)) 117 T ELT)) (|convert| (((|Vector| |#1|) $) 113 T ELT) (($ (|Vector| |#1|)) 112 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) #7#) 91 T ELT) (((|List| (|Polynomial| |#1|))) 115 T ELT)) (|commutator| (#18=($ $ $) 35 T ELT)) (|commutative?| (#17# 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 119 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 56 (|has| |#1| . #6#) ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|associative?| (#17# 72 T ELT)) (|apply| (($ (|Matrix| |#1|) $) 103 T ELT)) (|antiCommutator| (#18# 34 T ELT)) (|antiCommutative?| (#17# 73 T ELT)) (|antiAssociative?| (#17# 71 T ELT)) (|alternative?| (#17# 67 T ELT)) (|Zero| (#8# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#14# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #19=($)) 31 T ELT) (($ $ $) 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #19#) 46 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|unit| (#3=(#4=(|Union| $ #5="failed")) 49 #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|structuralConstants| ((#7=(|Vector| #8=(|Matrix| |#1|)) #9=(|Vector| $)) 90 T ELT) ((#7#) 116 T ELT)) (|someBasis| (#10=(#9#) 93 T ELT)) (|sample| (#11=($) 23 T CONST)) (|rightUnits| (#12=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) 52 #6# ELT)) (|rightUnit| (#3# 50 #6# ELT)) (|rightTraceMatrix| (#13=(#8# #9#) 77 T ELT) (#14=(#8#) 108 T ELT)) (|rightTrace| (#15=(|#1| $) 86 T ELT)) (|rightRegularRepresentation| (#16=(#8# $ #9#) 88 T ELT) (#17=(#8# $) 106 T ELT)) (|rightRecip| (#18=(#4# $) 57 #6# ELT)) (|rightRankPolynomial| (#19=((|SparseUnivariatePolynomial| #20=(|Polynomial| |#1|))) 104 #21=(|has| |#1| (|Field|)) ELT)) (|rightPower| (#22=($ $ #23=(|PositiveInteger|)) 38 T ELT)) (|rightNorm| (#15# 84 T ELT)) (|rightMinimalPolynomial| (#24=((|SparseUnivariatePolynomial| |#1|) $) 54 #6# ELT)) (|rightDiscriminant| (#25=(|#1| #9#) 79 T ELT) (#26=(|#1|) 110 T ELT)) (|rightCharacteristicPolynomial| (#24# 75 T ELT)) (|rightAlternative?| (#27=(#2#) 69 T ELT)) (|represents| (($ #28=(|Vector| |#1|) #9#) 81 T ELT) (#29=($ #28#) 114 T ELT)) (|recip| (#18# 59 #6# ELT)) (|rank| ((#23#) 92 T ELT)) (|powerAssociative?| (#27# 66 T ELT)) (|plenaryPower| (#22# 45 T ELT)) (|opposite?| (#1# 20 T ELT)) (|noncommutativeJordanAlgebra?| (#27# 62 T ELT)) (|lieAlgebra?| (#27# 60 T ELT)) (|lieAdmissible?| (#27# 64 T ELT)) (|leftUnits| (#12# 53 #6# ELT)) (|leftUnit| (#3# 51 #6# ELT)) (|leftTraceMatrix| (#13# 78 T ELT) (#14# 109 T ELT)) (|leftTrace| (#15# 87 T ELT)) (|leftRegularRepresentation| (#16# 89 T ELT) (#17# 107 T ELT)) (|leftRecip| (#18# 58 #6# ELT)) (|leftRankPolynomial| (#19# 105 #21# ELT)) (|leftPower| (#22# 39 T ELT)) (|leftNorm| (#15# 85 T ELT)) (|leftMinimalPolynomial| (#24# 55 #6# ELT)) (|leftDiscriminant| (#25# 80 T ELT) (#26# 111 T ELT)) (|leftCharacteristicPolynomial| (#24# 76 T ELT)) (|leftAlternative?| (#27# 70 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (#27# 61 T ELT)) (|jordanAdmissible?| (#27# 63 T ELT)) (|jacobiIdentity?| (#27# 65 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (#27# 68 T ELT)) (|elt| ((|#1| $ #30=(|Integer|)) 120 T ELT)) (|coordinates| ((#28# $ #9#) 83 T ELT) ((#8# #9# #9#) 82 T ELT) (#31=(#28# $) 118 T ELT) (#13# 117 T ELT)) (|convert| (#31# 113 T ELT) (#29# 112 T ELT)) (|conditionsForIdempotents| ((#32=(|List| #20#) #9#) 91 T ELT) ((#32#) 115 T ELT)) (|commutator| (#33=($ $ $) 35 T ELT)) (|commutative?| (#27# 74 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| (#10# 119 T ELT)) (|associatorDependence| (((|List| #28#)) 56 #6# ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|associative?| (#27# 72 T ELT)) (|apply| (($ #8# $) 103 T ELT)) (|antiCommutator| (#33# 34 T ELT)) (|antiCommutative?| (#27# 73 T ELT)) (|antiAssociative?| (#27# 71 T ELT)) (|alternative?| (#27# 67 T ELT)) (|Zero| (#11# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#33# 29 T ELT)) (+ (#33# 18 T ELT)) (** (#22# 40 T ELT)) (* (($ #23# $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ #30# . #34=($)) 31 T ELT) (#33# 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #34#) 46 T ELT))) (((|FramedNonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |FramedNonAssociativeAlgebra|)) -((|basis| (*1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *1)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|coordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *4)) (|ofCategory| *4 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *4)))) (|structuralConstants| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| (|Matrix| *3))))) (|conditionsForIdempotents| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|List| (|Polynomial| *3))))) (|represents| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|convert| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Vector| *3)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|leftDiscriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightDiscriminant| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|leftTraceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|rightTraceMatrix| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|leftRegularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|rightRegularRepresentation| (*1 *2 *1) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Matrix| *3)))) (|leftRankPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *3))))) (|rightRankPolynomial| (*1 *2) (AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| (|Polynomial| *3))))) (|apply| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Matrix| *3)) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|))))) -(|Join| (|FiniteRankNonAssociativeAlgebra| |t#1|) (|Eltable| (|Integer|) |t#1|) (CATEGORY |domain| (SIGNATURE |basis| ((|Vector| $))) (SIGNATURE |coordinates| ((|Vector| |t#1|) $)) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |t#1|)))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)))) (SIGNATURE |represents| ($ (|Vector| |t#1|))) (SIGNATURE |convert| ((|Vector| |t#1|) $)) (SIGNATURE |convert| ($ (|Vector| |t#1|))) (SIGNATURE |leftDiscriminant| (|t#1|)) (SIGNATURE |rightDiscriminant| (|t#1|)) (SIGNATURE |leftTraceMatrix| ((|Matrix| |t#1|))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |t#1|))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |t#1|) $)) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |t#1|) $)) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |t#1|)))) (SIGNATURE |rightRankPolynomial| ((|SparseUnivariatePolynomial| (|Polynomial| |t#1|))))) |%noBranch|) (SIGNATURE |apply| ($ (|Matrix| |t#1|) $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| (|Integer|) |#1|) . T) ((|FiniteRankNonAssociativeAlgebra| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeAlgebra| |#1|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|basis| #1=(*1 *2) (AND #2=(|ofCategory| *3 #3=(|CommutativeRing|)) (|isDomain| *2 #4=(|Vector| *1)) #5=(|ofCategory| *1 (|FramedNonAssociativeAlgebra| *3)))) (|coordinates| #6=(*1 *2 *1) #7=(AND #5# #2# #8=(|isDomain| *2 (|Vector| *3)))) (|coordinates| (*1 *2 *3) (AND (|isDomain| *3 #4#) (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *4)) (|ofCategory| *4 #3#) (|isDomain| *2 (|Matrix| *4)))) (|structuralConstants| #1# (AND #5# #2# (|isDomain| *2 (|Vector| #9=(|Matrix| *3))))) (|conditionsForIdempotents| #1# (AND #5# #2# (|isDomain| *2 (|List| #10=(|Polynomial| *3))))) (|represents| #11=(*1 *1 *2) #12=(AND #8# #2# #5#)) (|convert| #6# #7#) (|convert| #11# #12#) (|leftDiscriminant| #1# #13=(AND (|ofCategory| *1 (|FramedNonAssociativeAlgebra| *2)) (|ofCategory| *2 #3#))) (|rightDiscriminant| #1# #13#) (|leftTraceMatrix| #1# #14=(AND #5# #2# #15=(|isDomain| *2 #9#))) (|rightTraceMatrix| #1# #14#) (|leftRegularRepresentation| #6# #14#) (|rightRegularRepresentation| #6# #14#) (|leftRankPolynomial| #1# #16=(AND #5# #2# (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| #10#)))) (|rightRankPolynomial| #1# #16#) (|apply| (*1 *1 *2 *1) (AND #15# #5# #2#))) +(|Join| (|FiniteRankNonAssociativeAlgebra| |t#1|) (|Eltable| (|Integer|) |t#1|) (CATEGORY |domain| (SIGNATURE |basis| (#1=(|Vector| $))) (SIGNATURE |coordinates| #2=(#3=(|Vector| |t#1|) $)) (SIGNATURE |coordinates| (#4=(|Matrix| |t#1|) #1#)) (SIGNATURE |structuralConstants| ((|Vector| #4#))) (SIGNATURE |conditionsForIdempotents| ((|List| #5=(|Polynomial| |t#1|)))) (SIGNATURE |represents| #6=($ #3#)) (SIGNATURE |convert| #2#) (SIGNATURE |convert| #6#) (SIGNATURE |leftDiscriminant| #7=(|t#1|)) (SIGNATURE |rightDiscriminant| #7#) (SIGNATURE |leftTraceMatrix| #8=(#4#)) (SIGNATURE |rightTraceMatrix| #8#) (SIGNATURE |leftRegularRepresentation| #9=(#4# $)) (SIGNATURE |rightRegularRepresentation| #9#) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftRankPolynomial| #10=((|SparseUnivariatePolynomial| #5#))) (SIGNATURE |rightRankPolynomial| #10#)) |%noBranch|) (SIGNATURE |apply| ($ #4# $)))) +(((|AbelianGroup|) . 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(((|FunctionSpace| |#1|) (|Category|) (|SetCategory|)) (T |FunctionSpace|)) -((|ground?| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|ground| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionSpace| *2)) (|ofCategory| *2 (|SetCategory|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| (|Symbol|))))) (|applyQuote| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 (|SetCategory|)))) (|applyQuote| (*1 *1 *2 *1 *1 *1 *1) (AND (|isDomain| *2 (|Symbol|)) (|ofCategory| *1 (|FunctionSpace| *3)) (|ofCategory| *3 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T) ((|CoercibleFrom| #4=(|Polynomial| |#1|)) |has| |#1| (|Ring|)) ((|CoercibleFrom| #5=(|Symbol|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|IntegralDomain|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DivisionRing|) |has| |#1| (|IntegralDomain|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|EuclideanDomain|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|ExpressionSpace|) . T) ((|Field|) |has| |#1| (|IntegralDomain|)) ((|FullyLinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) |has| |#1| (|IntegralDomain|)) ((|Group|) |has| |#1| (|Group|)) ((|InnerEvalable| (|Kernel| $) $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| (|Integer|)) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianGroup|))) ((|LeftLinearSet| |#1|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|CommutativeRing|))) ((|LeftLinearSet| $) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|LeftModule| #1#) |has| |#1| (|IntegralDomain|)) ((|LeftModule| #6=(|Integer|)) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LeftModule| |#1|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|CommutativeRing|))) ((|LeftModule| $) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|LinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| #6#) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|Module| #1#) |has| |#1| (|IntegralDomain|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) OR (|has| |#1| (|SemiGroup|)) (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Group|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|PartialDifferentialDomain| $ #7=(|Symbol|)) |has| |#1| (|Ring|)) ((|PartialDifferentialRing| #7#) |has| |#1| (|Ring|)) ((|PartialDifferentialSpace| #7#) |has| |#1| (|Ring|)) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PrincipalIdealDomain|) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| (|Fraction| (|Integer|))) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|RetractableTo| (|Integer|))))) ((|RetractableTo| #2#) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #3#) . T) ((|RetractableTo| #4#) |has| |#1| (|Ring|)) ((|RetractableTo| #5#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|RightLinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightLinearSet| $) |has| |#1| (|IntegralDomain|)) ((|RightModule| #1#) |has| |#1| (|IntegralDomain|)) ((|RightModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightModule| $) |has| |#1| (|IntegralDomain|)) ((|Ring|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|Rng|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|SemiGroup|) OR (|has| |#1| (|SemiGroup|)) (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Group|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|SemiRing|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|IntegralDomain|))) +((|ground?| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|FunctionSpace| *3)) #3=(|ofCategory| *3 #4=(|SetCategory|)) (|isDomain| *2 (|Boolean|)))) (|ground| #1# (AND #5=(|ofCategory| *1 (|FunctionSpace| *2)) #6=(|ofCategory| *2 #4#))) (|variables| #1# (AND #2# #3# #7=(|isDomain| *2 (|List| #8=(|Symbol|))))) (|applyQuote| (*1 *1 *2 *1) #9=(AND #10=(|isDomain| *2 #8#) #2# #3#)) (|applyQuote| (*1 *1 *2 *1 *1) #9#) (|applyQuote| (*1 *1 *2 *1 *1 *1) #9#) (|applyQuote| (*1 *1 *2 *1 *1 *1 *1) #9#) (|applyQuote| (*1 *1 *2 *3) (AND #10# #11=(|isDomain| *3 #12=(|List| *1)) #13=(|ofCategory| *1 (|FunctionSpace| *4)) #14=(|ofCategory| *4 #4#))) (|eval| #15=(*1 *1 *1 *2) (AND #10# #2# #3# #16=(|ofCategory| *3 #17=(|ConvertibleTo| (|InputForm|))))) (|eval| #15# (AND #7# #2# #3# #16#)) (|eval| #18=(*1 *1 *1) (AND #5# #6# (|ofCategory| *2 #17#))) (|eval| (*1 *1 *1 *2 *1 *3) (AND (|isDomain| *2 #19=(|BasicOperator|)) #20=(|isDomain| *3 #8#) #13# #14# (|ofCategory| *4 #17#))) (|eval| #21=(*1 *1 *1 *2 *3 *4) (AND (|isDomain| *2 (|List| #19#)) #11# (|isDomain| *4 #8#) #22=(|ofCategory| *1 (|FunctionSpace| *5)) #23=(|ofCategory| *5 #4#) (|ofCategory| *5 #17#))) (|isTimes| #1# (|partial| AND #24=(|ofCategory| *3 (|SemiGroup|)) #3# #25=(|isDomain| *2 #12#) #2#)) (|isExpt| #1# (|partial| AND #24# #3# #26=(|isDomain| *2 (|Record| #27=(|:| |var| #28=(|Kernel| *1)) #29=(|:| |exponent| #30=(|Integer|)))) #2#)) (|isPlus| #1# (|partial| AND #31=(|ofCategory| *3 (|AbelianSemiGroup|)) #3# #25# #2#)) (|isMult| #1# (|partial| AND #31# #3# (|isDomain| *2 (|Record| (|:| |coef| #30#) #27#)) #2#)) (|coerce| #32=(*1 *1 *2) (AND #33=(|isDomain| *2 (|SparseMultivariatePolynomial| *3 #28#)) #34=(|ofCategory| *3 #35=(|Ring|)) #3# #2#)) (|numer| #1# (AND #34# #3# #33# #2#)) (|numerator| #18# (AND #5# #6# (|ofCategory| *2 #35#))) (|isExpt| #36=(*1 *2 *1 *3) (|partial| AND (|isDomain| *3 #19#) #37=(|ofCategory| *4 #35#) #14# #26# #13#)) (|isExpt| #36# (|partial| AND #20# #37# #14# #26# #13#)) (|isPower| #1# (|partial| AND #34# #3# (|isDomain| *2 (|Record| (|:| |val| *1) #29#)) #2#)) (|eval| #21# (AND #7# #38=(|isDomain| *3 (|List| #39=(|NonNegativeInteger|))) (|isDomain| *4 (|List| #40=(|Mapping| *1 *1))) #22# #23# #41=(|ofCategory| *5 #35#))) (|eval| #21# (AND #7# #38# (|isDomain| *4 (|List| #42=(|Mapping| *1 #12#))) #22# #23# #41#)) (|eval| #21# (AND #10# #43=(|isDomain| *3 #39#) (|isDomain| *4 #42#) #22# #23# #41#)) (|eval| #21# (AND #10# #43# (|isDomain| *4 #40#) #22# #23# #41#)) (|convert| #32# (AND (|isDomain| *2 (|Factored| *1)) #2# #44=(|ofCategory| *3 #45=(|IntegralDomain|)) #3#)) (|denom| #1# (AND #44# #3# #33# #2#)) (|denominator| #18# (AND #5# #6# (|ofCategory| *2 #45#))) (/ (*1 *1 *2 *2) (AND #33# #44# #3# #2#)) (|coerce| #32# (AND (|isDomain| *2 #46=(|Fraction| *3)) #44# #3# #2#)) (|coerce| #32# (AND (|isDomain| *2 #47=(|Polynomial| #46#)) #44# #3# #2#)) (|coerce| #32# (AND (|isDomain| *2 (|Fraction| #47#)) #44# #3# #2#)) (|univariate| #36# (AND (|isDomain| *3 #28#) #13# #14# (|ofCategory| *4 #45#) (|isDomain| *2 (|Fraction| (|SparseUnivariatePolynomial| *1))))) (** #15# (AND (|isDomain| *2 #39#) #2# #3# #24#))) +(|Join| (|ExpressionSpace|) (|RetractableTo| #1=(|Symbol|)) (|Patternable| |t#1|) (|FullyPatternMatchable| |t#1|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |ground?| ((|Boolean|) $)) (SIGNATURE |ground| (|t#1| $)) (SIGNATURE |variables| (#2=(|List| #1#) $)) (SIGNATURE |applyQuote| ($ #1# $)) (SIGNATURE |applyQuote| ($ #1# $ $)) (SIGNATURE |applyQuote| ($ #1# $ $ $)) (SIGNATURE |applyQuote| ($ #1# $ $ $ $)) (SIGNATURE |applyQuote| ($ #1# #3=(|List| $))) (IF (|has| |t#1| #4=(|ConvertibleTo| (|InputForm|))) (PROGN (ATTRIBUTE #4#) (SIGNATURE |eval| ($ $ #1#)) (SIGNATURE |eval| ($ $ #2#)) (SIGNATURE |eval| #5=($ $)) (SIGNATURE |eval| ($ $ #6=(|BasicOperator|) $ #1#)) (SIGNATURE |eval| ($ $ (|List| #6#) #3# #1#))) |%noBranch|) (IF (|has| |t#1| (|SemiGroup|)) (PROGN (ATTRIBUTE (|Monoid|)) (SIGNATURE ** ($ $ #7=(|NonNegativeInteger|))) (SIGNATURE |isTimes| #8=((|Union| #3# #9="failed") $)) (SIGNATURE |isExpt| (#10=(|Union| (|Record| #11=(|:| |var| #12=(|Kernel| $)) #13=(|:| |exponent| #14=(|Integer|))) #9#) $))) |%noBranch|) (IF (|has| |t#1| #15=(|Group|)) (ATTRIBUTE #15#) |%noBranch|) (IF (|has| |t#1| (|AbelianSemiGroup|)) (PROGN (ATTRIBUTE (|AbelianMonoid|)) (SIGNATURE |isPlus| #8#) (SIGNATURE |isMult| ((|Union| (|Record| (|:| |coef| #14#) #11#) #9#) $))) |%noBranch|) (IF (|has| |t#1| #16=(|AbelianGroup|)) (ATTRIBUTE #16#) |%noBranch|) (IF (|has| |t#1| #17=(|Ring|)) (PROGN (ATTRIBUTE #17#) (ATTRIBUTE (|RetractableTo| #18=(|Polynomial| |t#1|))) (ATTRIBUTE (|PartialDifferentialRing| #1#)) (ATTRIBUTE (|FullyLinearlyExplicitRingOver| |t#1|)) (SIGNATURE |coerce| ($ #19=(|SparseMultivariatePolynomial| |t#1| #12#))) (SIGNATURE |numer| #20=(#19# $)) (SIGNATURE |numerator| #5#) (SIGNATURE |isExpt| (#10# $ #6#)) (SIGNATURE |isExpt| (#10# $ #1#)) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| $) #13#) #9#) $)) (SIGNATURE |eval| ($ $ #2# #21=(|List| #7#) (|List| #22=(|Mapping| $ $)))) (SIGNATURE |eval| ($ $ #2# #21# (|List| #23=(|Mapping| $ #3#)))) (SIGNATURE |eval| ($ $ #1# #7# #23#)) (SIGNATURE |eval| ($ $ #1# #7# #22#))) |%noBranch|) (IF (|has| |t#1| #24=(|CharacteristicZero|)) (ATTRIBUTE #24#) |%noBranch|) (IF (|has| |t#1| #25=(|CharacteristicNonZero|)) (ATTRIBUTE #25#) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|Field|)) (ATTRIBUTE (|RetractableTo| (|Fraction| #18#))) (SIGNATURE |convert| ($ (|Factored| $))) (SIGNATURE |denom| #20#) (SIGNATURE |denominator| #5#) (SIGNATURE / ($ #19# #19#)) (SIGNATURE |coerce| ($ #26=(|Fraction| |t#1|))) (SIGNATURE |coerce| ($ #27=(|Polynomial| #26#))) (SIGNATURE |coerce| ($ (|Fraction| #27#))) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| $)) $ #12#)) (IF (|has| |t#1| (|RetractableTo| #14#)) (ATTRIBUTE (|RetractableTo| (|Fraction| #14#))) |%noBranch|)) |%noBranch|))) +(((|AbelianGroup|) OR (|has| |#1| (|AbelianGroup|)) (AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|)))) ((|AbelianMonoid|) OR (|has| |#1| (|AbelianSemiGroup|)) (AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|)))) ((|AbelianSemiGroup|) OR (|has| |#1| (|AbelianSemiGroup|)) (AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|)))) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|IntegralDomain|)) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|IntegralDomain|)) ((|BiModule| |#1| |#1|) |has| |#1| (|CommutativeRing|)) ((|BiModule| $ $) |has| |#1| (|IntegralDomain|)) ((|CancellationAbelianMonoid|) OR (|has| |#1| (|AbelianGroup|)) (AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|)))) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #3=(|Fraction| #4=(|Polynomial| |#1|))) |has| |#1| (|IntegralDomain|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#1| (|Ring|))) ((|CoercibleFrom| #5=(|Kernel| $)) . T) ((|CoercibleFrom| #4#) |has| |#1| (|Ring|)) ((|CoercibleFrom| #6=(|Symbol|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|IntegralDomain|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| #7=(|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| #2#)) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DivisionRing|) |has| |#1| (|IntegralDomain|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|EuclideanDomain|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|ExpressionSpace|) . T) ((|Field|) |has| |#1| (|IntegralDomain|)) ((|FullyLinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|FullyPatternMatchable| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) |has| |#1| (|IntegralDomain|)) ((|Group|) |has| |#1| (|Group|)) ((|InnerEvalable| #5# $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #2#) OR (|has| |#1| (|AbelianGroup|)) (AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|)))) ((|LeftLinearSet| |#1|) |has| |#1| (|Ring|)) ((|LeftLinearSet| $) |has| |#1| (|Ring|)) ((|LeftModule| #1#) |has| |#1| (|IntegralDomain|)) ((|LeftModule| #2#) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LeftModule| |#1|) |has| |#1| (|Ring|)) ((|LeftModule| $) |has| |#1| (|Ring|)) ((|LinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| #2#) AND (|has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) (|has| |#1| (|Ring|))) ((|LinearlyExplicitRingOver| |#1|) |has| |#1| (|Ring|)) ((|Module| #1#) |has| |#1| (|IntegralDomain|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) |has| |#1| (|SemiGroup|)) ((|PartialDifferentialDomain| $ #6#) |has| |#1| (|Ring|)) ((|PartialDifferentialRing| #6#) |has| |#1| (|Ring|)) ((|PartialDifferentialSpace| #6#) |has| |#1| (|Ring|)) ((|PatternMatchable| #7#) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| #2#) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PrincipalIdealDomain|) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| #1#) OR (AND (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|RetractableTo| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|RetractableTo| #3#) |has| |#1| (|IntegralDomain|)) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #5#) . T) ((|RetractableTo| #4#) |has| |#1| (|Ring|)) ((|RetractableTo| #6#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|IntegralDomain|)) ((|RightLinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightLinearSet| $) |has| |#1| (|IntegralDomain|)) ((|RightModule| #1#) |has| |#1| (|IntegralDomain|)) ((|RightModule| |#1|) |has| |#1| (|CommutativeRing|)) ((|RightModule| $) |has| |#1| (|IntegralDomain|)) ((|Ring|) |has| |#1| (|Ring|)) ((|Rng|) |has| |#1| (|Ring|)) ((|SemiGroup|) |has| |#1| (|SemiGroup|)) ((|SemiRing|) |has| |#1| (|Ring|)) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|IntegralDomain|))) ((|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 11 T ELT))) (((|FunctionSpaceFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) #1=(|Ring|) (|FunctionSpace| |#1|) #1# (|FunctionSpace| |#3|)) (T |FunctionSpaceFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|FunctionSpace| *6)) (|isDomain| *1 (|FunctionSpaceFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|FunctionSpace| *5))))) @@ -1227,11 +1227,11 @@ NIL ((|universe| (#1=($) 51 T ELT)) (|union| (($ |#2| $) NIL T ELT) #2=(($ $ |#2|) NIL T ELT) (#3=($ $ $) 47 T ELT)) (|symmetricDifference| (#3# 46 T ELT)) (|subset?| (#4=(#5=(|Boolean|) $ $) 35 T ELT)) (|size| ((#6=(|NonNegativeInteger|)) 55 T ELT)) (|set| (#7=($ (|List| |#2|)) 23 T ELT) #8=(#1# NIL T ELT)) (|random| (#1# 65 T ELT)) (|part?| (#4# 15 T ELT)) (|min| (#9=(|#2| $) 76 T ELT)) (|max| (#9# 74 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 69 T ELT)) (|intersect| (#3# 42 T ELT)) (|index| (($ #10#) 60 T ELT)) (|difference| #2# (#3# 45 T ELT)) (|count| ((#6# |#2| $) 31 T ELT) ((#6# (|Mapping| #5# |#2|) $) NIL T ELT)) (|construct| (#7# 27 T ELT)) (|complement| (($ $) 53 T ELT)) (|coerce| (((|OutputForm|) $) 40 T ELT)) (|cardinality| ((#6# $) 24 T ELT)) (|brace| (#7# 22 T ELT) #8#) (= (#4# 19 T ELT))) (((|FiniteSetAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |size| (#1=(|NonNegativeInteger|))) (SIGNATURE |index| (|#1| #2=(|PositiveInteger|))) (SIGNATURE |lookup| (#2# |#1|)) (SIGNATURE |random| #3=(|#1|)) (SIGNATURE |min| #4=(|#2| |#1|)) (SIGNATURE |max| #4#) (SIGNATURE |universe| #3#) (SIGNATURE |complement| (|#1| |#1|)) (SIGNATURE |cardinality| (#1# |#1|)) (SIGNATURE |count| (#1# (|Mapping| #5=(|Boolean|) |#2|) |#1|)) (SIGNATURE |count| (#1# |#2| |#1|)) (SIGNATURE = #6=(#5# |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |part?| #6#) (SIGNATURE |brace| #3#) (SIGNATURE |brace| #7=(|#1| (|List| |#2|))) (SIGNATURE |set| #3#) (SIGNATURE |set| #7#) (SIGNATURE |intersect| #8=(|#1| |#1| |#1|)) (SIGNATURE |difference| #8#) (SIGNATURE |difference| #9=(|#1| |#1| |#2|)) (SIGNATURE |symmetricDifference| #8#) (SIGNATURE |subset?| #6#) (SIGNATURE |union| #8#) (SIGNATURE |union| #9#) (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |construct| #7#)) (|FiniteSetAggregate| |#2|) (|SetCategory|)) (T |FiniteSetAggregate&|)) ((|size| (*1 *2) (AND (|ofCategory| *4 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FiniteSetAggregate&| *3 *4)) (|ofCategory| *3 (|FiniteSetAggregate| *4))))) -((~= (#1=((|Boolean|) $ $) 18 T ELT)) (|universe| (($) 61 (|has| |#1| (|Finite|)) ELT)) (|union| (($ |#1| $) 87 T ELT) (($ $ |#1|) 86 T ELT) (#2=($ $ $) 85 T ELT)) (|symmetricDifference| (#2# 83 T ELT)) (|subset?| (#3=((|Boolean|) $ $) 84 T ELT)) (|size| (((|NonNegativeInteger|)) 55 (|has| |#1| . #4=((|Finite|))) ELT)) (|set| (($ (|List| |#1|)) 79 T ELT) (#5=($) 78 T ELT)) (|select!| (($ (|Mapping| #6=(|Boolean|) |#1|) . #7=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #8=(|Boolean|) |#1|) . #9=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#10=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #11=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #6# |#1|) . #7#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #11#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #8# |#1|) . #9#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 74 (|has| |#1| . #12=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 70 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 69 T ELT)) (|random| (($) 58 (|has| |#1| . #4#) ELT)) (|part?| (#3# 75 T ELT)) (|min| ((|#1| $) 59 (|has| |#1| (|OrderedSet|)) ELT)) (|members| (((|List| |#1|) $) 68 T ELT)) (|member?| ((#13=(|Boolean|) |#1| $) 73 (|has| |#1| . #12#) ELT)) (|max| ((|#1| $) 60 (|has| |#1| (|OrderedSet|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 57 (|has| |#1| . #4#) ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 80 T ELT)) (|inspect| ((|#1| . #15=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|index| (($ #14#) 56 (|has| |#1| . #4#) ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #13# |#1|) $) 71 T ELT)) (|extract!| ((|#1| . #15#) 37 T ELT)) (|every?| ((#13# (|Mapping| #13# |#1|) . #16=($)) 66 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #17#)) ELT)) (|eq?| ((#18=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#18# $) 7 T ELT)) (|empty| (#10# 8 T ELT)) (|difference| (($ $ |#1|) 82 T ELT) (#2# 81 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|count| ((#19=(|NonNegativeInteger|) |#1| $) 72 (|has| |#1| . #12#) ELT) ((#19# (|Mapping| #13# |#1|) $) 67 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#20=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #20#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|complement| (($ $) 62 (|has| |#1| (|Finite|)) ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|cardinality| (((|NonNegativeInteger|) $) 63 T ELT)) (|brace| (($ (|List| |#1|)) 77 T ELT) (#5# 76 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#13# (|Mapping| #13# |#1|) . #16#) 65 T ELT)) (= (#1# 17 T ELT)) (|#| ((#19# $) 64 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 T ELT)) (|universe| (#3=($) 61 #4=(|has| |#1| (|Finite|)) ELT)) (|union| (#5=($ |#1| $) 87 T ELT) (#6=($ $ |#1|) 86 T ELT) (#7=($ $ $) 85 T ELT)) (|symmetricDifference| (#7# 83 T ELT)) (|subset?| (#1# 84 T ELT)) (|size| ((#8=(|NonNegativeInteger|)) 55 #4# ELT)) (|set| (#9=($ #10=(|List| |#1|)) 79 T ELT) (#3# 78 T ELT)) (|select!| (#11=($ #12=(|Mapping| #2# |#1|) $) 42 #13=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (#11# 49 #13# ELT)) (|sample| (#3# 6 T CONST)) (|removeDuplicates| (#14=($ $) 51 #15=(AND #16=(|has| |#1| (|BasicType|)) #13#) ELT)) (|remove!| (#5# 44 #13# ELT) (#11# 43 #13# ELT)) (|remove| (#5# 50 #15# ELT) (#11# 48 #13# ELT)) (|reduce| ((|#1| #17=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 74 #16# ELT) ((|#1| #17# $ |#1|) 70 T ELT) ((|#1| #17# $) 69 T ELT)) (|random| (#3# 58 #4# ELT)) (|part?| (#1# 75 T ELT)) (|min| (#18=(|#1| $) 59 #19=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#10# $) 68 T ELT)) (|member?| ((#2# |#1| $) 73 #16# ELT)) (|max| (#18# 60 #19# ELT)) (|map!| (#20=($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (#20# 26 T ELT)) (|lookup| ((#21=(|PositiveInteger|) $) 57 #4# ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#7# 80 T ELT)) (|inspect| (#18# 35 T ELT)) (|insert!| (#5# 36 T ELT)) (|index| (($ #21#) 56 #4# ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|find| (((|Union| |#1| "failed") #12# $) 71 T ELT)) (|extract!| (#18# 37 T ELT)) (|every?| (#22=(#2# #12# $) 66 T ELT)) (|eval| (($ $ (|List| #23=(|Equation| |#1|))) 25 #24=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ELT) (($ $ #23#) 24 #24# ELT) (($ $ |#1| |#1|) 23 #24# ELT) (($ $ #10# #10#) 22 #24# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|difference| (#6# 82 T ELT) (#7# 81 T ELT)) (|dictionary| (#3# 46 T ELT) (#9# 45 T ELT)) (|count| ((#8# |#1| $) 72 #16# ELT) ((#8# #12# $) 67 T ELT)) (|copy| (#14# 9 T ELT)) (|convert| ((#25=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #25#)) ELT)) (|construct| (#9# 47 T ELT)) (|complement| (#14# 62 #4# ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|cardinality| (#26=(#8# $) 63 T ELT)) (|brace| (#9# 77 T ELT) (#3# 76 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (#9# 38 T ELT)) (|any?| (#22# 65 T ELT)) (= (#1# 17 T ELT)) (|#| (#26# 64 T ELT))) (((|FiniteSetAggregate| |#1|) (|Category|) (|SetCategory|)) (T |FiniteSetAggregate|)) -((|cardinality| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|complement| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|Finite|)))) (|universe| (*1 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|Finite|)) (|ofCategory| *2 (|SetCategory|)))) (|max| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|)))) (|min| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *2)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *2 (|OrderedSet|))))) -(|Join| (|Dictionary| |t#1|) (|SetAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |cardinality| ((|NonNegativeInteger|) $)) (IF (|has| |t#1| (|Finite|)) (PROGN (ATTRIBUTE (|Finite|)) (SIGNATURE |complement| ($ $)) (SIGNATURE |universe| ($))) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (PROGN (SIGNATURE |max| (|t#1| $)) (SIGNATURE |min| (|t#1| $))) |%noBranch|))) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Dictionary| |#1|) . T) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Finite|) |has| |#1| (|Finite|)) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((|cardinality| #1=(*1 *2 *1) (AND (|ofCategory| *1 (|FiniteSetAggregate| *3)) (|ofCategory| *3 #2=(|SetCategory|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|complement| (*1 *1 *1) (AND #3=(|ofCategory| *1 (|FiniteSetAggregate| *2)) #4=(|ofCategory| *2 #2#) #5=(|ofCategory| *2 (|Finite|)))) (|universe| (*1 *1) (AND #3# #5# #4#)) (|max| #1# #6=(AND #3# #4# (|ofCategory| *2 (|OrderedSet|)))) (|min| #1# #6#)) +(|Join| (|Dictionary| |t#1|) (|SetAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |cardinality| ((|NonNegativeInteger|) $)) (IF (|has| |t#1| #1=(|Finite|)) (PROGN (ATTRIBUTE #1#) (SIGNATURE |complement| ($ $)) (SIGNATURE |universe| ($))) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (PROGN (SIGNATURE |max| #2=(|t#1| $)) (SIGNATURE |min| #2#)) |%noBranch|))) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Dictionary| |#1|) . T) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Finite|) |has| |#1| (|Finite|)) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((|scan| ((|#4| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|) 22 T ELT)) (|reduce| ((|#3| #1# |#2| |#3|) 20 T ELT)) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 17 T ELT))) (((|FiniteSetAggregateFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|)) (SIGNATURE |reduce| (|#3| #1=(|Mapping| |#3| |#1| |#3|) |#2| |#3|)) (SIGNATURE |scan| (|#4| #1# |#2| |#3|))) #2=(|SetCategory|) (|FiniteSetAggregate| |#1|) #2# (|FiniteSetAggregate| |#3|)) (T |FiniteSetAggregateFunctions2|)) ((|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) #1=(|ofCategory| *6 #2=(|SetCategory|)) #3=(|ofCategory| *5 #2#) (|ofCategory| *2 #4=(|FiniteSetAggregate| *5)) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *6 *4 *5 *2)) (|ofCategory| *4 #5=(|FiniteSetAggregate| *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #3# (|ofCategory| *2 #2#) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *2 *6)) #6=(|ofCategory| *4 #4#) (|ofCategory| *6 (|FiniteSetAggregate| *2)))) (|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #3# #1# (|ofCategory| *2 #5#) (|isDomain| *1 (|FiniteSetAggregateFunctions2| *5 *4 *6 *2)) #6#))) @@ -1269,7 +1269,7 @@ NIL (((|Functorial| |#1|) (|Category|) (|Type|)) (T |Functorial|)) ((|map| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) (|ofCategory| *1 (|Functorial| *3)) (|ofCategory| *3 (|Type|))))) (|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1|) $)))) -(((|Join|) . T) ((|Type|) . T)) +(((|Type|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|signature| (((|Signature|) $) 7 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| #1#) (= (#2# 9 T ELT))) (((|FunctionDescriptor|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |signature| ((|Signature|) $))))) (T |FunctionDescriptor|)) ((|signature| (*1 *2 *1) (AND (|isDomain| *2 (|Signature|)) (|isDomain| *1 (|FunctionDescriptor|))))) @@ -1303,11 +1303,11 @@ NIL ((|lcm| (#1=($ $ $) 14 T ELT) (#2=($ (|List| $)) 21 T ELT)) (|gcdPolynomial| ((#3=(|SparseUnivariatePolynomial| $) #3# #3#) 45 T ELT)) (|gcd| (#1# NIL T ELT) (#2# 22 T ELT))) (((|GcdDomain&| |#1|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| (#1=(|SparseUnivariatePolynomial| |#1|) #1# #1#)) (SIGNATURE |lcm| #2=(|#1| (|List| |#1|))) (SIGNATURE |lcm| #3=(|#1| |#1| |#1|)) (SIGNATURE |gcd| #2#) (SIGNATURE |gcd| #3#)) (|GcdDomain|)) (T |GcdDomain&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (($ $ $) 61 T ELT) (($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 59 T ELT)) (|gcd| (($ $ $) 63 T ELT) (($ (|List| $)) 62 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| ((#6=(|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|lcm| (#7=($ $ $) 61 T ELT) (#8=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#9=(|SparseUnivariatePolynomial| $) #9# #9#) 59 T ELT)) (|gcd| (#7# 63 T ELT) (#8# 62 T ELT)) (|exquo| ((#6# $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #10=(|Integer|)) 42 T ELT) (#4# 58 T ELT)) (|characteristic| ((#11=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (#5# 46 T CONST)) (= (#1# 8 T ELT)) (- (#4# 30 T ELT) (#7# 29 T ELT)) (+ (#7# 18 T ELT)) (** (($ $ #12=(|PositiveInteger|)) 36 T ELT) (($ $ #11#) 44 T ELT)) (* (($ #12# $) 17 T ELT) (($ #11# $) 21 T ELT) (($ #10# $) 31 T ELT) (#7# 35 T ELT))) (((|GcdDomain|) (|Category|)) (T |GcdDomain|)) -((|gcd| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|gcd| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|lcm| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|lcm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|GcdDomain|))))) -(|Join| (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (SIGNATURE |gcd| ($ (|List| $))) (SIGNATURE |lcm| ($ $ $)) (SIGNATURE |lcm| ($ (|List| $))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|gcd| #1=(*1 *1 *1 *1) #2=(|ofCategory| *1 (|GcdDomain|))) (|gcd| #3=(*1 *1 *2) #4=(AND (|isDomain| *2 (|List| *1)) #2#)) (|lcm| #1# #2#) (|lcm| #3# #4#) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) #2#))) +(|Join| (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| #1=($ $ $)) (SIGNATURE |gcd| #2=($ (|List| $))) (SIGNATURE |lcm| #1#) (SIGNATURE |lcm| #2#) (SIGNATURE |gcdPolynomial| (#3=(|SparseUnivariatePolynomial| $) #3# #3#)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| #7=(|Fraction| #8=(|Polynomial| |#1|)) #9=(|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| #7#)) #12=(|Vector| $)) NIL T ELT) ((#10#) NIL T ELT)) (|someBasis| (#13=(#12#) NIL T ELT)) (|sample| #14=(#15=($) NIL T CONST)) (|rightUnits| #16=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL T ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #17=((#11# #12#) NIL T ELT) #18=((#11#) NIL T ELT)) (|rightTrace| #19=(#20=(#7# $) NIL T ELT)) (|rightRegularRepresentation| #21=((#11# $ #12#) NIL T ELT) #22=((#11# $) NIL T ELT)) (|rightRecip| #23=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #24=(((|SparseUnivariatePolynomial| #25=(|Polynomial| #7#))) NIL (|has| #7# (|Field|)) ELT) (#26=(#27=(|SparseUnivariatePolynomial| #7#)) 89 #28=(|has| |#1| #9#) ELT)) (|rightPower| #29=(($ $ #30=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| (#31=(#27# $) 87 #6# ELT)) (|rightDiscriminant| #32=((#7# #12#) NIL T ELT) #33=(#34=(#7#) NIL T ELT)) (|rightCharacteristicPolynomial| #35=(#31# NIL T ELT)) (|rightAlternative?| #36=((#2#) NIL T ELT)) (|represents| (($ #37=(|Vector| #7#) #12#) 111 T ELT) #38=(#39=($ #37#) NIL T ELT)) (|recip| #23#) (|rank| ((#30#) NIL T ELT)) (|powerAssociative?| #36#) (|plenaryPower| #29#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #36#) (|lieAlgebra?| #36#) (|lieAdmissible?| #36#) (|leftUnits| #16#) (|leftUnit| #3#) (|leftTraceMatrix| #17# #18#) (|leftTrace| #19#) (|leftRegularRepresentation| #21# #22#) (|leftRecip| #23#) (|leftRankPolynomial| #24# (#26# 88 #28# ELT)) (|leftPower| #29#) (|leftNorm| #19#) (|leftMinimalPolynomial| (#31# 84 #6# ELT)) (|leftDiscriminant| #32# #33#) (|leftCharacteristicPolynomial| #35#) (|leftAlternative?| #36#) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| #36#) (|jordanAdmissible?| #36#) (|jacobiIdentity?| #36#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genericRightTraceForm| (#40=(#7# $ $) 75 #28# ELT)) (|genericRightTrace| (#20# 74 #28# ELT)) (|genericRightNorm| (#20# 101 #28# ELT)) (|genericRightMinimalPolynomial| (#31# 93 #28# ELT)) (|genericRightDiscriminant| (#34# 76 #28# ELT)) (|genericLeftTraceForm| (#40# 64 #28# ELT)) (|genericLeftTrace| (#20# 63 #28# ELT)) (|genericLeftNorm| (#20# 100 #28# ELT)) (|genericLeftMinimalPolynomial| (#31# 92 #28# ELT)) (|genericLeftDiscriminant| (#34# 73 #28# ELT)) (|generic| (#15# 107 T ELT) (($ #41=(|Symbol|)) 115 T ELT) (($ #42=(|Vector| #41#)) 114 T ELT) (($ #12#) 102 T ELT) (($ #41# #12#) 113 T ELT) (($ #42# #12#) 112 T ELT)) (|flexible?| #36#) (|elt| ((#7# $ #43=(|Integer|)) NIL T ELT)) (|coordinates| ((#37# $ #12#) 104 T ELT) ((#11# #12# #12#) NIL T ELT) (#44=(#37# $) 44 T ELT) #17#) (|convert| (#44# NIL T ELT) (#39# 41 T ELT)) (|conditionsForIdempotents| ((#45=(|List| #25#) #12#) NIL T ELT) ((#45#) NIL T ELT) ((#46=(|List| #8#) #12#) 105 #28# ELT) ((#46#) 106 #28# ELT)) (|commutator| #47=(#48=($ $ $) NIL T ELT)) (|commutative?| #36#) (|coerce| (((|OutputForm|) $) NIL T ELT) #38#) (|before?| #1#) (|basis| (#13# 66 T ELT)) (|associatorDependence| (((|List| #37#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| #36#) (|apply| (($ #11# $) NIL T ELT)) (|antiCommutator| #47#) (|antiCommutative?| #36#) (|antiAssociative?| #36#) (|alternative?| #36#) (|Zero| #14#) (= #1#) (- (($ $) NIL T ELT) (#48# 103 T ELT)) (+ #47#) (** #29#) (* (($ #30# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #43# . #49=($)) NIL T ELT) (#48# 62 T ELT) (($ $ #7#) NIL T ELT) (($ #7# . #49#) NIL T ELT) (($ (|SquareMatrix| |#2| #7#) . #49#) NIL T ELT))) (((|GenericNonAssociativeAlgebra| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| #1=(|Fraction| #2=(|Polynomial| |#1|))) (|LeftModule| (|SquareMatrix| |#2| #1#)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| #1#))) (SIGNATURE |leftUnits| #3=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed"))) (SIGNATURE |rightUnits| #3#) (SIGNATURE |generic| ($)) (SIGNATURE |generic| ($ #4=(|Symbol|))) (SIGNATURE |generic| ($ #5=(|Vector| #4#))) (SIGNATURE |generic| ($ #6=(|Vector| $))) (SIGNATURE |generic| ($ #4# #6#)) (SIGNATURE |generic| ($ #5# #6#)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |leftRankPolynomial| #7=(#8=(|SparseUnivariatePolynomial| #1#))) (SIGNATURE |genericLeftMinimalPolynomial| #9=(#8# $)) (SIGNATURE |genericLeftTrace| #10=(#1# $)) (SIGNATURE |genericLeftNorm| #10#) (SIGNATURE |rightRankPolynomial| #7#) (SIGNATURE |genericRightMinimalPolynomial| #9#) (SIGNATURE |genericRightTrace| #10#) (SIGNATURE |genericRightNorm| #10#) (SIGNATURE |genericLeftTraceForm| #11=(#1# $ $)) (SIGNATURE |genericLeftDiscriminant| #12=(#1#)) (SIGNATURE |genericRightTraceForm| #11#) (SIGNATURE |genericRightDiscriminant| #12#) (SIGNATURE |conditionsForIdempotents| (#13=(|List| #2#) #6#)) (SIGNATURE |conditionsForIdempotents| (#13#))) |%noBranch|))) (|CommutativeRing|) (|PositiveInteger|) (|List| #4#) (|Vector| (|Matrix| |#1|))) (T |GenericNonAssociativeAlgebra|)) ((|coerce| #1=(*1 *1 *2) (AND (|isDomain| *2 (|Vector| #2=(|Fraction| #3=(|Polynomial| *3)))) #4=(|ofCategory| *3 #5=(|CommutativeRing|)) #6=(|ofType| *6 (|Vector| (|Matrix| *3))) #7=(|isDomain| *1 #8=(|GenericNonAssociativeAlgebra| *3 *4 *5 *6)) #9=(|ofType| *4 #10=(|PositiveInteger|)) #11=(|ofType| *5 #12=(|List| #13=(|Symbol|))))) (|leftUnits| #14=(*1 *2) #15=(|partial| AND (|isDomain| *2 (|Record| (|:| |particular| #8#) (|:| |basis| (|List| #8#)))) #7# #4# #9# #11# #6#)) (|rightUnits| #14# #15#) (|generic| (*1 *1) (AND (|isDomain| *1 (|GenericNonAssociativeAlgebra| *2 *3 *4 *5)) (|ofCategory| *2 #5#) (|ofType| *3 #10#) (|ofType| *4 #12#) (|ofType| *5 (|Vector| (|Matrix| *2))))) (|generic| #1# (AND #16=(|isDomain| *2 #13#) #7# #4# #9# (|ofType| *5 #17=(|List| *2)) #6#)) (|generic| #1# (AND #18=(|isDomain| *2 (|Vector| #13#)) #7# #4# #9# #11# #6#)) (|generic| #1# (AND (|isDomain| *2 (|Vector| #8#)) #7# #4# #9# #11# #6#)) (|generic| #19=(*1 *1 *2 *3) (AND #16# #20=(|isDomain| *3 (|Vector| #21=(|GenericNonAssociativeAlgebra| *4 *5 *6 *7))) #22=(|isDomain| *1 #21#) #23=(|ofCategory| *4 #5#) #24=(|ofType| *5 #10#) (|ofType| *6 #17#) #25=(|ofType| *7 (|Vector| (|Matrix| *4))))) (|generic| #19# (AND #18# #20# #22# #23# #24# #26=(|ofType| *6 #12#) #25#)) (|leftRankPolynomial| #14# #27=(AND (|isDomain| *2 (|SparseUnivariatePolynomial| #2#)) #7# #28=(|ofCategory| *3 #29=(|IntegralDomain|)) #4# #9# #11# #6#)) (|genericLeftMinimalPolynomial| #30=(*1 *2 *1) #27#) (|genericLeftTrace| #30# #31=(AND (|isDomain| *2 #2#) #7# #28# #4# #9# #11# #6#)) (|genericLeftNorm| #30# #31#) (|rightRankPolynomial| #14# #27#) (|genericRightMinimalPolynomial| #30# #27#) (|genericRightTrace| #30# #31#) (|genericRightNorm| #30# #31#) (|genericLeftTraceForm| #32=(*1 *2 *1 *1) #31#) (|genericLeftDiscriminant| #14# #31#) (|genericRightTraceForm| #32# #31#) (|genericRightDiscriminant| #14# #31#) (|conditionsForIdempotents| (*1 *2 *3) (AND #20# (|isDomain| *2 (|List| (|Polynomial| *4))) #22# (|ofCategory| *4 #29#) #23# #24# #26# #25#)) (|conditionsForIdempotents| #14# (AND (|isDomain| *2 (|List| #3#)) #7# #28# #4# #9# #11# #6#))) @@ -1344,11 +1344,11 @@ NIL ((|Zero| (#1=($) 11 T CONST)) (|One| (#1# 13 T CONST)) (* (($ |#2| $) 15 T ELT) (($ $ |#2|) 16 T ELT))) (((|GradedAlgebra&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |One| #1=(|#1|) |constant|) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE |Zero| #1# |constant|)) (|GradedAlgebra| |#2| |#3|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 30 T ELT)) (|retract| ((|#1| $) 31 T ELT)) (|product| (($ $ $) 27 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| ((|#2| $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 29 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (($) 22 T CONST)) (|One| (($) 28 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 19 T ELT) (#2=($ $ $) 17 T ELT)) (+ (#2# 18 T ELT)) (* (($ |#1| $) 21 T ELT) (($ $ |#1|) 20 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 30 T ELT)) (|retract| ((|#1| $) 31 T ELT)) (|product| (#2=($ $ $) 27 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| ((|#2| $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ |#1|) 29 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3=($) 22 T CONST)) (|One| (#3# 28 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 19 T ELT) (#2# 17 T ELT)) (+ (#2# 18 T ELT)) (* (($ |#1| $) 21 T ELT) (($ $ |#1|) 20 T ELT))) (((|GradedAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedAlgebra|)) -((|One| (*1 *1) (AND (|ofCategory| *1 (|GradedAlgebra| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (|product| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedAlgebra| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|))))) +((|One| (*1 *1) #1=(AND (|ofCategory| *1 (|GradedAlgebra| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (|product| (*1 *1 *1 *1) #1#)) (|Join| (|GradedModule| |t#1| |t#2|) (|RetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |product| ($ $ $)))) -(((|BasicType|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|GradedModule| |#1| |#2|) . T) ((|Join|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|GradedModule| |#1| |#2|) . T) ((|RetractableTo| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|nextSubsetGray| ((#1=(|Vector| (|Vector| (|Integer|))) #1# #2=(|PositiveInteger|)) 26 T ELT)) (|firstSubsetGray| ((#1# #2#) 21 T ELT))) (((|GrayCode|) (CATEGORY |package| (SIGNATURE |nextSubsetGray| (#1=(|Vector| (|Vector| (|Integer|))) #1# #2=(|PositiveInteger|))) (SIGNATURE |firstSubsetGray| (#1# #2#)))) (T |GrayCode|)) ((|firstSubsetGray| (*1 *2 *3) (AND #1=(|isDomain| *3 (|PositiveInteger|)) #2=(|isDomain| *2 (|Vector| (|Vector| (|Integer|)))) #3=(|isDomain| *1 (|GrayCode|)))) (|nextSubsetGray| (*1 *2 *2 *3) (AND #2# #1# #3#))) @@ -1361,22 +1361,22 @@ NIL ((- (($ $) NIL T ELT) (($ $ $) 11 T ELT))) (((|GradedModule&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE - (|#1| |#1| |#1|)) (SIGNATURE - (|#1| |#1|))) (|GradedModule| |#2| |#3|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedModule&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| ((|#2| $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (($) 22 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 19 T ELT) (($ $ $) 17 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ |#1| $) 21 T ELT) (($ $ |#1|) 20 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| ((|#2| $) 23 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (($) 22 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 19 T ELT) (#2=($ $ $) 17 T ELT)) (+ (#2# 18 T ELT)) (* (($ |#1| $) 21 T ELT) (($ $ |#1|) 20 T ELT))) (((|GradedModule| |#1| |#2|) (|Category|) (|CommutativeRing|) (|AbelianMonoid|)) (T |GradedModule|)) -((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|GradedModule| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|AbelianMonoid|)))) (|Zero| (*1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (- (*1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (+ (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|)))) (- (*1 *1 *1 *1) (AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *3 (|AbelianMonoid|))))) -(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |Zero| ($) |constant|) (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#1|)) (SIGNATURE - ($ $)) (SIGNATURE + ($ $ $)) (SIGNATURE - ($ $ $)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|GradedModule| *3 *2)) (|ofCategory| *3 #1=(|CommutativeRing|)) (|ofCategory| *2 #2=(|AbelianMonoid|)))) (|Zero| (*1 *1) #3=(AND (|ofCategory| *1 (|GradedModule| *2 *3)) (|ofCategory| *2 #1#) (|ofCategory| *3 #2#))) (* (*1 *1 *2 *1) #3#) (* (*1 *1 *1 *2) #3#) (- (*1 *1 *1) #3#) (+ #4=(*1 *1 *1 *1) #3#) (- #4# #3#)) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |Zero| ($) |constant|) (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#1|)) (SIGNATURE - ($ $)) (SIGNATURE + #1=($ $ $)) (SIGNATURE - #1#))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|testDim| (((|Union| #1=(|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") #1# #2=(|List| (|OrderedVariableList| |#1|))) 134 T ELT)) (|groebSolve| (((|List| #3=(|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) #3# #2#) 131 T ELT)) (|genericPosition| (((|Record| (|:| |dpolys| #3#) (|:| |coords| (|List| (|Integer|)))) #3# #2#) 86 T ELT))) (((|GroebnerSolve| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |groebSolve| ((|List| #1=(|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) #1# #2=(|List| (|OrderedVariableList| |#1|)))) (SIGNATURE |testDim| ((|Union| #3=(|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") #3# #2#)) (SIGNATURE |genericPosition| ((|Record| (|:| |dpolys| #1#) (|:| |coords| (|List| (|Integer|)))) #1# #2#))) (|List| (|Symbol|)) #4=(|GcdDomain|) #4#) (T |GroebnerSolve|)) ((|genericPosition| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *4 (|List| (|OrderedVariableList| *5))) #3=(|ofType| *5 #4=(|List| (|Symbol|))) #5=(|ofCategory| *6 #6=(|GcdDomain|)) (|isDomain| *2 (|Record| (|:| |dpolys| #7=(|List| (|DistributedMultivariatePolynomial| *5 *6))) (|:| |coords| (|List| (|Integer|))))) #8=(|isDomain| *1 (|GroebnerSolve| *5 *6 *7)) #9=(|isDomain| *3 #7#) #10=(|ofCategory| *7 #6#))) (|testDim| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|HomogeneousDistributedMultivariatePolynomial| *4 *5))) (|isDomain| *3 (|List| (|OrderedVariableList| *4))) (|ofType| *4 #4#) (|ofCategory| *5 #6#) (|isDomain| *1 (|GroebnerSolve| *4 *5 *6)) #5#)) (|groebSolve| #1# (AND #2# #3# #5# (|isDomain| *2 (|List| #7#)) #8# #9# #10#))) ((|recip| (((|Union| $ "failed") $) 11 T ELT)) (|conjugate| (#1=($ $ $) 22 T ELT)) (|commutator| (#1# 23 T ELT)) (/ (#1# 9 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) 21 T ELT))) (((|Group&| |#1|) (CATEGORY |package| (SIGNATURE |commutator| #1=(|#1| |#1| |#1|)) (SIGNATURE |conjugate| #1#) (SIGNATURE ** (|#1| |#1| (|Integer|))) (SIGNATURE / #1#) (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|Group|)) (T |Group&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|sample| (#2=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|conjugate| (($ $ $) 27 T ELT)) (|commutator| (($ $ $) 26 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 29 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT) (($ $ (|Integer|)) 28 T ELT)) (* (($ $ $) 18 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|one?| ((#2# $) 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|conjugate| (#4=($ $ $) 27 T ELT)) (|commutator| (#4# 26 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (#4# 29 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT) (($ $ (|Integer|)) 28 T ELT)) (* (#4# 18 T ELT))) (((|Group|) (|Category|)) (T |Group|)) -((|inv| (*1 *1 *1) (|ofCategory| *1 (|Group|))) (/ (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Group|)) (|isDomain| *2 (|Integer|)))) (|conjugate| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|Group|)))) -(|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |inv| ($ $)) (SIGNATURE / ($ $ $)) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE |conjugate| ($ $ $)) (SIGNATURE |commutator| ($ $ $)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|inv| (*1 *1 *1) #1=(|ofCategory| *1 (|Group|))) (/ #2=(*1 *1 *1 *1) #1#) (** (*1 *1 *1 *2) (AND #1# (|isDomain| *2 (|Integer|)))) (|conjugate| #2# #1#) (|commutator| #2# #1#)) +(|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |inv| ($ $)) (SIGNATURE / #1=($ $ $)) (SIGNATURE ** ($ $ (|Integer|))) (SIGNATURE |conjugate| #1#) (SIGNATURE |commutator| #1#))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Monoid|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 18 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| #12=(#13=($ $ #14=(|Fraction| #15=(|Integer|))) NIL T ELT) (($ $ #14# #14#) NIL T ELT)) (|terms| ((#16=(|Stream| (|Record| (|:| |k| #14#) (|:| |c| |#1|))) $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|Algebra| #14#)) ELT)) (|tan| #17#) (|subtractIfCan| ((#19=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #20=(#11# NIL #21=(|has| |#1| (|Field|)) ELT)) (|squareFree| #22=(((|Factored| $) $) NIL #21# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #21# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #23=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| #24=(#25=($) NIL T CONST)) (|rem| #26=(#27=($ $ $) NIL #21# ELT)) (|reductum| #28=(#11# NIL T ELT)) (|recip| ((#29=(|Union| $ #30="failed") $) NIL T ELT)) (|quo| #26#) (|principalIdeal| (((|Record| (|:| |coef| #31=(|List| $)) #32=(|:| |generator| $)) #31#) NIL #21# ELT)) (|prime?| (#5# NIL #21# ELT)) (|pole?| #4#) (|pi| (#25# NIL #18# ELT)) (|order| #33=((#14# $) NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#34=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #35=(($ $ #36=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #31# #30#) #31# $) NIL #21# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) NIL T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 25 T ELT)) (|log| #17#) (|leadingMonomial| #28#) (|leadingCoefficient| (#37=(|#1| $) NIL T ELT)) (|lcm| #38=(($ #31#) NIL #21# ELT) #26#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #20#) (|integrate| (#11# 29 #18# ELT) (#39=($ $ #8#) 35 (OR (AND #18# (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #15#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|))) (AND #18# (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#40=(|List| #8#) |#1|))))) ELT) (#41=($ $ #42=(|Variable| |#2|)) 30 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#43=(|SparseUnivariatePolynomial| $) #43# #43#) NIL #21# ELT)) (|gcd| #38# #26#) (|factor| #22#) (|extendedEuclidean| (((|Union| (|Record| #44=(|:| |coef1| $) #45=(|:| |coef2| $)) #30#) $ $ $) NIL #21# ELT) (((|Record| #44# #45# #32#) $ $) NIL #21# ELT)) (|extend| #12#) (|exquo| ((#29# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #31#) #31# $) NIL #21# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #46=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#23# $) NIL #21# ELT)) (|elt| #47=(#48=(|#1| $ #14#) NIL T ELT) (#27# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #21# ELT)) (|differentiate| (#39# 28 #49=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #50=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #51=(($ $ #40#) NIL #49# ELT) #52=(($ $ #8# #23#) NIL #49# ELT) #53=(($ $ #40# (|List| #23#)) NIL #49# ELT) (#11# 14 #50# ELT) #54=(#55=($ $ #23#) NIL #50# ELT) (#41# 16 T ELT)) (|degree| #33#) (|csch| #17#) (|csc| #17#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|complete| #28#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL (|has| |#1| (|CommutativeRing|)) ELT) (($ #42#) NIL T ELT) (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) 9 T ELT) (($ #14#) NIL #18# ELT) #10#) (|coefficient| #47#) (|charthRoot| ((#19# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#23#) NIL T CONST)) (|center| (#37# 21 T ELT)) (|before?| #1#) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #9# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|approximate| (#48# NIL (AND #46# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|Zero| #24#) (|One| #24#) (D (#39# NIL #49# ELT) #51# #52# #53# (#11# NIL #50# ELT) #54# (#41# NIL T ELT)) (= #1#) (/ (#56=($ $ |#1|) NIL #21# ELT) #26#) (- #28# (#27# 27 T ELT)) (+ #57=(#27# NIL T ELT)) (** #35# (#55# NIL T ELT) (#34# NIL #21# ELT) (#27# NIL #18# ELT) #58=(#13# NIL #18# ELT)) (* (($ #36# $) NIL T ELT) (($ #23# $) NIL T ELT) (($ #15# . #59=($)) NIL T ELT) #57# (#56# NIL T ELT) (($ |#1| . #59#) 26 T ELT) (($ #14# . #59#) NIL #18# ELT) #58#)) (((|GeneralUnivariatePowerSeries| |#1| |#2| |#3|) (|Join| (|UnivariatePuiseuxSeriesCategory| |#1|) (|PartialDifferentialDomain| $ #1=(|Variable| |#2|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1#)) (SIGNATURE |coerce| ($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $ #1#)) |%noBranch|))) (|Ring|) (|Symbol|) |#1|) (T |GeneralUnivariatePowerSeries|)) ((|coerce| #1=(*1 *1 *2) (AND #2=(|isDomain| *2 (|Variable| *4)) #3=(|ofType| *4 (|Symbol|)) #4=(|isDomain| *1 (|GeneralUnivariatePowerSeries| *3 *4 *5)) #5=(|ofCategory| *3 (|Ring|)) #6=(|ofType| *5 *3))) (|coerce| #1# (AND (|isDomain| *2 (|UnivariatePuiseuxSeries| *3 *4 *5)) #5# #3# #6# #4#)) (|integrate| (*1 *1 *1 *2) (AND #2# #3# #4# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) #5# #6#))) @@ -1422,11 +1422,11 @@ NIL ((|eval| (($ $ (|List| #1=(|Equation| |#2|))) 13 T ELT) (($ $ #1#) NIL T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ #2=(|List| |#2|) #2#) NIL T ELT))) (((|HomogeneousAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |eval| (|#1| |#1| #1=(|List| |#2|) #1#)) (SIGNATURE |eval| (|#1| |#1| |#2| |#2|)) (SIGNATURE |eval| (|#1| |#1| #2=(|Equation| |#2|))) (SIGNATURE |eval| (|#1| |#1| (|List| #2#)))) (|HomogeneousAggregate| |#2|) (|Type|)) (T |HomogeneousAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #5#)) ELT)) (|eq?| ((#6=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#6# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|sample| (#4=($) 6 T CONST)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 #5=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) 20 #5# ELT)) (|eval| (($ $ (|List| #6=(|Equation| |#1|))) 25 #7=(AND (|has| |#1| (|Evalable| |#1|)) #5#) ELT) (($ $ #6#) 24 #7# ELT) (($ $ |#1| |#1|) 23 #7# ELT) (($ $ #8=(|List| |#1|) #8#) 22 #7# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#4# 8 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| ((#9=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #9#)) ELT)) (|before?| (#1# 19 #3# ELT)) (= (#1# 17 #3# ELT))) (((|HomogeneousAggregate| |#1|) (|Category|) (|Type|)) (T |HomogeneousAggregate|)) NIL -(|Join| (|Aggregate|) (|Functorial| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|CoercibleTo| (|OutputForm|))) (ATTRIBUTE (|CoercibleTo| (|OutputForm|))) |%noBranch|) (IF (|has| |t#1| (|BasicType|)) (ATTRIBUTE (|BasicType|)) |%noBranch|) (IF (|has| |t#1| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |%noBranch|) (IF (|has| |t#1| (|SetCategory|)) (IF (|has| |t#1| (|Evalable| |t#1|)) (ATTRIBUTE (|Evalable| |t#1|)) |%noBranch|) |%noBranch|))) -(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) +(|Join| (|Aggregate|) (|Functorial| |t#1|) (CATEGORY |package| (IF (|has| |t#1| #1=(|CoercibleTo| (|OutputForm|))) (ATTRIBUTE #1#) |%noBranch|) (IF (|has| |t#1| #2=(|BasicType|)) (ATTRIBUTE #2#) |%noBranch|) (IF #3=(|has| |t#1| #4=(|SetCategory|)) (ATTRIBUTE #4#) |%noBranch|) (IF #3# (IF (|has| |t#1| #5=(|Evalable| |t#1|)) (ATTRIBUTE #5#) |%noBranch|) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) ((|coerce| ((|#1| $) 6 T ELT) (($ |#1|) 9 T ELT))) (((|HomotopicTo| |#1|) (|Category|) (|Type|)) (T |HomotopicTo|)) NIL @@ -1438,10 +1438,10 @@ NIL ((|tanh| (#1=($ $) 15 T ELT)) (|sinh| (#1# 24 T ELT)) (|sech| (#1# 12 T ELT)) (|csch| (#1# 10 T ELT)) (|coth| (#1# 17 T ELT)) (|cosh| (#1# 22 T ELT))) (((|HyperbolicFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |cosh| #1=(|#1| |#1|)) (SIGNATURE |coth| #1#) (SIGNATURE |csch| #1#) (SIGNATURE |sech| #1#) (SIGNATURE |sinh| #1#) (SIGNATURE |tanh| #1#)) (|HyperbolicFunctionCategory|)) (T |HyperbolicFunctionCategory&|)) NIL -((|tanh| (($ $) 11 T ELT)) (|sinh| (($ $) 10 T ELT)) (|sech| (($ $) 9 T ELT)) (|csch| (($ $) 8 T ELT)) (|coth| (($ $) 7 T ELT)) (|cosh| (($ $) 6 T ELT))) +((|tanh| (#1=($ $) 11 T ELT)) (|sinh| (#1# 10 T ELT)) (|sech| (#1# 9 T ELT)) (|csch| (#1# 8 T ELT)) (|coth| (#1# 7 T ELT)) (|cosh| (#1# 6 T ELT))) (((|HyperbolicFunctionCategory|) (|Category|)) (T |HyperbolicFunctionCategory|)) -((|tanh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|sinh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|sech| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|csch| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|coth| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|cosh| (*1 *1 *1) (|ofCategory| *1 (|HyperbolicFunctionCategory|)))) -(|Join| (CATEGORY |domain| (SIGNATURE |cosh| ($ $)) (SIGNATURE |coth| ($ $)) (SIGNATURE |csch| ($ $)) (SIGNATURE |sech| ($ $)) (SIGNATURE |sinh| ($ $)) (SIGNATURE |tanh| ($ $)))) +((|tanh| #1=(*1 *1 *1) #2=(|ofCategory| *1 (|HyperbolicFunctionCategory|))) (|sinh| #1# #2#) (|sech| #1# #2#) (|csch| #1# #2#) (|coth| #1# #2#) (|cosh| #1# #2#)) +(|Join| (CATEGORY |domain| (SIGNATURE |cosh| #1=($ $)) (SIGNATURE |coth| #1#) (SIGNATURE |csch| #1#) (SIGNATURE |sech| #1#) (SIGNATURE |sinh| #1#) (SIGNATURE |tanh| #1#))) ((|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) 54 T ELT))) (((|InnerAlgFactor| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)))) #1=(|Field|) (|UnivariatePolynomialCategory| |#1|) (|Join| #1# (|CharacteristicZero|) (|MonogenicAlgebra| |#1| |#2|)) (|UnivariatePolynomialCategory| |#3|)) (T |InnerAlgFactor|)) ((|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|Factored| *6) *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #1=(|Field|)) (|ofCategory| *7 (|Join| #1# (|CharacteristicZero|) (|MonogenicAlgebra| *5 *6))) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|InnerAlgFactor| *5 *6 *7 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *7))))) @@ -1482,7 +1482,7 @@ NIL (((|IdempotentOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |IdempotentOperatorCategory|)) NIL (|Join| (|BinaryOperatorCategory| |t#1|) (CATEGORY |domain| (ATTRIBUTE (|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|)) (= (|f| |x| |x|) |x|)))))) -(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) +(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gensym| (($) 6 T ELT)) (|coerce| (((|OutputForm|) $) 10 T ELT)) (|before?| #1#) (= (#2# 8 T ELT))) (((|Identifier|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |gensym| ($))))) (T |Identifier|)) ((|gensym| (*1 *1) (|isDomain| *1 (|Identifier|)))) @@ -1492,11 +1492,11 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 16 T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 13 T ELT)) (|sample| (#5=($) NIL T CONST)) (|reductum| (($ $) 39 T ELT)) (|opposite?| (#2# 44 T ELT)) (|monomial| (($ |#1| |#2|) 36 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 38 T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) 41 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #4#) 11 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#5# 12 T CONST)) (= #1#) (+ (($ $ $) 30 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) 35 T ELT))) (((|IndexedDirectProductAbelianMonoid| |#1| |#2|) (|Join| #1=(|AbelianMonoid|) (|IndexedDirectProductCategory| |#1| |#2|)) #1# (|OrderedType|)) (T |IndexedDirectProductAbelianMonoid|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) 17 T ELT)) (|reductum| (($ $) 18 T ELT)) (|monomial| (($ |#1| |#2|) 21 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 23 T ELT)) (|leadingSupport| ((|#2| $) 19 T ELT)) (|leadingCoefficient| ((|#1| $) 20 T ELT)) (|latex| (((|String|) $) 16 (AND (|has| |#2| . #2=((|SetCategory|))) (|has| |#1| . #3=((|SetCategory|)))) ELT)) (|hash| (((|SingleInteger|) $) 15 (AND (|has| |#2| . #2#) (|has| |#1| . #3#)) ELT)) (|convert| (($ (|List| (|IndexedProductTerm| |#1| |#2|))) 22 T ELT)) (|coerce| (((|OutputForm|) $) 14 (AND (|has| |#2| . #2#) (|has| |#1| . #3#)) ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|terms| ((#2=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 17 T ELT)) (|reductum| (($ $) 18 T ELT)) (|monomial| (($ |#1| |#2|) 21 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 23 T ELT)) (|leadingSupport| ((|#2| $) 19 T ELT)) (|leadingCoefficient| ((|#1| $) 20 T ELT)) (|latex| (((|String|) $) 16 #3=(AND (|has| |#2| #4=(|SetCategory|)) (|has| |#1| #4#)) ELT)) (|hash| (((|SingleInteger|) $) 15 #3# ELT)) (|convert| (($ #2#) 22 T ELT)) (|coerce| (((|OutputForm|) $) 14 #3# ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) (((|IndexedDirectProductCategory| |#1| |#2|) (|Category|) (|BasicType|) (|OrderedType|)) (T |IndexedDirectProductCategory|)) -((|monomial| (*1 *1 *2 *3) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *3 (|OrderedType|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *3 (|OrderedType|)) (|ofCategory| *2 (|BasicType|)))) (|leadingSupport| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|OrderedType|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *3 (|OrderedType|)))) (|terms| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|OrderedType|)) (|isDomain| *2 (|List| (|IndexedProductTerm| *3 *4)))))) -(|Join| (|BasicType|) (|Functorial| |t#1|) (|ConvertibleFrom| (|List| (|IndexedProductTerm| |t#1| |t#2|))) (CATEGORY |domain| (IF (|has| |t#1| (|SetCategory|)) (IF (|has| |t#2| (|SetCategory|)) (ATTRIBUTE (|SetCategory|)) |%noBranch|) |%noBranch|) (SIGNATURE |monomial| ($ |t#1| |t#2|)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingSupport| (|t#2| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |terms| ((|List| (|IndexedProductTerm| |t#1| |t#2|)) $)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) AND (|has| |#1| (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|ConvertibleFrom| (|List| (|IndexedProductTerm| |#1| |#2|))) . T) ((|Functorial| |#1|) . T) ((|Join|) . T) ((|SetCategory|) AND (|has| |#1| (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|Type|) . T)) +((|monomial| (*1 *1 *2 *3) #1=(AND #2=(|ofCategory| *1 (|IndexedDirectProductCategory| *2 *3)) #3=(|ofCategory| *2 #4=(|BasicType|)) #5=(|ofCategory| *3 #6=(|OrderedType|)))) (|leadingCoefficient| #7=(*1 *2 *1) (AND #2# #5# #3#)) (|leadingSupport| #7# (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *2)) #8=(|ofCategory| *3 #4#) (|ofCategory| *2 #6#))) (|reductum| (*1 *1 *1) #1#) (|terms| #7# (AND (|ofCategory| *1 (|IndexedDirectProductCategory| *3 *4)) #8# (|ofCategory| *4 #6#) (|isDomain| *2 (|List| (|IndexedProductTerm| *3 *4)))))) +(|Join| (|BasicType|) (|Functorial| |t#1|) (|ConvertibleFrom| #1=(|List| (|IndexedProductTerm| |t#1| |t#2|))) (CATEGORY |domain| (IF (|has| |t#1| #2=(|SetCategory|)) (IF (|has| |t#2| #2#) (ATTRIBUTE #2#) |%noBranch|) |%noBranch|) (SIGNATURE |monomial| ($ |t#1| |t#2|)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |leadingSupport| (|t#2| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |terms| (#1# $)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) AND (|has| |#1| (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|ConvertibleFrom| (|List| (|IndexedProductTerm| |#1| |#2|))) . T) ((|Functorial| |#1|) . T) ((|SetCategory|) AND (|has| |#1| (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|terms| ((#4=(|List| (|IndexedProductTerm| |#1| |#2|)) $) 33 T ELT)) (|reductum| (($ $) 28 T ELT)) (|monomial| (($ |#1| |#2|) 24 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|leadingSupport| ((|#2| $) 32 T ELT)) (|leadingCoefficient| ((|#1| $) 31 T ELT)) (|latex| (((|String|) $) NIL #5=(AND (|has| |#1| #6=(|SetCategory|)) (|has| |#2| #6#)) ELT)) (|hash| (((|SingleInteger|) $) NIL #5# ELT)) (|convert| (($ #4#) 34 T ELT)) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| #3# |#1| |#1|)) 44 T ELT)) (|coerce| (((|OutputForm|) $) 18 #5# ELT)) (|before?| #1#) (= (#2# 22 T ELT))) (((|IndexedDirectProductObject| |#1| |#2|) (|Join| (|IndexedDirectProductCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |combineWithIf| ($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|))))) (|BasicType|) (|OrderedType|)) (T |IndexedDirectProductObject|)) ((|combineWithIf| (*1 *1 *1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *4 *4 *4)) (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) (|ofCategory| *4 (|BasicType|)) (|isDomain| *1 (|IndexedDirectProductObject| *4 *5)) (|ofCategory| *5 (|OrderedType|))))) @@ -1514,7 +1514,7 @@ NIL NIL ((|eval| (($ $ (|List| |#1|) (|List| |#2|)) 7 T ELT) (($ $ |#1| |#2|) 6 T ELT))) (((|InnerEvalable| |#1| |#2|) (|Category|) (|SetCategory|) (|Type|)) (T |InnerEvalable|)) -((|eval| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|InnerEvalable| *4 *5)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *5 (|Type|)))) (|eval| (*1 *1 *1 *2 *3) (AND (|ofCategory| *1 (|InnerEvalable| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|Type|))))) +((|eval| #1=(*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|InnerEvalable| *4 *5)) (|ofCategory| *4 #2=(|SetCategory|)) (|ofCategory| *5 #3=(|Type|)))) (|eval| #1# (AND (|ofCategory| *1 (|InnerEvalable| *2 *3)) (|ofCategory| *2 #2#) (|ofCategory| *3 #3#)))) (|Join| (CATEGORY |domain| (SIGNATURE |eval| ($ $ |t#1| |t#2|)) (SIGNATURE |eval| ($ $ (|List| |t#1|) (|List| |t#2|))))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#3# $) 17 T ELT)) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) 19 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|size| ((#4=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #6=(|Integer|)) 24 T ELT)) (|nthCoef| ((|#2| $ #6#) 22 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 48 T ELT)) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) 45 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#7=($ $ $) 55 (|has| |#2| (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 44 T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((|#2| |#1| $) 51 T ELT)) (|before?| #1#) (|Zero| (#5# 11 T CONST)) (= (#2# 30 T ELT)) (+ (#7# 28 T ELT) (($ |#1| $) 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #4# $) 37 T ELT) (($ |#2| |#1|) 32 T ELT))) (((|InnerFreeAbelianMonoid| |#1| |#2| |#3|) (|FreeAbelianMonoidCategory| |#1| |#2|) (|SetCategory|) (|CancellationAbelianMonoid|) |#2|) (T |InnerFreeAbelianMonoid|)) @@ -1545,7 +1545,7 @@ NIL NIL ((|readUInt8!| (((|Maybe| (|UInt8|)) $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|readByte!| (((|Maybe| (|Byte|)) $) 14 T ELT)) (|close!| (($ $) 6 T ELT))) (((|InputByteConduit|) (|Category|)) (T |InputByteConduit|)) -((|readByte!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Byte|))))) (|readInt8!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int8|))))) (|readUInt8!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt8|))))) (|readInt16!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int16|))))) (|readUInt16!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt16|))))) (|readInt32!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int32|))))) (|readUInt32!| (*1 *2 *1) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt32|))))) (|readBytes!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *3 (|ByteBuffer|)) (|isDomain| *2 (|NonNegativeInteger|))))) +((|readByte!| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|InputByteConduit|)) (|isDomain| *2 (|Maybe| (|Byte|))))) (|readInt8!| #1# (AND #2# (|isDomain| *2 (|Maybe| (|Int8|))))) (|readUInt8!| #1# (AND #2# (|isDomain| *2 (|Maybe| (|UInt8|))))) (|readInt16!| #1# (AND #2# (|isDomain| *2 (|Maybe| (|Int16|))))) (|readUInt16!| #1# (AND #2# (|isDomain| *2 (|Maybe| (|UInt16|))))) (|readInt32!| #1# (AND #2# (|isDomain| *2 (|Maybe| (|Int32|))))) (|readUInt32!| #1# (AND #2# (|isDomain| *2 (|Maybe| (|UInt32|))))) (|readBytes!| (*1 *2 *1 *3) (AND #2# (|isDomain| *3 (|ByteBuffer|)) (|isDomain| *2 (|NonNegativeInteger|))))) (|Join| (|Conduit|) (CATEGORY |domain| (SIGNATURE |readByte!| ((|Maybe| (|Byte|)) $)) (SIGNATURE |readInt8!| ((|Maybe| (|Int8|)) $)) (SIGNATURE |readUInt8!| ((|Maybe| (|UInt8|)) $)) (SIGNATURE |readInt16!| ((|Maybe| (|Int16|)) $)) (SIGNATURE |readUInt16!| ((|Maybe| (|UInt16|)) $)) (SIGNATURE |readInt32!| ((|Maybe| (|Int32|)) $)) (SIGNATURE |readUInt32!| ((|Maybe| (|UInt32|)) $)) (SIGNATURE |readBytes!| ((|NonNegativeInteger|) $ (|ByteBuffer|))))) (((|Conduit|) . T)) ((|xn| ((#1=(|SparseUnivariatePolynomial| |#1|) #2=(|NonNegativeInteger|)) 114 T ELT)) (|trace| (#3=(#4=(|Vector| |#1|) #4# #5=(|PositiveInteger|)) 107 T ELT)) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #6=(|SingleInteger|))))) |#1|) 122 T ELT)) (|repSq| ((#4# #4# #2#) 53 T ELT)) (|random| (#7=(#4# #5#) 109 T ELT)) (|qPot| (#8=(#4# #4# (|Integer|)) 30 T ELT)) (|pol| (#9=(#1# #4#) 115 T ELT)) (|normalElement| (#7# 136 T ELT)) (|normal?| (((|Boolean|) #4#) 119 T ELT)) (|norm| (#3# 99 T ELT)) (|minimalPolynomial| (#9# 130 T ELT)) (|lookup| ((#5# #4#) 95 T ELT)) (|inv| ((#4# #4#) 38 T ELT)) (|index| ((#4# #5# #5#) 139 T ELT)) (|expPot| ((#4# #4# #6# #6#) 29 T ELT)) (|dAndcExp| ((#4# #4# #2# #6#) 54 T ELT)) (|basis| (((|Vector| #4#) #5#) 135 T ELT)) (/ (#10=(#4# #4# #4#) 120 T ELT)) (** (#8# 67 T ELT)) (* (#10# 31 T ELT))) @@ -1599,11 +1599,11 @@ NIL ((|symmetricRemainder| (#1=($ $ $) 87 T ELT)) (|squareFree| (#2=((|Factored| $) $) 50 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) 62 T ELT)) (|retract| (#5=(#3# $) 40 T ELT)) (|rationalIfCan| (((|Union| #6=(|Fraction| #3#) #4#) $) 80 T ELT)) (|rational?| (#7=(#8=(|Boolean|) $) 24 T ELT)) (|rational| ((#6# $) 78 T ELT)) (|prime?| (#7# 53 T ELT)) (|powmod| (($ $ $ $) 94 T ELT)) (|permutation| (#1# 60 T ELT)) (|patternMatch| ((#9=(|PatternMatchResult| #3# $) $ #10=(|Pattern| #3#) #9#) 75 T ELT)) (|nextItem| (((|Maybe| $) $) 70 T ELT)) (|mask| (#11=($ $) 22 T ELT)) (|invmod| (#1# 92 T ELT)) (|init| (($) 63 T CONST)) (|factorial| (#11# 56 T ELT)) (|factor| (#2# 48 T ELT)) (|even?| (#7# 15 T ELT)) (|euclideanSize| ((#12=(|NonNegativeInteger|) $) 30 T ELT)) (|differentiate| (#11# 11 T ELT) (($ $ #12#) NIL T ELT)) (|copy| (#11# 16 T ELT)) (|convert| (#5# NIL T ELT) (((|InputForm|) $) 39 T ELT) ((#10# $) 43 T ELT) (((|Float|) $) 33 T ELT) (((|DoubleFloat|) $) 36 T ELT)) (|characteristic| ((#12#) 9 T CONST)) (|bit?| ((#8# $ $) 19 T ELT)) (|binomial| (#1# 58 T ELT))) (((|IntegerNumberSystem&| |#1|) (CATEGORY |package| (SIGNATURE |invmod| #1=(|#1| |#1| |#1|)) (SIGNATURE |powmod| (|#1| |#1| |#1| |#1|)) (SIGNATURE |mask| #2=(|#1| |#1|)) (SIGNATURE |copy| #2#) (SIGNATURE |rationalIfCan| ((|Union| #3=(|Fraction| #4=(|Integer|)) #5="failed") |#1|)) (SIGNATURE |rational| (#3# |#1|)) (SIGNATURE |rational?| #6=(#7=(|Boolean|) |#1|)) (SIGNATURE |symmetricRemainder| #1#) (SIGNATURE |bit?| (#7# |#1| |#1|)) (SIGNATURE |even?| #6#) (SIGNATURE |init| (|#1|) |constant|) (SIGNATURE |nextItem| ((|Maybe| |#1|) |#1|)) (SIGNATURE |convert| ((|DoubleFloat|) |#1|)) (SIGNATURE |convert| ((|Float|) |#1|)) (SIGNATURE |permutation| #1#) (SIGNATURE |factorial| #2#) (SIGNATURE |binomial| #1#) (SIGNATURE |patternMatch| (#8=(|PatternMatchResult| #4# |#1|) |#1| #9=(|Pattern| #4#) #8#)) (SIGNATURE |convert| (#9# |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4# #5#) |#1|)) (SIGNATURE |retract| #10=(#4# |#1|)) (SIGNATURE |convert| #10#) (SIGNATURE |differentiate| (|#1| |#1| #11=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #2#) (SIGNATURE |euclideanSize| (#11# |#1|)) (SIGNATURE |factor| #12=((|Factored| |#1|) |#1|)) (SIGNATURE |squareFree| #12#) (SIGNATURE |prime?| #6#) (SIGNATURE |characteristic| (#11#) |constant|)) (|IntegerNumberSystem|)) (T |IntegerNumberSystem&|)) ((|characteristic| (*1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|IntegerNumberSystem&| *3)) (|ofCategory| *3 (|IntegerNumberSystem|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|symmetricRemainder| (($ $ $) 103 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|submod| (($ $ $ $) 92 T ELT)) (|squareFreePart| (($ $) 67 T ELT)) (|squareFree| (#4=((|Factored| $) $) 68 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 146 T ELT)) (|sign| (((|Integer|) $) 135 T ELT)) (|shift| (($ $ $) 106 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) "failed") $) 127 T ELT)) (|retract| ((#6# $) 128 T ELT)) (|rem| (#7=($ $ $) 150 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #9=(|Matrix| $) #10=(|Vector| $)) 125 T ELT) (((|Matrix| #8#) #9#) 124 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 100 T ELT)) (|rational?| (((|Boolean|) $) 102 T ELT)) (|rational| (((|Fraction| (|Integer|)) $) 101 T ELT)) (|random| (($) 99 T ELT) (($ $) 98 T ELT)) (|quo| (#7# 149 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) (|:| |generator| $)) #11#) 144 T ELT)) (|prime?| (((|Boolean|) $) 69 T ELT)) (|powmod| (($ $ $ $) 90 T ELT)) (|positiveRemainder| (($ $ $) 104 T ELT)) (|positive?| (((|Boolean|) $) 137 T ELT)) (|permutation| (#12=($ $ $) 115 T ELT)) (|patternMatch| (((|PatternMatchResult| #13=(|Integer|) . #14=($)) $ (|Pattern| #13#) (|PatternMatchResult| #13# . #14#)) 118 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|odd?| (((|Boolean|) $) 110 T ELT)) (|nextItem| (((|Maybe| $) $) 112 T ELT)) (|negative?| (((|Boolean|) $) 136 T ELT)) (|multiEuclidean| (((|Union| #15=(|List| $) #16="failed") #15# $) 153 T ELT)) (|mulmod| (($ $ $ $) 91 T ELT)) (|min| (#17=($ $ $) 143 T ELT)) (|max| (#17# 142 T ELT)) (|mask| (($ $) 94 T ELT)) (|length| (($ $) 107 T ELT)) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| #8#)) (|:| |vec| (|Vector| #8#))) #10# $) 123 T ELT) (((|Matrix| #8#) #10#) 122 T ELT)) (|lcm| (#18=($ $ $) 61 T ELT) (#19=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|invmod| (($ $ $) 89 T ELT)) (|init| (($) 111 T CONST)) (|inc| (($ $) 96 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#20=(|SparseUnivariatePolynomial| $) #20# #20#) 59 T ELT)) (|gcd| (#18# 63 T ELT) (#19# 62 T ELT)) (|factorial| (($ $) 116 T ELT)) (|factor| (#4# 66 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #21=(|:| |coef1| $) #22=(|:| |coef2| $)) #16#) $ $ $) 152 T ELT) (((|Record| #21# #22# (|:| |generator| $)) $ $) 151 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) 145 T ELT)) (|even?| (((|Boolean|) $) 109 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 147 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 148 T ELT)) (|differentiate| (($ . #23=($)) 133 T ELT) (#24=($ $ (|NonNegativeInteger|)) 131 T ELT)) (|dec| (($ $) 95 T ELT)) (|copy| (($ $) 97 T ELT)) (|convert| (((|Integer|) . #25=($)) 129 T ELT) (((|InputForm|) . #25#) 120 T ELT) (((|Pattern| (|Integer|)) . #25#) 119 T ELT) (((|Float|) . #25#) 114 T ELT) (((|DoubleFloat|) . #25#) 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #6#) 126 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|bit?| (((|Boolean|) $ $) 105 T ELT)) (|binomial| (#12# 117 T ELT)) (|before?| (#1# 6 T ELT)) (|base| (($) 108 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|addmod| (($ $ $ $) 93 T ELT)) (|abs| (($ $) 134 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ . #23#) 132 T ELT) (#24# 130 T ELT)) (>= (#26=((|Boolean|) $ $) 141 T ELT)) (> (#26# 139 T ELT)) (= (#1# 8 T ELT)) (<= (#26# 140 T ELT)) (< (#26# 138 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #27=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ #8# . #27#) 121 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|symmetricRemainder| (#5=($ $ $) 103 T ELT)) (|subtractIfCan| ((#6=(|Maybe| $) $ $) 26 T ELT)) (|submod| (#7=($ $ $ $) 92 T ELT)) (|squareFreePart| (#4# 67 T ELT)) (|squareFree| (#8=((|Factored| $) $) 68 T ELT)) (|sizeLess?| (#1# 146 T ELT)) (|sign| (#9=(#10=(|Integer|) $) 135 T ELT)) (|shift| (#5# 106 T ELT)) (|sample| (#11=($) 23 T CONST)) (|retractIfCan| (((|Union| #10# #12="failed") $) 127 T ELT)) (|retract| (#9# 128 T ELT)) (|rem| (#5# 150 T ELT)) (|reducedSystem| ((#13=(|Record| (|:| |mat| #14=(|Matrix| #10#)) (|:| |vec| (|Vector| #10#))) #15=(|Matrix| $) #16=(|Vector| $)) 125 T ELT) ((#14# #15#) 124 T ELT)) (|recip| ((#17=(|Union| $ #12#) $) 43 T ELT)) (|rationalIfCan| (((|Union| #18=(|Fraction| #10#) #12#) $) 100 T ELT)) (|rational?| (#3# 102 T ELT)) (|rational| ((#18# $) 101 T ELT)) (|random| (#11# 99 T ELT) (#4# 98 T ELT)) (|quo| (#5# 149 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #19=(|List| $)) #20=(|:| |generator| $)) #19#) 144 T ELT)) (|prime?| (#3# 69 T ELT)) (|powmod| (#7# 90 T ELT)) (|positiveRemainder| (#5# 104 T ELT)) (|positive?| (#3# 137 T ELT)) (|permutation| (#5# 115 T ELT)) (|patternMatch| ((#21=(|PatternMatchResult| #10# $) $ #22=(|Pattern| #10#) #21#) 118 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|odd?| (#3# 110 T ELT)) (|nextItem| ((#6# $) 112 T ELT)) (|negative?| (#3# 136 T ELT)) (|multiEuclidean| (((|Union| #19# #12#) #19# $) 153 T ELT)) (|mulmod| (#7# 91 T ELT)) (|min| (#5# 143 T ELT)) (|max| (#5# 142 T ELT)) (|mask| (#4# 94 T ELT)) (|length| (#4# 107 T ELT)) (|leftReducedSystem| ((#13# #16# $) 123 T ELT) ((#14# #16#) 122 T ELT)) (|lcm| (#5# 61 T ELT) (#23=($ #19#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|invmod| (#5# 89 T ELT)) (|init| (#11# 111 T CONST)) (|inc| (#4# 96 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#24=(|SparseUnivariatePolynomial| $) #24# #24#) 59 T ELT)) (|gcd| (#5# 63 T ELT) (#23# 62 T ELT)) (|factorial| (#4# 116 T ELT)) (|factor| (#8# 66 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #25=(|:| |coef1| $) #26=(|:| |coef2| $)) #12#) $ $ $) 152 T ELT) (((|Record| #25# #26# #20#) $ $) 151 T ELT)) (|exquo| ((#17# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #19#) #19# $) 145 T ELT)) (|even?| (#3# 109 T ELT)) (|euclideanSize| ((#27=(|NonNegativeInteger|) $) 147 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 148 T ELT)) (|differentiate| (#4# 133 T ELT) (#28=($ $ #27#) 131 T ELT)) (|dec| (#4# 95 T ELT)) (|copy| (#4# 97 T ELT)) (|convert| (#9# 129 T ELT) (((|InputForm|) . #29=($)) 120 T ELT) ((#22# . #29#) 119 T ELT) (((|Float|) . #29#) 114 T ELT) (((|DoubleFloat|) . #29#) 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#30=($ #10#) 42 T ELT) (#4# 58 T ELT) (#30# 126 T ELT)) (|characteristic| ((#27#) 41 T CONST)) (|bit?| (#1# 105 T ELT)) (|binomial| (#5# 117 T ELT)) (|before?| (#1# 6 T ELT)) (|base| (#11# 108 T ELT)) (|associates?| (#1# 54 T 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CombinatorialFunctionCategory|) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|InputForm|)) . T) ((|ConvertibleTo| #1=(|Integer|)) . T) ((|ConvertibleTo| (|Pattern| #1#)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . 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T) ((|ConvertibleTo| #1#) . T) ((|ConvertibleTo| (|Pattern| #1#)) . T) ((|DifferentialDomain| $) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedIntegralDomain|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #1#) . T) ((|PrincipalIdealDomain|) . T) ((|RealConstant|) . T) ((|RetractableTo| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) . T) ((|Type|) . 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T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 10 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 76 T ELT)) (|unitCanonical| (#5=($ $) 77 T ELT)) (|unit?| #6=(#4# NIL T ELT)) (|symmetricRemainder| #7=(#8=($ $ $) NIL T ELT)) (|subtractIfCan| ((#9=(|Maybe| $) $ $) NIL T ELT)) (|submod| (#10=($ $ $ $) 29 T ELT)) (|squareFreePart| #11=(#5# NIL T ELT)) (|squareFree| (#12=((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sign| #13=(#14=(#15=(|Integer|) $) NIL T ELT)) (|shift| (#8# 71 T ELT)) (|sample| #16=(#17=($) NIL T CONST)) (|retractIfCan| (((|Union| #15# #18="failed") $) NIL T ELT)) (|retract| #13#) (|rem| (#8# 43 T ELT)) (|reducedSystem| ((#19=(|Record| (|:| |mat| #20=(|Matrix| #15#)) (|:| |vec| (|Vector| #15#))) #21=(|Matrix| $) #22=(|Vector| $)) 53 T ELT) ((#20# #21#) 49 T ELT)) (|recip| ((#23=(|Union| $ #18#) $) 73 T ELT)) (|rationalIfCan| (((|Union| #24=(|Fraction| #15#) #18#) $) NIL T ELT)) (|rational?| #6#) 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((#30=(|SparseUnivariatePolynomial| $) #30# #30#) 108 T ELT)) (|gcd| (#8# 74 T ELT) #29#) (|factorial| #11#) (|factor| (#12# 94 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #18#) $ $ $) NIL T ELT) (((|Record| #31# #32# #26#) $ $) NIL T ELT)) (|exquo| ((#23# $ $) 92 T ELT)) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|even?| (#4# 65 T ELT)) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 69 T ELT)) (|differentiate| #11# #34=(#35=($ $ #33#) NIL T ELT)) (|dec| (#5# 15 T ELT)) (|copy| (#5# 13 T ELT)) (|convert| (#14# 26 T ELT) (((|InputForm|) $) 39 T ELT) ((#28# $) NIL T ELT) (((|Float|) $) 33 T ELT) (((|DoubleFloat|) $) 36 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) #36=(($ #15#) 25 T ELT) #11# #36#) (|characteristic| ((#33#) NIL T CONST)) (|bit?| #1#) (|binomial| #7#) (|before?| #1#) (|base| (#17# 12 T ELT)) (|associates?| #1#) (|annihilate?| 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|exquo| (*1 *1 *1 *1) (|partial| |ofCategory| *1 #1=(|IntegralDomain|))) (|unitNormal| #2=(*1 *2 *1) (AND (|isDomain| *2 (|Record| (|:| |unit| *1) (|:| |canonical| *1) (|:| |associate| *1))) #3=(|ofCategory| *1 #1#))) (|unitCanonical| (*1 *1 *1) #3#) (|associates?| (*1 *2 *1 *1) #4=(AND #3# (|isDomain| *2 (|Boolean|)))) (|unit?| #2# #4#)) +(|Join| (|CommutativeRing|) (|Algebra| $) (|EntireRing|) (CATEGORY |domain| (SIGNATURE |exquo| ((|Union| $ "failed") $ $)) (SIGNATURE |unitNormal| ((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $)) (SIGNATURE |unitCanonical| ($ $)) (SIGNATURE |associates?| (#1=(|Boolean|) $ $)) (SIGNATURE |unit?| (#1# $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2="failed") |#2| #3=(|Symbol|) (|List| |#2|)) 38 T ELT)) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| #3#) 63 T ELT)) (|lfinfieldint| (((|Union| |#2| #2#) |#2| #3#) 156 T ELT)) (|lfextlimint| ((#4=(|Union| (|Record| (|:| |ratpart| |#2|) #1#) #2#) |#2| #3# #5=(|Kernel| |#2|) (|List| #5#)) 159 T ELT)) (|lfextendedint| ((#4# |#2| #3# |#2|) 41 T ELT))) (((|ElementaryIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |lfextendedint| (#1=(|Union| (|Record| (|:| |ratpart| |#2|) #2=(|:| |coeff| |#2|)) #3="failed") |#2| #4=(|Symbol|) |#2|)) (SIGNATURE |lflimitedint| ((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #2# (|:| |logand| |#2|))))) #3#) |#2| #4# (|List| |#2|))) (SIGNATURE |lfinfieldint| ((|Union| |#2| #3#) |#2| #4#)) (SIGNATURE |lfintegrate| ((|IntegrationResult| |#2|) |#2| #4#)) (SIGNATURE |lfextlimint| (#1# |#2| #4# #5=(|Kernel| |#2|) (|List| #5#)))) (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #6=(|Integer|)) (|LinearlyExplicitRingOver| #6#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ElementaryIntegration|)) ((|lfextlimint| (*1 *2 *3 *4 *5 *6) (|partial| AND #1=(|isDomain| *4 #2=(|Symbol|)) (|isDomain| *6 (|List| #3=(|Kernel| *3))) (|isDomain| *5 #3#) (|ofCategory| *3 (|Join| #4=(|AlgebraicallyClosedField|) #5=(|TranscendentalFunctionCategory|) (|FunctionSpace| *7))) (|ofCategory| *7 #6=(|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #7=(|Integer|)) (|LinearlyExplicitRingOver| #7#))) #8=(|isDomain| *2 (|Record| (|:| |ratpart| *3) #9=(|:| |coeff| *3))) (|isDomain| *1 (|ElementaryIntegration| *7 *3)))) (|lfintegrate| (*1 *2 *3 *4) (AND #1# #10=(|ofCategory| *5 #6#) (|isDomain| *2 (|IntegrationResult| *3)) #11=(|isDomain| *1 (|ElementaryIntegration| *5 *3)) #12=(|ofCategory| *3 (|Join| #4# #5# (|FunctionSpace| *5))))) (|lfinfieldint| (*1 *2 *2 *3) (|partial| AND (|isDomain| *3 #2#) (|ofCategory| *4 #6#) (|isDomain| *1 (|ElementaryIntegration| *4 *2)) (|ofCategory| *2 (|Join| #4# #5# (|FunctionSpace| *4))))) (|lflimitedint| (*1 *2 *3 *4 *5) (|partial| AND #1# (|isDomain| *5 (|List| *3)) (|ofCategory| *3 (|Join| #4# #5# (|FunctionSpace| *6))) (|ofCategory| *6 #6#) (|isDomain| *2 (|Record| (|:| |mainpart| *3) (|:| |limitedlogs| (|List| (|Record| #9# (|:| |logand| *3)))))) (|isDomain| *1 (|ElementaryIntegration| *6 *3)))) (|lfextendedint| (*1 *2 *3 *4 *3) (|partial| AND #1# #10# #8# #11# #12#))) @@ -1696,7 +1696,7 @@ NIL ((|inverseLaplace| (((|Union| |#2| "failed") |#2| #1=(|Symbol|) #1#) 10 T ELT))) (((|InverseLaplaceTransform| |#1| |#2|) (CATEGORY |package| (SIGNATURE |inverseLaplace| ((|Union| |#2| "failed") |#2| #1=(|Symbol|) #1#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|SpecialFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |InverseLaplaceTransform|)) ((|inverseLaplace| (*1 *2 *2 *3 *3) (|partial| AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#))) (|isDomain| *1 (|InverseLaplaceTransform| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|SpecialFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) -((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) 27 T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) 26 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 28 T ELT)) (|writeByte!| (((|Maybe| #3=(|Byte|)) $ #3#) 25 T ELT)) (|readUInt8!| (((|Maybe| (|UInt8|)) $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|readByte!| (((|Maybe| (|Byte|)) $) 14 T ELT)) (|close!| (($ $) 6 T ELT))) +((|writeUInt8!| ((#1=(|Maybe| #2=(|UInt8|)) $ #2#) 27 T ELT)) (|writeInt8!| ((#3=(|Maybe| #4=(|Int8|)) $ #4#) 26 T ELT)) (|writeBytes!| (#5=((|NonNegativeInteger|) $ (|ByteBuffer|)) 28 T ELT)) (|writeByte!| ((#6=(|Maybe| #7=(|Byte|)) $ #7#) 25 T ELT)) (|readUInt8!| ((#1# $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| ((#3# $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (#5# 7 T ELT)) (|readByte!| ((#6# $) 14 T ELT)) (|close!| (($ $) 6 T ELT))) (((|InputOutputByteConduit|) (|Category|)) (T |InputOutputByteConduit|)) NIL (|Join| (|InputByteConduit|) (|OutputByteConduit|)) @@ -1776,11 +1776,11 @@ NIL ((|swap!| (((|Void|) $ |#2| |#2|) 34 T ELT)) (|minIndex| (#1=(|#2| $) 23 T ELT)) (|maxIndex| (#1# 21 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) 30 T ELT)) (|first| ((|#3| $) 26 T ELT)) (|fill!| (($ $ |#3|) 32 T ELT)) (|entry?| (((|Boolean|) |#3| $) 17 T ELT)) (|entries| (((|List| |#3|) $) 15 T ELT)) (|elt| ((|#3| $ |#2| |#3|) 12 T ELT) ((|#3| $ |#2|) NIL T ELT))) (((|IndexedAggregate&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |swap!| ((|Void|) |#1| |#2| |#2|)) (SIGNATURE |fill!| (|#1| |#1| |#3|)) (SIGNATURE |first| (|#3| |#1|)) (SIGNATURE |minIndex| #1=(|#2| |#1|)) (SIGNATURE |maxIndex| #1#) (SIGNATURE |entry?| ((|Boolean|) |#3| |#1|)) (SIGNATURE |entries| ((|List| |#3|) |#1|)) (SIGNATURE |elt| (|#3| |#1| |#2|)) (SIGNATURE |elt| (|#3| |#1| |#2| |#3|)) (SIGNATURE |map| (|#1| (|Mapping| |#3| |#3|) |#1|))) (|IndexedAggregate| |#2| |#3|) (|BasicType|) (|Type|)) (T |IndexedAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#2| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ |#1| |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| ((|#2| $ |#1| |#2|) 47 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sample| (#3=($) 6 T CONST)) (|qsetelt!| ((|#2| $ |#1| |#2|) 48 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ |#1|) 46 T ELT)) (|minIndex| ((|#1| $) 38 (|has| |#1| (|OrderedSet|)) ELT)) (|maxIndex| ((|#1| $) 39 (|has| |#1| (|OrderedSet|)) ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#2| . #4=((|SetCategory|))) ELT)) (|indices| (((|List| |#1|) $) 41 T ELT)) (|index?| (((|Boolean|) |#1| $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#2| . #4#) ELT)) (|first| ((|#2| $) 37 (|has| |#1| (|OrderedSet|)) ELT)) (|fill!| (($ $ |#2|) 36 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|eval| (($ $ (|List| (|Equation| |#2|))) 25 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT) (($ $ (|Equation| |#2|)) 24 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT) (($ $ |#2| |#2|) 23 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 22 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|entry?| (((|Boolean|) |#2| $) 40 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| (|BasicType|))) ELT)) (|entries| (((|List| |#2|) $) 43 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|elt| ((|#2| $ |#1| |#2|) 45 T ELT) ((|#2| $ |#1|) 44 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#2| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#2| . #2#) ELT)) (= (#1# 17 (|has| |#2| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#2| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ |#1| |#1|) 35 #4=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| (#5=(|#2| $ |#1| |#2|) 47 #4# ELT)) (|sample| (#6=($) 6 T CONST)) (|qsetelt!| (#5# 48 #4# ELT)) (|qelt| (#7=(|#2| $ |#1|) 46 T ELT)) (|minIndex| (#8=(|#1| $) 38 #9=(|has| |#1| (|OrderedSet|)) ELT)) (|maxIndex| (#8# 39 #9# ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 26 T ELT)) (|latex| (((|String|) $) 21 #10=(|has| |#2| (|SetCategory|)) ELT)) (|indices| (((|List| |#1|) $) 41 T ELT)) (|index?| ((#2# |#1| $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 #10# ELT)) (|first| ((|#2| $) 37 #9# ELT)) (|fill!| (($ $ |#2|) 36 #4# ELT)) (|eval| (($ $ (|List| #11=(|Equation| |#2|))) 25 #12=(AND (|has| |#2| (|Evalable| |#2|)) #10#) ELT) (($ $ #11#) 24 #12# ELT) (($ $ |#2| |#2|) 23 #12# ELT) (($ $ #13=(|List| |#2|) #13#) 22 #12# ELT)) (|eq?| (#1# 10 T ELT)) (|entry?| ((#2# |#2| $) 40 (AND (|has| $ (|FiniteAggregate| |#2|)) #3#) ELT)) (|entries| ((#13# $) 43 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#6# 8 T ELT)) (|elt| (#5# 45 T ELT) (#7# 44 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| ((#14=(|OutputForm|) $) 16 (|has| |#2| (|CoercibleTo| #14#)) ELT)) (|before?| (#1# 19 #3# ELT)) (= (#1# 17 #3# ELT))) (((|IndexedAggregate| |#1| |#2|) (|Category|) (|BasicType|) (|Type|)) (T |IndexedAggregate|)) -((|entries| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|List| *4)))) (|index?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|indices| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|List| *3)))) (|entry?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *1 (|IndexedAggregate| *4 *3)) (|ofCategory| *4 (|BasicType|)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Boolean|)))) (|maxIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *2 (|OrderedSet|)))) (|minIndex| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|BasicType|)) (|ofCategory| *2 (|OrderedSet|)))) (|first| (*1 *2 *1) (AND (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|Type|)))) (|fill!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|IndexedAggregate| *3 *2)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *2 (|Type|)))) (|swap!| (*1 *2 *1 *3 *3) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *4)) (|ofCategory| *1 (|IndexedAggregate| *3 *4)) (|ofCategory| *3 (|BasicType|)) (|ofCategory| *4 (|Type|)) (|isDomain| *2 (|Void|))))) -(|Join| (|HomogeneousAggregate| |t#2|) (|EltableAggregate| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |entries| ((|List| |t#2|) $)) (SIGNATURE |index?| ((|Boolean|) |t#1| $)) (SIGNATURE |indices| ((|List| |t#1|) $)) (IF (|has| |t#2| (|BasicType|)) (IF (|has| $ (|FiniteAggregate| |t#2|)) (SIGNATURE |entry?| ((|Boolean|) |t#2| $)) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (PROGN (SIGNATURE |maxIndex| (|t#1| $)) (SIGNATURE |minIndex| (|t#1| $)) (SIGNATURE |first| (|t#2| $))) |%noBranch|) (IF (|has| $ (|ShallowlyMutableAggregate| |t#2|)) (PROGN (SIGNATURE |fill!| ($ $ |t#2|)) (SIGNATURE |swap!| ((|Void|) $ |t#1| |t#1|))) |%noBranch|))) -(((|Aggregate|) . T) ((|BasicType|) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#2| (|SetCategory|)) (|has| |#2| (|CoercibleTo| (|OutputForm|)))) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#2| (|SetCategory|)) ((|Type|) . T)) +((|entries| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|IndexedAggregate| *3 *4)) #3=(|ofCategory| *3 #4=(|BasicType|)) #5=(|ofCategory| *4 #6=(|Type|)) (|isDomain| *2 (|List| *4)))) (|index?| #7=(*1 *2 *3 *1) (AND #2# #3# #5# #8=(|isDomain| *2 (|Boolean|)))) (|indices| #1# (AND #2# #3# #5# (|isDomain| *2 (|List| *3)))) (|entry?| #7# (AND (|ofCategory| *1 (|FiniteAggregate| *3)) #3# (|ofCategory| *1 (|IndexedAggregate| *4 *3)) (|ofCategory| *4 #4#) #9=(|ofCategory| *3 #6#) #8#)) (|maxIndex| #1# #10=(AND (|ofCategory| *1 (|IndexedAggregate| *2 *3)) #9# (|ofCategory| *2 #4#) (|ofCategory| *2 #11=(|OrderedSet|)))) (|minIndex| #1# #10#) (|first| #1# (AND #12=(|ofCategory| *1 (|IndexedAggregate| *3 *2)) #3# (|ofCategory| *3 #11#) #13=(|ofCategory| *2 #6#))) (|fill!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) #12# #3# #13#)) (|swap!| (*1 *2 *1 *3 *3) (AND (|ofCategory| *1 (|ShallowlyMutableAggregate| *4)) #2# #3# #5# (|isDomain| *2 (|Void|))))) +(|Join| (|HomogeneousAggregate| |t#2|) (|EltableAggregate| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |entries| ((|List| |t#2|) $)) (SIGNATURE |index?| (#1=(|Boolean|) |t#1| $)) (SIGNATURE |indices| ((|List| |t#1|) $)) (IF (|has| |t#2| (|BasicType|)) (IF (|has| $ (|FiniteAggregate| |t#2|)) (SIGNATURE |entry?| (#1# |t#2| $)) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (PROGN (SIGNATURE |maxIndex| #2=(|t#1| $)) (SIGNATURE |minIndex| #2#) (SIGNATURE |first| (|t#2| $))) |%noBranch|) (IF (|has| $ (|ShallowlyMutableAggregate| |t#2|)) (PROGN (SIGNATURE |fill!| ($ $ |t#2|)) (SIGNATURE |swap!| ((|Void|) $ |t#1| |t#1|))) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#2| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#2| (|CoercibleTo| (|OutputForm|))) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|SetCategory|) |has| |#2| (|SetCategory|)) ((|Type|) . T)) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #2=($)) NIL T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# . #2#) NIL T ELT) ((#4=(|TypeAst|) $) 15 T ELT) (($ #5=(|List| #4#)) 14 T ELT)) (|categories| ((#5# $) 12 T ELT)) (|before?| #1#) (= #1#)) (((|JoinAst|) (|Join| (|SpadSyntaxCategory|) (|CoercibleTo| #1=(|TypeAst|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ #2=(|List| #1#))) (SIGNATURE |categories| (#2# $))))) (T |JoinAst|)) ((|coerce| (*1 *1 *2) #1=(AND (|isDomain| *2 (|List| (|TypeAst|))) (|isDomain| *1 (|JoinAst|)))) (|categories| (*1 *2 *1) #1#)) @@ -1811,11 +1811,11 @@ NIL ((|keys| (((|List| |#2|) $) 19 T ELT)) (|key?| (((|Boolean|) |#2| $) 12 T ELT)) (|elt| ((|#3| $ |#2|) 20 T ELT) ((|#3| $ |#2| |#3|) 21 T ELT))) (((|KeyedDictionary&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |keys| ((|List| |#2|) |#1|)) (SIGNATURE |key?| ((|Boolean|) |#2| |#1|)) (SIGNATURE |elt| (|#3| |#1| |#2| |#3|)) (SIGNATURE |elt| (|#3| |#1| |#2|))) (|KeyedDictionary| |#2| |#3|) #1=(|SetCategory|) #1#) (T |KeyedDictionary&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (OR (|has| |#2| . #2=((|BasicType|))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|swap!| (((|Void|) $ |#1| |#1|) 82 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| ((|#2| $ |#1| |#2|) 70 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|select!| (($ (|Mapping| #3=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #4=($)) 42 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #6=($)) 49 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|search| (((|Union| |#2| "failed") |#1| $) 59 T ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates| (($ $) 51 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . 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T) ((|BagAggregate| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| #1#) . T) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #1#) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Functorial| #1#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #1#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| #1# #1#) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| #1#) . T) ((|ShallowlyMutableAggregate| |#2|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|symbolIfCan| (((|Union| #4=(|Symbol|) "failed") $) 46 T ELT)) (|setPosition| (((|Void|) $ #5=(|NonNegativeInteger|)) 22 T ELT)) (|position| (#6=(#5# $) 20 T ELT)) (|operator| ((#7=(|BasicOperator|) $) 9 T ELT)) (|min| #8=(($ $ $) NIL T ELT)) (|max| #8#) (|latex| (((|String|) $) NIL T ELT)) (|kernel| (($ #7# #9=(|List| |#1|) #5#) 32 T ELT) (($ #4#) 33 T ELT)) (|is?| ((#3# $ #7#) 15 T ELT) ((#3# $ #4#) 13 T ELT)) (|height| (#6# 17 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| ((#10=(|Pattern| (|Integer|)) $) 99 (|has| |#1| (|ConvertibleTo| #10#)) ELT) ((#11=(|Pattern| (|Float|)) $) 106 (|has| |#1| (|ConvertibleTo| #11#)) ELT) ((#12=(|InputForm|) $) 92 (|has| |#1| (|ConvertibleTo| #12#)) ELT)) (|coerce| (((|OutputForm|) $) 74 T ELT)) (|before?| #1#) (|argument| ((#9# $) 19 T ELT)) (>= #1#) (> #1#) (= (#2# 51 T ELT)) (<= #1#) (< (#2# 53 T ELT))) (((|Kernel| |#1|) (|Join| (|CachableSet|) (|OrderedSet|) (|Patternable| |#1|) (CATEGORY |domain| (SIGNATURE |operator| (#1=(|BasicOperator|) $)) (SIGNATURE |argument| (#2=(|List| |#1|) $)) (SIGNATURE |height| (#3=(|NonNegativeInteger|) $)) (SIGNATURE |kernel| ($ #1# #2# #3#)) (SIGNATURE |kernel| ($ #4=(|Symbol|))) (SIGNATURE |symbolIfCan| ((|Union| #4# "failed") $)) (SIGNATURE |is?| (#5=(|Boolean|) $ #1#)) (SIGNATURE |is?| (#5# $ #4#)) (IF (|has| |#1| #6=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #6#) |%noBranch|))) (|SetCategory|)) (T |Kernel|)) ((|operator| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 #3=(|BasicOperator|)) #4=(|isDomain| *1 (|Kernel| *3)) #5=(|ofCategory| *3 #6=(|SetCategory|)))) (|argument| #1# (AND (|isDomain| *2 (|List| *3)) #4# #5#)) (|height| #1# (AND (|isDomain| *2 #7=(|NonNegativeInteger|)) #4# #5#)) (|kernel| (*1 *1 *2 *3 *4) (AND #2# (|isDomain| *3 (|List| *5)) (|isDomain| *4 #7#) (|ofCategory| *5 #6#) (|isDomain| *1 (|Kernel| *5)))) (|kernel| (*1 *1 *2) (AND #8=(|isDomain| *2 #9=(|Symbol|)) #4# #5#)) (|symbolIfCan| #1# (|partial| AND #8# #4# #5#)) (|is?| #10=(*1 *2 *1 *3) (AND (|isDomain| *3 #3#) #11=(|isDomain| *2 (|Boolean|)) #12=(|isDomain| *1 (|Kernel| *4)) #13=(|ofCategory| *4 #6#))) (|is?| #10# (AND (|isDomain| *3 #9#) #11# #12# #13#))) @@ -1850,11 +1850,11 @@ NIL ((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT))) (((|LeftAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|LeftAlgebra| |#2|) (|Ring|)) (T |LeftAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 50 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ |#1| . #4#) 51 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #5=(|Integer|)) 42 T ELT) (($ |#1|) 50 T ELT)) (|characteristic| ((#6=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#7=($ $ $) 29 T ELT)) (+ (#7# 18 T ELT)) (** (($ $ #8=(|PositiveInteger|)) 36 T ELT) (($ $ #6#) 44 T ELT)) (* (($ #8# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #5# . #9=($)) 31 T ELT) (#7# 35 T ELT) (($ |#1| . #9#) 51 T ELT))) (((|LeftAlgebra| |#1|) (|Category|) (|Ring|)) (T |LeftAlgebra|)) ((|coerce| (*1 *1 *2) (AND (|ofCategory| *1 (|LeftAlgebra| *2)) (|ofCategory| *2 (|Ring|))))) (|Join| (|Ring|) (|LeftModule| |t#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |t#1|)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|laplace| ((|#2| |#2| #1=(|Symbol|) #1#) 16 T ELT))) (((|LaplaceTransform| |#1| |#2|) (CATEGORY |package| (SIGNATURE |laplace| (|#2| |#2| #1=(|Symbol|) #1#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| |#1|))) (T |LaplaceTransform|)) ((|laplace| (*1 *2 *2 *3 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *4 (|Join| (|EuclideanDomain|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#))) (|isDomain| *1 (|LaplaceTransform| *4 *2)) (|ofCategory| *2 (|Join| (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|) (|AlgebraicallyClosedFunctionSpace| *4)))))) @@ -1879,10 +1879,10 @@ NIL ((|operator| ((#1=(|BasicOperator|) #1#) 88 T ELT)) (|li| (#2=(|#2| |#2|) 28 T ELT)) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) 84 T ELT) ((|#2| |#2| (|Symbol|)) 50 T ELT)) (|erf| (#2# 27 T ELT)) (|dilog| (#2# 29 T ELT)) (|belong?| (((|Boolean|) #1#) 33 T ELT)) (|Si| (#2# 24 T ELT)) (|Ei| (#2# 26 T ELT)) (|Ci| (#2# 25 T ELT))) (((|LiouvillianFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |belong?| ((|Boolean|) #1=(|BasicOperator|))) (SIGNATURE |operator| (#1# #1#)) (SIGNATURE |Ei| #2=(|#2| |#2|)) (SIGNATURE |Si| #2#) (SIGNATURE |Ci| #2#) (SIGNATURE |li| #2#) (SIGNATURE |erf| #2#) (SIGNATURE |dilog| #2#) (SIGNATURE |integral| (|#2| |#2| (|Symbol|))) (SIGNATURE |integral| (|#2| |#2| (|SegmentBinding| |#2|)))) (|IntegralDomain|) (|Join| (|FunctionSpace| |#1|) (|RadicalCategory|) (|TranscendentalFunctionCategory|))) (T |LiouvillianFunction|)) ((|integral| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|SegmentBinding| *2)) #2=(|ofCategory| *2 #3=(|Join| (|FunctionSpace| *4) #4=(|RadicalCategory|) #5=(|TranscendentalFunctionCategory|))) #6=(|ofCategory| *4 #7=(|IntegralDomain|)) #8=(|isDomain| *1 (|LiouvillianFunction| *4 *2)))) (|integral| #1# (AND (|isDomain| *3 (|Symbol|)) #6# #8# #2#)) (|dilog| #9=(*1 *2 *2) #10=(AND #11=(|ofCategory| *3 #7#) (|isDomain| *1 (|LiouvillianFunction| *3 *2)) (|ofCategory| *2 #12=(|Join| (|FunctionSpace| *3) #4# #5#)))) (|erf| #9# #10#) (|li| #9# #10#) (|Ci| #9# #10#) (|Si| #9# #10#) (|Ei| #9# #10#) (|operator| #9# (AND (|isDomain| *2 #13=(|BasicOperator|)) #11# (|isDomain| *1 (|LiouvillianFunction| *3 *4)) (|ofCategory| *4 #12#))) (|belong?| (*1 *2 *3) (AND (|isDomain| *3 #13#) #6# (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|LiouvillianFunction| *4 *5)) (|ofCategory| *5 #3#)))) -((|tanh| (#1=($ $) 38 T ELT)) (|tan| (#2=($ $) 21 T ELT)) (|sinh| (#1# 37 T ELT)) (|sin| (#2# 22 T ELT)) (|sech| (#1# 36 T ELT)) (|sec| (#2# 23 T ELT)) (|pi| (($) 48 T ELT)) (|log| (#3=($ $) 45 T ELT)) (|li| (($ $) 17 T ELT)) (|integral| (($ $ (|SegmentBinding| $)) 7 T ELT) (($ $ (|Symbol|)) 6 T ELT)) (|exp| (#3# 46 T ELT)) (|erf| (($ $) 15 T ELT)) (|dilog| (($ $) 16 T ELT)) (|csch| (#1# 35 T ELT)) (|csc| (#2# 24 T ELT)) (|coth| (#1# 34 T ELT)) (|cot| (#2# 25 T ELT)) (|cosh| (#1# 33 T ELT)) (|cos| (#2# 26 T ELT)) (|atanh| (#4=($ $) 44 T ELT)) (|atan| (#5=($ $) 32 T ELT)) (|asinh| (#4# 43 T ELT)) (|asin| (#5# 31 T ELT)) (|asech| (#4# 42 T ELT)) (|asec| (#5# 30 T ELT)) (|acsch| (#4# 41 T ELT)) (|acsc| (#5# 29 T ELT)) (|acoth| (#4# 40 T ELT)) (|acot| (#5# 28 T ELT)) (|acosh| (#4# 39 T ELT)) (|acos| (#5# 27 T ELT)) (|Si| (($ $) 19 T ELT)) (|Ei| (($ $) 20 T ELT)) (|Ci| (($ $) 18 T ELT)) (** (($ $ $) 47 T ELT))) +((|tanh| (#1=($ $) 38 T ELT)) (|tan| (#1# 21 T ELT)) (|sinh| (#1# 37 T ELT)) (|sin| (#1# 22 T ELT)) (|sech| (#1# 36 T ELT)) (|sec| (#1# 23 T ELT)) (|pi| (($) 48 T ELT)) (|log| (#1# 45 T ELT)) (|li| (#1# 17 T ELT)) (|integral| (($ $ (|SegmentBinding| $)) 7 T ELT) (($ $ (|Symbol|)) 6 T ELT)) (|exp| (#1# 46 T ELT)) (|erf| (#1# 15 T ELT)) (|dilog| (#1# 16 T ELT)) (|csch| (#1# 35 T ELT)) (|csc| (#1# 24 T ELT)) (|coth| (#1# 34 T ELT)) (|cot| (#1# 25 T ELT)) (|cosh| (#1# 33 T ELT)) (|cos| (#1# 26 T ELT)) (|atanh| (#1# 44 T ELT)) (|atan| (#1# 32 T ELT)) (|asinh| (#1# 43 T ELT)) (|asin| (#1# 31 T ELT)) (|asech| (#1# 42 T ELT)) (|asec| (#1# 30 T ELT)) (|acsch| (#1# 41 T ELT)) (|acsc| (#1# 29 T ELT)) (|acoth| (#1# 40 T ELT)) (|acot| (#1# 28 T ELT)) (|acosh| (#1# 39 T ELT)) (|acos| (#1# 27 T ELT)) (|Si| (#1# 19 T ELT)) (|Ei| (#1# 20 T ELT)) (|Ci| (#1# 18 T ELT)) (** (($ $ $) 47 T ELT))) (((|LiouvillianFunctionCategory|) (|Category|)) (T |LiouvillianFunctionCategory|)) -((|Ei| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Si| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Ci| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|li| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|dilog| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|erf| (*1 *1 *1) (|ofCategory| *1 (|LiouvillianFunctionCategory|)))) -(|Join| (|PrimitiveFunctionCategory|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |Ei| ($ $)) (SIGNATURE |Si| ($ $)) (SIGNATURE |Ci| ($ $)) (SIGNATURE |li| ($ $)) (SIGNATURE |dilog| ($ $)) (SIGNATURE |erf| ($ $)))) +((|Ei| #1=(*1 *1 *1) #2=(|ofCategory| *1 (|LiouvillianFunctionCategory|))) (|Si| #1# #2#) (|Ci| #1# #2#) (|li| #1# #2#) (|dilog| #1# #2#) (|erf| #1# #2#)) +(|Join| (|PrimitiveFunctionCategory|) (|TranscendentalFunctionCategory|) (CATEGORY |domain| (SIGNATURE |Ei| #1=($ $)) (SIGNATURE |Si| #1#) (SIGNATURE |Ci| #1#) (SIGNATURE |li| #1#) (SIGNATURE |dilog| #1#) (SIGNATURE |erf| #1#))) (((|ArcHyperbolicFunctionCategory|) . T) ((|ArcTrigonometricFunctionCategory|) . T) ((|ElementaryFunctionCategory|) . T) ((|HyperbolicFunctionCategory|) . T) ((|PrimitiveFunctionCategory|) . T) ((|TranscendentalFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . T)) ((|transform| ((#1=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) #2=(|DistributedMultivariatePolynomial| |#1| |#2|)) 65 T ELT)) (|totolex| ((#3=(|List| #2#) #4=(|List| #1#)) 90 T ELT)) (|minPol| ((#1# #4# #5=(|OrderedVariableList| |#1|)) 92 T ELT) ((#1# #4# #4# #5#) 91 T ELT)) (|linGenPos| (((|Record| (|:| |gblist| #3#) (|:| |gvlist| #6=(|List| (|Integer|)))) #4#) 135 T ELT)) (|intcompBasis| ((#4# #5# #4# #4#) 105 T ELT)) (|groebgen| (((|Record| (|:| |glbase| #3#) (|:| |glval| #6#)) #3#) 146 T ELT)) (|coord| (((|Vector| |#2|) #1# #4#) 70 T ELT)) (|computeBasis| ((#4# #4#) 47 T ELT)) (|choosemon| ((#2# #2# #3#) 61 T ELT)) (|anticoord| ((#2# (|List| |#2|) #2# #3#) 113 T ELT))) (((|LinGroebnerPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |linGenPos| ((|Record| (|:| |gblist| #1=(|List| #2=(|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| #3=(|List| (|Integer|)))) #4=(|List| #5=(|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)))) (SIGNATURE |groebgen| ((|Record| (|:| |glbase| #1#) (|:| |glval| #3#)) #1#)) (SIGNATURE |totolex| (#1# #4#)) (SIGNATURE |minPol| (#5# #4# #4# #6=(|OrderedVariableList| |#1|))) (SIGNATURE |minPol| (#5# #4# #6#)) (SIGNATURE |computeBasis| (#4# #4#)) (SIGNATURE |coord| ((|Vector| |#2|) #5# #4#)) (SIGNATURE |anticoord| (#2# (|List| |#2|) #2# #1#)) (SIGNATURE |intcompBasis| (#4# #6# #4# #4#)) (SIGNATURE |choosemon| (#2# #2# #1#)) (SIGNATURE |transform| (#5# #2#))) (|List| (|Symbol|)) (|GcdDomain|)) (T |LinGroebnerPackage|)) @@ -1896,11 +1896,11 @@ NIL ((/ (($ $ |#2|) 10 T ELT))) (((|LieAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE / (|#1| |#1| |#2|))) (|LieAlgebra| |#2|) (|CommutativeRing|)) (T |LieAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|construct| (($ $ $) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 40 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#1|) 38 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|construct| (#4=($ $ $) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (#5=($ $ |#1|) 40 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (#4# 29 T ELT)) (+ (#4# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 31 T ELT) (($ |#1| . #6#) 34 T ELT) (#5# 38 T ELT))) (((|LieAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |LieAlgebra|)) -((|construct| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LieAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|LieAlgebra| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|Field|))))) +((|construct| (*1 *1 *1 *1) (AND #1=(|ofCategory| *1 (|LieAlgebra| *2)) #2=(|ofCategory| *2 (|CommutativeRing|)))) (/ (*1 *1 *1 *2) (AND #1# #2# (|ofCategory| *2 (|Field|))))) (|Join| (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ $ $)) (IF (|has| |t#1| (|Field|)) (SIGNATURE / ($ $ |t#1|)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|limit| ((#1=(|Union| #2=(|OrderedCompletion| |#2|) #3="failed") |#2| (|Equation| |#2|) (|String|)) 105 T ELT) (((|Union| #2# (|Record| (|:| |leftHandLimit| #1#) (|:| |rightHandLimit| #1#)) #3#) |#2| (|Equation| #2#)) 130 T ELT)) (|complexLimit| (((|Union| #4=(|OnePointCompletion| |#2|) #3#) |#2| (|Equation| #4#)) 135 T ELT))) (((|PowerSeriesLimitPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |limit| ((|Union| #1=(|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| #2=(|Union| #1# #3="failed")) (|:| |rightHandLimit| #2#)) #3#) |#2| (|Equation| #1#))) (SIGNATURE |complexLimit| ((|Union| #4=(|OnePointCompletion| |#2|) #3#) |#2| (|Equation| #4#))) (SIGNATURE |limit| (#2# |#2| (|Equation| |#2|) (|String|)))) (|Join| (|GcdDomain|) (|RetractableTo| #5=(|Integer|)) (|LinearlyExplicitRingOver| #5#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |PowerSeriesLimitPackage|)) ((|limit| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Equation| *3)) (|isDomain| *5 (|String|)) (|ofCategory| *3 (|Join| #1=(|AlgebraicallyClosedField|) #2=(|TranscendentalFunctionCategory|) (|FunctionSpace| *6))) (|ofCategory| *6 #3=(|Join| (|GcdDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#))) (|isDomain| *2 #5=(|OrderedCompletion| *3)) (|isDomain| *1 (|PowerSeriesLimitPackage| *6 *3)))) (|complexLimit| #6=(*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Equation| #7=(|OnePointCompletion| *3))) #8=(|ofCategory| *5 #3#) (|isDomain| *2 #7#) #9=(|isDomain| *1 (|PowerSeriesLimitPackage| *5 *3)) #10=(|ofCategory| *3 (|Join| #1# #2# (|FunctionSpace| *5))))) (|limit| #6# (AND (|isDomain| *4 (|Equation| #5#)) #10# #8# (|isDomain| *2 (|Union| #5# (|Record| (|:| |leftHandLimit| #11=(|Union| #5# #12="failed")) (|:| |rightHandLimit| #11#)) #12#)) #9#))) @@ -1916,11 +1916,11 @@ NIL ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| #4=(|LinearBasis| |#2|))) $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|reductum| #6=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| #4#) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|linearElement| (($ (|List| |#1|)) 25 T ELT)) (|leadingSupport| ((#4# $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 16 T ELT)) (|coordinates| (((|Vector| |#1|) $) 44 T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4#) 11 T ELT)) (|before?| #1#) (|Zero| (#5# 20 T CONST)) (= #1#) (/ #7=(($ $ |#1|) NIL T ELT)) (- #6# (#8=($ $ $) NIL T ELT)) (+ (#8# 17 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #9=($)) NIL T ELT) (($ |#1| . #9#) NIL T ELT) #7#)) (((|LinearElement| |#1| |#2|) (|Join| (|VectorSpace| |#1|) (|CoercibleFrom| #1=(|LinearBasis| |#2|)) (|IndexedDirectProductCategory| |#1| #1#) (CATEGORY |domain| (SIGNATURE |linearElement| ($ (|List| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#1|) $)))) (|Field|) (|List| (|Symbol|))) (T |LinearElement|)) ((|linearElement| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Field|)) #2=(|isDomain| *1 (|LinearElement| *3 *4)) #3=(|ofType| *4 (|List| (|Symbol|))))) (|coordinates| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| *3)) #2# #1# #3#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| (((|Matrix| |#1|) (|Matrix| $)) 37 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) 36 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) (|Vector| $)) 39 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| ((#4=(|Matrix| |#1|) #5=(|Matrix| $)) 37 T ELT) ((#6=(|Record| (|:| |mat| #4#) (|:| |vec| (|Vector| |#1|))) #5# #7=(|Vector| $)) 36 T ELT)) (|opposite?| (#1# 20 T ELT)) (|leftReducedSystem| ((#4# #7#) 39 T ELT) ((#6# #7# $) 38 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#8=($ $ $) 29 T ELT)) (+ (#8# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #9=($)) 31 T ELT) (($ |#1| . #9#) 34 T ELT))) (((|LinearlyExplicitRingOver| |#1|) (|Category|) (|Ring|)) (T |LinearlyExplicitRingOver|)) -((|leftReducedSystem| (*1 *2 *3) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4)))) (|leftReducedSystem| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *4)) (|:| |vec| (|Vector| *4)))))) (|reducedSystem| (*1 *2 *3) (AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Matrix| *4)))) (|reducedSystem| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Matrix| *1)) (|isDomain| *4 (|Vector| *1)) (|ofCategory| *1 (|LinearlyExplicitRingOver| *5)) (|ofCategory| *5 (|Ring|)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *5)) (|:| |vec| (|Vector| *5))))))) -(|Join| (|LeftModule| |t#1|) (CATEGORY |domain| (SIGNATURE |leftReducedSystem| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |leftReducedSystem| ((|Record| (|:| |mat| (|Matrix| |t#1|)) (|:| |vec| (|Vector| |t#1|))) (|Vector| $) $)) (SIGNATURE |reducedSystem| ((|Matrix| |t#1|) (|Matrix| $))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| (|Matrix| |t#1|)) (|:| |vec| (|Vector| |t#1|))) (|Matrix| $) (|Vector| $))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|leftReducedSystem| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Vector| *1)) #4=(|ofCategory| *1 (|LinearlyExplicitRingOver| *4)) #5=(|ofCategory| *4 #6=(|Ring|)) #7=(|isDomain| *2 #8=(|Matrix| *4)))) (|leftReducedSystem| (*1 *2 *3 *1) (AND #2# #4# #5# (|isDomain| *2 (|Record| (|:| |mat| #8#) (|:| |vec| (|Vector| *4)))))) (|reducedSystem| #1# (AND #9=(|isDomain| *3 (|Matrix| *1)) #4# #5# #7#)) (|reducedSystem| (*1 *2 *3 *4) (AND #9# (|isDomain| *4 #3#) (|ofCategory| *1 (|LinearlyExplicitRingOver| *5)) (|ofCategory| *5 #6#) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *5)) (|:| |vec| (|Vector| *5))))))) +(|Join| (|LeftModule| |t#1|) (CATEGORY |domain| (SIGNATURE |leftReducedSystem| (#1=(|Matrix| |t#1|) #2=(|Vector| $))) (SIGNATURE |leftReducedSystem| (#3=(|Record| (|:| |mat| #1#) (|:| |vec| (|Vector| |t#1|))) #2# $)) (SIGNATURE |reducedSystem| (#1# #4=(|Matrix| $))) (SIGNATURE |reducedSystem| (#3# #4# #2#)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|opposite?| #1#) (|linearForm| (($ (|List| |#1|)) 23 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ (|LinearElement| |#1| |#2|)) 46 T ELT)) (|dimension| (((|CardinalNumber|)) 13 T ELT)) (|coordinates| (((|Vector| |#1|) $) 42 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| (#3# 18 T CONST)) (= #1#) (/ #4=(($ $ |#1|) NIL T ELT)) (- (($ $) NIL T ELT) (#5=($ $ $) NIL T ELT)) (+ (#5# 14 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #6=($)) NIL T ELT) (($ |#1| . #6#) NIL T ELT) #4#)) (((|LinearForm| |#1| |#2|) (|Join| (|VectorSpace| |#1|) (|Eltable| (|LinearElement| |#1| |#2|) |#1|) (CATEGORY |domain| (SIGNATURE |linearForm| ($ (|List| |#1|))) (SIGNATURE |coordinates| ((|Vector| |#1|) $)))) (|Field|) (|List| (|Symbol|))) (T |LinearForm|)) ((|linearForm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) #1=(|ofCategory| *3 (|Field|)) #2=(|isDomain| *1 (|LinearForm| *3 *4)) #3=(|ofType| *4 (|List| (|Symbol|))))) (|coordinates| (*1 *2 *1) (AND (|isDomain| *2 (|Vector| *3)) #2# #1# #3#))) @@ -1928,7 +1928,7 @@ NIL (((|LinearSet| |#1|) (|Category|) (|SemiGroup|)) (T |LinearSet|)) NIL (|Join| (|LeftLinearSet| |t#1|) (|RightLinearSet| |t#1|)) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| #5=(#6=(|#1| $) NIL T ELT)) (|third| #5#) (|tail| #7=(#8=($ $) NIL T ELT)) (|swap!| (((|Void|) $ #9=(|Integer|) #9#) NIL #10=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (#11=($ $ #9#) 68 #10# ELT)) (|sorted?| (#12=(#3# $) NIL #13=(|has| |#1| #14=(|OrderedSet|)) ELT) ((#3# #15=(|Mapping| #3# |#1| |#1|) $) NIL T ELT)) (|sort!| (#8# NIL (AND #10# #13#) ELT) (#16=($ #15# $) 65 #10# ELT)) (|sort| (#8# NIL #13# ELT) (#16# NIL T ELT)) (|size?| #17=((#3# $ #18=(|NonNegativeInteger|)) NIL T ELT)) (|setvalue!| #19=(#20=(|#1| $ |#1|) NIL #10# ELT)) (|setrest!| (#21=($ $ $) 26 #10# ELT)) (|setlast!| #19#) (|setfirst!| (#20# 24 #10# ELT)) (|setelt| ((|#1| $ #22="value" |#1|) NIL #10# ELT) ((|#1| $ #23="first" |#1|) 25 #10# ELT) (($ $ #24="rest" $) 27 #10# ELT) ((|#1| $ #25="last" |#1|) NIL #10# ELT) ((|#1| $ #26=(|UniversalSegment| #9#) |#1|) NIL #10# ELT) #27=(#28=(|#1| $ #9# |#1|) NIL #10# ELT)) (|setchildren!| (($ $ #29=(|List| $)) NIL #10# ELT)) (|setUnion| (#21# 74 #30=(|has| |#1| (|SetCategory|)) ELT)) (|setIntersection| (#21# 75 #30# ELT)) (|setDifference| (#21# 79 #30# ELT)) (|select!| #31=(#32=($ #33=(|Mapping| #3# |#1|) $) NIL T ELT)) (|select| #34=(#32# NIL #35=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|second| #5#) (|sample| (#36=($) NIL T CONST)) (|reverse!| (#8# 31 #10# ELT)) (|reverse| (#8# 32 T ELT)) (|rest| (#8# 21 T ELT) (#37=($ $ #18#) 35 T ELT)) (|removeDuplicates!| (#8# 63 #4# ELT)) (|removeDuplicates| (#8# 73 #38=(AND #35# #4#) ELT)) (|remove!| (#39=($ |#1| $) NIL #4# ELT) #31#) (|remove| #34# (#39# NIL #38# ELT)) (|reduce| ((|#1| #40=(|Mapping| |#1| |#1| |#1|) $) NIL T ELT) ((|#1| #40# $ |#1|) NIL T ELT) ((|#1| #40# $ |#1| |#1|) NIL #4# ELT)) (|qsetelt!| #27#) (|qelt| (#41=(|#1| $ #9#) NIL T ELT)) (|possiblyInfinite?| #42=(#12# NIL T ELT)) (|position| ((#9# |#1| $ #9#) NIL #4# ELT) ((#9# |#1| $) NIL #4# ELT) ((#9# #33# $) NIL T ELT)) (|null| (#12# 9 T ELT)) (|nodes| #43=((#29# $) NIL T ELT)) (|node?| #1#) (|nil| (#36# 7 T CONST)) (|new| (($ #18# |#1|) NIL T ELT)) (|more?| #17#) (|minIndex| (#44=(#9# $) 34 #45=(|has| #9# #14#) ELT)) (|min| #46=(#21# NIL #13# ELT)) (|merge!| #46# (#47=($ #15# $ $) 66 T ELT)) (|merge| #46# (#47# NIL T ELT)) (|members| (#48=(#49=(|List| |#1|) $) 30 T ELT)) (|member?| (#50=(#3# |#1| $) 61 #4# ELT)) (|maxIndex| (#44# NIL #45# ELT)) (|max| #46#) (|map!| (#51=($ (|Mapping| |#1| |#1|) $) 92 T ELT)) (|map| (#51# NIL T ELT) (($ #40# $ $) NIL T ELT)) (|list| (($ |#1|) NIL T ELT)) (|less?| #17#) (|leaves| #52=(#48# NIL T ELT)) (|leaf?| #42#) (|latex| (((|String|) $) 59 #30# ELT)) (|last| #5# #53=(#37# NIL T ELT)) (|insert!| #54=(#55=($ $ $ #9#) NIL T ELT) #56=(($ |#1| $ #9#) NIL T ELT)) (|insert| #54# #56#) (|indices| (((|List| #9#) $) NIL T ELT)) (|index?| ((#3# #9# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #30# ELT)) (|first| (#6# 16 T ELT) #53#) (|find| (((|Union| |#1| "failed") #33# $) NIL T ELT)) (|fill!| (#57=($ $ |#1|) NIL #10# ELT)) (|explicitlyFinite?| #42#) (|every?| #58=((#3# #33# $) NIL T ELT)) (|eval| (($ $ (|List| #59=(|Equation| |#1|))) NIL #60=(AND (|has| |#1| (|Evalable| |#1|)) #30#) ELT) (($ $ #59#) NIL #60# ELT) (($ $ |#1| |#1|) NIL #60# ELT) (($ $ #49# #49#) NIL #60# ELT)) (|eq?| (#2# 15 T ELT)) (|entry?| (#50# NIL #38# ELT)) (|entries| #52#) (|empty?| (#12# 20 T ELT)) (|empty| (#36# 19 T ELT)) (|elt| ((|#1| $ #22#) NIL T ELT) ((|#1| $ #23#) 18 T ELT) (($ $ #24#) 23 T ELT) ((|#1| $ #25#) NIL T ELT) #61=(($ $ #26#) NIL T ELT) (#41# 78 T ELT) (#28# NIL T ELT)) (|distance| ((#9# $ $) NIL T ELT)) (|delete!| #61# #62=(#11# NIL T ELT)) (|delete| #61# #62#) (|cyclic?| #42#) (|cycleTail| #7#) (|cycleSplit!| (#8# NIL #10# ELT)) (|cycleLength| (#63=(#18# $) NIL T ELT)) (|cycleEntry| (#8# 40 T ELT)) (|count| ((#18# #33# $) NIL T ELT) ((#18# |#1| $) NIL #4# ELT)) (|copyInto!| (#55# NIL #10# ELT)) (|copy| (#8# 36 T ELT)) (|convert| ((#64=(|InputForm|) $) 87 (|has| |#1| (|ConvertibleTo| #64#)) ELT)) (|construct| (($ #49#) 29 T ELT)) (|cons| (#39# 10 T ELT)) (|concat!| (#21# 62 T ELT) #65=(#57# NIL T ELT)) (|concat| (#21# 72 T ELT) (#39# 14 T ELT) (($ #29#) NIL T ELT) #65#) (|coerce| ((#66=(|OutputForm|) $) 51 (|has| |#1| (|CoercibleTo| #66#)) ELT)) (|children| #43#) (|child?| #1#) (|before?| #1#) (|append| (#21# 11 T ELT)) (|any?| #58#) (>= #67=(#2# NIL #13# ELT)) (> #67#) (= (#2# 55 #4# ELT)) (<= #67#) (< #67#) (|#| (#63# 13 T ELT))) (((|List| |#1|) (|Join| (|ListAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |nil| ($) |constant|) (SIGNATURE |null| ((|Boolean|) $)) (SIGNATURE |cons| ($ |#1| $)) (SIGNATURE |append| #1=($ $ $)) (IF (|has| |#1| (|SetCategory|)) (PROGN (SIGNATURE |setUnion| #1#) (SIGNATURE |setIntersection| #1#) (SIGNATURE |setDifference| #1#)) |%noBranch|))) (|Type|)) (T |List|)) ((|nil| (*1 *1) #1=(AND #2=(|isDomain| *1 (|List| *2)) #3=(|ofCategory| *2 #4=(|Type|)))) (|null| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|List| *3)) (|ofCategory| *3 #4#))) (|cons| (*1 *1 *2 *1) #1#) (|append| #5=(*1 *1 *1 *1) #1#) (|setUnion| #5# #6=(AND #2# (|ofCategory| *2 (|SetCategory|)) #3#)) (|setIntersection| #5# #6#) (|setDifference| #5# #6#)) @@ -1948,26 +1948,26 @@ NIL (((|LeftLinearSet| |#1|) (|Category|) (|SemiGroup|)) (T |LeftLinearSet|)) ((* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|LeftLinearSet| *2)) (|ofCategory| *2 (|SemiGroup|))))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ |t#1| $)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|substitute| (($ |#1| |#1| $) 45 T ELT)) (|select!| (#5=($ #6=(|Mapping| #3# |#1|) $) 61 #7=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| #8=(#5# NIL #7# ELT)) (|sample| (#9=($) NIL T CONST)) (|removeDuplicates!| (#10=($ $) 47 T ELT)) (|removeDuplicates| (#10# NIL #11=(AND #7# #4#) ELT)) (|remove!| (#12=($ |#1| $) 58 #7# ELT) (#5# 60 #7# ELT)) (|remove| (#12# NIL #11# ELT) #8#) (|reduce| ((|#1| #13=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #13# $ |#1|) NIL T ELT) ((|#1| #13# $) NIL T ELT)) (|members| ((#14=(|List| |#1|) $) 9 T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| (#15=($ (|Mapping| |#1| |#1|) $) 41 T ELT)) (|map| (#15# 39 T ELT)) (|latex| (((|String|) $) NIL #16=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#17=(|#1| $) 49 T ELT)) (|insert!| (#12# 30 T ELT) (($ |#1| $ #18=(|NonNegativeInteger|)) 44 T ELT)) (|hash| (((|SingleInteger|) $) NIL #16# ELT)) (|find| (((|Union| |#1| "failed") #6# $) NIL T ELT)) (|extract!| (#17# 52 T ELT)) (|every?| #19=((#3# #6# $) NIL T ELT)) (|eval| (($ $ (|List| #20=(|Equation| |#1|))) NIL #21=(AND (|has| |#1| (|Evalable| |#1|)) #16#) ELT) (($ $ #20#) NIL #21# ELT) (($ $ |#1| |#1|) NIL #21# ELT) (($ $ #14# #14#) NIL #21# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| (#22=(#3# $) 23 T ELT)) (|empty| (#9# 29 T ELT)) (|duplicates?| (#22# 56 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #18#))) $) 69 T ELT)) (|dictionary| (#9# 26 T ELT) (#23=($ #14#) 19 T ELT)) (|count| ((#18# |#1| $) 65 #4# ELT) ((#18# #6# $) NIL T ELT)) (|copy| (#10# 20 T ELT)) (|convert| ((#24=(|InputForm|) $) 36 (|has| |#1| (|ConvertibleTo| #24#)) ELT)) (|construct| (#23# NIL T ELT)) (|coerce| ((#25=(|OutputForm|) $) 14 (|has| |#1| (|CoercibleTo| #25#)) ELT)) (|before?| #1#) (|bag| (#23# 24 T ELT)) (|any?| #19#) (= (#2# 71 #4# ELT)) (|#| ((#18# $) 17 T ELT))) (((|ListMultiDictionary| |#1|) (|Join| (|MultiDictionary| |#1|) (|FiniteAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |duplicates?| ((|Boolean|) $)) (SIGNATURE |substitute| ($ |#1| |#1| $)))) (|SetCategory|)) (T |ListMultiDictionary|)) ((|duplicates?| (*1 *2 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|ListMultiDictionary| *3)) (|ofCategory| *3 #1=(|SetCategory|)))) (|substitute| (*1 *1 *2 *2 *1) (AND (|isDomain| *1 (|ListMultiDictionary| *2)) (|ofCategory| *2 #1#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#4=($ $ $) 29 T ELT)) (+ (#4# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 31 T ELT) (($ |#1| . #5#) 34 T ELT))) (((|LeftModule| |#1|) (|Category|) (|Rng|)) (T |LeftModule|)) NIL (|Join| (|AbelianGroup|) (|LeftLinearSet| |t#1|)) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|size| (((|NonNegativeInteger|) $) 17 T ELT)) (|rightMult| (($ $ |#1|) 68 T ELT)) (|reverse!| (#3=($ $) 39 T ELT)) (|reverse| (#3# 37 T ELT)) (|retractIfCan| (((|Union| |#1| "failed") $) 60 T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|plus| (($ |#1| |#2| $) 77 T ELT) (($ $ $) 79 T ELT)) (|outputForm| ((#4=(|OutputForm|) $ #5=(|Mapping| #4# #4# #4#) #5# #6=(|Integer|)) 55 T ELT)) (|nthFactor| ((|#1| $ #6#) 35 T ELT)) (|nthExpon| ((|#2| $ #6#) 34 T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 41 T ELT)) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) 46 T ELT)) (|makeUnit| (($) 13 T ELT)) (|makeTerm| (($ |#1| |#2|) 24 T ELT)) (|makeMulti| (($ #7=(|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) 25 T ELT)) (|listOfMonoms| ((#7# $) 14 T ELT)) (|leftMult| (($ |#1| $) 69 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|commutativeEquality| (#2# 74 T ELT)) (|coerce| ((#4# $) 21 T ELT) (($ |#1|) 18 T ELT)) (|before?| #1#) (= (#2# 27 T ELT))) (((|ListMonoidOps| |#1| |#2| |#3|) (|Join| #1=(|SetCategory|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| (#2=(|OutputForm|) $ #3=(|Mapping| #2# #2# #2#) #3# #4=(|Integer|))) (SIGNATURE |listOfMonoms| (#5=(|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $)) (SIGNATURE |makeTerm| ($ |#1| |#2|)) (SIGNATURE |makeMulti| ($ #5#)) (SIGNATURE |nthExpon| (|#2| $ #4#)) (SIGNATURE |nthFactor| (|#1| $ #4#)) (SIGNATURE |reverse| #6=($ $)) (SIGNATURE |reverse!| #6#) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |makeUnit| ($)) (SIGNATURE |rightMult| ($ $ |#1|)) (SIGNATURE |leftMult| ($ |#1| $)) (SIGNATURE |plus| ($ |#1| |#2| $)) (SIGNATURE |plus| ($ $ $)) (SIGNATURE |commutativeEquality| ((|Boolean|) $ $)) (SIGNATURE |mapExpon| ($ (|Mapping| |#2| |#2|) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)))) #1# (|AbelianMonoid|) |#2|) (T |ListMonoidOps|)) ((|outputForm| (*1 *2 *1 *3 *3 *4) (AND (|isDomain| *3 (|Mapping| #1=(|OutputForm|) #1# #1#)) (|isDomain| *4 #2=(|Integer|)) (|isDomain| *2 #1#) (|isDomain| *1 (|ListMonoidOps| *5 *6 *7)) (|ofCategory| *5 #3=(|SetCategory|)) (|ofCategory| *6 #4=(|AbelianMonoid|)) (|ofType| *7 *6))) (|listOfMonoms| #5=(*1 *2 *1) (AND #6=(|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| *4)))) #7=(|isDomain| *1 (|ListMonoidOps| *3 *4 *5)) #8=(|ofCategory| *3 #3#) #9=(|ofCategory| *4 #4#) #10=(|ofType| *5 *4))) (|makeTerm| (*1 *1 *2 *3) #11=(AND (|isDomain| *1 (|ListMonoidOps| *2 *3 *4)) #12=(|ofCategory| *2 #3#) (|ofCategory| *3 #4#) (|ofType| *4 *3))) (|makeMulti| (*1 *1 *2) (AND #6# #8# #9# #10# #7#)) (|nthExpon| #13=(*1 *2 *1 *3) (AND #14=(|isDomain| *3 #2#) (|ofCategory| *2 #4#) (|isDomain| *1 (|ListMonoidOps| *4 *2 *5)) (|ofCategory| *4 #3#) (|ofType| *5 *2))) (|nthFactor| #13# (AND #14# #12# (|isDomain| *1 (|ListMonoidOps| *2 *4 *5)) #9# #10#)) (|reverse| #15=(*1 *1 *1) #11#) (|reverse!| #15# #11#) (|size| #5# (AND (|isDomain| *2 (|NonNegativeInteger|)) #7# #8# #9# #10#)) (|makeUnit| (*1 *1) #11#) (|rightMult| (*1 *1 *1 *2) #11#) (|leftMult| #16=(*1 *1 *2 *1) #11#) (|plus| (*1 *1 *2 *3 *1) #11#) (|plus| (*1 *1 *1 *1) #11#) (|commutativeEquality| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) #7# #8# #9# #10#)) (|mapExpon| #16# (AND (|isDomain| *2 (|Mapping| *4 *4)) #9# #10# #7# #8#)) (|mapGen| #16# (AND (|isDomain| *2 (|Mapping| *3 *3)) #8# #7# #9# #10#))) ((|maxIndex| ((#1=(|Integer|) $) 30 T ELT)) (|insert| (($ |#2| $ #1#) 26 T ELT) (($ $ $ #1#) NIL T ELT)) (|indices| (((|List| #1#) $) 12 T ELT)) (|index?| (((|Boolean|) #1# $) 17 T ELT)) (|concat| (($ $ |#2|) 23 T ELT) (($ |#2| $) 24 T ELT) (($ $ $) NIL T ELT) (($ (|List| $)) NIL T ELT))) (((|LinearAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |insert| (|#1| |#1| |#1| #1=(|Integer|))) (SIGNATURE |insert| (|#1| |#2| |#1| #1#)) (SIGNATURE |concat| (|#1| (|List| |#1|))) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#2|)) (SIGNATURE |maxIndex| (#1# |#1|)) (SIGNATURE |indices| ((|List| #1#) |#1|)) (SIGNATURE |index?| ((|Boolean|) #1# |#1|))) (|LinearAggregate| |#2|) (|Type|)) (T |LinearAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #4=(|Boolean|) |#1|) . #5=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#6=($) 6 T CONST)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #7=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #7#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #4# |#1|) . #5#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #8=($)) 38 (|has| #3# . #9=((|OrderedSet|))) ELT)) (|maxIndex| ((#3# . #8#) 39 (|has| #3# . #9#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #10=((|SetCategory|))) ELT)) (|insert| (($ |#1| $ (|Integer|)) 57 T ELT) (($ $ $ (|Integer|)) 56 T ELT)) (|indices| (((|List| #3#) $) 41 T ELT)) (|index?| ((#11=(|Boolean|) #3# $) 42 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #10#) ELT)) (|first| ((|#1| $) 37 (|has| #3# . #9#) ELT)) (|fill!| (($ $ |#1|) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| 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T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) +((|new| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) #1=(|ofCategory| *1 (|LinearAggregate| *3)) #2=(|ofCategory| *3 #3=(|Type|)))) (|concat| #4=(*1 *1 *1 *2) #5=(AND #6=(|ofCategory| *1 (|LinearAggregate| *2)) #7=(|ofCategory| *2 #3#))) (|concat| (*1 *1 *2 *1) #5#) (|concat| (*1 *1 *1 *1) #5#) (|concat| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) #1# #2#)) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) #1# #2#)) (|delete| #4# #8=(AND (|isDomain| *2 #9=(|Integer|)) #1# #2#)) (|delete| #4# (AND (|isDomain| *2 #10=(|UniversalSegment| #9#)) #1# #2#)) (|insert| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 #9#) #6# #7#)) (|insert| (*1 *1 *1 *1 *2) #8#) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 #10#) (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) #6# #7#))) +(|Join| (|IndexedAggregate| #1=(|Integer|) |t#1|) (|Collection| |t#1|) (|Eltable| #2=(|UniversalSegment| #1#) $) (CATEGORY |domain| (SIGNATURE |new| ($ (|NonNegativeInteger|) |t#1|)) (SIGNATURE |concat| ($ $ |t#1|)) (SIGNATURE |concat| ($ |t#1| $)) (SIGNATURE |concat| ($ $ $)) (SIGNATURE |concat| ($ (|List| $))) (SIGNATURE |map| ($ (|Mapping| |t#1| |t#1| |t#1|) $ $)) (SIGNATURE |delete| ($ $ #1#)) (SIGNATURE |delete| ($ $ #2#)) (SIGNATURE |insert| ($ |t#1| $ #1#)) (SIGNATURE |insert| ($ $ $ #1#)) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (SIGNATURE |setelt| (|t#1| $ #2# |t#1|)) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| #1#) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sign| ((#5=(|Integer|) $) NIL #6=(|has| |#1| (|OrderedAbelianGroup|)) ELT)) (|sample| (#7=($) NIL T CONST)) (|positive?| #8=(#4# NIL #6# ELT)) (|opposite?| #1#) (|numer| ((|#1| $) 23 T ELT)) (|negative?| #8#) (|min| #9=(#10=($ $ $) NIL #6# ELT)) (|max| #9#) (|latex| (((|String|) $) 48 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|denom| ((|#3| $) 24 T ELT)) (|coerce| (((|OutputForm|) $) 43 T ELT)) (|before?| (#2# 22 T ELT)) (|abs| (#11=($ $) NIL #6# ELT)) (|Zero| (#7# 10 T CONST)) (>= #12=(#2# NIL #6# ELT)) (> #12#) (= (#2# 20 T ELT)) (<= #12#) (< (#2# 26 #6# ELT)) (/ (($ $ |#3|) 36 T ELT) (($ |#1| |#3|) 37 T ELT)) (- (#11# 17 T ELT) (#10# NIL T ELT)) (+ (#10# 29 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #5# $) 32 T ELT) (($ |#2| $) 34 T ELT) (($ $ |#2|) NIL T ELT))) (((|Localize| |#1| |#2| |#3|) (|Join| #1=(|Module| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|OrderedAbelianGroup|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE / ($ $ |#3|)) (SIGNATURE / ($ |#1| |#3|)) (SIGNATURE |numer| (|#1| $)) (SIGNATURE |denom| (|#3| $)))) #1# (|CommutativeRing|) (|SubsetCategory| (|Monoid|) |#2|)) (T |Localize|)) ((/ (*1 *1 *1 *2) (AND #1=(|ofCategory| *4 #2=(|CommutativeRing|)) #3=(|isDomain| *1 (|Localize| *3 *4 *2)) #4=(|ofCategory| *3 #5=(|Module| *4)) #6=(|ofCategory| *2 #7=(|SubsetCategory| #8=(|Monoid|) *4)))) (/ (*1 *1 *2 *3) (AND #1# (|isDomain| *1 (|Localize| *2 *4 *3)) (|ofCategory| *2 #5#) (|ofCategory| *3 #7#))) (|numer| #9=(*1 *2 *1) (AND (|ofCategory| *3 #2#) (|ofCategory| *2 (|Module| *3)) (|isDomain| *1 (|Localize| *2 *3 *4)) (|ofCategory| *4 (|SubsetCategory| #8# *3)))) (|denom| #9# (AND #1# #6# #3# #4#))) @@ -1986,11 +1986,11 @@ NIL ((|symmetricSquare| (#1=($ $) 29 T ELT)) (|adjoint| (#1# 27 T ELT)) (D (($) 13 T ELT))) (((|LinearOrdinaryDifferentialOperatorCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |symmetricSquare| #1=(|#1| |#1|)) (SIGNATURE |adjoint| #1#) (SIGNATURE D (|#1|))) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|Ring|)) (T |LinearOrdinaryDifferentialOperatorCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetricSquare| (($ $) 97 (|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (($ $ $) 99 (|has| |#1| (|Field|)) ELT)) (|symmetricPower| (($ $ (|NonNegativeInteger|)) 98 (|has| |#1| (|Field|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (#4=($ $ $) 59 (|has| |#1| . #5=((|Field|))) ELT)) (|rightQuotient| (#4# 60 (|has| |#1| . #5#) ELT)) (|rightLcm| (#4# 62 (|has| |#1| . #5#) ELT)) (|rightGcd| (#4# 57 (|has| |#1| . #5#) ELT)) (|rightExtendedGcd| (#6=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 56 (|has| |#1| . #5#) ELT)) (|rightExactQuotient| (#7=(#8=(|Union| $ "failed") $ $) 58 (|has| |#1| . #5#) ELT)) (|rightDivide| (#9=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 61 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=("failed")) . #12=($)) 89 (|has| |#1| . #13=((|RetractableTo| #10#))) ELT) (((|Union| #14=(|Fraction| #10#) . #11#) . #12#) 86 (|has| |#1| . #15=((|RetractableTo| #14#))) ELT) (((|Union| |#1| . #11#) . #12#) 83 T ELT)) (|retract| ((#10# . #16=($)) 88 (|has| |#1| . #13#) ELT) ((#14# . #16#) 85 (|has| |#1| . #15#) ELT) ((|#1| . #16#) 84 T ELT)) (|reductum| (#17=($ $) 78 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|primitivePart| (#17# 69 (|has| |#1| . #18=((|GcdDomain|))) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial| (($ |#1| #19=(|NonNegativeInteger|)) 76 T ELT)) (|monicRightDivide| (#9# 71 (|has| |#1| . #20=((|IntegralDomain|))) ELT)) (|monicLeftDivide| (#9# 72 (|has| |#1| . #20#) ELT)) (|minimumDegree| (#21=(#19# $) 80 T ELT)) (|leftRemainder| (#4# 66 (|has| |#1| . #5#) ELT)) (|leftQuotient| (#4# 67 (|has| |#1| . #5#) ELT)) (|leftLcm| (#4# 55 (|has| |#1| . #5#) ELT)) (|leftGcd| (#4# 64 (|has| |#1| . #5#) ELT)) (|leftExtendedGcd| (#6# 63 (|has| |#1| . #5#) ELT)) (|leftExactQuotient| (#7# 65 (|has| |#1| . #5#) ELT)) (|leftDivide| (#9# 68 (|has| |#1| . #5#) ELT)) (|leadingCoefficient| ((|#1| . #22=($)) 79 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#8# $ |#1|) 73 (|has| |#1| . #20#) ELT)) (|elt| ((|#1| $ |#1|) 102 T ELT)) (|directSum| (($ $ $) 96 (|has| |#1| (|Field|)) ELT)) (|degree| (#21# 81 T ELT)) (|content| ((|#1| . #22#) 70 (|has| |#1| . #18#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #14#) 87 (|has| |#1| . #15#) ELT) (($ |#1|) 82 T ELT)) (|coefficients| (((|List| |#1|) $) 75 T ELT)) (|coefficient| ((|#1| $ #19#) 77 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 74 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|adjoint| (($ $) 100 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($) 101 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #23=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 91 T ELT) (($ |#1| . #23#) 90 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|symmetricSquare| (#4=($ $) 97 #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (#6=($ $ $) 99 #5# ELT)) (|symmetricPower| (#7=($ $ #8=(|NonNegativeInteger|)) 98 #5# ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#9=($) 23 T CONST)) (|rightRemainder| (#6# 59 #5# ELT)) (|rightQuotient| (#6# 60 #5# ELT)) (|rightLcm| (#6# 62 #5# ELT)) (|rightGcd| (#6# 57 #5# ELT)) (|rightExtendedGcd| (#10=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 56 #5# ELT)) (|rightExactQuotient| (#11=(#12=(|Union| $ #13="failed") $ $) 58 #5# ELT)) (|rightDivide| (#14=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 61 #5# ELT)) (|retractIfCan| (((|Union| #15=(|Integer|) . #16=(#13#)) . #17=($)) 89 #18=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| #19=(|Fraction| #15#) . #16#) . #17#) 86 #20=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| |#1| . #16#) . #17#) 83 T ELT)) (|retract| ((#15# . #21=($)) 88 #18# ELT) ((#19# . #21#) 85 #20# ELT) (#22=(|#1| . #21#) 84 T ELT)) (|reductum| (#4# 78 T ELT)) (|recip| ((#12# $) 43 T ELT)) (|primitivePart| (#4# 69 #23=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|monomial| (($ |#1| #8#) 76 T ELT)) (|monicRightDivide| (#14# 71 #24=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#14# 72 #24# ELT)) (|minimumDegree| (#25=(#8# $) 80 T ELT)) (|leftRemainder| (#6# 66 #5# ELT)) (|leftQuotient| (#6# 67 #5# ELT)) (|leftLcm| (#6# 55 #5# ELT)) (|leftGcd| (#6# 64 #5# ELT)) (|leftExtendedGcd| (#10# 63 #5# ELT)) (|leftExactQuotient| (#11# 65 #5# ELT)) (|leftDivide| (#14# 68 #5# ELT)) (|leadingCoefficient| (#22# 79 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#12# $ |#1|) 73 #24# ELT)) (|elt| ((|#1| $ |#1|) 102 T ELT)) (|directSum| (#6# 96 #5# ELT)) (|degree| (#25# 81 T ELT)) (|content| (#22# 70 #23# ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #15#) 42 T ELT) (($ #19#) 87 #20# ELT) (($ |#1|) 82 T ELT)) (|coefficients| (((|List| |#1|) $) 75 T ELT)) (|coefficient| ((|#1| $ #8#) 77 T ELT)) (|characteristic| ((#8#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 74 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|adjoint| (#4# 100 T ELT)) (|Zero| (#9# 24 T CONST)) (|One| (#9# 46 T CONST)) (D (#9# 101 T ELT)) (= (#1# 8 T ELT)) (- (#4# 30 T ELT) (#6# 29 T ELT)) (+ (#6# 18 T ELT)) (** (($ $ #26=(|PositiveInteger|)) 36 T ELT) (#7# 44 T ELT)) (* (($ #26# $) 17 T ELT) (($ #8# $) 21 T ELT) (($ #15# . #27=($)) 31 T ELT) (#6# 35 T ELT) (($ $ |#1|) 91 T ELT) (($ |#1| . #27#) 90 T ELT))) (((|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Category|) (|Ring|)) (T |LinearOrdinaryDifferentialOperatorCategory|)) -((D (*1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|adjoint| (*1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|symmetricProduct| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|symmetricPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *3 (|Field|)))) (|symmetricSquare| (*1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|directSum| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) -(|Join| (|UnivariateSkewPolynomialCategory| |t#1|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE D ($)) (SIGNATURE |adjoint| ($ $)) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |symmetricProduct| ($ $ $)) (SIGNATURE |symmetricPower| ($ $ (|NonNegativeInteger|))) (SIGNATURE |symmetricSquare| ($ $)) (SIGNATURE |directSum| ($ $ $))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| |#1| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UnivariateSkewPolynomialCategory| |#1|) . T)) +((D (*1 *1) #1=(AND #2=(|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *2)) #3=(|ofCategory| *2 #4=(|Ring|)))) (|adjoint| #5=(*1 *1 *1) #1#) (|symmetricProduct| #6=(*1 *1 *1 *1) #7=(AND #2# #3# (|ofCategory| *2 #8=(|Field|)))) (|symmetricPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|LinearOrdinaryDifferentialOperatorCategory| *3)) (|ofCategory| *3 #4#) (|ofCategory| *3 #8#))) (|symmetricSquare| #5# #7#) (|directSum| #6# #7#)) +(|Join| (|UnivariateSkewPolynomialCategory| |t#1|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE D ($)) (SIGNATURE |adjoint| #1=($ $)) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |symmetricProduct| #2=($ $ $)) (SIGNATURE |symmetricPower| ($ $ (|NonNegativeInteger|))) (SIGNATURE |symmetricSquare| #1#) (SIGNATURE |directSum| #2#)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| |#1| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UnivariateSkewPolynomialCategory| |#1|) . T)) ((|factor1| (#1=(#2=(|List| #3=(|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) #3#) 86 #4=(|has| |#1| (|AlgebraicallyClosedField|)) ELT)) (|factor| (#1# 85 #4# ELT) ((#2# #3# (|Mapping| (|List| |#1|) |#2|)) 19 T ELT))) (((|LinearOrdinaryDifferentialOperatorFactorizer| |#1| |#2|) (CATEGORY |package| (SIGNATURE |factor| (#1=(|List| #2=(|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) #2# (|Mapping| (|List| |#1|) |#2|))) (IF (|has| |#1| (|AlgebraicallyClosedField|)) (PROGN (SIGNATURE |factor| #3=(#1# #2#)) (SIGNATURE |factor1| #3#)) |%noBranch|)) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #4=(|Integer|)) (|RetractableTo| (|Fraction| #4#))) (|UnivariatePolynomialCategory| |#1|)) (T |LinearOrdinaryDifferentialOperatorFactorizer|)) ((|factor1| #1=(*1 *2 *3) #2=(AND (|ofCategory| *4 (|AlgebraicallyClosedField|)) (|ofCategory| *4 #3=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #4=(|Integer|)) (|RetractableTo| (|Fraction| #4#)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| #5=(|LinearOrdinaryDifferentialOperator1| (|Fraction| *5)))) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *4 *5)) (|isDomain| *3 #5#))) (|factor| #1# #2#) (|factor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| (|List| *5) *6)) (|ofCategory| *5 #3#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| #6=(|LinearOrdinaryDifferentialOperator1| (|Fraction| *6)))) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorFactorizer| *5 *6)) (|isDomain| *3 #6#)))) @@ -2000,11 +2000,11 @@ NIL ((|\\/| (($ $ $) 9 T ELT))) (((|Logic&| |#1|) (CATEGORY |package| (SIGNATURE |\\/| (|#1| |#1| |#1|))) (|Logic|)) (T |Logic&|)) NIL -((~ (($ $) 8 T ELT)) (|\\/| (($ $ $) 6 T ELT)) (|/\\| (($ $ $) 7 T ELT))) +((~ (($ $) 8 T ELT)) (|\\/| (#1=($ $ $) 6 T ELT)) (|/\\| (#1# 7 T ELT))) (((|Logic|) (|Category|)) (T |Logic|)) -((~ (*1 *1 *1) (|ofCategory| *1 (|Logic|))) (|/\\| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|))) (|\\/| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|)))) -(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE ~ ($ $)) (SIGNATURE |/\\| ($ $ $)) (SIGNATURE |\\/| ($ $ $)))) -(((|Join|) . T) ((|Type|) . T)) +((~ (*1 *1 *1) #1=(|ofCategory| *1 (|Logic|))) (|/\\| #2=(*1 *1 *1 *1) #1#) (|\\/| #2# #1#)) +(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE ~ ($ $)) (SIGNATURE |/\\| #1=($ $ $)) (SIGNATURE |\\/| #1#))) +(((|Type|) . T)) ((|solveLinearPolynomialEquationByFractions| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#) 33 T ELT))) (((|LinearPolynomialEquationByFractions| |#1|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquationByFractions| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#))) (|PolynomialFactorizationExplicit|)) (T |LinearPolynomialEquationByFractions|)) ((|solveLinearPolynomialEquationByFractions| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| *4))) (|isDomain| *3 #1#) (|ofCategory| *4 (|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|LinearPolynomialEquationByFractions| *4))))) @@ -2014,11 +2014,11 @@ NIL ((|sorted?| ((#1=(|Boolean|) $) NIL T ELT) ((#1# #2=(|Mapping| #1# |#2| |#2|) $) 59 T ELT)) (|sort!| (#3=($ $) NIL T ELT) (($ #2# $) 12 T ELT)) (|select!| (#4=($ #5=(|Mapping| #1# |#2|) $) 29 T ELT)) (|reverse!| (#3# 65 T ELT)) (|removeDuplicates!| (#3# 74 T ELT)) (|remove!| (($ |#2| $) NIL T ELT) (#4# 43 T ELT)) (|reduce| ((|#2| #6=(|Mapping| |#2| |#2| |#2|) $) 21 T ELT) ((|#2| #6# $ |#2|) 60 T ELT) ((|#2| #6# $ |#2| |#2|) 62 T ELT)) (|position| ((#7=(|Integer|) |#2| $ #7#) 71 T ELT) ((#7# |#2| $) NIL T ELT) ((#7# #5# $) 54 T ELT)) (|new| (($ (|NonNegativeInteger|) |#2|) 63 T ELT)) (|merge!| #8=(($ $ $) NIL T ELT) (#9=($ #2# $ $) 31 T ELT)) (|merge| #8# (#9# 24 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT) (($ #6# $ $) 64 T ELT)) (|list| (($ |#2|) 15 T ELT)) (|insert!| (#10=($ $ $ #7#) 42 T ELT) (($ |#2| $ #7#) 40 T ELT)) (|find| (((|Union| |#2| "failed") #5# $) 53 T ELT)) (|delete!| (($ $ (|UniversalSegment| #7#)) 51 T ELT) (($ $ #7#) 44 T ELT)) (|copyInto!| (#10# 70 T ELT)) (|copy| (#3# 68 T ELT)) (< ((#1# $ $) 76 T ELT))) (((|ListAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |list| (|#1| |#2|)) (SIGNATURE |delete!| (|#1| |#1| #1=(|Integer|))) (SIGNATURE |delete!| (|#1| |#1| (|UniversalSegment| #1#))) (SIGNATURE |remove!| #2=(|#1| #3=(|Mapping| #4=(|Boolean|) |#2|) |#1|)) (SIGNATURE |insert!| (|#1| |#2| |#1| #1#)) (SIGNATURE |insert!| #5=(|#1| |#1| |#1| #1#)) (SIGNATURE |merge!| #6=(|#1| #7=(|Mapping| #4# |#2| |#2|) |#1| |#1|)) (SIGNATURE |select!| #2#) (SIGNATURE |remove!| (|#1| |#2| |#1|)) (SIGNATURE |removeDuplicates!| #8=(|#1| |#1|)) (SIGNATURE |merge!| #9=(|#1| |#1| |#1|)) (SIGNATURE |reduce| (|#2| #10=(|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |find| ((|Union| |#2| "failed") #3# |#1|)) (SIGNATURE |reduce| (|#2| #10# |#1| |#2|)) (SIGNATURE |reduce| (|#2| #10# |#1|)) (SIGNATURE |merge| #6#) (SIGNATURE |sorted?| (#4# #7# |#1|)) (SIGNATURE |position| (#1# #3# |#1|)) (SIGNATURE |position| (#1# |#2| |#1|)) (SIGNATURE |position| (#1# |#2| |#1| #1#)) (SIGNATURE |merge| #9#) (SIGNATURE |sorted?| (#4# |#1|)) (SIGNATURE |copyInto!| #5#) (SIGNATURE |reverse!| #8#) (SIGNATURE |sort!| (|#1| #7# |#1|)) (SIGNATURE |sort!| #8#) (SIGNATURE < (#4# |#1| |#1|)) (SIGNATURE |new| (|#1| (|NonNegativeInteger|) |#2|)) (SIGNATURE |map| (|#1| #10# |#1| |#1|)) (SIGNATURE |map| (|#1| (|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |copy| #8#)) (|ListAggregate| |#2|) (|Type|)) (T |ListAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|third| ((|#1| . #3=($)) 62 T ELT)) (|tail| (#4=($ $) 64 T ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) 99 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|split!| (($ $ (|Integer|)) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#6=(|Boolean|) $) 155 (|has| |#1| . #7=((|OrderedSet|))) ELT) ((#6# (|Mapping| #6# |#1| |#1|) $) 149 T ELT)) (|sort!| (#8=($ $) 159 (AND (|has| |#1| . #7#) (|has| $ (|ShallowlyMutableAggregate| |#1|))) ELT) (($ (|Mapping| #6# |#1| |#1|) . #9=($)) 158 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sort| (#8# 154 (|has| |#1| . #7#) ELT) (($ (|Mapping| #6# |#1| |#1|) . #9#) 148 T ELT)) (|size?| (#10=(#11=(|Boolean|) $ (|NonNegativeInteger|)) 82 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setrest!| (#12=($ $ $) 53 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #13="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #14="first" |#1|) 54 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ #15="rest" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #16="last" |#1|) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #17=(|UniversalSegment| #5#) |#1|) 115 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #5# |#1|) 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #18=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select!| (($ (|Mapping| #19=(|Boolean|) |#1|) . #20=($)) 131 T ELT)) (|select| (($ (|Mapping| #21=(|Boolean|) |#1|) . #22=($)) 103 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|second| ((|#1| . #3#) 63 T ELT)) (|sample| (#23=($) 6 T CONST)) (|reverse!| (#8# 157 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|reverse| (#8# 147 T ELT)) (|rest| (#4# 70 T ELT) (#24=($ $ #25=(|NonNegativeInteger|)) 68 T ELT)) (|removeDuplicates!| (($ $) 133 (|has| |#1| . #26=((|BasicType|))) ELT)) (|removeDuplicates| (($ $) 101 (AND (|has| |#1| . #27=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 132 (|has| |#1| . #26#) ELT) (($ (|Mapping| #19# |#1|) . #20#) 127 T ELT)) (|remove| (($ (|Mapping| #21# |#1|) . #22#) 104 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ |#1| $) 102 (AND (|has| |#1| . #27#) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 140 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 139 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 135 (|has| |#1| . #28=((|BasicType|))) ELT)) (|qsetelt!| 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T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| #1#) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|RecursiveAggregate| |#1|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|StreamAggregate| |#1|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| |#1|) . T)) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|head| (((|HeadAst|) $) 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|body| (((|SpadAst|) $) 17 T ELT)) (|before?| #1#) (= #1#)) (((|MacroAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |head| ((|HeadAst|) $)) (SIGNATURE |body| ((|SpadAst|) $))))) (T |MacroAst|)) ((|head| #1=(*1 *2 *1) (AND (|isDomain| *2 (|HeadAst|)) #2=(|isDomain| *1 (|MacroAst|)))) (|body| #1# (AND (|isDomain| *2 (|SpadAst|)) #2#))) @@ -2072,11 +2072,11 @@ NIL ((|zero| (($ #1=(|NonNegativeInteger|) #1#) 42 T ELT)) (|vertConcat| (#2=($ $ $) 73 T ELT)) (|transpose| (($ |#3|) 68 T ELT) (#3=($ $) 69 T ELT)) (|symmetric?| (#4=((|Boolean|) $) 36 T ELT)) (|swapRows!| (#5=($ $ #6=(|Integer|) #6#) 84 T ELT)) (|swapColumns!| (#5# 85 T ELT)) (|subMatrix| (($ $ #6# #6# #6# #6#) 90 T ELT)) (|squareTop| (#3# 71 T ELT)) (|square?| (#4# 15 T ELT)) (|setsubMatrix!| (($ $ #6# #6# $) 91 T ELT)) (|setelt| #7=((|#2| $ #6# #6# |#2|) NIL T ELT) (($ $ #8=(|List| #6#) #8# $) 89 T ELT)) (|scalarMatrix| (($ #1# |#2|) 55 T ELT)) (|matrix| (($ #9=(|List| #10=(|List| |#2|))) 51 T ELT) (($ #1# #1# (|Mapping| |#2| #6# #6#)) 53 T ELT)) (|listOfLists| ((#9# $) 80 T ELT)) (|horizConcat| (#2# 72 T ELT)) (|exquo| (((|Union| $ "failed") $ |#2|) 122 T ELT)) (|elt| ((|#2| $ #6# #6#) NIL T ELT) #7# (($ $ #8# #8#) 88 T ELT)) (|diagonalMatrix| (($ #10#) 56 T ELT) (($ (|List| $)) 58 T ELT)) (|diagonal?| (#4# 28 T ELT)) (|coerce| (($ |#4|) 63 T ELT) (((|OutputForm|) $) NIL T ELT)) (|antisymmetric?| (#4# 38 T ELT)) (/ (#11=($ $ |#2|) 124 T ELT)) (- (#2# 95 T ELT) (#3# 98 T ELT)) (+ (#2# 93 T ELT)) (** (($ $ #1#) 111 T ELT) (($ $ #6#) 128 T ELT)) (* (#2# 104 T ELT) (($ |#2| $) 100 T ELT) (#11# 101 T ELT) (($ #6# $) 103 T ELT) ((|#4| $ |#4|) 115 T ELT) ((|#3| |#3| $) 119 T ELT))) (((|MatrixCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| 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(SIGNATURE |diagonalMatrix| (|#1| (|List| |#1|))) (SIGNATURE |diagonalMatrix| (|#1| #9#)) (SIGNATURE |scalarMatrix| (|#1| #3# |#2|)) (SIGNATURE |matrix| (|#1| #3# #3# (|Mapping| |#2| #1# #1#))) (SIGNATURE |matrix| (|#1| #8#)) (SIGNATURE |zero| (|#1| #3# #3#)) (SIGNATURE |antisymmetric?| #10=((|Boolean|) |#1|)) (SIGNATURE |symmetric?| #10#) (SIGNATURE |diagonal?| #10#) (SIGNATURE |square?| #10#) (SIGNATURE |setelt| #11=(|#2| |#1| #1# #1# |#2|)) (SIGNATURE |elt| #11#) (SIGNATURE |elt| (|#2| |#1| #1# #1#))) (|MatrixCategory| |#2| |#3| |#4|) (|Ring|) #12=(|FiniteLinearAggregate| |#2|) #12#) (T |MatrixCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) 108 T ELT)) (|vertConcat| (($ $ $) 97 T ELT)) (|transpose| (($ |#2|) 101 T ELT) (($ $) 100 T ELT)) (|symmetric?| (((|Boolean|) $) 110 T ELT)) (|swapRows!| (($ $ (|Integer|) (|Integer|)) 93 T ELT)) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) 92 T ELT)) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) 91 T ELT)) (|squareTop| (($ $) 99 T ELT)) (|square?| (((|Boolean|) $) 112 T ELT)) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) 90 T ELT)) (|setelt| ((|#1| $ #3=(|Integer|) #3# |#1|) 52 T ELT) (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) 94 T ELT)) (|setRow!| (($ $ #3# |#2|) 50 T ELT)) (|setColumn!| (($ $ #3# |#3|) 49 T ELT)) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) 105 T ELT)) (|sample| (#4=($) 6 T CONST)) (|rowEchelon| (($ $) 77 (|has| |#1| (|EuclideanDomain|)) ELT)) (|row| ((|#2| $ #3#) 54 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 39 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 38 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 34 (|has| |#1| . #5=((|BasicType|))) ELT)) (|rank| (((|NonNegativeInteger|) $) 76 (|has| |#1| (|IntegralDomain|)) ELT)) (|qsetelt!| ((|#1| $ #3# #3# |#1|) 51 T ELT)) (|qelt| ((|#1| . #6=($ #3# #3#)) 56 T ELT)) (|nullity| (((|NonNegativeInteger|) $) 75 (|has| |#1| (|IntegralDomain|)) ELT)) (|nullSpace| (((|List| |#3|) $) 74 (|has| |#1| (|IntegralDomain|)) ELT)) (|nrows| (#7=(#8=(|NonNegativeInteger|) $) 59 T ELT)) (|new| (($ #8# #8# |#1|) 65 T ELT)) (|ncols| (#7# 58 T ELT)) (|minordet| ((|#1| $) 72 (|has| |#1| (ATTRIBUTE (|commutative| #9="*"))) ELT)) (|minRowIndex| (#10=(#3# $) 63 T ELT)) (|minColIndex| (#10# 61 T ELT)) (|members| (((|List| |#1|) $) 40 T ELT)) (|member?| ((#11=(|Boolean|) |#1| $) 35 (|has| |#1| . #5#) ELT)) (|maxRowIndex| (#10# 62 T ELT)) (|maxColIndex| (#10# 60 T ELT)) (|matrix| (($ (|List| (|List| |#1|))) 107 T ELT) (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) 106 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 66 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 48 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) 47 T ELT)) (|listOfLists| (((|List| (|List| |#1|)) $) 96 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #12=((|SetCategory|))) ELT)) (|inverse| (((|Union| $ "failed") $) 71 (|has| |#1| (|Field|)) ELT)) (|horizConcat| (($ $ $) 98 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #12#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #11# |#1|) $) 37 T ELT)) (|fill!| (($ $ |#1|) 64 T ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 79 (|has| |#1| (|IntegralDomain|)) ELT)) (|every?| ((#11# (|Mapping| #11# |#1|) . #13=($)) 42 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #12#)) ELT)) (|eq?| ((#14=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#14# $) 7 T ELT)) (|empty| (#4# 8 T ELT)) (|elt| ((|#1| . #6#) 57 T ELT) ((|#1| $ #3# #3# |#1|) 55 T ELT) (($ $ (|List| (|Integer|)) (|List| (|Integer|))) 95 T ELT)) (|diagonalMatrix| (($ (|List| |#1|)) 104 T ELT) (($ (|List| $)) 103 T ELT)) (|diagonal?| (((|Boolean|) $) 111 T ELT)) (|determinant| ((|#1| $) 73 (|has| |#1| (ATTRIBUTE (|commutative| #9#))) ELT)) (|count| ((#15=(|NonNegativeInteger|) (|Mapping| #11# |#1|) $) 41 T ELT) ((#15# |#1| $) 36 (|has| |#1| . #5#) ELT)) (|copy| (($ $) 9 T ELT)) (|column| ((|#3| $ #3#) 53 T ELT)) (|coerce| (($ |#3|) 102 T ELT) (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| ((#11# (|Mapping| #11# |#1|) . #13#) 43 T ELT)) (|antisymmetric?| (((|Boolean|) $) 109 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (/ (($ $ |#1|) 78 (|has| |#1| (|Field|)) ELT)) (- (($ $ $) 88 T ELT) (($ $) 87 T ELT)) (+ (($ $ $) 89 T ELT)) (** (($ $ (|NonNegativeInteger|)) 80 T ELT) (($ $ (|Integer|)) 70 (|has| |#1| (|Field|)) ELT)) (* (($ $ $) 86 T ELT) (($ |#1| $) 85 T ELT) (($ $ |#1|) 84 T ELT) (($ (|Integer|) $) 83 T 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(|FiniteLinearAggregate| *3)))) (|transpose| (*1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|squareTop| (*1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|horizConcat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|vertConcat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|MatrixCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|FiniteLinearAggregate| *2)) (|ofCategory| *4 (|FiniteLinearAggregate| *2)))) (|listOfLists| (*1 *2 *1) (AND (|ofCategory| *1 (|MatrixCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|FiniteLinearAggregate| *3)) (|ofCategory| *5 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T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|TwoDimensionalArrayCategory| |#1| |#2| |#3|) . T) ((|Type|) . T)) ((|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) 39 T ELT)) (|map| (((|Union| |#8| #1="failed") (|Mapping| (|Union| |#5| #1#) |#1|) |#4|) 37 T ELT) ((|#8| (|Mapping| |#5| |#1|) |#4|) 31 T ELT))) (((|MatrixCategoryFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| (|#8| (|Mapping| |#5| |#1|) |#4|)) (SIGNATURE |map| ((|Union| |#8| #1="failed") (|Mapping| (|Union| |#5| #1#) |#1|) |#4|)) (SIGNATURE |reduce| (|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|))) #2=(|Ring|) #3=(|FiniteLinearAggregate| |#1|) #3# (|MatrixCategory| |#1| |#2| |#3|) #2# #4=(|FiniteLinearAggregate| |#5|) #4# (|MatrixCategory| |#5| |#6| |#7|)) (T |MatrixCategoryFunctions2|)) ((|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #1=(|ofCategory| *5 #2=(|Ring|)) (|ofCategory| *2 #2#) #3=(|ofCategory| *6 #4=(|FiniteLinearAggregate| *5)) #5=(|ofCategory| *7 #4#) (|ofCategory| *8 #6=(|FiniteLinearAggregate| *2)) (|ofCategory| *9 #6#) (|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *2 *8 *9 *10)) #7=(|ofCategory| *4 (|MatrixCategory| *5 *6 *7)) (|ofCategory| *10 (|MatrixCategory| *2 *8 *9)))) (|map| #8=(*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Mapping| (|Union| *8 "failed") *5)) #1# #9=(|ofCategory| *8 #2#) #3# #5# #10=(|ofCategory| *2 (|MatrixCategory| *8 *9 *10)) #11=(|isDomain| *1 (|MatrixCategoryFunctions2| *5 *6 *7 *4 *8 *9 *10 *2)) #7# #12=(|ofCategory| *9 #13=(|FiniteLinearAggregate| *8)) #14=(|ofCategory| *10 #13#))) (|map| #8# (AND (|isDomain| *3 (|Mapping| *8 *5)) #1# #9# #3# #5# #10# #11# #7# #12# #14#))) @@ -2095,11 +2095,11 @@ NIL ((|splitDenominator| (((|Record| (|:| |num| #1=(|Matrix| |#1|)) (|:| |den| |#1|)) #2=(|Matrix| |#2|)) 20 T ELT)) (|commonDenominator| ((|#1| #2#) 9 T ELT)) (|clearDenominator| ((#1# #2#) 18 T ELT))) (((|MatrixCommonDenominator| |#1| |#2|) (CATEGORY |package| (SIGNATURE |commonDenominator| (|#1| #1=(|Matrix| |#2|))) (SIGNATURE |clearDenominator| (#2=(|Matrix| |#1|) #1#)) (SIGNATURE |splitDenominator| ((|Record| (|:| |num| #2#) (|:| |den| |#1|)) #1#))) (|IntegralDomain|) (|QuotientFieldCategory| |#1|)) (T |MatrixCommonDenominator|)) ((|splitDenominator| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|Matrix| *5)) #3=(|ofCategory| *5 (|QuotientFieldCategory| *4)) #4=(|ofCategory| *4 #5=(|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |num| #6=(|Matrix| *4)) (|:| |den| *4))) #7=(|isDomain| *1 (|MatrixCommonDenominator| *4 *5)))) (|clearDenominator| #1# (AND #2# #3# #4# (|isDomain| *2 #6#) #7#)) (|commonDenominator| #1# (AND (|isDomain| *3 #6#) (|ofCategory| *4 (|QuotientFieldCategory| *2)) (|ofCategory| *2 #5#) (|isDomain| *1 (|MatrixCommonDenominator| *2 *4))))) -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|select!| (($ (|Mapping| #3=(|Boolean|) |#1|) . #4=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#7=($) 6 T CONST)) (|removeDuplicates!| (($ $) 55 T ELT)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #8=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #3# |#1|) . #4#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #8#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #5# |#1|) . #6#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #9=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #10=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT) (($ |#1| $ (|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #9#) ELT)) (|extract!| ((|#1| . #10#) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #9#)) ELT)) (|eq?| ((#11=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#11# $) 7 T ELT)) (|empty| (#7# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) 54 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#12=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #12#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|select!| (#4=($ (|Mapping| #2# |#1|) $) 42 #5=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (#4# 49 #5# ELT)) (|sample| (#6=($) 6 T CONST)) (|removeDuplicates!| (#7=($ $) 55 T ELT)) (|removeDuplicates| (#7# 51 #8=(AND #3# #5#) ELT)) (|remove!| (#9=($ |#1| $) 44 #5# ELT) (#4# 43 #5# ELT)) (|remove| (#9# 50 #8# ELT) (#4# 48 #5# ELT)) (|map!| (#10=($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (#10# 26 T ELT)) (|latex| (((|String|) $) 21 #11=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#12=(|#1| $) 35 T ELT)) (|insert!| (#9# 36 T ELT) (($ |#1| $ #13=(|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 #11# ELT)) (|extract!| (#12# 37 T ELT)) (|eval| (($ $ (|List| #14=(|Equation| |#1|))) 25 #15=(AND (|has| |#1| (|Evalable| |#1|)) #11#) ELT) (($ $ #14#) 24 #15# ELT) (($ $ |#1| |#1|) 23 #15# ELT) (($ $ #16=(|List| |#1|) #16#) 22 #15# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#6# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #13#))) $) 54 T ELT)) (|dictionary| (#6# 46 T ELT) (#17=($ #16#) 45 T ELT)) (|copy| (#7# 9 T ELT)) (|convert| ((#18=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #18#)) ELT)) (|construct| (#17# 47 T ELT)) (|coerce| ((#19=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #19#)) ELT)) (|before?| (#1# 19 #3# ELT)) (|bag| (#17# 38 T ELT)) (= (#1# 17 #3# ELT))) (((|MultiDictionary| |#1|) (|Category|) (|SetCategory|)) (T |MultiDictionary|)) -((|insert!| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MultiDictionary| *2)) (|ofCategory| *2 (|SetCategory|)))) (|removeDuplicates!| (*1 *1 *1) (AND (|ofCategory| *1 (|MultiDictionary| *2)) (|ofCategory| *2 (|SetCategory|)))) (|duplicates| (*1 *2 *1) (AND (|ofCategory| *1 (|MultiDictionary| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|List| (|Record| (|:| |entry| *3) (|:| |count| (|NonNegativeInteger|)))))))) -(|Join| (|DictionaryOperations| |t#1|) (CATEGORY |domain| (SIGNATURE |insert!| ($ |t#1| $ (|NonNegativeInteger|))) (SIGNATURE |removeDuplicates!| ($ $)) (SIGNATURE |duplicates| ((|List| (|Record| (|:| |entry| |t#1|) (|:| |count| (|NonNegativeInteger|)))) $)))) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((|insert!| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 #1=(|NonNegativeInteger|)) #2=(|ofCategory| *1 (|MultiDictionary| *2)) #3=(|ofCategory| *2 #4=(|SetCategory|)))) (|removeDuplicates!| (*1 *1 *1) (AND #2# #3#)) (|duplicates| (*1 *2 *1) (AND (|ofCategory| *1 (|MultiDictionary| *3)) (|ofCategory| *3 #4#) (|isDomain| *2 (|List| (|Record| (|:| |entry| *3) (|:| |count| #1#))))))) +(|Join| (|DictionaryOperations| |t#1|) (CATEGORY |domain| (SIGNATURE |insert!| ($ |t#1| $ #1=(|NonNegativeInteger|))) (SIGNATURE |removeDuplicates!| ($ $)) (SIGNATURE |duplicates| ((|List| (|Record| (|:| |entry| |t#1|) (|:| |count| #1#))) $)))) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((|separateFactors| ((#1=(|List| |#1|) #2=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #3=(|Integer|)))) #3#) 66 T ELT)) (|linears| ((|#1| |#1| #3#) 63 T ELT)) (|gcd| ((|#1| |#1| |#1| #3#) 46 T ELT)) (|factor| ((#1# |#1| #3#) 49 T ELT)) (|exptMod| ((|#1| |#1| #3# |#1| #3#) 40 T ELT)) (|ddFact| ((#2# |#1| #3#) 62 T ELT))) (((|ModularDistinctDegreeFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |gcd| (|#1| |#1| |#1| #1=(|Integer|))) (SIGNATURE |linears| (|#1| |#1| #1#)) (SIGNATURE |factor| (#2=(|List| |#1|) |#1| #1#)) (SIGNATURE |ddFact| (#3=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #1#))) |#1| #1#)) (SIGNATURE |separateFactors| (#2# #3# #1#)) (SIGNATURE |exptMod| (|#1| |#1| #1# |#1| #1#))) (|UnivariatePolynomialCategory| #1#)) (T |ModularDistinctDegreeFactorizer|)) ((|exptMod| (*1 *2 *2 *3 *2 *3) #1=(AND (|isDomain| *3 #2=(|Integer|)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|separateFactors| #3=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| (|Record| (|:| |factor| *5) (|:| |degree| #2#)))) #4=(|isDomain| *4 #2#) (|ofCategory| *5 #5=(|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|ModularDistinctDegreeFactorizer| *5)))) (|ddFact| #3# (AND #4# (|isDomain| *2 (|List| (|Record| (|:| |factor| *3) (|:| |degree| *4)))) #6=(|isDomain| *1 (|ModularDistinctDegreeFactorizer| *3)) #7=(|ofCategory| *3 #5#))) (|factor| #3# (AND #4# (|isDomain| *2 (|List| *3)) #6# #7#)) (|linears| (*1 *2 *2 *3) #1#) (|gcd| (*1 *2 *2 *2 *3) #1#)) @@ -2130,11 +2130,11 @@ NIL ((|lifting1| ((#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #3# #4=(|List| |#2|) #2# #5=(|List| |#3|) #6=(|List| |#4|) (|List| (|List| (|Record| (|:| |expt| #7=(|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) #8=(|List| #7#) #9=(|Vector| #10=(|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) 92 T ELT)) (|lifting| ((#1# #3# #4# #10# #5# #6# #8# |#3|) 110 T ELT)) (|corrPoly| ((#1# #3# #4# #5# #8# #2# #9# |#3|) 48 T ELT))) (((|MultivariateLifting| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |corrPoly| (#1=(|Union| #2=(|List| #3=(|SparseUnivariatePolynomial| |#4|)) "failed") #3# #4=(|List| |#2|) #5=(|List| |#3|) #6=(|List| #7=(|NonNegativeInteger|)) #2# #8=(|Vector| #9=(|List| (|SparseUnivariatePolynomial| |#3|))) |#3|)) (SIGNATURE |lifting| (#1# #3# #4# #9# #5# #10=(|List| |#4|) #6# |#3|)) (SIGNATURE |lifting1| (#1# #3# #4# #2# #5# #10# (|List| (|List| (|Record| (|:| |expt| #7#) (|:| |pcoef| |#4|)))) #6# #8# |#3|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |MultivariateLifting|)) ((|lifting1| (*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| *13))) (|isDomain| *3 #1#) (|isDomain| *4 #2=(|List| *12)) (|isDomain| *5 #3=(|List| *10)) (|isDomain| *6 (|List| *13)) (|isDomain| *7 (|List| (|List| (|Record| (|:| |expt| #4=(|NonNegativeInteger|)) (|:| |pcoef| *13))))) #5=(|isDomain| *8 #6=(|List| #4#)) (|isDomain| *9 (|Vector| (|List| (|SparseUnivariatePolynomial| *10)))) (|ofCategory| *12 #7=(|OrderedSet|)) (|ofCategory| *10 #8=(|EuclideanDomain|)) (|ofCategory| *13 (|PolynomialCategory| *10 *11 *12)) (|ofCategory| *11 #9=(|OrderedAbelianMonoidSup|)) (|isDomain| *1 (|MultivariateLifting| *11 *12 *10 *13)))) (|lifting| (*1 *2 *3 *4 *5 *6 *7 *8 *9) (|partial| AND (|isDomain| *4 (|List| *11)) (|isDomain| *5 (|List| (|SparseUnivariatePolynomial| *9))) (|isDomain| *6 (|List| *9)) (|isDomain| *7 #2#) #5# (|ofCategory| *11 #7#) (|ofCategory| *9 #8#) (|ofCategory| *12 (|PolynomialCategory| *9 *10 *11)) (|ofCategory| *10 #9#) (|isDomain| *2 (|List| #10=(|SparseUnivariatePolynomial| *12))) (|isDomain| *1 (|MultivariateLifting| *10 *11 *9 *12)) (|isDomain| *3 #10#))) (|corrPoly| (*1 *2 *3 *4 *5 *6 *2 *7 *8) (|partial| AND (|isDomain| *2 (|List| #11=(|SparseUnivariatePolynomial| *11))) (|isDomain| *3 #11#) (|isDomain| *4 #3#) (|isDomain| *5 (|List| *8)) (|isDomain| *6 #6#) (|isDomain| *7 (|Vector| (|List| (|SparseUnivariatePolynomial| *8)))) (|ofCategory| *10 #7#) (|ofCategory| *8 #8#) (|ofCategory| *11 (|PolynomialCategory| *8 *9 *10)) (|ofCategory| *9 #9#) (|isDomain| *1 (|MultivariateLifting| *9 *10 *8 *11))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reductum| (($ $) 57 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 55 T ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 59 T ELT)) (|leadingCoefficient| ((|#1| $) 58 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| (((|NonNegativeInteger|) $) 60 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 54 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 56 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 62 T ELT) (($ |#1| . #4#) 61 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|reductum| (#5=($ $) 57 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|monomial| (($ |#1| #6=(|NonNegativeInteger|)) 55 T ELT)) (|minimumDegree| (#7=(#6# $) 59 T ELT)) (|leadingCoefficient| ((|#1| $) 58 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|degree| (#7# 60 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #8=(|Integer|)) 42 T ELT) (($ |#1|) 54 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ #6#) 56 T ELT)) (|characteristic| ((#6#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (= (#1# 8 T ELT)) (- (#5# 30 T ELT) (#9=($ $ $) 29 T ELT)) (+ (#9# 18 T ELT)) (** (($ $ #10=(|PositiveInteger|)) 36 T ELT) (($ $ #6#) 44 T ELT)) (* (($ #10# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #8# . #11=($)) 31 T ELT) (#9# 35 T ELT) (($ $ |#1|) 62 T ELT) (($ |#1| . #11#) 61 T ELT))) (((|MonogenicLinearOperator| |#1|) (|Category|) (|Ring|)) (T |MonogenicLinearOperator|)) -((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|MonogenicLinearOperator| *2)) (|ofCategory| *2 (|Ring|))))) -(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ |t#1| (|NonNegativeInteger|))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|degree| #1=(*1 *2 *1) #2=(AND (|ofCategory| *1 (|MonogenicLinearOperator| *3)) (|ofCategory| *3 #3=(|Ring|)) (|isDomain| *2 #4=(|NonNegativeInteger|)))) (|minimumDegree| #1# #2#) (|leadingCoefficient| #1# #5=(AND #6=(|ofCategory| *1 (|MonogenicLinearOperator| *2)) #7=(|ofCategory| *2 #3#))) (|reductum| (*1 *1 *1) #5#) (|coefficient| (*1 *2 *1 *3) #8=(AND (|isDomain| *3 #4#) #6# #7#)) (|monomial| (*1 *1 *2 *3) #8#)) +(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (SIGNATURE |degree| #1=(#2=(|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| #1#) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ #2#)) (SIGNATURE |monomial| ($ |t#1| #2#)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) 23 T ELT))) (((|MultipleMap| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| (|#6| (|Mapping| |#4| |#1|) |#3|))) #1=(|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) #1# (|UnivariatePolynomialCategory| |#4|) (|UnivariatePolynomialCategory| (|Fraction| |#5|))) (T |MultipleMap|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *7 #1#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *2 (|UnivariatePolynomialCategory| (|Fraction| *8))) (|isDomain| *1 (|MultipleMap| *5 *6 *4 *7 *8 *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|UnivariatePolynomialCategory| *7))))) @@ -2159,54 +2159,54 @@ NIL ((* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ |#2|) 9 T ELT))) (((|Module&| |#1| |#2|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| (|Integer|) |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|Module| |#2|) (|CommutativeRing|)) (T |Module&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#1|) 38 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#4=($ $ $) 29 T ELT)) (+ (#4# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 31 T ELT) (($ |#1| . #5#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|Module| |#1|) (|Category|) (|CommutativeRing|)) (T |Module|)) NIL (|Join| (|BiModule| |t#1| |t#1|) (|LinearSet| |t#1|)) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|shift| (#4=($ |#1|) 17 T ELT) (#5=($ $ |#1|) 20 T ELT)) (|scale| (#4# 18 T ELT) (#5# 21 T ELT)) (|sample| (#6=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT) (#6# 19 T ELT) (#7=($ $) 22 T ELT)) (|one?| ((#3# $) NIL T ELT)) (|moebius| (($ |#1| |#1| |#1| |#1|) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#7# 16 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| ((|#1| $ |#1|) 24 T ELT) ((#8=(|OnePointCompletion| |#1|) $ #8#) 32 T ELT)) (|conjugate| #9=(#10=($ $ $) NIL T ELT)) (|commutator| #9#) (|coerce| (((|OutputForm|) $) 39 T ELT)) (|before?| #1#) (|One| (#6# 9 T CONST)) (= (#2# 48 T ELT)) (/ #9#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) NIL T ELT)) (* (#10# 14 T ELT))) (((|MoebiusTransform| |#1|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |moebius| ($ |#1| |#1| |#1| |#1|)) (SIGNATURE |shift| #1=($ |#1|)) (SIGNATURE |scale| #1#) (SIGNATURE |recip| ($)) (SIGNATURE |shift| #2=($ $ |#1|)) (SIGNATURE |scale| #2#) (SIGNATURE |recip| ($ $)) (SIGNATURE |eval| (|#1| $ |#1|)) (SIGNATURE |eval| (#3=(|OnePointCompletion| |#1|) $ #3#)))) (|Field|)) (T |MoebiusTransform|)) ((|moebius| (*1 *1 *2 *2 *2 *2) #1=(AND (|isDomain| *1 (|MoebiusTransform| *2)) (|ofCategory| *2 #2=(|Field|)))) (|shift| #3=(*1 *1 *2) #1#) (|scale| #3# #1#) (|recip| (*1 *1) #1#) (|shift| #4=(*1 *1 *1 *2) #1#) (|scale| #4# #1#) (|recip| (*1 *1 *1) #1#) (|eval| #5=(*1 *2 *1 *2) #1#) (|eval| #5# (AND (|isDomain| *2 (|OnePointCompletion| *3)) (|ofCategory| *3 #2#) (|isDomain| *1 (|MoebiusTransform| *3))))) ((|rightPower| (#1=($ $ (|PositiveInteger|)) 19 T ELT)) (|leftPower| (#1# 20 T ELT)) (** (#1# 10 T ELT))) (((|Monad&| |#1|) (CATEGORY |package| (SIGNATURE ** #1=(|#1| |#1| (|PositiveInteger|))) (SIGNATURE |leftPower| #1#) (SIGNATURE |rightPower| #1#)) (|Monad|)) (T |Monad&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|rightPower| (($ $ (|PositiveInteger|)) 19 T ELT)) (|leftPower| (($ $ (|PositiveInteger|)) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT)) (* (($ $ $) 20 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|rightPower| (#2=($ $ (|PositiveInteger|)) 19 T ELT)) (|leftPower| (#2# 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (** (#2# 17 T ELT)) (* (($ $ $) 20 T ELT))) (((|Monad|) (|Category|)) (T |Monad|)) -((* (*1 *1 *1 *1) (|ofCategory| *1 (|Monad|))) (|rightPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|)))) (|leftPower| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monad|)) (|isDomain| *2 (|PositiveInteger|))))) -(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |rightPower| ($ $ (|PositiveInteger|))) (SIGNATURE |leftPower| ($ $ (|PositiveInteger|))) (SIGNATURE ** ($ $ (|PositiveInteger|))))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((* (*1 *1 *1 *1) #1=(|ofCategory| *1 (|Monad|))) (|rightPower| #2=(*1 *1 *1 *2) #3=(AND #1# (|isDomain| *2 (|PositiveInteger|)))) (|leftPower| #2# #3#) (** #2# #3#)) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE |rightPower| #1=($ $ (|PositiveInteger|))) (SIGNATURE |leftPower| #1#) (SIGNATURE ** #1#))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . 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#54# ELT) (#56# 151 #54# ELT) (#57# 147 #54# ELT) (#58# 143 #4# ELT) (#60# 142 #4# ELT)) (= (#1# 8 T ELT)) (/ (#28# 141 #4# ELT)) (- (#5# 30 T ELT) (#28# 29 T ELT)) (+ (#28# 18 T ELT)) (** (($ $ #10#) 36 T ELT) (#40# 44 T ELT) (($ $ #12#) 138 #4# ELT)) (* (($ #10# $) 17 T ELT) (($ #11# $) 21 T ELT) (($ #12# . #62=($)) 31 T ELT) (#28# 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #62#) 54 T ELT) (($ #23# . #62#) 140 #4# ELT) (($ $ #23#) 139 #4# ELT))) (((|MonogenicAlgebra| |#1| |#2|) (|Category|) (|CommutativeRing|) (|UnivariatePolynomialCategory| |t#1|)) (T |MonogenicAlgebra|)) -((|generator| (*1 *1) (AND (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|definingPolynomial| (*1 *2) (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|reduce| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|convert| (*1 *1 *2) (AND (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|lift| (*1 *2 *1) (AND (|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|reduce| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Fraction| *4)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *3 *4)))) (|derivationCoordinates| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Vector| *1)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 (|Field|)) (|ofCategory| *1 (|MonogenicAlgebra| *5 *6)) (|ofCategory| *5 (|CommutativeRing|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Matrix| *5))))) -(|Join| (|FramedAlgebra| |t#1| |t#2|) (|CommutativeRing|) (|ConvertibleTo| |t#2|) (|FullyRetractableTo| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |generator| ($)) (SIGNATURE |definingPolynomial| (|t#2|)) (SIGNATURE |reduce| ($ |t#2|)) (SIGNATURE |convert| ($ |t#2|)) (SIGNATURE |lift| (|t#2| $)) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|Finite|)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (ATTRIBUTE (|Field|)) (ATTRIBUTE (|DifferentialExtension| |t#1|)) (SIGNATURE |reduce| ((|Union| $ "failed") (|Fraction| |t#2|))) (SIGNATURE |derivationCoordinates| ((|Matrix| |t#1|) (|Vector| $) (|Mapping| |t#1| |t#1|)))) |%noBranch|) (IF (|has| |t#1| (|FiniteFieldCategory|)) (ATTRIBUTE (|FiniteFieldCategory|)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Algebra| |#1|) . T) ((|Algebra| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|BasicType|) . T) ((|BiModule| #1# #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#2|) . T) ((|DifferentialDomain| $) OR (|has| |#1| (|FiniteFieldCategory|)) (AND (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|Field|))) (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))) ((|DifferentialExtension| |#1|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))) ((|DifferentialSpace|) OR (|has| |#1| (|FiniteFieldCategory|)) (AND (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|Field|))) (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|)))) ((|DifferentialSpaceExtension| |#1|) |has| |#1| (|Field|)) ((|DivisionRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|EntireRing|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Field|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|FieldOfPrimeCharacteristic|) |has| |#1| (|FiniteFieldCategory|)) ((|Finite|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Finite|))) ((|FiniteFieldCategory|) |has| |#1| (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| |#1| |#2|) . T) ((|FramedAlgebra| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|IntegralDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LinearSet| |#1|) . T) ((|LinearSet| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Module| |#1|) . T) ((|Module| $) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) OR (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialRing| (|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialSpace| #3#) OR (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|))))) ((|PrincipalIdealDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|))) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)))) +((|generator| (*1 *1) (AND (|ofCategory| *2 #1=(|CommutativeRing|)) (|ofCategory| *1 (|MonogenicAlgebra| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|definingPolynomial| (*1 *2) #2=(AND #3=(|ofCategory| *1 (|MonogenicAlgebra| *3 *2)) #4=(|ofCategory| *3 #1#) #5=(|ofCategory| *2 #6=(|UnivariatePolynomialCategory| *3)))) (|reduce| #7=(*1 *1 *2) #8=(AND #4# #3# #5#)) (|convert| #7# #8#) (|lift| (*1 *2 *1) #2#) (|reduce| #7# (|partial| AND (|isDomain| *2 (|Fraction| *4)) (|ofCategory| *4 #6#) (|ofCategory| *3 #9=(|Field|)) #4# (|ofCategory| *1 (|MonogenicAlgebra| *3 *4)))) (|derivationCoordinates| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Vector| *1)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 #9#) (|ofCategory| *1 (|MonogenicAlgebra| *5 *6)) (|ofCategory| *5 #1#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Matrix| *5))))) +(|Join| (|FramedAlgebra| |t#1| |t#2|) (|CommutativeRing|) (|ConvertibleTo| |t#2|) (|FullyRetractableTo| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |generator| ($)) (SIGNATURE |definingPolynomial| (|t#2|)) (SIGNATURE |reduce| #1=($ |t#2|)) (SIGNATURE |convert| #1#) (SIGNATURE |lift| (|t#2| $)) (IF (|has| |t#1| #2=(|Finite|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |t#1| #3=(|Field|)) (PROGN (ATTRIBUTE #3#) (ATTRIBUTE (|DifferentialExtension| |t#1|)) (SIGNATURE |reduce| ((|Union| $ "failed") (|Fraction| |t#2|))) (SIGNATURE |derivationCoordinates| ((|Matrix| |t#1|) (|Vector| $) (|Mapping| |t#1| |t#1|)))) |%noBranch|) (IF (|has| |t#1| #4=(|FiniteFieldCategory|)) (ATTRIBUTE #4#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Field|)) ((|Algebra| |#1|) . T) ((|Algebra| $) |has| |#1| (|Field|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Field|)) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) |has| |#1| (|Field|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| |#2|) . T) ((|DifferentialDomain| $) OR (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (AND (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|))) ((|DifferentialExtension| |#1|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|))) ((|DifferentialSpace|) OR (AND (|has| |#1| (|DifferentialRing|)) (|has| |#1| (|Field|))) (AND (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|Field|))) (|has| |#1| (|FiniteFieldCategory|))) ((|DifferentialSpaceExtension| |#1|) |has| |#1| (|Field|)) ((|DivisionRing|) |has| |#1| (|Field|)) ((|EntireRing|) |has| |#1| (|Field|)) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|FieldOfPrimeCharacteristic|) |has| |#1| (|FiniteFieldCategory|)) ((|Finite|) |has| |#1| (|Finite|)) ((|FiniteFieldCategory|) |has| |#1| (|FiniteFieldCategory|)) ((|FiniteRankAlgebra| |#1| |#2|) . T) ((|FramedAlgebra| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|IntegralDomain|) |has| |#1| (|Field|)) ((|LeftLinearSet| #1#) |has| |#1| (|Field|)) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Field|)) ((|LeftModule| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Field|)) ((|LinearSet| |#1|) . T) ((|LinearSet| $) |has| |#1| (|Field|)) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Field|)) ((|Module| |#1|) . T) ((|Module| $) |has| |#1| (|Field|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) OR (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialSpace| #3#) OR (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))))) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Field|)) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) |has| |#1| (|Field|)) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|))) ((|sample| (($) 11 T CONST)) (|recip| (((|Union| $ "failed") $) 14 T ELT)) (|one?| (((|Boolean|) $) 10 T ELT)) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) 20 T ELT))) (((|Monoid&| |#1|) (CATEGORY |package| (SIGNATURE |recip| ((|Union| |#1| "failed") |#1|)) (SIGNATURE ** (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |one?| ((|Boolean|) |#1|)) (SIGNATURE |sample| (|#1|) |constant|) (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|Monoid|)) (T |Monoid&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|sample| (($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (($) 24 T CONST)) (= (#1# 8 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT)) (* (($ $ $) 18 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|one?| ((#2# $) 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT)) (* (($ $ $) 18 T ELT))) (((|Monoid|) (|Category|)) (T |Monoid|)) -((|One| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|sample| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|one?| (*1 *2 *1) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|Boolean|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 (|Monoid|)))) -(|Join| (|SemiGroup|) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |sample| ($) |constant|) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE |recip| ((|Union| $ "failed") $)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|One| #1=(*1 *1) #2=(|ofCategory| *1 #3=(|Monoid|))) (|sample| #1# #2#) (|one?| (*1 *2 *1) (AND #2# (|isDomain| *2 (|Boolean|)))) (** (*1 *1 *1 *2) (AND #2# (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 #3#))) +(|Join| (|SemiGroup|) (CATEGORY |domain| (SIGNATURE |One| #1=($) |constant|) (SIGNATURE |sample| #1# |constant|) (SIGNATURE |one?| ((|Boolean|) $)) (SIGNATURE ** ($ $ (|NonNegativeInteger|))) (SIGNATURE |recip| ((|Union| $ "failed") $)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|neutralValue| ((|#1| $) 16 T ELT)) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ |#1| |#1|) 14 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (((|SemiGroupOperation| |#1|) $) 17 T ELT)) (|before?| #1#) (= #1#)) (((|MonoidOperation| |#1|) (|Join| (|MonoidOperatorCategory| |#1|) (|SetCategory|) (|CoercibleTo| (|SemiGroupOperation| |#1|)) (CATEGORY |domain| (SIGNATURE |monoidOperation| ($ (|Mapping| |#1| |#1| |#1|) |#1|)))) (|BasicType|)) (T |MonoidOperation|)) ((|monoidOperation| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *1 (|MonoidOperation| *3))))) ((|neutralValue| ((|#1| $) 8 T ELT)) (|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) (((|MonoidOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |MonoidOperatorCategory|)) ((|neutralValue| (*1 *2 *1) (AND (|ofCategory| *1 (|MonoidOperatorCategory| *2)) (|ofCategory| *2 (|BasicType|))))) -(|Join| (|SemiGroupOperatorCategory| |t#1|) (CATEGORY |domain| (SIGNATURE |neutralValue| (|t#1| $)) (ATTRIBUTE (|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|)) (SEQ (= (|f| |x| (|neutralValue| |f|)) |x|) (|exit| 1 (= (|f| (|neutralValue| |f|) |x|) |x|)))))))) -(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|SemiGroupOperatorCategory| |#1|) . T) ((|Type|) . T)) +(|Join| (|SemiGroupOperatorCategory| |t#1|) (CATEGORY |domain| (SIGNATURE |neutralValue| (|t#1| $)) (ATTRIBUTE (|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|)) (SEQ (= (|f| |x| #1=(|neutralValue| |f|)) |x|) (|exit| 1 (= (|f| #1# |x|) |x|)))))))) +(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|SemiGroupOperatorCategory| |#1|) . T)) ((|splitSquarefree| (((|Record| (|:| |normal| #1=(|Factored| |#2|)) (|:| |special| #1#)) |#2| #2=(|Mapping| |#2| |#2|)) 39 T ELT)) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| #2#) 12 T ELT)) (|normalDenom| ((|#2| #3=(|Fraction| |#2|) #2#) 13 T ELT)) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| #3#) (|:| |special| #3#)) #3# #2#) 48 T ELT))) (((|MonomialExtensionTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |split| ((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| #1=(|Mapping| |#2| |#2|))) (SIGNATURE |splitSquarefree| ((|Record| (|:| |normal| #2=(|Factored| |#2|)) (|:| |special| #2#)) |#2| #1#)) (SIGNATURE |normalDenom| (|#2| #3=(|Fraction| |#2|) #1#)) (SIGNATURE |decompose| ((|Record| (|:| |poly| |#2|) (|:| |normal| #3#) (|:| |special| #3#)) #3# #1#))) (|Field|) (|UnivariatePolynomialCategory| |#1|)) (T |MonomialExtensionTools|)) ((|decompose| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 #2=(|UnivariatePolynomialCategory| *5)) #3=(|ofCategory| *5 (|Field|)) (|isDomain| *2 (|Record| (|:| |poly| *6) (|:| |normal| #4=(|Fraction| *6)) (|:| |special| #4#))) (|isDomain| *1 (|MonomialExtensionTools| *5 *6)) (|isDomain| *3 #4#))) (|normalDenom| #1# (AND (|isDomain| *3 (|Fraction| *2)) (|isDomain| *4 (|Mapping| *2 *2)) (|ofCategory| *2 #2#) (|isDomain| *1 (|MonomialExtensionTools| *5 *2)) #3#)) (|splitSquarefree| #1# (AND #5=(|isDomain| *4 (|Mapping| *3 *3)) #6=(|ofCategory| *3 #2#) #3# (|isDomain| *2 (|Record| (|:| |normal| #7=(|Factored| *3)) (|:| |special| #7#))) #8=(|isDomain| *1 (|MonomialExtensionTools| *5 *3)))) (|split| #1# (AND #5# #6# #3# (|isDomain| *2 (|Record| (|:| |normal| *3) (|:| |special| *3))) #8#))) @@ -2237,22 +2237,22 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|unique| (#4=(#5=(|List| |#1|) $) 38 T ELT)) (|union| (#6=($ |#1| $) NIL T ELT) #7=(($ $ |#1|) NIL T ELT) (#8=($ $ $) 95 T ELT)) (|symmetricDifference| (#8# 99 T ELT)) (|subset?| (#2# 107 T ELT)) (|set| (#9=($ #5#) 26 T ELT) (#10=($) 17 T ELT)) (|select!| (#11=($ #12=(|Mapping| #3# |#1|) $) 86 #13=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| #14=(#11# NIL #13# ELT)) (|sample| (#10# NIL T CONST)) (|removeDuplicates!| (#15=($ $) 88 T ELT)) (|removeDuplicates| (#15# NIL #16=(AND #13# #17=(|has| |#1| (|BasicType|))) ELT)) (|remove!| (#6# 71 #13# ELT) (#11# 80 #13# ELT) (#18=($ |#1| $ #19=(|Integer|)) 78 T ELT) (#20=($ #12# $ #19#) 81 T ELT)) (|remove| (#6# NIL #16# ELT) #14# (#18# 83 T ELT) (#20# 84 T ELT)) (|reduce| ((|#1| #21=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #17# ELT) ((|#1| #21# $ |#1|) NIL T ELT) ((|#1| #21# $) NIL T ELT)) (|part?| (#2# 106 T ELT)) (|multiset| (#10# 15 T ELT) (($ |#1|) 28 T ELT) (#9# 23 T ELT)) (|members| (#4# 32 T ELT)) (|member?| ((#3# |#1| $) 66 #17# ELT)) (|map!| (#22=($ (|Mapping| |#1| |#1|) $) 91 T ELT)) (|map| (#22# 92 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|intersect| (#8# 97 T ELT)) (|inspect| (#23=(|#1| $) 63 T ELT)) (|insert!| (#6# 64 T ELT) (($ |#1| $ #24=(|NonNegativeInteger|)) 89 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|find| (((|Union| |#1| "failed") #12# $) NIL T ELT)) (|extract!| (#23# 62 T ELT)) (|every?| #25=((#3# #12# $) NIL T ELT)) (|eval| (($ $ (|List| #26=(|Equation| |#1|))) NIL #27=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ELT) (($ $ #26#) NIL #27# ELT) (($ $ |#1| |#1|) NIL #27# ELT) (($ $ #5# #5#) NIL #27# ELT)) (|eq?| #1#) (|empty?| ((#3# $) 57 T ELT)) (|empty| (#10# 14 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #24#))) $) 56 T ELT)) (|difference| #7# (#8# 98 T ELT)) (|dictionary| (#10# 16 T ELT) (#9# 25 T ELT)) (|count| ((#24# |#1| $) 69 #17# ELT) ((#24# #12# $) NIL T ELT)) (|copy| (#15# 82 T ELT)) (|convert| ((#28=(|InputForm|) $) 36 (|has| |#1| (|ConvertibleTo| #28#)) ELT)) (|construct| (#9# 22 T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT)) (|brace| (#9# 27 T ELT) (#10# 18 T ELT)) (|before?| #1#) (|bag| (#9# 24 T ELT)) (|any?| #25#) (= (#2# 103 T ELT)) (|#| ((#24# $) 68 T ELT))) (((|Multiset| |#1|) (|Join| (|MultisetAggregate| |#1|) (|FiniteAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |multiset| ($)) (SIGNATURE |multiset| ($ |#1|)) (SIGNATURE |multiset| ($ #1=(|List| |#1|))) (SIGNATURE |unique| (#1# $)) (SIGNATURE |remove| #2=($ |#1| $ #3=(|Integer|))) (SIGNATURE |remove| #4=($ (|Mapping| (|Boolean|) |#1|) $ #3#)) (SIGNATURE |remove!| #2#) (SIGNATURE |remove!| #4#))) (|SetCategory|)) (T |Multiset|)) ((|multiset| (*1 *1) #1=(AND #2=(|isDomain| *1 (|Multiset| *2)) #3=(|ofCategory| *2 #4=(|SetCategory|)))) (|multiset| #5=(*1 *1 *2) #1#) (|multiset| #5# (AND #6=(|isDomain| *2 (|List| *3)) #7=(|ofCategory| *3 #4#) #8=(|isDomain| *1 (|Multiset| *3)))) (|unique| (*1 *2 *1) (AND #6# #8# #7#)) (|remove| #9=(*1 *1 *2 *1 *3) #10=(AND #11=(|isDomain| *3 (|Integer|)) #2# #3#)) (|remove| #9# #12=(AND (|isDomain| *2 (|Mapping| (|Boolean|) *4)) #11# (|ofCategory| *4 #4#) (|isDomain| *1 (|Multiset| *4)))) (|remove!| #9# #10#) (|remove!| #9# #12#)) -((~= (#1=((|Boolean|) $ $) 18 T ELT)) (|union| (($ |#1| $) 71 T ELT) (($ $ |#1|) 70 T ELT) (#2=($ $ $) 69 T ELT)) (|symmetricDifference| (#2# 67 T ELT)) (|subset?| (#3=((|Boolean|) $ $) 68 T ELT)) (|set| (($ (|List| |#1|)) 63 T ELT) (#4=($) 62 T ELT)) (|select!| (($ (|Mapping| #5=(|Boolean|) |#1|) . #6=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #7=(|Boolean|) |#1|) . #8=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#9=($) 6 T CONST)) (|removeDuplicates!| (($ $) 55 T ELT)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #10=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #5# |#1|) . #6#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #10#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #7# |#1|) . #8#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|part?| (#3# 59 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 64 T ELT)) (|inspect| ((|#1| . #11=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT) (($ |#1| $ #12=(|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|extract!| ((|#1| . #11#) 37 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13=((|SetCategory|)))) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #13#)) ELT)) (|eq?| ((#14=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#14# $) 7 T ELT)) (|empty| (#9# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #12#))) $) 54 T ELT)) (|difference| (($ $ |#1|) 66 T ELT) (#2# 65 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#15=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #15#)) ELT)) (|construct| (($ (|List| |#1|)) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|brace| (($ (|List| |#1|)) 61 T ELT) (#4# 60 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (= (#1# 17 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 T ELT)) (|union| (#3=($ |#1| $) 71 T ELT) (#4=($ $ |#1|) 70 T ELT) (#5=($ $ $) 69 T ELT)) (|symmetricDifference| (#5# 67 T ELT)) (|subset?| (#1# 68 T ELT)) (|set| (#6=($ #7=(|List| |#1|)) 63 T ELT) (#8=($) 62 T ELT)) (|select!| (#9=($ (|Mapping| #2# |#1|) $) 42 #10=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (#9# 49 #10# ELT)) (|sample| (#8# 6 T CONST)) (|removeDuplicates!| (#11=($ $) 55 T ELT)) (|removeDuplicates| (#11# 51 #12=(AND (|has| |#1| (|BasicType|)) #10#) ELT)) (|remove!| (#3# 44 #10# ELT) (#9# 43 #10# ELT)) (|remove| (#3# 50 #12# ELT) (#9# 48 #10# ELT)) (|part?| (#1# 59 T ELT)) (|map!| (#13=($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (#13# 26 T ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#5# 64 T ELT)) (|inspect| (#14=(|#1| $) 35 T ELT)) (|insert!| (#3# 36 T ELT) (($ |#1| $ #15=(|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|extract!| (#14# 37 T ELT)) (|eval| (($ $ (|List| #16=(|Equation| |#1|))) 25 #17=(AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ELT) (($ $ #16#) 24 #17# ELT) (($ $ |#1| |#1|) 23 #17# ELT) (($ $ #7# #7#) 22 #17# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#8# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #15#))) $) 54 T ELT)) (|difference| (#4# 66 T ELT) (#5# 65 T ELT)) (|dictionary| (#8# 46 T ELT) (#6# 45 T ELT)) (|copy| (#11# 9 T ELT)) (|convert| ((#18=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #18#)) ELT)) (|construct| (#6# 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT)) (|brace| (#6# 61 T ELT) (#8# 60 T ELT)) (|before?| (#1# 19 T ELT)) (|bag| (#6# 38 T ELT)) (= (#1# 17 T ELT))) (((|MultisetAggregate| |#1|) (|Category|) (|SetCategory|)) (T |MultisetAggregate|)) NIL (|Join| (|MultiDictionary| |t#1|) (|SetAggregate| |t#1|)) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|MultiDictionary| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|MultiDictionary| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . 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T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|Functorial| |#1|) . T) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| |#2| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#2|) . T) ((|PartialDifferentialRing| |#2|) . T) ((|PartialDifferentialSpace| |#2|) . T) ((|PowerSeriesCategory| |#1| #1# |#2|) . T) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T)) +((|coefficient| #1=(*1 *1 *1 *2 *3) #2=(AND #3=(|isDomain| *3 #4=(|NonNegativeInteger|)) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *2)) #5=(|ofCategory| *4 #6=(|Ring|)) #7=(|ofCategory| *2 #8=(|OrderedSet|)))) (|coefficient| #1# #9=(AND (|isDomain| *2 (|List| *5)) (|isDomain| *3 (|List| #4#)) #10=(|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *5)) #5# #11=(|ofCategory| *5 #8#))) (|extend| #12=(*1 *1 *1 *2) (AND #13=(|isDomain| *2 #4#) (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *4)) #14=(|ofCategory| *3 #6#) (|ofCategory| *4 #8#))) (|monomial| #1# #2#) (|monomial| #1# #9#) (|order| #15=(*1 *2 *1 *3) (AND #16=(|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *4 *3)) #5# #17=(|ofCategory| *3 #8#) #13#)) (|order| (*1 *2 *1 *3 *2) (AND #13# #16# #5# #17#)) (|polynomial| #15# #18=(AND #3# #10# #5# #11# (|isDomain| *2 (|Polynomial| *4)))) (|polynomial| (*1 *2 *1 *3 *3) #18#) (|integrate| #12# (AND (|ofCategory| *1 (|MultivariateTaylorSeriesCategory| *3 *2)) #14# #7# (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))) +(|Join| (|PartialDifferentialRing| |t#2|) (|PowerSeriesCategory| |t#1| (|IndexedExponents| |t#2|) |t#2|) (|InnerEvalable| |t#2| $) (|Evalable| $) (CATEGORY |domain| (SIGNATURE |coefficient| #1=($ $ |t#2| #2=(|NonNegativeInteger|))) (SIGNATURE |coefficient| #3=($ $ (|List| |t#2|) (|List| #2#))) (SIGNATURE |extend| ($ $ #2#)) (SIGNATURE |monomial| #1#) (SIGNATURE |monomial| #3#) (SIGNATURE |order| (#2# $ |t#2|)) (SIGNATURE |order| (#2# $ |t#2| #2#)) (SIGNATURE |polynomial| (#4=(|Polynomial| |t#1|) $ #2#)) (SIGNATURE |polynomial| (#4# $ #2# #2#)) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ |t#2|)) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|IndexedExponents| |#2|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| #3=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #3#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|Functorial| |#1|) . T) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| |#2| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #3#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#2|) . T) ((|PartialDifferentialRing| |#2|) . T) ((|PartialDifferentialSpace| |#2|) . T) ((|PowerSeriesCategory| |#1| #1# |#2|) . T) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T)) ((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#) 30 T ELT) (((|Factored| |#4|) |#4|) 26 T ELT))) (((|MultivariateFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|PolynomialCategory| |#3| |#2| |#1|)) (T |MultivariateFactorize|)) ((|factor| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 (|OrderedSet|)) #3=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *6 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (|ofCategory| *7 #5=(|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *7)) (|isDomain| *3 #6#))) (|factor| #1# (AND #2# #3# #4# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultivariateFactorize| *4 *5 *6 *3)) (|ofCategory| *3 #5#)))) @@ -2262,27 +2262,27 @@ NIL ((|plenaryPower| (($ $ (|PositiveInteger|)) 17 T ELT))) (((|NonAssociativeAlgebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |plenaryPower| (|#1| |#1| (|PositiveInteger|)))) (|NonAssociativeAlgebra| |#2|) (|CommutativeRing|)) (T |NonAssociativeAlgebra&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 38 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 45 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#5=($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (#5# 34 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 31 T ELT) (($ $ $) 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #6#) 46 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ #5=(|PositiveInteger|)) 38 T ELT)) (|plenaryPower| (#4# 45 T ELT)) (|opposite?| (#1# 20 T ELT)) (|leftPower| (#4# 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#6=($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (#6# 34 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#6# 29 T ELT)) (+ (#6# 18 T ELT)) (** (#4# 40 T ELT)) (* (($ #5# $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 31 T ELT) (#6# 37 T ELT) (($ $ |#1|) 47 T ELT) (($ |#1| . #7#) 46 T ELT))) (((|NonAssociativeAlgebra| |#1|) (|Category|) (|CommutativeRing|)) (T |NonAssociativeAlgebra|)) ((|plenaryPower| (*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|NonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|))))) (|Join| (|NonAssociativeRng|) (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE |plenaryPower| ($ $ (|PositiveInteger|))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monad|) . T) ((|NonAssociativeRng|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|commutator| (#1=($ $ $) 10 T ELT)) (|associator| (($ $ $ $) 9 T ELT)) (|antiCommutator| (#1# 12 T ELT))) (((|NonAssociativeRng&| |#1|) (CATEGORY |package| (SIGNATURE |antiCommutator| #1=(|#1| |#1| |#1|)) (SIGNATURE |commutator| #1#) (SIGNATURE |associator| (|#1| |#1| |#1| |#1|))) (|NonAssociativeRng|)) (T |NonAssociativeRng&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 38 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftPower| (#4# 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (($ $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 40 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 37 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightPower| (#4=($ $ #5=(|PositiveInteger|)) 38 T ELT)) (|opposite?| (#1# 20 T ELT)) (|leftPower| (#4# 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#6=($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (#6# 34 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#6# 29 T ELT)) (+ (#6# 18 T ELT)) (** (#4# 40 T ELT)) (* (($ #5# $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (#6# 37 T ELT))) (((|NonAssociativeRng|) (|Category|)) (T |NonAssociativeRng|)) -((|associator| (*1 *1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|commutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|))) (|antiCommutator| (*1 *1 *1 *1) (|ofCategory| *1 (|NonAssociativeRng|)))) -(|Join| (|AbelianGroup|) (|Monad|) (CATEGORY |domain| (SIGNATURE |associator| ($ $ $ $)) (SIGNATURE |commutator| ($ $ $)) (SIGNATURE |antiCommutator| ($ $ $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|Monad|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|associator| (*1 *1 *1 *1 *1) #1=(|ofCategory| *1 (|NonAssociativeRng|))) (|commutator| #2=(*1 *1 *1 *1) #1#) (|antiCommutator| #2# #1#)) +(|Join| (|AbelianGroup|) (|Monad|) (CATEGORY |domain| (SIGNATURE |associator| ($ $ $ $)) (SIGNATURE |commutator| #1=($ $ $)) (SIGNATURE |antiCommutator| #1#))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|Monad|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) 10 T ELT))) (((|NonAssociativeRing&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|NonAssociativeRing|)) (T |NonAssociativeRing&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRecip| (#4=((|Union| $ "failed") $) 50 T ELT)) (|rightPower| (#5=($ $ (|PositiveInteger|)) 38 T ELT) (#6=($ $ (|NonNegativeInteger|)) 45 T ELT)) (|recip| (#4# 48 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|leftRecip| (#4# 49 T ELT)) (|leftPower| (#5# 39 T ELT) (#6# 46 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#7=($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 42 T CONST)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (#7# 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 43 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#5# 40 T ELT) (#6# 47 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 37 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rightRecip| (#5=((|Union| $ "failed") $) 50 T ELT)) (|rightPower| (#6=($ $ #7=(|PositiveInteger|)) 38 T ELT) (#8=($ $ #9=(|NonNegativeInteger|)) 45 T ELT)) (|recip| (#5# 48 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 44 T ELT)) (|leftRecip| (#5# 49 T ELT)) (|leftPower| (#6# 39 T ELT) (#8# 46 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|commutator| (#10=($ $ $) 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #11=(|Integer|)) 41 T ELT)) (|characteristic| ((#9#) 42 T CONST)) (|before?| (#1# 6 T ELT)) (|associator| (($ $ $ $) 36 T ELT)) (|antiCommutator| (#10# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 43 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#10# 29 T ELT)) (+ (#10# 18 T ELT)) (** (#6# 40 T ELT) (#8# 47 T ELT)) (* (($ #7# $) 17 T ELT) (($ #9# $) 21 T ELT) (($ #11# $) 31 T ELT) (#10# 37 T ELT))) (((|NonAssociativeRing|) (|Category|)) (T |NonAssociativeRing|)) -((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|NonAssociativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|NonAssociativeRing|))))) +((|characteristic| (*1 *2) (AND #1=(|ofCategory| *1 (|NonAssociativeRing|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #1#))) (|Join| (|NonAssociativeRng|) (|MonadWithUnit|) (CATEGORY |domain| (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|) (SIGNATURE |coerce| ($ (|Integer|))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|Monad|) . T) ((|MonadWithUnit|) . T) ((|NonAssociativeRng|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|Monad|) . T) ((|MonadWithUnit|) . T) ((|NonAssociativeRng|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|complexEigenvectors| (((|List| (|Record| (|:| |outval| #1=(|Complex| |#1|)) (|:| |outmult| #2=(|Integer|)) (|:| |outvect| (|List| (|Matrix| #1#))))) #3=(|Matrix| #4=(|Complex| (|Fraction| #2#))) |#1|) 33 T ELT)) (|complexEigenvalues| (((|List| #1#) #3# |#1|) 23 T ELT)) (|characteristicPolynomial| ((#5=(|Polynomial| #4#) #3# (|Symbol|)) 20 T ELT) ((#5# #3#) 19 T ELT))) (((|NumericComplexEigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (#1=(|Polynomial| #2=(|Complex| (|Fraction| #3=(|Integer|)))) #4=(|Matrix| #2#))) (SIGNATURE |characteristicPolynomial| (#1# #4# (|Symbol|))) (SIGNATURE |complexEigenvalues| ((|List| #5=(|Complex| |#1|)) #4# |#1|)) (SIGNATURE |complexEigenvectors| ((|List| (|Record| (|:| |outval| #5#) (|:| |outmult| #3#) (|:| |outvect| (|List| (|Matrix| #5#))))) #4# |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |NumericComplexEigenPackage|)) ((|complexEigenvectors| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Matrix| #3=(|Complex| (|Fraction| #4=(|Integer|))))) (|isDomain| *2 (|List| (|Record| (|:| |outval| #5=(|Complex| *4)) (|:| |outmult| #4#) (|:| |outvect| (|List| (|Matrix| #5#)))))) #6=(|isDomain| *1 (|NumericComplexEigenPackage| *4)) #7=(|ofCategory| *4 #8=(|Join| (|Field|) (|OrderedRing|))))) (|complexEigenvalues| #1# (AND #2# (|isDomain| *2 (|List| #5#)) #6# #7#)) (|characteristicPolynomial| #1# (AND #2# (|isDomain| *4 (|Symbol|)) #9=(|isDomain| *2 (|Polynomial| #3#)) (|isDomain| *1 (|NumericComplexEigenPackage| *5)) (|ofCategory| *5 #8#))) (|characteristicPolynomial| (*1 *2 *3) (AND #2# #9# #6# #7#))) @@ -2292,9 +2292,9 @@ NIL ((|leftRemainder| (#1=(|#1| |#1| |#1|) 28 T ELT)) (|leftQuotient| (#1# 27 T ELT)) (|leftLcm| (#1# 38 T ELT)) (|leftGcd| (#1# 33 T ELT)) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) 31 T ELT)) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 26 T ELT))) (((|NonCommutativeOperatorDivision| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|)) (SIGNATURE |leftQuotient| #1=(|#1| |#1| |#1|)) (SIGNATURE |leftRemainder| #1#) (SIGNATURE |leftExactQuotient| ((|Union| |#1| "failed") |#1| |#1|)) (SIGNATURE |leftGcd| #1#) (SIGNATURE |leftLcm| #1#)) (|MonogenicLinearOperator| |#2|) (|Field|)) (T |NonCommutativeOperatorDivision|)) ((|leftLcm| #1=(*1 *2 *2 *2) #2=(AND #3=(|ofCategory| *3 #4=(|Field|)) #5=(|isDomain| *1 (|NonCommutativeOperatorDivision| *2 *3)) #6=(|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|leftGcd| #1# #2#) (|leftExactQuotient| #1# (|partial| AND #3# #5# #6#)) (|leftRemainder| #1# #2#) (|leftQuotient| #1# #2#) (|leftDivide| (*1 *2 *3 *3) (AND (|ofCategory| *4 #4#) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|NonCommutativeOperatorDivision| *3 *4)) (|ofCategory| *3 (|MonogenicLinearOperator| *4))))) -((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) 27 T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) 26 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 28 T ELT)) (|writeByte!| (((|Maybe| #3=(|Byte|)) $ #3#) 25 T ELT)) (|readUInt8!| (((|Maybe| (|UInt8|)) $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| (((|Maybe| (|Int8|)) $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|readByte!| (((|Maybe| (|Byte|)) $) 14 T ELT)) (|isConnected?| (((|Boolean|) $) 32 T ELT)) (|connectTo| (((|Maybe| $) |#1| (|PortNumber|)) 33 T ELT)) (|close!| (($ $) 6 T ELT))) +((|writeUInt8!| ((#1=(|Maybe| #2=(|UInt8|)) $ #2#) 27 T ELT)) (|writeInt8!| ((#3=(|Maybe| #4=(|Int8|)) $ #4#) 26 T ELT)) (|writeBytes!| (#5=((|NonNegativeInteger|) $ (|ByteBuffer|)) 28 T ELT)) (|writeByte!| ((#6=(|Maybe| #7=(|Byte|)) $ #7#) 25 T ELT)) (|readUInt8!| ((#1# $) 12 T ELT)) (|readUInt32!| (((|Maybe| (|UInt32|)) $) 8 T ELT)) (|readUInt16!| (((|Maybe| (|UInt16|)) $) 10 T ELT)) (|readInt8!| ((#3# $) 13 T ELT)) (|readInt32!| (((|Maybe| (|Int32|)) $) 9 T ELT)) (|readInt16!| (((|Maybe| (|Int16|)) $) 11 T ELT)) (|readBytes!| (#5# 7 T ELT)) (|readByte!| ((#6# $) 14 T ELT)) (|isConnected?| (((|Boolean|) $) 32 T ELT)) (|connectTo| (((|Maybe| $) |#1| (|PortNumber|)) 33 T ELT)) (|close!| (($ $) 6 T ELT))) (((|NetworkClientSocket| |#1|) (|Category|) (|SetCategory|)) (T |NetworkClientSocket|)) -((|connectTo| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PortNumber|)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|NetworkClientSocket| *3)))) (|isConnected?| (*1 *2 *1) (AND (|ofCategory| *1 (|NetworkClientSocket| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) +((|connectTo| (*1 *2 *3 *4) (AND (|isDomain| *4 (|PortNumber|)) #1=(|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Maybe| *1)) #2=(|ofCategory| *1 (|NetworkClientSocket| *3)))) (|isConnected?| (*1 *2 *1) (AND #2# #1# (|isDomain| *2 (|Boolean|))))) (|Join| (|InputOutputByteConduit|) (CATEGORY |domain| (SIGNATURE |connectTo| ((|Maybe| $) |t#1| (|PortNumber|))) (SIGNATURE |isConnected?| ((|Boolean|) $)))) (((|Conduit|) . T) ((|InputByteConduit|) . T) ((|InputOutputByteConduit|) . T) ((|OutputByteConduit|) . T)) ((|localIntegralBasis| ((#1=(|Record| (|:| |basis| #2=(|Matrix| #3=(|Integer|))) (|:| |basisDen| #3#) (|:| |basisInv| #2#)) #3#) 72 T ELT)) (|integralBasis| ((#1#) 70 T ELT)) (|discriminant| ((#3#) 86 T ELT))) @@ -2343,11 +2343,11 @@ NIL ((|eulerE| (#1=(|#1| (|NonNegativeInteger|) |#1|) 33 #2=(|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|cyclotomic| (#1# 23 T ELT)) (|bernoulliB| (#1# 35 #2# ELT))) (((|NumberTheoreticPolynomialFunctions| |#1|) (CATEGORY |package| (SIGNATURE |cyclotomic| #1=(|#1| (|NonNegativeInteger|) |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |bernoulliB| #1#) (SIGNATURE |eulerE| #1#)) |%noBranch|)) (|CommutativeRing|)) (T |NumberTheoreticPolynomialFunctions|)) ((|eulerE| #1=(*1 *2 *3 *2) #2=(AND #3=(|isDomain| *3 (|NonNegativeInteger|)) #4=(|isDomain| *1 (|NumberTheoreticPolynomialFunctions| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) #5=(|ofCategory| *2 (|CommutativeRing|)))) (|bernoulliB| #1# #2#) (|cyclotomic| #1# (AND #3# #4# #5#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) ((#2=(|List| $) (|List| |#4|) #3=(|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #4=($)) 39 T ELT)) (|trivialIdeal?| (#5=(#6=(|Boolean|) $) 32 T ELT)) (|triangular?| (#5# 23 (|has| |#1| . #7=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#8=(|Boolean|) |#4| . #9=($)) 107 T ELT) (#10=(#8# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #11=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) . #12=(#13=(|:| |tower| $)))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #14=(|Boolean|) |#4|) . #15=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #16=(#17="failed")) $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#5# 28 (|has| |#1| . #7#) ELT)) (|roughSubIdeal?| (#19=(#6# $ $) 30 (|has| |#1| . #7#) ELT)) (|roughEqualIdeals?| (#19# 29 (|has| |#1| . #7#) ELT)) (|roughBase?| (#5# 31 (|has| |#1| . #7#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #20=($)) 24 (|has| |#1| . #7#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #20#) 25 (|has| |#1| . #7#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#21=(|Union| $ #17#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #11#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #22=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #22#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #14# |#4|) . #15#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #7#) ELT)) (|reduced?| ((#8# |#4| $ (|Mapping| #8# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #11#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #23=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| ((#3# |#4| . #24=($)) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| ((#3# |#4| . #24#) 142 T ELT)) (|purelyAlgebraic?| ((#3# |#4| . #24#) 146 T ELT) ((#3# $) 143 T ELT)) (|normalized?| ((#8# |#4| . #9#) 110 T ELT) (#10# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#25=(|Boolean|) |#4| $) 53 (|has| |#4| . #23#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #4#) 38 T ELT)) (|mainVariable?| ((#6# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #2#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) . #12#)) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #16#) . #26=($)) 89 T ELT)) (|invertibleSet| ((#2# |#4| . #27=($)) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #2#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #13#)) |#4| $) 140 T ELT) ((#3# |#4| . #24#) 139 T ELT)) (|intersect| ((#2# |#4| . #27#) 134 T ELT) ((#2# (|List| |#4|) . #28=($)) 133 T ELT) ((#2# (|List| |#4|) . #29=(#2#)) 132 T ELT) ((#2# |#4| . #30=(#2#)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#8# |#4| . #9#) 105 T ELT) (#10# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #11#) 96 T ELT)) (|infRittWu?| ((#8# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #7#) ELT)) (|headReduced?| ((#8# |#4| . #9#) 106 T ELT) (#10# 102 T ELT)) (|headReduce| ((|#4| |#4| . #11#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #16#) . #26#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #25# |#4|) $) 51 T ELT)) (|extendIfCan| ((#21# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) ((#2# |#4| . #27#) 124 T ELT) ((#2# |#4| . #30#) 123 T ELT) ((#2# (|List| |#4|) . #28#) 122 T ELT) ((#2# (|List| |#4|) . #29#) 121 T ELT)) (|every?| ((#25# (|Mapping| #25# |#4|) . #31=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT)) (|eq?| ((#33=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#33# $) 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#34=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#35=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #23#) ELT) ((#35# (|Mapping| #25# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#36=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #36#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #37=($)) 13 T ELT) (((|List| |#4|) . #37#) 43 T ELT)) (|coHeight| (#34# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #38=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #39=(#17#)) (|List| |#4|) (|Mapping| #8# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #38# (|:| |top| (|List| |#4|))) . #39#) (|List| |#4|) (|Mapping| #8# |#4|) (|Mapping| #8# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#8# $ (|Mapping| #8# |#4| (|List| |#4|))) 104 T ELT)) (|augment| ((#2# |#4| . #27#) 130 T ELT) ((#2# |#4| . #30#) 129 T ELT) ((#2# (|List| |#4|) . #28#) 128 T ELT) ((#2# (|List| |#4|) . #29#) 127 T ELT)) (|any?| ((#25# (|Mapping| #25# |#4|) . #31#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| ((#3# |#4| . #24#) 144 T ELT)) (|algebraic?| ((#8# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#35# $) 44 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #3=(|:| |open| #4=(|List| |#4|)))) #4#) 91 T ELT)) (|zeroSetSplit| ((#5=(|List| $) #4#) 92 T ELT) ((#5# #4# #2#) 120 T ELT)) (|variables| (#6=((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (#7=(#2# $) 32 T ELT)) (|triangular?| (#7# 23 #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| (#9=(#2# |#4| $) 107 T ELT) (#7# 103 T ELT)) (|stronglyReduce| (#10=(|#4| |#4| $) 98 T ELT)) (|squareFreePart| ((#11=(|List| (|Record| (|:| |val| |#4|) #12=(|:| |tower| $))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (#13=($ #14=(|Mapping| #2# |#4|) $) 67 #15=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#16=(|Union| |#4| #17="failed") $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#7# 28 #8# ELT)) (|roughSubIdeal?| (#1# 30 #8# ELT)) (|roughEqualIdeals?| (#1# 29 #8# ELT)) (|roughBase?| (#7# 31 #8# ELT)) (|rewriteSetWithReduction| ((#4# #4# $ #19=(|Mapping| |#4| |#4| |#4|) #20=(|Mapping| #2# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (#21=(#4# #4# $) 24 #8# ELT)) (|rewriteIdealWithHeadRemainder| (#21# 25 #8# ELT)) (|retractIfCan| ((#22=(|Union| $ #17#) #4#) 42 T ELT)) (|retract| (#23=($ #4#) 41 T ELT)) (|rest| ((#22# $) 88 T ELT)) (|removeZero| (#10# 95 T ELT)) (|removeDuplicates| (#24=($ $) 69 #25=(AND #26=(|has| |#4| (|BasicType|)) #15#) ELT)) (|remove| (#27=($ |#4| $) 68 #25# ELT) (#13# 66 #15# ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #28=(|:| |den| |#1|)) |#4| $) 26 #8# ELT)) (|reduced?| ((#2# |#4| $ #20#) 108 T ELT)) (|reduceByQuasiMonic| (#10# 93 T ELT)) (|reduce| ((|#4| #19# $ |#4| |#4|) 54 #26# ELT) ((|#4| #19# $ |#4|) 50 T ELT) ((|#4| #19# $) 49 T ELT) ((|#4| |#4| $ #19# #20#) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #4#) #3#) $) 111 T ELT)) (|purelyTranscendental?| (#9# 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#9# 142 T ELT)) (|purelyAlgebraic?| (#9# 146 T ELT) (#7# 143 T ELT)) (|normalized?| (#9# 110 T ELT) (#7# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (#29=(#4# $) 48 T ELT)) (|member?| (#9# 53 #26# ELT)) (|map!| (#30=($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (#30# 60 T ELT)) (|mainVariables| (#6# 38 T ELT)) (|mainVariable?| (#31=(#2# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #5#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| ((#11# |#4| |#4| $) 136 T ELT)) (|last| (#32=(#16# $) 89 T ELT)) (|invertibleSet| (#33=(#5# |#4| $) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #2# #5#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #2#) #12#)) |#4| $) 140 T ELT) (#9# 139 T ELT)) (|intersect| (#33# 134 T ELT) (#34=(#5# #4# $) 133 T ELT) (#35=(#5# #4# #5#) 132 T ELT) (#36=(#5# |#4| #5#) 131 T ELT)) (|internalAugment| (#27# 126 T ELT) (($ #4# $) 125 T ELT)) (|initials| (#29# 113 T ELT)) (|initiallyReduced?| (#9# 105 T ELT) (#7# 101 T ELT)) (|initiallyReduce| (#10# 96 T ELT)) (|infRittWu?| (#1# 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #28#) |#4| $) 27 #8# ELT)) (|headReduced?| (#9# 106 T ELT) (#7# 102 T ELT)) (|headReduce| (#10# 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (#32# 90 T ELT)) (|find| ((#16# #14# $) 51 T ELT)) (|extendIfCan| ((#22# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) (#33# 124 T ELT) (#36# 123 T ELT) (#34# 122 T ELT) (#35# 121 T ELT)) (|every?| (#37=(#2# #14# $) 46 T ELT)) (|eval| (($ $ #4# #4#) 64 #38=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) 63 #38# ELT) (($ $ #39=(|Equation| |#4|)) 62 #38# ELT) (($ $ (|List| #39#)) 61 #38# ELT)) (|eq?| (#1# 55 T ELT)) (|empty?| (#7# 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#40=(#41=(|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#41# |#4| $) 52 #26# ELT) ((#41# #14# $) 47 T ELT)) (|copy| (#24# 56 T ELT)) (|convert| ((#42=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #42#)) ELT)) (|construct| (#23# 65 T ELT)) (|collectUpper| (#43=($ $ |#3|) 34 T ELT)) (|collectUnder| (#43# 36 T ELT)) (|collectQuasiMonic| (#24# 94 T ELT)) (|collect| (#43# 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#29# 43 T ELT)) (|coHeight| (#40# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| ((#44=(|Union| (|Record| (|:| |bas| $) (|:| |top| #4#)) #17#) #4# #20#) 115 T ELT) ((#44# #4# #14# #20#) 114 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#4| #4#)) 104 T ELT)) (|augment| (#33# 130 T ELT) (#36# 129 T ELT) (#34# 128 T ELT) (#35# 127 T ELT)) (|any?| (#37# 45 T ELT)) (|algebraicVariables| (#6# 87 T ELT)) (|algebraicCoefficients?| (#9# 144 T ELT)) (|algebraic?| (#31# 86 T ELT)) (= (#1# 8 T ELT)) (|#| (#40# 44 T ELT))) (((|NormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |NormalizedTriangularSetCategory|)) NIL (|Join| (|RegularTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|)) -(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) +(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) ((|numericIfCan| ((#1=(|Union| #2=(|Float|) #3="failed") #4=(|Expression| |#1|) #5=(|PositiveInteger|)) 60 #6=(AND #7=(|has| |#1| (|IntegralDomain|)) (|has| |#1| (|OrderedSet|))) ELT) ((#1# #4#) 52 #6# ELT) ((#1# #8=(|Fraction| #9=(|Polynomial| |#1|)) #5#) 39 #7# ELT) ((#1# #8#) 35 #7# ELT) ((#1# #9# #5#) 30 #10=(|has| |#1| (|Ring|)) ELT) ((#1# #9#) 24 #10# ELT)) (|numeric| ((#2# #4# #5#) 92 #6# ELT) ((#2# #4#) 87 #6# ELT) ((#2# #8# #5#) 84 #7# ELT) ((#2# #8#) 81 #7# ELT) ((#2# #9# #5#) 80 #10# ELT) ((#2# #9#) 77 #10# ELT) ((#2# |#1| #5#) 73 T ELT) ((#2# |#1|) 22 T ELT)) (|complexNumericIfCan| ((#11=(|Union| #12=(|Complex| #2#) #3#) #13=(|Expression| #14=(|Complex| |#1|)) #5#) 68 #6# ELT) ((#11# #13#) 58 #6# ELT) ((#11# #4# #5#) 61 #6# ELT) ((#11# #4#) 59 #6# ELT) ((#11# #15=(|Fraction| #16=(|Polynomial| #14#)) #5#) 44 #7# ELT) ((#11# #15#) 43 #7# ELT) ((#11# #8# #5#) 38 #7# ELT) ((#11# #8#) 37 #7# ELT) ((#11# #9# #5#) 28 #10# ELT) ((#11# #9#) 26 #10# ELT) ((#11# #16# #5#) 18 #17=(|has| |#1| (|CommutativeRing|)) ELT) ((#11# #16#) 15 #17# ELT)) (|complexNumeric| ((#12# #13# #5#) 95 #6# ELT) ((#12# #13#) 94 #6# ELT) ((#12# #4# #5#) 93 #6# ELT) ((#12# #4#) 91 #6# ELT) ((#12# #15# #5#) 86 #7# ELT) ((#12# #15#) 85 #7# ELT) ((#12# #8# #5#) 83 #7# ELT) ((#12# #8#) 82 #7# ELT) ((#12# #9# #5#) 79 #10# ELT) ((#12# #9#) 78 #10# ELT) ((#12# #16# #5#) 75 #17# ELT) ((#12# #16#) 74 #17# ELT) ((#12# #14# #5#) 17 #17# ELT) ((#12# #14#) 13 #17# ELT) ((#12# |#1| #5#) 27 T ELT) ((#12# |#1|) 25 T ELT))) (((|Numeric| |#1|) (CATEGORY |package| (SIGNATURE |numeric| (#1=(|Float|) |#1|)) (SIGNATURE |numeric| (#1# |#1| #2=(|PositiveInteger|))) (SIGNATURE |complexNumeric| (#3=(|Complex| #1#) |#1|)) (SIGNATURE |complexNumeric| (#3# |#1| #2#)) (IF #4=(|has| |#1| (|CommutativeRing|)) (PROGN (SIGNATURE |complexNumeric| (#3# #5=(|Complex| |#1|))) (SIGNATURE |complexNumeric| (#3# #5# #2#)) (SIGNATURE |complexNumeric| (#3# #6=(|Polynomial| #5#))) (SIGNATURE |complexNumeric| (#3# #6# #2#))) |%noBranch|) (IF #7=(|has| |#1| (|Ring|)) (PROGN (SIGNATURE |numeric| (#1# #8=(|Polynomial| |#1|))) (SIGNATURE |numeric| (#1# #8# #2#)) (SIGNATURE |complexNumeric| (#3# #8#)) (SIGNATURE |complexNumeric| (#3# #8# #2#))) |%noBranch|) (IF #9=(|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |numeric| (#1# #10=(|Fraction| #8#))) (SIGNATURE |numeric| (#1# #10# #2#)) (SIGNATURE |complexNumeric| (#3# #10#)) (SIGNATURE |complexNumeric| (#3# #10# #2#)) (SIGNATURE |complexNumeric| (#3# #11=(|Fraction| #6#))) (SIGNATURE |complexNumeric| (#3# #11# #2#)) (IF #12=(|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |numeric| (#1# #13=(|Expression| |#1|))) (SIGNATURE |numeric| (#1# #13# #2#)) (SIGNATURE |complexNumeric| (#3# #13#)) (SIGNATURE |complexNumeric| (#3# #13# #2#)) (SIGNATURE |complexNumeric| (#3# #14=(|Expression| #5#))) (SIGNATURE |complexNumeric| (#3# #14# #2#))) |%noBranch|)) |%noBranch|) (IF #4# (PROGN (SIGNATURE |complexNumericIfCan| (#15=(|Union| #3# #16="failed") #6#)) (SIGNATURE |complexNumericIfCan| (#15# #6# #2#))) |%noBranch|) (IF #7# (PROGN (SIGNATURE |numericIfCan| (#17=(|Union| #1# #16#) #8#)) (SIGNATURE |numericIfCan| (#17# #8# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #8#)) (SIGNATURE |complexNumericIfCan| (#15# #8# #2#))) |%noBranch|) (IF #9# (PROGN (SIGNATURE |numericIfCan| (#17# #10#)) (SIGNATURE |numericIfCan| (#17# #10# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #10#)) (SIGNATURE |complexNumericIfCan| (#15# #10# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #11#)) (SIGNATURE |complexNumericIfCan| (#15# #11# #2#)) (IF #12# (PROGN (SIGNATURE |numericIfCan| (#17# #13#)) (SIGNATURE |numericIfCan| (#17# #13# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #13#)) (SIGNATURE |complexNumericIfCan| (#15# #13# #2#)) (SIGNATURE |complexNumericIfCan| (#15# #14#)) (SIGNATURE |complexNumericIfCan| (#15# #14# #2#))) |%noBranch|)) |%noBranch|)) (|ConvertibleTo| #1#)) (T |Numeric|)) ((|complexNumericIfCan| #1=(*1 *2 *3 *4) (|partial| AND #2=(|isDomain| *3 (|Expression| #3=(|Complex| *5))) #4=(|isDomain| *4 (|PositiveInteger|)) #5=(|ofCategory| *5 #6=(|IntegralDomain|)) #7=(|ofCategory| *5 #8=(|OrderedSet|)) #9=(|ofCategory| *5 #10=(|ConvertibleTo| #11=(|Float|))) #12=(|isDomain| *2 (|Complex| #11#)) #13=(|isDomain| *1 (|Numeric| *5)))) (|complexNumericIfCan| #14=(*1 *2 *3) (|partial| AND #15=(|isDomain| *3 (|Expression| #16=(|Complex| *4))) #17=(|ofCategory| *4 #6#) #18=(|ofCategory| *4 #8#) #19=(|ofCategory| *4 #10#) #12# #20=(|isDomain| *1 (|Numeric| *4)))) (|complexNumericIfCan| #1# (|partial| AND #21=(|isDomain| *3 (|Expression| *5)) #4# #5# #7# #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #22=(|isDomain| *3 (|Expression| *4)) #17# #18# #19# #12# #20#)) (|numericIfCan| #1# (|partial| AND #21# #4# #5# #7# #23=(|ofCategory| *5 #24=(|ConvertibleTo| *2)) #25=(|isDomain| *2 #11#) #13#)) (|numericIfCan| #14# (|partial| AND #22# #17# #18# #26=(|ofCategory| *4 #24#) #25# #20#)) (|complexNumericIfCan| #1# (|partial| AND #27=(|isDomain| *3 (|Fraction| #28=(|Polynomial| #3#))) #4# #5# #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #29=(|isDomain| *3 (|Fraction| #30=(|Polynomial| #16#))) #17# #19# #12# #20#)) (|complexNumericIfCan| #1# (|partial| AND #31=(|isDomain| *3 (|Fraction| #32=(|Polynomial| *5))) #4# #5# #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #33=(|isDomain| *3 (|Fraction| #34=(|Polynomial| *4))) #17# #19# #12# #20#)) (|numericIfCan| #1# (|partial| AND #31# #4# #5# #23# #25# #13#)) (|numericIfCan| #14# (|partial| AND #33# #17# #26# #25# #20#)) (|complexNumericIfCan| #1# (|partial| AND #35=(|isDomain| *3 #32#) #4# #36=(|ofCategory| *5 #37=(|Ring|)) #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #38=(|isDomain| *3 #34#) #39=(|ofCategory| *4 #37#) #19# #12# #20#)) (|numericIfCan| #1# (|partial| AND #35# #4# #36# #23# #25# #13#)) (|numericIfCan| #14# (|partial| AND #38# #39# #26# #25# #20#)) (|complexNumericIfCan| #1# (|partial| AND #40=(|isDomain| *3 #28#) #4# #41=(|ofCategory| *5 #42=(|CommutativeRing|)) #9# #12# #13#)) (|complexNumericIfCan| #14# (|partial| AND #43=(|isDomain| *3 #30#) #44=(|ofCategory| *4 #42#) #19# #12# #20#)) (|complexNumeric| #1# (AND #2# #4# #5# #7# #9# #12# #13#)) (|complexNumeric| #14# (AND #15# #17# #18# #19# #12# #20#)) (|complexNumeric| #1# (AND #21# #4# #5# #7# #9# #12# #13#)) (|complexNumeric| #14# (AND #22# #17# #18# #19# #12# #20#)) (|numeric| #1# (AND #21# #4# #5# #7# #23# #25# #13#)) (|numeric| #14# (AND #22# #17# #18# #26# #25# #20#)) (|complexNumeric| #1# (AND #27# #4# #5# #9# #12# #13#)) (|complexNumeric| #14# (AND #29# #17# #19# #12# #20#)) (|complexNumeric| #1# (AND #31# #4# #5# #9# #12# #13#)) (|complexNumeric| #14# (AND #33# #17# #19# #12# #20#)) (|numeric| #1# (AND #31# #4# #5# #23# #25# #13#)) (|numeric| #14# (AND #33# #17# #26# #25# #20#)) (|complexNumeric| #1# (AND #35# #4# #36# #9# #12# #13#)) (|complexNumeric| #14# (AND #38# #39# #19# #12# #20#)) (|numeric| #1# (AND #35# #4# #36# #23# #25# #13#)) (|numeric| #14# (AND #38# #39# #26# #25# #20#)) (|complexNumeric| #1# (AND #40# #4# #41# #9# #12# #13#)) (|complexNumeric| #14# (AND #43# #44# #19# #12# #20#)) (|complexNumeric| #1# (AND (|isDomain| *3 #3#) #4# #41# #9# #12# #13#)) (|complexNumeric| #14# (AND (|isDomain| *3 #16#) #44# #19# #12# #20#)) (|complexNumeric| #1# (AND #4# #12# #45=(|isDomain| *1 (|Numeric| *3)) #46=(|ofCategory| *3 #10#))) (|complexNumeric| #14# (AND #12# #45# #46#)) (|numeric| #1# (AND #4# #25# #45# #47=(|ofCategory| *3 #24#))) (|numeric| #14# (AND #25# #45# #47#))) @@ -2366,42 +2366,42 @@ NIL ((|sign| (((|Integer|) $) 17 T ELT)) (|negative?| (((|Boolean|) $) 10 T ELT)) (|abs| (($ $) 19 T ELT))) (((|OrderedAbelianGroup&| |#1|) (CATEGORY |package| (SIGNATURE |abs| (|#1| |#1|)) (SIGNATURE |sign| ((|Integer|) |#1|)) (SIGNATURE |negative?| ((|Boolean|) |#1|))) (|OrderedAbelianGroup|)) (T |OrderedAbelianGroup&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sign| (((|Integer|) $) 39 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|negative?| (((|Boolean|) $) 40 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|abs| (($ $) 38 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 43 T ELT) (($ $) 42 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 41 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sign| ((#4=(|Integer|) $) 39 T ELT)) (|sample| (#5=($) 30 T CONST)) (|positive?| (#3# 28 T ELT)) (|opposite?| (#1# 33 T ELT)) (|negative?| (#3# 40 T ELT)) (|min| (#6=($ $ $) 23 T ELT)) (|max| (#6# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|abs| (#7=($ $) 38 T ELT)) (|Zero| (#5# 29 T CONST)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT)) (- (#6# 43 T ELT) (#7# 42 T ELT)) (+ (#6# 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ #4# $) 41 T ELT))) (((|OrderedAbelianGroup|) (|Category|)) (T |OrderedAbelianGroup|)) -((|negative?| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Boolean|)))) (|sign| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Integer|)))) (|abs| (*1 *1 *1) (|ofCategory| *1 (|OrderedAbelianGroup|)))) +((|negative?| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|OrderedAbelianGroup|)) (|isDomain| *2 (|Boolean|)))) (|sign| #1# (AND #2# (|isDomain| *2 (|Integer|)))) (|abs| (*1 *1 *1) #2#)) (|Join| (|OrderedCancellationAbelianMonoid|) (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |negative?| ((|Boolean|) $)) (SIGNATURE |sign| ((|Integer|) $)) (SIGNATURE |abs| ($ $)))) -(((|AbelianGroup|) . 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T)) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT)) (+ (#2# 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT))) (((|OrderedAbelianSemiGroup|) (|Category|)) (T |OrderedAbelianSemiGroup|)) NIL (|Join| (|OrderedSet|) (|AbelianSemiGroup|)) -(((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . 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109 (|has| |#1| . #8#) ELT) ((#9# . #11#) 106 (|has| |#1| . #10#) ELT) ((|#1| . #11#) 105 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|real| ((|#1| $) 94 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 81 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 83 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 82 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|random| (($) 71 (|has| |#1| . #3#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 85 T ELT)) (|norm| ((|#1| $) 86 T ELT)) (|min| (#12=($ $ $) 72 (|has| |#1| . #13=((|OrderedSet|))) ELT)) (|max| (#12# 73 (|has| |#1| . #13#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 96 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 70 (|has| |#1| . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 80 (|has| |#1| (|Field|)) ELT)) (|index| (($ #14#) 69 (|has| |#1| . #3#) ELT)) (|imagk| ((|#1| $) 91 T ELT)) (|imagj| ((|#1| $) 92 T ELT)) (|imagi| ((|#1| $) 93 T ELT)) (|imagK| ((|#1| $) 87 T ELT)) (|imagJ| ((|#1| $) 88 T ELT)) (|imagI| ((|#1| $) 89 T ELT)) (|imagE| ((|#1| $) 90 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 102 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 101 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|Equation| |#1|)) 100 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| (|Equation| |#1|))) 99 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ (|List| #15=(|Symbol|)) (|List| |#1|)) 98 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT) (($ $ #15# |#1|) 97 (|has| |#1| (|InnerEvalable| #15# |#1|)) ELT)) (|elt| (($ $ |#1|) 103 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| (((|InputForm|) $) 78 (|has| |#1| (|ConvertibleTo| (|InputForm|))) ELT)) (|conjugate| (($ $) 95 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 53 T ELT) (($ #9#) 108 (|has| |#1| . #10#) ELT)) (|charthRoot| (((|Maybe| $) $) 79 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| ((|#1| $) 84 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#16=((|Boolean|) $ $) 74 (|has| |#1| . #13#) ELT)) (> (#16# 76 (|has| |#1| . #13#) ELT)) (= (#1# 8 T ELT)) (<= (#16# 75 (|has| |#1| . #13#) ELT)) (< (#16# 77 (|has| |#1| . #13#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #17#) 54 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| ((#4=(|Maybe| $) $ $) 26 T ELT)) (|size| (#5=(#6=(|NonNegativeInteger|)) 68 #7=(|has| |#1| (|Finite|)) ELT)) (|sample| (#8=($) 23 T CONST)) (|retractIfCan| (((|Union| #9=(|Integer|) . #10=(#11="failed")) . #12=($)) 110 #13=(|has| |#1| (|RetractableTo| #9#)) ELT) (#14=((|Union| #15=(|Fraction| #9#) #11#) $) 107 #16=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| |#1| . #10#) . #12#) 104 T ELT)) (|retract| ((#9# . #17=($)) 109 #13# ELT) (#18=(#15# $) 106 #16# ELT) (#19=(|#1| . #17#) 105 T ELT)) (|recip| (((|Union| $ #11#) $) 43 T ELT)) (|real| (#19# 94 T ELT)) (|rationalIfCan| (#14# 81 #20=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#3# 83 #20# ELT)) (|rational| (#18# 82 #20# ELT)) (|random| (#8# 71 #7# ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 85 T ELT)) (|norm| (#19# 86 T ELT)) (|min| (#21=($ $ $) 72 #22=(|has| |#1| (|OrderedSet|)) ELT)) (|max| (#21# 73 #22# ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 96 T ELT)) (|lookup| ((#23=(|PositiveInteger|) $) 70 #7# ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#24=($ $) 80 (|has| |#1| (|Field|)) ELT)) (|index| (($ #23#) 69 #7# ELT)) (|imagk| (#19# 91 T ELT)) (|imagj| (#19# 92 T ELT)) (|imagi| (#19# 93 T ELT)) (|imagK| (#19# 87 T ELT)) (|imagJ| (#19# 88 T ELT)) (|imagI| (#19# 89 T ELT)) (|imagE| (#19# 90 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ #25=(|List| |#1|) #25#) 102 #26=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 101 #26# ELT) (($ $ #27=(|Equation| |#1|)) 100 #26# ELT) (($ $ (|List| #27#)) 99 #26# ELT) (($ $ (|List| #28=(|Symbol|)) #25#) 98 #29=(|has| |#1| (|InnerEvalable| #28# |#1|)) ELT) (($ $ #28# |#1|) 97 #29# ELT)) (|elt| (#30=($ $ |#1|) 103 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| ((#31=(|InputForm|) $) 78 (|has| |#1| (|ConvertibleTo| #31#)) ELT)) (|conjugate| (#24# 95 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #9#) 42 T ELT) (($ |#1|) 53 T ELT) (($ #15#) 108 #16# ELT)) (|charthRoot| ((#4# $) 79 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (#5# 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|abs| (#19# 84 (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#8# 24 T CONST)) (|One| (#8# 46 T CONST)) (>= (#1# 74 #22# ELT)) (> (#1# 76 #22# ELT)) (= (#1# 8 T ELT)) (<= (#1# 75 #22# ELT)) (< (#1# 77 #22# ELT)) (- (#24# 30 T ELT) (#21# 29 T ELT)) (+ (#21# 18 T ELT)) (** (($ $ #23#) 36 T ELT) (($ $ #6#) 44 T ELT)) (* (($ #23# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #9# . #32=($)) 31 T ELT) (#21# 35 T ELT) (#30# 55 T ELT) (($ |#1| . #32#) 54 T ELT))) (((|OctonionCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |OctonionCategory|)) -((|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagi| (*1 *2 *1) (AND (|ofCategory| *1 (|OctonionCategory| *2)) (|ofCategory| *2 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(|has| |t#1| (|Field|)) (SIGNATURE |inv| ($ $)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Finite|) |has| |#1| (|Finite|)) ((|FullyEvalableOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sample| (#3=($) 30 T CONST)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (+ (($ $ $) 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT))) +((|conjugate| #1=(*1 *1 *1) #2=(AND #3=(|ofCategory| *1 (|OctonionCategory| *2)) #4=(|ofCategory| *2 #5=(|CommutativeRing|)))) (|real| #6=(*1 *2 *1) #2#) (|imagi| #6# #2#) (|imagj| #6# #2#) (|imagk| #6# #2#) (|imagE| #6# #2#) (|imagI| #6# #2#) (|imagJ| #6# #2#) (|imagK| #6# #2#) (|norm| #6# #2#) (|octon| (*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) #2#) (|abs| #6# (AND #3# #4# (|ofCategory| *2 (|RealNumberSystem|)))) (|rational?| #6# (AND #7=(|ofCategory| *1 (|OctonionCategory| *3)) #8=(|ofCategory| *3 #5#) #9=(|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| #6# (AND #7# #8# #9# #10=(|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| #6# (|partial| AND #7# #8# #9# #10#)) (|inv| #1# (AND #3# #4# (|ofCategory| *2 (|Field|))))) +(|Join| (|Algebra| |t#1|) (|FullyRetractableTo| |t#1|) (|FullyEvalableOver| |t#1|) (CATEGORY |domain| (SIGNATURE |conjugate| #1=($ $)) (SIGNATURE |real| #2=(|t#1| $)) (SIGNATURE |imagi| #2#) (SIGNATURE |imagj| #2#) (SIGNATURE |imagk| #2#) (SIGNATURE |imagE| #2#) (SIGNATURE |imagI| #2#) (SIGNATURE |imagJ| #2#) (SIGNATURE |imagK| #2#) (SIGNATURE |norm| #2#) (SIGNATURE |octon| ($ |t#1| |t#1| |t#1| |t#1| |t#1| |t#1| |t#1| |t#1|)) (IF (|has| |t#1| #3=(|Finite|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |t#1| #4=(|OrderedSet|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |t#1| #5=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #5#) |%noBranch|) (IF (|has| |t#1| #6=(|CharacteristicZero|)) (ATTRIBUTE #6#) |%noBranch|) (IF (|has| |t#1| #7=(|CharacteristicNonZero|)) (ATTRIBUTE #7#) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| #2#) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| (#8=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #8# "failed") $))) |%noBranch|) (IF (|has| |t#1| (|Field|)) (SIGNATURE |inv| #1#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Finite|) |has| |#1| (|Finite|)) ((|FullyEvalableOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sample| (#4=($) 30 T CONST)) (|positive?| (#3# 28 T ELT)) (|opposite?| (#1# 33 T ELT)) (|min| (#5=($ $ $) 23 T ELT)) (|max| (#5# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#4# 29 T CONST)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT)) (+ (#5# 25 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT))) (((|OrderedCancellationAbelianMonoid|) (|Category|)) (T |OrderedCancellationAbelianMonoid|)) NIL (|Join| (|OrderedAbelianMonoid|) (|CancellationAbelianMonoid|)) -(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Maybe| $) $ $) NIL T ELT)) (|size| (#7=(#8=(|NonNegativeInteger|)) NIL #9=(|has| |#1| (|Finite|)) ELT)) (|sample| (#10=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #11=(#12="failed")) . #13=($)) NIL T ELT) (((|Union| #14=(|Quaternion| |#1|) . #11#) $) 35 T ELT) (#15=((|Union| #16=(|Fraction| #17=(|Integer|)) . #11#) . #13#) NIL #18=(OR (|has| #14# #19=(|RetractableTo| #16#)) (|has| |#1| #19#)) ELT) (((|Union| #17# . #11#) . #13#) NIL #20=(OR (|has| #14# #21=(|RetractableTo| #17#)) (|has| |#1| #21#)) ELT)) (|retract| #22=(#23=(|#1| . #24=($)) NIL T ELT) ((#14# $) 33 T ELT) (#25=(#16# . #24#) NIL #18# ELT) ((#17# . #24#) NIL #20# ELT)) (|recip| (((|Union| $ #12#) $) NIL T ELT)) (|real| (#23# 16 T ELT)) (|rationalIfCan| (#15# NIL #26=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#5# NIL #26# ELT)) (|rational| (#25# NIL #26# ELT)) (|random| (#10# NIL #9# ELT)) (|opposite?| #1#) (|one?| #4#) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 28 T ELT) (($ #14# #14#) 29 T ELT)) (|norm| #22#) (|min| #27=(#28=($ $ $) NIL #29=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #27#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|lookup| ((#30=(|PositiveInteger|) $) NIL #9# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#31=($ $) NIL (|has| |#1| (|Field|)) ELT)) (|index| (($ #30#) NIL #9# ELT)) (|imagk| (#23# 22 T ELT)) (|imagj| (#23# 20 T ELT)) (|imagi| (#23# 18 T ELT)) (|imagK| (#23# 26 T ELT)) (|imagJ| (#23# 25 T ELT)) (|imagI| (#23# 24 T ELT)) (|imagE| (#23# 23 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ #32=(|List| |#1|) #32#) NIL #33=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #33# ELT) (($ $ #34=(|Equation| |#1|)) NIL #33# ELT) (($ $ (|List| #34#)) NIL #33# ELT) (($ $ (|List| #35=(|Symbol|)) #32#) NIL #36=(|has| |#1| (|InnerEvalable| #35# |#1|)) ELT) (($ $ #35# |#1|) NIL #36# ELT)) (|elt| (#37=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| ((#38=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #38#)) ELT)) (|conjugate| #39=(#31# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #17#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #14#) 30 T ELT) (($ #16#) NIL #18# ELT)) (|charthRoot| ((#6# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#23# NIL (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#10# 8 T CONST)) (|One| (#10# 12 T CONST)) (>= #40=(#2# NIL #29# ELT)) (> #40#) (= #1#) (<= #40#) (< #40#) (- #39# #41=(#28# NIL T ELT)) (+ #41#) (** (($ $ #30#) NIL T ELT) (($ $ #8#) NIL T ELT)) (* (($ #30# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #17# . #42=($)) NIL T ELT) (#28# 40 T ELT) (#37# NIL T ELT) (($ |#1| . #42#) NIL T ELT))) (((|Octonion| |#1|) (|Join| (|OctonionCategory| |#1|) (|FullyRetractableTo| #1=(|Quaternion| |#1|)) (CATEGORY |domain| (SIGNATURE |octon| ($ #1# #1#)))) (|CommutativeRing|)) (T |Octonion|)) ((|octon| (*1 *1 *2 *2) (AND (|isDomain| *2 (|Quaternion| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *1 (|Octonion| *3))))) @@ -2456,19 +2456,19 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 39 T ELT)) (|size| (#4=(#5=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|rquo| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT) (#10=(#8# $ |#1|) 29 T ELT)) (|retractIfCan| (((|Union| |#1| #9#) $) NIL T ELT)) (|retract| (#11=(|#1| $) NIL T ELT)) (|rest| (#12=($ $) 43 T ELT)) (|recip| ((#8# $) NIL T ELT)) (|overlap| (((|Record| #13=(|:| |lm| $) (|:| |mm| $) #14=(|:| |rm| $)) $ $) NIL T ELT)) (|one?| ((#3# $) NIL T ELT)) (|nthFactor| ((|#1| $ #15=(|Integer|)) NIL T ELT)) (|nthExpon| ((#5# $ #15#) NIL T ELT)) (|mirror| (#12# 55 T ELT)) (|min| #16=(($ $ $) NIL T ELT)) (|max| #16#) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapExpon| (($ (|Mapping| #5# #5#) $) NIL T ELT)) (|lquo| #7# 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((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sign| (((|Integer|) $) 70 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|positive?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|negative?| (((|Boolean|) $) 69 T ELT)) (|min| (#5=($ $ $) 62 T ELT)) (|max| (#5# 63 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|abs| (($ $) 71 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (>= (#6=((|Boolean|) $ $) 64 T ELT)) (> (#6# 66 T ELT)) (= (#1# 8 T ELT)) (<= (#6# 65 T ELT)) (< (#6# 67 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . 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T)) ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sample| #4=(($) NIL T CONST)) (|reductum| #5=(#6=($ $) NIL T ELT)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|po| ((|#1| $) 10 T ELT)) (|opposite?| #1#) (|op| (($ |#1|) 9 T ELT)) (|one?| #3#) (|monomial| (($ |#2| #7=(|NonNegativeInteger|)) NIL T ELT)) (|minimumDegree| #8=((#7# $) NIL T ELT)) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #9=(#6# NIL #10=(|has| |#1| (|DifferentialRing|)) ELT) #11=(#12=($ $ #7#) NIL #10# ELT)) (|degree| #8#) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #13=(|Integer|)) NIL T ELT) (($ |#2|) NIL (|has| |#2| (|CommutativeRing|)) ELT)) (|coefficient| ((|#2| $ #7#) NIL T ELT)) (|characteristic| ((#7#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #4#) (|One| #4#) (D #9# #11#) (= #1#) (- #5# #14=(#15=($ $ $) NIL T ELT)) (+ 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#5=(|Boolean|) |#1|) . #6=($)) 42 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #7=(|Boolean|) |#1|) . #8=($)) 49 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#9=($) 6 T CONST)) (|removeDuplicates!| (($ $) 55 T ELT)) (|removeDuplicates| (($ $) 51 (AND (|has| |#1| . #10=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove!| (($ |#1| $) 44 (|has| $ (|FiniteAggregate| |#1|)) ELT) (($ (|Mapping| #5# |#1|) . #6#) 43 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|remove| (($ |#1| $) 50 (AND (|has| |#1| . #10#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #7# |#1|) . #8#) 48 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $) 80 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 79 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 75 (|has| |#1| . #11=((|BasicType|))) ELT)) (|part?| (#3# 59 T ELT)) (|min| ((|#1| $) 74 T ELT)) (|merge!| (#12=($ $ $) 88 T ELT)) (|merge| (#12# 87 T ELT)) (|members| (((|List| 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(#19# 84 T ELT)) (= (#1# 17 T ELT)) (|#| ((#18# $) 85 T ELT))) (((|OrderedMultisetAggregate| |#1|) (|Category|) (|OrderedSet|)) (T |OrderedMultisetAggregate|)) ((|min| (*1 *2 *1) (AND (|ofCategory| *1 (|OrderedMultisetAggregate| *2)) (|ofCategory| *2 (|OrderedSet|))))) (|Join| (|MultisetAggregate| |t#1|) (|PriorityQueueAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |min| (|t#1| $)))) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|MultiDictionary| |#1|) . T) ((|MultisetAggregate| |#1|) . T) ((|PriorityQueueAggregate| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DictionaryOperations| |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|MultiDictionary| |#1|) . T) ((|MultisetAggregate| |#1|) . T) ((|PriorityQueueAggregate| |#1|) . T) ((|SetAggregate| |#1|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((~= (#1=(#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL #4=(|has| |#1| (|AbelianGroup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL #4# ELT)) (|sign| (#5=(#6=(|Integer|) $) NIL #7=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#8=($) NIL #4# CONST)) (|retractIfCan| (((|Union| #6# . #9=(#10="failed")) $) NIL #11=(|has| |#1| (|RetractableTo| #6#)) ELT) (#12=((|Union| #13=(|Fraction| #6#) #10#) $) NIL #14=(|has| |#1| (|RetractableTo| #13#)) ELT) (((|Union| |#1| . #9#) $) 15 T ELT)) (|retract| (#5# NIL #11# ELT) (#15=(#13# $) NIL #14# ELT) ((|#1| $) 9 T ELT)) (|recip| (((|Union| $ #10#) $) 42 #7# ELT)) (|rationalIfCan| (#12# 51 #16=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#3# 46 #16# ELT)) (|rational| (#15# 48 #16# ELT)) (|positive?| #17=(#3# NIL #7# ELT)) (|opposite?| (#1# NIL #4# ELT)) (|one?| #17#) (|negative?| #17#) (|min| #18=(#19=($ $ $) NIL #7# ELT)) (|max| #18#) (|latex| (((|String|) $) NIL T ELT)) (|infinity| (#8# 13 T ELT)) (|infinite?| (#3# 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|finite?| (#3# 11 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #13#) NIL #14# ELT) (($ |#1|) 8 T ELT) (($ #6#) NIL (OR #7# #11#) ELT)) (|characteristic| ((#20=(|NonNegativeInteger|)) 36 #7# CONST)) (|before?| (#1# 53 T ELT)) (|annihilate?| #21=(#1# NIL #7# ELT)) (|abs| (#22=($ $) NIL #7# ELT)) (|Zero| (#8# 23 #4# CONST)) (|One| (#8# 33 #7# CONST)) (>= #21#) (> #21#) (= (#1# 21 T ELT)) (<= #21#) (< (#1# 45 #7# ELT)) (- (#19# NIL #4# ELT) (#22# 29 #4# ELT)) (+ (#19# 31 #4# ELT)) (** (($ $ #23=(|PositiveInteger|)) NIL #7# ELT) (($ $ #20#) NIL #7# ELT)) (* (#19# 39 #7# ELT) (($ #6# $) 27 #4# ELT) (($ #20# $) NIL #4# ELT) (($ #23# $) NIL #4# ELT))) (((|OnePointCompletion| |#1|) (|Join| #1=(|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |infinity| ($)) (SIGNATURE |finite?| #2=((|Boolean|) $)) (SIGNATURE |infinite?| #2#) (IF (|has| |#1| #3=(|AbelianGroup|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|OrderedRing|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| #2#) (SIGNATURE |rational| (#5=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #5# "failed") $))) |%noBranch|))) #1#) (T |OnePointCompletion|)) ((|infinity| (*1 *1) (AND (|isDomain| *1 (|OnePointCompletion| *2)) (|ofCategory| *2 #1=(|SetCategory|)))) (|finite?| #2=(*1 *2 *1) #3=(AND #4=(|isDomain| *2 (|Boolean|)) #5=(|isDomain| *1 (|OnePointCompletion| *3)) #6=(|ofCategory| *3 #1#))) (|infinite?| #2# #3#) (|rational?| #2# (AND #4# #5# #7=(|ofCategory| *3 (|IntegerNumberSystem|)) #6#)) (|rational| #2# (AND #8=(|isDomain| *2 (|Fraction| (|Integer|))) #5# #7# #6#)) (|rationalIfCan| #2# (|partial| AND #8# #5# #7# #6#))) @@ -2481,11 +2481,11 @@ NIL ((|is?| (((|Boolean|) $ |#2|) 14 T ELT)) (|coerce| (((|OutputForm|) $) 11 T ELT))) (((|OperatorCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |is?| ((|Boolean|) |#1| |#2|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|OperatorCategory| |#2|) (|SetCategory|)) (T |OperatorCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|name| ((|#1| $) 19 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|is?| (((|Boolean|) $ |#1|) 17 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|arity| (((|Arity|) $) 18 T ELT)) (= (#1# 8 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|name| ((|#1| $) 19 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|is?| ((#2# $ |#1|) 17 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|arity| (((|Arity|) $) 18 T ELT)) (= (#1# 8 T ELT))) (((|OperatorCategory| |#1|) (|Category|) (|SetCategory|)) (T |OperatorCategory|)) -((|name| (*1 *2 *1) (AND (|ofCategory| *1 (|OperatorCategory| *2)) (|ofCategory| *2 (|SetCategory|)))) (|arity| (*1 *2 *1) (AND (|ofCategory| *1 (|OperatorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Arity|)))) (|is?| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OperatorCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) +((|name| #1=(*1 *2 *1) (AND (|ofCategory| *1 (|OperatorCategory| *2)) (|ofCategory| *2 #2=(|SetCategory|)))) (|arity| #1# (AND #3=(|ofCategory| *1 (|OperatorCategory| *3)) #4=(|ofCategory| *3 #2#) (|isDomain| *2 (|Arity|)))) (|is?| (*1 *2 *1 *3) (AND #3# #4# (|isDomain| *2 (|Boolean|))))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |name| (|t#1| $)) (SIGNATURE |arity| ((|Arity|) $)) (SIGNATURE |is?| ((|Boolean|) $ |t#1|)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|getDatabase| (((|Database| (|IndexCard|)) (|String|)) 9 T ELT))) (((|OperationsQuery|) (CATEGORY |package| (SIGNATURE |getDatabase| ((|Database| (|IndexCard|)) (|String|))))) (T |OperationsQuery|)) ((|getDatabase| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Database| (|IndexCard|))) (|isDomain| *1 (|OperationsQuery|))))) @@ -2498,48 +2498,48 @@ NIL ((|map| ((#1=(|OrderedCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OrderedCompletion| |#1|) #1# #1#) 13 T ELT) ((#1# #2# #3#) 14 T ELT))) (((|OrderedCompletionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (#1=(|OrderedCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OrderedCompletion| |#1|))) (SIGNATURE |map| (#1# #2# #3# #1# #1#))) #4=(|SetCategory|) #4#) (T |OrderedCompletionFunctions2|)) ((|map| (*1 *2 *3 *4 *2 *2) (AND #1=(|isDomain| *2 (|OrderedCompletion| *6)) #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|OrderedCompletion| *5)) #4=(|ofCategory| *5 #5=(|SetCategory|)) #6=(|ofCategory| *6 #5#) #7=(|isDomain| *1 (|OrderedCompletionFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND #2# #3# #4# #6# #1# #7#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|size| (((|NonNegativeInteger|)) 27 T ELT)) (|random| (($) 30 T ELT)) (|min| (#2=($ $ $) 23 T ELT) (($) 26 T CONST)) (|max| (#2# 22 T ELT) (($) 25 T CONST)) (|lookup| ((#3=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|index| (($ #3#) 28 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#4=((|Boolean|) $ $) 21 T ELT)) (> (#4# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#4# 20 T ELT)) (< (#4# 18 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|size| (((|NonNegativeInteger|)) 27 T ELT)) (|random| (#2=($) 30 T ELT)) (|min| (#3=($ $ $) 23 T ELT) (#2# 26 T CONST)) (|max| (#3# 22 T ELT) (#2# 25 T CONST)) (|lookup| ((#4=(|PositiveInteger|) $) 29 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|index| (($ #4#) 28 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT))) (((|OrderedFinite|) (|Category|)) (T |OrderedFinite|)) -((|min| (*1 *1) (|ofCategory| *1 (|OrderedFinite|))) (|max| (*1 *1) (|ofCategory| *1 (|OrderedFinite|)))) -(|Join| (|OrderedSet|) (|Finite|) (CATEGORY |domain| (SIGNATURE |min| ($) |constant|) (SIGNATURE |max| ($) |constant|))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Finite|) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|min| #1=(*1 *1) #2=(|ofCategory| *1 (|OrderedFinite|))) (|max| #1# #2#)) +(|Join| (|OrderedSet|) (|Finite|) (CATEGORY |domain| (SIGNATURE |min| #1=($) |constant|) (SIGNATURE |max| #1# |constant|))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Finite|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|totalLex| (#1=((|Boolean|) #2=(|Vector| |#2|) #2#) 19 T ELT)) (|reverseLex| (#1# 20 T ELT)) (|pureLex| (#1# 16 T ELT))) (((|OrderingFunctions| |#1| |#2|) (CATEGORY |package| (SIGNATURE |pureLex| #1=((|Boolean|) #2=(|Vector| |#2|) #2#)) (SIGNATURE |totalLex| #1#) (SIGNATURE |reverseLex| #1#)) (|NonNegativeInteger|) (|OrderedAbelianMonoid|)) (T |OrderingFunctions|)) ((|reverseLex| #1=(*1 *2 *3 *3) #2=(AND (|isDomain| *3 (|Vector| *5)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|OrderingFunctions| *4 *5)) (|ofType| *4 (|NonNegativeInteger|)))) (|totalLex| #1# #2#) (|pureLex| #1# #2#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|sample| (#2=($) 29 T CONST)) (|recip| (((|Union| $ "failed") $) 32 T ELT)) (|one?| (((|Boolean|) $) 30 T ELT)) (|min| (#3=($ $ $) 23 T ELT)) (|max| (#3# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 28 T CONST)) (>= (#4=((|Boolean|) $ $) 21 T ELT)) (> (#4# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#4# 20 T ELT)) (< (#4# 18 T ELT)) (** (($ $ (|PositiveInteger|)) 26 T ELT) (($ $ (|NonNegativeInteger|)) 31 T ELT)) (* (($ $ $) 25 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|sample| (#3=($) 29 T CONST)) (|recip| (((|Union| $ "failed") $) 32 T ELT)) (|one?| ((#2# $) 30 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#3# 28 T CONST)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT)) (** (($ $ (|PositiveInteger|)) 26 T ELT) (($ $ (|NonNegativeInteger|)) 31 T ELT)) (* (#4# 25 T ELT))) (((|OrderedMonoid|) (|Category|)) (T |OrderedMonoid|)) NIL (|Join| (|OrderedSemiGroup|) (|Monoid|)) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sign| (((|Integer|) $) 39 T ELT)) (|sample| (#3=($) 30 T CONST)) (|recip| (((|Union| $ "failed") $) 56 T ELT)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|one?| (((|Boolean|) $) 54 T ELT)) (|negative?| (((|Boolean|) $) 40 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 58 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 52 T ELT)) (|abs| (($ $) 38 T ELT)) (|Zero| (#3# 29 T CONST)) (|One| (($) 53 T CONST)) (>= (#5=((|Boolean|) $ $) 21 T ELT)) (> (#5# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#5# 20 T ELT)) (< (#5# 18 T ELT)) (- (($ $ $) 43 T ELT) (($ $) 42 T ELT)) (+ (($ $ $) 25 T ELT)) (** (($ $ (|NonNegativeInteger|)) 55 T ELT) (($ $ (|PositiveInteger|)) 50 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ (|Integer|) $) 41 T ELT) (($ $ $) 51 T ELT))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Monoid|) . T) ((|OrderedSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 31 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 35 T ELT)) (|sign| ((#4=(|Integer|) $) 39 T ELT)) (|sample| (#5=($) 30 T CONST)) (|recip| (((|Union| $ "failed") $) 56 T ELT)) (|positive?| (#3# 28 T ELT)) (|opposite?| (#1# 33 T ELT)) (|one?| (#3# 54 T ELT)) (|negative?| (#3# 40 T ELT)) (|min| (#6=($ $ $) 23 T ELT)) (|max| (#6# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #4#) 57 T ELT)) (|characteristic| ((#7=(|NonNegativeInteger|)) 58 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 52 T ELT)) (|abs| (#8=($ $) 38 T ELT)) (|Zero| (#5# 29 T CONST)) (|One| (#5# 53 T CONST)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT)) (- (#6# 43 T ELT) (#8# 42 T ELT)) (+ (#6# 25 T ELT)) (** (($ $ #7#) 55 T ELT) (($ $ #9=(|PositiveInteger|)) 50 T ELT)) (* (($ #9# $) 26 T ELT) (($ #7# $) 32 T ELT) (($ #4# $) 41 T ELT) (#6# 51 T ELT))) (((|OrderedRing|) (|Category|)) (T |OrderedRing|)) NIL (|Join| (|OrderedAbelianGroup|) (|CharacteristicZero|) (|Monoid|)) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#3=((|Boolean|) $ $) 21 T ELT)) (> (#3# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#3# 20 T ELT)) (< (#3# 18 T ELT))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT))) (((|OrderedSet|) (|Category|)) (T |OrderedSet|)) NIL (|Join| (|SetCategory|) (|OrderedType|)) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT)) (|max| #3#) (|coerce| (($ |#1|) 10 T ELT) ((|#1| $) 9 T ELT) ((#4=(|OutputForm|) $) 15 (|has| |#1| (|CoercibleTo| #4#)) ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 12 T ELT))) (((|OrderedStructure| |#1| |#2|) (|Join| (|OrderedType|) (|HomotopicTo| |#1|) (CATEGORY |package| (IF (|has| |#1| #1=(|CoercibleTo| (|OutputForm|))) (ATTRIBUTE #1#) |%noBranch|))) (|Type|) (|Mapping| (|Boolean|) |#1| |#1|)) (T |OrderedStructure|)) NIL ((|min| (#1=($ $ $) 16 T ELT)) (|max| (#1# 15 T ELT)) (|before?| (#2=((|Boolean|) $ $) 17 T ELT)) (>= (#2# 12 T ELT)) (> (#2# 9 T ELT)) (= (#2# 14 T ELT)) (<= (#2# 11 T ELT))) (((|OrderedType&| |#1|) (CATEGORY |package| (SIGNATURE |min| #1=(|#1| |#1| |#1|)) (SIGNATURE |max| #1#) (SIGNATURE >= #2=((|Boolean|) |#1| |#1|)) (SIGNATURE <= #2#) (SIGNATURE > #2#) (SIGNATURE |before?| #2#) (SIGNATURE = #2#)) (|OrderedType|)) (T |OrderedType&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (($ $ $) 10 T ELT)) (|max| (($ $ $) 11 T ELT)) (|before?| (#1# 6 T ELT)) (>= (((|Boolean|) $ $) 12 T ELT)) (> (((|Boolean|) $ $) 14 T ELT)) (= (#1# 8 T ELT)) (<= (((|Boolean|) $ $) 13 T ELT)) (< (((|Boolean|) $ $) 15 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 10 T ELT)) (|max| (#2# 11 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#1# 12 T ELT)) (> (#1# 14 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 13 T ELT)) (< (#1# 15 T ELT))) (((|OrderedType|) (|Category|)) (T |OrderedType|)) -((< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (> (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (<= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (>= (*1 *2 *1 *1) (AND (|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (|max| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedType|))) (|min| (*1 *1 *1 *1) (|ofCategory| *1 (|OrderedType|)))) -(|Join| (|BasicType|) (CATEGORY |domain| (SIGNATURE < ((|Boolean|) $ $)) (SIGNATURE > ((|Boolean|) $ $)) (SIGNATURE <= ((|Boolean|) $ $)) (SIGNATURE >= ((|Boolean|) $ $)) (SIGNATURE |max| ($ $ $)) (SIGNATURE |min| ($ $ $)))) -(((|BasicType|) . T) ((|Join|) . T) ((|Type|) . T)) +((< #1=(*1 *2 *1 *1) #2=(AND #3=(|ofCategory| *1 (|OrderedType|)) (|isDomain| *2 (|Boolean|)))) (> #1# #2#) (<= #1# #2#) (>= #1# #2#) (|max| #4=(*1 *1 *1 *1) #3#) (|min| #4# #3#)) +(|Join| (|BasicType|) (CATEGORY |domain| (SIGNATURE < #1=((|Boolean|) $ $)) (SIGNATURE > #1#) (SIGNATURE <= #1#) (SIGNATURE >= #1#) (SIGNATURE |max| #2=($ $ $)) (SIGNATURE |min| #2#))) +(((|BasicType|) . T) ((|Type|) . T)) ((|rightRemainder| (#1=($ $ $) 49 T ELT)) (|rightQuotient| (#1# 48 T ELT)) (|rightLcm| (#1# 46 T ELT)) (|rightGcd| (#1# 55 T ELT)) (|rightExtendedGcd| (#2=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 50 T ELT)) (|rightExactQuotient| (#3=(#4=(|Union| $ #5="failed") $ $) 53 T ELT)) (|retractIfCan| (((|Union| #6=(|Integer|) #5#) $) NIL T ELT) (((|Union| #7=(|Fraction| #6#) #5#) $) NIL T ELT) (((|Union| |#2| #5#) $) 29 T ELT)) (|primitivePart| (($ $) 39 T ELT)) (|leftRemainder| (#1# 43 T ELT)) (|leftQuotient| (#1# 42 T ELT)) (|leftLcm| (#1# 51 T ELT)) (|leftGcd| (#1# 57 T ELT)) (|leftExtendedGcd| (#2# 45 T ELT)) (|leftExactQuotient| (#3# 52 T ELT)) (|exquo| ((#4# $ |#2|) 32 T ELT)) (|content| ((|#2| $) 36 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6#) NIL T ELT) (($ #7#) NIL T ELT) (($ |#2|) 13 T ELT)) (|coefficients| (((|List| |#2|) $) 21 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #6# $) NIL T ELT) (#1# NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 25 T ELT))) (((|UnivariateSkewPolynomialCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftLcm| #1=(|#1| |#1| |#1|)) (SIGNATURE |rightExtendedGcd| #2=((|Record| (|:| |coef1| |#1|) (|:| |coef2| |#1|) (|:| |generator| |#1|)) |#1| |#1|)) (SIGNATURE |rightGcd| #1#) (SIGNATURE |rightExactQuotient| #3=(#4=(|Union| |#1| #5="failed") |#1| |#1|)) (SIGNATURE |rightRemainder| #1#) (SIGNATURE |rightQuotient| #1#) (SIGNATURE |rightLcm| #1#) (SIGNATURE |leftExtendedGcd| #2#) (SIGNATURE |leftGcd| #1#) (SIGNATURE |leftExactQuotient| #3#) (SIGNATURE |leftRemainder| #1#) (SIGNATURE |leftQuotient| #1#) (SIGNATURE |primitivePart| (|#1| |#1|)) (SIGNATURE |content| (|#2| |#1|)) (SIGNATURE |exquo| (#4# |#1| |#2|)) (SIGNATURE |coefficients| ((|List| |#2|) |#1|)) (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |retractIfCan| ((|Union| |#2| #5#) |#1|)) (SIGNATURE |retractIfCan| ((|Union| #6=(|Fraction| #7=(|Integer|)) #5#) |#1|)) (SIGNATURE |coerce| (|#1| #6#)) (SIGNATURE |retractIfCan| ((|Union| #7# #5#) |#1|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * (|#1| |#1| |#2|)) (SIGNATURE |coerce| (|#1| #7#)) (SIGNATURE * #1#) (SIGNATURE * (|#1| #7# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|UnivariateSkewPolynomialCategory| |#2|) (|Ring|)) (T |UnivariateSkewPolynomialCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (($ $ $) 59 (|has| |#1| (|Field|)) ELT)) (|rightQuotient| (($ $ $) 60 (|has| |#1| (|Field|)) ELT)) (|rightLcm| (($ $ $) 62 (|has| |#1| (|Field|)) ELT)) (|rightGcd| (($ $ $) 57 (|has| |#1| (|Field|)) ELT)) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 56 (|has| |#1| (|Field|)) ELT)) (|rightExactQuotient| (((|Union| $ "failed") $ $) 58 (|has| |#1| (|Field|)) ELT)) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 61 (|has| |#1| (|Field|)) ELT)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 89 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 86 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 83 T ELT)) (|retract| ((#4# . #10=($)) 88 (|has| |#1| . #7#) ELT) ((#8# . #10#) 85 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 84 T ELT)) (|reductum| (($ $) 78 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|primitivePart| (($ $) 69 (|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 76 T ELT)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 71 (|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 72 (|has| |#1| (|IntegralDomain|)) ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 80 T ELT)) (|leftRemainder| (($ $ $) 66 (|has| |#1| (|Field|)) ELT)) (|leftQuotient| (($ $ $) 67 (|has| |#1| (|Field|)) ELT)) (|leftLcm| (($ $ $) 55 (|has| |#1| (|Field|)) ELT)) (|leftGcd| (($ $ $) 64 (|has| |#1| (|Field|)) ELT)) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 63 (|has| |#1| (|Field|)) ELT)) (|leftExactQuotient| (((|Union| $ "failed") $ $) 65 (|has| |#1| (|Field|)) ELT)) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 68 (|has| |#1| (|Field|)) ELT)) (|leadingCoefficient| ((|#1| $) 79 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 73 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| (((|NonNegativeInteger|) $) 81 T ELT)) (|content| ((|#1| $) 70 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #8#) 87 (|has| |#1| . #9#) ELT) (($ |#1|) 82 T ELT)) (|coefficients| (((|List| |#1|) $) 75 T ELT)) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) 77 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 74 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #11=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 91 T ELT) (($ |#1| . #11#) 90 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rightRemainder| (#5=($ $ $) 59 #6=(|has| |#1| (|Field|)) ELT)) (|rightQuotient| (#5# 60 #6# ELT)) (|rightLcm| (#5# 62 #6# ELT)) (|rightGcd| (#5# 57 #6# ELT)) (|rightExtendedGcd| (#7=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 56 #6# ELT)) (|rightExactQuotient| (#8=(#9=(|Union| $ #10="failed") $ $) 58 #6# ELT)) (|rightDivide| (#11=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 61 #6# ELT)) (|retractIfCan| (((|Union| #12=(|Integer|) . #13=(#10#)) . #14=($)) 89 #15=(|has| |#1| (|RetractableTo| #12#)) ELT) (((|Union| #16=(|Fraction| #12#) . #13#) . #14#) 86 #17=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| |#1| . #13#) . #14#) 83 T ELT)) (|retract| ((#12# . #18=($)) 88 #15# ELT) ((#16# . #18#) 85 #17# ELT) (#19=(|#1| . #18#) 84 T ELT)) (|reductum| (#20=($ $) 78 T ELT)) (|recip| ((#9# $) 43 T ELT)) (|primitivePart| (#20# 69 #21=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|monomial| (($ |#1| #22=(|NonNegativeInteger|)) 76 T ELT)) (|monicRightDivide| (#11# 71 #23=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#11# 72 #23# ELT)) (|minimumDegree| (#24=(#22# $) 80 T ELT)) (|leftRemainder| (#5# 66 #6# ELT)) (|leftQuotient| (#5# 67 #6# ELT)) (|leftLcm| (#5# 55 #6# ELT)) (|leftGcd| (#5# 64 #6# ELT)) (|leftExtendedGcd| (#7# 63 #6# ELT)) (|leftExactQuotient| (#8# 65 #6# ELT)) (|leftDivide| (#11# 68 #6# ELT)) (|leadingCoefficient| (#19# 79 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#9# $ |#1|) 73 #23# ELT)) (|degree| (#24# 81 T ELT)) (|content| (#19# 70 #21# ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #12#) 42 T ELT) (($ #16#) 87 #17# ELT) (($ |#1|) 82 T ELT)) (|coefficients| (((|List| |#1|) $) 75 T ELT)) (|coefficient| ((|#1| $ #22#) 77 T ELT)) (|characteristic| ((#22#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 74 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (= (#1# 8 T ELT)) (- (#20# 30 T ELT) (#5# 29 T ELT)) (+ (#5# 18 T ELT)) (** (($ $ #25=(|PositiveInteger|)) 36 T ELT) (($ $ #22#) 44 T ELT)) (* (($ #25# $) 17 T ELT) (($ #22# $) 21 T ELT) (($ #12# . #26=($)) 31 T ELT) (#5# 35 T ELT) (($ $ |#1|) 91 T ELT) (($ |#1| . #26#) 90 T ELT))) (((|UnivariateSkewPolynomialCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariateSkewPolynomialCategory|)) -((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|minimumDegree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|reductum| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|List| *3)))) (|apply| (*1 *2 *1 *2 *2) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|exquo| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|IntegralDomain|)))) (|monicLeftDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|monicRightDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|content| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|GcdDomain|)))) (|leftDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|leftQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftRemainder| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftExactQuotient| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|leftExtendedGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|rightLcm| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|rightQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightRemainder| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightExactQuotient| (*1 *1 *1 *1) (|partial| AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|rightExtendedGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)))) (|leftLcm| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|))))) -(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| ((|NonNegativeInteger|) $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |coefficient| (|t#1| $ (|NonNegativeInteger|))) (SIGNATURE |monomial| ($ |t#1| (|NonNegativeInteger|))) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |apply| (|t#1| $ |t#1| |t#1|)) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |exquo| ((|Union| $ "failed") $ |t#1|)) (SIGNATURE |monicLeftDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |monicRightDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |content| (|t#1| $)) (SIGNATURE |primitivePart| ($ $))) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |leftQuotient| ($ $ $)) (SIGNATURE |leftRemainder| ($ $ $)) (SIGNATURE |leftExactQuotient| ((|Union| $ "failed") $ $)) (SIGNATURE |leftGcd| ($ $ $)) (SIGNATURE |leftExtendedGcd| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |rightLcm| ($ $ $)) (SIGNATURE |rightDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |rightQuotient| ($ $ $)) (SIGNATURE |rightRemainder| ($ $ $)) (SIGNATURE |rightExactQuotient| ((|Union| $ "failed") $ $)) (SIGNATURE |rightGcd| ($ $ $)) (SIGNATURE |rightExtendedGcd| ((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |leftLcm| ($ $ $))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FullyRetractableTo| |#1|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|degree| #1=(*1 *2 *1) #2=(AND #3=(|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *3)) #4=(|ofCategory| *3 #5=(|Ring|)) (|isDomain| *2 #6=(|NonNegativeInteger|)))) (|minimumDegree| #1# #2#) (|leadingCoefficient| #1# #7=(AND #8=(|ofCategory| *1 (|UnivariateSkewPolynomialCategory| *2)) #9=(|ofCategory| *2 #5#))) (|reductum| #10=(*1 *1 *1) #7#) (|coefficient| (*1 *2 *1 *3) #11=(AND (|isDomain| *3 #6#) #8# #9#)) (|monomial| (*1 *1 *2 *3) #11#) (|coefficients| #1# (AND #3# #4# (|isDomain| *2 (|List| *3)))) (|apply| (*1 *2 *1 *2 *2) #7#) (|exquo| (*1 *1 *1 *2) (|partial| AND #8# #9# (|ofCategory| *2 #12=(|IntegralDomain|)))) (|monicLeftDivide| #13=(*1 *2 *1 *1) #14=(AND (|ofCategory| *3 #12#) #4# #15=(|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) #3#)) (|monicRightDivide| #13# #14#) (|content| #1# #16=(AND #8# #9# (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart| #10# #16#) (|leftDivide| #13# #17=(AND #18=(|ofCategory| *3 #19=(|Field|)) #4# #15# #3#)) (|leftQuotient| #20=(*1 *1 *1 *1) #21=(AND #8# #9# #22=(|ofCategory| *2 #19#))) (|leftRemainder| #20# #21#) (|leftExactQuotient| #20# #23=(|partial| AND #8# #9# #22#)) (|leftGcd| #20# #21#) (|leftExtendedGcd| #13# #24=(AND #18# #4# (|isDomain| *2 (|Record| (|:| |coef1| *1) (|:| |coef2| *1) (|:| |generator| *1))) #3#)) (|rightLcm| #20# #21#) (|rightDivide| #13# #17#) (|rightQuotient| #20# #21#) (|rightRemainder| #20# #21#) (|rightExactQuotient| #20# #23#) (|rightGcd| #20# #21#) (|rightExtendedGcd| #13# #24#) (|leftLcm| #20# #21#)) +(|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|FullyRetractableTo| |t#1|) (CATEGORY |domain| (SIGNATURE |degree| #1=(#2=(|NonNegativeInteger|) $)) (SIGNATURE |minimumDegree| #1#) (SIGNATURE |leadingCoefficient| #3=(|t#1| $)) (SIGNATURE |reductum| #4=($ $)) (SIGNATURE |coefficient| (|t#1| $ #2#)) (SIGNATURE |monomial| ($ |t#1| #2#)) (SIGNATURE |coefficients| ((|List| |t#1|) $)) (SIGNATURE |apply| (|t#1| $ |t#1| |t#1|)) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |exquo| (#5=(|Union| $ "failed") $ |t#1|)) (SIGNATURE |monicLeftDivide| #6=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |monicRightDivide| #6#)) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |content| #3#) (SIGNATURE |primitivePart| #4#)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| #6#) (SIGNATURE |leftQuotient| #7=($ $ $)) (SIGNATURE |leftRemainder| #7#) (SIGNATURE |leftExactQuotient| #8=(#5# $ $)) (SIGNATURE |leftGcd| #7#) (SIGNATURE |leftExtendedGcd| #9=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $)) (SIGNATURE |rightLcm| #7#) (SIGNATURE |rightDivide| #6#) (SIGNATURE |rightQuotient| #7#) (SIGNATURE |rightRemainder| #7#) (SIGNATURE |rightExactQuotient| #8#) (SIGNATURE |rightGcd| #7#) (SIGNATURE |rightExtendedGcd| #9#) (SIGNATURE |leftLcm| #7#)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|FullyRetractableTo| |#1|) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|times| ((|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|)) 20 T ELT)) (|rightDivide| (#3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#) 51 #4=(|has| |#1| (|Field|)) ELT)) (|monicRightDivide| (#3# 48 #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#3# 47 #5# ELT)) (|leftDivide| (#3# 50 #4# ELT)) (|apply| ((|#1| |#2| |#1| |#1| #1# #2#) 37 T ELT))) (((|UnivariateSkewPolynomialCategoryOps| |#1| |#2|) (CATEGORY |package| (SIGNATURE |times| (|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|))) (SIGNATURE |apply| (|#1| |#2| |#1| |#1| #1# #2#)) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |monicLeftDivide| #3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#)) (SIGNATURE |monicRightDivide| #3#)) |%noBranch|) (IF (|has| |#1| (|Field|)) (PROGN (SIGNATURE |leftDivide| #3#) (SIGNATURE |rightDivide| #3#)) |%noBranch|)) (|Ring|) (|UnivariateSkewPolynomialCategory| |#1|)) (T |UnivariateSkewPolynomialCategoryOps|)) ((|rightDivide| #1=(*1 *2 *3 *3 *4) #2=(AND #3=(|isDomain| *4 #4=(|Automorphism| *5)) (|ofCategory| *5 (|Field|)) #5=(|ofCategory| *5 #6=(|Ring|)) #7=(|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) #8=(|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *3)) #9=(|ofCategory| *3 #10=(|UnivariateSkewPolynomialCategory| *5)))) (|leftDivide| #1# #2#) (|monicRightDivide| #1# #11=(AND #3# (|ofCategory| *5 (|IntegralDomain|)) #5# #7# #8# #9#)) (|monicLeftDivide| #1# #11#) (|apply| (*1 *2 *3 *2 *2 *4 *5) (AND (|isDomain| *4 (|Automorphism| *2)) (|isDomain| *5 (|Mapping| *2 *2)) (|ofCategory| *2 #6#) (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *2 *3)) (|ofCategory| *3 (|UnivariateSkewPolynomialCategory| *2)))) (|times| (*1 *2 *2 *2 *3 *4) (AND (|isDomain| *3 #4#) (|isDomain| *4 (|Mapping| *5 *5)) #5# (|isDomain| *1 (|UnivariateSkewPolynomialCategoryOps| *5 *2)) (|ofCategory| *2 #10#)))) @@ -2552,11 +2552,11 @@ NIL ((|legendreP| (#1=(|#1| #2=(|NonNegativeInteger|) |#1|) 45 (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ELT)) (|laguerreL| ((|#1| #2# #2# |#1|) 36 T ELT) (#1# 24 T ELT)) (|hermiteH| (#1# 40 T ELT)) (|chebyshevU| (#1# 38 T ELT)) (|chebyshevT| (#1# 37 T ELT))) (((|OrthogonalPolynomialFunctions| |#1|) (CATEGORY |package| (SIGNATURE |chebyshevT| #1=(|#1| #2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |chebyshevU| #1#) (SIGNATURE |hermiteH| #1#) (SIGNATURE |laguerreL| #1#) (SIGNATURE |laguerreL| (|#1| #2# #2# |#1|)) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |legendreP| #1#) |%noBranch|)) (|CommutativeRing|)) (T |OrthogonalPolynomialFunctions|)) ((|legendreP| #1=(*1 *2 *3 *2) (AND #2=(|isDomain| *3 (|NonNegativeInteger|)) #3=(|isDomain| *1 (|OrthogonalPolynomialFunctions| *2)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))) #4=(|ofCategory| *2 (|CommutativeRing|)))) (|laguerreL| (*1 *2 *3 *3 *2) #5=(AND #2# #3# #4#)) (|laguerreL| #1# #5#) (|hermiteH| #1# #5#) (|chebyshevU| #1# #5#) (|chebyshevT| #1# #5#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#3=((|Boolean|) $ $) 21 T ELT)) (> (#3# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#3# 20 T ELT)) (< (#3# 18 T ELT)) (** (($ $ (|PositiveInteger|)) 26 T ELT)) (* (($ $ $) 25 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|min| (#2=($ $ $) 23 T ELT)) (|max| (#2# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (>= (#1# 21 T ELT)) (> (#1# 19 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 20 T ELT)) (< (#1# 18 T ELT)) (** (($ $ (|PositiveInteger|)) 26 T ELT)) (* (#2# 25 T ELT))) (((|OrderedSemiGroup|) (|Category|)) (T |OrderedSemiGroup|)) NIL (|Join| (|OrderedSet|) (|SemiGroup|)) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|value| ((#3=(|Integer|) $) 14 T ELT)) (|min| #4=(($ $ $) NIL T ELT)) (|max| #4#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #3#) 13 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= (#2# 10 T ELT)) (<= #1#) (< (#2# 12 T ELT))) (((|OrdSetInts|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|Integer|))) (SIGNATURE |value| (#1# $))))) (T |OrdSetInts|)) ((|coerce| (*1 *1 *2) #1=(AND (|isDomain| *2 (|Integer|)) (|isDomain| *1 (|OrdSetInts|)))) (|value| (*1 *2 *1) #1#)) @@ -2566,10 +2566,10 @@ NIL ((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) 15 T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) 12 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 30 T ELT))) (((|OutputByteConduit&| |#1|) (CATEGORY |package| (SIGNATURE |writeBytes!| ((|NonNegativeInteger|) |#1| (|ByteBuffer|))) (SIGNATURE |writeUInt8!| ((|Maybe| #1=(|UInt8|)) |#1| #1#)) (SIGNATURE |writeInt8!| ((|Maybe| #2=(|Int8|)) |#1| #2#))) (|OutputByteConduit|)) (T |OutputByteConduit&|)) NIL -((|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) 8 T ELT)) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) 9 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) 10 T ELT)) (|close!| (($ $) 6 T ELT))) +((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) 8 T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) 9 T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) 7 T ELT)) (|writeByte!| (((|Maybe| #3=(|Byte|)) $ #3#) 10 T ELT)) (|close!| (($ $) 6 T ELT))) (((|OutputByteConduit|) (|Category|)) (T |OutputByteConduit|)) -((|writeByte!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *2 (|Maybe| (|Byte|))) (|isDomain| *3 (|Byte|)))) (|writeInt8!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *2 (|Maybe| (|Int8|))) (|isDomain| *3 (|Int8|)))) (|writeUInt8!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *2 (|Maybe| (|UInt8|))) (|isDomain| *3 (|UInt8|)))) (|writeBytes!| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *3 (|ByteBuffer|)) (|isDomain| *2 (|NonNegativeInteger|))))) -(|Join| (|Conduit|) (CATEGORY |domain| (SIGNATURE |writeByte!| ((|Maybe| (|Byte|)) $ (|Byte|))) (SIGNATURE |writeInt8!| ((|Maybe| (|Int8|)) $ (|Int8|))) (SIGNATURE |writeUInt8!| ((|Maybe| (|UInt8|)) $ (|UInt8|))) (SIGNATURE |writeBytes!| ((|NonNegativeInteger|) $ (|ByteBuffer|))))) +((|writeByte!| #1=(*1 *2 *1 *3) (AND #2=(|ofCategory| *1 (|OutputByteConduit|)) (|isDomain| *2 (|Maybe| #3=(|Byte|))) (|isDomain| *3 #3#))) (|writeInt8!| #1# (AND #2# (|isDomain| *2 (|Maybe| #4=(|Int8|))) (|isDomain| *3 #4#))) (|writeUInt8!| #1# (AND #2# (|isDomain| *2 (|Maybe| #5=(|UInt8|))) (|isDomain| *3 #5#))) (|writeBytes!| #1# (AND #2# (|isDomain| *3 (|ByteBuffer|)) (|isDomain| *2 (|NonNegativeInteger|))))) +(|Join| (|Conduit|) (CATEGORY |domain| (SIGNATURE |writeByte!| ((|Maybe| #1=(|Byte|)) $ #1#)) (SIGNATURE |writeInt8!| ((|Maybe| #2=(|Int8|)) $ #2#)) (SIGNATURE |writeUInt8!| ((|Maybe| #3=(|UInt8|)) $ #3#)) (SIGNATURE |writeBytes!| ((|NonNegativeInteger|) $ (|ByteBuffer|))))) (((|Conduit|) . T)) ((|writeUInt8!| (((|Maybe| #1=(|UInt8|)) $ #1#) NIL T ELT)) (|writeInt8!| (((|Maybe| #2=(|Int8|)) $ #2#) NIL T ELT)) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) NIL T ELT)) (|writeByte!| (((|Maybe| #3=(|Byte|)) $ #3#) 22 T ELT)) (|outputBinaryFile| (($ (|FileName|)) 12 T ELT) (($ (|String|)) 14 T ELT)) (|isOpen?| (((|Boolean|) $) 19 T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT)) (|close!| (($ $) 23 T ELT))) (((|OutputBinaryFile|) (|Join| (|OutputByteConduit|) (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |outputBinaryFile| ($ (|FileName|))) (SIGNATURE |outputBinaryFile| ($ (|String|))) (SIGNATURE |isOpen?| ((|Boolean|) $))))) (T |OutputBinaryFile|)) @@ -2595,11 +2595,11 @@ NIL ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(($ $) NIL T ELT)) (|unit?| #3#) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sqrt| #5=(($ $ #6=(|Integer|)) NIL T ELT)) (|sizeLess?| #1#) (|sample| #7=(($) NIL T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #6#) #6#) NIL T ELT)) (|rem| #8=(($ $ $) NIL T ELT)) (|recip| ((#9=(|Union| $ #10="failed") $) NIL T ELT)) (|quotientByP| #4#) (|quo| #8#) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) #12=(|:| |generator| $)) #11#) NIL T ELT)) (|order| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|multiEuclidean| (((|Union| #11# #10#) #11# $) NIL T ELT)) (|modulus| ((#6#) NIL T ELT)) (|moduloP| ((#6# $) NIL T ELT)) (|lcm| #8# #15=(($ #11#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#16=(|SparseUnivariatePolynomial| $) #16# #16#) NIL T ELT)) (|gcd| #8# #15#) (|extendedEuclidean| (((|Record| #17=(|:| |coef1| $) #18=(|:| |coef2| $) #12#) $ $) NIL T ELT) (((|Union| (|Record| #17# #18#) #10#) $ $ $) NIL T ELT)) (|extend| #5#) (|exquo| ((#9# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) NIL T ELT)) (|euclideanSize| #13#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (((|Stream| #6#) $) NIL T ELT)) (|complete| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #6#) NIL T ELT) #4#) (|characteristic| ((#14#) NIL T CONST)) (|before?| #1#) (|associates?| #1#) (|approximate| ((#6# $ #6#) NIL T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| #7#) (= #1#) (- #4# #8#) (+ #8#) (** (($ $ #19=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #19# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #6# $) NIL T ELT) #8#)) (((|PAdicInteger| |#1|) (|PAdicIntegerCategory| |#1|) (|Integer|)) (T |PAdicInteger|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sqrt| (($ $ (|Integer|)) 79 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#4=($) 23 T CONST)) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) 78 T ELT)) (|rem| (#5=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quotientByP| (($ $) 81 T ELT)) (|quo| (#5# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #6=(|List| $)) (|:| |generator| $)) #6#) 67 T ELT)) (|order| (((|NonNegativeInteger|) $) 86 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #7=(|List| $) #8="failed") #7# $) 69 T ELT)) (|modulus| (((|Integer|)) 83 T ELT)) (|moduloP| (((|Integer|) $) 82 T ELT)) (|lcm| (#9=($ $ $) 61 T ELT) (#10=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#11=(|SparseUnivariatePolynomial| $) #11# #11#) 59 T ELT)) (|gcd| (#9# 63 T ELT) (#10# 62 T ELT)) (|extendedEuclidean| (((|Record| #12=(|:| |coef1| $) #13=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #12# #13#) #8#) $ $ $) 70 T ELT)) (|extend| (($ $ (|Integer|)) 85 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #6#) #6# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|digits| (((|Stream| (|Integer|)) $) 87 T ELT)) (|complete| (($ $) 84 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|approximate| (((|Integer|) $ (|Integer|)) 80 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sqrt| (#5=($ $ #6=(|Integer|)) 79 T ELT)) (|sizeLess?| (#1# 76 T ELT)) (|sample| (#7=($) 23 T CONST)) (|root| (($ (|SparseUnivariatePolynomial| #6#) #6#) 78 T ELT)) (|rem| (#8=($ $ $) 72 T ELT)) (|recip| ((#9=(|Union| $ #10="failed") $) 43 T ELT)) (|quotientByP| (#4# 81 T ELT)) (|quo| (#8# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #11=(|List| $)) #12=(|:| |generator| $)) #11#) 67 T ELT)) (|order| (#13=(#14=(|NonNegativeInteger|) $) 86 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|multiEuclidean| (((|Union| #11# #10#) #11# $) 69 T ELT)) (|modulus| ((#6#) 83 T ELT)) (|moduloP| ((#6# $) 82 T ELT)) (|lcm| (#8# 61 T ELT) (#15=($ #11#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#16=(|SparseUnivariatePolynomial| $) #16# #16#) 59 T ELT)) (|gcd| (#8# 63 T ELT) (#15# 62 T ELT)) (|extendedEuclidean| (((|Record| #17=(|:| |coef1| $) #18=(|:| |coef2| $) #12#) $ $) 71 T ELT) (((|Union| (|Record| #17# #18#) #10#) $ $ $) 70 T ELT)) (|extend| (#5# 85 T ELT)) (|exquo| ((#9# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #11#) #11# $) 66 T ELT)) (|euclideanSize| (#13# 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|digits| (((|Stream| #6#) $) 87 T ELT)) (|complete| (#4# 84 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #6#) 42 T ELT) (#4# 58 T ELT)) (|characteristic| ((#14#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|approximate| ((#6# $ #6#) 80 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#7# 24 T CONST)) (|One| (#7# 46 T CONST)) (= (#1# 8 T ELT)) (- (#4# 30 T ELT) (#8# 29 T ELT)) (+ (#8# 18 T ELT)) (** (($ $ #19=(|PositiveInteger|)) 36 T ELT) (($ $ #14#) 44 T ELT)) (* (($ #19# $) 17 T ELT) (($ #14# $) 21 T ELT) (($ #6# $) 31 T ELT) (#8# 35 T ELT))) (((|PAdicIntegerCategory| |#1|) (|Category|) (|Integer|)) (T |PAdicIntegerCategory|)) -((|digits| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Stream| (|Integer|))))) (|order| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|NonNegativeInteger|)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|complete| (*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2))) (|modulus| (*1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|moduloP| (*1 *2 *1) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|quotientByP| (*1 *1 *1) (|ofCategory| *1 (|PAdicIntegerCategory| *2))) (|approximate| (*1 *2 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|sqrt| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Integer|)))) (|root| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|PAdicIntegerCategory| *4))))) -(|Join| (|EuclideanDomain|) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |digits| ((|Stream| (|Integer|)) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |extend| ($ $ (|Integer|))) (SIGNATURE |complete| ($ $)) (SIGNATURE |modulus| ((|Integer|))) (SIGNATURE |moduloP| ((|Integer|) $)) (SIGNATURE |quotientByP| ($ $)) (SIGNATURE |approximate| ((|Integer|) $ (|Integer|))) (SIGNATURE |sqrt| ($ $ (|Integer|))) (SIGNATURE |root| ($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|digits| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|PAdicIntegerCategory| *3)) (|isDomain| *2 (|Stream| #3=(|Integer|))))) (|order| #1# (AND #2# (|isDomain| *2 (|NonNegativeInteger|)))) (|extend| #4=(*1 *1 *1 *2) #5=(AND #2# (|isDomain| *2 #3#))) (|complete| #6=(*1 *1 *1) #7=(|ofCategory| *1 (|PAdicIntegerCategory| *2))) (|modulus| (*1 *2) #5#) (|moduloP| #1# #5#) (|quotientByP| #6# #7#) (|approximate| (*1 *2 *1 *2) #5#) (|sqrt| #4# #5#) (|root| (*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| #3#)) (|isDomain| *3 #3#) (|ofCategory| *1 (|PAdicIntegerCategory| *4))))) +(|Join| (|EuclideanDomain|) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |digits| ((|Stream| #1=(|Integer|)) $)) (SIGNATURE |order| ((|NonNegativeInteger|) $)) (SIGNATURE |extend| #2=($ $ #1#)) (SIGNATURE |complete| #3=($ $)) (SIGNATURE |modulus| (#1#)) (SIGNATURE |moduloP| (#1# $)) (SIGNATURE |quotientByP| #3#) (SIGNATURE |approximate| (#1# $ #1#)) (SIGNATURE |sqrt| #2#) (SIGNATURE |root| ($ (|SparseUnivariatePolynomial| #1#) #1#)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|PrincipalIdealDomain|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholePart| (#6=(#7=(|PAdicInteger| |#1|) $) NIL #8=(|has| #7# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #9=(#10=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| ((#11=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #12=(((|Factored| #13=(|SparseUnivariatePolynomial| $)) #13#) NIL #14=(|has| #7# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #9#) (|squareFree| #15=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #16=(|List| #13#) #17="failed") #16# #13#) NIL #14# ELT)) (|sizeLess?| #1#) (|sign| (#18=(#19=(|Integer|) $) NIL #20=(|has| #7# (|OrderedIntegralDomain|)) ELT)) (|sample| #21=(#22=($) NIL T CONST)) (|retractIfCan| (((|Union| #7# . #23=(#17#)) . #24=($)) NIL T ELT) (((|Union| #25=(|Symbol|) . #23#) . #24#) NIL #26=(|has| #7# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #19#) . #23#) . #24#) NIL #28=(|has| #7# (|RetractableTo| #19#)) ELT) (((|Union| #19# . #23#) . #24#) NIL #28# ELT)) (|retract| #29=(#6# NIL T ELT) ((#25# . #30=($)) NIL #26# ELT) ((#27# . #30#) NIL #28# ELT) (#18# NIL #28# ELT)) (|removeZeroes| #9# #31=(($ #19# $) NIL T ELT)) (|rem| #32=(#33=($ $ $) NIL T ELT)) (|reducedSystem| ((#34=(|Matrix| #19#) . #35=(#36=(|Matrix| $))) NIL #37=(|has| #7# (|LinearlyExplicitRingOver| #19#)) ELT) ((#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #19#))) . #39=(#36# #40=(|Vector| $))) NIL #37# ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| #7#)) (|:| |vec| (|Vector| #7#))) . #39#) NIL T ELT) ((#42# . #35#) NIL T ELT)) (|recip| ((#43=(|Union| $ #17#) $) NIL T ELT)) (|random| (#22# NIL #44=(|has| #7# (|IntegerNumberSystem|)) ELT)) (|quo| #32#) (|principalIdeal| (((|Record| (|:| |coef| #45=(|List| $)) #46=(|:| |generator| $)) #45#) NIL T ELT)) (|prime?| #4#) (|positive?| #47=(#5# NIL #20# ELT)) (|patternMatch| ((#48=(|PatternMatchResult| #19# . #49=($)) $ #50=(|Pattern| #19#) #48#) NIL (|has| #7# (|PatternMatchable| #19#)) ELT) ((#51=(|PatternMatchResult| #52=(|Float|) . #49#) $ #53=(|Pattern| #52#) #51#) NIL (|has| #7# (|PatternMatchable| #52#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #9#) (|numer| #29#) (|nextItem| (#54=(#11# $) NIL #55=(|has| #7# (|StepThrough|)) ELT)) (|negative?| #47#) (|multiEuclidean| (((|Union| #45# #17#) #45# $) NIL T ELT)) (|min| #56=(#33# NIL #57=(|has| #7# (|OrderedSet|)) ELT)) (|max| #56#) (|map| (($ #58=(|Mapping| #7# #7#) $) NIL T ELT)) (|leftReducedSystem| ((#34# . #59=(#40#)) NIL #37# ELT) ((#38# . #60=(#40# $)) NIL #37# ELT) ((#41# . #60#) NIL T ELT) ((#42# . #59#) NIL T ELT)) (|lcm| #32# #61=(($ #45#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #9#) (|init| (#22# NIL #55# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#13# #13# #13#) NIL T ELT)) (|gcd| #32# #61#) (|fractionPart| (#10# NIL #8# ELT)) (|floor| #62=(#6# NIL #44# ELT)) (|factorSquareFreePolynomial| #12#) (|factorPolynomial| #12#) (|factor| #15#) (|extendedEuclidean| (((|Record| #63=(|:| |coef1| $) #64=(|:| |coef2| $) #46#) $ $) NIL T ELT) (((|Union| (|Record| #63# #64#) #17#) $ $ $) NIL T ELT)) (|exquo| ((#43# $ $) NIL T ELT)) (|expressIdealMember| (((|Maybe| #45#) #45# $) NIL T ELT)) (|eval| (($ $ #65=(|List| #7#) #65#) NIL #66=(|has| #7# (|Evalable| #7#)) ELT) (($ $ #7# #7#) NIL #66# ELT) (($ $ #67=(|Equation| #7#)) NIL #66# ELT) (($ $ (|List| #67#)) NIL #66# ELT) (($ $ #68=(|List| #25#) #65#) NIL #69=(|has| #7# (|InnerEvalable| #25# #7#)) ELT) (($ $ #25# #7#) NIL #69# ELT)) (|euclideanSize| ((#70=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#71=($ $ #7#) NIL (|has| #7# (|Eltable| #7# #7#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #72=(($ $ #58#) NIL T ELT) #73=(($ $ #58# #70#) NIL T ELT) #74=(($ $ #25#) NIL #75=(|has| #7# (|PartialDifferentialSpace| #25#)) ELT) #76=(($ $ #68#) NIL #75# ELT) #77=(($ $ #25# #70#) NIL #75# ELT) #78=(($ $ #68# (|List| #70#)) NIL #75# ELT) #79=(#10# NIL #80=(|has| #7# (|DifferentialSpace|)) ELT) #81=(#82=($ $ #70#) NIL #80# ELT)) (|denominator| #9#) (|denom| #29#) (|convert| ((#50# . #83=($)) NIL (|has| #7# (|ConvertibleTo| #50#)) ELT) ((#53# . #83#) NIL (|has| #7# (|ConvertibleTo| #53#)) ELT) ((#84=(|InputForm|) . #83#) NIL (|has| #7# (|ConvertibleTo| #84#)) ELT) ((#52# . #83#) NIL #85=(|has| #7# (|RealConstant|)) ELT) (((|DoubleFloat|) . #83#) NIL #85# ELT)) (|continuedFraction| (((|ContinuedFraction| #27#) $) NIL T ELT)) (|conditionP| (((|Union| #40# #17#) #36#) NIL #86=(AND (|has| $ #87=(|CharacteristicNonZero|)) #14#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) #9# (($ #27#) NIL T ELT) (($ #7#) NIL T ELT) (($ #25#) NIL #26# ELT)) (|charthRoot| (#54# NIL (OR #86# (|has| #7# #87#)) ELT)) (|characteristic| ((#70#) NIL T CONST)) (|ceiling| #62#) (|before?| #1#) (|associates?| #1#) (|approximate| ((#27# $ #19#) NIL T ELT)) (|annihilate?| #1#) (|abs| (#10# NIL #20# ELT)) (|Zero| #21#) (|One| #21#) (D #72# #73# #74# #76# #77# #78# #79# #81#) (>= #88=(#2# NIL #57# ELT)) (> #88#) (= #1#) (<= #88#) (< #88#) (/ #32# (($ #7# #7#) NIL T ELT)) (- #9# #32#) (+ #32#) (** (($ $ #89=(|PositiveInteger|)) NIL T ELT) (#82# NIL T ELT) (($ $ #19#) NIL T ELT)) (* (($ #89# $) NIL T ELT) (($ #70# $) NIL T ELT) #31# #32# (($ $ #27#) NIL T ELT) (($ #27# . #90=($)) NIL T ELT) (($ #7# . #90#) NIL T ELT) (#71# NIL T ELT))) (((|PAdicRational| |#1|) (|Join| (|QuotientFieldCategory| (|PAdicInteger| |#1|)) (CATEGORY |domain| (SIGNATURE |approximate| (#1=(|Fraction| #2=(|Integer|)) $ #2#)) (SIGNATURE |continuedFraction| ((|ContinuedFraction| #1#) $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ #2# $)))) #2#) (T |PAdicRational|)) ((|approximate| (*1 *2 *1 *3) (AND (|isDomain| *2 #1=(|Fraction| #2=(|Integer|))) (|isDomain| *1 (|PAdicRational| *4)) (|ofType| *4 *3) (|isDomain| *3 #2#))) (|continuedFraction| (*1 *2 *1) (AND (|isDomain| *2 (|ContinuedFraction| #1#)) #3=(|isDomain| *1 (|PAdicRational| *3)) (|ofType| *3 #2#))) (|removeZeroes| (*1 *1 *1) (AND (|isDomain| *1 (|PAdicRational| *2)) (|ofType| *2 #2#))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 #2#) #3# (|ofType| *3 *2)))) @@ -2642,19 +2642,19 @@ NIL ((|shufflein| ((#1=(|Stream| #2=(|List| #3=(|Integer|))) #2# #1#) 41 T ELT)) (|shuffle| (#4=(#1# #2# #2#) 31 T ELT)) (|sequences| ((#1# #2#) 53 T ELT) (#4# 50 T ELT)) (|permutations| ((#1# #3#) 55 T ELT)) (|conjugates| ((#5=(|Stream| #6=(|List| (|PositiveInteger|))) #5#) 22 T ELT)) (|conjugate| ((#6# #6#) 18 T ELT))) (((|PartitionsAndPermutations|) (CATEGORY |package| (SIGNATURE |conjugate| (#1=(|List| (|PositiveInteger|)) #1#)) (SIGNATURE |conjugates| (#2=(|Stream| #1#) #2#)) (SIGNATURE |shuffle| #3=(#4=(|Stream| #5=(|List| #6=(|Integer|))) #5# #5#)) (SIGNATURE |shufflein| (#4# #5# #4#)) (SIGNATURE |sequences| #3#) (SIGNATURE |sequences| (#4# #5#)) (SIGNATURE |permutations| (#4# #6#)))) (T |PartitionsAndPermutations|)) ((|permutations| #1=(*1 *2 *3) (AND #2=(|isDomain| *2 (|Stream| #3=(|List| #4=(|Integer|)))) #5=(|isDomain| *1 (|PartitionsAndPermutations|)) (|isDomain| *3 #4#))) (|sequences| #1# #6=(AND #2# #5# #7=(|isDomain| *3 #3#))) (|sequences| #8=(*1 *2 *3 *3) #6#) (|shufflein| (*1 *2 *3 *2) (AND #2# #7# #5#)) (|shuffle| #8# #6#) (|conjugates| #9=(*1 *2 *2) (AND (|isDomain| *2 (|Stream| #10=(|List| (|PositiveInteger|)))) #5#)) (|conjugate| #9# (AND (|isDomain| *2 #10#) #5#))) -((|convert| (((|Pattern| (|Float|)) . #1=($)) 9 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ELT) (((|Pattern| (|Integer|)) . #1#) 8 (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ELT))) +((|convert| ((#1=(|Pattern| (|Float|)) . #2=($)) 9 (|has| |#1| (|ConvertibleTo| #1#)) ELT) ((#3=(|Pattern| (|Integer|)) . #2#) 8 (|has| |#1| (|ConvertibleTo| #3#)) ELT))) (((|Patternable| |#1|) (|Category|) (|Type|)) (T |Patternable|)) NIL -(|Join| (CATEGORY |package| (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Integer|)))) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (ATTRIBUTE (|ConvertibleTo| (|Pattern| (|Float|)))) |%noBranch|))) +(|Join| (CATEGORY |package| (IF (|has| |t#1| #1=(|ConvertibleTo| (|Pattern| (|Integer|)))) (ATTRIBUTE #1#) |%noBranch|) (IF (|has| |t#1| #2=(|ConvertibleTo| (|Pattern| (|Float|)))) (ATTRIBUTE #2#) |%noBranch|))) (((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|new| (#4=($) 14 T ELT)) (|makeResult| (($ #5=(|PatternMatchResult| |#1| |#2|) #6=(|PatternMatchResult| |#1| |#3|)) 28 T ELT)) (|lists| ((#6# $) 16 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|failed?| ((#3# $) 22 T ELT)) (|failed| (#4# 19 T ELT)) (|coerce| (((|OutputForm|) $) 31 T ELT)) (|before?| #1#) (|atoms| ((#5# $) 15 T ELT)) (= (#2# 26 T ELT))) (((|PatternMatchListResult| |#1| |#2| |#3|) (|Join| #1=(|SetCategory|) (CATEGORY |domain| (SIGNATURE |failed?| ((|Boolean|) $)) (SIGNATURE |failed| #2=($)) (SIGNATURE |new| #2#) (SIGNATURE |makeResult| ($ #3=(|PatternMatchResult| |#1| |#2|) #4=(|PatternMatchResult| |#1| |#3|))) (SIGNATURE |atoms| (#3# $)) (SIGNATURE |lists| (#4# $)))) #1# #1# (|ListAggregate| |#2|)) (T |PatternMatchListResult|)) ((|failed?| #1=(*1 *2 *1) (AND #2=(|ofCategory| *4 #3=(|SetCategory|)) (|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 (|PatternMatchListResult| *3 *4 *5)) #5=(|ofCategory| *3 #3#) #6=(|ofCategory| *5 (|ListAggregate| *4)))) (|failed| #7=(*1 *1) #8=(AND #5# (|isDomain| *1 (|PatternMatchListResult| *2 *3 *4)) (|ofCategory| *2 #3#) (|ofCategory| *4 (|ListAggregate| *3)))) (|new| #7# #8#) (|makeResult| (*1 *1 *2 *3) (AND (|isDomain| *2 (|PatternMatchResult| *4 *5)) (|isDomain| *3 (|PatternMatchResult| *4 *6)) #2# (|ofCategory| *5 #3#) (|ofCategory| *6 (|ListAggregate| *5)) (|isDomain| *1 (|PatternMatchListResult| *4 *5 *6)))) (|atoms| #1# (AND #2# (|isDomain| *2 (|PatternMatchResult| *3 *4)) #4# #5# #6#)) (|lists| #1# (AND #2# (|isDomain| *2 (|PatternMatchResult| *3 *5)) #4# #5# #6#))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) 17 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|patternMatch| ((#2=(|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) #2#) 17 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) (((|PatternMatchable| |#1|) (|Category|) (|SetCategory|)) (T |PatternMatchable|)) ((|patternMatch| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|PatternMatchResult| *4 *1)) (|isDomain| *3 (|Pattern| *4)) (|ofCategory| *1 (|PatternMatchable| *4)) (|ofCategory| *4 (|SetCategory|))))) -(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |patternMatch| ((|PatternMatchResult| |t#1| $) $ (|Pattern| |t#1|) (|PatternMatchResult| |t#1| $))))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |t#1| $) $ (|Pattern| |t#1|) #1#)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|is?| ((#1=(|Boolean|) #2=(|List| |#2|) |#3|) 23 T ELT) ((#1# |#2| |#3|) 18 T ELT)) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) 45 (AND #3=(|not| #4=(|has| |#2| (|RetractableTo| (|Symbol|)))) (|not| #5=(|has| |#2| (|Ring|)))) ELT) (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) 44 (AND #5# #3#) ELT) (((|List| (|Equation| |#2|)) |#2| |#3|) 36 #4# ELT) (((|PatternMatchListResult| |#1| |#2| #2#) #2# |#3|) 21 T ELT))) (((|PatternMatch| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |is?| (#1=(|Boolean|) |#2| |#3|)) (SIGNATURE |is?| (#1# #2=(|List| |#2|) |#3|)) (SIGNATURE |Is| ((|PatternMatchListResult| |#1| |#2| #2#) #2# |#3|)) (IF (|has| |#2| (|RetractableTo| (|Symbol|))) (SIGNATURE |Is| ((|List| (|Equation| |#2|)) |#2| |#3|)) (IF (|has| |#2| (|Ring|)) (SIGNATURE |Is| ((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|)) (SIGNATURE |Is| ((|PatternMatchResult| |#1| |#2|) |#2| |#3|))))) (|SetCategory|) (|PatternMatchable| |#1|) (|ConvertibleTo| (|Pattern| |#1|))) (T |PatternMatch|)) ((|Is| #1=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 (|SetCategory|)) (|isDomain| *2 (|PatternMatchResult| *5 *3)) #3=(|isDomain| *1 (|PatternMatch| *5 *3 *4)) #4=(|not| #5=(|ofCategory| *3 (|RetractableTo| (|Symbol|)))) (|not| #6=(|ofCategory| *3 (|Ring|))) #7=(|ofCategory| *3 #8=(|PatternMatchable| *5)) #9=(|ofCategory| *4 (|ConvertibleTo| (|Pattern| *5))))) (|Is| #1# (AND #2# (|isDomain| *2 (|List| (|Equation| (|Polynomial| *3)))) #3# #6# #4# #7# #9#)) (|Is| #1# (AND #2# (|isDomain| *2 (|List| (|Equation| *3))) #3# #5# #7# #9#)) (|Is| #1# (AND #2# #10=(|ofCategory| *6 #8#) (|isDomain| *2 (|PatternMatchListResult| *5 *6 #11=(|List| *6))) #12=(|isDomain| *1 (|PatternMatch| *5 *6 *4)) #13=(|isDomain| *3 #11#) #9#)) (|is?| #1# (AND #13# #10# #2# #14=(|isDomain| *2 (|Boolean|)) #12# #9#)) (|is?| #1# (AND #2# #14# #3# #7# #9#))) @@ -2682,32 +2682,32 @@ NIL ((D ((|#2| $ |#3|) 10 T ELT))) (((|PartialDifferentialDomain&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE D (|#2| |#1| |#3|))) (|PartialDifferentialDomain| |#2| |#3|) #1=(|Type|) #1#) (T |PartialDifferentialDomain&|)) NIL -((|differentiate| ((|#1| $ |#2|) 7 T ELT)) (D ((|#1| $ |#2|) 6 T ELT))) -(((|PartialDifferentialDomain| |#1| |#2|) (|Category|) (|Type|) (|Type|)) (T |PartialDifferentialDomain|)) -((|differentiate| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PartialDifferentialDomain| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|Type|)))) (D (*1 *2 *1 *3) (AND (|ofCategory| *1 (|PartialDifferentialDomain| *2 *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *2 (|Type|))))) -(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| (|t#1| $ |t#2|)) (SIGNATURE D (|t#1| $ |t#2|)))) -(((|Join|) . T) ((|Type|) . T)) +((|differentiate| (#1=(|#1| $ |#2|) 7 T ELT)) (D (#1# 6 T ELT))) +(((|PartialDifferentialDomain| |#1| |#2|) (|Category|) #1=(|Type|) #1#) (T |PartialDifferentialDomain|)) +((|differentiate| #1=(*1 *2 *1 *3) #2=(AND (|ofCategory| *1 (|PartialDifferentialDomain| *2 *3)) (|ofCategory| *3 #3=(|Type|)) (|ofCategory| *2 #3#))) (D #1# #2#)) +(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE |differentiate| #1=(|t#1| $ |t#2|)) (SIGNATURE D #1#))) +(((|Type|) . T)) ((|rightFactorCandidate| ((|#1| |#1| #1=(|NonNegativeInteger|)) 26 T ELT)) (|leftFactor| (((|Union| |#1| #2="failed") |#1| |#1|) 23 T ELT)) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) #2#) |#1| #1# #1#) 29 T ELT) (((|List| |#1|) |#1|) 38 T ELT))) (((|PolynomialDecomposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |decompose| ((|List| |#1|) |#1|)) (SIGNATURE |decompose| ((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) #1="failed") |#1| #2=(|NonNegativeInteger|) #2#)) (SIGNATURE |leftFactor| ((|Union| |#1| #1#) |#1| |#1|)) (SIGNATURE |rightFactorCandidate| (|#1| |#1| #2#))) (|UnivariatePolynomialCategory| |#2|) (|Field|)) (T |PolynomialDecomposition|)) ((|rightFactorCandidate| (*1 *2 *2 *3) (AND (|isDomain| *3 #1=(|NonNegativeInteger|)) #2=(|ofCategory| *4 #3=(|Field|)) (|isDomain| *1 (|PolynomialDecomposition| *2 *4)) (|ofCategory| *2 #4=(|UnivariatePolynomialCategory| *4)))) (|leftFactor| (*1 *2 *2 *2) (|partial| AND (|ofCategory| *3 #3#) (|isDomain| *1 (|PolynomialDecomposition| *2 *3)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|decompose| (*1 *2 *3 *4 *4) (|partial| AND (|isDomain| *4 #1#) (|ofCategory| *5 #3#) (|isDomain| *2 (|Record| (|:| |left| *3) (|:| |right| *3))) (|isDomain| *1 (|PolynomialDecomposition| *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|decompose| (*1 *2 *3) (AND #2# (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialDecomposition| *3 *4)) (|ofCategory| *3 #4#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#2|) . #4=((|List| #5=(|NonNegativeInteger|)))) 46 T ELT) (($ $ |#2| . #6=(#5#)) 45 T ELT) (($ $ (|List| |#2|)) 44 T ELT) (($ $ |#2|) 42 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ $ (|List| |#2|) . #4#) 49 T ELT) (($ $ |#2| . #6#) 48 T ELT) (($ $ (|List| |#2|)) 47 T ELT) (($ $ |#2|) 43 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 31 T ELT) (($ |#1| . #7#) 34 T ELT) (($ $ |#1|) 38 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ #5=(|List| |#2|) (|List| #6=(|NonNegativeInteger|))) 46 T ELT) (#7=($ $ |#2| #6#) 45 T ELT) (#8=($ $ #5#) 44 T ELT) (#9=($ $ |#2|) 42 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (#4# 49 T ELT) (#7# 48 T ELT) (#8# 47 T ELT) (#9# 43 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#10=($ $ $) 29 T ELT)) (+ (#10# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ #6# $) 21 T ELT) (($ (|Integer|) . #11=($)) 31 T ELT) (($ |#1| . #11#) 34 T ELT) (($ $ |#1|) 38 T ELT))) (((|PartialDifferentialModule| |#1| |#2|) (|Category|) (|Ring|) (|BasicType|)) (T |PartialDifferentialModule|)) NIL (|Join| (|BiModule| |t#1| |t#1|) (|PartialDifferentialSpace| |t#2|) (CATEGORY |package| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#1|)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|PartialDifferentialDomain| $ |#2|) . T) ((|PartialDifferentialSpace| |#2|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#1|) . #4=((|List| #5=(|NonNegativeInteger|)))) 53 T ELT) (($ $ |#1| . #6=(#5#)) 52 T ELT) (($ $ (|List| |#1|)) 51 T ELT) (($ $ |#1|) 49 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ (|List| |#1|) . #4#) 56 T ELT) (($ $ |#1| . #6#) 55 T ELT) (($ $ (|List| |#1|)) 54 T ELT) (($ $ |#1|) 50 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|PartialDifferentialDomain| $ |#2|) . T) ((|PartialDifferentialSpace| |#2|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#5=($ $ #6=(|List| |#1|) (|List| #7=(|NonNegativeInteger|))) 53 T ELT) (#8=($ $ |#1| #7#) 52 T ELT) (#9=($ $ #6#) 51 T ELT) (#10=($ $ |#1|) 49 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #11=(|Integer|)) 42 T ELT)) (|characteristic| ((#7#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (D (#5# 56 T ELT) (#8# 55 T ELT) (#9# 54 T ELT) (#10# 50 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#12=($ $ $) 29 T ELT)) (+ (#12# 18 T ELT)) (** (($ $ #13=(|PositiveInteger|)) 36 T ELT) (($ $ #7#) 44 T ELT)) (* (($ #13# $) 17 T ELT) (($ #7# $) 21 T ELT) (($ #11# $) 31 T ELT) (#12# 35 T ELT))) (((|PartialDifferentialRing| |#1|) (|Category|) (|BasicType|)) (T |PartialDifferentialRing|)) NIL (|Join| (|Ring|) (|PartialDifferentialSpace| |t#1|)) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#1|) . T) ((|PartialDifferentialSpace| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#1|) . T) ((|PartialDifferentialSpace| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|differentiate| (#1=($ $ |#2|) NIL T ELT) (#2=($ $ #3=(|List| |#2|)) 10 T ELT) (#4=($ $ |#2| #5=(|NonNegativeInteger|)) 12 T ELT) (#6=($ $ #3# (|List| #5#)) 15 T ELT)) (D (#1# 16 T ELT) (#2# 18 T ELT) (#4# 19 T ELT) (#6# 21 T ELT))) (((|PartialDifferentialSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE D #1=(|#1| |#1| #2=(|List| |#2|) (|List| #3=(|NonNegativeInteger|)))) (SIGNATURE D #4=(|#1| |#1| |#2| #3#)) (SIGNATURE D #5=(|#1| |#1| #2#)) (SIGNATURE |differentiate| #1#) (SIGNATURE |differentiate| #4#) (SIGNATURE |differentiate| #5#) (SIGNATURE D #6=(|#1| |#1| |#2|)) (SIGNATURE |differentiate| #6#)) (|PartialDifferentialSpace| |#2|) (|BasicType|)) (T |PartialDifferentialSpace&|)) NIL -((|differentiate| (($ $ |#1|) 7 T ELT) (($ $ (|List| |#1|)) 15 T ELT) (($ $ |#1| (|NonNegativeInteger|)) 14 T ELT) (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) 13 T ELT)) (D (($ $ |#1|) 6 T ELT) (($ $ (|List| |#1|)) 12 T ELT) (($ $ |#1| (|NonNegativeInteger|)) 11 T ELT) (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) 10 T ELT))) +((|differentiate| (#1=($ $ |#1|) 7 T ELT) (#2=($ $ #3=(|List| |#1|)) 15 T ELT) (#4=($ $ |#1| #5=(|NonNegativeInteger|)) 14 T ELT) (#6=($ $ #3# (|List| #5#)) 13 T ELT)) (D (#1# 6 T ELT) (#2# 12 T ELT) (#4# 11 T ELT) (#6# 10 T ELT))) (((|PartialDifferentialSpace| |#1|) (|Category|) (|BasicType|)) (T |PartialDifferentialSpace|)) -((|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PartialDifferentialSpace| *3)) (|ofCategory| *3 (|BasicType|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PartialDifferentialSpace| *2)) (|ofCategory| *2 (|BasicType|)))) (|differentiate| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PartialDifferentialSpace| *4)) (|ofCategory| *4 (|BasicType|)))) (D (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PartialDifferentialSpace| *3)) (|ofCategory| *3 (|BasicType|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|PartialDifferentialSpace| *2)) (|ofCategory| *2 (|BasicType|)))) (D (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| (|NonNegativeInteger|))) (|ofCategory| *1 (|PartialDifferentialSpace| *4)) (|ofCategory| *4 (|BasicType|))))) -(|Join| (|PartialDifferentialDomain| $ |t#1|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $ (|List| |t#1|))) (SIGNATURE |differentiate| ($ $ |t#1| (|NonNegativeInteger|))) (SIGNATURE |differentiate| ($ $ (|List| |t#1|) (|List| (|NonNegativeInteger|)))) (SIGNATURE D ($ $ (|List| |t#1|))) (SIGNATURE D ($ $ |t#1| (|NonNegativeInteger|))) (SIGNATURE D ($ $ (|List| |t#1|) (|List| (|NonNegativeInteger|)))))) -(((|Join|) . T) ((|PartialDifferentialDomain| $ |#1|) . T) ((|Type|) . T)) +((|differentiate| #1=(*1 *1 *1 *2) #2=(AND (|isDomain| *2 (|List| *3)) (|ofCategory| *1 (|PartialDifferentialSpace| *3)) (|ofCategory| *3 #3=(|BasicType|)))) (|differentiate| #4=(*1 *1 *1 *2 *3) #5=(AND (|isDomain| *3 #6=(|NonNegativeInteger|)) (|ofCategory| *1 (|PartialDifferentialSpace| *2)) (|ofCategory| *2 #3#))) (|differentiate| #4# #7=(AND (|isDomain| *2 (|List| *4)) (|isDomain| *3 (|List| #6#)) (|ofCategory| *1 (|PartialDifferentialSpace| *4)) (|ofCategory| *4 #3#))) (D #1# #2#) (D #4# #5#) (D #4# #7#)) +(|Join| (|PartialDifferentialDomain| $ |t#1|) (CATEGORY |domain| (SIGNATURE |differentiate| #1=($ $ #2=(|List| |t#1|))) (SIGNATURE |differentiate| #3=($ $ |t#1| #4=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #5=($ $ #2# (|List| #4#))) (SIGNATURE D #1#) (SIGNATURE D #3#) (SIGNATURE D #5#))) +(((|PartialDifferentialDomain| $ |#1|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 26 T ELT)) (|setvalue!| ((|#1| $ |#1|) NIL #5=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setright!| #6=(#7=($ $ $) NIL #5# ELT)) (|setleft!| #6#) (|setelt| ((|#1| $ #8="value" |#1|) NIL #5# ELT) (($ $ #9="left" $) NIL #5# ELT) (($ $ #10="right" $) NIL #5# ELT)) (|setchildren!| (($ $ #11=(|List| $)) NIL #5# ELT)) (|sample| (#12=($) NIL T CONST)) (|right| (#13=($ $) 25 T ELT)) (|ptree| (($ |#1|) 12 T ELT) (#7# 17 T ELT)) (|nodes| #14=((#11# $) NIL T ELT)) (|node?| #1#) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|left| (#13# 23 T ELT)) (|leaves| ((#15=(|List| |#1|) $) NIL T ELT)) (|leaf?| (#16=(#3# $) 20 T ELT)) (|latex| (((|String|) $) NIL #17=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) NIL #17# ELT)) (|eval| (($ $ (|List| #18=(|Equation| |#1|))) NIL #19=(AND (|has| |#1| (|Evalable| |#1|)) #17#) ELT) (($ $ #18#) NIL #19# ELT) (($ $ |#1| |#1|) NIL #19# ELT) (($ $ #15# #15#) NIL #19# ELT)) (|eq?| (#2# NIL T ELT)) (|empty?| #20=(#16# NIL T ELT)) (|empty| (#12# NIL T ELT)) (|elt| ((|#1| $ #8#) NIL T ELT) (($ $ #9#) NIL T ELT) (($ $ #10#) NIL T ELT)) (|distance| (((|Integer|) $ $) NIL T ELT)) (|cyclic?| #20#) (|copy| (#13# NIL T ELT)) (|coerce| (((|Tree| |#1|) $) 9 T ELT) ((#21=(|OutputForm|) $) 29 (|has| |#1| (|CoercibleTo| #21#)) ELT)) (|children| #14#) (|child?| #1#) (|before?| #1#) (= (#2# 21 #4# ELT))) (((|PendantTree| |#1|) (|Join| (|BinaryRecursiveAggregate| |#1|) (|CoercibleTo| (|Tree| |#1|)) (CATEGORY |domain| (SIGNATURE |ptree| ($ |#1|)) (SIGNATURE |ptree| ($ $ $)))) (|SetCategory|)) (T |PendantTree|)) ((|ptree| (*1 *1 *2) #1=(AND (|isDomain| *1 (|PendantTree| *2)) (|ofCategory| *2 (|SetCategory|)))) (|ptree| (*1 *1 *1 *1) #1#)) @@ -2717,11 +2717,11 @@ NIL ((|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) 48 T ELT))) (((|Permanent| |#1| |#2|) (CATEGORY |package| (SIGNATURE |permanent| (|#2| (|SquareMatrix| |#1| |#2|)))) (|PositiveInteger|) (|Join| (|Ring|) (CATEGORY |package| (ATTRIBUTE (|commutative| "*"))))) (T |Permanent|)) ((|permanent| (*1 *2 *3) (AND (|isDomain| *3 (|SquareMatrix| *4 *2)) (|ofType| *4 (|PositiveInteger|)) (|ofCategory| *2 (|Join| (|Ring|) (CATEGORY |package| (ATTRIBUTE (|commutative| "*"))))) (|isDomain| *1 (|Permanent| *4 *2))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|support| (((|Set| |#1|) $) 42 T ELT)) (|sample| (#2=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|orbit| (((|Set| |#1|) $ |#1|) 41 T ELT)) (|one?| (((|Boolean|) $) 22 T ELT)) (|min| (#3=($ $ $) 35 (OR (|has| |#1| . #4=((|OrderedSet|))) (|has| |#1| . #5=((|Finite|)))) ELT)) (|max| (#3# 36 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|elt| ((|#1| $ |#1|) 45 T ELT)) (|cycles| (($ (|List| (|List| |#1|))) 43 T ELT)) (|cycle| (($ (|List| |#1|)) 44 T ELT)) (|conjugate| (#6=($ $ $) 27 T ELT)) (|commutator| (#6# 26 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|One| (#2# 24 T CONST)) (>= (#7=((|Boolean|) $ $) 37 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (> (#7# 39 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (= (#1# 8 T ELT)) (<= (#7# 38 (OR (|has| |#1| . #4#) (|has| |#1| . #5#)) ELT)) (< (((|Boolean|) $ $) 40 T ELT)) (/ (#6# 29 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT) (($ $ (|Integer|)) 28 T ELT)) (* (($ $ $) 18 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|support| ((#3=(|Set| |#1|) $) 42 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 20 T ELT)) (|orbit| ((#3# $ |#1|) 41 T ELT)) (|one?| ((#2# $) 22 T ELT)) (|min| (#5=($ $ $) 35 #6=(OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ELT)) (|max| (#5# 36 #6# ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 30 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|elt| ((|#1| $ |#1|) 45 T ELT)) 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*2 *1 *3) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Set| *3)))) (< (*1 *2 *1 *1) (AND (|ofCategory| *1 (|PermutationCategory| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *2 (|Boolean|))))) -(|Join| (|Group|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |cycle| ($ (|List| |t#1|))) (SIGNATURE |cycles| ($ (|List| (|List| |t#1|)))) (SIGNATURE |support| ((|Set| |t#1|) $)) (SIGNATURE |orbit| ((|Set| |t#1|) $ |t#1|)) (SIGNATURE < ((|Boolean|) $ $)) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|) (IF (|has| |t#1| (|Finite|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| |#1| |#1|) . T) ((|Group|) . T) ((|Join|) . T) ((|Monoid|) . T) ((|OrderedSet|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ((|OrderedType|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|Finite|))) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|cycle| #1=(*1 *1 *2) (AND (|isDomain| *2 #2=(|List| *3)) #3=(|ofCategory| *3 (|SetCategory|)) #4=(|ofCategory| *1 (|PermutationCategory| *3)))) (|cycles| #1# (AND (|isDomain| *2 (|List| #2#)) #3# #4#)) (|support| (*1 *2 *1) #5=(AND #4# #3# (|isDomain| *2 (|Set| *3)))) (|orbit| (*1 *2 *1 *3) #5#) (< (*1 *2 *1 *1) (AND #4# #3# (|isDomain| *2 (|Boolean|))))) +(|Join| (|Group|) (|Eltable| |t#1| |t#1|) (CATEGORY |domain| (SIGNATURE |cycle| ($ #1=(|List| |t#1|))) (SIGNATURE |cycles| ($ (|List| #1#))) (SIGNATURE |support| (#2=(|Set| |t#1|) $)) (SIGNATURE |orbit| (#2# $ |t#1|)) (SIGNATURE < ((|Boolean|) $ $)) (IF (|has| |t#1| #3=(|OrderedSet|)) #4=(ATTRIBUTE #3#) |%noBranch|) (IF (|has| |t#1| (|Finite|)) #4# |%noBranch|))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Eltable| |#1| |#1|) . T) ((|Group|) . T) ((|Monoid|) . T) ((|OrderedSet|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))) ((|OrderedType|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|OrderedSet|))) ((|SemiGroup|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|wordsForStrongGenerators| (((|List| #4=(|List| #5=(|NonNegativeInteger|))) $) 162 T ELT)) (|wordInStrongGenerators| (#6=(#4# #7=(|Permutation| |#1|) $) 190 T ELT)) (|wordInGenerators| (#6# 191 T ELT)) (|support| ((#8=(|Set| |#1|) $) 154 T ELT)) (|strongGenerators| (#9=(#10=(|List| #7#) $) 151 T ELT)) (|random| ((#7# $ #11=(|Integer|)) 156 T ELT) ((#7# $) 157 T ELT)) (|permutationGroup| (#12=($ #10#) 164 T ELT)) (|order| (#13=(#5# $) 158 T ELT)) (|orbits| ((#14=(|Set| #8#) $) 188 T ELT)) (|orbit| ((#8# $ |#1|) 179 T ELT) ((#14# $ #8#) 200 T ELT) (((|Set| #15=(|List| |#1|)) $ #15#) 203 T ELT)) (|member?| ((#3# #7# $) 139 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|initializeGroupForWordProblem| ((#16=(|Void|) $) 144 T ELT) ((#16# $ #11# #11#) 204 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generators| (#9# 145 T ELT)) (|elt| ((#7# $ #5#) 152 T ELT)) (|degree| (#13# 159 T ELT)) (|coerce| (((|OutputForm|) $) 176 T ELT) (#12# 163 T ELT) (#9# 28 T ELT)) (|before?| #1#) (|base| ((#15# $) 161 T ELT)) (= (#2# 197 T ELT)) (<= (#2# 194 T ELT)) (< (#2# 193 T ELT))) (((|PermutationGroup| |#1|) (|Join| #1=(|SetCategory|) (|HomotopicTo| #2=(|List| #3=(|Permutation| |#1|))) (CATEGORY |domain| (SIGNATURE |generators| #4=(#2# $)) (SIGNATURE |elt| (#3# $ #5=(|NonNegativeInteger|))) (SIGNATURE |random| (#3# $ #6=(|Integer|))) (SIGNATURE |random| (#3# $)) (SIGNATURE |order| #7=(#5# $)) (SIGNATURE |degree| #7#) (SIGNATURE |base| (#8=(|List| |#1|) $)) (SIGNATURE |strongGenerators| #4#) (SIGNATURE |wordsForStrongGenerators| ((|List| #9=(|List| #5#)) $)) (SIGNATURE |permutationGroup| ($ #2#)) (SIGNATURE |orbit| (#10=(|Set| |#1|) $ |#1|)) (SIGNATURE |orbits| (#11=(|Set| #10#) $)) (SIGNATURE |orbit| (#11# $ #10#)) (SIGNATURE |orbit| ((|Set| #8#) $ #8#)) (SIGNATURE |member?| (#12=(|Boolean|) #3# $)) (SIGNATURE |wordInStrongGenerators| #13=(#9# #3# $)) (SIGNATURE |wordInGenerators| #13#) (SIGNATURE |support| (#10# $)) (SIGNATURE < #14=(#12# $ $)) (SIGNATURE <= #14#) (SIGNATURE |initializeGroupForWordProblem| (#15=(|Void|) $)) (SIGNATURE |initializeGroupForWordProblem| (#15# $ #6# #6#)))) #1#) (T |PermutationGroup|)) ((|generators| #1=(*1 *2 *1) #2=(AND #3=(|isDomain| *2 (|List| #4=(|Permutation| *3))) #5=(|isDomain| *1 (|PermutationGroup| *3)) #6=(|ofCategory| *3 #7=(|SetCategory|)))) (|elt| #8=(*1 *2 *1 *3) (AND (|isDomain| *3 #9=(|NonNegativeInteger|)) #10=(|isDomain| *2 #11=(|Permutation| *4)) #12=(|isDomain| *1 (|PermutationGroup| *4)) #13=(|ofCategory| *4 #7#))) (|random| #8# (AND #14=(|isDomain| *3 (|Integer|)) #10# #12# #13#)) (|random| #1# (AND (|isDomain| *2 #4#) #5# #6#)) (|order| #1# #15=(AND (|isDomain| *2 #9#) #5# #6#)) (|degree| #1# #15#) (|base| #1# (AND (|isDomain| *2 (|List| *3)) #5# #6#)) (|strongGenerators| #1# #2#) (|wordsForStrongGenerators| #1# (AND (|isDomain| *2 (|List| #16=(|List| #9#))) #5# #6#)) (|permutationGroup| (*1 *1 *2) (AND #3# #6# #5#)) (|orbit| #8# #17=(AND (|isDomain| *2 #18=(|Set| *3)) #5# #6#)) (|orbits| #1# (AND (|isDomain| *2 (|Set| #18#)) #5# #6#)) (|orbit| #8# (AND #13# (|isDomain| *2 (|Set| #19=(|Set| *4))) #12# (|isDomain| *3 #19#))) (|orbit| #8# (AND #13# (|isDomain| *2 (|Set| #20=(|List| *4))) #12# (|isDomain| *3 #20#))) (|member?| #21=(*1 *2 *3 *1) (AND #22=(|isDomain| *3 #11#) #13# #23=(|isDomain| *2 (|Boolean|)) #12#)) (|wordInStrongGenerators| #21# #24=(AND #22# #13# (|isDomain| *2 #16#) #12#)) (|wordInGenerators| #21# #24#) (|support| #1# #17#) (< #25=(*1 *2 *1 *1) #26=(AND #23# #5# #6#)) (<= #25# #26#) (|initializeGroupForWordProblem| #1# (AND #27=(|isDomain| *2 (|Void|)) #5# #6#)) (|initializeGroupForWordProblem| (*1 *2 *1 *3 *3) (AND #14# #27# #12# #13#))) @@ -2737,11 +2737,11 @@ NIL ((|solveLinearPolynomialEquation| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| $)) "failed") #1# #2#) 46 T ELT)) (|gcdPolynomial| ((#2# #2# #2#) 18 T ELT)) (|charthRoot| (((|Maybe| $) $) 40 T ELT))) (((|PolynomialFactorizationExplicit&| |#1|) (CATEGORY |package| (SIGNATURE |charthRoot| ((|Maybe| |#1|) |#1|)) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#1|)) "failed") #1# #2#)) (SIGNATURE |gcdPolynomial| (#2# #2# #2#))) (|PolynomialFactorizationExplicit|)) (T |PolynomialFactorizationExplicit&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 76 T ELT)) (|squareFreePart| (($ $) 67 T ELT)) (|squareFree| (#4=((|Factored| $) $) 68 T ELT)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 73 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|prime?| (((|Boolean|) $) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (#6=($ $ $) 61 T ELT) (#7=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#8=(|SparseUnivariatePolynomial| $) #8# #8#) 59 T ELT)) (|gcd| (#6# 63 T ELT) (#7# 62 T ELT)) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 74 T ELT)) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 75 T ELT)) (|factor| (#4# 66 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) 72 (|has| $ (|CharacteristicNonZero|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|charthRoot| (((|Maybe| $) $) 71 (|has| $ (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|subtractIfCan| ((#5=(|Maybe| $) $ $) 26 T ELT)) (|squareFreePolynomial| (#6=((|Factored| #7=(|SparseUnivariatePolynomial| $)) #7#) 76 T ELT)) (|squareFreePart| (#4# 67 T ELT)) (|squareFree| (#8=((|Factored| $) $) 68 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #9=(|List| #7#) #10="failed") #9# #7#) 73 T ELT)) (|sample| (#11=($) 23 T CONST)) (|recip| ((#12=(|Union| $ #10#) $) 43 T ELT)) (|prime?| (#3# 69 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|lcm| (#13=($ $ $) 61 T ELT) (#14=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7# #7# #7#) 59 T ELT)) (|gcd| (#13# 63 T ELT) (#14# 62 T ELT)) (|factorSquareFreePolynomial| (#6# 74 T ELT)) (|factorPolynomial| (#6# 75 T ELT)) (|factor| (#8# 66 T ELT)) (|exquo| ((#12# $ $) 57 T ELT)) (|conditionP| (((|Union| (|Vector| $) #10#) (|Matrix| $)) 72 #15=(|has| $ (|CharacteristicNonZero|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #16=(|Integer|)) 42 T ELT) (#4# 58 T ELT)) (|charthRoot| ((#5# $) 71 #15# ELT)) (|characteristic| ((#17=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#11# 24 T CONST)) (|One| (#11# 46 T CONST)) (= (#1# 8 T ELT)) (- (#4# 30 T ELT) (#13# 29 T ELT)) (+ (#13# 18 T ELT)) (** (($ $ #18=(|PositiveInteger|)) 36 T ELT) (($ $ #17#) 44 T ELT)) (* (($ #18# $) 17 T ELT) (($ #17# $) 21 T ELT) (($ #16# $) 31 T ELT) (#13# 35 T ELT))) (((|PolynomialFactorizationExplicit|) (|Category|)) (T |PolynomialFactorizationExplicit|)) -((|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)))) (|squareFreePolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|factorPolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|factorSquareFreePolynomial| (*1 *2 *3) (AND (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Factored| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)))) (|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| (|SparseUnivariatePolynomial| *1))) (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)))) (|conditionP| (*1 *2 *3) (|partial| AND (|isDomain| *3 (|Matrix| *1)) (|ofCategory| *1 (|CharacteristicNonZero|)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|)) (|isDomain| *2 (|Vector| *1)))) (|charthRoot| (*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) (|ofCategory| *1 (|CharacteristicNonZero|)) (|ofCategory| *1 (|PolynomialFactorizationExplicit|))))) -(|Join| (|UniqueFactorizationDomain|) (CATEGORY |domain| (SIGNATURE |squareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |factorPolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |factorSquareFreePolynomial| ((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $))) (IF (|has| $ (|CharacteristicNonZero|)) (PROGN (SIGNATURE |conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) (SIGNATURE |charthRoot| ((|Maybe| $) $))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 #1=(|SparseUnivariatePolynomial| *1)) #2=(|ofCategory| *1 (|PolynomialFactorizationExplicit|)))) (|squareFreePolynomial| #3=(*1 *2 *3) #4=(AND #2# (|isDomain| *2 (|Factored| #1#)) #5=(|isDomain| *3 #1#))) (|factorPolynomial| #3# #4#) (|factorSquareFreePolynomial| #3# #4#) (|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #1#)) #5# #2#)) (|conditionP| #3# (|partial| AND (|isDomain| *3 (|Matrix| *1)) #6=(|ofCategory| *1 (|CharacteristicNonZero|)) #2# (|isDomain| *2 (|Vector| *1)))) (|charthRoot| (*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *1)) #6# #2#))) +(|Join| (|UniqueFactorizationDomain|) (CATEGORY |domain| (SIGNATURE |squareFreePolynomial| #1=((|Factored| #2=(|SparseUnivariatePolynomial| $)) #2#)) (SIGNATURE |factorPolynomial| #1#) (SIGNATURE |factorSquareFreePolynomial| #1#) (SIGNATURE |gcdPolynomial| (#2# #2# #2#)) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #3=(|List| #2#) #4="failed") #3# #2#)) (IF (|has| $ (|CharacteristicNonZero|)) (PROGN (SIGNATURE |conditionP| ((|Union| (|Vector| $) #4#) (|Matrix| $))) (SIGNATURE |charthRoot| ((|Maybe| $) $))) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((|torsionIfCan| (((|Union| (|Record| (|:| |order| #1=(|NonNegativeInteger|)) (|:| |function| |#5|)) #2="failed") #3=(|FiniteDivisor| |#2| |#3| |#4| |#5|)) 78 T ELT)) (|torsion?| (((|Boolean|) #3#) 17 T ELT)) (|order| (((|Union| #1# #2#) #3#) 15 T ELT))) (((|PointsOfFiniteOrder| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |order| ((|Union| #1=(|NonNegativeInteger|) #2="failed") #3=(|FiniteDivisor| |#2| |#3| |#4| |#5|))) (SIGNATURE |torsion?| ((|Boolean|) #3#)) (SIGNATURE |torsionIfCan| ((|Union| (|Record| (|:| |order| #1#) (|:| |function| |#5|)) #2#) #3#))) (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|))) (|FunctionSpace| |#1|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| (|Fraction| |#3|)) (|FunctionFieldCategory| |#2| |#3| |#4|)) (T |PointsOfFiniteOrder|)) ((|torsionIfCan| #1=(*1 *2 *3) (|partial| AND #2=(|isDomain| *3 (|FiniteDivisor| *5 *6 *7 *8)) #3=(|ofCategory| *5 (|FunctionSpace| *4)) #4=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) #5=(|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) #6=(|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) #7=(|ofCategory| *4 (|Join| (|IntegralDomain|) (|RetractableTo| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |order| #8=(|NonNegativeInteger|)) (|:| |function| *8))) #9=(|isDomain| *1 (|PointsOfFiniteOrder| *4 *5 *6 *7 *8)))) (|torsion?| #1# (AND #2# #3# #4# #5# #6# #7# (|isDomain| *2 (|Boolean|)) #9#)) (|order| #1# (|partial| AND #2# #3# #4# #5# #6# #7# (|isDomain| *2 #8#) #9#))) @@ -2773,11 +2773,11 @@ NIL ((|coerce| (((|Expression| |#1|) (|Pi|)) 16 T ELT))) (((|PiCoercions| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|Expression| |#1|) (|Pi|)))) (|IntegralDomain|)) (T |PiCoercions|)) ((|coerce| (*1 *2 *3) (AND (|isDomain| *3 (|Pi|)) (|isDomain| *2 (|Expression| *4)) (|isDomain| *1 (|PiCoercions| *4)) (|ofCategory| *4 (|IntegralDomain|))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 67 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (#5=($ $ $) 61 T ELT) (#6=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 59 T ELT)) (|gcd| (#5# 63 T ELT) (#6# 62 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) 66 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| ((#6=(|Union| $ "failed") $) 43 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|lcm| (#8=($ $ $) 61 T ELT) (#9=($ #7#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#10=(|SparseUnivariatePolynomial| $) #10# #10#) 59 T ELT)) (|gcd| (#8# 63 T ELT) (#9# 62 T ELT)) (|exquo| ((#6# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #11=(|Integer|)) 42 T ELT) (#4# 58 T ELT)) (|characteristic| ((#12=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (#5# 46 T CONST)) (= (#1# 8 T ELT)) (- (#4# 30 T ELT) (#8# 29 T ELT)) (+ (#8# 18 T ELT)) (** (($ $ #13=(|PositiveInteger|)) 36 T ELT) (($ $ #12#) 44 T ELT)) (* (($ #13# $) 17 T ELT) (($ #12# $) 21 T ELT) (($ #11# $) 31 T ELT) (#8# 35 T ELT))) (((|PrincipalIdealDomain|) (|Category|)) (T |PrincipalIdealDomain|)) -((|principalIdeal| (*1 *2 *3) (AND (|ofCategory| *1 (|PrincipalIdealDomain|)) (|isDomain| *2 (|Record| (|:| |coef| (|List| *1)) (|:| |generator| *1))) (|isDomain| *3 (|List| *1)))) (|expressIdealMember| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|PrincipalIdealDomain|)) (|isDomain| *2 (|Maybe| (|List| *1))) (|isDomain| *3 (|List| *1))))) -(|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $))) (SIGNATURE |expressIdealMember| ((|Maybe| (|List| $)) (|List| $) $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|principalIdeal| (*1 *2 *3) (AND #1=(|ofCategory| *1 (|PrincipalIdealDomain|)) (|isDomain| *2 (|Record| (|:| |coef| #2=(|List| *1)) (|:| |generator| *1))) #3=(|isDomain| *3 #2#))) (|expressIdealMember| (*1 *2 *3 *1) (AND #1# (|isDomain| *2 (|Maybe| #2#)) #3#))) +(|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |principalIdeal| ((|Record| (|:| |coef| #1=(|List| $)) (|:| |generator| $)) #1#)) (SIGNATURE |expressIdealMember| ((|Maybe| #1#) #1# $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|interpolate| (((|SparseUnivariatePolynomial| |#2|) #1=(|List| |#2|) #1#) 17 T ELT) ((#2=(|UnivariatePolynomial| |#1| |#2|) #2# #1# #1#) 13 T ELT))) (((|PolynomialInterpolation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |interpolate| (#1=(|UnivariatePolynomial| |#1| |#2|) #1# #2=(|List| |#2|) #2#)) (SIGNATURE |interpolate| ((|SparseUnivariatePolynomial| |#2|) #2# #2#))) (|Symbol|) (|Field|)) (T |PolynomialInterpolation|)) ((|interpolate| (*1 *2 *3 *3) (AND #1=(|isDomain| *3 (|List| *5)) #2=(|ofCategory| *5 (|Field|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *5)) #3=(|isDomain| *1 (|PolynomialInterpolation| *4 *5)) #4=(|ofType| *4 (|Symbol|)))) (|interpolate| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 (|UnivariatePolynomial| *4 *5)) #1# #4# #2# #3#))) @@ -2862,11 +2862,11 @@ NIL ((|totalDegree| ((#1=(|NonNegativeInteger|) $) 88 T ELT) ((#1# $ #2=(|List| |#4|)) 93 T ELT)) (|squareFreePart| (#3=($ $) 214 T ELT)) (|squareFree| (#4=((|Factored| $) $) 206 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #5=(|List| #6=(|SparseUnivariatePolynomial| $)) #7="failed") #5# #6#) 141 T ELT)) (|retractIfCan| (((|Union| |#2| #7#) $) NIL T ELT) (((|Union| #8=(|Fraction| #9=(|Integer|)) #7#) $) NIL T ELT) (((|Union| #9# #7#) $) NIL T ELT) (((|Union| |#4| #7#) $) 74 T ELT)) (|retract| #10=((|#2| $) NIL T ELT) ((#8# $) NIL T ELT) ((#9# $) NIL T ELT) ((|#4| $) 73 T ELT)) (|resultant| (($ $ $ |#4|) 95 T ELT)) (|reducedSystem| ((#11=(|Matrix| #9#) #12=(|Matrix| $)) NIL T ELT) (((|Record| (|:| |mat| #11#) (|:| |vec| (|Vector| #9#))) #12# #13=(|Vector| $)) NIL T ELT) (((|Record| (|:| |mat| #14=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) #12# #13#) 131 T ELT) ((#14# #12#) 121 T ELT)) (|primitivePart| (#3# 221 T ELT) (#15=($ $ |#4|) 224 T ELT)) (|primitiveMonomials| (#16=(#17=(|List| $) $) 77 T ELT)) (|patternMatch| ((#18=(|PatternMatchResult| #19=(|Float|) $) $ #20=(|Pattern| #19#) #18#) 240 T ELT) ((#21=(|PatternMatchResult| #9# $) $ #22=(|Pattern| #9#) #21#) 233 T ELT)) (|monomials| (#16# 34 T ELT)) (|monomial| (($ |#2| |#3|) NIL T ELT) (#23=($ $ |#4| #1#) NIL T ELT) (#24=($ $ #2# (|List| #1#)) 71 T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) 203 T ELT)) (|isTimes| (#25=((|Union| #17# #7#) $) 52 T ELT)) (|isPlus| (#25# 39 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| #1#)) #7#) $) 57 T ELT)) (|gcdPolynomial| ((#6# #6# #6#) 134 T ELT)) (|factorSquareFreePolynomial| (#26=((|Factored| #6#) #6#) 147 T ELT)) (|factorPolynomial| (#26# 145 T ELT)) (|factor| (#4# 165 T ELT)) (|eval| (($ $ (|List| #27=(|Equation| $))) 24 T ELT) (($ $ #27#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #17# #17#) NIL T ELT) (($ $ |#4| |#2|) NIL T ELT) (($ $ #2# (|List| |#2|)) NIL T ELT) (($ $ |#4| $) NIL T ELT) (($ $ #2# #17#) NIL T ELT)) (|discriminant| (#15# 97 T ELT)) (|convert| ((#20# $) 254 T ELT) ((#22# $) 247 T ELT) (((|InputForm|) $) 262 T ELT)) (|content| #10# (#15# 216 T ELT)) (|conditionP| (((|Union| #13# #7#) #12#) 185 T ELT)) (|coefficient| ((|#2| $ |#3|) NIL T ELT) (#23# 62 T ELT) (#24# 69 T ELT)) (|charthRoot| (((|Maybe| $) $) 195 T ELT)) (|before?| (((|Boolean|) $ $) 227 T ELT))) (((|PolynomialCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| (#1=(|SparseUnivariatePolynomial| |#1|) #1# #1#)) (SIGNATURE |squareFree| #2=((|Factored| |#1|) |#1|)) (SIGNATURE |squareFreePart| #3=(|#1| |#1|)) (SIGNATURE |charthRoot| ((|Maybe| |#1|) |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| (#4=(|Pattern| #5=(|Integer|)) |#1|)) (SIGNATURE |convert| (#6=(|Pattern| #7=(|Float|)) |#1|)) (SIGNATURE |patternMatch| (#8=(|PatternMatchResult| #5# |#1|) |#1| #4# #8#)) (SIGNATURE |patternMatch| (#9=(|PatternMatchResult| #7# |#1|) |#1| #6# #9#)) (SIGNATURE |factor| #2#) (SIGNATURE |factorPolynomial| #10=((|Factored| #1#) #1#)) (SIGNATURE |factorSquareFreePolynomial| #10#) (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #11=(|List| #1#) 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T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| |#3|) . T) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#3|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) +((|primitivePart| #1=(*1 *1 *1) #2=(AND (|ofCategory| *1 (|PolynomialCategory| *2 *3 *4)) (|ofCategory| *2 #3=(|Ring|)) (|ofCategory| *3 #4=(|OrderedAbelianMonoidSup|)) (|ofCategory| *4 #5=(|OrderedSet|)) (|ofCategory| *2 #6=(|GcdDomain|)))) (|degree| #7=(*1 *2 *1 *3) #8=(AND #9=(|ofCategory| *1 (|PolynomialCategory| *4 *5 *3)) #10=(|ofCategory| *4 #3#) #11=(|ofCategory| *5 #4#) #12=(|ofCategory| *3 #5#) #13=(|isDomain| *2 #14=(|NonNegativeInteger|)))) (|degree| #7# #15=(AND #16=(|isDomain| *3 #17=(|List| *6)) #18=(|ofCategory| *1 (|PolynomialCategory| *4 *5 *6)) #10# #11# #19=(|ofCategory| *6 #5#) (|isDomain| *2 #20=(|List| #14#)))) (|coefficient| #21=(*1 *1 *1 *2 *3) #22=(AND (|isDomain| *3 #14#) (|ofCategory| *1 (|PolynomialCategory| *4 *5 *2)) #10# #11# #23=(|ofCategory| *2 #5#))) (|coefficient| #21# #24=(AND (|isDomain| *2 #17#) (|isDomain| *3 #20#) #18# #10# #11# #19#)) (|monomials| #25=(*1 *2 *1) #26=(AND #27=(|ofCategory| *3 #3#) #28=(|ofCategory| *4 #4#) #29=(|ofCategory| *5 #5#) #30=(|isDomain| *2 (|List| *1)) #31=(|ofCategory| *1 (|PolynomialCategory| *3 *4 *5)))) (|univariate| #7# (AND #10# #11# #12# #32=(|isDomain| *2 (|SparseUnivariatePolynomial| *1)) #9#)) (|univariate| #25# (AND #31# #27# #28# #29# (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|mainVariable| #25# (|partial| AND #33=(|ofCategory| *1 (|PolynomialCategory| *3 *4 *2)) #27# #28# #23#)) (|minimumDegree| #7# #8#) (|minimumDegree| #7# #15#) (|monicDivide| (*1 *2 *1 *1 *3) (AND #10# #11# #12# (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) #9#)) (|monomial| #21# #22#) (|monomial| #21# #24#) (|multivariate| #34=(*1 *1 *2 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) #10# #9# #11# #12#)) (|multivariate| #34# (AND #32# #9# #10# #11# #12#)) (|isPlus| #25# #35=(|partial| AND #27# #28# #29# #30# #31#)) (|isTimes| #25# #35#) (|isExpt| #25# (|partial| AND #31# #27# #28# #29# (|isDomain| *2 (|Record| (|:| |var| *5) (|:| |exponent| #14#))))) (|totalDegree| #25# (AND #31# #27# #28# #29# #13#)) (|totalDegree| #7# (AND #16# #18# #10# #11# #19# #13#)) (|variables| #25# (AND #31# #27# #28# #29# (|isDomain| *2 (|List| *5)))) (|primitiveMonomials| #25# #26#) (|resultant| (*1 *1 *1 *1 *2) #36=(AND #33# #27# #28# #23# (|ofCategory| *3 (|CommutativeRing|)))) (|discriminant| #37=(*1 *1 *1 *2) #36#) (|content| #37# #38=(AND #33# #27# #28# #23# #39=(|ofCategory| *3 #6#))) (|primitivePart| #37# #38#) (|squareFreePart| #1# #2#) (|squareFree| #25# (AND #39# #27# #28# #29# (|isDomain| *2 (|Factored| *1)) #31#))) +(|Join| (|PartialDifferentialRing| |t#3|) (|FiniteAbelianMonoidRing| |t#1| |t#2|) (|Evalable| $) (|InnerEvalable| |t#3| |t#1|) (|InnerEvalable| |t#3| $) (|RetractableTo| |t#3|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |degree| #1=(#2=(|NonNegativeInteger|) $ |t#3|)) (SIGNATURE |degree| #3=(#4=(|List| #2#) $ #5=(|List| |t#3|))) (SIGNATURE |coefficient| #6=($ $ |t#3| #2#)) (SIGNATURE |coefficient| #7=($ $ #5# #4#)) (SIGNATURE |monomials| #8=(#9=(|List| $) $)) (SIGNATURE |univariate| (#10=(|SparseUnivariatePolynomial| $) $ |t#3|)) (SIGNATURE |univariate| (#11=(|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |mainVariable| ((|Union| |t#3| #12="failed") $)) (SIGNATURE |minimumDegree| #1#) (SIGNATURE |minimumDegree| #3#) (SIGNATURE |monicDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |monomial| #6#) (SIGNATURE |monomial| #7#) (SIGNATURE |multivariate| ($ #11# |t#3|)) (SIGNATURE |multivariate| ($ #10# |t#3|)) (SIGNATURE |isPlus| #13=((|Union| #9# #12#) $)) (SIGNATURE |isTimes| #13#) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |t#3|) (|:| |exponent| #2#)) #12#) $)) (SIGNATURE |totalDegree| (#2# $)) (SIGNATURE |totalDegree| (#2# $ #5#)) (SIGNATURE |variables| (#5# $)) (SIGNATURE |primitiveMonomials| #8#) (IF (|has| |t#1| #14=(|ConvertibleTo| (|InputForm|))) (IF (|has| |t#3| #14#) (ATTRIBUTE #14#) |%noBranch|) |%noBranch|) (IF (|has| |t#1| #15=(|ConvertibleTo| (|Pattern| #16=(|Integer|)))) (IF (|has| |t#3| #15#) (ATTRIBUTE #15#) |%noBranch|) |%noBranch|) (IF (|has| |t#1| #17=(|ConvertibleTo| (|Pattern| #18=(|Float|)))) (IF (|has| |t#3| #17#) (ATTRIBUTE #17#) |%noBranch|) |%noBranch|) (IF (|has| |t#1| #19=(|PatternMatchable| #16#)) (IF (|has| |t#3| #19#) (ATTRIBUTE #19#) |%noBranch|) |%noBranch|) (IF (|has| |t#1| #20=(|PatternMatchable| #18#)) (IF (|has| |t#3| #20#) (ATTRIBUTE #20#) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (SIGNATURE |resultant| ($ $ $ |t#3|)) (SIGNATURE |discriminant| #21=($ $ |t#3|))) |%noBranch|) (IF (|has| |t#1| #22=(|GcdDomain|)) (PROGN (ATTRIBUTE #22#) (SIGNATURE |content| #21#) (SIGNATURE |primitivePart| #23=($ $)) (SIGNATURE |primitivePart| #21#) (SIGNATURE |squareFree| ((|Factored| $) $)) (SIGNATURE |squareFreePart| #23#)) |%noBranch|) (IF (|has| |t#1| #24=(ATTRIBUTE |canonicalUnitNormal|)) #24# |%noBranch|) (IF (|has| |t#1| #25=(|PolynomialFactorizationExplicit|)) (ATTRIBUTE #25#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| #3=(|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| #2#)) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|GcdDomain|)) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| |#3|) . T) ((|PatternMatchable| #3#) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| #2#) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#3|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) ((|variables| (((|List| |#2|) |#5|) 40 T ELT)) (|univariate| ((#1=(|SparseUnivariatePolynomial| |#5|) |#5| |#2| #1#) 23 T ELT) ((#2=(|Fraction| #1#) |#5| |#2|) 16 T ELT)) (|multivariate| ((|#5| #2# |#2|) 30 T ELT)) (|mainVariable| (((|Union| |#2| #3="failed") |#5|) 70 T ELT)) (|isTimes| (#4=((|Union| (|List| |#5|) #3#) |#5|) 64 T ELT)) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) #5=(|:| |exponent| (|Integer|))) #3#) |#5|) 53 T ELT)) (|isPlus| (#4# 66 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) #5#) #3#) |#5|) 56 T ELT))) (((|PolynomialCategoryQuotientFunctions| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |variables| ((|List| |#2|) |#5|)) (SIGNATURE |mainVariable| ((|Union| |#2| #1="failed") |#5|)) (SIGNATURE |univariate| (#2=(|Fraction| #3=(|SparseUnivariatePolynomial| |#5|)) |#5| |#2|)) (SIGNATURE |multivariate| (|#5| #2# |#2|)) (SIGNATURE |univariate| (#3# |#5| |#2| #3#)) (SIGNATURE |isPlus| #4=((|Union| (|List| |#5|) #1#) |#5|)) (SIGNATURE |isTimes| #4#) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| |#2|) #5=(|:| |exponent| (|Integer|))) #1#) |#5|)) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| |#5|) #5#) #1#) |#5|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|Ring|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |numer| #6=(|#4| $)) (SIGNATURE |denom| #6#)))) (T |PolynomialCategoryQuotientFunctions|)) ((|isPower| #1=(*1 *2 *3) (|partial| AND #2=(|ofCategory| *4 #3=(|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *5 #5=(|OrderedSet|)) #6=(|ofCategory| *6 #7=(|Ring|)) #8=(|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Record| (|:| |val| *3) #9=(|:| |exponent| (|Integer|)))) #10=(|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *5 *6 *7 *3)) #11=(|ofCategory| *3 #12=(|Join| #13=(|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7)) (SIGNATURE |numer| #14=(*7 $)) (SIGNATURE |denom| #14#)))))) (|isExpt| #1# (|partial| AND #2# #4# #6# #8# (|isDomain| *2 (|Record| (|:| |var| *5) #9#)) #10# #11#)) (|isTimes| #1# #15=(|partial| AND #2# #4# #6# #8# (|isDomain| *2 (|List| *3)) #10# #11#)) (|isPlus| #1# #15#) (|univariate| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 #16=(|SparseUnivariatePolynomial| *3)) #11# #17=(|ofCategory| *7 (|PolynomialCategory| *6 *5 *4)) #18=(|ofCategory| *5 #3#) #19=(|ofCategory| *4 #5#) #6# #20=(|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *3)))) (|multivariate| #21=(*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|SparseUnivariatePolynomial| *2))) #18# #19# #6# (|ofCategory| *2 #12#) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *5 *4 *6 *7 *2)) #17#)) (|univariate| #21# (AND #18# #19# #6# #17# (|isDomain| *2 (|Fraction| #16#)) #20# #11#)) (|mainVariable| #1# (|partial| AND #2# (|ofCategory| *5 #7#) (|ofCategory| *6 (|PolynomialCategory| *5 *4 *2)) (|ofCategory| *2 #5#) (|isDomain| *1 (|PolynomialCategoryQuotientFunctions| *4 *2 *5 *6 *3)) (|ofCategory| *3 (|Join| #13# (CATEGORY |domain| (SIGNATURE |coerce| ($ *6)) (SIGNATURE |numer| #22=(*6 $)) (SIGNATURE |denom| #22#)))))) (|variables| #1# (AND #2# #4# #6# #8# (|isDomain| *2 (|List| *5)) #10# #11#))) @@ -2879,10 +2879,10 @@ NIL ((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|port| (($ #3=(|SingleInteger|)) 8 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (#4=(#3# $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 15 T ELT) (#4# 12 T ELT)) (|before?| #1#) (= (#2# 11 T ELT))) (((|PortNumber|) (|Join| (|SetCategory|) (|CoercibleTo| #1=(|SingleInteger|)) (CATEGORY |domain| (SIGNATURE |port| ($ #1#))))) (T |PortNumber|)) ((|port| (*1 *1 *2) (AND (|isDomain| *2 (|SingleInteger|)) (|isDomain| *1 (|PortNumber|))))) -((|yRange| (((|Segment| (|DoubleFloat|)) $) 8 T ELT)) (|xRange| (((|Segment| (|DoubleFloat|)) $) 9 T ELT)) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 6 T ELT))) +((|yRange| (#1=((|Segment| #2=(|DoubleFloat|)) $) 8 T ELT)) (|xRange| (#1# 9 T ELT)) (|listBranches| (((|List| (|List| (|Point| #2#))) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 6 T ELT))) (((|PlottablePlaneCurveCategory|) (|Category|)) (T |PlottablePlaneCurveCategory|)) -((|listBranches| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))))) (|xRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|yRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) -(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |xRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |yRange| ((|Segment| (|DoubleFloat|)) $)))) +((|listBranches| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|PlottablePlaneCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| #3=(|DoubleFloat|))))))) (|xRange| #1# #4=(AND #2# (|isDomain| *2 (|Segment| #3#)))) (|yRange| #1# #4#)) +(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| #1=(|DoubleFloat|)))) $)) (SIGNATURE |xRange| #2=((|Segment| #1#) $)) (SIGNATURE |yRange| #2#))) (((|CoercibleTo| (|OutputForm|)) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 80 #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#7=($ $) 81 #6# ELT)) (|unit?| (#5# NIL #6# ELT)) (|subtractIfCan| ((#8=(|Maybe| $) $ $) NIL T ELT)) (|sample| (#9=($) NIL T CONST)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=(#12="failed")) . #13=($)) NIL #14=(|has| |#1| (|RetractableTo| #10#)) ELT) (((|Union| #15=(|Fraction| #10#) . #11#) . #13#) NIL #16=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| |#1| . #11#) $) 35 T ELT)) (|retract| ((#10# . #17=($)) NIL #14# ELT) ((#15# . #17#) NIL #16# ELT) #18=(#19=(|#1| . #17#) NIL T ELT)) (|reductum| (#7# 32 T ELT)) (|recip| ((#20=(|Union| $ #12#) $) 43 T ELT)) (|primitivePart| (#7# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 64 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| ((#22=(|NonNegativeInteger|) $) 18 T ELT)) (|monomial?| #4#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|minimumDegree| (#23=(|#2| $) 25 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingMonomial| (#7# 29 T ELT)) (|leadingCoefficient| (#19# 27 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#5# 52 T ELT)) (|ground| #18#) (|fmecg| (($ $ |#2| |#1| $) 90 (AND (|has| |#2| (|CancellationAbelianMonoid|)) #6#) ELT)) (|exquo| ((#20# $ $) 97 #6# ELT) ((#20# $ |#1|) 87 #6# ELT)) (|degree| (#23# 23 T ELT)) (|content| (#19# NIL #21# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #10#) 47 T ELT) (#7# NIL #6# ELT) (($ |#1|) 42 T ELT) (($ #15#) NIL (OR #24=(|has| |#1| (|Algebra| #15#)) #16#) ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ |#2|) 38 T ELT)) (|charthRoot| ((#8# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#22#) 15 T CONST)) (|binomThmExpt| (($ $ $ #22#) 76 (|has| |#1| (|CommutativeRing|)) ELT)) (|before?| #1#) (|associates?| (#2# 86 #6# ELT)) (|annihilate?| #1#) (|Zero| (#9# 28 T CONST)) (|One| (#9# 12 T CONST)) (= (#2# 85 T ELT)) (/ (#25=($ $ |#1|) 98 (|has| |#1| (|Field|)) ELT)) (- (#7# NIL T ELT) #26=(#27=($ $ $) NIL T ELT)) (+ #26#) (** (($ $ #28=(|PositiveInteger|)) 71 T ELT) (($ $ #22#) 69 T ELT)) (* (($ #28# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #10# . #29=($)) NIL T ELT) (#27# 68 T ELT) (#25# 66 T ELT) (($ |#1| . #29#) 65 T ELT) (($ #15# . #29#) NIL #24# ELT) (($ $ #15#) NIL #24# ELT))) (((|PolynomialRing| |#1| |#2|) (|Join| (|FiniteAbelianMonoidRing| |#1| |#2|) (CATEGORY |domain| (IF (|has| |#1| (|IntegralDomain|)) (IF (|has| |#2| (|CancellationAbelianMonoid|)) (SIGNATURE |fmecg| ($ $ |#2| |#1| $)) |%noBranch|) |%noBranch|) (IF (|has| |#1| #1=(ATTRIBUTE |canonicalUnitNormal|)) #1# |%noBranch|))) (|Ring|) (|OrderedAbelianMonoid|)) (T |PolynomialRing|)) @@ -2898,7 +2898,7 @@ NIL ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) #1=(|isDomain| *4 #2=(|PrimitiveArray| *5)) #3=(|ofCategory| *5 #4=(|Type|)) #5=(|ofCategory| *6 #4#) (|isDomain| *2 #6=(|PrimitiveArray| *6)) (|isDomain| *1 (|PrimitiveArrayFunctions2| *5 *6)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *5 *2)) #1# #3# (|ofCategory| *2 #4#) (|isDomain| *1 (|PrimitiveArrayFunctions2| *5 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *6 *5)) (|isDomain| *4 #6#) #5# #3# (|isDomain| *2 #2#) (|isDomain| *1 (|PrimitiveArrayFunctions2| *6 *5))))) ((|integral| (($ $ (|SegmentBinding| $)) 7 T ELT) (($ $ (|Symbol|)) 6 T ELT))) (((|PrimitiveFunctionCategory|) (|Category|)) (T |PrimitiveFunctionCategory|)) -((|integral| (*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) (|ofCategory| *1 (|PrimitiveFunctionCategory|)))) (|integral| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PrimitiveFunctionCategory|)) (|isDomain| *2 (|Symbol|))))) +((|integral| #1=(*1 *1 *1 *2) (AND (|isDomain| *2 (|SegmentBinding| *1)) #2=(|ofCategory| *1 (|PrimitiveFunctionCategory|)))) (|integral| #1# (AND #2# (|isDomain| *2 (|Symbol|))))) (|Join| (CATEGORY |domain| (SIGNATURE |integral| ($ $ (|Symbol|))) (SIGNATURE |integral| ($ $ (|SegmentBinding| $))))) ((|primitiveElement| ((#1=(|Record| (|:| |coef| (|List| #2=(|Integer|))) (|:| |poly| (|List| #3=(|SparseUnivariatePolynomial| |#1|))) #4=(|:| |prim| #3#)) #5=(|List| #6=(|Polynomial| |#1|)) #7=(|List| #8=(|Symbol|)) #8#) 26 T ELT) ((#1# #5# #7#) 27 T ELT) (((|Record| (|:| |coef1| #2#) (|:| |coef2| #2#) #4#) #6# #8# #6# #8#) 49 T ELT))) (((|PrimitiveElement| |#1|) (CATEGORY |package| (SIGNATURE |primitiveElement| ((|Record| (|:| |coef1| #1=(|Integer|)) (|:| |coef2| #1#) #2=(|:| |prim| #3=(|SparseUnivariatePolynomial| |#1|))) #4=(|Polynomial| |#1|) #5=(|Symbol|) #4# #5#)) (SIGNATURE |primitiveElement| (#6=(|Record| (|:| |coef| (|List| #1#)) (|:| |poly| (|List| #3#)) #2#) #7=(|List| #4#) #8=(|List| #5#))) (SIGNATURE |primitiveElement| (#6# #7# #8# #5#))) (|Join| (|Field|) (|CharacteristicZero|))) (T |PrimitiveElement|)) @@ -2924,16 +2924,16 @@ NIL ((|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) 29 T ELT))) (((|PropositionalFormulaFunctions2| |#1| |#2|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |map| ((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|))))) #1=(|SetCategory|) #1#) (T |PropositionalFormulaFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|PropositionalFormula| *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|PropositionalFormula| *6)) (|isDomain| *1 (|PropositionalFormulaFunctions2| *5 *6))))) -((~= (#1=((|Boolean|) $ $) 19 T ELT)) (~ (($ $) 8 T ELT)) (|true| (($) 17 T CONST)) (|or| (#2=($ $ $) 9 T ELT)) (|not| (($ $) 11 T ELT)) (|latex| (((|String|) $) 23 T ELT)) (|implies| (($ $ $) 15 T ELT)) (|hash| (((|SingleInteger|) $) 22 T ELT)) (|false| (($) 16 T CONST)) (|equiv| (($ $ $) 14 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|before?| (#1# 20 T ELT)) (|and| (#2# 10 T ELT)) (|\\/| (#3=($ $ $) 6 T ELT)) (= (#1# 18 T ELT)) (|/\\| (#3# 7 T ELT))) +((~= (#1=((|Boolean|) $ $) 19 T ELT)) (~ (#2=($ $) 8 T ELT)) (|true| (#3=($) 17 T CONST)) (|or| (#4=($ $ $) 9 T ELT)) (|not| (#2# 11 T ELT)) (|latex| (((|String|) $) 23 T ELT)) (|implies| (#4# 15 T ELT)) (|hash| (((|SingleInteger|) $) 22 T ELT)) (|false| (#3# 16 T CONST)) (|equiv| (#4# 14 T ELT)) (|coerce| (((|OutputForm|) $) 21 T ELT)) (|before?| (#1# 20 T ELT)) (|and| (#4# 10 T ELT)) (|\\/| (#4# 6 T ELT)) (= (#1# 18 T ELT)) (|/\\| (#4# 7 T ELT))) (((|PropositionalLogic|) (|Category|)) (T |PropositionalLogic|)) -((|true| (*1 *1) (|ofCategory| *1 (|PropositionalLogic|))) (|false| (*1 *1) (|ofCategory| *1 (|PropositionalLogic|))) (|implies| (*1 *1 *1 *1) (|ofCategory| *1 (|PropositionalLogic|))) (|equiv| (*1 *1 *1 *1) (|ofCategory| *1 (|PropositionalLogic|)))) -(|Join| (|BooleanLogic|) (|SetCategory|) (CATEGORY |domain| (SIGNATURE |true| ($) |constant|) (SIGNATURE |false| ($) |constant|) (SIGNATURE |implies| ($ $ $)) (SIGNATURE |equiv| ($ $ $)))) -(((|BasicType|) . T) ((|BooleanLogic|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Logic|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 54 (|has| |#1| . #4=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 50 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 49 T ELT)) (|merge!| (($ $ $) 41 T ELT)) (|merge| (($ $ $) 42 T ELT)) (|members| (((|List| |#1|) $) 48 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 53 (|has| |#1| . #4#) ELT)) (|max| ((|#1| $) 43 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #7=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 51 T ELT)) (|extract!| ((|#1| . #7#) 37 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #8=($)) 46 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#9=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#9# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|count| ((#10=(|NonNegativeInteger|) |#1| $) 52 (|has| |#1| . #4#) ELT) ((#10# (|Mapping| #5# |#1|) $) 47 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|any?| ((#5# (|Mapping| #5# |#1|) . #8#) 45 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#10# $) 44 T ELT))) +((|true| #1=(*1 *1) #2=(|ofCategory| *1 (|PropositionalLogic|))) (|false| #1# #2#) (|implies| #3=(*1 *1 *1 *1) #2#) (|equiv| #3# #2#)) +(|Join| (|BooleanLogic|) (|SetCategory|) (CATEGORY |domain| (SIGNATURE |true| #1=($) |constant|) (SIGNATURE |false| #1# |constant|) (SIGNATURE |implies| #2=($ $ $)) (SIGNATURE |equiv| #2#))) +(((|BasicType|) . T) ((|BooleanLogic|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Logic|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|sample| (#4=($) 6 T CONST)) (|reduce| ((|#1| #5=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 54 #3# ELT) ((|#1| #5# $ |#1|) 50 T ELT) ((|#1| #5# $) 49 T ELT)) (|merge!| (#6=($ $ $) 41 T ELT)) (|merge| (#6# 42 T ELT)) (|members| ((#7=(|List| |#1|) $) 48 T ELT)) (|member?| ((#2# |#1| $) 53 #3# ELT)) (|max| (#8=(|#1| $) 43 T ELT)) (|map!| (#9=($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (#9# 26 T ELT)) (|latex| (((|String|) $) 21 #10=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#8# 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 #10# ELT)) (|find| (((|Union| |#1| "failed") #11=(|Mapping| #2# |#1|) $) 51 T ELT)) (|extract!| (#8# 37 T ELT)) (|every?| (#12=(#2# #11# $) 46 T ELT)) (|eval| (($ $ (|List| #13=(|Equation| |#1|))) 25 #14=(AND (|has| |#1| (|Evalable| |#1|)) #10#) ELT) (($ $ #13#) 24 #14# ELT) (($ $ |#1| |#1|) 23 #14# ELT) (($ $ #7# #7#) 22 #14# ELT)) (|eq?| (#1# 10 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#4# 8 T ELT)) (|count| ((#15=(|NonNegativeInteger|) |#1| $) 52 #3# ELT) ((#15# #11# $) 47 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| ((#16=(|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| #16#)) ELT)) (|before?| (#1# 19 #3# ELT)) (|bag| (($ #7#) 38 T ELT)) (|any?| (#12# 45 T ELT)) (= (#1# 17 #3# ELT)) (|#| ((#15# $) 44 T ELT))) (((|PriorityQueueAggregate| |#1|) (|Category|) (|OrderedSet|)) (T |PriorityQueueAggregate|)) -((|max| (*1 *2 *1) (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|merge| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|merge!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|PriorityQueueAggregate| *2)) (|ofCategory| *2 (|OrderedSet|))))) -(|Join| (|BagAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |max| (|t#1| $)) (SIGNATURE |merge| ($ $ $)) (SIGNATURE |merge!| ($ $ $)))) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((|max| (*1 *2 *1) #1=(AND (|ofCategory| *1 (|PriorityQueueAggregate| *2)) (|ofCategory| *2 (|OrderedSet|)))) (|merge| #2=(*1 *1 *1 *1) #1#) (|merge!| #2# #1#)) +(|Join| (|BagAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |max| (|t#1| $)) (SIGNATURE |merge| #1=($ $ $)) (SIGNATURE |merge!| #1#))) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((|subResultantGcdEuclidean| (((|Record| #1=(|:| |coef1| |#2|) #2=(|:| |coef2| |#2|) #3=(|:| |gcd| |#2|)) |#2| |#2|) 105 T ELT)) (|subResultantGcd| (#4=(|#2| |#2| |#2|) 103 T ELT)) (|semiSubResultantGcdEuclidean2| (((|Record| #2# #3#) |#2| |#2|) 107 T ELT)) (|semiSubResultantGcdEuclidean1| (((|Record| #1# #3#) |#2| |#2|) 109 T ELT)) (|semiResultantReduitEuclidean| (((|Record| #2# #5=(|:| |resultantReduit| |#1|)) |#2| |#2|) 132 #6=(|has| |#1| (|GcdDomain|)) ELT)) (|semiResultantEuclideannaif| (#7=((|Record| #2# #8=(|:| |resultant| |#1|)) |#2| |#2|) 56 T ELT)) (|semiResultantEuclidean2| (#7# 80 T ELT)) (|semiResultantEuclidean1| (((|Record| #1# #8#) |#2| |#2|) 82 T ELT)) (|semiLastSubResultantEuclidean| ((#9=(|Record| #2# #10=(|:| |subResultant| |#2|)) |#2| |#2|) 96 T ELT)) (|semiIndiceSubResultantEuclidean| (#11=(#9# |#2| |#2| #12=(|NonNegativeInteger|)) 89 T ELT)) (|semiDiscriminantEuclidean| (((|Record| #2# #13=(|:| |discriminant| |#1|)) |#2|) 121 T ELT)) (|semiDegreeSubResultantEuclidean| (#11# 92 T ELT)) (|schema| (((|List| #12#) |#2| |#2|) 102 T ELT)) (|resultantnaif| (#14=(|#1| |#2| |#2|) 50 T ELT)) (|resultantReduitEuclidean| (((|Record| #1# #2# #5#) |#2| |#2|) 130 #6# ELT)) (|resultantReduit| (#14# 128 #6# ELT)) (|resultantEuclideannaif| (#15=((|Record| #1# #2# #8#) |#2| |#2|) 54 T ELT)) (|resultantEuclidean| (#15# 79 T ELT)) (|resultant| (#14# 76 T ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) #16=(|:| |quotient| |#2|) #17=(|:| |remainder| |#2|)) |#2| |#2|) 41 T ELT)) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) 67 T ELT)) (|lastSubResultantEuclidean| ((#18=(|Record| #1# #2# #10#) |#2| |#2|) 94 T ELT)) (|lastSubResultant| (#4# 93 T ELT)) (|indiceSubResultantEuclidean| (#19=(#18# |#2| |#2| #12#) 87 T ELT)) (|indiceSubResultant| (#20=(|#2| |#2| |#2| #12#) 85 T ELT)) (|gcd| (#4# 136 #6# ELT)) (|exquo| ((#21=(|Vector| |#2|) #21# |#1|) 22 T ELT)) (|divide| (((|Record| #16# #17#) |#2| |#2|) 46 T ELT)) (|discriminantEuclidean| (((|Record| #1# #2# #13#) |#2|) 119 T ELT)) (|discriminant| ((|#1| |#2|) 116 T ELT)) (|degreeSubResultantEuclidean| (#19# 91 T ELT)) (|degreeSubResultant| (#20# 90 T ELT)) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) 99 T ELT)) (|Lazard2| ((|#2| |#2| |#1| |#1| #12#) 62 T ELT)) (|Lazard| ((|#1| |#1| |#1| #12#) 61 T ELT)) (* ((#21# |#1| #21#) 17 T ELT))) (((|PseudoRemainderSequence| |#1| |#2|) (CATEGORY |package| (SIGNATURE |resultant| #1=(|#1| |#2| |#2|)) (SIGNATURE |resultantEuclidean| #2=((|Record| #3=(|:| |coef1| |#2|) #4=(|:| |coef2| |#2|) #5=(|:| |resultant| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean2| #6=((|Record| #4# #5#) |#2| |#2|)) (SIGNATURE |semiResultantEuclidean1| ((|Record| #3# #5#) |#2| |#2|)) (SIGNATURE |indiceSubResultant| #7=(|#2| |#2| |#2| #8=(|NonNegativeInteger|))) (SIGNATURE |indiceSubResultantEuclidean| #9=(#10=(|Record| #3# #4# #11=(|:| |subResultant| |#2|)) |#2| |#2| #8#)) (SIGNATURE |semiIndiceSubResultantEuclidean| #12=(#13=(|Record| #4# #11#) |#2| |#2| #8#)) (SIGNATURE |degreeSubResultant| #7#) (SIGNATURE |degreeSubResultantEuclidean| #9#) (SIGNATURE |semiDegreeSubResultantEuclidean| #12#) (SIGNATURE |lastSubResultant| #14=(|#2| |#2| |#2|)) (SIGNATURE |lastSubResultantEuclidean| (#10# |#2| |#2|)) (SIGNATURE |semiLastSubResultantEuclidean| (#13# |#2| |#2|)) (SIGNATURE |subResultantGcd| #14#) (SIGNATURE |subResultantGcdEuclidean| ((|Record| #3# #4# #15=(|:| |gcd| |#2|)) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean2| ((|Record| #4# #15#) |#2| |#2|)) (SIGNATURE |semiSubResultantGcdEuclidean1| ((|Record| #3# #15#) |#2| |#2|)) (SIGNATURE |discriminant| (|#1| |#2|)) (SIGNATURE |discriminantEuclidean| ((|Record| #3# #4# #16=(|:| |discriminant| |#1|)) |#2|)) (SIGNATURE |semiDiscriminantEuclidean| ((|Record| #4# #16#) |#2|)) (SIGNATURE |chainSubResultants| ((|List| |#2|) |#2| |#2|)) (SIGNATURE |schema| ((|List| #8#) |#2| |#2|)) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |resultantReduit| #1#) (SIGNATURE |resultantReduitEuclidean| ((|Record| #3# #4# #17=(|:| |resultantReduit| |#1|)) |#2| |#2|)) (SIGNATURE |semiResultantReduitEuclidean| ((|Record| #4# #17#) |#2| |#2|)) (SIGNATURE |gcd| #14#)) |%noBranch|) (SIGNATURE * (#18=(|Vector| |#2|) |#1| #18#)) (SIGNATURE |exquo| (#18# #18# |#1|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |#1|) #19=(|:| |quotient| |#2|) #20=(|:| |remainder| |#2|)) |#2| |#2|)) (SIGNATURE |divide| ((|Record| #19# #20#) |#2| |#2|)) (SIGNATURE |Lazard| (|#1| |#1| |#1| #8#)) (SIGNATURE |Lazard2| (|#2| |#2| |#1| |#1| #8#)) (SIGNATURE |nextsousResultant2| (|#2| |#2| |#2| |#2| |#1|)) (SIGNATURE |resultantnaif| #1#) (SIGNATURE |resultantEuclideannaif| #2#) (SIGNATURE |semiResultantEuclideannaif| #6#)) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |PseudoRemainderSequence|)) ((|semiResultantEuclideannaif| #1=(*1 *2 *3 *3) #2=(AND #3=(|ofCategory| *4 #4=(|IntegralDomain|)) (|isDomain| *2 (|Record| #5=(|:| |coef2| *3) #6=(|:| |resultant| *4))) #7=(|isDomain| *1 (|PseudoRemainderSequence| *4 *3)) #8=(|ofCategory| *3 #9=(|UnivariatePolynomialCategory| *4)))) (|resultantEuclideannaif| #1# #10=(AND #3# (|isDomain| *2 (|Record| #11=(|:| |coef1| *3) #5# #6#)) #7# #8#)) (|resultantnaif| #1# #12=(AND #13=(|ofCategory| *2 #4#) #14=(|isDomain| *1 (|PseudoRemainderSequence| *2 *3)) #15=(|ofCategory| *3 #16=(|UnivariatePolynomialCategory| *2)))) (|nextsousResultant2| (*1 *2 *2 *2 *2 *3) #17=(AND #18=(|ofCategory| *3 #4#) #19=(|isDomain| *1 (|PseudoRemainderSequence| *3 *2)) #20=(|ofCategory| *2 #21=(|UnivariatePolynomialCategory| *3)))) (|Lazard2| (*1 *2 *2 *3 *3 *4) (AND #22=(|isDomain| *4 #23=(|NonNegativeInteger|)) #18# #19# #20#)) (|Lazard| #24=(*1 *2 *2 *2 *3) (AND #25=(|isDomain| *3 #23#) #13# (|isDomain| *1 (|PseudoRemainderSequence| *2 *4)) (|ofCategory| *4 #16#))) (|divide| #1# (AND #3# (|isDomain| *2 (|Record| #26=(|:| |quotient| *3) #27=(|:| |remainder| *3))) #7# #8#)) (|pseudoDivide| #1# (AND #3# (|isDomain| *2 (|Record| (|:| |coef| *4) #26# #27#)) #7# #8#)) (|exquo| (*1 *2 *2 *3) #28=(AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 #21#) #18# (|isDomain| *1 (|PseudoRemainderSequence| *3 *4)))) (* (*1 *2 *3 *2) #28#) (|gcd| #29=(*1 *2 *2 *2) (AND (|ofCategory| *3 #30=(|GcdDomain|)) #18# #19# #20#)) (|semiResultantReduitEuclidean| #1# (AND #31=(|ofCategory| *4 #30#) #3# (|isDomain| *2 (|Record| #5# #32=(|:| |resultantReduit| *4))) #7# #8#)) (|resultantReduitEuclidean| #1# (AND #31# #3# (|isDomain| *2 (|Record| #11# #5# #32#)) #7# #8#)) (|resultantReduit| #1# (AND #13# (|ofCategory| *2 #30#) #14# #15#)) (|schema| #1# (AND #3# (|isDomain| *2 (|List| #23#)) #7# #8#)) (|chainSubResultants| #1# (AND #3# (|isDomain| *2 (|List| *3)) #7# #8#)) (|semiDiscriminantEuclidean| #33=(*1 *2 *3) (AND #3# (|isDomain| *2 (|Record| #5# #34=(|:| |discriminant| *4))) #7# #8#)) (|discriminantEuclidean| #33# (AND #3# (|isDomain| *2 (|Record| #11# #5# #34#)) #7# #8#)) (|discriminant| #33# #12#) (|semiSubResultantGcdEuclidean1| #1# (AND #3# (|isDomain| *2 (|Record| #11# #35=(|:| |gcd| *3))) #7# #8#)) (|semiSubResultantGcdEuclidean2| #1# (AND #3# (|isDomain| *2 (|Record| #5# #35#)) #7# #8#)) (|subResultantGcdEuclidean| #1# (AND #3# (|isDomain| *2 (|Record| #11# #5# #35#)) #7# #8#)) (|subResultantGcd| #29# #17#) (|semiLastSubResultantEuclidean| #1# (AND #3# #36=(|isDomain| *2 (|Record| #5# #37=(|:| |subResultant| *3))) #7# #8#)) (|lastSubResultantEuclidean| #1# (AND #3# #38=(|isDomain| *2 (|Record| #11# #5# #37#)) #7# #8#)) (|lastSubResultant| #29# #17#) (|semiDegreeSubResultantEuclidean| #39=(*1 *2 *3 *3 *4) #40=(AND #22# #41=(|ofCategory| *5 #4#) #36# #42=(|isDomain| *1 (|PseudoRemainderSequence| *5 *3)) #43=(|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|degreeSubResultantEuclidean| #39# #44=(AND #22# #41# #38# #42# #43#)) (|degreeSubResultant| #24# #45=(AND #25# #3# (|isDomain| *1 (|PseudoRemainderSequence| *4 *2)) (|ofCategory| *2 #9#))) (|semiIndiceSubResultantEuclidean| #39# #40#) (|indiceSubResultantEuclidean| #39# #44#) (|indiceSubResultant| #24# #45#) (|semiResultantEuclidean1| #1# (AND #3# (|isDomain| *2 (|Record| #11# #6#)) #7# #8#)) (|semiResultantEuclidean2| #1# #2#) (|resultantEuclidean| #1# #10#) (|resultant| #1# #12#)) @@ -2946,24 +2946,24 @@ NIL ((/ (#1=($ $ |#2|) 31 T ELT)) (- (($ $) 23 T ELT) #2=(($ $ $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #3=(|Integer|) $) 17 T ELT) #2# (#1# 21 T ELT) (($ |#2| $) 20 T ELT) (($ #4=(|Fraction| #3#) $) 27 T ELT) (($ $ #4#) 29 T ELT))) (((|PowerSeriesCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE * (|#1| |#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE / #3=(|#1| |#1| |#2|)) (SIGNATURE * (|#1| |#2| |#1|)) (SIGNATURE * #3#) (SIGNATURE * #4=(|#1| |#1| |#1|)) (SIGNATURE - #4#) (SIGNATURE - (|#1| |#1|)) (SIGNATURE * (|#1| #2# |#1|)) (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)) (SIGNATURE * (|#1| (|PositiveInteger|) |#1|))) (|PowerSeriesCategory| |#2| |#3| |#4|) (|Ring|) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |PowerSeriesCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#3|) $) 96 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 76 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (#6=($ $) 82 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial?| (((|Boolean|) $) 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT) (($ $ |#3| |#2|) 98 T ELT) (($ $ (|List| |#3|) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#6# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 72 (|has| |#1| . #3#) ELT)) (|degree| ((|#2| $) 85 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #7=(|Fraction| (|Integer|))) 79 (|has| |#1| . #8=((|Algebra| #7#))) ELT) (($ $) 71 (|has| |#1| . #3#) ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 75 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #9=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #9#) 89 T ELT) (($ #7# . #9#) 78 (|has| |#1| . #8#) ELT) (($ $ #7#) 77 (|has| |#1| . #8#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|variables| ((#4=(|List| |#3|) $) 96 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#6=($ $) 74 #5# ELT)) (|unit?| (#3# 76 #5# ELT)) (|subtractIfCan| ((#7=(|Maybe| $) $ $) 26 T ELT)) (|sample| (#8=($) 23 T CONST)) (|reductum| (#6# 82 T ELT)) (|recip| ((#9=(|Union| $ "failed") $) 43 T ELT)) (|pole?| (#3# 95 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|monomial?| (#3# 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT) (($ $ |#3| |#2|) 98 T ELT) (($ $ #4# (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#6# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#9# $ $) 72 #5# ELT)) (|degree| ((|#2| $) 85 T ELT)) (|complete| (#6# 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #10=(|Integer|)) 42 T ELT) (($ #11=(|Fraction| #10#)) 79 #12=(|has| |#1| (|Algebra| #11#)) ELT) (#6# 71 #5# ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| ((#7# $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#13=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 75 #5# ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#8# 24 T CONST)) (|One| (#8# 46 T CONST)) (= (#1# 8 T ELT)) (/ (#14=($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (#6# 30 T ELT) (#15=($ $ $) 29 T ELT)) (+ (#15# 18 T ELT)) (** (($ $ #16=(|PositiveInteger|)) 36 T ELT) (($ $ #13#) 44 T ELT)) (* (($ #16# $) 17 T ELT) (($ #13# $) 21 T ELT) (($ #10# . #17=($)) 31 T ELT) (#15# 35 T ELT) (#14# 90 T ELT) (($ |#1| . #17#) 89 T ELT) (($ #11# . #17#) 78 #12# ELT) (($ $ #11#) 77 #12# ELT))) (((|PowerSeriesCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoid|) (|OrderedSet|)) (T |PowerSeriesCategory|)) -((|leadingCoefficient| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|Ring|)))) (|leadingMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *2 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|ofCategory| *1 (|PowerSeriesCategory| *4 *3 *2)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *2 (|OrderedSet|)))) (|monomial| (*1 *1 *1 *2 *3) (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 (|List| *5)) (|ofCategory| *1 (|PowerSeriesCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoid|)) (|ofCategory| *6 (|OrderedSet|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *5)))) (|pole?| (*1 *2 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|complete| (*1 *1 *1) (AND (|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|ofCategory| *4 (|OrderedSet|))))) -(|Join| (|AbelianMonoidRing| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |monomial| ($ $ |t#3| |t#2|)) (SIGNATURE |monomial| ($ $ (|List| |t#3|) (|List| |t#2|))) (SIGNATURE |leadingMonomial| ($ $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |variables| ((|List| |t#3|) $)) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |complete| ($ $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((|zRange| (((|Segment| (|DoubleFloat|)) $) 8 T ELT)) (|yRange| (((|Segment| (|DoubleFloat|)) $) 9 T ELT)) (|xRange| (((|Segment| (|DoubleFloat|)) $) 10 T ELT)) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 6 T ELT))) +((|leadingCoefficient| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|PowerSeriesCategory| *2 *3 *4)) #3=(|ofCategory| *3 #4=(|OrderedAbelianMonoid|)) #5=(|ofCategory| *4 #6=(|OrderedSet|)) #7=(|ofCategory| *2 #8=(|Ring|)))) (|leadingMonomial| #9=(*1 *1 *1) #10=(AND #2# #7# #3# #5#)) (|degree| #1# (AND (|ofCategory| *1 (|PowerSeriesCategory| *3 *2 *4)) #11=(|ofCategory| *3 #8#) #5# (|ofCategory| *2 #4#))) (|monomial| #12=(*1 *1 *1 *2 *3) (AND (|ofCategory| *1 (|PowerSeriesCategory| *4 *3 *2)) #13=(|ofCategory| *4 #8#) #3# (|ofCategory| *2 #6#))) (|monomial| #12# (AND (|isDomain| *2 (|List| *6)) (|isDomain| *3 #14=(|List| *5)) (|ofCategory| *1 (|PowerSeriesCategory| *4 *5 *6)) #13# (|ofCategory| *5 #4#) (|ofCategory| *6 #6#))) (|variables| #1# (AND #15=(|ofCategory| *1 (|PowerSeriesCategory| *3 *4 *5)) #11# #16=(|ofCategory| *4 #4#) #17=(|ofCategory| *5 #6#) (|isDomain| *2 #14#))) (|pole?| #1# (AND #15# #11# #16# #17# (|isDomain| *2 (|Boolean|)))) (|complete| #9# #10#)) +(|Join| (|AbelianMonoidRing| |t#1| |t#2|) (CATEGORY |domain| (SIGNATURE |monomial| ($ $ |t#3| |t#2|)) (SIGNATURE |monomial| ($ $ #1=(|List| |t#3|) (|List| |t#2|))) (SIGNATURE |leadingMonomial| #2=($ $)) (SIGNATURE |leadingCoefficient| (|t#1| $)) (SIGNATURE |degree| (|t#2| $)) (SIGNATURE |variables| (#1# $)) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |complete| #2#))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|zRange| (#1=((|Segment| #2=(|DoubleFloat|)) $) 8 T ELT)) (|yRange| (#1# 9 T ELT)) (|xRange| (#1# 10 T ELT)) (|listBranches| (((|List| (|List| (|Point| #2#))) $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 6 T ELT))) (((|PlottableSpaceCurveCategory|) (|Category|)) (T |PlottableSpaceCurveCategory|)) -((|listBranches| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| (|DoubleFloat|))))))) (|xRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|yRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|))))) (|zRange| (*1 *2 *1) (AND (|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|Segment| (|DoubleFloat|)))))) -(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |xRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |yRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |zRange| ((|Segment| (|DoubleFloat|)) $)))) +((|listBranches| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|PlottableSpaceCurveCategory|)) (|isDomain| *2 (|List| (|List| (|Point| #3=(|DoubleFloat|))))))) (|xRange| #1# #4=(AND #2# (|isDomain| *2 (|Segment| #3#)))) (|yRange| #1# #4#) (|zRange| #1# #4#)) +(|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| #1=(|DoubleFloat|)))) $)) (SIGNATURE |xRange| #2=((|Segment| #1#) $)) (SIGNATURE |yRange| #2#) (SIGNATURE |zRange| #2#))) (((|CoercibleTo| (|OutputForm|)) . T)) ((|variables| (#1=((|List| |#4|) $) 23 T ELT)) (|trivialIdeal?| (#2=(#3=(|Boolean|) $) 55 T ELT)) (|triangular?| (#2# 54 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) 42 T ELT)) (|roughUnitIdeal?| (#2# 56 T ELT)) (|roughSubIdeal?| (#4=(#3# $ $) 62 T ELT)) (|roughEqualIdeals?| (#4# 65 T ELT)) (|roughBase?| (#2# 60 T ELT)) (|rewriteIdealWithRemainder| (#5=(#6=(|List| |#5|) #6# $) 103 T ELT)) (|rewriteIdealWithHeadRemainder| (#5# 100 T ELT)) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #7=(|:| |den| |#2|)) |#5| $) 93 T ELT)) (|mainVariables| (#1# 27 T ELT)) (|mainVariable?| ((#3# |#4| $) 34 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#5|) #7#) |#5| $) 86 T ELT)) (|collectUpper| (#8=($ $ |#4|) 39 T ELT)) (|collectUnder| (#8# 38 T ELT)) (|collect| (#8# 40 T ELT)) (= (#4# 46 T ELT))) (((|PolynomialSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |triangular?| #1=(#2=(|Boolean|) |#1|)) (SIGNATURE |rewriteIdealWithRemainder| #3=(#4=(|List| |#5|) #4# |#1|)) (SIGNATURE |rewriteIdealWithHeadRemainder| #3#) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #5=(|:| |den| |#2|)) |#5| |#1|)) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |#5|) #5#) |#5| |#1|)) (SIGNATURE |roughUnitIdeal?| #1#) (SIGNATURE |roughEqualIdeals?| #6=(#2# |#1| |#1|)) (SIGNATURE |roughSubIdeal?| #6#) (SIGNATURE |roughBase?| #1#) (SIGNATURE |trivialIdeal?| #1#) (SIGNATURE |sort| ((|Record| (|:| |under| |#1|) (|:| |floor| |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (SIGNATURE |collectUpper| #7=(|#1| |#1| |#4|)) (SIGNATURE |collect| #7#) (SIGNATURE |collectUnder| #7#) (SIGNATURE |mainVariable?| (#2# |#4| |#1|)) (SIGNATURE |mainVariables| #8=((|List| |#4|) |#1|)) (SIGNATURE |variables| #8#) (SIGNATURE = #6#)) (|PolynomialSetCategory| |#2| |#3| |#4| |#5|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |PolynomialSetCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|variables| (((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (((|Boolean|) $) 32 T ELT)) (|triangular?| (((|Boolean|) $) 23 (|has| |#1| (|IntegralDomain|)) ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #2=(|Boolean|) |#4|) . #3=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|sample| (#4=($) 59 T CONST)) (|roughUnitIdeal?| (((|Boolean|) $) 28 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughSubIdeal?| (((|Boolean|) $ $) 30 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughEqualIdeals?| (((|Boolean|) $ $) 29 (|has| |#1| (|IntegralDomain|)) ELT)) (|roughBase?| (((|Boolean|) $) 31 (|has| |#1| (|IntegralDomain|)) ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) 24 (|has| |#1| (|IntegralDomain|)) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) 25 (|has| |#1| (|IntegralDomain|)) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #5=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #5#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #2# |#4|) . #3#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| (|IntegralDomain|)) ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #6=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#7=(|Boolean|) |#4| $) 53 (|has| |#4| . #6#) ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) $) 38 T ELT)) (|mainVariable?| (((|Boolean|) |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| (|IntegralDomain|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #7# |#4|) $) 51 T ELT)) (|every?| ((#7# (|Mapping| #7# |#4|) . #8=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #9#)) ELT)) (|eq?| ((#10=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#10# $) 58 T ELT)) (|empty| (#4# 57 T ELT)) (|count| ((#11=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #6#) ELT) ((#11# (|Mapping| #7# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#12=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #12#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #13=($)) 13 T ELT) (((|List| |#4|) . #13#) 43 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#7# (|Mapping| #7# |#4|) . #8#) 45 T ELT)) (= (#1# 8 T ELT)) (|#| ((#11# $) 44 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|variables| (#3=((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (#4=(#2# $) 32 T ELT)) (|triangular?| (#4# 23 #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (#6=($ #7=(|Mapping| #2# |#4|) $) 67 #8=(|has| $ (|FiniteAggregate| |#4|)) ELT)) (|sample| (#9=($) 59 T CONST)) (|roughUnitIdeal?| (#4# 28 #5# ELT)) (|roughSubIdeal?| (#1# 30 #5# ELT)) (|roughEqualIdeals?| (#1# 29 #5# ELT)) (|roughBase?| (#4# 31 #5# ELT)) (|rewriteIdealWithRemainder| (#10=(#11=(|List| |#4|) #11# $) 24 #5# ELT)) (|rewriteIdealWithHeadRemainder| (#10# 25 #5# ELT)) (|retractIfCan| (((|Union| $ #12="failed") #11#) 42 T ELT)) (|retract| (#13=($ #11#) 41 T ELT)) (|removeDuplicates| (#14=($ $) 69 #15=(AND #16=(|has| |#4| (|BasicType|)) #8#) ELT)) (|remove| (($ |#4| $) 68 #15# ELT) (#6# 66 #8# ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #17=(|:| |den| |#1|)) |#4| $) 26 #5# ELT)) (|reduce| ((|#4| #18=(|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 #16# ELT) ((|#4| #18# $ |#4|) 50 T ELT) ((|#4| #18# $) 49 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (#19=(#11# $) 48 T ELT)) (|member?| ((#2# |#4| $) 53 #16# ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (#3# 38 T ELT)) (|mainVariable?| ((#2# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #17#) |#4| $) 27 #5# ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#4| #12#) #7# $) 51 T ELT)) (|every?| (#20=(#2# #7# $) 46 T ELT)) (|eval| (($ $ #11# #11#) 64 #21=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) 63 #21# ELT) (($ $ #22=(|Equation| |#4|)) 62 #21# ELT) (($ $ (|List| #22#)) 61 #21# ELT)) (|eq?| (#1# 55 T ELT)) (|empty?| (#4# 58 T ELT)) (|empty| (#9# 57 T ELT)) (|count| ((#23=(|NonNegativeInteger|) |#4| $) 52 #16# ELT) ((#23# #7# $) 47 T ELT)) (|copy| (#14# 56 T ELT)) (|convert| ((#24=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #24#)) ELT)) (|construct| (#13# 65 T ELT)) (|collectUpper| (#25=($ $ |#3|) 34 T ELT)) (|collectUnder| (#25# 36 T ELT)) (|collect| (#25# 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#19# 43 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| (#20# 45 T ELT)) (= (#1# 8 T ELT)) (|#| ((#23# $) 44 T ELT))) (((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |PolynomialSetCategory|)) -((|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)))) (|mvar| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *2 (|OrderedSet|)))) (|variables| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *5)))) (|mainVariables| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *5)))) (|mainVariable?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *3 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3)) (|isDomain| *2 (|Boolean|)))) (|collectUnder| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)))) (|collect| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)))) (|collectUpper| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)))) (|sort| (*1 *2 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3)) (|isDomain| *2 (|Record| (|:| |under| *1) (|:| |floor| *1) (|:| |upper| *1))) (|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *3 *6)))) (|trivialIdeal?| (*1 *2 *1) (AND (|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) 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T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|retractIfCan| #1=(*1 *1 *2) (|partial| AND #2=(|isDomain| *2 (|List| *6)) #3=(|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #4=(|ofCategory| *3 #5=(|Ring|)) #6=(|ofCategory| *4 #7=(|OrderedAbelianMonoidSup|)) #8=(|ofCategory| *5 #9=(|OrderedSet|)) #10=(|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *5 *6)))) (|retract| #1# (AND #2# #3# #4# #6# #8# #10#)) (|mvar| #11=(*1 *2 *1) (AND #12=(|ofCategory| *1 (|PolynomialSetCategory| *3 *4 *2 *5)) #4# #6# #13=(|ofCategory| *5 (|RecursivePolynomialCategory| *3 *4 *2)) #14=(|ofCategory| *2 #9#))) (|variables| #11# #15=(AND #10# #4# #6# #8# #3# (|isDomain| *2 (|List| *5)))) (|mainVariables| #11# #15#) (|mainVariable?| #16=(*1 *2 *3 *1) (AND #17=(|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *3 *6)) #18=(|ofCategory| *4 #5#) #19=(|ofCategory| *5 #7#) #20=(|ofCategory| *3 #9#) #21=(|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3)) #22=(|isDomain| *2 (|Boolean|)))) (|collectUnder| #23=(*1 *1 *1 *2) #24=(AND #12# #4# #6# #14# #13#)) (|collect| #23# #24#) (|collectUpper| #23# #24#) (|sort| (*1 *2 *1 *3) (AND #18# #19# #20# #21# (|isDomain| *2 (|Record| (|:| |under| *1) (|:| |floor| *1) (|:| |upper| *1))) #17#)) (|trivialIdeal?| #11# (AND #10# #4# #6# #8# #3# #22#)) (|roughBase?| #11# #25=(AND #10# #4# #6# #8# #3# #26=(|ofCategory| *3 #27=(|IntegralDomain|)) #22#)) (|roughSubIdeal?| #28=(*1 *2 *1 *1) #25#) (|roughEqualIdeals?| #28# #25#) (|roughUnitIdeal?| #11# #25#) (|headRemainder| #16# (AND #29=(|ofCategory| *1 (|PolynomialSetCategory| *4 *5 *6 *3)) #18# #19# #30=(|ofCategory| *6 #9#) #31=(|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) #32=(|ofCategory| *4 #27#) (|isDomain| *2 (|Record| (|:| |num| *3) #33=(|:| |den| *4))))) (|remainder| #16# (AND #29# #18# #19# #30# #31# #32# (|isDomain| *2 (|Record| (|:| |rnum| *4) (|:| |polnum| *3) #33#)))) (|rewriteIdealWithHeadRemainder| #34=(*1 *2 *2 *1) #35=(AND #2# #10# #4# #6# #8# #3# #26#)) (|rewriteIdealWithRemainder| #34# #35#) (|triangular?| #11# #25#)) +(|Join| (|SetCategory|) (|Collection| |t#4|) (|FiniteAggregate| |t#4|) (|CoercibleTo| #1=(|List| |t#4|)) (CATEGORY |domain| (SIGNATURE |retractIfCan| ((|Union| $ "failed") #1#)) (SIGNATURE |retract| ($ #1#)) (SIGNATURE |mvar| (|t#3| $)) (SIGNATURE |variables| #2=((|List| |t#3|) $)) (SIGNATURE |mainVariables| #2#) (SIGNATURE |mainVariable?| (#3=(|Boolean|) |t#3| $)) (SIGNATURE |collectUnder| #4=($ $ |t#3|)) (SIGNATURE |collect| #4#) (SIGNATURE |collectUpper| #4#) (SIGNATURE |sort| ((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |t#3|)) (SIGNATURE |trivialIdeal?| #5=(#3# $)) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |roughBase?| #5#) (SIGNATURE |roughSubIdeal?| #6=(#3# $ $)) (SIGNATURE |roughEqualIdeals?| #6#) (SIGNATURE |roughUnitIdeal?| #5#) (SIGNATURE |headRemainder| ((|Record| (|:| |num| |t#4|) #7=(|:| |den| |t#1|)) |t#4| $)) (SIGNATURE |remainder| ((|Record| (|:| |rnum| |t#1|) (|:| |polnum| |t#4|) #7#) |t#4| $)) (SIGNATURE |rewriteIdealWithHeadRemainder| #8=(#1# #1# $)) (SIGNATURE |rewriteIdealWithRemainder| #8#) (SIGNATURE |triangular?| #5#)) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|SetCategory|) . T) ((|Type|) . T)) ((|unprotectedRemoveRedundantFactors| (#1=(#2=(|List| |#4|) |#4| |#4|) 135 T ELT)) (|univariatePolynomialsGcds| ((#2# #2# #3=(|Boolean|)) 123 #4=(|has| |#1| (|GcdDomain|)) ELT) (#5=(#2# #2#) 124 #4# ELT)) (|univariatePolynomials| (#6=(#7=(|Record| (|:| |goodPols| #2#) (|:| |badPols| #2#)) #2#) 44 T ELT)) (|univariate?| (#8=(#3# |#4|) 43 T ELT)) (|squareFreeFactors| ((#2# |#4|) 120 #4# ELT)) (|selectPolynomials| ((#7# #9=(|Mapping| #3# |#4|) #2#) 24 T ELT)) (|selectOrPolynomials| (#10=(#7# (|List| #9#) #2#) 30 T ELT)) (|selectAndPolynomials| (#10# 31 T ELT)) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| #2#)) "failed") #2#) 90 T ELT)) (|rewriteSetByReducingWithParticularGenerators| ((#2# #2# #9# #11=(|Mapping| #3# |#4| |#4|) #12=(|Mapping| |#4| |#4| |#4|)) 103 T ELT)) (|rewriteIdealWithQuasiMonicGenerators| ((#2# #2# #11# #12#) 127 T ELT)) (|removeSquaresIfCan| (#5# 126 T ELT)) (|removeRoughlyRedundantFactorsInPols| ((#2# #2# #2# #3#) 59 T ELT) (#13=(#2# #2# #2#) 61 T ELT)) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| #2#) 60 T ELT)) (|removeRoughlyRedundantFactorsInContents| (#13# 131 #4# ELT)) (|removeRedundantFactorsInPols| (#13# 134 #4# ELT)) (|removeRedundantFactorsInContents| (#13# 133 #4# ELT)) (|removeRedundantFactors| ((#2# #2# #2# (|Mapping| #2# #2#)) 105 T ELT) (#13# 107 T ELT) ((#2# #2# |#4|) 139 T ELT) (#1# 136 T ELT) (#5# 106 T ELT)) (|removeIrreducibleRedundantFactors| (#13# 117 #14=(AND (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|EuclideanDomain|))) ELT)) (|quasiMonicPolynomials| (#6# 52 T ELT)) (|probablyZeroDim?| ((#3# #2#) 79 T ELT)) (|possiblyNewVariety?| ((#3# #2# (|List| #2#)) 67 T ELT)) (|linearPolynomials| (#6# 37 T ELT)) (|linear?| (#8# 36 T ELT)) (|lazyIrreducibleFactors| (#5# 116 #14# ELT)) (|irreducibleFactors| (#5# 115 #14# ELT)) (|interReduce| (#5# 83 T ELT)) (|crushedSet| (#5# 97 T ELT)) (|certainlySubVariety?| ((#3# #2# #2#) 65 T ELT)) (|bivariatePolynomials| (#6# 50 T ELT)) (|bivariate?| (#8# 45 T ELT))) (((|PolynomialSetUtilitiesPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |removeRedundantFactors| #1=(#2=(|List| |#4|) #2#)) (SIGNATURE |removeRedundantFactors| #3=(#2# |#4| |#4|)) (SIGNATURE |removeSquaresIfCan| #1#) (SIGNATURE |unprotectedRemoveRedundantFactors| #3#) (SIGNATURE |removeRedundantFactors| (#2# #2# |#4|)) (SIGNATURE |removeRedundantFactors| #4=(#2# #2# #2#)) (SIGNATURE |removeRedundantFactors| (#2# #2# #2# (|Mapping| #2# #2#))) (SIGNATURE |certainlySubVariety?| (#5=(|Boolean|) #2# #2#)) (SIGNATURE |possiblyNewVariety?| (#5# #2# (|List| #2#))) (SIGNATURE |probablyZeroDim?| (#5# #2#)) (SIGNATURE |selectPolynomials| (#6=(|Record| (|:| |goodPols| #2#) (|:| |badPols| #2#)) #7=(|Mapping| #5# |#4|) #2#)) (SIGNATURE |selectOrPolynomials| #8=(#6# (|List| #7#) #2#)) (SIGNATURE |selectAndPolynomials| #8#) (SIGNATURE |quasiMonicPolynomials| #9=(#6# #2#)) (SIGNATURE |univariate?| #10=(#5# |#4|)) (SIGNATURE 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|removeRedundantFactorsInContents| #4#) (SIGNATURE |removeRedundantFactorsInPols| #4#)) |%noBranch|) (IF (|has| |#1| (|EuclideanDomain|)) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |irreducibleFactors| #1#) (SIGNATURE |lazyIrreducibleFactors| #1#) (SIGNATURE |removeIrreducibleRedundantFactors| #4#)) |%noBranch|) |%noBranch|)) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |PolynomialSetUtilitiesPackage|)) ((|removeIrreducibleRedundantFactors| #1=(*1 *2 *2 *2) #2=(AND #3=(|isDomain| *2 (|List| *6)) #4=(|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|CharacteristicZero|)) (|ofCategory| *3 (|EuclideanDomain|)) #5=(|ofCategory| *3 #6=(|IntegralDomain|)) #7=(|ofCategory| *4 #8=(|OrderedAbelianMonoidSup|)) #9=(|ofCategory| *5 #10=(|OrderedSet|)) #11=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *3 *4 *5 *6)))) (|lazyIrreducibleFactors| #12=(*1 *2 *2) #2#) (|irreducibleFactors| #12# #2#) (|removeRedundantFactorsInPols| #1# #13=(AND #3# #4# (|ofCategory| *3 #14=(|GcdDomain|)) #5# #7# #9# #11#)) (|removeRedundantFactorsInContents| #1# #13#) (|removeRoughlyRedundantFactorsInContents| #1# #13#) (|univariatePolynomialsGcds| #15=(*1 *2 *2 *3) (AND #16=(|isDomain| *2 #17=(|List| *7)) #18=(|isDomain| *3 #19=(|Boolean|)) #20=(|ofCategory| *7 #21=(|RecursivePolynomialCategory| *4 *5 *6)) #22=(|ofCategory| *4 #14#) #23=(|ofCategory| *4 #6#) #24=(|ofCategory| *5 #8#) #25=(|ofCategory| *6 #10#) #26=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *7)))) (|univariatePolynomialsGcds| #12# #13#) (|squareFreeFactors| #27=(*1 *2 *3) (AND #22# #23# #24# #25# #28=(|isDomain| *2 (|List| *3)) #29=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *3)) #30=(|ofCategory| *3 #21#))) (|rewriteIdealWithQuasiMonicGenerators| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 #31=(|List| *8)) (|isDomain| *3 (|Mapping| #19# *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) #32=(|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) #33=(|ofCategory| *5 #6#) #34=(|ofCategory| *6 #8#) #35=(|ofCategory| *7 #10#) #36=(|isDomain| *1 (|PolynomialSetUtilitiesPackage| *5 *6 *7 *8)))) (|rewriteSetByReducingWithParticularGenerators| (*1 *2 *2 *3 *4 *5) (AND (|isDomain| *2 (|List| *9)) (|isDomain| *3 (|Mapping| #19# *9)) (|isDomain| *4 (|Mapping| #19# *9 *9)) (|isDomain| *5 (|Mapping| *9 *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #6#) (|ofCategory| *7 #8#) (|ofCategory| *8 #10#) (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *6 *7 *8 *9)))) (|crushedSet| #12# #37=(AND #3# #4# #5# #7# #9# #11#)) (|roughBasicSet| #27# (|partial| AND #23# #24# #25# #20# (|isDomain| *2 (|Record| (|:| |bas| (|GeneralTriangularSet| *4 *5 *6 *7)) (|:| |top| #17#))) #26# #38=(|isDomain| *3 #17#))) (|interReduce| #12# #37#) (|removeRoughlyRedundantFactorsInPol| #15# (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #21#) #23# #24# #25# (|isDomain| *1 (|PolynomialSetUtilitiesPackage| *4 *5 *6 *2)))) (|removeRoughlyRedundantFactorsInPols| #39=(*1 *2 *2 *2 *3) (AND #16# #18# #20# #23# #24# #25# #26#)) (|removeRoughlyRedundantFactorsInPols| #1# #37#) (|bivariatePolynomials| #27# #40=(AND #23# #24# #25# #20# (|isDomain| *2 (|Record| (|:| |goodPols| #17#) (|:| |badPols| #17#))) #26# #38#)) (|bivariate?| #27# #41=(AND #23# #24# #25# #42=(|isDomain| *2 #19#) #29# #30#)) (|linearPolynomials| #27# #40#) (|linear?| #27# #41#) (|univariatePolynomials| #27# #40#) (|univariate?| #27# #41#) (|quasiMonicPolynomials| #27# #40#) (|selectAndPolynomials| #43=(*1 *2 *3 *4) #44=(AND (|isDomain| *3 (|List| #45=(|Mapping| #19# *8))) #32# #33# #34# #35# #46=(|isDomain| *2 (|Record| (|:| |goodPols| #31#) (|:| |badPols| #31#))) #36# #47=(|isDomain| *4 #31#))) (|selectOrPolynomials| #43# #44#) (|selectPolynomials| #43# (AND (|isDomain| *3 #45#) #32# #33# #34# #35# #46# #36# #47#)) (|probablyZeroDim?| #27# #48=(AND #38# #20# #23# #24# #25# #42# #26#)) (|possiblyNewVariety?| #43# (AND (|isDomain| *4 (|List| #31#)) (|isDomain| *3 #31#) #32# #33# #34# #35# #42# #36#)) (|certainlySubVariety?| #49=(*1 *2 *3 *3) #48#) (|removeRedundantFactors| #39# (AND (|isDomain| *3 (|Mapping| #17# #17#)) #16# #20# #23# #24# #25# #26#)) (|removeRedundantFactors| #1# #37#) (|removeRedundantFactors| #15# (AND #28# #30# #23# #24# #25# #29#)) (|unprotectedRemoveRedundantFactors| #49# #50=(AND #23# #24# #25# #28# #29# #30#)) (|removeSquaresIfCan| #12# #37#) (|removeRedundantFactors| #49# #50#) (|removeRedundantFactors| #12# #37#)) @@ -2973,21 +2973,21 @@ NIL ((|squareFree| (((|Factored| |#4|) |#4|) 61 T ELT))) (((|PolynomialSquareFree| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#4|) |#4|))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|GcdDomain|) (|PolynomialCategory| |#3| |#2| |#1|)) (T |PolynomialSquareFree|)) ((|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|GcdDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|PolynomialSquareFree| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4))))) -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|zero| (($ (|NonNegativeInteger|)) 123 (|has| |#1| (|AbelianMonoid|)) ELT)) (|swap!| (((|Void|) $ #3=(|Integer|) #3#) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#4=(|Boolean|) (|Mapping| #4# |#1| |#1|) $) 96 T ELT) ((#4# $) 90 (|has| |#1| . #5=((|OrderedSet|))) ELT)) (|sort!| (($ (|Mapping| #4# |#1| |#1|) . #6=($)) 87 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (#7=($ $) 86 (AND (|has| |#1| . #5#) (|has| $ (|ShallowlyMutableAggregate| |#1|))) ELT)) (|sort| (($ (|Mapping| #4# |#1| |#1|) . #6#) 97 T ELT) (#7# 91 (|has| |#1| . #5#) ELT)) (|setelt| ((|#1| $ #3# |#1|) 47 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ #8=(|UniversalSegment| #3#) |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|select| (($ (|Mapping| #9=(|Boolean|) |#1|) . #10=($)) 69 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#11=($) 6 T CONST)) (|reverse!| (#7# 88 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|reverse| (#7# 98 T ELT)) (|removeDuplicates| (($ $) 71 (AND (|has| |#1| . #12=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 70 (AND (|has| |#1| . #12#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #9# |#1|) . #10#) 68 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 110 (|has| |#1| . #13=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 106 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 105 T ELT)) (|qsetelt!| ((|#1| $ #3# |#1|) 48 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|qelt| ((|#1| $ #3#) 46 T ELT)) (|position| ((#14=(|Integer|) (|Mapping| #4# |#1|) $) 95 T ELT) ((#14# |#1| $) 94 (|has| |#1| . #15=((|BasicType|))) ELT) ((#14# |#1| $ #14#) 93 (|has| |#1| . #15#) ELT)) (|point| (($ (|List| |#1|)) 129 T ELT)) (|outerProduct| (((|Matrix| |#1|) $ $) 116 (|has| |#1| . #16=((|Ring|))) ELT)) (|new| (($ (|NonNegativeInteger|) |#1|) 65 T ELT)) (|minIndex| ((#3# . #17=($)) 38 (|has| #3# . #18=((|OrderedSet|))) ELT)) (|min| (#19=($ $ $) 80 (|has| |#1| . #5#) ELT)) (|merge| (($ (|Mapping| #4# |#1| |#1|) $ $) 99 T ELT) (($ $ $) 92 (|has| |#1| . #5#) ELT)) (|members| (((|List| |#1|) $) 104 T ELT)) (|member?| ((#20=(|Boolean|) |#1| $) 109 (|has| |#1| . #13#) ELT)) (|maxIndex| ((#3# . #17#) 39 (|has| #3# . #18#) ELT)) (|max| (#19# 81 (|has| |#1| . #5#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 112 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT) (($ (|Mapping| |#1| |#1| |#1|) $ $) 60 T ELT)) (|magnitude| ((|#1| . #21=($)) 113 (AND (|has| |#1| . #16#) (|has| |#1| . #22=((|RadicalCategory|)))) ELT)) (|length| ((|#1| . #21#) 114 (AND (|has| |#1| . #16#) (|has| |#1| . #22#)) ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #23=((|SetCategory|))) ELT)) 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|#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#26# $) 7 T ELT)) (|empty| (#11# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ #8#) 66 T ELT)) (|dot| ((|#1| $ $) 117 (|has| |#1| . #16#) ELT)) (|dimension| (((|PositiveInteger|) $) 128 T ELT)) (|delete| (($ $ #3#) 59 T ELT) (($ $ #8#) 58 T ELT)) (|cross| (($ $ $) 115 T ELT)) (|count| ((#27=(|NonNegativeInteger|) |#1| $) 108 (|has| |#1| . #13#) ELT) ((#27# (|Mapping| #20# |#1|) $) 103 T ELT)) (|copyInto!| (($ $ $ #14#) 89 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#28=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #28#)) ELT) (($ (|List| |#1|)) 130 T ELT)) (|construct| (($ (|List| |#1|)) 67 T ELT)) (|concat| (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|any?| 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|t#1|))))) -(((|Aggregate|) . 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*4 (|Ring|)) #3=(|ofCategory| *2 (|PolynomialCategory| #1# *5 *6)) #4=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #5=(|ofCategory| *6 #6=(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#7=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #7#))))) #8=(|isDomain| *1 (|PushVariables| *4 *5 *6 *2)))) (|pushup| #9=(*1 *2 *2 *3) #10=(AND (|isDomain| *3 (|List| *6)) #5# #2# #4# #8# #3#)) (|pushup| #9# #11=(AND #2# #4# (|ofCategory| *3 #6#) (|isDomain| *1 (|PushVariables| *4 *5 *3 *2)) (|ofCategory| *2 (|PolynomialCategory| #1# *5 *3)))) (|pushdown| #9# #10#) (|pushdown| #9# #11#)) @@ -3009,11 +3009,11 @@ NIL ((|retractIfCan| (((|Union| |#2| #1="failed") $) NIL T ELT) (((|Union| #2=(|Symbol|) #1#) $) 72 T ELT) (((|Union| #3=(|Fraction| #4=(|Integer|)) #1#) $) NIL T ELT) (((|Union| #4# #1#) $) 102 T ELT)) (|retract| ((|#2| $) NIL T ELT) ((#2# $) 67 T ELT) ((#3# $) NIL T ELT) ((#4# $) 99 T ELT)) (|reducedSystem| ((#5=(|Matrix| #4#) #6=(|Matrix| $)) NIL T ELT) 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#22#) 87 T ELT) (($ #22# . #76#) 86 T ELT) (($ |#1| . #76#) 207 T ELT) (#60# 206 T ELT))) (((|QuotientFieldCategory| |#1|) (|Category|) (|IntegralDomain|)) (T |QuotientFieldCategory|)) -((/ (*1 *1 *2 *2) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|numer| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|denom| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|numerator| (*1 *1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|denominator| (*1 *1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)))) (|wholePart| (*1 *2 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|EuclideanDomain|)))) (|fractionPart| (*1 *1 *1) (AND (|ofCategory| *1 (|QuotientFieldCategory| *2)) (|ofCategory| *2 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| |#1|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) OR (|has| |#1| (|OrderedIntegralDomain|)) (|has| |#1| (|CharacteristicZero|))) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #2=(|Symbol|)) |has| |#1| (|RetractableTo| (|Symbol|))) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|Float|)) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| (|Float|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| (|Integer|))) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DifferentialDomain| $) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|DivisionRing|) . T) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Field|) . T) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyPatternMatchable| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #3=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #3#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedAbelianMonoid|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedAbelianSemiGroup|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedCancellationAbelianMonoid|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedIntegralDomain|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedRing|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedSet|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|OrderedIntegralDomain|))) ((|OrderedType|) OR (|has| |#1| (|OrderedSet|)) (|has| |#1| (|OrderedIntegralDomain|))) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|PrincipalIdealDomain|) . T) ((|RealConstant|) |has| |#1| (|RealConstant|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Symbol|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((/ (*1 *1 *2 *2) #1=(AND #2=(|ofCategory| *1 (|QuotientFieldCategory| *2)) #3=(|ofCategory| *2 (|IntegralDomain|)))) (|numer| #4=(*1 *2 *1) #1#) (|denom| #4# #1#) (|numerator| #5=(*1 *1 *1) #1#) (|denominator| #5# #1#) (|wholePart| #4# #6=(AND #2# #3# (|ofCategory| *2 (|EuclideanDomain|)))) (|fractionPart| #5# #6#) (|random| (*1 *1) (AND #2# #7=(|ofCategory| *2 (|IntegerNumberSystem|)) #3#)) (|ceiling| #4# #8=(AND #2# #3# #7#)) (|floor| #4# #8#)) +(|Join| (|Field|) (|Algebra| |t#1|) (|RetractableTo| |t#1|) (|FullyEvalableOver| |t#1|) (|DifferentialExtension| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (|Patternable| |t#1|) (|FullyPatternMatchable| |t#1|) (CATEGORY |domain| (SIGNATURE / ($ |t#1| |t#1|)) (SIGNATURE |numer| #1=(|t#1| $)) (SIGNATURE |denom| #1#) (SIGNATURE |numerator| #2=($ $)) (SIGNATURE |denominator| #2#) (IF (|has| |t#1| #3=(|StepThrough|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |t#1| #4=(|RetractableTo| #5=(|Integer|))) (PROGN (ATTRIBUTE #4#) (ATTRIBUTE (|RetractableTo| (|Fraction| #5#)))) |%noBranch|) (IF (|has| |t#1| #6=(|OrderedSet|)) (ATTRIBUTE #6#) |%noBranch|) (IF (|has| |t#1| #7=(|OrderedIntegralDomain|)) (ATTRIBUTE #7#) |%noBranch|) (IF (|has| |t#1| #8=(|RealConstant|)) (ATTRIBUTE #8#) |%noBranch|) (IF (|has| |t#1| #9=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #9#) |%noBranch|) (IF (|has| |t#1| #10=(|CharacteristicZero|)) (ATTRIBUTE #10#) |%noBranch|) (IF (|has| |t#1| #11=(|CharacteristicNonZero|)) (ATTRIBUTE #11#) |%noBranch|) (IF (|has| |t#1| #12=(|RetractableTo| (|Symbol|))) (ATTRIBUTE #12#) |%noBranch|) (IF (|has| |t#1| (|EuclideanDomain|)) (PROGN (SIGNATURE |wholePart| #1#) (SIGNATURE |fractionPart| #2#)) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |random| ($)) (SIGNATURE |ceiling| #1#) (SIGNATURE |floor| #1#)) |%noBranch|) (IF (|has| |t#1| #13=(|PolynomialFactorizationExplicit|)) (ATTRIBUTE #13#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| |#1|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| #3=(|Symbol|)) |has| |#1| (|RetractableTo| (|Symbol|))) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| #4=(|Float|)) |has| |#1| (|RealConstant|)) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|ConvertibleTo| (|Pattern| #4#)) |has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) ((|ConvertibleTo| (|Pattern| #2#)) |has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) ((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpaceExtension| |#1|) . T) ((|DivisionRing|) . T) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Field|) . T) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyPatternMatchable| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) . T) ((|InnerEvalable| #3# |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| |#1|) . T) ((|LinearSet| $) . T) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) . T) ((|Module| |#1|) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedAbelianMonoid|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedAbelianSemiGroup|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedCancellationAbelianMonoid|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedIntegralDomain|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedRing|) |has| |#1| (|OrderedIntegralDomain|)) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialDomain| $ #3#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialRing| #3#) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #3#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PatternMatchable| #4#) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| #2#) |has| |#1| (|PatternMatchable| (|Integer|))) ((|Patternable| |#1|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|PrincipalIdealDomain|) . T) ((|RealConstant|) |has| |#1| (|RealConstant|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #3#) |has| |#1| (|RetractableTo| (|Symbol|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| |#1|) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) 14 T ELT))) (((|QuotientFieldCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#2| |#1|) |#3|))) #1=(|IntegralDomain|) #1# (|QuotientFieldCategory| |#1|) (|QuotientFieldCategory| |#2|)) (T |QuotientFieldCategoryFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|QuotientFieldCategory| *6)) (|isDomain| *1 (|QuotientFieldCategoryFunctions2| *5 *6 *4 *2)) (|ofCategory| *4 (|QuotientFieldCategory| *5))))) @@ -3023,22 +3023,22 @@ NIL ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|expression| (((|SpadAst|) $) 10 T ELT)) (|coerce| (((|OutputForm|) $) 16 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) (((|QuasiquoteAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |expression| ((|SpadAst|) $))))) (T |QuasiquoteAst|)) ((|expression| (*1 *2 *1) (AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|QuasiquoteAst|))))) -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|sample| (#3=($) 6 T CONST)) (|rotate!| (($ $) 44 T ELT)) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) 57 (|has| |#1| . #4=((|BasicType|))) ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) 53 T ELT) ((|#1| (|Mapping| |#1| |#1| |#1|) $) 52 T ELT)) (|members| (((|List| |#1|) $) 51 T ELT)) (|member?| ((#5=(|Boolean|) |#1| $) 56 (|has| |#1| . #4#) ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|length| (((|NonNegativeInteger|) $) 43 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #6=((|SetCategory|))) ELT)) (|inspect| ((|#1| . #7=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #6#) ELT)) (|front| ((|#1| $) 42 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #5# |#1|) $) 54 T ELT)) (|extract!| ((|#1| . #7#) 37 T ELT)) (|every?| ((#5# (|Mapping| #5# |#1|) . #8=($)) 49 T ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#9=(|Boolean|) $ $) 10 T ELT)) (|enqueue!| ((|#1| |#1| $) 46 T ELT)) (|empty?| ((#9# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|dequeue!| ((|#1| $) 45 T ELT)) (|count| ((#10=(|NonNegativeInteger|) |#1| $) 55 (|has| |#1| . #4#) ELT) ((#10# (|Mapping| #5# |#1|) $) 50 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (|bag| (($ (|List| |#1|)) 38 T ELT)) (|back| ((|#1| $) 41 T ELT)) (|any?| 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(|ofCategory| *3 (|Type|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|front| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|back| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|))))) -(|Join| (|BagAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |enqueue!| (|t#1| |t#1| $)) (SIGNATURE |dequeue!| (|t#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |front| (|t#1| $)) (SIGNATURE |back| (|t#1| $)))) -(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((|enqueue!| (*1 *2 *2 *1) #1=(AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 #2=(|Type|)))) (|dequeue!| #3=(*1 *2 *1) #1#) (|rotate!| (*1 *1 *1) #1#) (|length| #3# (AND (|ofCategory| *1 (|QueueAggregate| *3)) (|ofCategory| *3 #2#) (|isDomain| *2 (|NonNegativeInteger|)))) (|front| #3# #1#) (|back| #3# #1#)) +(|Join| (|BagAggregate| |t#1|) (|FiniteAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |enqueue!| (|t#1| |t#1| $)) (SIGNATURE |dequeue!| #1=(|t#1| $)) (SIGNATURE |rotate!| ($ $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |front| #1#) (SIGNATURE |back| #1#))) +(((|Aggregate|) . T) ((|BagAggregate| |#1|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . 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#7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 142 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 139 T ELT)) (|retract| ((#4# . #10=($)) 143 (|has| |#1| . #7#) ELT) ((#8# . #10#) 141 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 140 T ELT)) (|reducedSystem| (((|Matrix| #11=(|Integer|)) . #12=(#13=(|Matrix| $))) 124 (|has| |#1| . #14=((|LinearlyExplicitRingOver| #11#))) ELT) (((|Record| (|:| |mat| (|Matrix| #11#)) (|:| |vec| (|Vector| #11#))) . #15=(#13# #16=(|Vector| $))) 123 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #15#) 122 T ELT) (((|Matrix| |#1|) . #12#) 121 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|real| ((|#1| $) 112 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 108 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 110 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 109 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 113 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|norm| ((|#1| $) 114 T ELT)) (|min| (#17=($ $ $) 96 (|has| |#1| . #18=((|OrderedSet|))) ELT)) (|max| (#17# 97 (|has| |#1| . #18#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 127 T ELT)) (|leftReducedSystem| (((|Matrix| #11#) . #19=(#16#)) 126 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| #11#)) (|:| |vec| (|Vector| #11#))) . #20=(#16# $)) 125 (|has| |#1| . #14#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #20#) 120 T ELT) (((|Matrix| |#1|) . #19#) 119 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 105 (|has| |#1| . #21=((|Field|))) ELT)) (|imagK| ((|#1| $) 115 T ELT)) (|imagJ| ((|#1| $) 116 T ELT)) (|imagI| ((|#1| $) 117 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 133 (|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 132 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8 T ELT)) (<= (#32# 99 (|has| |#1| . #18#) ELT)) (< (#32# 101 (|has| |#1| . #18#) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #33=(|Integer|)) 104 (|has| |#1| . #21#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #34=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 55 T ELT) (($ |#1| . #34#) 54 T ELT) (($ $ #35=(|Fraction| #33#)) 103 (|has| |#1| . #21#) ELT) (($ #35# . #34#) 102 (|has| |#1| . #21#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| ((#4=(|Maybe| $) $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| #6=(|Integer|) . #7=(#8="failed")) . #9=($)) 144 #10=(|has| |#1| (|RetractableTo| #6#)) ELT) (#11=((|Union| #12=(|Fraction| #6#) #8#) $) 142 #13=(|has| |#1| (|RetractableTo| #12#)) ELT) (((|Union| |#1| . #7#) . #9#) 139 T ELT)) (|retract| ((#6# . #14=($)) 143 #10# ELT) (#15=(#12# $) 141 #13# ELT) (#16=(|#1| . #14#) 140 T ELT)) (|reducedSystem| ((#17=(|Matrix| #6#) . #18=(#19=(|Matrix| $))) 124 #20=(|has| |#1| (|LinearlyExplicitRingOver| #6#)) ELT) ((#21=(|Record| (|:| |mat| #17#) (|:| |vec| (|Vector| #6#))) . #22=(#19# #23=(|Vector| $))) 123 #20# ELT) ((#24=(|Record| (|:| |mat| #25=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #22#) 122 T ELT) ((#25# . #18#) 121 T ELT)) (|recip| (((|Union| $ #8#) $) 43 T ELT)) (|real| (#16# 112 T ELT)) (|rationalIfCan| (#11# 108 #26=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#3# 110 #26# ELT)) (|rational| (#15# 109 #26# ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 113 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|norm| (#16# 114 T ELT)) (|min| (#27=($ $ $) 96 #28=(|has| |#1| (|OrderedSet|)) ELT)) (|max| (#27# 97 #28# ELT)) (|map| (($ #29=(|Mapping| |#1| |#1|) $) 127 T ELT)) (|leftReducedSystem| ((#17# . #30=(#23#)) 126 #20# ELT) ((#21# . #31=(#23# $)) 125 #20# ELT) ((#24# . #31#) 120 T ELT) ((#25# . #30#) 119 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#32=($ $) 105 #33=(|has| |#1| (|Field|)) ELT)) (|imagK| (#16# 115 T ELT)) (|imagJ| (#16# 116 T ELT)) (|imagI| (#16# 117 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ #34=(|List| |#1|) #34#) 133 #35=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) 132 #35# ELT) (($ $ #36=(|Equation| |#1|)) 131 #35# ELT) (($ $ (|List| #36#)) 130 #35# ELT) (($ $ #37=(|List| #38=(|Symbol|)) #34#) 129 #39=(|has| |#1| (|InnerEvalable| #38# |#1|)) ELT) (($ $ #38# |#1|) 128 #39# ELT)) (|elt| (#40=($ $ |#1|) 134 (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|differentiate| (#41=($ $ #29#) 138 T ELT) (#42=($ $ #29# #43=(|NonNegativeInteger|)) 137 T ELT) (#32# 95 #44=(|has| |#1| (|DifferentialSpace|)) ELT) (#45=($ $ #43#) 93 #44# ELT) (#46=($ $ #38#) 91 #47=(|has| |#1| (|PartialDifferentialSpace| #38#)) ELT) (#48=($ $ #37#) 89 #47# ELT) (#49=($ $ #38# #43#) 88 #47# ELT) (#50=($ $ #37# 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31 T ELT) (#27# 35 T ELT) (#40# 55 T ELT) (($ |#1| . #53#) 54 T ELT) (($ $ #12#) 103 #33# ELT) (($ #12# . #53#) 102 #33# ELT))) (((|QuaternionCategory| |#1|) (|Category|) (|CommutativeRing|)) (T |QuaternionCategory|)) -((|conjugate| (*1 *1 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagI| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagJ| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|imagK| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|norm| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|quatern| (*1 *1 *2 *2 *2 *2) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|real| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)))) (|abs| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *2)) (|ofCategory| *2 (|CommutativeRing|)) (|ofCategory| *2 (|RealNumberSystem|)))) (|rational?| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| (*1 *2 *1) (AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|QuaternionCategory| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) -(|Join| (|Algebra| |t#1|) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |conjugate| ($ $)) (SIGNATURE |imagI| (|t#1| $)) (SIGNATURE |imagJ| (|t#1| $)) (SIGNATURE |imagK| (|t#1| $)) (SIGNATURE |norm| (|t#1| $)) (SIGNATURE |quatern| ($ |t#1| |t#1| |t#1| |t#1|)) (SIGNATURE |real| (|t#1| $)) (IF (|has| |t#1| (|EntireRing|)) (ATTRIBUTE (|EntireRing|)) |%noBranch|) (IF (|has| |t#1| (|OrderedSet|)) (ATTRIBUTE (|OrderedSet|)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|DivisionRing|)) |%noBranch|) (IF (|has| |t#1| (|ConvertibleTo| (|InputForm|))) (ATTRIBUTE (|ConvertibleTo| (|InputForm|))) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| (|t#1| $)) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| ((|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| (|Fraction| (|Integer|)) "failed") $))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) |has| |#1| (|Field|)) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Field|)) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Field|))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DifferentialDomain| $) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#1| (|DifferentialSpace|)) (|has| |#1| (|DifferentialRing|))) ((|DifferentialSpaceExtension| |#1|) . T) ((|DivisionRing|) |has| |#1| (|Field|)) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|InnerEvalable| (|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Field|)) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Field|)) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Field|)) ((|LinearSet| |#1|) . T) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Field|)) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #3#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Field|)) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|RightModule| #1#) |has| |#1| (|Field|)) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|Field|)) (|has| |#1| (|EntireRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|conjugate| (*1 *1 *1) #1=(AND #2=(|ofCategory| *1 (|QuaternionCategory| *2)) #3=(|ofCategory| *2 #4=(|CommutativeRing|)))) (|imagI| #5=(*1 *2 *1) #1#) (|imagJ| #5# #1#) (|imagK| #5# #1#) (|norm| #5# #1#) (|quatern| (*1 *1 *2 *2 *2 *2) #1#) (|real| #5# #1#) (|abs| #5# (AND #2# #3# (|ofCategory| *2 (|RealNumberSystem|)))) (|rational?| #5# (AND #6=(|ofCategory| *1 (|QuaternionCategory| *3)) #7=(|ofCategory| *3 #4#) #8=(|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *2 (|Boolean|)))) (|rational| #5# (AND #6# #7# #8# #9=(|isDomain| *2 (|Fraction| (|Integer|))))) (|rationalIfCan| #5# (|partial| AND #6# #7# #8# #9#))) +(|Join| (|Algebra| |t#1|) (|FullyRetractableTo| |t#1|) (|DifferentialExtension| |t#1|) (|FullyEvalableOver| |t#1|) (|FullyLinearlyExplicitRingOver| |t#1|) (CATEGORY |domain| (SIGNATURE |conjugate| ($ $)) (SIGNATURE |imagI| #1=(|t#1| $)) (SIGNATURE |imagJ| #1#) (SIGNATURE |imagK| #1#) (SIGNATURE |norm| #1#) (SIGNATURE |quatern| ($ |t#1| |t#1| |t#1| |t#1|)) (SIGNATURE |real| #1#) (IF (|has| |t#1| #2=(|EntireRing|)) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |t#1| #3=(|OrderedSet|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|DivisionRing|)) |%noBranch|) (IF (|has| |t#1| #4=(|ConvertibleTo| (|InputForm|))) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |t#1| #5=(|CharacteristicZero|)) (ATTRIBUTE #5#) |%noBranch|) (IF (|has| |t#1| #6=(|CharacteristicNonZero|)) (ATTRIBUTE #6#) |%noBranch|) (IF (|has| |t#1| (|RealNumberSystem|)) (SIGNATURE |abs| #1#) |%noBranch|) (IF (|has| |t#1| (|IntegerNumberSystem|)) (PROGN (SIGNATURE |rational?| ((|Boolean|) $)) (SIGNATURE |rational| (#7=(|Fraction| (|Integer|)) $)) (SIGNATURE |rationalIfCan| ((|Union| #7# "failed") $))) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Field|)) ((|Algebra| |#1|) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Field|)) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|EntireRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|Field|)) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|DifferentialDomain| $) |has| |#1| (|DifferentialSpace|)) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) |has| |#1| (|DifferentialRing|)) ((|DifferentialSpace|) |has| |#1| (|DifferentialSpace|)) ((|DifferentialSpaceExtension| |#1|) . T) ((|DivisionRing|) |has| |#1| (|Field|)) ((|Eltable| |#1| $) |has| |#1| (|Eltable| |#1| |#1|)) ((|EntireRing|) |has| |#1| (|EntireRing|)) ((|Evalable| |#1|) |has| |#1| (|Evalable| |#1|)) ((|FullyEvalableOver| |#1|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|InnerEvalable| #3=(|Symbol|) |#1|) |has| |#1| (|InnerEvalable| (|Symbol|) |#1|)) ((|InnerEvalable| |#1| |#1|) |has| |#1| (|Evalable| |#1|)) ((|LeftLinearSet| #1#) |has| |#1| (|Field|)) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Field|)) ((|LeftModule| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Field|)) ((|LinearSet| |#1|) . T) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Field|)) ((|Module| |#1|) . T) ((|Monoid|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|PartialDifferentialDomain| $ #3#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialRing| #3#) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #3#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Field|)) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|EntireRing|)) ((|RightModule| #1#) |has| |#1| (|Field|)) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|EntireRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 16 T ELT))) (((|QuaternionCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|QuaternionCategory| |#2|) #1=(|CommutativeRing|) (|QuaternionCategory| |#4|) #1#) (T |QuaternionCategoryFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|QuaternionCategory| *6)) (|isDomain| *1 (|QuaternionCategoryFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|QuaternionCategory| *5))))) @@ -3048,10 +3048,10 @@ NIL ((|sqrt| (($ $) 12 T ELT)) (|nthRoot| (($ $ (|Integer|)) 13 T ELT))) (((|RadicalCategory&| |#1|) (CATEGORY |package| (SIGNATURE |sqrt| (|#1| |#1|)) (SIGNATURE |nthRoot| (|#1| |#1| (|Integer|)))) (|RadicalCategory|)) (T |RadicalCategory&|)) NIL -((|sqrt| (($ $) 6 T ELT)) (|nthRoot| (($ $ (|Integer|)) 7 T ELT)) (** (($ $ (|Fraction| (|Integer|))) 8 T ELT))) +((|sqrt| (($ $) 6 T ELT)) (|nthRoot| (($ $ #1=(|Integer|)) 7 T ELT)) (** (($ $ (|Fraction| #1#)) 8 T ELT))) (((|RadicalCategory|) (|Category|)) (T |RadicalCategory|)) -((** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|nthRoot| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Integer|)))) (|sqrt| (*1 *1 *1) (|ofCategory| *1 (|RadicalCategory|)))) -(|Join| (CATEGORY |domain| (SIGNATURE |sqrt| ($ $)) (SIGNATURE |nthRoot| ($ $ (|Integer|))) (SIGNATURE ** ($ $ (|Fraction| (|Integer|)))))) +((** #1=(*1 *1 *1 *2) (AND #2=(|ofCategory| *1 (|RadicalCategory|)) (|isDomain| *2 (|Fraction| #3=(|Integer|))))) (|nthRoot| #1# (AND #2# (|isDomain| *2 #3#))) (|sqrt| (*1 *1 *1) #2#)) +(|Join| (CATEGORY |domain| (SIGNATURE |sqrt| ($ $)) (SIGNATURE |nthRoot| ($ $ #1=(|Integer|))) (SIGNATURE ** ($ $ (|Fraction| #1#))))) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|yCoordinates| (#6=((|Record| (|:| |num| #7=(|Vector| |#2|)) #8=(|:| |den| |#2|)) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| #10=(|Fraction| |#2|) #11=(|Field|)) ELT)) (|unitCanonical| #12=(#13=($ $) NIL #9# ELT)) (|unit?| #14=(#5# NIL #9# ELT)) (|traceMatrix| #15=((#16=(|Matrix| #10#) #17=(|Vector| $)) NIL T ELT) (#18=(#16#) NIL T ELT)) (|trace| #19=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #20=(|PositiveInteger|) #21=(|NonNegativeInteger|)) #22=(|Integer|)) NIL #23=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| ((#24=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #25=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #26=(#2# NIL #9# ELT)) (|size| (#27=(#21#) NIL #28=(|has| #10# #29=(|Finite|)) ELT)) (|singularAtInfinity?| #30=(#31=(#3#) NIL T ELT)) (|singular?| (#32=(#3# |#1|) 162 T ELT) (#33=(#3# |#2|) 166 T ELT)) (|sample| #34=(#35=($) NIL T CONST)) (|retractIfCan| (((|Union| #22# . #36=(#37="failed")) . #38=($)) NIL #39=(|has| #10# (|RetractableTo| #22#)) ELT) (((|Union| #40=(|Fraction| #22#) . #36#) . #38#) NIL #41=(|has| #10# (|RetractableTo| #40#)) ELT) (((|Union| #10# . #36#) . #38#) NIL T ELT)) (|retract| ((#22# . #42=($)) NIL #39# ELT) ((#40# . #42#) NIL #41# ELT) #19#) (|represents| (($ #43=(|Vector| #10#) #17#) NIL T ELT) (#44=($ #43#) 79 T ELT) (#45=($ #7# |#2|) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #23# ELT)) (|rem| #46=(#47=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#16# $ #17#) NIL T ELT) ((#16# $) NIL T ELT)) (|reducedSystem| ((#48=(|Matrix| #22#) . #49=(#50=(|Matrix| $))) NIL #51=(|has| #10# (|LinearlyExplicitRingOver| #22#)) ELT) ((#52=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #22#))) . #53=(#50# #17#)) NIL #51# ELT) ((#54=(|Record| (|:| |mat| #16#) (|:| |vec| #43#)) . #53#) NIL T ELT) ((#16# . #49#) NIL T ELT)) (|reduceBasisAtInfinity| #55=((#17# #17#) NIL T ELT)) (|reduce| (#56=($ |#3|) 73 T ELT) ((#57=(|Union| $ #37#) (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#57# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #29#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#20#) NIL T ELT)) (|random| (#35# NIL #28# ELT)) (|ramifiedAtInfinity?| #30#) (|ramified?| (#32# 61 T ELT) (#33# 164 T ELT)) (|quo| #46#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #9# ELT)) (|primitivePart| #60=(#13# NIL T ELT)) (|primitiveElement| #61=(#35# NIL #23# ELT)) (|primitive?| (#5# NIL #23# ELT)) (|primeFrobenius| (#62=($ $ #21#) NIL #23# ELT) #63=(#13# NIL #23# ELT)) (|prime?| #14#) (|order| (#64=(#20# $) NIL #23# ELT) (((|OnePointCompletion| #20#) $) NIL #23# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #65=(#27# NIL T ELT)) (|normalizeAtInfinity| #55#) (|norm| #19#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #66=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#67=(#24# $) NIL #23# ELT)) (|multiEuclidean| (((|Union| #58# #37#) #58# $) NIL #9# ELT)) (|minimalPolynomial| (#68=(|#3| $) NIL #9# ELT)) (|lookup| (#64# NIL #28# ELT)) (|lift| #69=(#68# NIL T ELT)) (|leftReducedSystem| ((#48# #17#) NIL #51# ELT) ((#52# . #70=(#17# $)) NIL #51# ELT) ((#54# . #70#) NIL T ELT) #15#) (|lcm| #71=(($ #58#) NIL #9# ELT) #46#) (|latex| (((|String|) $) NIL T ELT)) (|inverseIntegralMatrixAtInfinity| (#18# 57 T ELT)) (|inverseIntegralMatrix| (#18# 56 T ELT)) (|inv| #12#) (|integralRepresents| (#45# 80 T ELT)) (|integralMatrixAtInfinity| (#18# 55 T ELT)) (|integralMatrix| (#18# 54 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #72=(|Mapping| |#2| |#2|)) 95 T ELT)) (|integralCoordinates| (#6# 86 T ELT)) (|integralBasisAtInfinity| (#73=(#17#) 51 T ELT)) (|integralBasis| (#73# 50 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#35# NIL #23# CONST)) (|index| (($ #20#) NIL #28# ELT)) (|hyperelliptic| (#74=((|Union| |#2| #37#)) 70 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #65#) (|generator| (#35# NIL T ELT)) (|gcdPolynomial| ((#75=(|SparseUnivariatePolynomial| $) #75# #75#) NIL #9# ELT)) (|gcd| #71# #46#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #22#) (|:| |exponent| #22#)))) NIL #23# ELT)) (|factor| #25#) (|extendedEuclidean| (((|Union| (|Record| #76=(|:| |coef1| $) #77=(|:| |coef2| $)) #37#) $ $ $) NIL #9# ELT) (((|Record| #76# #77# #59#) $ $) NIL #9# ELT)) (|exquo| ((#57# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #9# ELT)) (|euclideanSize| (#78=(#21# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| (#74# 68 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #17#) NIL T ELT) ((#10#) 47 T ELT)) (|discreteLog| (#78# NIL #23# ELT) (((|Union| #21# #37#) $ $) NIL #23# ELT)) (|differentiate| #79=(($ $ #80=(|Mapping| #10# #10#)) NIL #9# ELT) #81=(($ $ #80# #21#) NIL #9# ELT) (($ $ #72#) NIL T ELT) #82=(#62# NIL #83=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #23#) ELT) #84=(#13# NIL #83# ELT) #85=(($ $ #86=(|List| #66#) (|List| #21#)) NIL #87=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #66#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #66#)))) ELT) #88=(($ $ #66# #21#) NIL #87# ELT) #89=(($ $ #86#) NIL #87# ELT) #90=(($ $ #66#) NIL #87# ELT)) (|derivationCoordinates| ((#16# #17# #80#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 58 T ELT)) (|createPrimitiveElement| #61#) (|coordinates| ((#43# $ #17#) NIL T ELT) ((#16# #17# #17#) NIL T ELT) (#91=(#43# $) 81 T ELT) #15#) (|convert| (#91# NIL T ELT) (#44# NIL T ELT) #69# (#56# NIL T ELT)) (|conditionP| (((|Union| #17# #37#) #50#) NIL #23# ELT)) (|complementaryBasis| #55#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #22#) NIL T ELT) (($ #10#) NIL T ELT) (($ #40#) NIL (OR #9# #41#) ELT) #12#) (|charthRoot| #63# (#67# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #69#) (|characteristic| (#27# NIL T CONST)) (|branchPointAtInfinity?| (#31# 65 T ELT)) (|branchPoint?| (#32# 167 T ELT) (#33# 168 T ELT)) (|before?| #1#) (|basis| (#73# NIL T ELT)) (|associates?| #26#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #72#) NIL T ELT)) (|absolutelyIrreducible?| #30#) (|Zero| #34#) (|One| #34#) (D #79# #81# #82# #84# #85# #88# #89# #90#) (= #1#) (/ #46#) (- #60# #92=(#47# NIL T ELT)) (+ #92#) (** (($ $ #20#) NIL T ELT) (#62# NIL T ELT) (($ $ #22#) NIL #9# ELT)) (* (($ #20# $) NIL T ELT) (($ #21# $) NIL T ELT) (($ #22# . #93=($)) NIL T ELT) #92# (($ $ #10#) NIL T ELT) (($ #10# . #93#) NIL T ELT) (($ #40# . #93#) NIL #9# ELT) (($ $ #40#) NIL #9# ELT))) (((|RadicalFunctionField| |#1| |#2| |#3| |#4| |#5|) (|FunctionFieldCategory| |#1| |#2| |#3|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| #1=(|Fraction| |#2|)) #1# (|NonNegativeInteger|)) (T |RadicalFunctionField|)) NIL @@ -3073,19 +3073,19 @@ NIL ((|setelt| ((|#2| $ #1="value" |#2|) 12 T ELT)) (|elt| ((|#2| $ #1#) 10 T ELT)) (|child?| (((|Boolean|) $ $) 18 T ELT))) (((|RecursiveAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |setelt| (|#2| |#1| #1="value" |#2|)) (SIGNATURE |child?| ((|Boolean|) |#1| |#1|)) (SIGNATURE |elt| (|#2| |#1| #1#))) (|RecursiveAggregate| |#2|) (|Type|)) (T |RecursiveAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ "value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ (|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sample| (#3=($) 6 T CONST)) (|nodes| (((|List| $) $) 45 T ELT)) (|node?| (((|Boolean|) $ $) 37 (|has| |#1| (|BasicType|)) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|leaves| (((|List| |#1|) $) 40 T ELT)) (|leaf?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 21 (|has| |#1| . #4=((|SetCategory|))) ELT)) (|hash| (((|SingleInteger|) $) 20 (|has| |#1| . #4#) ELT)) (|eval| (($ $ (|List| (|Equation| |#1|))) 25 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|Equation| |#1|)) 24 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ |#1| |#1|) 23 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #4#)) ELT)) (|eq?| ((#5=(|Boolean|) $ $) 10 T ELT)) (|empty?| ((#5# $) 7 T ELT)) (|empty| (#3# 8 T ELT)) (|elt| ((|#1| $ "value") 42 T ELT)) (|distance| (((|Integer|) $ $) 39 T ELT)) (|cyclic?| (((|Boolean|) $) 41 T ELT)) (|copy| (($ $) 9 T ELT)) (|coerce| (((|OutputForm|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|children| (((|List| $) $) 46 T ELT)) (|child?| (((|Boolean|) $ $) 38 (|has| |#1| (|BasicType|)) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(|has| |#1| (|BasicType|)) ELT)) (|value| ((|#1| $) 43 T ELT)) (|setvalue!| ((|#1| $ |#1|) 34 #4=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #5="value" |#1|) 35 #4# ELT)) (|setchildren!| (($ $ #6=(|List| $)) 36 #4# ELT)) (|sample| (#7=($) 6 T CONST)) (|nodes| (#8=(#6# $) 45 T ELT)) (|node?| (#1# 37 #3# ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|leaves| ((#9=(|List| |#1|) $) 40 T ELT)) (|leaf?| (#10=(#2# $) 44 T ELT)) (|latex| (((|String|) $) 21 #11=(|has| |#1| (|SetCategory|)) ELT)) (|hash| (((|SingleInteger|) $) 20 #11# ELT)) (|eval| (($ $ (|List| #12=(|Equation| |#1|))) 25 #13=(AND (|has| |#1| (|Evalable| |#1|)) #11#) ELT) (($ $ #12#) 24 #13# ELT) (($ $ |#1| |#1|) 23 #13# ELT) (($ $ #9# #9#) 22 #13# ELT)) (|eq?| (#1# 10 T 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(#25# 118 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#4# 135 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#16# #16# #16#) 120 T ELT)) (|gcd| (#30# 117 T ELT) (#25# 116 T ELT)) (|factor| (#5# 131 T ELT)) (|extendedEuclidean| (((|Union| (|Record| #31=(|:| |coef1| $) #32=(|:| |coef2| $)) #15#) $ $ $) 129 T ELT) (((|Record| #31# #32# #27#) $ $) 128 T ELT)) (|exquo| ((#14# $ $) 111 T ELT)) (|expressIdealMember| (((|Maybe| #26#) #26# $) 122 T ELT)) (|euclideanSize| ((#33=(|NonNegativeInteger|) $) 124 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 125 T ELT)) (|coerce| ((#17# $) 13 T ELT) (#11# 42 T ELT) (#8# 139 T ELT) (#4# 110 T ELT) (#8# 103 T ELT) (#11# 102 T ELT) (#8# 99 T ELT)) (|characteristic| ((#33#) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 114 T ELT)) (|approximate| ((#9# $ $) 77 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|allRootsOf| ((#26# #16#) 88 T ELT) ((#26# (|SparseUnivariatePolynomial| #9#)) 87 T 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(|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|mainValue| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|rootOf| (*1 *1 *2 *3 *4) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|OutputForm|)) (|ofCategory| *1 (|RealClosedField|)))) (|rootOf| (*1 *1 *2 *3) (|partial| AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|isDomain| *3 (|PositiveInteger|)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|List| *1)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| (|Integer|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| *1)) (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|List| *1)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| (|Fraction| (|Integer|)))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|allRootsOf| (*1 *2 *3) (AND (|isDomain| *3 (|Polynomial| (|Integer|))) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RealClosedField|)))) (|sqrt| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|PositiveInteger|)))) (|sqrt| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *1 (|RealClosedField|)))) (|sqrt| (*1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|RealClosedField|)))) (|rename!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|rename| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|OutputForm|)))) (|approximate| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RealClosedField|)) (|isDomain| *2 (|Fraction| (|Integer|)))))) -(|Join| (|CharacteristicZero|) (|OrderedRing|) (|CommutativeRing|) (|Field|) (|FullyRetractableTo| (|Fraction| (|Integer|))) (|Algebra| (|Integer|)) (|Algebra| (|Fraction| (|Integer|))) (|RadicalCategory|) (CATEGORY |domain| (SIGNATURE |mainForm| ((|Union| (|OutputForm|) "failed") $)) (SIGNATURE |mainDefiningPolynomial| ((|Union| (|SparseUnivariatePolynomial| $) "failed") $)) (SIGNATURE |mainValue| ((|Union| (|SparseUnivariatePolynomial| $) "failed") $)) (SIGNATURE |rootOf| ((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|))) (SIGNATURE |rootOf| ((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| $) (|SparseUnivariatePolynomial| (|Integer|)))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |allRootsOf| ((|List| $) (|Polynomial| (|Integer|)))) (SIGNATURE |sqrt| ($ $ (|PositiveInteger|))) (SIGNATURE |sqrt| ($ $)) (SIGNATURE |sqrt| ($ (|Fraction| (|Integer|)))) (SIGNATURE |sqrt| ($ (|Integer|))) (SIGNATURE |rename!| ($ $ (|OutputForm|))) (SIGNATURE |rename| ($ $ (|OutputForm|))) (SIGNATURE |approximate| ((|Fraction| (|Integer|)) $ $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| #2=(|Integer|)) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| #2# #2#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FullyRetractableTo| (|Fraction| (|Integer|))) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #2#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| #2#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| #2#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| (|Fraction| (|Integer|))) . T) ((|RetractableTo| (|Integer|)) |has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|))) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| #2#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| #2#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((|sqrt| (*1 *1 *1) #1=(|ofCategory| *1 (|RealClosedField|))) (|mainForm| #2=(*1 *2 *1) (|partial| AND #1# #3=(|isDomain| *2 #4=(|OutputForm|)))) (|mainDefiningPolynomial| #2# #5=(|partial| AND #6=(|isDomain| *2 #7=(|SparseUnivariatePolynomial| *1)) #1#)) (|mainValue| #2# #5#) (|rootOf| (*1 *1 *2 *3 *4) (|partial| AND #6# #8=(|isDomain| *3 #9=(|PositiveInteger|)) (|isDomain| *4 #4#) #1#)) (|rootOf| (*1 *1 *2 *3) (|partial| AND #6# #8# #1#)) (|allRootsOf| #10=(*1 *2 *3) (AND (|isDomain| *3 #7#) #1# #11=(|isDomain| *2 (|List| *1)))) (|allRootsOf| #10# (AND (|isDomain| *3 (|SparseUnivariatePolynomial| #12=(|Fraction| #13=(|Integer|)))) #11# #1#)) (|allRootsOf| #10# (AND (|isDomain| *3 (|SparseUnivariatePolynomial| #13#)) #11# #1#)) (|allRootsOf| #10# (AND (|isDomain| *3 (|Polynomial| *1)) #1# #11#)) (|allRootsOf| #10# (AND (|isDomain| *3 (|Polynomial| #12#)) #11# #1#)) (|allRootsOf| #10# (AND (|isDomain| *3 (|Polynomial| #13#)) #11# #1#)) (|sqrt| #14=(*1 *1 *1 *2) (AND #1# (|isDomain| *2 #9#))) (|sqrt| #15=(*1 *1 *2) (AND #16=(|isDomain| *2 #12#) #1#)) (|sqrt| #15# (AND (|isDomain| *2 #13#) #1#)) (|rename!| #14# #17=(AND #1# #3#)) (|rename| #14# #17#) (|approximate| (*1 *2 *1 *1) (AND #1# #16#))) +(|Join| (|CharacteristicZero|) (|OrderedRing|) (|CommutativeRing|) (|Field|) (|FullyRetractableTo| #1=(|Fraction| #2=(|Integer|))) (|Algebra| #2#) (|Algebra| #1#) (|RadicalCategory|) (CATEGORY |domain| (SIGNATURE |mainForm| ((|Union| #3=(|OutputForm|) #4="failed") $)) (SIGNATURE |mainDefiningPolynomial| #5=((|Union| #6=(|SparseUnivariatePolynomial| $) #4#) $)) (SIGNATURE |mainValue| #5#) (SIGNATURE |rootOf| (#7=(|Union| $ #4#) #6# #8=(|PositiveInteger|) #3#)) (SIGNATURE |rootOf| (#7# #6# #8#)) (SIGNATURE |allRootsOf| (#9=(|List| $) #6#)) (SIGNATURE |allRootsOf| (#9# (|SparseUnivariatePolynomial| #1#))) (SIGNATURE |allRootsOf| (#9# (|SparseUnivariatePolynomial| #2#))) (SIGNATURE |allRootsOf| (#9# (|Polynomial| $))) (SIGNATURE |allRootsOf| (#9# (|Polynomial| #1#))) (SIGNATURE |allRootsOf| (#9# (|Polynomial| #2#))) (SIGNATURE |sqrt| ($ $ #8#)) (SIGNATURE |sqrt| ($ $)) (SIGNATURE |sqrt| ($ #1#)) (SIGNATURE |sqrt| ($ #2#)) (SIGNATURE |rename!| #10=($ $ #3#)) (SIGNATURE |rename| #10#) (SIGNATURE |approximate| (#1# $ $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| #2#) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| #2# #2#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FullyRetractableTo| #1#) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| #2#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| #2#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| #2#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RetractableTo| #1#) . T) ((|RetractableTo| #2#) |has| (|Fraction| (|Integer|)) (|RetractableTo| (|Integer|))) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| #2#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| #2#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2="failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #1#) #2#) |#2| |#2|)) 67 T ELT))) (((|ElementaryRischDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rischDE| ((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) #1=(|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #2=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #2#) #3#) |#2| |#2|)))) (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #1#) (|LinearlyExplicitRingOver| #1#)) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| |#1|))) (T |ElementaryRischDE|)) ((|rischDE| (*1 *2 *3 *4 *4 *5 *6 *7) (AND (|isDomain| *5 (|Symbol|)) (|isDomain| *6 (|Mapping| (|Union| (|Record| (|:| |mainpart| *4) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| *4) (|:| |logand| *4))))) #2="failed") *4 (|List| *4))) (|isDomain| *7 (|Mapping| (|Union| (|Record| (|:| |ratpart| *4) #1#) #2#) *4 *4)) (|ofCategory| *4 (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| *8))) (|ofCategory| *8 (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| *3) (|LinearlyExplicitRingOver| *3))) (|isDomain| *3 (|Integer|)) (|isDomain| *2 (|Record| (|:| |ans| *4) (|:| |right| *4) (|:| |sol?| (|Boolean|)))) (|isDomain| *1 (|ElementaryRischDE| *8 *4))))) @@ -3162,7 +3162,7 @@ NIL NIL ((|retractIfCan| (((|Union| |#1| "failed") $) 9 T ELT)) (|retract| ((|#1| $) 8 T ELT)) (|coerce| (($ |#1|) 6 T ELT))) (((|RetractableTo| |#1|) (|Category|) (|Type|)) (T |RetractableTo|)) -((|retractIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|)))) (|retract| (*1 *2 *1) (AND (|ofCategory| *1 (|RetractableTo| *2)) (|ofCategory| *2 (|Type|))))) +((|retractIfCan| #1=(*1 *2 *1) (|partial| AND #2=(|ofCategory| *1 (|RetractableTo| *2)) #3=(|ofCategory| *2 (|Type|)))) (|retract| #1# (AND #2# #3#))) (|Join| (|CoercibleFrom| |t#1|) (CATEGORY |domain| (SIGNATURE |retractIfCan| ((|Union| |t#1| "failed") $)) (SIGNATURE |retract| (|t#1| $)))) (((|CoercibleFrom| |#1|) . T)) ((|solveRetract| (((|List| (|List| (|Equation| (|Fraction| #1=(|Polynomial| |#2|))))) (|List| #1#) (|List| (|Symbol|))) 38 T ELT))) @@ -3180,16 +3180,16 @@ NIL ((|factorFraction| (((|Fraction| (|Factored| #1=(|Polynomial| |#1|))) (|Fraction| #1#)) 14 T ELT))) (((|RationalFunctionFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |factorFraction| ((|Fraction| (|Factored| #1=(|Polynomial| |#1|))) (|Fraction| #1#)))) (|EuclideanDomain|)) (T |RationalFunctionFactorizer|)) ((|factorFraction| (*1 *2 *3) (AND (|isDomain| *3 (|Fraction| #1=(|Polynomial| *4))) (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Fraction| (|Factored| #1#))) (|isDomain| *1 (|RationalFunctionFactorizer| *4))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|sample| (#3=($) 23 T CONST)) (|red| ((|#1| $) 29 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|green| ((|#1| $) 28 T ELT)) (|componentUpperBound| ((|#1|) 26 T CONST)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|blue| ((|#1| $) 27 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|sample| (#3=($) 23 T CONST)) (|red| (#4=(|#1| $) 29 T ELT)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|green| (#4# 28 T ELT)) (|componentUpperBound| ((|#1|) 26 T CONST)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|blue| (#4# 27 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) (((|RGBColorModel| |#1|) (|Category|) (|AbelianMonoid|)) (T |RGBColorModel|)) -((|red| (*1 *2 *1) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|)))) (|green| (*1 *2 *1) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|)))) (|blue| (*1 *2 *1) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|)))) (|componentUpperBound| (*1 *2) (AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|))))) -(|Join| (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |red| (|t#1| $)) (SIGNATURE |green| (|t#1| $)) (SIGNATURE |blue| (|t#1| $)) (SIGNATURE |componentUpperBound| (|t#1|) |constant|))) -(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|whitePoint| (($) 31 T CONST)) (|sample| (#3=($) 23 T CONST)) (|red| ((|#1| . #4=($)) 29 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|green| ((|#1| . #4#) 28 T ELT)) (|componentUpperBound| ((|#1|) 26 T CONST)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|blue| ((|#1| . #4#) 27 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) +((|red| #1=(*1 *2 *1) #2=(AND (|ofCategory| *1 (|RGBColorModel| *2)) (|ofCategory| *2 (|AbelianMonoid|)))) (|green| #1# #2#) (|blue| #1# #2#) (|componentUpperBound| (*1 *2) #2#)) +(|Join| (|AbelianMonoid|) (CATEGORY |domain| (SIGNATURE |red| #1=(|t#1| $)) (SIGNATURE |green| #1#) (SIGNATURE |blue| #1#) (SIGNATURE |componentUpperBound| (|t#1|) |constant|))) +(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|whitePoint| (#3=($) 31 T CONST)) (|sample| (#3# 23 T CONST)) (|red| (#4=(|#1| $) 29 T ELT)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|green| (#4# 28 T ELT)) (|componentUpperBound| ((|#1|) 26 T CONST)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|blue| (#4# 27 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT))) (((|RGBColorSpace| |#1|) (|Category|) (|AbelianMonoid|)) (T |RGBColorSpace|)) ((|whitePoint| (*1 *1) (AND (|ofCategory| *1 (|RGBColorSpace| *2)) (|ofCategory| *2 (|AbelianMonoid|))))) (|Join| (|RGBColorModel| |t#1|) (CATEGORY |domain| (SIGNATURE |whitePoint| ($) |constant|))) -(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|RGBColorModel| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|RGBColorModel| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| #6=(|NewSparseMultivariatePolynomial| |#1| #7=(|OrderedVariableList| |#2|)))))) #5#) NIL T ELT)) (|zeroSetSplit| ((#8=(|List| $) #5#) NIL T ELT) ((#8# #5# #3#) NIL T ELT) ((#8# #5# #3# #3#) NIL T ELT)) (|variables| #9=(((|List| #7#) $) NIL T ELT)) (|trivialIdeal?| #10=(#11=(#3# $) NIL T ELT)) (|triangular?| #12=(#11# NIL #13=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #14=(#15=(#3# #6# $) NIL T ELT) #10#) (|stronglyReduce| #16=((#6# #6# $) NIL T ELT)) (|squareFreePart| ((#17=(|List| (|Record| (|:| |val| #6#) #18=(|:| |tower| $))) #6# $) NIL T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ #7#) NIL T ELT)) (|select| #19=(($ #20=(|Mapping| #3# #6#) $) NIL #21=(|has| $ (|FiniteAggregate| #6#)) ELT) ((#22=(|Union| #6# #23="failed") $ #7#) NIL T ELT)) (|sample| (#24=($) NIL T CONST)) (|roughUnitIdeal?| #12#) (|roughSubIdeal?| #25=(#2# NIL #13# ELT)) (|roughEqualIdeals?| #25#) (|roughBase?| #12#) (|rewriteSetWithReduction| ((#5# #5# $ #26=(|Mapping| #6# #6# #6#) #27=(|Mapping| #3# #6# #6#)) NIL T ELT)) (|rewriteIdealWithRemainder| #28=((#5# #5# $) NIL #13# ELT)) (|rewriteIdealWithHeadRemainder| #28#) (|retractIfCan| ((#29=(|Union| $ #23#) #5#) NIL T ELT)) (|retract| #30=(($ #5#) NIL T ELT)) (|rest| ((#29# $) NIL T ELT)) (|removeZero| #16#) (|removeDuplicates| (#31=($ $) NIL #32=(AND #21# #33=(|has| #6# (|BasicType|))) ELT)) (|remove| (#34=($ #6# $) NIL #32# ELT) #19#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| #6#) #35=(|:| |den| |#1|)) #6# $) NIL #13# ELT)) (|reduced?| ((#3# #6# $ #27#) NIL T ELT)) (|reduceByQuasiMonic| #16#) (|reduce| ((#6# #26# $ #6# #6#) NIL #33# ELT) ((#6# #26# $ #6#) NIL T ELT) ((#6# #26# $) NIL T ELT) ((#6# #6# $ #26# #27#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|purelyTranscendental?| #14#) (|purelyAlgebraicLeadingMonomial?| #14#) (|purelyAlgebraic?| #14# #10#) (|normalized?| #14# #10#) (|mvar| ((#7# $) NIL T ELT)) (|members| #36=((#5# $) NIL T ELT)) (|member?| (#15# NIL #33# ELT)) (|map!| #37=(($ (|Mapping| #6# #6#) $) NIL T ELT)) (|map| #37#) (|mainVariables| #9#) (|mainVariable?| #38=((#3# #7# $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultantElseSplit| (((|Union| #6# #8#) #6# #6# $) NIL T ELT)) (|lastSubResultant| ((#17# #6# #6# $) NIL T ELT)) (|last| #39=((#22# $) NIL T ELT)) (|invertibleSet| #40=((#8# #6# $) NIL T ELT)) (|invertibleElseSplit?| (((|Union| #3# #8#) #6# $) NIL T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #18#)) #6# $) NIL T ELT) #14#) (|intersect| #40# #41=((#8# #5# $) NIL T ELT) #42=((#8# #5# #8#) NIL T ELT) #43=((#8# #6# #8#) NIL T ELT)) (|internalAugment| (#34# NIL T ELT) (($ #5# $) NIL T ELT)) (|initials| #36#) (|initiallyReduced?| #14# #10#) (|initiallyReduce| #16#) (|infRittWu?| #1#) (|headRemainder| (((|Record| (|:| |num| #6#) #35#) #6# $) NIL #13# ELT)) (|headReduced?| #14# #10#) (|headReduce| #16#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| #39#) (|find| ((#22# #20# $) NIL T ELT)) (|extendIfCan| ((#29# $ #6#) NIL T ELT)) (|extend| (($ $ #6#) NIL T ELT) #40# #43# #41# #42#) (|every?| #44=((#3# #20# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #45=(AND (|has| #6# (|Evalable| #6#)) (|has| #6# (|SetCategory|))) ELT) (($ $ #6# #6#) NIL #45# ELT) (($ $ #46=(|Equation| #6#)) NIL #45# ELT) (($ $ (|List| #46#)) NIL #45# ELT)) (|eq?| #1#) (|empty?| #10#) (|empty| (#24# NIL T ELT)) (|degree| #47=(#48=(#49=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#49# #6# $) NIL #33# ELT) ((#49# #20# $) NIL T ELT)) (|copy| #50=(#31# NIL T ELT)) (|convert| ((#51=(|InputForm|) $) NIL (|has| #6# (|ConvertibleTo| #51#)) ELT)) (|construct| #30#) (|collectUpper| #52=(($ $ #7#) NIL T ELT)) (|collectUnder| #52#) (|collectQuasiMonic| #50#) (|collect| #52#) (|coerce| (((|OutputForm|) $) NIL T ELT) #36#) (|coHeight| (#48# NIL (|has| #7# (|Finite|)) ELT)) (|before?| #1#) (|basicSet| ((#53=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #23#) #5# #27#) NIL T ELT) ((#53# #5# #20# #27#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# #6# #5#)) NIL T ELT)) (|augment| #40# #43# #41# #42#) (|any?| #44#) (|algebraicVariables| #9#) (|algebraicCoefficients?| #14#) (|algebraic?| #38#) (= #1#) (|#| #47#)) (((|RegularChain| |#1| |#2|) (|Join| (|RegularTriangularSetCategory| |#1| (|IndexedExponents| #1=(|OrderedVariableList| |#2|)) #1# #2=(|NewSparseMultivariatePolynomial| |#1| #1#)) (CATEGORY |domain| (SIGNATURE |zeroSetSplit| ((|List| $) (|List| #2#) #3=(|Boolean|) #3#)))) (|GcdDomain|) (|List| (|Symbol|))) (T |RegularChain|)) ((|zeroSetSplit| (*1 *2 *3 *4 *4) (AND (|isDomain| *3 (|List| (|NewSparseMultivariatePolynomial| *5 (|OrderedVariableList| *6)))) (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 (|GcdDomain|)) (|ofType| *6 (|List| (|Symbol|))) (|isDomain| *2 (|List| #1=(|RegularChain| *5 *6))) (|isDomain| *1 #1#)))) @@ -3199,11 +3199,11 @@ NIL ((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) 10 T ELT))) (((|Ring&| |#1|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Ring|)) (T |Ring&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #5=(|Integer|)) 42 T ELT)) (|characteristic| ((#6=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#7=($ $ $) 29 T ELT)) (+ (#7# 18 T ELT)) (** (($ $ #8=(|PositiveInteger|)) 36 T ELT) (($ $ #6#) 44 T ELT)) (* (($ #8# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #5# $) 31 T ELT) (#7# 35 T ELT))) (((|Ring|) (|Category|)) (T |Ring|)) ((|characteristic| (*1 *2) (AND (|ofCategory| *1 (|Ring|)) (|isDomain| *2 (|NonNegativeInteger|))))) (|Join| (|Rng|) (|SemiRing|) (|LeftModule| $) (|CoercibleFrom| (|Integer|)) (CATEGORY |package| (SIGNATURE |characteristic| ((|NonNegativeInteger|)) |constant|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|Monoid|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|interpolate| (((|Fraction| (|Polynomial| |#2|)) #1=(|List| |#2|) #1# #2=(|NonNegativeInteger|) #2#) 55 T ELT))) (((|RationalInterpolation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |interpolate| ((|Fraction| (|Polynomial| |#2|)) #1=(|List| |#2|) #1# #2=(|NonNegativeInteger|) #2#))) (|Symbol|) (|Field|)) (T |RationalInterpolation|)) ((|interpolate| (*1 *2 *3 *3 *4 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *6 (|Field|)) (|isDomain| *2 (|Fraction| (|Polynomial| *6))) (|isDomain| *1 (|RationalInterpolation| *5 *6)) (|ofType| *5 (|Symbol|))))) @@ -3211,45 +3211,45 @@ NIL (((|RightLinearSet| |#1|) (|Category|) (|SemiGroup|)) (T |RightLinearSet|)) ((* (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RightLinearSet| *2)) (|ofCategory| *2 (|SemiGroup|))))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ |t#1|)))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|symmetric?| (#1=((|Boolean|) $) 38 T ELT)) (|square?| (#1# 17 T ELT)) (|nrows| (#2=((|NonNegativeInteger|) $) 13 T ELT)) (|ncols| (#2# 14 T ELT)) (|diagonal?| (#1# 30 T ELT)) (|antisymmetric?| (#1# 40 T ELT))) (((|RectangularMatrixCategory&| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |ncols| #1=(#2=(|NonNegativeInteger|) |#1|)) (SIGNATURE |nrows| #1#) (SIGNATURE |antisymmetric?| #3=((|Boolean|) |#1|)) (SIGNATURE |symmetric?| #3#) (SIGNATURE |diagonal?| #3#) (SIGNATURE |square?| #3#)) (|RectangularMatrixCategory| |#2| |#3| |#4| |#5| |#6|) #2# #2# (|Ring|) (|DirectProductCategory| |#3| |#4|) (|DirectProductCategory| |#2| |#4|)) (T |RectangularMatrixCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|symmetric?| (((|Boolean|) $) 64 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|square?| (((|Boolean|) $) 66 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rowEchelon| (($ $) 47 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| ((|#4| $ (|Integer|)) 52 T ELT)) (|reduce| ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) 87 (|has| |#3| . #4=((|BasicType|))) ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $ |#3|) 83 T ELT) ((|#3| (|Mapping| |#3| |#3| |#3|) $) 82 T ELT)) (|rank| (((|NonNegativeInteger|) $) 46 (|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) 54 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|nullity| (((|NonNegativeInteger|) $) 45 (|has| |#3| (|IntegralDomain|)) ELT)) (|nullSpace| (((|List| |#5|) $) 44 (|has| |#3| (|IntegralDomain|)) ELT)) (|nrows| (((|NonNegativeInteger|) $) 58 T ELT)) (|ncols| (((|NonNegativeInteger|) $) 57 T ELT)) (|minRowIndex| (((|Integer|) $) 62 T ELT)) (|minColIndex| (((|Integer|) $) 60 T ELT)) (|members| (((|List| |#3|) $) 81 T ELT)) (|member?| ((#5=(|Boolean|) |#3| $) 86 (|has| |#3| . #4#) ELT)) (|maxRowIndex| (((|Integer|) $) 61 T ELT)) (|maxColIndex| (((|Integer|) $) 59 T ELT)) (|matrix| (($ (|List| (|List| |#3|))) 67 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) 72 T ELT) (($ (|Mapping| |#3| |#3| |#3|) $ $) 50 T ELT)) (|listOfLists| (((|List| (|List| |#3|)) $) 56 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#3| "failed") (|Mapping| #5# |#3|) $) 84 T ELT)) (|exquo| (((|Union| $ "failed") $ |#3|) 49 (|has| |#3| (|IntegralDomain|)) ELT)) (|every?| ((#5# (|Mapping| #5# |#3|) . #6=($)) 79 T ELT)) (|eval| (($ $ (|List| |#3|) (|List| |#3|)) 76 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7=((|SetCategory|)))) ELT) (($ $ |#3| |#3|) 75 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|Equation| |#3|)) 74 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT) (($ $ (|List| (|Equation| |#3|))) 73 (AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| . #7#)) ELT)) (|eq?| ((#8=(|Boolean|) $ $) 68 T ELT)) (|empty?| ((#8# $) 71 T ELT)) (|empty| (($) 70 T ELT)) (|elt| ((|#3| $ (|Integer|) (|Integer|)) 55 T ELT) ((|#3| $ (|Integer|) (|Integer|) |#3|) 53 T ELT)) (|diagonal?| (((|Boolean|) $) 65 T ELT)) (|count| ((#9=(|NonNegativeInteger|) |#3| $) 85 (|has| |#3| . #4#) ELT) ((#9# (|Mapping| #5# |#3|) $) 80 T ELT)) (|copy| (($ $) 69 T ELT)) (|column| ((|#5| $ (|Integer|)) 51 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|any?| ((#5# (|Mapping| #5# |#3|) . #6#) 78 T ELT)) (|antisymmetric?| (((|Boolean|) $) 63 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#3|) 48 (|has| |#3| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #10=($)) 31 T ELT) (($ |#3| . #10#) 34 T ELT) (($ $ |#3|) 38 T ELT)) (|#| ((#9# $) 77 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|symmetric?| (#3# 64 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|square?| (#3# 66 T ELT)) (|sample| (#4=($) 23 T CONST)) (|rowEchelon| (#5=($ $) 47 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| ((|#4| $ #6=(|Integer|)) 52 T ELT)) (|reduce| ((|#3| #7=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) 87 #8=(|has| |#3| (|BasicType|)) ELT) ((|#3| #7# $ |#3|) 83 T ELT) ((|#3| #7# $) 82 T ELT)) (|rank| (#9=(#10=(|NonNegativeInteger|) $) 46 #11=(|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| (#12=(|#3| $ #6# #6#) 54 T ELT)) (|opposite?| (#1# 20 T ELT)) (|nullity| (#9# 45 #11# ELT)) (|nullSpace| (((|List| |#5|) $) 44 #11# ELT)) (|nrows| (#9# 58 T ELT)) (|ncols| (#9# 57 T ELT)) (|minRowIndex| (#13=(#6# $) 62 T ELT)) (|minColIndex| (#13# 60 T ELT)) (|members| ((#14=(|List| |#3|) $) 81 T ELT)) (|member?| ((#2# |#3| $) 86 #8# ELT)) (|maxRowIndex| (#13# 61 T ELT)) (|maxColIndex| (#13# 59 T ELT)) (|matrix| (($ #15=(|List| #14#)) 67 T ELT)) (|map| (($ (|Mapping| |#3| |#3|) $) 72 T ELT) (($ #7# $ $) 50 T ELT)) (|listOfLists| ((#15# $) 56 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|find| (((|Union| |#3| #16="failed") 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(|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#6=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|truncate| (#6# 107 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (#6# 92 T ELT)) (|squareFree| (#7=((|Factored| $) $) 91 T ELT)) (|sqrt| (#6# 117 T ELT)) (|sizeLess?| (#1# 76 T ELT)) (|sign| (#4# 134 T ELT)) (|sample| (#8=($) 23 T CONST)) (|round| (#6# 106 T ELT)) (|retractIfCan| (((|Union| #5# . #9=(#10="failed")) . #11=($)) 122 T ELT) (((|Union| #12=(|Fraction| #5#) . #9#) . #11#) 119 T ELT)) (|retract| (#4# 123 T ELT) ((#12# $) 120 T ELT)) (|rem| (#13=($ $ $) 72 T ELT)) (|recip| ((#14=(|Union| $ #10#) $) 43 T ELT)) (|quo| (#13# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) 67 T ELT)) (|prime?| (#3# 90 T ELT)) (|positive?| (#3# 132 T ELT)) (|patternMatch| ((#17=(|PatternMatchResult| #18=(|Float|) $) $ #19=(|Pattern| #18#) #17#) 113 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|nthRoot| (#20=($ $ #5#) 116 T ELT)) (|norm| (#6# 112 T ELT)) (|negative?| (#3# 133 T ELT)) (|multiEuclidean| (((|Union| #15# #10#) #15# $) 69 T ELT)) (|min| (#13# 126 T ELT)) (|max| (#13# 127 T ELT)) (|lcm| (#13# 61 T ELT) (#21=($ #15#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#6# 89 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#22=(|SparseUnivariatePolynomial| $) #22# #22#) 59 T ELT)) (|gcd| (#13# 63 T ELT) (#21# 62 T ELT)) (|fractionPart| (#6# 108 T ELT)) (|floor| (#6# 110 T ELT)) (|factor| (#7# 93 T ELT)) (|extendedEuclidean| (((|Record| #23=(|:| |coef1| $) #24=(|:| |coef2| $) #16#) $ $) 71 T ELT) (((|Union| (|Record| #23# #24#) #10#) $ $ $) 70 T ELT)) (|exquo| ((#14# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #15#) #15# $) 66 T ELT)) (|euclideanSize| ((#25=(|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|convert| ((#18# . #26=($)) 125 T ELT) (((|DoubleFloat|) . #26#) 124 T ELT) ((#19# . #26#) 114 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#27=($ #5#) 42 T ELT) (#6# 58 T ELT) (#28=($ #12#) 85 T ELT) (#27# 121 T ELT) (#28# 118 T ELT)) (|characteristic| ((#25#) 41 T CONST)) (|ceiling| (#6# 111 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|abs| (#6# 135 T ELT)) (|Zero| (#8# 24 T CONST)) (|One| (#8# 46 T CONST)) (>= (#1# 128 T ELT)) (> (#1# 130 T ELT)) (= (#1# 8 T ELT)) (<= (#1# 129 T ELT)) (< (#1# 131 T ELT)) (/ (#13# 84 T ELT)) (- (#6# 30 T ELT) (#13# 29 T ELT)) (+ (#13# 18 T ELT)) (** (($ $ #29=(|PositiveInteger|)) 36 T ELT) (($ $ #25#) 44 T ELT) (#20# 88 T ELT) (#30=($ $ #12#) 115 T ELT)) (* (($ #29# $) 17 T ELT) (($ #25# $) 21 T ELT) (($ #5# . #31=($)) 31 T ELT) (#13# 35 T ELT) (#30# 87 T ELT) (($ #12# . #31#) 86 T ELT))) (((|RealNumberSystem|) (|Category|)) (T |RealNumberSystem|)) -((|norm| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|ceiling| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|floor| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|wholePart| (*1 *2 *1) (AND (|ofCategory| *1 (|RealNumberSystem|)) (|isDomain| *2 (|Integer|)))) (|fractionPart| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|truncate| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) (|round| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|)))) +((|norm| #1=(*1 *1 *1) #2=(|ofCategory| *1 (|RealNumberSystem|))) (|ceiling| #1# #2#) (|floor| #1# #2#) (|wholePart| (*1 *2 *1) (AND #2# (|isDomain| *2 (|Integer|)))) (|fractionPart| #1# #2#) (|truncate| #1# #2#) (|round| #1# #2#)) (|Join| (|Field|) (|OrderedRing|) (|RealConstant|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#)) (|RadicalCategory|) (|ConvertibleTo| (|Pattern| #2=(|Float|))) (|PatternMatchable| #2#) (|CharacteristicZero|) (CATEGORY |domain| (SIGNATURE |norm| #3=($ $)) (SIGNATURE |ceiling| #3#) (SIGNATURE |floor| #3#) (SIGNATURE |wholePart| (#1# $)) (SIGNATURE |fractionPart| #3#) (SIGNATURE |truncate| #3#) (SIGNATURE |round| #3#))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T) ((|ConvertibleTo| (|Pattern| #2=(|Float|))) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #2#) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RetractableTo| (|Fraction| #3=(|Integer|))) . T) ((|RetractableTo| #3#) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicZero|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| #3=(|Float|)) . T) ((|ConvertibleTo| (|Pattern| #3#)) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|LinearSet| $) . T) ((|Module| #1#) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|OrderedAbelianGroup|) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedRing|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|PatternMatchable| #3#) . T) ((|PrincipalIdealDomain|) . T) ((|RadicalCategory|) . T) ((|RealConstant|) . T) ((|RetractableTo| #1#) . T) ((|RetractableTo| #2#) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# |#2| $) 26 T ELT)) (|size| (#5=(|#1| $) 10 T ELT)) (|sign| (((|Integer|) |#2| $) 119 T ELT)) (|rootOf| (((|Union| $ #6="failed") |#2| (|PositiveInteger|)) 76 T ELT)) (|right| (#5# 31 T ELT)) (|relativeApprox| (#7=(|#1| |#2| $ |#1|) 40 T ELT)) (|refine| (($ $) 28 T ELT)) (|recip| (((|Union| |#2| #6#) |#2| $) 113 T ELT)) (|positive?| #8=(#4# NIL T ELT)) (|negative?| #8#) (|mightHaveRoots| (#4# 27 T ELT)) (|middle| (#5# 120 T ELT)) (|left| (#5# 30 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|definingPolynomial| ((|#2| $) 104 T ELT)) (|coerce| (((|OutputForm|) $) 95 T ELT)) (|before?| #1#) (|approximate| (#7# 41 T ELT)) (|allRootsOf| (((|List| $) |#2|) 78 T ELT)) (= (#2# 99 T ELT))) (((|RightOpenIntervalRootCharacterization| |#1| |#2|) (|Join| (|RealRootCharacterizationCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |left| #1=(|#1| $)) (SIGNATURE |right| #1#) (SIGNATURE |size| #1#) (SIGNATURE |middle| #1#) (SIGNATURE |refine| ($ $)) (SIGNATURE |mightHaveRoots| ((|Boolean|) |#2| $)) (SIGNATURE |relativeApprox| (|#1| |#2| $ |#1|)))) (|Join| (|OrderedRing|) (|Field|)) (|UnivariatePolynomialCategory| |#1|)) (T |RightOpenIntervalRootCharacterization|)) ((|relativeApprox| (*1 *2 *3 *1 *2) #1=(AND (|ofCategory| *2 #2=(|Join| (|OrderedRing|) (|Field|))) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *2 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|left| #3=(*1 *2 *1) #1#) (|right| #3# #1#) (|size| #3# #1#) (|middle| #3# #1#) (|refine| (*1 *1 *1) #1#) (|mightHaveRoots| (*1 *2 *3 *1) (AND (|ofCategory| *4 #2#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|RightOpenIntervalRootCharacterization| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) @@ -3259,33 +3259,33 @@ NIL ((|tail| (#1=($ $) 46 T ELT)) (|supRittWu?| (#2=(#3=(|Boolean|) $ $) 82 T ELT)) (|retractIfCan| (((|Union| |#2| #4="failed") $) NIL T ELT) (((|Union| #5=(|Fraction| #6=(|Integer|)) #4#) $) NIL T ELT) (((|Union| #6# #4#) $) NIL T ELT) (((|Union| |#4| #4#) $) NIL T ELT) ((#7=(|Union| $ #4#) #8=(|Polynomial| #5#)) 247 T ELT) ((#7# #9=(|Polynomial| #6#)) 246 T ELT) ((#7# #10=(|Polynomial| |#2|)) 249 T ELT)) (|retract| #11=((|#2| $) NIL T ELT) ((#5# $) NIL T ELT) ((#6# $) NIL T ELT) (#12=(|#4| $) NIL T ELT) (#13=($ #8#) 235 T ELT) (#14=($ #9#) 231 T ELT) (#15=($ #10#) 255 T ELT)) (|reductum| #16=(#1# NIL T ELT) (#17=($ $ |#4|) 44 T ELT)) (|reduced?| (#2# 131 T ELT) (#18=(#3# $ #19=(|List| $)) 135 T ELT)) (|quasiMonic?| (#20=(#3# $) 60 T ELT)) (|pseudoDivide| (((|Record| #21=(|:| |quotient| $) #22=(|:| |remainder| $)) $ $) 125 T ELT)) (|primitivePart!| (#1# 160 T ELT)) (|primPartElseUnitCanonical!| (#1# 156 T ELT)) (|primPartElseUnitCanonical| (#1# 155 T ELT)) (|prem| (#23=($ $ $) 87 T ELT) (#24=($ $ $ |#4|) 92 T ELT)) (|pquo| (#23# 90 T ELT) (#24# 94 T ELT)) (|normalized?| (#2# 143 T ELT) (#18# 144 T ELT)) (|mvar| (#12# 32 T ELT)) (|monicModulo| (#23# 128 T ELT)) (|monic?| (#20# 59 T ELT)) (|mdeg| ((#25=(|NonNegativeInteger|) $) 35 T ELT)) (|mainSquareFreePart| (#1# 174 T ELT)) (|mainPrimitivePart| (#1# 171 T ELT)) (|mainMonomials| (#26=(#19# $) 72 T ELT)) (|mainMonomial| (#1# 62 T ELT)) (|mainContent| (#1# 167 T ELT)) (|mainCoefficients| (#26# 69 T ELT)) (|leastMonomial| (#1# 64 T ELT)) (|leadingCoefficient| #11# (#17# 39 T ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #25#)) $ $) 130 T ELT)) (|lazyPseudoDivide| ((#27=(|Record| #28=(|:| |coef| $) #29=(|:| |gap| #25#) #21# #22#) $ $) 126 T ELT) ((#27# $ $ |#4|) 127 T ELT)) (|lazyPremWithDefault| ((#30=(|Record| #28# #29# #22#) $ $) 121 T ELT) ((#30# $ $ |#4|) 123 T ELT)) (|lazyPrem| (#23# 97 T ELT) (#24# 106 T ELT)) (|lazyPquo| (#23# 98 T ELT) (#24# 107 T ELT)) (|iteratedInitials| (#26# 54 T ELT)) (|initiallyReduced?| (#2# 140 T ELT) (#18# 141 T ELT)) (|initiallyReduce| (#23# 116 T ELT)) (|init| (#1# 37 T ELT)) (|infRittWu?| (#2# 80 T ELT)) (|headReduced?| (#2# 136 T ELT) (#18# 138 T ELT)) (|headReduce| (#23# 112 T ELT)) (|head| (#1# 41 T ELT)) (|gcd| ((|#2| |#2| $) 164 T ELT) (($ #19#) NIL T ELT) (#23# NIL T ELT)) (|exactQuotient!| (#31=($ $ |#2|) NIL T ELT) (#23# 153 T ELT)) (|exactQuotient| (#31# 148 T ELT) (#23# 151 T ELT)) (|deepestTail| (#1# 49 T ELT)) (|deepestInitial| (#1# 55 T ELT)) (|convert| (((|Pattern| (|Float|)) $) NIL T ELT) (((|Pattern| #6#) $) NIL T ELT) (((|InputForm|) $) NIL T ELT) (#13# 237 T ELT) (#14# 233 T ELT) (#15# 248 T ELT) (((|String|) $) 278 T ELT) (#32=(#10# $) 184 T ELT)) (|coerce| (((|OutputForm|) $) 29 T ELT) (($ #6#) NIL T ELT) (($ |#2|) NIL T ELT) (($ |#4|) NIL T ELT) (#32# 185 T ELT) (($ #5#) NIL T ELT) #16#) (|RittWuCompare| (((|Union| #3# #4#) $ $) 79 T ELT))) (((|RecursivePolynomialCategory&| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |coerce| #1=(|#1| |#1|)) (SIGNATURE |gcd| #2=(|#1| |#1| |#1|)) (SIGNATURE |gcd| (|#1| #3=(|List| |#1|))) (SIGNATURE |coerce| (|#1| #4=(|Fraction| #5=(|Integer|)))) (SIGNATURE |coerce| #6=(#7=(|Polynomial| |#2|) |#1|)) (SIGNATURE |convert| #6#) (SIGNATURE |convert| ((|String|) |#1|)) (SIGNATURE |mainSquareFreePart| #1#) (SIGNATURE |mainPrimitivePart| #1#) (SIGNATURE |mainContent| #1#) (SIGNATURE |primitivePart!| #1#) (SIGNATURE |gcd| (|#2| |#2| |#1|)) (SIGNATURE |exactQuotient!| #2#) (SIGNATURE |exactQuotient| #2#) (SIGNATURE |exactQuotient!| #8=(|#1| |#1| |#2|)) (SIGNATURE |exactQuotient| #8#) (SIGNATURE |primPartElseUnitCanonical!| #1#) (SIGNATURE |primPartElseUnitCanonical| #1#) (SIGNATURE |convert| #9=(|#1| #7#)) (SIGNATURE |retract| #9#) (SIGNATURE |retractIfCan| (#10=(|Union| |#1| #11="failed") #7#)) (SIGNATURE |convert| #12=(|#1| #13=(|Polynomial| #5#))) (SIGNATURE |retract| #12#) (SIGNATURE |retractIfCan| (#10# #13#)) (SIGNATURE |convert| #14=(|#1| #15=(|Polynomial| #4#))) (SIGNATURE |retract| #14#) (SIGNATURE |retractIfCan| (#10# #15#)) (SIGNATURE |initiallyReduce| #2#) (SIGNATURE 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|headReduced?| #24#) (SIGNATURE |headReduced?| #26#) (SIGNATURE |reduced?| #24#) (SIGNATURE |reduced?| #26#) (SIGNATURE |supRittWu?| #26#) (SIGNATURE |infRittWu?| #26#) (SIGNATURE |RittWuCompare| ((|Union| #25# #11#) |#1| |#1|)) (SIGNATURE |mainMonomials| #27=(#3# |#1|)) (SIGNATURE |mainCoefficients| #27#) (SIGNATURE |leastMonomial| #1#) (SIGNATURE |mainMonomial| #1#) (SIGNATURE |quasiMonic?| #28=(#25# |#1|)) (SIGNATURE |monic?| #28#) (SIGNATURE |reductum| #29=(|#1| |#1| |#4|)) (SIGNATURE |leadingCoefficient| #29#) (SIGNATURE |deepestInitial| #1#) (SIGNATURE |iteratedInitials| #27#) (SIGNATURE |deepestTail| #1#) (SIGNATURE |tail| #1#) (SIGNATURE |head| #1#) (SIGNATURE |init| #1#) (SIGNATURE |mdeg| (#16# |#1|)) (SIGNATURE |mvar| #30=(|#4| |#1|)) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |convert| ((|Pattern| #5#) |#1|)) (SIGNATURE |convert| ((|Pattern| (|Float|)) |#1|)) (SIGNATURE |coerce| (|#1| |#4|)) (SIGNATURE |retractIfCan| ((|Union| |#4| #11#) |#1|)) (SIGNATURE 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((#28=(|Union| $ #19#) #29=(|Polynomial| #23#)) 254 #30=(AND #31=(|has| |#1| (|Algebra| #23#)) #32=(|has| |#3| (|ConvertibleTo| (|Symbol|)))) ELT) ((#28# #33=(|Polynomial| #24#)) 251 #34=(OR (AND #35=(|not| #31#) #36=(|has| |#1| (|Algebra| #24#)) #32#) #30#) ELT) ((#28# #37=(|Polynomial| |#1|)) 248 #38=(OR (AND #35# (|not| #36#) #32#) (AND (|not| (|has| |#1| (|IntegerNumberSystem|))) #35# #36# #32#) (AND (|not| (|has| |#1| (|QuotientFieldCategory| #24#))) #31# #32#)) ELT)) (|retract| (#39=(|#1| . #40=($)) 182 T ELT) ((#23# . #40#) 181 #25# ELT) ((#24# . #40#) 179 #26# ELT) (#41=(|#3| . #40#) 156 T ELT) (#42=($ #29#) 253 #30# ELT) (#43=($ #33#) 250 #34# ELT) (#44=($ #37#) 247 #38# ELT)) (|resultant| (#45=($ $ $ |#3|) 123 #46=(|has| |#1| (|CommutativeRing|)) ELT) (#12# 235 #7# ELT)) (|reductum| (#8# 173 T ELT) (#47=($ $ |#3|) 289 T ELT)) (|reducedSystem| ((#48=(|Matrix| #24#) . #49=(#50=(|Matrix| $))) 151 #51=(|has| |#1| (|LinearlyExplicitRingOver| #24#)) ELT) ((#52=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #24#))) . #53=(#50# #54=(|Vector| $))) 150 #51# ELT) ((#55=(|Record| (|:| |mat| #56=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #53#) 149 T ELT) ((#56# . #49#) 148 T ELT)) (|reduced?| (#1# 279 T ELT) (#57=(#2# $ #13#) 278 T ELT)) (|recip| ((#28# $) 43 T ELT)) (|quasiMonic?| (#3# 287 T ELT)) (|pseudoDivide| ((#58=(|Record| #59=(|:| |quotient| $) #60=(|:| |remainder| $)) $ $) 259 T ELT)) (|primitivePart!| (#8# 228 #16# ELT)) (|primitivePart| (#8# 195 #16# ELT) (#47# 120 #16# ELT)) (|primitiveMonomials| (#61=(#13# $) 124 T ELT)) (|prime?| (#3# 111 #15# ELT)) (|primPartElseUnitCanonical!| (#8# 244 #7# ELT)) (|primPartElseUnitCanonical| (#8# 245 #7# ELT)) (|prem| (#12# 271 T ELT) (#45# 269 T ELT)) (|pquo| (#12# 270 T ELT) (#45# 268 T ELT)) (|pomopo!| (($ $ |#1| |#2| $) 191 T ELT)) (|patternMatch| ((#62=(|PatternMatchResult| #63=(|Float|) . #64=($)) $ #65=(|Pattern| #63#) #62#) 99 (AND (|has| |#3| #66=(|PatternMatchable| #63#)) (|has| |#1| #66#)) ELT) ((#67=(|PatternMatchResult| #24# . #64#) $ #68=(|Pattern| #24#) #67#) 98 (AND (|has| |#3| #69=(|PatternMatchable| #24#)) (|has| |#1| #69#)) ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|numberOfMonomials| (#9# 188 T ELT)) (|normalized?| (#1# 273 T ELT) (#57# 272 T ELT)) (|nextsubResultant2| (($ $ $ $ $) 230 #7# ELT)) (|mvar| (#41# 298 T ELT)) (|multivariate| (($ #6# |#3|) 132 T ELT) (($ #5# |#3|) 131 T ELT)) (|monomials| (#61# 141 T ELT)) (|monomial?| (#3# 171 T ELT)) (|monomial| (($ |#1| |#2|) 172 T ELT) (#70=($ $ |#3| #10#) 134 T ELT) (#71=($ $ #4# #72=(|List| #10#)) 133 T ELT)) (|monicModulo| (#12# 258 T ELT)) (|monicDivide| ((#58# $ $ |#3|) 135 T ELT)) (|monic?| (#3# 288 T ELT)) (|minimumDegree| (#73=(|#2| $) 189 T ELT) (#74=(#10# $ |#3|) 137 T ELT) (#75=(#72# $ #4#) 136 T ELT)) (|mdeg| (#9# 297 T ELT)) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) 190 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 167 T ELT)) (|mainVariable| (#27# 138 T ELT)) (|mainSquareFreePart| (#8# 225 #16# ELT)) (|mainPrimitivePart| (#8# 226 #16# ELT)) (|mainMonomials| (#61# 283 T ELT)) (|mainMonomial| (#8# 286 T ELT)) (|mainContent| (#8# 227 #16# ELT)) (|mainCoefficients| (#61# 284 T ELT)) (|leftReducedSystem| ((#48# . #76=(#54#)) 153 #51# ELT) ((#52# . #77=(#54# $)) 152 #51# ELT) ((#55# . #77#) 147 T ELT) ((#56# . #76#) 146 T ELT)) (|leastMonomial| (#8# 285 T ELT)) (|leadingMonomial| (#8# 169 T ELT)) (|leadingCoefficient| (#39# 168 T ELT) (#47# 290 T ELT)) (|lcm| (#78=($ #13#) 109 #16# ELT) (#12# 108 #16# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #10#)) $ $) 257 T ELT)) (|lazyPseudoDivide| ((#79=(|Record| #80=(|:| |coef| $) #81=(|:| |gap| #10#) #59# #60#) $ $) 261 T ELT) ((#79# $ $ |#3|) 260 T ELT)) (|lazyPremWithDefault| ((#82=(|Record| #80# #81# #60#) $ $) 263 T ELT) ((#82# $ $ |#3|) 262 T ELT)) (|lazyPrem| (#12# 267 T ELT) (#45# 265 T ELT)) (|lazyPquo| (#12# 266 T ELT) (#45# 264 T ELT)) (|latex| (#83=((|String|) $) 11 T ELT)) (|lastSubResultant| (#12# 233 #7# ELT)) (|iteratedInitials| (#61# 292 T ELT)) (|isTimes| (#84=((|Union| #13# #19#) $) 129 T ELT)) (|isPlus| (#84# 130 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| #10#)) #19#) $) 128 T ELT)) (|initiallyReduced?| (#1# 275 T ELT) (#57# 274 T ELT)) (|initiallyReduce| (#12# 255 T ELT)) (|init| (#8# 296 T ELT)) (|infRittWu?| (#1# 281 T ELT)) (|headReduced?| (#1# 277 T ELT) (#57# 276 T ELT)) (|headReduce| (#12# 256 T ELT)) (|head| (#8# 295 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #85=(|:| |gcd| $) #86=(|:| |coef2| $)) $ $) 236 #7# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #85# #87=(|:| |coef1| $)) $ $) 237 #7# ELT)) (|ground?| (#3# 185 T ELT)) (|ground| (#39# 186 T ELT)) (|gcdPolynomial| ((#5# #5# #5#) 110 #16# ELT)) (|gcd| ((|#1| |#1| $) 229 #16# ELT) (#78# 107 #16# ELT) (#12# 106 #16# ELT)) (|factorSquareFreePolynomial| (#14# 117 #15# ELT)) (|factorPolynomial| (#14# 116 #15# ELT)) (|factor| (#17# 114 #15# ELT)) (|extendedSubResultantGcd| (((|Record| #85# #87# #86#) $ $) 238 #7# ELT)) (|exquo| ((#28# $ |#1|) 193 #7# ELT) ((#28# $ $) 101 #7# ELT)) (|exactQuotient!| (#88=($ $ |#1|) 242 #7# ELT) (#12# 240 #7# ELT)) (|exactQuotient| (#88# 243 #7# ELT) (#12# 241 #7# ELT)) (|eval| (($ $ (|List| #89=(|Equation| $))) 164 T ELT) (($ $ #89#) 163 T ELT) (($ $ $ $) 162 T ELT) (($ $ #13# #13#) 161 T ELT) (($ $ |#3| |#1|) 160 T ELT) (($ $ #4# #90=(|List| |#1|)) 159 T ELT) (($ $ |#3| $) 158 T ELT) (($ $ #4# #13#) 157 T ELT)) (|discriminant| (#47# 122 #46# ELT)) (|differentiate| (#71# 53 T ELT) (#70# 52 T ELT) (#91=($ $ #4#) 51 T ELT) (#47# 49 T ELT)) (|degree| (#73# 170 T ELT) (#74# 145 T ELT) (#75# 144 T ELT)) (|deepestTail| (#8# 293 T ELT)) (|deepestInitial| (#8# 291 T ELT)) (|convert| ((#65# . #92=($)) 97 (AND (|has| |#3| #93=(|ConvertibleTo| #65#)) (|has| |#1| #93#)) ELT) ((#68# . #92#) 96 (AND (|has| |#3| #94=(|ConvertibleTo| #68#)) (|has| |#1| #94#)) ELT) ((#95=(|InputForm|) . #92#) 95 (AND (|has| |#3| #96=(|ConvertibleTo| #95#)) (|has| |#1| #96#)) ELT) (#42# 252 #30# ELT) (#43# 249 #34# ELT) (#44# 246 #32# ELT) (#83# 224 (AND #26# #32#) ELT) (#97=(#37# . #92#) 223 #32# ELT)) (|content| (#39# 194 #16# ELT) (#47# 121 #16# ELT)) (|conditionP| (((|Union| #54# #19#) #50#) 119 #98=(|and| (|has| $ #99=(|CharacteristicNonZero|)) #15#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #24#) 42 T ELT) (($ |#1|) 184 T ELT) (($ |#3|) 154 T ELT) (#97# 222 #32# ELT) (($ #23#) 93 (OR #25# #31#) ELT) (#8# 100 #7# ELT)) (|coefficients| ((#90# $) 187 T ELT)) (|coefficient| ((|#1| $ |#2|) 174 T ELT) (#70# 143 T ELT) (#71# 142 T ELT)) (|charthRoot| ((#11# $) 94 (OR #98# (|has| |#1| #99#)) ELT)) (|characteristic| ((#10#) 41 T CONST)) (|binomThmExpt| (#100=($ $ $ #10#) 192 #46# ELT)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 104 #7# ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#20# 24 T CONST)) (|RittWuCompare| (((|Union| #2# #19#) $ $) 282 T ELT)) (|One| (#20# 46 T CONST)) (|LazardQuotient2| (($ $ $ $ #10#) 231 #7# ELT)) (|LazardQuotient| (#100# 232 #7# ELT)) (D (#71# 56 T ELT) (#70# 55 T ELT) (#91# 54 T ELT) (#47# 50 T ELT)) (= (#1# 8 T ELT)) (/ (#88# 175 (|has| |#1| (|Field|)) ELT)) (- (#8# 30 T ELT) (#12# 29 T ELT)) (+ (#12# 18 T ELT)) (** (($ $ #101=(|PositiveInteger|)) 36 T ELT) (($ $ #10#) 44 T ELT)) (* (($ #101# $) 17 T ELT) (($ #10# $) 21 T ELT) (($ #24# . #102=($)) 31 T ELT) (#12# 35 T ELT) (($ $ #23#) 177 #31# ELT) (($ #23# . #102#) 176 #31# ELT) (($ |#1| . #102#) 166 T ELT) (#88# 165 T ELT))) (((|RecursivePolynomialCategory| |#1| |#2| |#3|) (|Category|) (|Ring|) (|OrderedAbelianMonoidSup|) (|OrderedSet|)) (T |RecursivePolynomialCategory|)) -((|mvar| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|mdeg| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|init| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|head| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|tail| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|deepestTail| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|iteratedInitials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|deepestInitial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|leadingCoefficient| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|reductum| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|monic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|quasiMonic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|mainMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|leastMonomial| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|mainCoefficients| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|mainMonomials| (*1 *2 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|RittWuCompare| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|infRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|supRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|Boolean|)))) (|prem| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|pquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|prem| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|pquo| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPrem| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyPquo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyPrem| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPquo| (*1 *1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *2 (|OrderedSet|)))) (|lazyPremWithDefault| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lazyPremWithDefault| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3)))) (|lazyPseudoDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lazyPseudoDivide| (*1 *2 *1 *1 *3) (AND (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |coef| *1) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3)))) (|pseudoDivide| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |quotient| *1) (|:| |remainder| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|monicModulo| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|lazyResidueClass| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |polnum| *1) (|:| |polden| *1) (|:| |power| (|NonNegativeInteger|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|headReduce| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|initiallyReduce| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)))) (|retractIfCan| (*1 *1 *2) (|partial| AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|retract| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| (|Fraction| (|Integer|)))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|retractIfCan| (*1 *1 *2) (|partial| OR (AND #1=(|isDomain| *2 (|Polynomial| (|Integer|))) #2=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #3=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #1# #2# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #3#))) (|retract| (*1 *1 *2) (OR (AND #4=(|isDomain| *2 (|Polynomial| (|Integer|))) #5=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #6=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #4# #5# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #6#))) (|convert| (*1 *1 *2) (OR (AND #7=(|isDomain| *2 (|Polynomial| (|Integer|))) #8=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #9=((|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #7# #8# (AND (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #9#))) (|retractIfCan| (*1 *1 *2) (|partial| OR (AND #10=(|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11=((|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #10# (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11#) (AND #10# (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #11#))) (|retract| (*1 *1 *2) (OR (AND #12=(|isDomain| *2 (|Polynomial| *3)) (AND (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|not| (|ofCategory| *3 (|Algebra| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13=((|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (AND #12# (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) (|not| (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))) (|ofCategory| *3 (|Algebra| (|Integer|))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13#) (AND #12# (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| (|Integer|)))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|)))) . #13#))) (|convert| (*1 *1 *2) (AND (|isDomain| *2 (|Polynomial| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)))) (|primPartElseUnitCanonical| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|primPartElseUnitCanonical!| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient!| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|exactQuotient!| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|subResultantGcd| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|extendedSubResultantGcd| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef1| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|halfExtendedSubResultantGcd1| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef1| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|halfExtendedSubResultantGcd2| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |gcd| *1) (|:| |coef2| *1))) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|resultant| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|subResultantChain| (*1 *2 *1 *1) (AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)))) (|lastSubResultant| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|LazardQuotient| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|)))) (|LazardQuotient2| (*1 *1 *1 *1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *3 (|IntegralDomain|)))) (|nextsubResultant2| (*1 *1 *1 *1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|IntegralDomain|)))) (|gcd| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart!| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainContent| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainPrimitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|)))) (|mainSquareFreePart| (*1 *1 *1) (AND (|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 (|GcdDomain|))))) -(|Join| (|PolynomialCategory| |t#1| |t#2| |t#3|) (CATEGORY |domain| (SIGNATURE |mvar| (|t#3| $)) (SIGNATURE |mdeg| ((|NonNegativeInteger|) $)) (SIGNATURE |init| ($ $)) (SIGNATURE |head| ($ $)) (SIGNATURE |tail| ($ $)) (SIGNATURE |deepestTail| ($ $)) (SIGNATURE |iteratedInitials| ((|List| $) $)) (SIGNATURE |deepestInitial| ($ $)) (SIGNATURE |leadingCoefficient| ($ $ |t#3|)) (SIGNATURE |reductum| ($ $ |t#3|)) (SIGNATURE |monic?| ((|Boolean|) $)) (SIGNATURE |quasiMonic?| ((|Boolean|) $)) (SIGNATURE |mainMonomial| ($ $)) (SIGNATURE |leastMonomial| ($ $)) (SIGNATURE |mainCoefficients| ((|List| $) $)) (SIGNATURE |mainMonomials| ((|List| $) $)) (SIGNATURE |RittWuCompare| ((|Union| (|Boolean|) "failed") $ $)) (SIGNATURE |infRittWu?| ((|Boolean|) $ $)) (SIGNATURE |supRittWu?| ((|Boolean|) $ $)) (SIGNATURE |reduced?| ((|Boolean|) $ $)) (SIGNATURE |reduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |headReduced?| ((|Boolean|) $ $)) (SIGNATURE |headReduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |initiallyReduced?| ((|Boolean|) $ $)) (SIGNATURE |initiallyReduced?| ((|Boolean|) $ (|List| $))) (SIGNATURE |normalized?| ((|Boolean|) $ $)) (SIGNATURE |normalized?| ((|Boolean|) $ (|List| $))) (SIGNATURE |prem| ($ $ $)) (SIGNATURE |pquo| ($ $ $)) (SIGNATURE |prem| ($ $ $ |t#3|)) (SIGNATURE |pquo| ($ $ $ |t#3|)) (SIGNATURE |lazyPrem| ($ $ $)) (SIGNATURE |lazyPquo| ($ $ $)) (SIGNATURE |lazyPrem| ($ $ $ |t#3|)) (SIGNATURE |lazyPquo| ($ $ $ |t#3|)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPremWithDefault| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |t#3|)) (SIGNATURE |pseudoDivide| ((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |monicModulo| ($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $)) (SIGNATURE |headReduce| ($ $ $)) (SIGNATURE |initiallyReduce| ($ $ $)) (IF (|has| |t#3| (|ConvertibleTo| (|Symbol|))) (PROGN (ATTRIBUTE (|CoercibleTo| (|Polynomial| |t#1|))) (ATTRIBUTE (|ConvertibleTo| (|Polynomial| |t#1|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retract| ($ (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |convert| ($ (|Polynomial| (|Fraction| (|Integer|))))) (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |convert| ($ (|Polynomial| (|Integer|)))) (IF (|has| |t#1| (|QuotientFieldCategory| (|Integer|))) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|)))))) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Integer|))) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| (|Integer|)))) (SIGNATURE |retract| ($ (|Polynomial| (|Integer|)))) (SIGNATURE |convert| ($ (|Polynomial| (|Integer|)))) (IF (|has| |t#1| (|IntegerNumberSystem|)) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|))))))) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Integer|))) |%noBranch| (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) |%noBranch| (PROGN (SIGNATURE |retractIfCan| ((|Union| $ "failed") (|Polynomial| |t#1|))) (SIGNATURE |retract| ($ (|Polynomial| |t#1|)))))) (SIGNATURE |convert| ($ (|Polynomial| |t#1|))) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|ConvertibleTo| (|String|))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |primPartElseUnitCanonical| ($ $)) (SIGNATURE |primPartElseUnitCanonical!| ($ $)) (SIGNATURE |exactQuotient| ($ $ |t#1|)) (SIGNATURE |exactQuotient!| ($ $ |t#1|)) (SIGNATURE |exactQuotient| ($ $ $)) (SIGNATURE |exactQuotient!| ($ $ $)) (SIGNATURE |subResultantGcd| ($ $ $)) (SIGNATURE |extendedSubResultantGcd| ((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $)) (SIGNATURE |resultant| ($ $ $)) (SIGNATURE |subResultantChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| ($ $ $)) (SIGNATURE |LazardQuotient| ($ $ $ (|NonNegativeInteger|))) (SIGNATURE |LazardQuotient2| ($ $ $ $ (|NonNegativeInteger|))) (SIGNATURE |nextsubResultant2| ($ $ $ $ $))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |gcd| (|t#1| |t#1| $)) (SIGNATURE |primitivePart!| ($ $)) (SIGNATURE |mainContent| ($ $)) (SIGNATURE |mainPrimitivePart| ($ $)) (SIGNATURE |mainSquareFreePart| ($ $))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| (|Polynomial| |#1|)) |has| |#3| (|ConvertibleTo| (|Symbol|))) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|ConvertibleTo| (|Polynomial| |#1|)) |has| |#3| (|ConvertibleTo| (|Symbol|))) ((|ConvertibleTo| (|String|)) AND (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|))) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| |#3|) . T) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| |#2| |#3|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#3|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) +((|mvar| #1=(*1 *2 *1) #2=(AND (|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *2)) #3=(|ofCategory| *3 #4=(|Ring|)) #5=(|ofCategory| *4 #6=(|OrderedAbelianMonoidSup|)) (|ofCategory| *2 #7=(|OrderedSet|)))) (|mdeg| #1# (AND #8=(|ofCategory| *1 (|RecursivePolynomialCategory| *3 *4 *5)) #3# #5# #9=(|ofCategory| *5 #7#) #10=(|isDomain| *2 #11=(|NonNegativeInteger|)))) (|init| #12=(*1 *1 *1) #13=(AND #14=(|ofCategory| *1 (|RecursivePolynomialCategory| *2 *3 *4)) #15=(|ofCategory| *2 #4#) #16=(|ofCategory| *3 #6#) #17=(|ofCategory| *4 #7#))) (|head| #12# #13#) (|tail| #12# #13#) (|deepestTail| #12# #13#) (|iteratedInitials| #1# #18=(AND #3# #5# #9# #19=(|isDomain| *2 #20=(|List| *1)) #8#)) (|deepestInitial| #12# #13#) (|leadingCoefficient| #21=(*1 *1 *1 *2) #2#) (|reductum| #21# #2#) (|monic?| #1# #22=(AND #8# #3# #5# #9# #23=(|isDomain| *2 (|Boolean|)))) (|quasiMonic?| #1# #22#) (|mainMonomial| #12# #13#) (|leastMonomial| #12# #13#) (|mainCoefficients| #1# #18#) (|mainMonomials| #1# #18#) (|RittWuCompare| #24=(*1 *2 *1 *1) (|partial| AND #8# #3# #5# #9# #23#)) (|infRittWu?| #24# #22#) (|supRittWu?| #24# #22#) (|reduced?| #24# #22#) (|reduced?| #25=(*1 *2 *1 *3) #26=(AND (|isDomain| *3 #20#) (|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *6)) #27=(|ofCategory| *4 #4#) #28=(|ofCategory| *5 #6#) (|ofCategory| *6 #7#) #23#)) (|headReduced?| #24# #22#) (|headReduced?| #25# #26#) (|initiallyReduced?| #24# #22#) (|initiallyReduced?| #25# #26#) (|normalized?| #24# #22#) (|normalized?| #25# #26#) (|prem| #29=(*1 *1 *1 *1) #13#) (|pquo| #29# #13#) (|prem| #30=(*1 *1 *1 *1 *2) #2#) (|pquo| #30# #2#) (|lazyPrem| #29# #13#) (|lazyPquo| #29# #13#) (|lazyPrem| #30# #2#) (|lazyPquo| #30# #2#) (|lazyPremWithDefault| #24# (AND #3# #5# #9# #31=(|isDomain| *2 (|Record| #32=(|:| |coef| *1) #33=(|:| |gap| #11#) #34=(|:| |remainder| *1))) #8#)) (|lazyPremWithDefault| #35=(*1 *2 *1 *1 *3) (AND #27# #28# #36=(|ofCategory| *3 #7#) #31# #37=(|ofCategory| *1 (|RecursivePolynomialCategory| *4 *5 *3)))) (|lazyPseudoDivide| #24# (AND #3# #5# #9# #38=(|isDomain| *2 (|Record| #32# #33# #39=(|:| |quotient| *1) #34#)) #8#)) (|lazyPseudoDivide| #35# (AND #27# #28# #36# #38# #37#)) (|pseudoDivide| #24# (AND #3# #5# #9# (|isDomain| *2 (|Record| #39# #34#)) #8#)) (|monicModulo| #29# #13#) (|lazyResidueClass| #24# (AND #3# #5# #9# (|isDomain| *2 (|Record| (|:| |polnum| *1) (|:| |polden| *1) (|:| |power| #11#))) #8#)) (|headReduce| #29# #13#) (|initiallyReduce| #29# #13#) (|retractIfCan| #40=(*1 *1 *2) (|partial| AND #41=(|isDomain| *2 (|Polynomial| #42=(|Fraction| #43=(|Integer|)))) #8# #44=(|ofCategory| *3 (|Algebra| #42#)) #45=(|ofCategory| *5 (|ConvertibleTo| (|Symbol|))) #3# #5# #9#)) (|retract| #40# #46=(AND #41# #8# #44# #45# #3# #5# #9#)) (|convert| #40# #46#) (|retractIfCan| #40# (|partial| OR #47=(AND #48=(|isDomain| *2 (|Polynomial| #43#)) #8# (AND #49=(|not| #44#) #50=(|ofCategory| *3 (|Algebra| #43#)) #45#) . #51=(#3# #5# #9#)) #52=(AND #48# #8# (AND #44# #45#) . #51#))) (|retract| #40# #53=(OR #47# #52#)) (|convert| #40# #53#) (|retractIfCan| #40# (|partial| OR #54=(AND #55=(|isDomain| *2 (|Polynomial| *3)) (AND #49# (|not| #50#) #45#) . #56=(#3# #8# #5# #9#)) #57=(AND #55# (AND (|not| (|ofCategory| *3 (|IntegerNumberSystem|))) #49# #50# #45#) . #56#) #58=(AND #55# (AND (|not| (|ofCategory| *3 (|QuotientFieldCategory| #43#))) #44# #45#) . #56#))) (|retract| #40# (OR #54# #57# #58#)) (|convert| #40# (AND #55# #3# #8# #45# #5# #9#)) (|primPartElseUnitCanonical| #12# #59=(AND #14# #15# #16# #17# (|ofCategory| *2 #60=(|IntegralDomain|)))) (|primPartElseUnitCanonical!| #12# #59#) (|exactQuotient| #21# #59#) (|exactQuotient!| #21# #59#) (|exactQuotient| #29# #59#) (|exactQuotient!| #29# #59#) (|subResultantGcd| #29# #59#) (|extendedSubResultantGcd| #24# (AND #61=(|ofCategory| *3 #60#) #3# #5# #9# (|isDomain| *2 (|Record| #62=(|:| |gcd| *1) #63=(|:| |coef1| *1) #64=(|:| |coef2| *1))) #8#)) (|halfExtendedSubResultantGcd1| #24# (AND #61# #3# #5# #9# (|isDomain| *2 (|Record| #62# #63#)) #8#)) (|halfExtendedSubResultantGcd2| #24# (AND #61# #3# #5# #9# (|isDomain| *2 (|Record| #62# #64#)) #8#)) (|resultant| #29# #59#) (|subResultantChain| #24# (AND #61# #3# #5# #9# #19# #8#)) (|lastSubResultant| #29# #59#) (|LazardQuotient| #30# #65=(AND #10# #8# #3# #5# #9# #61#)) (|LazardQuotient2| (*1 *1 *1 *1 *1 *2) #65#) (|nextsubResultant2| (*1 *1 *1 *1 *1 *1) #59#) (|gcd| (*1 *2 *2 *1) #66=(AND #14# #15# #16# #17# (|ofCategory| *2 (|GcdDomain|)))) (|primitivePart!| #12# #66#) (|mainContent| #12# #66#) (|mainPrimitivePart| #12# #66#) (|mainSquareFreePart| #12# #66#)) +(|Join| (|PolynomialCategory| |t#1| |t#2| |t#3|) (CATEGORY |domain| (SIGNATURE |mvar| (|t#3| $)) (SIGNATURE |mdeg| (#1=(|NonNegativeInteger|) $)) (SIGNATURE |init| #2=($ $)) (SIGNATURE |head| #2#) (SIGNATURE |tail| #2#) (SIGNATURE |deepestTail| #2#) (SIGNATURE |iteratedInitials| #3=(#4=(|List| $) $)) (SIGNATURE |deepestInitial| #2#) (SIGNATURE |leadingCoefficient| #5=($ $ |t#3|)) (SIGNATURE |reductum| #5#) (SIGNATURE |monic?| #6=(#7=(|Boolean|) $)) (SIGNATURE |quasiMonic?| #6#) (SIGNATURE |mainMonomial| #2#) (SIGNATURE |leastMonomial| #2#) (SIGNATURE |mainCoefficients| #3#) (SIGNATURE |mainMonomials| #3#) (SIGNATURE |RittWuCompare| ((|Union| #7# #8="failed") $ $)) (SIGNATURE |infRittWu?| #9=(#7# $ $)) (SIGNATURE |supRittWu?| #9#) (SIGNATURE |reduced?| #9#) (SIGNATURE |reduced?| #10=(#7# $ #4#)) (SIGNATURE |headReduced?| #9#) (SIGNATURE |headReduced?| #10#) (SIGNATURE |initiallyReduced?| #9#) (SIGNATURE |initiallyReduced?| #10#) (SIGNATURE |normalized?| #9#) (SIGNATURE |normalized?| #10#) (SIGNATURE |prem| #11=($ $ $)) (SIGNATURE |pquo| #11#) (SIGNATURE |prem| #12=($ $ $ |t#3|)) (SIGNATURE |pquo| #12#) (SIGNATURE |lazyPrem| #11#) (SIGNATURE |lazyPquo| #11#) (SIGNATURE |lazyPrem| #12#) (SIGNATURE |lazyPquo| #12#) (SIGNATURE |lazyPremWithDefault| (#13=(|Record| #14=(|:| |coef| $) #15=(|:| |gap| #1#) #16=(|:| |remainder| $)) $ $)) (SIGNATURE |lazyPremWithDefault| (#13# $ $ |t#3|)) (SIGNATURE |lazyPseudoDivide| (#17=(|Record| #14# #15# #18=(|:| |quotient| $) #16#) $ $)) (SIGNATURE |lazyPseudoDivide| (#17# $ $ |t#3|)) (SIGNATURE |pseudoDivide| ((|Record| #18# #16#) $ $)) (SIGNATURE |monicModulo| #11#) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #1#)) $ $)) (SIGNATURE |headReduce| #11#) (SIGNATURE |initiallyReduce| #11#) (IF (|has| |t#3| (|ConvertibleTo| (|Symbol|))) (PROGN (ATTRIBUTE (|CoercibleTo| #19=(|Polynomial| |t#1|))) (ATTRIBUTE (|ConvertibleTo| #19#)) (IF #20=(|has| |t#1| (|Algebra| #21=(|Fraction| #22=(|Integer|)))) (PROGN (SIGNATURE |retractIfCan| (#23=(|Union| $ #8#) #24=(|Polynomial| #21#))) (SIGNATURE |retract| #25=($ #24#)) (SIGNATURE |convert| #25#) #26=(SIGNATURE |retractIfCan| (#23# #27=(|Polynomial| #22#))) #28=(SIGNATURE |retract| #29=($ #27#)) #30=(SIGNATURE |convert| #29#) (IF (|has| |t#1| (|QuotientFieldCategory| #22#)) |%noBranch| #31=(PROGN (SIGNATURE |retractIfCan| (#23# #19#)) (SIGNATURE |retract| #32=($ #19#))))) |%noBranch|) (IF #33=(|has| |t#1| (|Algebra| #22#)) (IF #20# |%noBranch| (PROGN #26# #28# #30# (IF (|has| |t#1| (|IntegerNumberSystem|)) |%noBranch| #31#))) |%noBranch|) (IF #33# |%noBranch| (IF #20# |%noBranch| #31#)) (SIGNATURE |convert| #32#) (IF (|has| |t#1| (|RetractableTo| #22#)) (ATTRIBUTE (|ConvertibleTo| (|String|))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |primPartElseUnitCanonical| #2#) (SIGNATURE |primPartElseUnitCanonical!| #2#) (SIGNATURE |exactQuotient| #34=($ $ |t#1|)) (SIGNATURE |exactQuotient!| #34#) (SIGNATURE |exactQuotient| #11#) (SIGNATURE |exactQuotient!| #11#) (SIGNATURE |subResultantGcd| #11#) (SIGNATURE |extendedSubResultantGcd| ((|Record| #35=(|:| |gcd| $) #36=(|:| |coef1| $) #37=(|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| #35# #36#) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| #35# #37#) $ $)) (SIGNATURE |resultant| #11#) (SIGNATURE |subResultantChain| (#4# $ $)) (SIGNATURE |lastSubResultant| #11#) (SIGNATURE |LazardQuotient| ($ $ $ #1#)) (SIGNATURE |LazardQuotient2| ($ $ $ $ #1#)) (SIGNATURE |nextsubResultant2| ($ $ $ $ $))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (PROGN (SIGNATURE |gcd| (|t#1| |t#1| $)) (SIGNATURE |primitivePart!| #2#) (SIGNATURE |mainContent| #2#) (SIGNATURE |mainPrimitivePart| #2#) (SIGNATURE |mainSquareFreePart| #2#)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| |#3|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #3=(|Polynomial| |#1|)) |has| |#3| (|ConvertibleTo| (|Symbol|))) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| |#3| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| #4=(|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| #2#)) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| |#3| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|ConvertibleTo| #3#) |has| |#3| (|ConvertibleTo| (|Symbol|))) ((|ConvertibleTo| (|String|)) AND (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#3| (|ConvertibleTo| (|Symbol|)))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|GcdDomain|)) ((|InnerEvalable| |#3| |#1|) . T) ((|InnerEvalable| |#3| $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| #2#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ |#3|) . T) ((|PartialDifferentialRing| |#3|) . T) ((|PartialDifferentialSpace| |#3|) . T) ((|PatternMatchable| #4#) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| |#3| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| #2#) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#3| (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| |#2| |#3|) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|RetractableTo| #1#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . T) ((|RetractableTo| |#3|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . 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T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|iterators| (((|List| #2=(|SpadAst|)) $) 18 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 27 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|body| ((#2# $) 20 T ELT)) (|before?| #1#) (= #1#)) (((|RepeatAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |iterators| ((|List| #1=(|SpadAst|)) $)) (SIGNATURE |body| (#1# $))))) (T |RepeatAst|)) ((|iterators| #1=(*1 *2 *1) (AND (|isDomain| *2 (|List| #2=(|SpadAst|))) #3=(|isDomain| *1 (|RepeatAst|)))) (|body| #1# (AND (|isDomain| *2 #2#) #3#))) ((|zero?| (#1=((|Boolean|) |#3| $) 15 T ELT)) (|rootOf| (((|Union| $ #2="failed") |#3| (|PositiveInteger|)) 29 T ELT)) (|recip| (((|Union| |#3| #2#) |#3| $) 45 T ELT)) (|positive?| (#1# 19 T ELT)) (|negative?| (#1# 17 T ELT))) (((|RealRootCharacterizationCategory&| |#1| |#2| |#3|) 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T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . 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T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|upDateBranches| ((#1=(|List| #2=(|Record| (|:| |val| #3=(|List| |#4|)) (|:| |tower| |#5|))) #3# #4=(|List| |#5|) #1# #5=(|Record| (|:| |done| #4#) (|:| |todo| #1#)) #6=(|NonNegativeInteger|)) 114 T ELT)) (|transcendentalDecompose| (#7=(#5# |#4| |#5|) 64 T ELT) (#8=(#5# |#4| |#5| #6#) 63 T ELT)) (|printInfo| (((|Void|) #1# #6#) 99 T ELT)) (|numberOfVariables| (#9=(#6# #3# #4#) 30 T ELT)) (|internalDecompose| (#7# 66 T ELT) (#8# 65 T ELT) ((#5# |#4| |#5| #6# #10=(|Boolean|)) 67 T ELT)) (|decompose| ((#4# #3# #4# #10# #10# #10# #10# #10#) 86 T ELT) ((#4# #3# #4# #10# #10#) 87 T ELT)) (|convert| (((|String|) #2#) 92 T ELT)) (|algebraicDecompose| ((#5# |#4| |#5| #10#) 62 T ELT)) (|KrullNumber| (#9# 21 T ELT))) (((|RegularSetDecompositionPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |KrullNumber| #1=(#2=(|NonNegativeInteger|) #3=(|List| |#4|) #4=(|List| |#5|))) (SIGNATURE |numberOfVariables| #1#) (SIGNATURE |algebraicDecompose| (#5=(|Record| (|:| |done| #4#) (|:| 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#6# #4#) 94 T ELT) (#8=(#4# |#5| #4#) 97 T ELT)) (|extend| (($ $ |#5|) NIL T ELT) #3# (#8# 75 T ELT) (#5# 77 T ELT) (#7# 79 T ELT)) (|augment| #3# (#8# 66 T ELT) (#5# 71 T ELT) (#7# 73 T ELT)) (|algebraicCoefficients?| (#1# 32 T ELT))) (((|RegularTriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |extend| #1=(#2=(|List| |#1|) #3=(|List| |#5|) #2#)) (SIGNATURE |extend| #4=(#2# #3# |#1|)) (SIGNATURE |extend| #5=(#2# |#5| #2#)) (SIGNATURE |extend| #6=(#2# |#5| |#1|)) (SIGNATURE |augment| #1#) (SIGNATURE |augment| #4#) (SIGNATURE |augment| #5#) (SIGNATURE |augment| #6#) (SIGNATURE |intersect| #5#) (SIGNATURE |intersect| #1#) (SIGNATURE |intersect| #4#) (SIGNATURE |intersect| #6#) (SIGNATURE |purelyAlgebraicLeadingMonomial?| #7=(#8=(|Boolean|) |#5| |#1|)) (SIGNATURE |purelyAlgebraic?| (#8# |#1|)) (SIGNATURE |algebraicCoefficients?| #7#) (SIGNATURE |purelyTranscendental?| #7#) (SIGNATURE |purelyAlgebraic?| #7#) (SIGNATURE |extend| (|#1| |#1| |#5|))) (|RegularTriangularSetCategory| |#2| |#3| |#4| |#5|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |RegularTriangularSetCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) (((|List| $) (|List| |#4|) (|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #2=($)) 39 T ELT)) (|trivialIdeal?| (#3=(#4=(|Boolean|) $) 32 T ELT)) (|triangular?| (#3# 23 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#6=(|Boolean|) |#4| . #7=($)) 107 T ELT) (#8=(#6# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #9=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #10=(|Boolean|) |#4|) . #11=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #12=(#13="failed")) $ |#3|) 85 T ELT)) (|sample| (#14=($) 59 T CONST)) (|roughUnitIdeal?| (#3# 28 (|has| |#1| . #5#) ELT)) (|roughSubIdeal?| (#15=(#4# $ $) 30 (|has| |#1| . #5#) ELT)) (|roughEqualIdeals?| (#15# 29 (|has| |#1| . #5#) ELT)) (|roughBase?| (#3# 31 (|has| |#1| . #5#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #6# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #16=($)) 24 (|has| |#1| . #5#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #16#) 25 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#17=(|Union| $ #13#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #9#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #18=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #18#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #10# |#4|) . #11#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #5#) ELT)) (|reduced?| ((#6# |#4| $ (|Mapping| #6# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #9#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #19=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #6# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| (((|Boolean|) |#4| $) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) 142 T ELT)) (|purelyAlgebraic?| (((|Boolean|) |#4| $) 146 T ELT) (((|Boolean|) $) 143 T ELT)) (|normalized?| ((#6# |#4| . #7#) 110 T ELT) (#8# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#20=(|Boolean|) |#4| $) 53 (|has| |#4| . #19#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #2#) 38 T ELT)) (|mainVariable?| ((#4# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #12#) . #21=($)) 89 T ELT)) (|invertibleSet| (((|List| $) |#4| $) 138 T ELT)) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) 140 T ELT) (((|Boolean|) |#4| $) 139 T ELT)) (|intersect| (((|List| $) |#4| $) 134 T ELT) (((|List| $) (|List| |#4|) $) 133 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 132 T ELT) (((|List| $) |#4| (|List| $)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#6# |#4| . #7#) 105 T ELT) (#8# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #9#) 96 T ELT)) (|infRittWu?| ((#6# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #5#) ELT)) (|headReduced?| ((#6# |#4| . #7#) 106 T ELT) (#8# 102 T ELT)) (|headReduce| ((|#4| |#4| . #9#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #12#) . #21#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #20# |#4|) $) 51 T ELT)) (|extendIfCan| ((#17# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) (((|List| $) |#4| $) 124 T ELT) (((|List| $) |#4| (|List| $)) 123 T ELT) (((|List| $) (|List| |#4|) $) 122 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 121 T ELT)) (|every?| ((#20# (|Mapping| #20# |#4|) . #22=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #23#)) ELT)) (|eq?| ((#24=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#24# $) 58 T ELT)) (|empty| (#14# 57 T ELT)) (|degree| (#25=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#26=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #19#) ELT) ((#26# (|Mapping| #20# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#27=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #27#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #28=($)) 13 T ELT) (((|List| |#4|) . #28#) 43 T ELT)) (|coHeight| (#25# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #29=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #30=(#13#)) (|List| |#4|) (|Mapping| #6# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #29# (|:| |top| (|List| |#4|))) . #30#) (|List| |#4|) (|Mapping| #6# |#4|) (|Mapping| #6# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#6# $ (|Mapping| #6# |#4| (|List| |#4|))) 104 T ELT)) (|augment| (((|List| $) |#4| $) 130 T ELT) (((|List| $) |#4| (|List| $)) 129 T ELT) (((|List| $) (|List| |#4|) $) 128 T ELT) (((|List| $) (|List| |#4|) (|List| $)) 127 T ELT)) (|any?| ((#20# (|Mapping| #20# |#4|) . #22#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| (((|Boolean|) |#4| $) 144 T ELT)) (|algebraic?| ((#6# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#26# $) 44 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #3=(|:| |open| #4=(|List| |#4|)))) #4#) 91 T ELT)) (|zeroSetSplit| ((#5=(|List| $) #4#) 92 T ELT) ((#5# #4# #2#) 120 T ELT)) (|variables| (#6=((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (#7=(#2# $) 32 T ELT)) (|triangular?| (#7# 23 #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| (#9=(#2# |#4| $) 107 T ELT) (#7# 103 T ELT)) (|stronglyReduce| (#10=(|#4| |#4| $) 98 T ELT)) (|squareFreePart| ((#11=(|List| (|Record| (|:| |val| |#4|) #12=(|:| |tower| $))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (#13=($ #14=(|Mapping| #2# |#4|) $) 67 #15=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#16=(|Union| |#4| #17="failed") $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#7# 28 #8# ELT)) (|roughSubIdeal?| (#1# 30 #8# ELT)) (|roughEqualIdeals?| (#1# 29 #8# ELT)) (|roughBase?| (#7# 31 #8# ELT)) (|rewriteSetWithReduction| ((#4# #4# $ #19=(|Mapping| |#4| |#4| |#4|) #20=(|Mapping| #2# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (#21=(#4# #4# $) 24 #8# ELT)) (|rewriteIdealWithHeadRemainder| (#21# 25 #8# ELT)) (|retractIfCan| ((#22=(|Union| $ #17#) #4#) 42 T ELT)) (|retract| (#23=($ #4#) 41 T ELT)) (|rest| ((#22# $) 88 T ELT)) (|removeZero| (#10# 95 T ELT)) (|removeDuplicates| (#24=($ $) 69 #25=(AND #26=(|has| |#4| (|BasicType|)) #15#) ELT)) (|remove| (#27=($ |#4| $) 68 #25# ELT) (#13# 66 #15# ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #28=(|:| |den| |#1|)) |#4| $) 26 #8# ELT)) (|reduced?| ((#2# |#4| $ #20#) 108 T ELT)) (|reduceByQuasiMonic| (#10# 93 T ELT)) (|reduce| ((|#4| #19# $ |#4| |#4|) 54 #26# ELT) ((|#4| #19# $ |#4|) 50 T ELT) ((|#4| #19# $) 49 T ELT) ((|#4| |#4| $ #19# #20#) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #4#) #3#) $) 111 T ELT)) (|purelyTranscendental?| (#9# 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#9# 142 T ELT)) (|purelyAlgebraic?| (#9# 146 T ELT) (#7# 143 T ELT)) (|normalized?| (#9# 110 T ELT) (#7# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (#29=(#4# $) 48 T ELT)) (|member?| (#9# 53 #26# ELT)) (|map!| (#30=($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (#30# 60 T ELT)) (|mainVariables| (#6# 38 T ELT)) (|mainVariable?| (#31=(#2# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #5#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| ((#11# |#4| |#4| $) 136 T ELT)) (|last| (#32=(#16# $) 89 T ELT)) (|invertibleSet| (#33=(#5# |#4| $) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #2# #5#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #2#) #12#)) |#4| $) 140 T ELT) (#9# 139 T ELT)) (|intersect| (#33# 134 T ELT) (#34=(#5# #4# $) 133 T ELT) (#35=(#5# #4# #5#) 132 T ELT) (#36=(#5# |#4| #5#) 131 T ELT)) (|internalAugment| (#27# 126 T ELT) (($ #4# $) 125 T ELT)) (|initials| (#29# 113 T ELT)) (|initiallyReduced?| (#9# 105 T ELT) (#7# 101 T ELT)) (|initiallyReduce| (#10# 96 T ELT)) (|infRittWu?| (#1# 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #28#) |#4| $) 27 #8# ELT)) (|headReduced?| (#9# 106 T ELT) (#7# 102 T ELT)) (|headReduce| (#10# 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (#32# 90 T ELT)) (|find| ((#16# #14# $) 51 T ELT)) (|extendIfCan| ((#22# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) (#33# 124 T ELT) (#36# 123 T ELT) (#34# 122 T ELT) (#35# 121 T ELT)) (|every?| (#37=(#2# #14# $) 46 T ELT)) (|eval| (($ $ #4# #4#) 64 #38=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) 63 #38# ELT) (($ $ #39=(|Equation| |#4|)) 62 #38# ELT) (($ $ (|List| #39#)) 61 #38# ELT)) (|eq?| (#1# 55 T ELT)) (|empty?| (#7# 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#40=(#41=(|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#41# |#4| $) 52 #26# ELT) ((#41# #14# $) 47 T ELT)) (|copy| (#24# 56 T ELT)) (|convert| ((#42=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #42#)) ELT)) (|construct| (#23# 65 T ELT)) (|collectUpper| (#43=($ $ |#3|) 34 T ELT)) (|collectUnder| (#43# 36 T ELT)) (|collectQuasiMonic| (#24# 94 T ELT)) (|collect| (#43# 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#29# 43 T ELT)) (|coHeight| (#40# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| ((#44=(|Union| (|Record| (|:| |bas| $) (|:| |top| #4#)) #17#) #4# #20#) 115 T ELT) ((#44# #4# #14# #20#) 114 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#4| #4#)) 104 T ELT)) (|augment| (#33# 130 T ELT) (#36# 129 T ELT) (#34# 128 T ELT) (#35# 127 T ELT)) (|any?| (#37# 45 T ELT)) (|algebraicVariables| (#6# 87 T ELT)) (|algebraicCoefficients?| (#9# 144 T ELT)) (|algebraic?| (#31# 86 T ELT)) (= (#1# 8 T ELT)) (|#| (#40# 44 T ELT))) (((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |RegularTriangularSetCategory|)) -((|purelyAlgebraic?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|purelyTranscendental?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|algebraicCoefficients?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|purelyAlgebraic?| (*1 *2 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|purelyAlgebraicLeadingMonomial?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|invertibleElseSplit?| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Union| (|Boolean|) (|List| *1))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|invertible?| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| *1)))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|invertible?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|invertibleSet| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|lastSubResultantElseSplit| (*1 *2 *3 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Union| *3 (|List| *1))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|lastSubResultant| (*1 *2 *3 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *1)))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|squareFreePart| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *1)))) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|intersect| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|intersect| (*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|intersect| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)))) (|intersect| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|augment| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|augment| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|augment| (*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|augment| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)))) (|internalAugment| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|internalAugment| (*1 *1 *2 *1) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|GcdDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)))) (|extend| (*1 *2 *3 *1) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)))) (|extend| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)))) (|extend| (*1 *2 *3 *1) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|extend| (*1 *2 *3 *2) (AND (|isDomain| *2 (|List| *1)) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)))) (|zeroSetSplit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 (|Boolean|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|GcdDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|RegularTriangularSetCategory| *5 *6 *7 *8))))) -(|Join| (|TriangularSetCategory| |t#1| |t#2| |t#3| |t#4|) (CATEGORY |domain| (SIGNATURE |purelyAlgebraic?| ((|Boolean|) |t#4| $)) (SIGNATURE |purelyTranscendental?| ((|Boolean|) |t#4| $)) (SIGNATURE |algebraicCoefficients?| ((|Boolean|) |t#4| $)) (SIGNATURE |purelyAlgebraic?| ((|Boolean|) $)) (SIGNATURE |purelyAlgebraicLeadingMonomial?| ((|Boolean|) |t#4| $)) (SIGNATURE |invertibleElseSplit?| ((|Union| (|Boolean|) (|List| $)) |t#4| $)) (SIGNATURE |invertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |t#4| $)) (SIGNATURE |invertible?| ((|Boolean|) |t#4| $)) (SIGNATURE |invertibleSet| ((|List| $) |t#4| $)) (SIGNATURE |lastSubResultantElseSplit| ((|Union| |t#4| (|List| $)) |t#4| |t#4| $)) (SIGNATURE |lastSubResultant| ((|List| (|Record| (|:| |val| |t#4|) (|:| |tower| $))) |t#4| |t#4| $)) (SIGNATURE |squareFreePart| ((|List| (|Record| (|:| |val| |t#4|) (|:| |tower| $))) |t#4| $)) (SIGNATURE |intersect| ((|List| $) |t#4| $)) (SIGNATURE |intersect| ((|List| $) (|List| |t#4|) $)) (SIGNATURE |intersect| ((|List| $) (|List| |t#4|) (|List| $))) (SIGNATURE |intersect| ((|List| $) |t#4| (|List| $))) (SIGNATURE |augment| ((|List| $) |t#4| $)) (SIGNATURE |augment| ((|List| $) |t#4| (|List| $))) (SIGNATURE |augment| ((|List| $) (|List| |t#4|) $)) (SIGNATURE |augment| ((|List| $) (|List| |t#4|) (|List| $))) (SIGNATURE |internalAugment| ($ |t#4| $)) (SIGNATURE |internalAugment| ($ (|List| |t#4|) $)) (SIGNATURE |extend| ((|List| $) |t#4| $)) (SIGNATURE |extend| ((|List| $) |t#4| (|List| $))) (SIGNATURE |extend| ((|List| $) (|List| |t#4|) $)) (SIGNATURE |extend| ((|List| $) (|List| |t#4|) (|List| $))) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |t#4|) (|Boolean|))))) -(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) +((|purelyAlgebraic?| #1=(*1 *2 *3 *1) #2=(AND #3=(|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *3)) #4=(|ofCategory| *4 #5=(|GcdDomain|)) #6=(|ofCategory| *5 #7=(|OrderedAbelianMonoidSup|)) #8=(|ofCategory| *6 #9=(|OrderedSet|)) #10=(|ofCategory| *3 #11=(|RecursivePolynomialCategory| *4 *5 *6)) #12=(|isDomain| *2 #13=(|Boolean|)))) (|purelyTranscendental?| #1# #2#) (|algebraicCoefficients?| #1# #2#) (|purelyAlgebraic?| (*1 *2 *1) (AND #14=(|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *6)) #15=(|ofCategory| *3 #5#) #16=(|ofCategory| *4 #7#) #17=(|ofCategory| *5 #9#) #18=(|ofCategory| *6 #19=(|RecursivePolynomialCategory| *3 *4 *5)) #12#)) (|purelyAlgebraicLeadingMonomial?| #1# #2#) (|invertibleElseSplit?| #1# (AND #4# #6# #8# #10# (|isDomain| *2 (|Union| #13# #20=(|List| *1))) #3#)) (|invertible?| #1# (AND #4# #6# #8# #10# (|isDomain| *2 (|List| (|Record| (|:| |val| #13#) #21=(|:| |tower| *1)))) #3#)) (|invertible?| #1# #2#) (|invertibleSet| #1# #22=(AND #4# #6# #8# #10# #23=(|isDomain| *2 #20#) #3#)) (|lastSubResultantElseSplit| #24=(*1 *2 *3 *3 *1) (AND #4# #6# #8# #10# (|isDomain| *2 (|Union| *3 #20#)) #3#)) (|lastSubResultant| #24# #25=(AND #4# #6# #8# #10# (|isDomain| *2 (|List| (|Record| (|:| |val| *3) #21#))) #3#)) (|squareFreePart| #1# #25#) (|intersect| #1# #22#) (|intersect| #1# #26=(AND #27=(|isDomain| *3 (|List| *7)) #28=(|ofCategory| *7 #11#) #4# #6# #8# #23# #29=(|ofCategory| *1 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|intersect| #30=(*1 *2 *3 *2) #31=(AND #23# #27# #29# #4# #6# #8# #28#)) (|intersect| #30# #32=(AND #23# #3# #4# #6# #8# #10#)) (|augment| #1# #22#) (|augment| #30# #32#) (|augment| #1# #26#) (|augment| #30# #31#) (|internalAugment| #33=(*1 *1 *2 *1) (AND (|ofCategory| *1 (|RegularTriangularSetCategory| *3 *4 *5 *2)) #15# #16# #17# (|ofCategory| *2 #19#))) (|internalAugment| #33# (AND (|isDomain| *2 (|List| *6)) #14# #15# #16# #17# #18#)) (|extend| #1# #22#) (|extend| #30# #32#) (|extend| #1# #26#) (|extend| #30# #31#) (|zeroSetSplit| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *8)) (|isDomain| *4 #13#) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 #5#) (|ofCategory| *6 #7#) (|ofCategory| *7 #9#) #23# (|ofCategory| *1 (|RegularTriangularSetCategory| *5 *6 *7 *8))))) +(|Join| (|TriangularSetCategory| |t#1| |t#2| |t#3| |t#4|) (CATEGORY |domain| (SIGNATURE |purelyAlgebraic?| #1=(#2=(|Boolean|) |t#4| $)) (SIGNATURE |purelyTranscendental?| #1#) (SIGNATURE |algebraicCoefficients?| #1#) (SIGNATURE |purelyAlgebraic?| (#2# $)) (SIGNATURE |purelyAlgebraicLeadingMonomial?| #1#) (SIGNATURE |invertibleElseSplit?| ((|Union| #2# #3=(|List| $)) |t#4| $)) (SIGNATURE |invertible?| ((|List| (|Record| (|:| |val| #2#) #4=(|:| |tower| $))) |t#4| $)) (SIGNATURE |invertible?| #1#) (SIGNATURE |invertibleSet| #5=(#3# |t#4| $)) (SIGNATURE |lastSubResultantElseSplit| ((|Union| |t#4| #3#) |t#4| |t#4| $)) (SIGNATURE |lastSubResultant| (#6=(|List| (|Record| (|:| |val| |t#4|) #4#)) |t#4| |t#4| $)) (SIGNATURE |squareFreePart| (#6# |t#4| $)) (SIGNATURE |intersect| #5#) (SIGNATURE |intersect| #7=(#3# #8=(|List| |t#4|) $)) (SIGNATURE |intersect| #9=(#3# #8# #3#)) (SIGNATURE |intersect| #10=(#3# |t#4| #3#)) (SIGNATURE |augment| #5#) (SIGNATURE |augment| #10#) (SIGNATURE |augment| #7#) (SIGNATURE |augment| #9#) (SIGNATURE |internalAugment| ($ |t#4| $)) (SIGNATURE |internalAugment| ($ #8# $)) (SIGNATURE |extend| #5#) (SIGNATURE |extend| #10#) (SIGNATURE |extend| #7#) (SIGNATURE |extend| #9#) (SIGNATURE |zeroSetSplit| (#3# #8# #2#)))) +(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) ((|toseSquareFreePart| ((#1=(|List| (|Record| (|:| |val| |#4|) #2=(|:| |tower| |#5|))) |#4| |#5|) 86 T ELT)) (|toseLastSubResultant| (#3=(#1# |#4| |#4| |#5|) 125 T ELT)) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) 74 T ELT)) (|toseInvertible?| (((|List| (|Record| (|:| |val| #4=(|Boolean|)) #2#)) |#4| |#5|) 47 T ELT) ((#4# |#4| |#5|) 55 T ELT)) (|stopTableInvSet!| (#5=(#6=(|Void|)) 36 T ELT)) (|stopTableGcd!| (#5# 25 T ELT)) (|startTableInvSet!| (#7=(#6# #8=(|String|) #8# #8#) 32 T ELT)) (|startTableGcd!| (#7# 21 T ELT)) (|prepareSubResAlgo| ((#9=(|List| (|Record| (|:| |val| (|List| |#4|)) #2#)) |#4| |#4| |#5|) 106 T ELT)) (|internalLastSubResultant| ((#1# #9# |#3| #4#) 117 T ELT) ((#1# |#4| |#4| |#5| #4# #4#) 52 T ELT)) (|integralLastSubResultant| (#3# 112 T ELT))) (((|RegularTriangularSetGcdPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTableGcd!| #1=(#2=(|Void|) #3=(|String|) #3# #3#)) (SIGNATURE |stopTableGcd!| #4=(#2#)) (SIGNATURE |startTableInvSet!| #1#) (SIGNATURE |stopTableInvSet!| #4#) (SIGNATURE |prepareSubResAlgo| (#5=(|List| (|Record| (|:| |val| (|List| |#4|)) #6=(|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |internalLastSubResultant| (#7=(|List| (|Record| (|:| |val| |#4|) #6#)) |#4| |#4| |#5| #8=(|Boolean|) #8#)) (SIGNATURE |internalLastSubResultant| (#7# #5# |#3| #8#)) (SIGNATURE |integralLastSubResultant| #9=(#7# |#4| |#4| |#5|)) (SIGNATURE |toseLastSubResultant| #9#) (SIGNATURE |toseInvertible?| (#8# |#4| |#5|)) (SIGNATURE |toseInvertible?| ((|List| (|Record| (|:| |val| #8#) #6#)) |#4| |#5|)) (SIGNATURE |toseInvertibleSet| ((|List| |#5|) |#4| |#5|)) (SIGNATURE |toseSquareFreePart| (#7# |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |RegularTriangularSetGcdPackage|)) ((|toseSquareFreePart| #1=(*1 *2 *3 *4) #2=(AND #3=(|ofCategory| *5 #4=(|GcdDomain|)) #5=(|ofCategory| *6 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *7 #8=(|OrderedSet|)) #9=(|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) #10=(|isDomain| *2 (|List| (|Record| (|:| |val| *3) #11=(|:| |tower| *4)))) #12=(|isDomain| *1 (|RegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) #13=(|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|toseInvertibleSet| #1# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| *4)) #12# #13#)) (|toseInvertible?| #1# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| (|:| |val| #14=(|Boolean|)) #11#))) #12# #13#)) (|toseInvertible?| #1# (AND #3# #5# #7# #9# (|isDomain| *2 #14#) #12# #13#)) (|toseLastSubResultant| #15=(*1 *2 *3 *3 *4) #2#) (|integralLastSubResultant| #15# #2#) (|internalLastSubResultant| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) #16=(|:| |tower| *9)))) #17=(|isDomain| *5 #14#) (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4)) (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8)) #18=(|ofCategory| *6 #4#) #19=(|ofCategory| *7 #6#) (|ofCategory| *4 #8#) (|isDomain| *2 (|List| (|Record| (|:| |val| *8) #16#))) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *4 *8 *9)))) (|internalLastSubResultant| (*1 *2 *3 *3 *4 *5 *5) (AND #17# #18# #19# (|ofCategory| *8 #8#) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #10# (|isDomain| *1 (|RegularTriangularSetGcdPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|prepareSubResAlgo| #15# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *3)) #11#))) #12# #13#)) (|stopTableInvSet!| #20=(*1 *2) #21=(AND (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #22=(|isDomain| *2 (|Void|)) (|isDomain| *1 (|RegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableInvSet!| #23=(*1 *2 *3 *3 *3) #24=(AND (|isDomain| *3 (|String|)) (|ofCategory| *4 #4#) (|ofCategory| *5 #6#) (|ofCategory| *6 #8#) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) #22# (|isDomain| *1 (|RegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTableGcd!| #20# #21#) (|startTableGcd!| #23# #24#)) @@ -3323,7 +3323,7 @@ NIL (((|SpadSyntaxCategory|) (|Category|)) (T |SpadSyntaxCategory|)) NIL (|Join| (|AbstractSyntaxCategory|)) -(((|AbstractSyntaxCategory|) . T) ((|BasicType|) . T) ((|CoercibleFrom| #1=(|Syntax|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbstractSyntaxCategory|) . T) ((|BasicType|) . T) ((|CoercibleFrom| #1=(|Syntax|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CoercibleTo| #1#) . T) ((|HomotopicTo| #1#) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) 41 T ELT) ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) 33 T ELT)) (|clearCache| (((|Void|)) 21 T ELT)) (|cache| (((|List| |#1|)) 13 T ELT))) (((|SortedCache| |#1|) (CATEGORY |package| (SIGNATURE |clearCache| ((|Void|))) (SIGNATURE |cache| ((|List| |#1|))) (SIGNATURE |enterInCache| (|#1| |#1| (|Mapping| (|Boolean|) |#1|))) (SIGNATURE |enterInCache| (|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)))) (|CachableSet|)) (T |SortedCache|)) ((|enterInCache| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| (|Integer|) *2 *2)) #2=(|ofCategory| *2 #3=(|CachableSet|)) #4=(|isDomain| *1 (|SortedCache| *2)))) (|enterInCache| #1# (AND (|isDomain| *3 (|Mapping| (|Boolean|) *2)) #2# #4#)) (|cache| #5=(*1 *2) (AND (|isDomain| *2 (|List| *3)) #6=(|isDomain| *1 (|SortedCache| *3)) #7=(|ofCategory| *3 #3#))) (|clearCache| #5# (AND (|isDomain| *2 (|Void|)) #6# #7#))) @@ -3354,14 +3354,14 @@ NIL ((|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) 19 T ELT))) (((|SegmentBindingFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)))) #1=(|Type|) #1#) (T |SegmentBindingFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|SegmentBinding| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|SegmentBinding| *6)) (|isDomain| *1 (|SegmentBindingFunctions2| *5 *6))))) -((|segment| (($ |#1| |#1|) 8 T ELT)) (|low| ((|#1| $) 11 T ELT)) (|lo| ((|#1| $) 13 T ELT)) (|incr| (((|Integer|) $) 9 T ELT)) (|high| ((|#1| $) 10 T ELT)) (|hi| ((|#1| $) 12 T ELT)) (|convert| (($ |#1|) 6 T ELT)) (SEGMENT (($ |#1| |#1|) 15 T ELT)) (BY (($ $ (|Integer|)) 14 T ELT))) +((|segment| (#1=($ |#1| |#1|) 8 T ELT)) (|low| (#2=(|#1| $) 11 T ELT)) (|lo| (#2# 13 T ELT)) (|incr| ((#3=(|Integer|) $) 9 T ELT)) (|high| (#2# 10 T ELT)) (|hi| (#2# 12 T ELT)) (|convert| (($ |#1|) 6 T ELT)) (SEGMENT (#1# 15 T ELT)) (BY (($ $ #3#) 14 T ELT))) (((|SegmentCategory| |#1|) (|Category|) (|Type|)) (T |SegmentCategory|)) -((SEGMENT (*1 *1 *2 *2) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (BY (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|SegmentCategory| *3)) (|ofCategory| *3 (|Type|)))) (|lo| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|hi| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|low| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|high| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|)))) (|incr| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentCategory| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *2 (|Integer|)))) (|segment| (*1 *1 *2 *2) (AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 (|Type|))))) -(|Join| (|ConvertibleFrom| |t#1|) (CATEGORY |domain| (SIGNATURE SEGMENT ($ |t#1| |t#1|)) (SIGNATURE BY ($ $ (|Integer|))) (SIGNATURE |lo| (|t#1| $)) (SIGNATURE |hi| (|t#1| $)) (SIGNATURE |low| (|t#1| $)) (SIGNATURE |high| (|t#1| $)) (SIGNATURE |incr| ((|Integer|) $)) (SIGNATURE |segment| ($ |t#1| |t#1|)))) +((SEGMENT #1=(*1 *1 *2 *2) #2=(AND (|ofCategory| *1 (|SegmentCategory| *2)) (|ofCategory| *2 #3=(|Type|)))) (BY (*1 *1 *1 *2) (AND #4=(|isDomain| *2 (|Integer|)) #5=(|ofCategory| *1 (|SegmentCategory| *3)) #6=(|ofCategory| *3 #3#))) (|lo| #7=(*1 *2 *1) #2#) (|hi| #7# #2#) (|low| #7# #2#) (|high| #7# #2#) (|incr| #7# (AND #5# #6# #4#)) (|segment| #1# #2#)) +(|Join| (|ConvertibleFrom| |t#1|) (CATEGORY |domain| (SIGNATURE SEGMENT #1=($ |t#1| |t#1|)) (SIGNATURE BY ($ $ #2=(|Integer|))) (SIGNATURE |lo| #3=(|t#1| $)) (SIGNATURE |hi| #3#) (SIGNATURE |low| #3#) (SIGNATURE |high| #3#) (SIGNATURE |incr| (#2# $)) (SIGNATURE |segment| #1#))) (((|ConvertibleFrom| |#1|) . T)) -((|segment| (($ |#1| |#1|) 8 T ELT)) (|map| ((|#2| (|Mapping| |#1| |#1|) $) 17 T ELT)) (|low| ((|#1| . #1=($)) 11 T ELT)) (|lo| ((|#1| . #1#) 13 T ELT)) (|incr| ((#2=(|Integer|) $) 9 T ELT)) (|high| ((|#1| . #1#) 10 T ELT)) (|hi| ((|#1| . #1#) 12 T ELT)) (|expand| ((|#2| (|List| $)) 19 T ELT) ((|#2| $) 18 T ELT)) (|convert| (($ |#1|) 6 T ELT)) (SEGMENT (($ |#1| |#1|) 15 T ELT)) (BY (($ $ #2#) 14 T ELT))) +((|segment| (#1=($ |#1| |#1|) 8 T ELT)) (|map| ((|#2| (|Mapping| |#1| |#1|) $) 17 T ELT)) (|low| (#2=(|#1| $) 11 T ELT)) (|lo| (#2# 13 T ELT)) (|incr| ((#3=(|Integer|) $) 9 T ELT)) (|high| (#2# 10 T ELT)) (|hi| (#2# 12 T ELT)) (|expand| ((|#2| (|List| $)) 19 T ELT) ((|#2| $) 18 T ELT)) (|convert| (($ |#1|) 6 T ELT)) (SEGMENT (#1# 15 T ELT)) (BY (($ $ #3#) 14 T ELT))) (((|SegmentExpansionCategory| |#1| |#2|) (|Category|) (|OrderedRing|) (|StreamAggregate| |t#1|)) (T |SegmentExpansionCategory|)) -((|expand| (*1 *2 *3) (AND (|isDomain| *3 (|List| *1)) (|ofCategory| *1 (|SegmentExpansionCategory| *4 *2)) (|ofCategory| *4 (|OrderedRing|)) (|ofCategory| *2 (|StreamAggregate| *4)))) (|expand| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentExpansionCategory| *3 *2)) (|ofCategory| *3 (|OrderedRing|)) (|ofCategory| *2 (|StreamAggregate| *3)))) (|map| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *1 (|SegmentExpansionCategory| *4 *2)) (|ofCategory| *4 (|OrderedRing|)) (|ofCategory| *2 (|StreamAggregate| *4))))) +((|expand| (*1 *2 *3) (AND (|isDomain| *3 (|List| *1)) #1=(|ofCategory| *1 (|SegmentExpansionCategory| *4 *2)) #2=(|ofCategory| *4 #3=(|OrderedRing|)) #4=(|ofCategory| *2 (|StreamAggregate| *4)))) (|expand| (*1 *2 *1) (AND (|ofCategory| *1 (|SegmentExpansionCategory| *3 *2)) (|ofCategory| *3 #3#) (|ofCategory| *2 (|StreamAggregate| *3)))) (|map| (*1 *2 *3 *1) (AND (|isDomain| *3 (|Mapping| *4 *4)) #1# #2# #4#))) (|Join| (|SegmentCategory| |t#1|) (CATEGORY |domain| (SIGNATURE |expand| (|t#2| (|List| $))) (SIGNATURE |expand| (|t#2| $)) (SIGNATURE |map| (|t#2| (|Mapping| |t#1| |t#1|) $)))) (((|ConvertibleFrom| |#1|) . T) ((|SegmentCategory| |#1|) . T)) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|last| ((#2=(|SpadAst|) $) 14 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|body| (((|List| #2#) $) 12 T ELT)) (|before?| #1#) (= #1#)) @@ -3373,11 +3373,11 @@ NIL ((|union| #1=(#2=($ $ $) NIL T ELT) (#3=($ $ |#2|) 13 T ELT) (($ |#2| $) 14 T ELT)) (|symmetricDifference| (#2# 10 T ELT)) (|difference| #1# (#3# 15 T ELT))) (((|SetAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |union| (|#1| |#2| |#1|)) (SIGNATURE |union| #1=(|#1| |#1| |#2|)) (SIGNATURE |union| #2=(|#1| |#1| |#1|)) (SIGNATURE |symmetricDifference| #2#) (SIGNATURE |difference| #1#) (SIGNATURE |difference| #2#)) (|SetAggregate| |#2|) (|SetCategory|)) (T |SetAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|union| (($ $ $) 23 T ELT) (($ $ |#1|) 22 T ELT) (($ |#1| $) 21 T ELT)) (|symmetricDifference| (($ $ $) 25 T ELT)) (|subset?| (((|Boolean|) $ $) 24 T ELT)) (|set| (($) 30 T ELT) (($ (|List| |#1|)) 29 T ELT)) (|select| (($ (|Mapping| #2=(|Boolean|) |#1|) . #3=($)) 46 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#4=($) 38 T CONST)) (|removeDuplicates| (($ $) 48 (AND (|has| |#1| . #5=((|BasicType|))) (|has| $ (|FiniteAggregate| |#1|))) ELT)) (|remove| (($ |#1| $) 47 (AND (|has| |#1| . #5#) (|has| $ (|FiniteAggregate| |#1|))) ELT) (($ (|Mapping| #2# |#1|) . #3#) 45 (|has| $ (|FiniteAggregate| |#1|)) ELT)) (|part?| (((|Boolean|) $ $) 33 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|intersect| (($ $ $) 28 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|eval| (($ $ (|List| |#1|) (|List| |#1|)) 43 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6=((|SetCategory|)))) ELT) (($ $ |#1| |#1|) 42 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|Equation| |#1|)) 41 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT) (($ $ (|List| (|Equation| |#1|))) 40 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #6#)) ELT)) (|eq?| ((#7=(|Boolean|) $ $) 34 T ELT)) (|empty?| ((#7# $) 37 T ELT)) (|empty| (#4# 36 T ELT)) (|difference| (($ $ $) 27 T ELT) (($ $ |#1|) 26 T ELT)) (|copy| (($ $) 35 T ELT)) (|convert| ((#8=(|InputForm|) $) 49 (|has| |#1| (|ConvertibleTo| #8#)) ELT)) (|construct| (($ (|List| |#1|)) 44 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|brace| (($) 32 T ELT) (($ (|List| |#1|)) 31 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|union| (#3=($ $ $) 23 T ELT) (#4=($ $ |#1|) 22 T ELT) (#5=($ |#1| $) 21 T ELT)) (|symmetricDifference| (#3# 25 T ELT)) (|subset?| (#1# 24 T ELT)) (|set| (#6=($) 30 T ELT) (#7=($ #8=(|List| |#1|)) 29 T ELT)) (|select| (#9=($ (|Mapping| #2# |#1|) $) 46 #10=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#6# 38 T CONST)) (|removeDuplicates| (#11=($ $) 48 #12=(AND (|has| |#1| (|BasicType|)) #10#) ELT)) (|remove| (#5# 47 #12# ELT) 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T)) +((|eq| (*1 *2 *1 *1) #1=(AND #2=(|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *7)) #3=(|ofCategory| *3 #4=(|SetCategory|)) #5=(|ofCategory| *4 #4#) #6=(|ofCategory| *5 #4#) #7=(|ofCategory| *6 #4#) #8=(|ofCategory| *7 #4#) (|isDomain| *2 (|Boolean|)))) (|null?| #9=(*1 *2 *1) #1#) (|atom?| #9# #1#) (|pair?| #9# #1#) (|list?| #9# #1#) (|string?| #9# #1#) (|symbol?| #9# #1#) (|integer?| #9# #1#) (|float?| #9# #1#) (|destruct| #9# (AND #3# #5# #6# #7# #8# (|isDomain| *2 (|List| *1)) #2#)) (|string| #9# (AND #10=(|ofCategory| *1 (|SExpressionCategory| *2 *3 *4 *5 *6)) #3# #5# #6# #7# #11=(|ofCategory| *2 #4#))) (|symbol| #9# (AND (|ofCategory| *1 (|SExpressionCategory| *3 *2 *4 *5 *6)) #3# #5# #6# #7# #11#)) (|integer| #9# (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *2 *5 *6)) #3# #5# #6# #7# #11#)) (|float| #9# (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *2 *6)) #3# #5# #6# #7# #11#)) (|expr| #9# (AND (|ofCategory| *1 (|SExpressionCategory| *3 *4 *5 *6 *2)) #3# #5# #6# #7# #11#)) (|car| #12=(*1 *1 *1) #13=(AND #10# #11# #3# #5# #6# #7#)) (|cdr| #12# #13#) (|#| #9# (AND #2# #3# #5# #6# #7# #8# (|isDomain| *2 (|Integer|))))) +(|Join| (|SetCategory|) (|ConvertibleFrom| |t#1|) (|ConvertibleFrom| |t#2|) (|ConvertibleFrom| |t#3|) #1=(|ConvertibleFrom| |t#4|) #1# (|ConvertibleFrom| |t#5|) (|ConvertibleFrom| #2=(|List| $)) (|Eltable| #3=(|Integer|) $) (|Eltable| (|List| #3#) $) (CATEGORY |domain| (SIGNATURE |eq| (#4=(|Boolean|) $ $)) (SIGNATURE |null?| #5=(#4# $)) (SIGNATURE |atom?| #5#) (SIGNATURE |pair?| #5#) (SIGNATURE |list?| #5#) (SIGNATURE |string?| #5#) (SIGNATURE |symbol?| #5#) (SIGNATURE |integer?| #5#) (SIGNATURE |float?| #5#) (SIGNATURE |destruct| (#2# $)) (SIGNATURE |string| (|t#1| $)) (SIGNATURE |symbol| (|t#2| $)) (SIGNATURE |integer| (|t#3| $)) (SIGNATURE |float| (|t#4| $)) (SIGNATURE |expr| (|t#5| $)) (SIGNATURE |car| #6=($ $)) (SIGNATURE |cdr| #6#) (SIGNATURE |#| (#3# $)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|ConvertibleFrom| (|List| $)) . T) ((|ConvertibleFrom| |#1|) . T) ((|ConvertibleFrom| |#2|) . T) ((|ConvertibleFrom| |#3|) . T) ((|ConvertibleFrom| |#4|) . T) ((|ConvertibleFrom| |#5|) . T) ((|Eltable| #1=(|Integer|) $) . T) ((|Eltable| (|List| #1#) $) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|symbol?| (#4=(#3# $) 45 T ELT)) (|symbol| ((|#2| $) 48 T ELT)) (|string?| (#4# 20 T ELT)) (|string| ((|#1| $) 21 T ELT)) (|pair?| (#4# 42 T ELT)) (|null?| (#4# 14 T ELT)) (|list?| (#4# 44 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integer?| (#4# 46 T ELT)) (|integer| ((|#3| $) 50 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|float?| (#4# 47 T ELT)) (|float| ((|#4| $) 49 T ELT)) (|expr| ((|#5| $) 51 T ELT)) (|eq| (#2# 41 T ELT)) (|elt| (($ $ #5=(|Integer|)) 62 T ELT) (($ $ (|List| #5#)) 64 T ELT)) (|destruct| ((#6=(|List| $) $) 27 T ELT)) (|convert| (($ |#1|) 53 T ELT) (($ |#2|) 54 T ELT) (($ |#3|) 55 T ELT) (($ |#4|) 56 T ELT) (($ |#5|) 57 T ELT) (($ #6#) 52 T ELT)) (|coerce| (((|OutputForm|) $) 28 T ELT)) (|cdr| (#7=($ $) 26 T ELT)) (|car| (#7# 58 T ELT)) (|before?| #1#) (|atom?| (#4# 23 T ELT)) (= (#2# 40 T ELT)) (|#| ((#5# $) 60 T ELT))) (((|SExpressionOf| |#1| |#2| |#3| |#4| |#5|) (|SExpressionCategory| |#1| |#2| |#3| 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(#10=(#9# #11=(|String|) #11# #11#) 32 T ELT)) (|startTableGcd!| (#10# 21 T ELT))) (((|SquareFreeRegularTriangularSetGcdPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |startTableGcd!| #1=(#2=(|Void|) #3=(|String|) #3# #3#)) (SIGNATURE |stopTableGcd!| #4=(#2#)) (SIGNATURE |startTableInvSet!| #1#) (SIGNATURE |stopTableInvSet!| #4#) (SIGNATURE |stosePrepareSubResAlgo| (#5=(|List| (|Record| (|:| |val| (|List| |#4|)) #6=(|:| |tower| |#5|))) |#4| |#4| |#5|)) (SIGNATURE |stoseInternalLastSubResultant| (#7=(|List| (|Record| (|:| |val| |#4|) #6#)) |#4| |#4| |#5| #8=(|Boolean|) #8#)) (SIGNATURE |stoseInternalLastSubResultant| (#7# #5# |#3| #8#)) (SIGNATURE |stoseIntegralLastSubResultant| #9=(#7# |#4| |#4| |#5|)) (SIGNATURE |stoseLastSubResultant| #9#) (SIGNATURE |stoseInvertible?| (#8# |#4| |#5|)) (SIGNATURE |stoseInvertible?sqfreg| #10=((|List| (|Record| (|:| |val| #8#) #6#)) |#4| |#5|)) (SIGNATURE |stoseInvertibleSetsqfreg| #11=((|List| |#5|) |#4| |#5|)) (SIGNATURE 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#9# (|isDomain| *2 (|List| (|Record| (|:| |val| #16=(|Boolean|)) #11#))) #12# #13#)) (|stoseInvertibleSetreg| #1# #14#) (|stoseInvertible?reg| #1# #15#) (|stoseInvertibleSetsqfreg| #1# #14#) (|stoseInvertible?sqfreg| #1# #15#) (|stoseInvertible?| #1# (AND #3# #5# #7# #9# (|isDomain| *2 #16#) #12# #13#)) (|stoseLastSubResultant| #17=(*1 *2 *3 *3 *4) #2#) (|stoseIntegralLastSubResultant| #17# #2#) (|stoseInternalLastSubResultant| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| (|List| *8)) #18=(|:| |tower| *9)))) #19=(|isDomain| *5 #16#) (|ofCategory| *8 (|RecursivePolynomialCategory| *6 *7 *4)) (|ofCategory| *9 (|RegularTriangularSetCategory| *6 *7 *4 *8)) #20=(|ofCategory| *6 #4#) #21=(|ofCategory| *7 #6#) (|ofCategory| *4 #8#) (|isDomain| *2 (|List| (|Record| (|:| |val| *8) #18#))) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *4 *8 *9)))) (|stoseInternalLastSubResultant| (*1 *2 *3 *3 *4 *5 *5) (AND #19# #20# #21# (|ofCategory| *8 #8#) (|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #10# (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *6 *7 *8 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|stosePrepareSubResAlgo| #17# (AND #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *3)) #11#))) #12# #13#)) (|stopTableInvSet!| #22=(*1 *2) #23=(AND (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #24=(|isDomain| *2 (|Void|)) (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *3 *4 *5 *6 *7)) (|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)))) (|startTableInvSet!| #25=(*1 *2 *3 *3 *3) #26=(AND (|isDomain| *3 (|String|)) (|ofCategory| *4 #4#) (|ofCategory| *5 #6#) (|ofCategory| *6 #8#) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) #24# (|isDomain| *1 (|SquareFreeRegularTriangularSetGcdPackage| *4 *5 *6 *7 *8)) (|ofCategory| *8 (|RegularTriangularSetCategory| *4 *5 *6 *7)))) (|stopTableGcd!| #22# #23#) (|startTableGcd!| #25# #26#)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) ((#2=(|List| $) (|List| |#4|) #3=(|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #4=($)) 39 T ELT)) (|trivialIdeal?| (#5=(#6=(|Boolean|) $) 32 T ELT)) (|triangular?| (#5# 23 (|has| |#1| . #7=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#8=(|Boolean|) |#4| . #9=($)) 107 T ELT) (#10=(#8# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #11=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) . #12=(#13=(|:| |tower| $)))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #14=(|Boolean|) |#4|) . #15=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #16=(#17="failed")) $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#5# 28 (|has| |#1| . #7#) ELT)) (|roughSubIdeal?| (#19=(#6# $ $) 30 (|has| |#1| . #7#) ELT)) (|roughEqualIdeals?| (#19# 29 (|has| |#1| . #7#) ELT)) (|roughBase?| (#5# 31 (|has| |#1| . #7#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #20=($)) 24 (|has| |#1| . #7#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #20#) 25 (|has| |#1| . #7#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#21=(|Union| $ #17#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #11#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #22=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #22#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #14# |#4|) . #15#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #7#) ELT)) (|reduced?| ((#8# |#4| $ (|Mapping| #8# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #11#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #23=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| ((#3# |#4| . #24=($)) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| ((#3# |#4| . #24#) 142 T ELT)) (|purelyAlgebraic?| ((#3# |#4| . #24#) 146 T ELT) ((#3# $) 143 T ELT)) (|normalized?| ((#8# |#4| . #9#) 110 T ELT) (#10# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) 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$) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#8# |#4| . #9#) 105 T ELT) (#10# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #11#) 96 T ELT)) (|infRittWu?| ((#8# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #7#) ELT)) (|headReduced?| ((#8# |#4| . #9#) 106 T ELT) (#10# 102 T ELT)) (|headReduce| ((|#4| |#4| . #11#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #16#) . #26#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #25# |#4|) $) 51 T ELT)) (|extendIfCan| ((#21# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) ((#2# |#4| . #27#) 124 T ELT) ((#2# |#4| . #30#) 123 T ELT) ((#2# (|List| |#4|) . #28#) 122 T ELT) ((#2# (|List| |#4|) . #29#) 121 T ELT)) (|every?| ((#25# (|Mapping| #25# |#4|) . #31=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT)) (|eq?| ((#33=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#33# $) 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#34=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#35=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #23#) ELT) ((#35# (|Mapping| #25# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#36=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #36#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #37=($)) 13 T ELT) (((|List| |#4|) . #37#) 43 T ELT)) (|coHeight| (#34# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #38=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #39=(#17#)) (|List| |#4|) (|Mapping| #8# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #38# (|:| |top| (|List| |#4|))) . #39#) (|List| |#4|) (|Mapping| #8# |#4|) (|Mapping| #8# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#8# $ (|Mapping| #8# |#4| (|List| |#4|))) 104 T ELT)) (|augment| ((#2# |#4| . #27#) 130 T ELT) ((#2# |#4| . #30#) 129 T ELT) ((#2# (|List| |#4|) . #28#) 128 T ELT) ((#2# (|List| |#4|) . #29#) 127 T ELT)) (|any?| ((#25# (|Mapping| #25# |#4|) . #31#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| ((#3# |#4| . #24#) 144 T ELT)) (|algebraic?| ((#8# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#35# $) 44 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #3=(|:| |open| #4=(|List| |#4|)))) #4#) 91 T ELT)) (|zeroSetSplit| ((#5=(|List| $) #4#) 92 T ELT) ((#5# #4# #2#) 120 T ELT)) (|variables| (#6=((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (#7=(#2# $) 32 T ELT)) (|triangular?| (#7# 23 #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| (#9=(#2# |#4| $) 107 T ELT) (#7# 103 T ELT)) (|stronglyReduce| (#10=(|#4| |#4| $) 98 T ELT)) (|squareFreePart| ((#11=(|List| (|Record| (|:| |val| |#4|) #12=(|:| |tower| $))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (#13=($ #14=(|Mapping| #2# |#4|) $) 67 #15=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#16=(|Union| |#4| #17="failed") $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#7# 28 #8# ELT)) (|roughSubIdeal?| (#1# 30 #8# ELT)) (|roughEqualIdeals?| (#1# 29 #8# ELT)) (|roughBase?| (#7# 31 #8# ELT)) (|rewriteSetWithReduction| ((#4# #4# $ #19=(|Mapping| |#4| |#4| |#4|) #20=(|Mapping| #2# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (#21=(#4# #4# $) 24 #8# ELT)) (|rewriteIdealWithHeadRemainder| (#21# 25 #8# ELT)) (|retractIfCan| ((#22=(|Union| $ #17#) #4#) 42 T ELT)) (|retract| (#23=($ #4#) 41 T ELT)) (|rest| ((#22# $) 88 T ELT)) (|removeZero| (#10# 95 T ELT)) (|removeDuplicates| (#24=($ $) 69 #25=(AND #26=(|has| |#4| (|BasicType|)) #15#) ELT)) (|remove| (#27=($ |#4| $) 68 #25# ELT) (#13# 66 #15# ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #28=(|:| |den| |#1|)) |#4| $) 26 #8# ELT)) (|reduced?| ((#2# |#4| $ #20#) 108 T ELT)) (|reduceByQuasiMonic| (#10# 93 T ELT)) (|reduce| ((|#4| #19# $ |#4| |#4|) 54 #26# ELT) ((|#4| #19# $ |#4|) 50 T ELT) ((|#4| #19# $) 49 T ELT) ((|#4| |#4| $ #19# #20#) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #4#) #3#) $) 111 T ELT)) (|purelyTranscendental?| (#9# 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#9# 142 T ELT)) (|purelyAlgebraic?| (#9# 146 T ELT) (#7# 143 T ELT)) (|normalized?| (#9# 110 T ELT) (#7# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (#29=(#4# $) 48 T ELT)) (|member?| (#9# 53 #26# ELT)) (|map!| (#30=($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (#30# 60 T ELT)) (|mainVariables| (#6# 38 T ELT)) (|mainVariable?| (#31=(#2# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #5#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| ((#11# |#4| |#4| $) 136 T ELT)) (|last| (#32=(#16# $) 89 T ELT)) (|invertibleSet| (#33=(#5# |#4| $) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #2# #5#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #2#) #12#)) |#4| $) 140 T ELT) (#9# 139 T ELT)) (|intersect| (#33# 134 T ELT) (#34=(#5# #4# $) 133 T ELT) (#35=(#5# #4# #5#) 132 T ELT) (#36=(#5# |#4| #5#) 131 T ELT)) (|internalAugment| (#27# 126 T ELT) (($ #4# $) 125 T ELT)) (|initials| (#29# 113 T ELT)) (|initiallyReduced?| (#9# 105 T ELT) (#7# 101 T ELT)) (|initiallyReduce| (#10# 96 T ELT)) (|infRittWu?| (#1# 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #28#) |#4| $) 27 #8# ELT)) (|headReduced?| (#9# 106 T ELT) (#7# 102 T ELT)) (|headReduce| (#10# 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (#32# 90 T ELT)) (|find| ((#16# #14# $) 51 T ELT)) (|extendIfCan| ((#22# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) (#33# 124 T ELT) (#36# 123 T ELT) (#34# 122 T ELT) (#35# 121 T ELT)) (|every?| (#37=(#2# #14# $) 46 T ELT)) (|eval| (($ $ #4# #4#) 64 #38=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) 63 #38# ELT) (($ $ #39=(|Equation| |#4|)) 62 #38# ELT) (($ $ (|List| #39#)) 61 #38# ELT)) (|eq?| (#1# 55 T ELT)) (|empty?| (#7# 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#40=(#41=(|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#41# |#4| $) 52 #26# ELT) ((#41# #14# $) 47 T ELT)) (|copy| (#24# 56 T ELT)) (|convert| ((#42=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #42#)) ELT)) (|construct| (#23# 65 T ELT)) (|collectUpper| (#43=($ $ |#3|) 34 T ELT)) (|collectUnder| (#43# 36 T ELT)) (|collectQuasiMonic| (#24# 94 T ELT)) (|collect| (#43# 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#29# 43 T ELT)) (|coHeight| (#40# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| ((#44=(|Union| (|Record| (|:| |bas| $) (|:| |top| #4#)) #17#) #4# #20#) 115 T ELT) ((#44# #4# #14# #20#) 114 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#4| #4#)) 104 T ELT)) (|augment| (#33# 130 T ELT) (#36# 129 T ELT) (#34# 128 T ELT) (#35# 127 T ELT)) (|any?| (#37# 45 T ELT)) (|algebraicVariables| (#6# 87 T ELT)) (|algebraicCoefficients?| (#9# 144 T ELT)) (|algebraic?| (#31# 86 T ELT)) (= (#1# 8 T ELT)) (|#| (#40# 44 T ELT))) (((|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |SquareFreeRegularTriangularSetCategory|)) NIL (|Join| (|RegularTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|)) -(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) +(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) ((|unrankImproperPartitions1| (#1=(#2=(|List| #3=(|Integer|)) #3# #3# #3#) 40 T ELT)) (|unrankImproperPartitions0| (#1# 30 T ELT)) (|subSet| (#1# 35 T ELT)) (|numberOfImproperPartitions| ((#3# #3# #3#) 22 T ELT)) (|nextPartition| ((#4=(|Vector| #3#) #2# #4# #3#) 78 T ELT) ((#4# #4# #4# #3#) 73 T ELT)) (|nextLatticePermutation| ((#2# #5=(|List| (|PositiveInteger|)) #2# (|Boolean|)) 56 T ELT)) (|nextColeman| ((#6=(|Matrix| #3#) #2# #2# #6#) 77 T ELT)) (|makeYoungTableau| ((#6# #5# #2#) 61 T ELT)) (|listYoungTableaus| (((|List| #6#) #5#) 66 T ELT)) (|inverseColeman| ((#2# #2# #2# #6#) 81 T ELT)) (|coleman| ((#6# #2# #2# #2#) 91 T ELT))) (((|SymmetricGroupCombinatoricFunctions|) (CATEGORY |package| (SIGNATURE |coleman| (#1=(|Matrix| #2=(|Integer|)) #3=(|List| #2#) #3# #3#)) (SIGNATURE |inverseColeman| (#3# #3# #3# #1#)) (SIGNATURE |listYoungTableaus| ((|List| #1#) #4=(|List| (|PositiveInteger|)))) (SIGNATURE |makeYoungTableau| (#1# #4# #3#)) (SIGNATURE |nextColeman| (#1# #3# #3# #1#)) (SIGNATURE |nextLatticePermutation| (#3# #4# #3# (|Boolean|))) (SIGNATURE |nextPartition| (#5=(|Vector| #2#) #5# #5# #2#)) (SIGNATURE |nextPartition| (#5# #3# #5# #2#)) (SIGNATURE |numberOfImproperPartitions| (#2# #2# #2#)) (SIGNATURE |subSet| #6=(#3# #2# #2# #2#)) (SIGNATURE |unrankImproperPartitions0| #6#) (SIGNATURE |unrankImproperPartitions1| #6#))) (T |SymmetricGroupCombinatoricFunctions|)) ((|unrankImproperPartitions1| #1=(*1 *2 *3 *3 *3) #2=(AND #3=(|isDomain| *2 #4=(|List| #5=(|Integer|))) #6=(|isDomain| *1 (|SymmetricGroupCombinatoricFunctions|)) #7=(|isDomain| *3 #5#))) (|unrankImproperPartitions0| #1# #2#) (|subSet| #1# #2#) (|numberOfImproperPartitions| (*1 *2 *2 *2) (AND (|isDomain| *2 #5#) #6#)) (|nextPartition| #8=(*1 *2 *3 *2 *4) (AND #9=(|isDomain| *2 (|Vector| #5#)) #10=(|isDomain| *3 #4#) (|isDomain| *4 #5#) #6#)) (|nextPartition| #11=(*1 *2 *2 *2 *3) (AND #9# #7# #6#)) (|nextLatticePermutation| #8# (AND #3# #12=(|isDomain| *3 (|List| (|PositiveInteger|))) (|isDomain| *4 (|Boolean|)) #6#)) (|nextColeman| (*1 *2 *3 *3 *2) (AND #13=(|isDomain| *2 #14=(|Matrix| #5#)) #10# #6#)) (|makeYoungTableau| (*1 *2 *3 *4) (AND #12# (|isDomain| *4 #4#) #13# #6#)) (|listYoungTableaus| (*1 *2 *3) (AND #12# (|isDomain| *2 (|List| #14#)) #6#)) (|inverseColeman| #11# (AND #3# (|isDomain| *3 #14#) #6#)) (|coleman| #1# (AND #10# #13# #6#))) @@ -3421,15 +3421,15 @@ NIL (((|SemiGroupOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |SemiGroupOperatorCategory|)) NIL (|Join| (|BinaryOperatorCategory| |t#1|) (CATEGORY |domain| (ATTRIBUTE (|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|) (|:| |y| |t#1|) (|:| |z| |t#1|)) (= (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|)))))))) -(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) +(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T)) ((** (($ $ (|PositiveInteger|)) 10 T ELT))) (((|SemiGroup&| |#1|) (CATEGORY |package| (SIGNATURE ** (|#1| |#1| (|PositiveInteger|)))) (|SemiGroup|)) (T |SemiGroup&|)) NIL ((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (** (($ $ (|PositiveInteger|)) 17 T ELT)) (* (($ $ $) 18 T ELT))) (((|SemiGroup|) (|Category|)) (T |SemiGroup|)) -((* (*1 *1 *1 *1) (|ofCategory| *1 (|SemiGroup|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) +((* (*1 *1 *1 *1) #1=(|ofCategory| *1 (|SemiGroup|))) (** (*1 *1 *1 *2) (AND #1# (|isDomain| *2 (|PositiveInteger|))))) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|PositiveInteger|))))) -(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#3| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#3| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#3| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#3|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#3| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL (|has| |#3| (|CancellationAbelianMonoid|)) ELT)) (|size| (#14=(#15=(|NonNegativeInteger|)) NIL #16=(|has| |#3| (|Finite|)) ELT)) (|setelt| #17=(#18=(|#3| $ #10# |#3|) NIL #11# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #20=(#21="failed")) . #22=($)) NIL #23=(AND (|has| |#3| (|RetractableTo| #10#)) #24=(|has| |#3| (|SetCategory|))) ELT) (((|Union| #25=(|Fraction| #10#) . #20#) . #22#) NIL #26=(AND (|has| |#3| (|RetractableTo| #25#)) #24#) ELT) ((#27=(|Union| |#3| . #20#) . #22#) NIL #24# ELT)) (|retract| (#28=(#10# . #29=($)) NIL #23# ELT) ((#25# . #29#) NIL #26# ELT) (#30=(|#3| . #29#) NIL #24# ELT)) (|reducedSystem| ((#31=(|Matrix| #10#) . #32=(#33=(|Matrix| $))) NIL #34=(AND (|has| |#3| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#35=(|Record| (|:| |mat| #31#) (|:| |vec| (|Vector| #10#))) . #36=(#33# #37=(|Vector| $))) NIL #34# ELT) ((#38=(|Record| (|:| |mat| #39=(|Matrix| |#3|)) (|:| |vec| #40=(|Vector| |#3|))) . #36#) NIL #9# ELT) ((#39# . #32#) NIL #9# ELT)) (|reduce| ((|#3| #41=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #4# ELT) ((|#3| #41# $ |#3|) NIL T ELT) ((|#3| #41# $) NIL T ELT)) (|recip| (((|Union| $ #21#) $) NIL #9# ELT)) (|random| (#19# NIL #16# ELT)) (|qsetelt!| #17#) (|qelt| (#42=(|#3| $ #10#) 12 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| #43=(#28# NIL #44=(|has| #10# #45=(|OrderedSet|)) ELT)) (|min| #46=(#12# NIL #47=(|has| |#3| #45#) ELT)) (|members| #48=((#49=(|List| |#3|) $) NIL T ELT)) (|member?| (#50=(#3# |#3| $) NIL #4# ELT)) (|maxIndex| #43#) (|max| #46#) (|map| (($ #51=(|Mapping| |#3| |#3|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #16# ELT)) (|leftReducedSystem| ((#31# . #52=(#37#)) NIL #34# ELT) ((#35# . #53=(#37# $)) NIL #34# ELT) ((#38# . #53#) NIL #9# ELT) ((#39# . #52#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #24# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #16# ELT)) (|hash| (((|SingleInteger|) $) NIL #24# ELT)) (|first| (#30# NIL #44# ELT)) (|find| ((#27# #54=(|Mapping| #3# |#3|) $) NIL T ELT)) (|fill!| (#55=($ $ |#3|) NIL #11# ELT)) (|every?| #56=((#3# #54# $) NIL T ELT)) (|eval| (($ $ (|List| #57=(|Equation| |#3|))) NIL #58=(AND (|has| |#3| (|Evalable| |#3|)) #24#) ELT) (($ $ #57#) NIL #58# ELT) (($ $ |#3| |#3|) NIL #58# ELT) (($ $ #49# #49#) NIL #58# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#50# NIL (AND (|has| $ (|FiniteAggregate| |#3|)) #4#) ELT)) (|entries| #48#) (|empty?| (#5# NIL T ELT)) (|empty| (#19# NIL T ELT)) (|elt| (#18# NIL T ELT) (#42# NIL T ELT)) (|dot| ((|#3| $ $) NIL #9# ELT)) (|directProduct| (($ #40#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #59=(|has| |#3| (|Field|)) ELT)) (|differentiate| #60=(#61=($ $ #15#) NIL #62=(AND (|has| |#3| (|DifferentialSpace|)) #9#) ELT) #63=(#64=($ $) NIL #62# ELT) #65=(($ $ #66=(|List| #67=(|Symbol|)) (|List| #15#)) NIL #68=(AND (|has| |#3| (|PartialDifferentialSpace| #67#)) #9#) ELT) #69=(($ $ #67# #15#) NIL #68# ELT) #70=(($ $ #66#) NIL #68# ELT) #71=(($ $ #67#) NIL #68# ELT) #72=(($ $ #51#) NIL #9# ELT) #73=(($ $ #51# #15#) NIL #9# ELT)) (|count| ((#15# |#3| $) NIL #4# ELT) ((#15# #54# $) NIL T ELT)) (|copy| (#64# NIL T ELT)) (|coerce| ((#40# . #74=($)) NIL T ELT) (($ #10#) NIL (OR #23# #9#) ELT) (($ #25#) NIL #26# ELT) (($ |#3|) NIL #24# ELT) ((#75=(|OutputForm|) . #74#) NIL (|has| |#3| (|CoercibleTo| #75#)) ELT)) (|characteristic| (#14# NIL #9# CONST)) (|before?| #1#) (|any?| #56#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#19# NIL #6# 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#14=(|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *2 *5)) #8# #10# #15=(|ofCategory| *2 #11#))) (|trace| #13# #16=(AND #4# #5# #7# #2#)) (|diagonalProduct| #13# #16#) (* (*1 *2 *1 *2) (AND (|ofCategory| *1 (|SquareMatrixCategory| *3 *4 *5 *2)) #8# #10# #15#)) (* (*1 *2 *2 *1) (AND #14# #8# #15# #10#)) (|determinant| #13# #17=(AND #4# #5# #7# (|has| *2 (ATTRIBUTE (|commutative| "*"))) #2#)) (|minordet| #13# #17#) (|inverse| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|SquareMatrixCategory| *2 *3 *4 *5)) (|ofCategory| *3 #3#) (|ofCategory| *4 #18=(|DirectProductCategory| *2 *3)) (|ofCategory| *5 #18#) (|ofCategory| *3 #19=(|Field|)))) (** (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) #9# #8# #10# #12# (|ofCategory| *4 #19#)))) +(|Join| (|DifferentialExtension| |t#2|) (|BiModule| |t#2| |t#2|) (|RectangularMatrixCategory| |t#1| |t#1| |t#2| |t#3| |t#4|) (|FullyRetractableTo| |t#2|) (|FullyLinearlyExplicitRingOver| |t#2|) (CATEGORY |domain| (IF (|has| |t#2| (|CommutativeRing|)) (ATTRIBUTE (|Module| |t#2|)) |%noBranch|) (SIGNATURE |scalarMatrix| ($ |t#2|)) (SIGNATURE |diagonalMatrix| ($ (|List| |t#2|))) (SIGNATURE |diagonal| (|t#3| $)) (SIGNATURE |trace| #1=(|t#2| $)) (SIGNATURE |diagonalProduct| #1#) (SIGNATURE * (|t#4| $ |t#4|)) (SIGNATURE * (|t#3| |t#3| $)) (IF (|has| |t#2| (ATTRIBUTE (|commutative| "*"))) (PROGN (ATTRIBUTE (|Algebra| |t#2|)) (SIGNATURE |determinant| #1#) (SIGNATURE |minordet| #1#)) |%noBranch|) (IF (|has| |t#2| (|Field|)) (PROGN (SIGNATURE |inverse| ((|Union| $ "failed") $)) (SIGNATURE ** ($ $ (|Integer|)))) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Aggregate|) . T) ((|Algebra| |#2|) |has| |#2| (ATTRIBUTE (|commutative| #1="*"))) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #2=(|Fraction| #3=(|Integer|))) |has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #3#) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) |has| |#2| (|DifferentialSpace|)) ((|DifferentialExtension| |#2|) . T) ((|DifferentialRing|) |has| |#2| (|DifferentialRing|)) ((|DifferentialSpace|) |has| |#2| (|DifferentialSpace|)) ((|DifferentialSpaceExtension| |#2|) . T) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|FiniteAggregate| |#2|) . T) ((|FullyLinearlyExplicitRingOver| |#2|) . T) ((|FullyRetractableTo| |#2|) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| |#2|) . T) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|LeftLinearSet| #3#) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #3#) |has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#2|) OR (|has| |#2| (ATTRIBUTE (|commutative| #1#))) (|has| |#2| (|CommutativeRing|))) ((|LinearlyExplicitRingOver| #3#) |has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#2|) . T) ((|Module| |#2|) OR (|has| |#2| (ATTRIBUTE (|commutative| #1#))) (|has| |#2| (|CommutativeRing|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) OR (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialRing| #4#) |has| |#2| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) OR (|has| |#2| (|PartialDifferentialRing| (|Symbol|))) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) ((|RectangularMatrixCategory| |#1| |#1| |#2| |#3| |#4|) . T) ((|RetractableTo| #2#) |has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #3#) |has| |#2| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|smith| (#1=(|#4| |#4|) 81 T ELT)) (|hermite| (#1# 76 T ELT)) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) 91 T ELT)) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) 80 T ELT)) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) 78 T ELT))) (((|SmithNormalForm| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |hermite| #1=(|#4| |#4|)) (SIGNATURE |completeHermite| ((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|)) (SIGNATURE |smith| #1#) (SIGNATURE |completeSmith| ((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|)) (SIGNATURE |diophantineSystem| ((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|))) (|EuclideanDomain|) #2=(|FiniteLinearAggregate| |#1|) #2# (|MatrixCategory| |#1| |#2| |#3|)) (T |SmithNormalForm|)) ((|diophantineSystem| (*1 *2 *3 *4) (AND (|ofCategory| *5 #1=(|EuclideanDomain|)) (|ofCategory| *6 #2=(|FiniteLinearAggregate| *5)) (|ofCategory| *4 #2#) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|SmithNormalForm| *5 *6 *4 *3)) (|ofCategory| *3 (|MatrixCategory| *5 *6 *4)))) (|completeSmith| #3=(*1 *2 *3) (AND #4=(|ofCategory| *4 #1#) #5=(|ofCategory| *5 #6=(|FiniteLinearAggregate| *4)) #7=(|ofCategory| *6 #6#) (|isDomain| *2 (|Record| (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3))) #8=(|isDomain| *1 (|SmithNormalForm| *4 *5 *6 *3)) #9=(|ofCategory| *3 (|MatrixCategory| *4 *5 *6)))) (|smith| #10=(*1 *2 *2) #11=(AND (|ofCategory| *3 #1#) (|ofCategory| *4 #12=(|FiniteLinearAggregate| *3)) (|ofCategory| *5 #12#) (|isDomain| *1 (|SmithNormalForm| *3 *4 *5 *2)) (|ofCategory| *2 (|MatrixCategory| *3 *4 *5)))) (|completeHermite| #3# (AND #4# #5# #7# (|isDomain| *2 (|Record| (|:| |Hermite| *3) (|:| |eqMat| *3))) #8# #9#)) (|hermite| #10# #11#)) @@ -3482,11 +3482,11 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #7=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #8=(#9=($ $) NIL #7# ELT)) (|unit?| (#5# NIL #7# ELT)) (|tanh| (#9# 149 #10=(|has| |#1| (|Algebra| #11=(|Fraction| #12=(|Integer|)))) ELT)) (|tan| (#9# 125 #10# ELT)) (|subtractIfCan| ((#13=(|Maybe| $) $ $) NIL T ELT)) (|sqrt| (#9# NIL #10# ELT)) (|sinh| (#9# 145 #10# ELT)) (|sin| (#9# 121 #10# ELT)) (|sech| (#9# 153 #10# ELT)) (|sec| (#9# 129 #10# ELT)) (|sample| (#14=($) NIL T CONST)) (|reductum| #15=(#9# NIL T ELT)) (|recip| ((#16=(|Union| $ "failed") $) NIL T ELT)) (|polynomial| ((#17=(|Polynomial| |#1|) $ #18=(|NonNegativeInteger|)) NIL T ELT) ((#17# $ #18# #18#) NIL T ELT)) (|pole?| #4#) (|pi| (#14# NIL #10# ELT)) (|order| ((#18# $ |#2|) NIL T ELT) ((#18# $ |#2| #18#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (($ $ #12#) NIL #10# ELT)) (|monomial?| #4#) (|monomial| (($ $ #6# (|List| #19=(|IndexedExponents| |#2|))) NIL T ELT) (($ $ |#2| #19#) NIL T ELT) (($ |#1| #19#) NIL T ELT) (#20=($ $ |#2| #18#) 63 T ELT) #21=(($ $ #6# (|List| #18#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| (#9# 119 #10# ELT)) (|leadingMonomial| #15#) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#22=($ $ |#2|) NIL #10# ELT) (($ $ |#2| |#1|) 171 #10# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) 170 #10# ELT)) (|extend| (#23=($ $ #18#) 17 T ELT)) (|exquo| ((#16# $ $) NIL #7# ELT)) (|exp| (#9# 117 #10# ELT)) (|eval| (($ $ |#2| $) 104 T ELT) (($ $ #6# #24=(|List| $)) 99 T ELT) (($ $ (|List| #25=(|Equation| $))) NIL T ELT) (($ $ #25#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #24# #24#) NIL T ELT)) (|differentiate| #21# #26=(#20# NIL T ELT) #27=(($ $ #6#) NIL T ELT) (#22# 106 T ELT)) (|degree| ((#19# $) NIL T ELT)) (|csubst| (((|Mapping| #28=(|Stream| |#3|) |#3|) #6# (|List| #28#)) 87 T ELT)) (|csch| (#9# 155 #10# ELT)) (|csc| (#9# 131 #10# ELT)) (|coth| (#9# 151 #10# ELT)) (|cot| (#9# 127 #10# ELT)) (|cosh| (#9# 147 #10# ELT)) (|cos| (#9# 123 #10# ELT)) (|complete| (#9# 19 T ELT)) (|coerce| (((|OutputForm|) $) 194 T ELT) (($ #12#) NIL T ELT) (($ |#1|) 45 (|has| |#1| (|CommutativeRing|)) ELT) #8# (($ #11#) NIL #10# ELT) (($ |#2|) 70 T ELT) (($ |#3|) 68 T ELT)) (|coefficient| ((|#1| $ #19#) NIL T ELT) #26# #21# ((|#3| $ #18#) 43 T ELT)) (|charthRoot| ((#13# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#18#) NIL T CONST)) (|before?| #1#) (|atanh| (#9# 161 #10# ELT)) (|atan| (#9# 137 #10# ELT)) (|associates?| (#2# NIL #7# ELT)) (|asinh| (#9# 157 #10# ELT)) (|asin| (#9# 133 #10# ELT)) (|asech| (#9# 165 #10# ELT)) (|asec| (#9# 141 #10# ELT)) (|annihilate?| #1#) (|acsch| (#9# 167 #10# ELT)) (|acsc| (#9# 143 #10# ELT)) (|acoth| (#9# 163 #10# ELT)) (|acot| (#9# 139 #10# ELT)) (|acosh| (#9# 159 #10# ELT)) (|acos| (#9# 135 #10# ELT)) (|Zero| (#14# 52 T CONST)) (|One| (#14# 62 T CONST)) (D #21# #26# #27# (#22# NIL T ELT)) (= #1#) (/ (#29=($ $ |#1|) 196 (|has| |#1| (|Field|)) ELT)) (- #15# (#30=($ $ $) NIL T ELT)) (+ (#30# 66 T ELT)) (** (($ $ #31=(|PositiveInteger|)) NIL T ELT) (#23# 77 T ELT) (#30# NIL #10# ELT) (#32=($ $ #11#) 109 #10# ELT)) (* (($ #31# $) NIL T ELT) (($ #18# $) NIL T ELT) (($ #12# $) NIL T ELT) (#30# 65 T ELT) (#32# 114 #10# ELT) (($ #11# $) 112 #10# ELT) (($ |#1| $) 48 T ELT) (#29# 49 T ELT) (($ |#3| $) 47 T ELT))) (((|SparseMultivariateTaylorSeries| |#1| |#2| |#3|) (|Join| (|MultivariateTaylorSeriesCategory| |#1| |#2|) (CATEGORY |domain| (SIGNATURE |coefficient| (|#3| $ (|NonNegativeInteger|))) (SIGNATURE |coerce| ($ |#2|)) (SIGNATURE |coerce| ($ |#3|)) (SIGNATURE * ($ |#3| $)) (SIGNATURE |csubst| ((|Mapping| #1=(|Stream| |#3|) |#3|) (|List| |#2|) (|List| #1#))) (IF (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $ |#2| |#1|)) (SIGNATURE |fintegrate| ($ (|Mapping| $) |#2| |#1|))) |%noBranch|))) (|Ring|) (|OrderedSet|) (|PolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|)) (T |SparseMultivariateTaylorSeries|)) ((|coefficient| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *2 (|PolynomialCategory| *4 (|IndexedExponents| *5) *5)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *4 *5 *2)) #1=(|ofCategory| *4 #2=(|Ring|)) (|ofCategory| *5 #3=(|OrderedSet|)))) (|coerce| #4=(*1 *1 *2) (AND #5=(|ofCategory| *3 #2#) #6=(|ofCategory| *2 #3#) #7=(|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *2 *4)) #8=(|ofCategory| *4 (|PolynomialCategory| *3 (|IndexedExponents| *2) *2)))) (|coerce| #4# #9=(AND #5# (|ofCategory| *4 #3#) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *3 *4 *2)) (|ofCategory| *2 (|PolynomialCategory| *3 (|IndexedExponents| *4) *4)))) (* (*1 *1 *2 *1) #9#) (|csubst| (*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *6)) (|isDomain| *4 (|List| #10=(|Stream| *7))) (|ofCategory| *6 #3#) (|ofCategory| *7 (|PolynomialCategory| *5 (|IndexedExponents| *6) *6)) (|ofCategory| *5 #2#) (|isDomain| *2 (|Mapping| #10# *7)) (|isDomain| *1 (|SparseMultivariateTaylorSeries| *5 *6 *7)))) (|integrate| (*1 *1 *1 *2 *3) (AND (|ofCategory| *3 #11=(|Algebra| (|Fraction| (|Integer|)))) #5# #6# #7# #8#)) (|fintegrate| (*1 *1 *2 *3 *4) (AND (|isDomain| *2 (|Mapping| #12=(|SparseMultivariateTaylorSeries| *4 *3 *5))) (|ofCategory| *4 #11#) #1# (|ofCategory| *3 #3#) (|isDomain| *1 #12#) (|ofCategory| *5 (|PolynomialCategory| *4 (|IndexedExponents| *3) *3))))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT) ((#2=(|List| $) (|List| |#4|) #3=(|Boolean|)) 120 T ELT)) (|variables| (((|List| |#3|) . #4=($)) 39 T ELT)) (|trivialIdeal?| (#5=(#6=(|Boolean|) $) 32 T ELT)) (|triangular?| (#5# 23 (|has| |#1| . #7=((|IntegralDomain|))) ELT)) (|stronglyReduced?| ((#8=(|Boolean|) |#4| . #9=($)) 107 T ELT) (#10=(#8# $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| . #11=($)) 98 T ELT)) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) . #12=(#13=(|:| |tower| $)))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #14=(|Boolean|) |#4|) . #15=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| . #16=(#17="failed")) $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#5# 28 (|has| |#1| . #7#) ELT)) (|roughSubIdeal?| (#19=(#6# $ $) 30 (|has| |#1| . #7#) ELT)) (|roughEqualIdeals?| (#19# 29 (|has| |#1| . #7#) ELT)) (|roughBase?| (#5# 31 (|has| |#1| . #7#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #20=($)) 24 (|has| |#1| . #7#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #20#) 25 (|has| |#1| . #7#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| ((#21=(|Union| $ #17#) $) 88 T ELT)) (|removeZero| ((|#4| |#4| . #11#) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #22=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #22#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #14# |#4|) . #15#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #7#) ELT)) (|reduced?| ((#8# |#4| $ (|Mapping| #8# |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| . #11#) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #23=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| #8# |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|purelyTranscendental?| ((#3# |#4| . #24=($)) 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| ((#3# |#4| . #24#) 142 T ELT)) (|purelyAlgebraic?| ((#3# |#4| . #24#) 146 T ELT) ((#3# $) 143 T ELT)) (|normalized?| ((#8# |#4| . #9#) 110 T ELT) (#10# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#25=(|Boolean|) |#4| $) 53 (|has| |#4| . #23#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #4#) 38 T ELT)) (|mainVariable?| ((#6# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #2#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) . #12#)) |#4| |#4| $) 136 T ELT)) (|last| (((|Union| |#4| . #16#) . #26=($)) 89 T ELT)) (|invertibleSet| ((#2# |#4| . #27=($)) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #2#) |#4| $) 141 T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #13#)) |#4| $) 140 T ELT) ((#3# |#4| . #24#) 139 T ELT)) (|intersect| ((#2# |#4| . #27#) 134 T ELT) ((#2# (|List| |#4|) . #28=($)) 133 T ELT) ((#2# (|List| |#4|) . #29=(#2#)) 132 T ELT) ((#2# |#4| . #30=(#2#)) 131 T ELT)) (|internalAugment| (($ |#4| $) 126 T ELT) (($ (|List| |#4|) $) 125 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| ((#8# |#4| . #9#) 105 T ELT) (#10# 101 T ELT)) (|initiallyReduce| ((|#4| |#4| . #11#) 96 T ELT)) (|infRittWu?| ((#8# $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #7#) ELT)) (|headReduced?| ((#8# |#4| . #9#) 106 T ELT) (#10# 102 T ELT)) (|headReduce| ((|#4| |#4| . #11#) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| . #16#) . #26#) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #25# |#4|) $) 51 T ELT)) (|extendIfCan| ((#21# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT) ((#2# |#4| . #27#) 124 T ELT) ((#2# |#4| . #30#) 123 T ELT) ((#2# (|List| |#4|) . #28#) 122 T ELT) ((#2# (|List| |#4|) . #29#) 121 T ELT)) (|every?| ((#25# (|Mapping| #25# |#4|) . #31=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #32#)) ELT)) (|eq?| ((#33=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#33# $) 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#34=((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#35=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #23#) ELT) ((#35# (|Mapping| #25# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#36=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #36#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #37=($)) 13 T ELT) (((|List| |#4|) . #37#) 43 T ELT)) (|coHeight| (#34# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| #38=(|:| |bas| $) (|:| |top| (|List| |#4|))) . #39=(#17#)) (|List| |#4|) (|Mapping| #8# |#4| |#4|)) 115 T ELT) (((|Union| (|Record| #38# (|:| |top| (|List| |#4|))) . #39#) (|List| |#4|) (|Mapping| #8# |#4|) (|Mapping| #8# |#4| |#4|)) 114 T ELT)) (|autoReduced?| ((#8# $ (|Mapping| #8# |#4| (|List| |#4|))) 104 T ELT)) (|augment| ((#2# |#4| . #27#) 130 T ELT) ((#2# |#4| . #30#) 129 T ELT) ((#2# (|List| |#4|) . #28#) 128 T ELT) ((#2# (|List| |#4|) . #29#) 127 T ELT)) (|any?| ((#25# (|Mapping| #25# |#4|) . #31#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraicCoefficients?| ((#3# |#4| . #24#) 144 T ELT)) (|algebraic?| ((#8# |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#35# $) 44 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #3=(|:| |open| #4=(|List| |#4|)))) #4#) 91 T ELT)) (|zeroSetSplit| ((#5=(|List| $) #4#) 92 T ELT) ((#5# #4# #2#) 120 T ELT)) (|variables| (#6=((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (#7=(#2# $) 32 T ELT)) (|triangular?| (#7# 23 #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| (#9=(#2# |#4| $) 107 T ELT) (#7# 103 T ELT)) (|stronglyReduce| (#10=(|#4| |#4| $) 98 T ELT)) (|squareFreePart| ((#11=(|List| (|Record| (|:| |val| |#4|) #12=(|:| |tower| $))) |#4| $) 135 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (#13=($ #14=(|Mapping| #2# |#4|) $) 67 #15=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#16=(|Union| |#4| #17="failed") $ |#3|) 85 T ELT)) (|sample| (#18=($) 59 T CONST)) (|roughUnitIdeal?| (#7# 28 #8# ELT)) (|roughSubIdeal?| (#1# 30 #8# ELT)) (|roughEqualIdeals?| (#1# 29 #8# ELT)) (|roughBase?| (#7# 31 #8# ELT)) (|rewriteSetWithReduction| ((#4# #4# $ #19=(|Mapping| |#4| |#4| |#4|) #20=(|Mapping| #2# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (#21=(#4# #4# $) 24 #8# ELT)) (|rewriteIdealWithHeadRemainder| (#21# 25 #8# ELT)) (|retractIfCan| ((#22=(|Union| $ #17#) #4#) 42 T ELT)) (|retract| (#23=($ #4#) 41 T ELT)) (|rest| ((#22# $) 88 T ELT)) (|removeZero| (#10# 95 T ELT)) (|removeDuplicates| (#24=($ $) 69 #25=(AND #26=(|has| |#4| (|BasicType|)) #15#) ELT)) (|remove| (#27=($ |#4| $) 68 #25# ELT) (#13# 66 #15# ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #28=(|:| |den| |#1|)) |#4| $) 26 #8# ELT)) (|reduced?| ((#2# |#4| $ #20#) 108 T ELT)) (|reduceByQuasiMonic| (#10# 93 T ELT)) (|reduce| ((|#4| #19# $ |#4| |#4|) 54 #26# ELT) ((|#4| #19# $ |#4|) 50 T ELT) ((|#4| #19# $) 49 T ELT) ((|#4| |#4| $ #19# #20#) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #4#) #3#) $) 111 T ELT)) (|purelyTranscendental?| (#9# 145 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#9# 142 T ELT)) (|purelyAlgebraic?| (#9# 146 T ELT) (#7# 143 T ELT)) (|normalized?| (#9# 110 T ELT) (#7# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (#29=(#4# $) 48 T ELT)) (|member?| (#9# 53 #26# ELT)) (|map!| (#30=($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (#30# 60 T ELT)) (|mainVariables| (#6# 38 T ELT)) (|mainVariable?| (#31=(#2# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #5#) |#4| |#4| $) 137 T ELT)) (|lastSubResultant| ((#11# |#4| |#4| $) 136 T ELT)) (|last| (#32=(#16# $) 89 T ELT)) (|invertibleSet| (#33=(#5# |#4| $) 138 T ELT)) (|invertibleElseSplit?| (((|Union| #2# #5#) |#4| $) 141 T ELT)) (|invertible?| (((|List| 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#38# ELT) (($ $ (|List| #39#)) 61 #38# ELT)) (|eq?| (#1# 55 T ELT)) (|empty?| (#7# 58 T ELT)) (|empty| (#18# 57 T ELT)) (|degree| (#40=(#41=(|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#41# |#4| $) 52 #26# ELT) ((#41# #14# $) 47 T ELT)) (|copy| (#24# 56 T ELT)) (|convert| ((#42=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #42#)) ELT)) (|construct| (#23# 65 T ELT)) (|collectUpper| (#43=($ $ |#3|) 34 T ELT)) (|collectUnder| (#43# 36 T ELT)) (|collectQuasiMonic| (#24# 94 T ELT)) (|collect| (#43# 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#29# 43 T ELT)) (|coHeight| (#40# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| ((#44=(|Union| (|Record| (|:| |bas| $) (|:| |top| #4#)) #17#) #4# #20#) 115 T ELT) ((#44# #4# #14# #20#) 114 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#4| #4#)) 104 T ELT)) (|augment| (#33# 130 T ELT) (#36# 129 T ELT) (#34# 128 T ELT) (#35# 127 T ELT)) (|any?| (#37# 45 T ELT)) (|algebraicVariables| (#6# 87 T ELT)) (|algebraicCoefficients?| (#9# 144 T ELT)) (|algebraic?| (#31# 86 T ELT)) (= (#1# 8 T ELT)) (|#| (#40# 44 T ELT))) (((|SquareFreeNormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |SquareFreeNormalizedTriangularSetCategory|)) NIL (|Join| (|SquareFreeRegularTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|) (|NormalizedTriangularSetCategory| |t#1| |t#2| |t#3| |t#4|)) -(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|NormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) +(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|NormalizedTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|TriangularSetCategory| |#1| |#2| |#3| |#4|) . T) ((|Type|) . T)) ((|solve| (#1=(#2=(|List| |#2|) |#1|) 15 T ELT)) (|quartic| ((#2# |#2| |#2| |#2| |#2| |#2|) 47 T ELT) (#1# 61 T ELT)) (|quadratic| ((#2# |#2| |#2| |#2|) 45 T ELT) (#1# 59 T ELT)) (|particularSolution| ((|#2| |#1|) 54 T ELT)) (|mapSolve| (((|Record| (|:| |solns| #2#) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) 20 T ELT)) (|linear| ((#2# |#2| |#2|) 42 T ELT) (#1# 58 T ELT)) (|cubic| ((#2# |#2| |#2| |#2| |#2|) 46 T ELT) (#1# 60 T ELT)) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) 53 T ELT)) (|aQuadratic| ((|#2| |#2| |#2| |#2|) 51 T ELT)) (|aLinear| ((|#2| |#2| |#2|) 50 T ELT)) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) 52 T ELT))) (((|PolynomialSolveByFormulas| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| #1=(#2=(|List| |#2|) |#1|)) (SIGNATURE |particularSolution| (|#2| |#1|)) (SIGNATURE |mapSolve| ((|Record| (|:| |solns| #2#) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|))) (SIGNATURE |linear| #1#) (SIGNATURE |quadratic| #1#) (SIGNATURE |cubic| #1#) (SIGNATURE |quartic| #1#) (SIGNATURE |linear| (#2# |#2| |#2|)) (SIGNATURE |quadratic| (#2# |#2| |#2| |#2|)) (SIGNATURE |cubic| (#2# |#2| |#2| |#2| |#2|)) (SIGNATURE |quartic| (#2# |#2| |#2| |#2| |#2| |#2|)) (SIGNATURE |aLinear| (|#2| |#2| |#2|)) (SIGNATURE |aQuadratic| (|#2| |#2| |#2| |#2|)) (SIGNATURE |aCubic| (|#2| |#2| |#2| |#2| |#2|)) (SIGNATURE |aQuartic| (|#2| |#2| |#2| |#2| |#2| |#2|))) (|UnivariatePolynomialCategory| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (T |PolynomialSolveByFormulas|)) ((|aQuartic| (*1 *2 *2 *2 *2 *2 *2) #1=(AND (|ofCategory| *2 #2=(|Join| (|Field|) (CATEGORY |domain| (SIGNATURE ** ($ $ (|Fraction| (|Integer|))))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *2)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)))) (|aCubic| (*1 *2 *2 *2 *2 *2) #1#) (|aQuadratic| (*1 *2 *2 *2 *2) #1#) (|aLinear| (*1 *2 *2 *2) #1#) (|quartic| (*1 *2 *3 *3 *3 *3 *3) #3=(AND (|ofCategory| *3 #2#) (|isDomain| *2 (|List| *3)) (|isDomain| *1 (|PolynomialSolveByFormulas| *4 *3)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)))) (|cubic| (*1 *2 *3 *3 *3 *3) #3#) (|quadratic| (*1 *2 *3 *3 *3) #3#) (|linear| (*1 *2 *3 *3) #3#) (|quartic| #4=(*1 *2 *3) #5=(AND (|ofCategory| *4 #2#) (|isDomain| *2 (|List| *4)) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *4)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|cubic| #4# #5#) (|quadratic| #4# #5#) (|linear| #4# #5#) (|mapSolve| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 #2#) (|isDomain| *2 (|Record| (|:| |solns| (|List| *5)) (|:| |maps| (|List| (|Record| (|:| |arg| *5) (|:| |res| *5)))))) (|isDomain| *1 (|PolynomialSolveByFormulas| *3 *5)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|particularSolution| #4# #1#) (|solve| #4# #5#)) @@ -3505,29 +3505,29 @@ NIL ((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|subspace| ((#3=(|SubSpace| 3 |#1|) $) 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(SIGNATURE |setValue!| ($ $ |#1|)) (SIGNATURE |setCondition!| ($ $ |#2|)) (SIGNATURE |setStatus!| ($ $ #3#)) (SIGNATURE |setEmpty!| #6#) (SIGNATURE |infLex?| (#3# $ $ (|Mapping| #3# |#1| |#1|) #7=(|Mapping| #3# |#2| |#2|))) (SIGNATURE |subNode?| (#3# $ $ #7#)))) #8=(|Join| #1# (|Aggregate|)) #8#) (T |SplittingNode|)) ((|empty| (*1 *1) #1=(AND #2=(|isDomain| *1 (|SplittingNode| *2 *3)) #3=(|ofCategory| *2 #4=(|Join| (|SetCategory|) (|Aggregate|))) #5=(|ofCategory| *3 #4#))) (|empty?| #6=(*1 *2 *1) #7=(AND #8=(|isDomain| *2 #9=(|Boolean|)) #10=(|isDomain| *1 (|SplittingNode| *3 *4)) #5# #11=(|ofCategory| *4 #4#))) (|value| #6# (AND #3# #2# #5#)) (|condition| #6# (AND #3# #12=(|isDomain| *1 (|SplittingNode| *3 *2)) #5#)) (|status| #6# #7#) (|construct| (*1 *1 *2 *3 *4) (AND (|isDomain| *4 #9#) #2# #3# #5#)) (|construct| (*1 *1 *2 *3) #1#) (|construct| (*1 *1 *2) (AND (|isDomain| *2 (|Record| (|:| |val| *3) (|:| |tower| *4))) #5# #11# #10#)) (|construct| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |val| *4) (|:| |tower| *5)))) #11# #13=(|ofCategory| *5 #4#) (|isDomain| *2 (|List| #14=(|SplittingNode| *4 *5))) #15=(|isDomain| *1 #14#))) (|construct| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *5)) #13# (|isDomain| *2 (|List| #16=(|SplittingNode| *3 *5))) (|isDomain| *1 #16#) #5#)) (|copy| #17=(*1 *1 *1) #1#) (|setValue!| #18=(*1 *1 *1 *2) #1#) (|setCondition!| #18# (AND #12# #5# #3#)) (|setStatus!| #18# #7#) (|setEmpty!| #17# #1#) (|infLex?| (*1 *2 *1 *1 *3 *4) (AND #19=(|isDomain| *3 (|Mapping| #9# *5 *5)) (|isDomain| *4 (|Mapping| #9# *6 *6)) #13# (|ofCategory| *6 #4#) #8# (|isDomain| *1 (|SplittingNode| *5 *6)))) (|subNode?| (*1 *2 *1 *1 *3) (AND #19# #13# #8# #15# #11#))) @@ -3540,41 +3540,41 @@ NIL ((|upperCase| (#1=($ $) 19 T ELT)) (|trim| (($ $ #2=(|Character|)) 10 T ELT) (($ $ (|CharacterClass|)) 14 T ELT)) (|prefix?| (((|Boolean|) $ $) 24 T ELT)) (|lowerCase| (#1# 17 T ELT)) (|elt| ((#2# $ #3=(|Integer|) #2#) NIL T ELT) ((#2# $ #3#) NIL T ELT) (($ $ 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(|Integer|)) 123 T ELT)) (|new| (($ (|NonNegativeInteger|) #2#) 65 T ELT)) (|minIndex| ((#4# . #17=($)) 38 (|has| #4# . #18=((|OrderedSet|))) ELT)) (|min| (#19=($ $ $) 80 (|has| #2# . #6#) ELT)) (|merge| (($ (|Mapping| #5# #2# #2#) $ $) 99 T ELT) (($ $ $) 92 (|has| #2# . #6#) ELT)) (|members| (((|List| #2#) $) 104 T ELT)) (|member?| ((#20=(|Boolean|) #2# $) 109 (|has| #2# . #14#) ELT)) (|maxIndex| ((#4# . #17#) 39 (|has| #4# . #18#) ELT)) (|max| (#19# 81 (|has| #2# . #6#) ELT)) (|match?| (((|Boolean|) $ $ (|Character|)) 126 T ELT)) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) 127 T ELT)) (|map!| (($ (|Mapping| #2# #2#) $) 112 T ELT)) (|map| (($ (|Mapping| #2# #2#) $) 26 T ELT) (($ (|Mapping| #2# #2# #2#) $ $) 60 T ELT)) (|lowerCase!| (($ $) 133 T ELT)) (|lowerCase| (($ $) 134 T ELT)) (|leftTrim| (($ $ (|Character|)) 117 T ELT) (($ $ (|CharacterClass|)) 116 T ELT)) (|latex| (((|String|) $) 21 (|has| #2# . #21=((|SetCategory|))) ELT)) (|insert| (($ #2# $ #4#) 57 T ELT) (($ $ $ 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|key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT) (($ $ (|List| (|Equation| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) 97 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #17#)) ELT)) (|eq?| ((#21=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#19# |#2| $) 77 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| (|BasicType|))) ELT)) (|entries| (((|List| |#2|) $) 74 T ELT)) (|empty?| ((#21# $) 7 T ELT)) (|empty| (#9# 8 T ELT)) (|elt| ((|#2| $ |#1|) 73 T ELT) ((|#2| $ |#1| |#2|) 72 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 45 T ELT)) (|count| ((#22=(|NonNegativeInteger|) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 109 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #11#) ELT) ((#22# (|Mapping| #14# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) $) 104 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#23=(|InputForm|) $) 52 (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| #23#)) ELT)) (|construct| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 47 T ELT)) (|coerce| (((|OutputForm|) $) 16 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #24=((|CoercibleTo| (|OutputForm|)))) (|has| |#2| . #24#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #24#)) ELT)) (|before?| (#1# 19 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|bag| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) 38 T ELT)) (|any?| ((#14# (|Mapping| #14# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #20#) 102 T ELT)) (= (#1# 17 (OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#) (|has| |#2| . #2#) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #2#)) ELT)) (|#| ((#22# $) 101 T ELT))) -(((|TableAggregate| |#1| |#2|) (|Category|) (|SetCategory|) (|SetCategory|)) (T |TableAggregate|)) -((|table| (*1 *1) (AND (|ofCategory| *1 (|TableAggregate| *2 *3)) (|ofCategory| *2 (|SetCategory|)) (|ofCategory| *3 (|SetCategory|)))) (|table| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| *3) (|:| |entry| *4)))) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *1 (|TableAggregate| *3 *4)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *4 *4 *4)) (|ofCategory| *1 (|TableAggregate| *3 *4)) (|ofCategory| *3 (|SetCategory|)) (|ofCategory| *4 (|SetCategory|))))) -(|Join| (|KeyedDictionary| |t#1| |t#2|) (|FiniteAggregate| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))) (CATEGORY |domain| (SIGNATURE |table| ($)) (SIGNATURE |table| ($ (|List| (|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))))) (SIGNATURE |map| ($ (|Mapping| |t#2| |t#2| |t#2|) $ $)))) -(((|Aggregate|) . T) ((|BagAggregate| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|BasicType|)) (|has| |#2| (|SetCategory|)) (|has| |#2| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|SetCategory|)) (|has| |#2| (|CoercibleTo| (|OutputForm|)))) ((|Collection| #1#) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #2=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|FiniteAggregate| #2#) . T) ((|Functorial| #2#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #2#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| #2# #2#) AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|Join|) . T) ((|KeyedDictionary| |#1| |#2|) . T) ((|SetCategory|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| |#2| (|SetCategory|))) ((|ShallowlyMutableAggregate| #1#) . T) ((|ShallowlyMutableAggregate| |#2|) . T) ((|Type|) . T)) +((~= (#1=(#2=(|Boolean|) $ $) 18 #3=(OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #6=((|BasicType|))) #7=(|has| |#2| . #6#) #4#) ELT)) (|table| (#8=($) 95 T ELT) (#9=($ #10=(|List| #5#)) 94 T ELT)) (|swap!| (((|Void|) $ |#1| |#1|) 82 #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|setelt| (#12=(|#2| $ |#1| |#2|) 70 #11# ELT)) (|select!| (#13=($ #14=(|Mapping| #2# #5#) $) 42 #15=(|has| $ (|FiniteAggregate| #5#)) ELT)) (|select| (#13# 49 #15# ELT)) (|search| (#16=((|Union| |#2| #17="failed") |#1| $) 59 T ELT)) (|sample| (#8# 6 T CONST)) (|removeDuplicates| (#18=($ $) 51 #19=(AND #4# #15#) ELT)) (|remove!| (#20=($ #5# $) 44 #15# ELT) (#13# 43 #15# ELT) (#16# 60 T ELT)) (|remove| (#20# 50 #19# ELT) (#13# 48 #15# ELT)) (|reduce| ((#5# #21=(|Mapping| #5# #5# #5#) $ #5# #5#) 111 #4# ELT) ((#5# #21# $ #5#) 107 T ELT) ((#5# #21# $) 106 T ELT)) (|qsetelt!| (#12# 69 #11# ELT)) (|qelt| (#22=(|#2| $ |#1|) 71 T ELT)) (|minIndex| (#23=(|#1| $) 79 #24=(|has| |#1| (|OrderedSet|)) ELT)) (|members| ((#10# $) 105 T ELT)) (|member?| ((#2# #5# $) 110 #4# ELT)) (|maxIndex| (#23# 78 #24# ELT)) (|map!| (#25=($ (|Mapping| #5# #5#) . #26=($)) 39 T ELT) (#27=($ (|Mapping| |#2| |#2|) . #26#) 63 T ELT)) (|map| (#25# 26 T ELT) (#27# 64 T ELT) (#25# 96 T ELT) (($ (|Mapping| |#2| |#2| |#2|) $ $) 93 T ELT)) (|latex| (((|String|) $) 21 #28=(OR #29=(|has| #5# . #30=((|SetCategory|))) #31=(|has| |#2| . #30#) #29#) ELT)) (|keys| (#32=((|List| |#1|) $) 61 T ELT)) (|key?| (#33=(#2# |#1| $) 62 T ELT)) (|inspect| (#34=(#5# $) 35 T ELT)) (|insert!| (#20# 36 T ELT)) (|indices| (#32# 76 T ELT)) (|index?| (#33# 75 T ELT)) (|hash| (((|SingleInteger|) $) 20 #28# ELT)) (|first| ((|#2| $) 80 #24# ELT)) (|find| (((|Union| #5# #17#) #14# $) 108 T ELT)) (|fill!| (($ $ |#2|) 81 #11# ELT)) (|extract!| (#34# 37 T ELT)) (|every?| (#35=(#2# #14# $) 103 T ELT)) (|eval| (#36=($ $ (|List| #37=(|Equation| #5#))) 25 #38=(AND (|has| #5# (|Evalable| #5#)) #29#) ELT) (#39=($ $ #37#) 24 #38# ELT) (#40=($ $ #5# #5#) 23 #38# ELT) (#41=($ $ #10# #10#) 22 #38# ELT) (($ $ #42=(|List| |#2|) #42#) 68 #43=(AND (|has| |#2| (|Evalable| |#2|)) #31#) ELT) (($ $ |#2| |#2|) 67 #43# ELT) (($ $ #44=(|Equation| |#2|)) 66 #43# ELT) (($ $ (|List| #44#)) 65 #43# ELT) (#41# 100 #38# ELT) (#40# 99 #38# ELT) (#39# 98 #38# ELT) (#36# 97 #38# ELT)) (|eq?| (#1# 10 T ELT)) (|entry?| ((#2# |#2| $) 77 (AND (|has| $ (|FiniteAggregate| |#2|)) #7#) ELT)) (|entries| ((#42# $) 74 T ELT)) (|empty?| ((#2# $) 7 T ELT)) (|empty| (#8# 8 T ELT)) (|elt| (#22# 73 T ELT) (#12# 72 T ELT)) (|dictionary| (#8# 46 T ELT) (#9# 45 T ELT)) (|count| ((#45=(|NonNegativeInteger|) #5# $) 109 #4# ELT) ((#45# #14# $) 104 T ELT)) (|copy| (#18# 9 T ELT)) (|convert| ((#46=(|InputForm|) $) 52 (|has| #5# (|ConvertibleTo| #46#)) ELT)) (|construct| (#9# 47 T ELT)) (|coerce| ((#47=(|OutputForm|) $) 16 (OR #48=(|has| #5# . #49=((|CoercibleTo| #47#))) (|has| |#2| . #49#) #48#) ELT)) (|before?| (#1# 19 #3# ELT)) (|bag| (#9# 38 T ELT)) (|any?| (#35# 102 T ELT)) (= (#1# 17 #3# ELT)) (|#| ((#45# $) 101 T ELT))) +(((|TableAggregate| |#1| |#2|) (|Category|) #1=(|SetCategory|) #1#) (T |TableAggregate|)) +((|table| (*1 *1) (AND (|ofCategory| *1 (|TableAggregate| *2 *3)) (|ofCategory| *2 #1=(|SetCategory|)) #2=(|ofCategory| *3 #1#))) (|table| (*1 *1 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |key| *3) (|:| |entry| *4)))) #2# #3=(|ofCategory| *4 #1#) #4=(|ofCategory| *1 (|TableAggregate| *3 *4)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *4 *4 *4)) #4# #2# #3#))) +(|Join| (|KeyedDictionary| |t#1| |t#2|) (|FiniteAggregate| #1=(|Record| (|:| |key| |t#1|) (|:| |entry| |t#2|))) (CATEGORY |domain| (SIGNATURE |table| ($)) (SIGNATURE |table| ($ (|List| #1#))) (SIGNATURE |map| ($ (|Mapping| |t#2| |t#2| |t#2|) $ $)))) +(((|Aggregate|) . T) ((|BagAggregate| #1=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| #1#) . T) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #1#) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ((|Evalable| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|FiniteAggregate| #1#) . T) ((|Functorial| #1#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #1#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| |#1| |#2|) . T) ((|InnerEvalable| #1# #1#) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Evalable| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| (|SetCategory|))) ((|KeyedDictionary| |#1| |#2|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| #1#) . T) ((|ShallowlyMutableAggregate| |#2|) . T) ((|Type|) . T)) ((|usingTable?| (#1=((|Boolean|)) 29 T ELT)) (|startStats!| ((#2=(|Void|) #3=(|String|)) 31 T ELT)) (|printingInfo?| (#1# 41 T ELT)) (|printStats!| (#4=(#2#) 39 T ELT)) (|printInfo!| ((#2# #3# #3#) 30 T ELT)) (|makingStats?| (#1# 42 T ELT)) (|insert!| ((#2# |#1| |#2|) 53 T ELT)) (|initTable!| (#4# 26 T ELT)) (|extractIfCan| (((|Union| |#2| "failed") |#1|) 51 T ELT)) (|clearTable!| (#4# 40 T ELT))) (((|TabulatedComputationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |initTable!| #1=(#2=(|Void|))) (SIGNATURE |printInfo!| (#2# #3=(|String|) #3#)) (SIGNATURE |startStats!| (#2# #3#)) (SIGNATURE |printStats!| #1#) (SIGNATURE |clearTable!| #1#) (SIGNATURE |usingTable?| #4=((|Boolean|))) (SIGNATURE |printingInfo?| #4#) (SIGNATURE |makingStats?| #4#) (SIGNATURE |extractIfCan| ((|Union| |#2| "failed") |#1|)) (SIGNATURE |insert!| (#2# |#1| |#2|))) #5=(|SetCategory|) #5#) (T |TabulatedComputationPackage|)) ((|insert!| (*1 *2 *3 *4) #1=(AND #2=(|isDomain| *2 (|Void|)) #3=(|isDomain| *1 (|TabulatedComputationPackage| *3 *4)) #4=(|ofCategory| *3 #5=(|SetCategory|)) #6=(|ofCategory| *4 #5#))) (|extractIfCan| #7=(*1 *2 *3) (|partial| AND (|ofCategory| *2 #5#) (|isDomain| *1 (|TabulatedComputationPackage| *3 *2)) #4#)) (|makingStats?| #8=(*1 *2) #9=(AND (|isDomain| *2 (|Boolean|)) #3# #4# #6#)) (|printingInfo?| #8# #9#) (|usingTable?| #8# #9#) (|clearTable!| #8# #1#) (|printStats!| #8# #1#) (|startStats!| #7# #10=(AND (|isDomain| *3 (|String|)) #2# (|isDomain| *1 (|TabulatedComputationPackage| *4 *5)) #6# (|ofCategory| *5 #5#))) (|printInfo!| (*1 *2 *3 *3) #10#) (|initTable!| #8# #1#)) @@ -3723,7 +3723,7 @@ NIL ((|pi| (($) 12 T ELT)) (|atanh| (#1=($ $) 36 T ELT)) (|asinh| (#1# 34 T ELT)) (|asin| (#1# 26 T ELT)) (|asech| (#1# 18 T ELT)) (|acsch| (#1# 16 T ELT)) (|acoth| (#1# 20 T ELT)) (|acot| (#1# 31 T ELT)) (|acosh| (#1# 35 T ELT)) (|acos| (#1# 30 T ELT))) (((|TranscendentalFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |pi| (|#1|)) (SIGNATURE |atanh| #1=(|#1| |#1|)) (SIGNATURE |asinh| #1#) (SIGNATURE |asech| #1#) (SIGNATURE |acsch| #1#) (SIGNATURE |acoth| #1#) (SIGNATURE |acosh| #1#) (SIGNATURE |asin| #1#) (SIGNATURE |acot| #1#) (SIGNATURE |acos| #1#)) (|TranscendentalFunctionCategory|)) (T |TranscendentalFunctionCategory&|)) NIL -((|tanh| (#1=($ $) 26 T ELT)) (|tan| (#2=($ $) 11 T ELT)) (|sinh| (#1# 27 T ELT)) (|sin| (#2# 10 T ELT)) (|sech| (#1# 28 T ELT)) (|sec| (#2# 9 T ELT)) (|pi| (($) 16 T ELT)) (|log| (#3=($ $) 19 T ELT)) (|exp| (#3# 18 T ELT)) (|csch| (#1# 29 T ELT)) (|csc| (#2# 8 T ELT)) (|coth| (#1# 30 T ELT)) (|cot| (#2# 7 T ELT)) (|cosh| (#1# 31 T ELT)) (|cos| (#2# 6 T ELT)) (|atanh| (#4=($ $) 20 T ELT)) (|atan| (#5=($ $) 32 T ELT)) (|asinh| (#4# 21 T ELT)) (|asin| (#5# 33 T ELT)) (|asech| (#4# 22 T ELT)) (|asec| (#5# 34 T ELT)) (|acsch| (#4# 23 T ELT)) (|acsc| (#5# 35 T ELT)) (|acoth| (#4# 24 T ELT)) (|acot| (#5# 36 T ELT)) (|acosh| (#4# 25 T ELT)) (|acos| (#5# 37 T ELT)) (** (($ $ $) 17 T ELT))) +((|tanh| (#1=($ $) 26 T ELT)) (|tan| (#1# 11 T ELT)) (|sinh| (#1# 27 T ELT)) (|sin| (#1# 10 T ELT)) (|sech| (#1# 28 T ELT)) (|sec| (#1# 9 T ELT)) (|pi| (($) 16 T ELT)) (|log| (#1# 19 T ELT)) (|exp| (#1# 18 T ELT)) (|csch| (#1# 29 T ELT)) (|csc| (#1# 8 T ELT)) (|coth| (#1# 30 T ELT)) (|cot| (#1# 7 T ELT)) (|cosh| (#1# 31 T ELT)) (|cos| (#1# 6 T ELT)) (|atanh| (#1# 20 T ELT)) (|atan| (#1# 32 T ELT)) (|asinh| (#1# 21 T ELT)) (|asin| (#1# 33 T ELT)) (|asech| (#1# 22 T ELT)) (|asec| (#1# 34 T ELT)) (|acsch| (#1# 23 T ELT)) (|acsc| (#1# 35 T ELT)) (|acoth| (#1# 24 T ELT)) (|acot| (#1# 36 T ELT)) (|acosh| (#1# 25 T ELT)) (|acos| (#1# 37 T ELT)) (** (($ $ $) 17 T ELT))) (((|TranscendentalFunctionCategory|) (|Category|)) (T |TranscendentalFunctionCategory|)) ((|pi| (*1 *1) (|ofCategory| *1 (|TranscendentalFunctionCategory|)))) (|Join| (|TrigonometricFunctionCategory|) (|ArcTrigonometricFunctionCategory|) (|HyperbolicFunctionCategory|) (|ArcHyperbolicFunctionCategory|) (|ElementaryFunctionCategory|) (CATEGORY |domain| (SIGNATURE |pi| ($)))) @@ -3734,10 +3734,10 @@ NIL ((|tan| (#1=($ $) 15 T ELT)) (|sec| (#1# 12 T ELT)) (|csc| (#1# 10 T ELT)) (|cot| (#1# 17 T ELT))) (((|TrigonometricFunctionCategory&| |#1|) (CATEGORY |package| (SIGNATURE |cot| #1=(|#1| |#1|)) (SIGNATURE |csc| #1#) (SIGNATURE |sec| #1#) (SIGNATURE |tan| #1#)) (|TrigonometricFunctionCategory|)) (T |TrigonometricFunctionCategory&|)) NIL -((|tan| (($ $) 11 T ELT)) (|sin| (($ $) 10 T ELT)) (|sec| (($ $) 9 T ELT)) (|csc| (($ $) 8 T ELT)) (|cot| (($ $) 7 T ELT)) (|cos| (($ $) 6 T ELT))) +((|tan| (#1=($ $) 11 T ELT)) (|sin| (#1# 10 T ELT)) (|sec| (#1# 9 T ELT)) (|csc| (#1# 8 T ELT)) (|cot| (#1# 7 T ELT)) (|cos| (#1# 6 T ELT))) (((|TrigonometricFunctionCategory|) (|Category|)) (T |TrigonometricFunctionCategory|)) -((|tan| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|sin| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|sec| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|csc| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|cot| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|cos| (*1 *1 *1) (|ofCategory| *1 (|TrigonometricFunctionCategory|)))) -(|Join| (CATEGORY |domain| (SIGNATURE |cos| ($ $)) (SIGNATURE |cot| ($ $)) (SIGNATURE |csc| ($ $)) (SIGNATURE |sec| ($ $)) (SIGNATURE |sin| ($ $)) (SIGNATURE |tan| ($ $)))) +((|tan| #1=(*1 *1 *1) #2=(|ofCategory| *1 (|TrigonometricFunctionCategory|))) (|sin| #1# #2#) (|sec| #1# #2#) (|csc| #1# #2#) (|cot| #1# #2#) (|cos| #1# #2#)) +(|Join| (CATEGORY |domain| (SIGNATURE |cos| #1=($ $)) (SIGNATURE |cot| #1#) (SIGNATURE |csc| #1#) (SIGNATURE |sec| #1#) (SIGNATURE |sin| #1#) (SIGNATURE |tan| #1#))) ((|trigs| (#1=(|#2| |#2|) 95 T ELT)) (|real?| (((|Boolean|) |#2|) 29 T ELT)) (|real| (#1# 33 T ELT)) (|imag| (#1# 35 T ELT)) (|complexNormalize| (#2=(|#2| |#2| (|Symbol|)) 89 T ELT) (#1# 90 T ELT)) (|complexForm| (((|Complex| |#2|) |#2|) 31 T ELT)) (|complexElementary| (#2# 91 T ELT) (#1# 92 T ELT))) (((|TrigonometricManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |complexNormalize| #1=(|#2| |#2|)) (SIGNATURE |complexNormalize| #2=(|#2| |#2| (|Symbol|))) (SIGNATURE |complexElementary| #1#) (SIGNATURE |complexElementary| #2#) (SIGNATURE |trigs| #1#) (SIGNATURE |real| #1#) (SIGNATURE |imag| #1#) (SIGNATURE |real?| ((|Boolean|) |#2|)) (SIGNATURE |complexForm| ((|Complex| |#2|) |#2|))) (|Join| (|GcdDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |TrigonometricManipulations|)) ((|complexForm| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|Join| (|GcdDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#))) (|isDomain| *2 (|Complex| *3)) #5=(|isDomain| *1 (|TrigonometricManipulations| *4 *3)) #6=(|ofCategory| *3 #7=(|Join| #8=(|AlgebraicallyClosedField|) #9=(|TranscendentalFunctionCategory|) (|FunctionSpace| *4))))) (|real?| #1# (AND #2# (|isDomain| *2 (|Boolean|)) #5# #6#)) (|imag| #10=(*1 *2 *2) #11=(AND (|ofCategory| *3 #3#) (|isDomain| *1 (|TrigonometricManipulations| *3 *2)) (|ofCategory| *2 (|Join| #8# #9# (|FunctionSpace| *3))))) (|real| #10# #11#) (|trigs| #10# #11#) (|complexElementary| #12=(*1 *2 *2 *3) #13=(AND (|isDomain| *3 (|Symbol|)) #2# (|isDomain| *1 (|TrigonometricManipulations| *4 *2)) (|ofCategory| *2 #7#))) (|complexElementary| #10# #11#) (|complexNormalize| #12# #13#) (|complexNormalize| #10# #11#)) @@ -3753,11 +3753,11 @@ NIL ((|stronglyReduced?| (#1=(#2=(|Boolean|) |#5| $) 68 T ELT) (#3=(#2# $) 109 T ELT)) (|stronglyReduce| (#4=(|#5| |#5| $) 83 T ELT)) (|select| (($ #5=(|Mapping| #2# |#5|) $) NIL T ELT) ((#6=(|Union| |#5| #7="failed") $ |#4|) 126 T ELT)) (|rewriteSetWithReduction| ((#8=(|List| |#5|) #8# $ #9=(|Mapping| |#5| |#5| |#5|) #10=(|Mapping| #2# |#5| |#5|)) 81 T ELT)) (|retractIfCan| ((#11=(|Union| $ #7#) #8#) 134 T ELT)) (|rest| ((#11# $) 119 T ELT)) (|removeZero| (#4# 101 T ELT)) (|reduced?| ((#2# |#5| $ #10#) 36 T ELT)) (|reduceByQuasiMonic| (#4# 105 T ELT)) (|reduce| ((|#5| #9# $ |#5| |#5|) NIL T ELT) ((|#5| #9# $ |#5|) NIL T ELT) ((|#5| #9# $) NIL T ELT) ((|#5| |#5| $ #9# #10#) 77 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #8#) (|:| |open| #8#)) $) 63 T ELT)) (|normalized?| (#1# 66 T ELT) (#3# 110 T ELT)) (|mvar| ((|#4| $) 115 T ELT)) (|last| (#12=(#6# $) 117 T ELT)) (|initials| (#13=(#8# $) 55 T ELT)) (|initiallyReduced?| (#1# 75 T ELT) (#3# 114 T ELT)) (|initiallyReduce| (#4# 89 T ELT)) (|infRittWu?| (#14=(#2# $ $) 29 T ELT)) (|headReduced?| (#1# 71 T ELT) (#3# 112 T ELT)) (|headReduce| (#4# 86 T ELT)) (|first| (#12# 116 T ELT)) (|extend| (($ $ |#5|) 135 T ELT)) (|degree| (#15=((|NonNegativeInteger|) $) 60 T ELT)) (|construct| (($ #8#) 132 T ELT)) (|collectUpper| (#16=($ $ |#4|) 130 T ELT)) (|collectUnder| (#16# 128 T ELT)) (|collectQuasiMonic| (($ $) 127 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (#13# 120 T ELT)) (|coHeight| (#15# 142 T ELT)) (|basicSet| ((#17=(|Union| (|Record| (|:| |bas| $) (|:| |top| #8#)) #7#) #8# #10#) 49 T ELT) ((#17# #8# #5# #10#) 51 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#5| #8#)) 107 T ELT)) (|algebraicVariables| (((|List| |#4|) $) 122 T ELT)) (|algebraic?| ((#2# |#4| $) 125 T ELT)) (= (#14# 20 T ELT))) (((|TriangularSetCategory&| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |coHeight| #1=((|NonNegativeInteger|) |#1|)) (SIGNATURE |extend| (|#1| |#1| |#5|)) (SIGNATURE |select| (#2=(|Union| |#5| #3="failed") |#1| |#4|)) (SIGNATURE |algebraic?| (#4=(|Boolean|) |#4| |#1|)) (SIGNATURE |algebraicVariables| ((|List| |#4|) |#1|)) (SIGNATURE |rest| (#5=(|Union| |#1| #3#) |#1|)) (SIGNATURE |last| #6=(#2# |#1|)) (SIGNATURE |first| #6#) (SIGNATURE |reduceByQuasiMonic| #7=(|#5| |#5| |#1|)) (SIGNATURE |collectQuasiMonic| (|#1| |#1|)) (SIGNATURE |removeZero| #7#) (SIGNATURE |initiallyReduce| #7#) (SIGNATURE |headReduce| #7#) (SIGNATURE |stronglyReduce| #7#) (SIGNATURE |rewriteSetWithReduction| (#8=(|List| |#5|) #8# |#1| #9=(|Mapping| |#5| |#5| |#5|) #10=(|Mapping| #4# |#5| |#5|))) (SIGNATURE |reduce| (|#5| |#5| |#1| #9# #10#)) (SIGNATURE |initiallyReduced?| #11=(#4# |#1|)) (SIGNATURE |headReduced?| #11#) (SIGNATURE |stronglyReduced?| #11#) (SIGNATURE |autoReduced?| (#4# |#1| (|Mapping| #4# |#5| #8#))) (SIGNATURE |initiallyReduced?| #12=(#4# |#5| |#1|)) (SIGNATURE |headReduced?| #12#) (SIGNATURE |stronglyReduced?| #12#) (SIGNATURE |reduced?| (#4# |#5| |#1| #10#)) (SIGNATURE |normalized?| #11#) (SIGNATURE |normalized?| #12#) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| #8#) (|:| |open| #8#)) |#1|)) (SIGNATURE |degree| #1#) (SIGNATURE |initials| #13=(#8# |#1|)) (SIGNATURE |basicSet| (#14=(|Union| (|Record| (|:| |bas| |#1|) (|:| |top| #8#)) #3#) #8# #15=(|Mapping| #4# |#5|) #10#)) (SIGNATURE |basicSet| (#14# #8# #10#)) (SIGNATURE |infRittWu?| #16=(#4# |#1| |#1|)) (SIGNATURE |collectUpper| #17=(|#1| |#1| |#4|)) (SIGNATURE |collectUnder| #17#) (SIGNATURE |mvar| (|#4| |#1|)) (SIGNATURE |retractIfCan| (#5# #8#)) (SIGNATURE |coerce| #13#) (SIGNATURE |reduce| (|#5| #9# |#1|)) (SIGNATURE |reduce| (|#5| #9# |#1| |#5|)) (SIGNATURE |reduce| (|#5| #9# |#1| |#5| |#5|)) (SIGNATURE |construct| (|#1| #8#)) (SIGNATURE |select| (|#1| #15# |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE = #16#)) (|TriangularSetCategory| |#2| |#3| |#4| |#5|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#2| |#3| |#4|)) (T |TriangularSetCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) 91 T ELT)) (|zeroSetSplit| (((|List| $) (|List| |#4|)) 92 T ELT)) (|variables| (((|List| |#3|) . #2=($)) 39 T ELT)) (|trivialIdeal?| (#3=(#4=(|Boolean|) $) 32 T ELT)) (|triangular?| (#3# 23 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|stronglyReduced?| (((|Boolean|) |#4| $) 107 T ELT) (((|Boolean|) $) 103 T ELT)) (|stronglyReduce| ((|#4| |#4| $) 98 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (($ (|Mapping| #6=(|Boolean|) |#4|) . #7=($)) 67 (|has| $ (|FiniteAggregate| |#4|)) ELT) (((|Union| |#4| "failed") $ |#3|) 85 T ELT)) (|sample| (#8=($) 59 T CONST)) (|roughUnitIdeal?| (#3# 28 (|has| |#1| . #5#) ELT)) (|roughSubIdeal?| (#9=(#4# $ $) 30 (|has| |#1| . #5#) ELT)) (|roughEqualIdeals?| (#9# 29 (|has| |#1| . #5#) ELT)) (|roughBase?| (#3# 31 (|has| |#1| . #5#) ELT)) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) . #10=($)) 24 (|has| |#1| . #5#) ELT)) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) . #10#) 25 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) 42 T ELT)) (|retract| (($ (|List| |#4|)) 41 T ELT)) (|rest| (((|Union| $ "failed") $) 88 T ELT)) (|removeZero| ((|#4| |#4| $) 95 T ELT)) (|removeDuplicates| (($ $) 69 (AND (|has| |#4| . #11=((|BasicType|))) (|has| $ (|FiniteAggregate| |#4|))) ELT)) (|remove| (($ |#4| $) 68 (AND (|has| |#4| . #11#) (|has| $ (|FiniteAggregate| |#4|))) ELT) (($ (|Mapping| #6# |#4|) . #7#) 66 (|has| $ (|FiniteAggregate| |#4|)) ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) 26 (|has| |#1| . #5#) ELT)) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) 108 T ELT)) (|reduceByQuasiMonic| ((|#4| |#4| $) 93 T ELT)) (|reduce| ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4| |#4|) 54 (|has| |#4| . #12=((|BasicType|))) ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $ |#4|) 50 T ELT) ((|#4| (|Mapping| |#4| |#4| |#4|) $) 49 T ELT) ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) 111 T ELT)) (|normalized?| (((|Boolean|) |#4| $) 110 T ELT) (((|Boolean|) $) 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (((|List| |#4|) $) 48 T ELT)) (|member?| ((#13=(|Boolean|) |#4| $) 53 (|has| |#4| . #12#) ELT)) (|map!| (($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (($ (|Mapping| |#4| |#4|) $) 60 T ELT)) (|mainVariables| (((|List| |#3|) . #2#) 38 T ELT)) (|mainVariable?| ((#4# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|last| (((|Union| |#4| "failed") $) 89 T ELT)) (|initials| (((|List| |#4|) $) 113 T ELT)) (|initiallyReduced?| (((|Boolean|) |#4| $) 105 T ELT) (((|Boolean|) $) 101 T ELT)) (|initiallyReduce| ((|#4| |#4| $) 96 T ELT)) (|infRittWu?| (((|Boolean|) $ $) 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) 27 (|has| |#1| . #5#) ELT)) (|headReduced?| (((|Boolean|) |#4| $) 106 T ELT) (((|Boolean|) $) 102 T ELT)) (|headReduce| ((|#4| |#4| $) 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (((|Union| |#4| "failed") $) 90 T ELT)) (|find| (((|Union| |#4| "failed") (|Mapping| #13# |#4|) $) 51 T ELT)) (|extendIfCan| (((|Union| $ "failed") $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT)) (|every?| ((#13# (|Mapping| #13# |#4|) . #14=($)) 46 T ELT)) (|eval| (($ $ (|List| |#4|) (|List| |#4|)) 64 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15=((|SetCategory|)))) ELT) (($ $ |#4| |#4|) 63 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT) (($ $ (|Equation| |#4|)) 62 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT) (($ $ (|List| (|Equation| |#4|))) 61 (AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| . #15#)) ELT)) (|eq?| ((#16=(|Boolean|) $ $) 55 T ELT)) (|empty?| ((#16# $) 58 T ELT)) (|empty| (#8# 57 T ELT)) (|degree| (((|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#17=(|NonNegativeInteger|) |#4| $) 52 (|has| |#4| . #12#) ELT) ((#17# (|Mapping| #13# |#4|) $) 47 T ELT)) (|copy| (($ $) 56 T ELT)) (|convert| ((#18=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #18#)) ELT)) (|construct| (($ (|List| |#4|)) 65 T ELT)) (|collectUpper| (($ $ |#3|) 34 T ELT)) (|collectUnder| (($ $ |#3|) 36 T ELT)) (|collectQuasiMonic| (($ $) 94 T ELT)) (|collect| (($ $ |#3|) 35 T ELT)) (|coerce| (((|OutputForm|) . #19=($)) 13 T ELT) (((|List| |#4|) . #19#) 43 T ELT)) (|coHeight| (((|NonNegativeInteger|) $) 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 115 T ELT) (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) 114 T ELT)) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) 104 T ELT)) (|any?| ((#13# (|Mapping| #13# |#4|) . #14#) 45 T ELT)) (|algebraicVariables| (((|List| |#3|) $) 87 T ELT)) (|algebraic?| (((|Boolean|) |#3| $) 86 T ELT)) (= (#1# 8 T ELT)) (|#| ((#17# $) 44 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #3=(|:| |open| #4=(|List| |#4|)))) #4#) 91 T ELT)) (|zeroSetSplit| (((|List| $) #4#) 92 T ELT)) (|variables| (#5=((|List| |#3|) $) 39 T ELT)) (|trivialIdeal?| (#6=(#2# $) 32 T ELT)) (|triangular?| (#6# 23 #7=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| (#8=(#2# |#4| $) 107 T ELT) (#6# 103 T ELT)) (|stronglyReduce| (#9=(|#4| |#4| $) 98 T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) 33 T ELT)) (|select| (#10=($ #11=(|Mapping| #2# |#4|) $) 67 #12=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#13=(|Union| |#4| #14="failed") $ |#3|) 85 T ELT)) (|sample| (#15=($) 59 T CONST)) (|roughUnitIdeal?| (#6# 28 #7# ELT)) (|roughSubIdeal?| (#1# 30 #7# ELT)) (|roughEqualIdeals?| (#1# 29 #7# ELT)) (|roughBase?| (#6# 31 #7# ELT)) (|rewriteSetWithReduction| ((#4# #4# $ #16=(|Mapping| |#4| |#4| |#4|) #17=(|Mapping| #2# |#4| |#4|)) 99 T ELT)) (|rewriteIdealWithRemainder| (#18=(#4# #4# $) 24 #7# ELT)) (|rewriteIdealWithHeadRemainder| (#18# 25 #7# ELT)) (|retractIfCan| ((#19=(|Union| $ #14#) #4#) 42 T ELT)) (|retract| (#20=($ #4#) 41 T ELT)) (|rest| ((#19# $) 88 T ELT)) (|removeZero| (#9# 95 T ELT)) (|removeDuplicates| (#21=($ $) 69 #22=(AND #23=(|has| |#4| (|BasicType|)) #12#) ELT)) (|remove| (($ |#4| $) 68 #22# ELT) (#10# 66 #12# ELT)) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #24=(|:| |den| |#1|)) |#4| $) 26 #7# ELT)) (|reduced?| ((#2# |#4| $ #17#) 108 T ELT)) (|reduceByQuasiMonic| (#9# 93 T ELT)) (|reduce| ((|#4| #16# $ |#4| |#4|) 54 #23# ELT) ((|#4| #16# $ |#4|) 50 T ELT) ((|#4| #16# $) 49 T ELT) ((|#4| |#4| $ #16# #17#) 100 T ELT)) (|quasiComponent| (((|Record| (|:| |close| #4#) #3#) $) 111 T ELT)) (|normalized?| (#8# 110 T ELT) (#6# 109 T ELT)) (|mvar| ((|#3| $) 40 T ELT)) (|members| (#25=(#4# $) 48 T ELT)) (|member?| (#8# 53 #23# ELT)) (|map!| (#26=($ (|Mapping| |#4| |#4|) $) 117 T ELT)) (|map| (#26# 60 T ELT)) (|mainVariables| (#5# 38 T ELT)) (|mainVariable?| (#27=(#2# |#3| $) 37 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|last| (#28=(#13# $) 89 T ELT)) (|initials| (#25# 113 T ELT)) (|initiallyReduced?| (#8# 105 T ELT) (#6# 101 T ELT)) (|initiallyReduce| (#9# 96 T ELT)) (|infRittWu?| (#1# 116 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #24#) |#4| $) 27 #7# ELT)) (|headReduced?| (#8# 106 T ELT) (#6# 102 T ELT)) (|headReduce| (#9# 97 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|first| (#28# 90 T ELT)) (|find| ((#13# #11# $) 51 T ELT)) (|extendIfCan| ((#19# $ |#4|) 84 T ELT)) (|extend| (($ $ |#4|) 83 T ELT)) (|every?| (#29=(#2# #11# $) 46 T ELT)) (|eval| (($ $ #4# #4#) 64 #30=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) 63 #30# ELT) (($ $ #31=(|Equation| |#4|)) 62 #30# ELT) (($ $ (|List| #31#)) 61 #30# ELT)) (|eq?| (#1# 55 T ELT)) (|empty?| (#6# 58 T ELT)) (|empty| (#15# 57 T ELT)) (|degree| (#32=(#33=(|NonNegativeInteger|) $) 112 T ELT)) (|count| ((#33# |#4| $) 52 #23# ELT) ((#33# #11# $) 47 T ELT)) (|copy| (#21# 56 T ELT)) (|convert| ((#34=(|InputForm|) $) 70 (|has| |#4| (|ConvertibleTo| #34#)) ELT)) (|construct| (#20# 65 T ELT)) (|collectUpper| (#35=($ $ |#3|) 34 T ELT)) (|collectUnder| (#35# 36 T ELT)) (|collectQuasiMonic| (#21# 94 T ELT)) (|collect| (#35# 35 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (#25# 43 T ELT)) (|coHeight| (#32# 82 (|has| |#3| (|Finite|)) ELT)) (|before?| (#1# 6 T ELT)) (|basicSet| ((#36=(|Union| (|Record| (|:| |bas| $) (|:| |top| #4#)) #14#) #4# #17#) 115 T ELT) ((#36# #4# #11# #17#) 114 T ELT)) (|autoReduced?| ((#2# $ (|Mapping| #2# |#4| #4#)) 104 T ELT)) (|any?| (#29# 45 T ELT)) (|algebraicVariables| (#5# 87 T ELT)) (|algebraic?| (#27# 86 T ELT)) (= (#1# 8 T ELT)) (|#| (#32# 44 T ELT))) (((|TriangularSetCategory| |#1| |#2| |#3| |#4|) (|Category|) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |t#1| |t#2| |t#3|)) (T |TriangularSetCategory|)) -((|infRittWu?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|basicSet| (*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| (|Boolean|) *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |bas| *1) (|:| |top| (|List| *8)))) (|isDomain| *3 (|List| *8)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *8)))) (|basicSet| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Mapping| (|Boolean|) *9)) (|isDomain| *5 (|Mapping| (|Boolean|) *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *7 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 (|OrderedSet|)) (|isDomain| *2 (|Record| (|:| |bas| *1) (|:| |top| (|List| *9)))) (|isDomain| *3 (|List| *9)) (|ofCategory| *1 (|TriangularSetCategory| *6 *7 *8 *9)))) (|initials| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *6)))) (|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|NonNegativeInteger|)))) (|quasiComponent| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Record| (|:| |close| (|List| *6)) (|:| |open| (|List| *6)))))) (|normalized?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|normalized?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|reduced?| (*1 *2 *3 *1 *4) (AND (|isDomain| *4 (|Mapping| (|Boolean|) *3 *3)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *3)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 (|Boolean|)))) (|stronglyReduced?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *3 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|autoReduced?| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| (|Boolean|) *7 (|List| *7))) (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|Boolean|)))) (|stronglyReduced?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|headReduced?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|initiallyReduced?| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|Boolean|)))) (|reduce| (*1 *2 *2 *1 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|isDomain| *4 (|Mapping| (|Boolean|) *2 *2)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *2)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *5 *6 *7)))) (|rewriteSetWithReduction| (*1 *2 *2 *1 *3 *4) (AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| *8 *8 *8)) (|isDomain| *4 (|Mapping| (|Boolean|) *8 *8)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 (|IntegralDomain|)) (|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 (|OrderedSet|)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)))) (|stronglyReduce| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|headReduce| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|initiallyReduce| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|removeZero| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|collectQuasiMonic| (*1 *1 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *2 *3 *4)))) (|reduceByQuasiMonic| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|zeroSetSplit| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7)))) (|zeroSetSplitIntoTriangularSystems| (*1 *2 *3) (AND (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|OrderedSet|)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| (|Record| (|:| |close| *1) (|:| |open| (|List| *7))))) (|isDomain| *3 (|List| *7)) (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7)))) (|first| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|last| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|rest| (*1 *1 *1) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *3 (|OrderedAbelianMonoidSup|)) (|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *5 (|RecursivePolynomialCategory| *2 *3 *4)))) (|algebraicVariables| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|isDomain| *2 (|List| *5)))) (|algebraic?| (*1 *2 *3 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *6)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *4 *5 *3)) (|isDomain| *2 (|Boolean|)))) (|select| (*1 *2 *1 *3) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *2)) (|ofCategory| *4 (|IntegralDomain|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *3)))) (|extendIfCan| (*1 *1 *1 *2) (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *2 (|RecursivePolynomialCategory| *3 *4 *5)))) (|coHeight| (*1 *2 *1) (AND (|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *5 (|Finite|)) (|isDomain| *2 (|NonNegativeInteger|))))) -(|Join| (|PolynomialSetCategory| |t#1| |t#2| |t#3| |t#4|) (|ShallowlyMutableAggregate| |t#4|) (CATEGORY |domain| (SIGNATURE |infRittWu?| ((|Boolean|) $ $)) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |t#4|))) "failed") (|List| |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |basicSet| ((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |t#4|))) "failed") (|List| |t#4|) (|Mapping| (|Boolean|) |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |initials| ((|List| |t#4|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| (|List| |t#4|)) (|:| |open| (|List| |t#4|))) $)) (SIGNATURE |normalized?| ((|Boolean|) |t#4| $)) (SIGNATURE |normalized?| ((|Boolean|) $)) (SIGNATURE |reduced?| ((|Boolean|) |t#4| $ (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |stronglyReduced?| ((|Boolean|) |t#4| $)) (SIGNATURE |headReduced?| ((|Boolean|) |t#4| $)) (SIGNATURE |initiallyReduced?| ((|Boolean|) |t#4| $)) (SIGNATURE |autoReduced?| ((|Boolean|) $ (|Mapping| (|Boolean|) |t#4| (|List| |t#4|)))) (SIGNATURE |stronglyReduced?| ((|Boolean|) $)) (SIGNATURE |headReduced?| ((|Boolean|) $)) (SIGNATURE |initiallyReduced?| ((|Boolean|) $)) (SIGNATURE |reduce| (|t#4| |t#4| $ (|Mapping| |t#4| |t#4| |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |rewriteSetWithReduction| ((|List| |t#4|) (|List| |t#4|) $ (|Mapping| |t#4| |t#4| |t#4|) (|Mapping| (|Boolean|) |t#4| |t#4|))) (SIGNATURE |stronglyReduce| (|t#4| |t#4| $)) (SIGNATURE |headReduce| (|t#4| |t#4| $)) (SIGNATURE |initiallyReduce| (|t#4| |t#4| $)) (SIGNATURE |removeZero| (|t#4| |t#4| $)) (SIGNATURE |collectQuasiMonic| ($ $)) (SIGNATURE |reduceByQuasiMonic| (|t#4| |t#4| $)) (SIGNATURE |zeroSetSplit| ((|List| $) (|List| |t#4|))) (SIGNATURE |zeroSetSplitIntoTriangularSystems| ((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |t#4|)))) (|List| |t#4|))) (SIGNATURE |first| ((|Union| |t#4| "failed") $)) (SIGNATURE |last| ((|Union| |t#4| "failed") $)) (SIGNATURE |rest| ((|Union| $ "failed") $)) (SIGNATURE |algebraicVariables| ((|List| |t#3|) $)) (SIGNATURE |algebraic?| ((|Boolean|) |t#3| $)) (SIGNATURE |select| ((|Union| |t#4| "failed") $ |t#3|)) (SIGNATURE |extendIfCan| ((|Union| $ "failed") $ |t#4|)) (SIGNATURE |extend| ($ $ |t#4|)) (IF (|has| |t#3| (|Finite|)) (SIGNATURE |coHeight| ((|NonNegativeInteger|) $)) |%noBranch|))) -(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|Type|) . T)) +((|infRittWu?| (*1 *2 *1 *1) #1=(AND #2=(|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *6)) #3=(|ofCategory| *3 #4=(|IntegralDomain|)) #5=(|ofCategory| *4 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *5 #8=(|OrderedSet|)) #9=(|ofCategory| *6 #10=(|RecursivePolynomialCategory| *3 *4 *5)) #11=(|isDomain| *2 #12=(|Boolean|)))) (|basicSet| (*1 *2 *3 *4) (|partial| AND #13=(|isDomain| *4 (|Mapping| #12# *8 *8)) #14=(|ofCategory| *8 #15=(|RecursivePolynomialCategory| *5 *6 *7)) #16=(|ofCategory| *5 #4#) #17=(|ofCategory| *6 #6#) #18=(|ofCategory| *7 #8#) (|isDomain| *2 (|Record| #19=(|:| |bas| *1) (|:| |top| #20=(|List| *8)))) (|isDomain| *3 #20#) #21=(|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *8)))) (|basicSet| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *4 (|Mapping| #12# *9)) (|isDomain| *5 (|Mapping| #12# *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #4#) (|ofCategory| *7 #6#) (|ofCategory| *8 #8#) (|isDomain| *2 (|Record| #19# (|:| |top| #22=(|List| *9)))) (|isDomain| *3 #22#) (|ofCategory| *1 (|TriangularSetCategory| *6 *7 *8 *9)))) (|initials| #23=(*1 *2 *1) (AND #2# #3# #5# #7# #9# (|isDomain| *2 #24=(|List| *6)))) (|degree| #23# (AND #2# #3# #5# #7# #9# #25=(|isDomain| *2 (|NonNegativeInteger|)))) (|quasiComponent| #23# (AND #2# #3# #5# #7# #9# (|isDomain| *2 (|Record| (|:| |close| #24#) (|:| |open| #24#))))) (|normalized?| #26=(*1 *2 *3 *1) #27=(AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *3)) #28=(|ofCategory| *4 #4#) #29=(|ofCategory| *5 #6#) #30=(|ofCategory| *6 #8#) (|ofCategory| *3 #31=(|RecursivePolynomialCategory| *4 *5 *6)) #11#)) (|normalized?| #23# #1#) (|reduced?| (*1 *2 *3 *1 *4) (AND (|isDomain| *4 (|Mapping| #12# *3 *3)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *3)) #16# #17# #18# (|ofCategory| *3 #15#) #11#)) (|stronglyReduced?| #26# #27#) (|headReduced?| #26# #27#) (|initiallyReduced?| #26# #27#) (|autoReduced?| #32=(*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| #12# *7 #33=(|List| *7))) #34=(|ofCategory| *1 (|TriangularSetCategory| *4 *5 *6 *7)) #28# #29# #30# #35=(|ofCategory| *7 #31#) #11#)) (|stronglyReduced?| #23# #1#) (|headReduced?| #23# #1#) (|initiallyReduced?| #23# #1#) (|reduce| #36=(*1 *2 *2 *1 *3 *4) (AND (|isDomain| *3 (|Mapping| *2 *2 *2)) (|isDomain| *4 (|Mapping| #12# *2 *2)) (|ofCategory| *1 (|TriangularSetCategory| *5 *6 *7 *2)) #16# #17# #18# (|ofCategory| *2 #15#))) (|rewriteSetWithReduction| #36# (AND (|isDomain| *2 #20#) (|isDomain| *3 (|Mapping| *8 *8 *8)) #13# #21# #16# #17# #18# #14#)) (|stronglyReduce| #37=(*1 *2 *2 *1) #38=(AND #39=(|ofCategory| *1 (|TriangularSetCategory| *3 *4 *5 *2)) #3# #5# #7# #40=(|ofCategory| *2 #10#))) (|headReduce| #37# #38#) (|initiallyReduce| #37# #38#) (|removeZero| #37# #38#) (|collectQuasiMonic| #41=(*1 *1 *1) (AND #42=(|ofCategory| *1 (|TriangularSetCategory| *2 *3 *4 *5)) #43=(|ofCategory| *2 #4#) #44=(|ofCategory| *3 #6#) #45=(|ofCategory| *4 #8#) #46=(|ofCategory| *5 (|RecursivePolynomialCategory| *2 *3 *4)))) (|reduceByQuasiMonic| #37# #38#) (|zeroSetSplit| #47=(*1 *2 *3) (AND #48=(|isDomain| *3 #33#) #35# #28# #29# #30# (|isDomain| *2 (|List| *1)) #34#)) (|zeroSetSplitIntoTriangularSystems| #47# (AND #28# #29# #30# #35# (|isDomain| *2 (|List| (|Record| (|:| |close| *1) (|:| |open| #33#)))) #48# #34#)) (|first| #23# #49=(|partial| AND #39# #3# #5# #7# #40#)) (|last| #23# #49#) (|rest| #41# (|partial| AND #42# #43# #44# #45# #46#)) (|algebraicVariables| #23# (AND #2# #3# #5# #7# #9# (|isDomain| *2 (|List| *5)))) (|algebraic?| #26# (AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *6)) #28# #29# #50=(|ofCategory| *3 #8#) (|ofCategory| *6 #51=(|RecursivePolynomialCategory| *4 *5 *3)) #11#)) (|select| #32# (|partial| AND (|ofCategory| *1 (|TriangularSetCategory| *4 *5 *3 *2)) #28# #29# #50# (|ofCategory| *2 #51#))) (|extendIfCan| #52=(*1 *1 *1 *2) #49#) (|extend| #52# #38#) (|coHeight| #23# (AND #2# #3# #5# #7# #9# (|ofCategory| *5 (|Finite|)) #25#))) +(|Join| (|PolynomialSetCategory| |t#1| |t#2| |t#3| |t#4|) (|ShallowlyMutableAggregate| |t#4|) (CATEGORY |domain| (SIGNATURE |infRittWu?| (#1=(|Boolean|) $ $)) (SIGNATURE |basicSet| (#2=(|Union| (|Record| (|:| |bas| $) (|:| |top| #3=(|List| |t#4|))) #4="failed") #3# #5=(|Mapping| #1# |t#4| |t#4|))) (SIGNATURE |basicSet| (#2# #3# (|Mapping| #1# |t#4|) #5#)) (SIGNATURE |initials| (#3# $)) (SIGNATURE |degree| #6=((|NonNegativeInteger|) $)) (SIGNATURE |quasiComponent| ((|Record| (|:| |close| #3#) #7=(|:| |open| #3#)) $)) (SIGNATURE |normalized?| #8=(#1# |t#4| $)) (SIGNATURE |normalized?| #9=(#1# $)) (SIGNATURE |reduced?| (#1# |t#4| $ #5#)) (SIGNATURE |stronglyReduced?| #8#) (SIGNATURE |headReduced?| #8#) (SIGNATURE |initiallyReduced?| #8#) (SIGNATURE |autoReduced?| (#1# $ (|Mapping| #1# |t#4| #3#))) (SIGNATURE |stronglyReduced?| #9#) (SIGNATURE |headReduced?| #9#) (SIGNATURE |initiallyReduced?| #9#) (SIGNATURE |reduce| (|t#4| |t#4| $ #10=(|Mapping| |t#4| |t#4| |t#4|) #5#)) (SIGNATURE |rewriteSetWithReduction| (#3# #3# $ #10# #5#)) (SIGNATURE |stronglyReduce| #11=(|t#4| |t#4| $)) (SIGNATURE |headReduce| #11#) (SIGNATURE |initiallyReduce| #11#) (SIGNATURE |removeZero| #11#) (SIGNATURE |collectQuasiMonic| ($ $)) (SIGNATURE |reduceByQuasiMonic| #11#) (SIGNATURE |zeroSetSplit| ((|List| $) #3#)) (SIGNATURE |zeroSetSplitIntoTriangularSystems| ((|List| (|Record| (|:| |close| $) #7#)) #3#)) (SIGNATURE |first| #12=(#13=(|Union| |t#4| #4#) $)) (SIGNATURE |last| #12#) (SIGNATURE |rest| (#14=(|Union| $ #4#) $)) (SIGNATURE |algebraicVariables| ((|List| |t#3|) $)) (SIGNATURE |algebraic?| (#1# |t#3| $)) (SIGNATURE |select| (#13# $ |t#3|)) (SIGNATURE |extendIfCan| (#14# $ |t#4|)) (SIGNATURE |extend| ($ $ |t#4|)) (IF (|has| |t#3| (|Finite|)) (SIGNATURE |coHeight| #6#) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|Type|) . T)) ((|tube| (($ |#1| #1=(|List| (|List| (|Point| (|DoubleFloat|)))) #2=(|Boolean|)) 19 T ELT)) (|setClosed| ((#2# $ #2#) 18 T ELT)) (|open?| (#3=(#2# $) 17 T ELT)) (|listLoops| ((#1# $) 13 T ELT)) (|getCurve| ((|#1| $) 8 T ELT)) (|closed?| (#3# 15 T ELT))) (((|TubePlot| |#1|) (CATEGORY |domain| (SIGNATURE |getCurve| (|#1| $)) (SIGNATURE |listLoops| (#1=(|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |closed?| #2=(#3=(|Boolean|) $)) (SIGNATURE |open?| #2#) (SIGNATURE |setClosed| (#3# $ #3#)) (SIGNATURE |tube| ($ |#1| #1# #3#))) (|PlottableSpaceCurveCategory|)) (T |TubePlot|)) ((|tube| (*1 *1 *2 *3 *4) (AND (|isDomain| *3 #1=(|List| (|List| (|Point| (|DoubleFloat|))))) (|isDomain| *4 #2=(|Boolean|)) #3=(|isDomain| *1 (|TubePlot| *2)) #4=(|ofCategory| *2 #5=(|PlottableSpaceCurveCategory|)))) (|setClosed| (*1 *2 *1 *2) #6=(AND (|isDomain| *2 #2#) #7=(|isDomain| *1 (|TubePlot| *3)) #8=(|ofCategory| *3 #5#))) (|open?| #9=(*1 *2 *1) #6#) (|closed?| #9# #6#) (|listLoops| #9# (AND (|isDomain| *2 #1#) #7# #8#)) (|getCurve| #9# (AND #3# #4#))) @@ -3787,11 +3787,11 @@ NIL ((|squareFreePart| (($ $) 17 T ELT)) (|prime?| (((|Boolean|) $) 27 T ELT))) (((|UniqueFactorizationDomain&| |#1|) (CATEGORY |package| (SIGNATURE |squareFreePart| (|#1| |#1|)) (SIGNATURE |prime?| ((|Boolean|) |#1|))) (|UniqueFactorizationDomain|)) (T |UniqueFactorizationDomain&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 67 T ELT)) (|squareFree| (((|Factored| $) $) 68 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|prime?| (((|Boolean|) $) 69 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|lcm| (#5=($ $ $) 61 T ELT) (#6=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 59 T ELT)) (|gcd| (#5# 63 T ELT) (#6# 62 T ELT)) (|factor| (((|Factored| $) $) 66 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 31 T ELT) (($ $ $) 35 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (#4# 67 T ELT)) (|squareFree| (#5=((|Factored| $) $) 68 T ELT)) (|sample| (#6=($) 23 T CONST)) (|recip| ((#7=(|Union| $ "failed") $) 43 T ELT)) (|prime?| (#3# 69 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|lcm| (#8=($ $ $) 61 T ELT) (#9=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#10=(|SparseUnivariatePolynomial| $) #10# #10#) 59 T ELT)) (|gcd| (#8# 63 T ELT) (#9# 62 T ELT)) (|factor| (#5# 66 T ELT)) (|exquo| ((#7# $ $) 57 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #11=(|Integer|)) 42 T ELT) (#4# 58 T ELT)) (|characteristic| ((#12=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (#6# 46 T CONST)) (= (#1# 8 T ELT)) (- (#4# 30 T ELT) (#8# 29 T ELT)) (+ (#8# 18 T ELT)) (** (($ $ #13=(|PositiveInteger|)) 36 T ELT) (($ $ #12#) 44 T ELT)) (* (($ #13# $) 17 T ELT) (($ #12# $) 21 T ELT) (($ #11# $) 31 T ELT) (#8# 35 T ELT))) (((|UniqueFactorizationDomain|) (|Category|)) (T |UniqueFactorizationDomain|)) -((|prime?| (*1 *2 *1) (AND (|ofCategory| *1 (|UniqueFactorizationDomain|)) (|isDomain| *2 (|Boolean|)))) (|squareFree| (*1 *2 *1) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|UniqueFactorizationDomain|)))) (|squareFreePart| (*1 *1 *1) (|ofCategory| *1 (|UniqueFactorizationDomain|))) (|factor| (*1 *2 *1) (AND (|isDomain| *2 (|Factored| *1)) (|ofCategory| *1 (|UniqueFactorizationDomain|))))) -(|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |prime?| ((|Boolean|) $)) (SIGNATURE |squareFree| ((|Factored| $) $)) (SIGNATURE |squareFreePart| ($ $)) (SIGNATURE |factor| ((|Factored| $) $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|prime?| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|UniqueFactorizationDomain|)) (|isDomain| *2 (|Boolean|)))) (|squareFree| #1# #3=(AND (|isDomain| *2 (|Factored| *1)) #2#)) (|squareFreePart| (*1 *1 *1) #2#) (|factor| #1# #3#)) +(|Join| (|GcdDomain|) (CATEGORY |domain| (SIGNATURE |prime?| ((|Boolean|) $)) (SIGNATURE |squareFree| #1=((|Factored| $) $)) (SIGNATURE |squareFreePart| ($ $)) (SIGNATURE |factor| #1#))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|EntireRing|) . T) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| $) . T) ((|LinearSet| $) . T) ((|Module| $) . T) ((|Monoid|) . T) ((|RightLinearSet| $) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (($ $) NIL T ELT)) (|size| (((|NonNegativeInteger|)) NIL T ELT)) (|sample| #2=(#3=($) NIL T CONST)) (|random| (#3# NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT) #2#) (|max| #4# #2#) (|lookup| ((#5=(|PositiveInteger|) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|index| (($ #5#) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|bitior| #4#) (|bitand| #4#) (|before?| #1#) (|\\/| #4#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (|/\\| #4#)) (((|UInt16|) (|Join| (|OrderedFinite|) (|Logic|) (CATEGORY |domain| (SIGNATURE |bitand| #1=($ $ $)) (SIGNATURE |bitior| #1#) (SIGNATURE |sample| ($) |constant|)))) (T |UInt16|)) ((|bitand| #1=(*1 *1 *1 *1) #2=(|isDomain| *1 (|UInt16|))) (|bitior| #1# #2#) (|sample| (*1 *1) #2#)) @@ -3814,19 +3814,19 @@ NIL ((|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) 23 T ELT))) (((|UnivariateLaurentSeriesFunctions2| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)))) #1=(|Ring|) #1# #2=(|Symbol|) #2# |#1| |#2|) (T |UnivariateLaurentSeriesFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UnivariateLaurentSeries| *5 *7 *9)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofType| *7 #2=(|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6) (|isDomain| *2 (|UnivariateLaurentSeries| *6 *8 *10)) (|isDomain| *1 (|UnivariateLaurentSeriesFunctions2| *5 *6 *7 *8 *9 *10)) (|ofType| *8 #2#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#4=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 76 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|Integer|)) 125 T ELT) (($ $ #7# #7#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#8=($ $) 164 (|has| |#1| . #9=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|tan| (#10=($ $) 147 (|has| |#1| . #9#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #11=((|Field|))) ELT)) (|squareFree| (#12=((|Factored| $) $) 192 (|has| |#1| . #11#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #13=((|Algebra| (|Fraction| (|Integer|))))) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #11#) ELT)) (|sinh| (#8# 163 (|has| |#1| . #9#) ELT)) (|sin| (#10# 148 (|has| |#1| . #9#) ELT)) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) 202 T ELT)) (|sech| (#8# 162 (|has| |#1| . #9#) ELT)) (|sec| (#10# 149 (|has| |#1| . #9#) ELT)) (|sample| (#14=($) 23 T 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T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|Integer|) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) +((|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| #1=(|Integer|)) (|:| |c| *3)))) #2=(|ofCategory| *3 #3=(|Ring|)) #4=(|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *3)))) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 #1#)) #4# #2#)) (|rationalFunction| (*1 *2 *1 *3) #5=(AND (|isDomain| *3 #1#) (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *4)) (|ofCategory| *4 #3#) (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Fraction| (|Polynomial| *4))))) (|rationalFunction| (*1 *2 *1 *3 *3) #5#) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesCategory| *2)) (|ofCategory| *2 #3#) (|ofCategory| *2 #6=(|Algebra| (|Fraction| #1#))))) (|integrate| (*1 *1 *1 *2) (OR (AND #7=(|isDomain| *2 (|Symbol|)) #4# #2# (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| #1#)) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) #8=(|ofCategory| *3 #6#))) (AND #7# #4# #2# (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3))) (|has| *3 (SIGNATURE |integrate| (*3 *3 *2))) #8#))))) +(|Join| (|UnivariatePowerSeriesCategory| |t#1| #1=(|Integer|)) (CATEGORY |domain| (SIGNATURE |series| ($ (|Stream| (|Record| (|:| |k| #1#) (|:| |c| |t#1|))))) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |t#1| #1#) $)) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (SIGNATURE |rationalFunction| (#2=(|Fraction| (|Polynomial| |t#1|)) $ #1#)) (SIGNATURE |rationalFunction| (#2# $ #1# #1#))) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| #1#))) (PROGN (SIGNATURE |integrate| ($ $)) (IF (|has| |t#1| (SIGNATURE |integrate| (|t#1| |t#1| #3=(|Symbol|)))) (IF (|has| |t#1| (SIGNATURE |variables| ((|List| #3#) |t#1|))) #4=(SIGNATURE |integrate| ($ $ #3#)) |%noBranch|) |%noBranch|) (IF (|has| |t#1| #5=(|TranscendentalFunctionCategory|)) (IF (|has| |t#1| (|PrimitiveFunctionCategory|)) (IF (|has| |t#1| (|AlgebraicallyClosedFunctionSpace| #1#)) #4# |%noBranch|) |%noBranch|) |%noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE #5#)) |%noBranch|) (IF (|has| |t#1| #6=(|Field|)) (ATTRIBUTE #6#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| #1#)) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) . T) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) ((|zero?| (((|Boolean|) $) 12 T ELT)) (|retractIfCan| (((|Union| |#3| #1="failed") $) 17 T ELT) (((|Union| #2=(|Symbol|) #1#) $) NIL T ELT) (((|Union| #3=(|Fraction| #4=(|Integer|)) #1#) $) NIL T ELT) (((|Union| #4# #1#) $) NIL T ELT)) (|retract| ((|#3| $) 14 T ELT) ((#2# $) NIL T ELT) ((#3# $) NIL T ELT) ((#4# $) NIL T ELT))) (((|UnivariateLaurentSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |retractIfCan| ((|Union| #1=(|Integer|) #2="failed") |#1|)) (SIGNATURE |retract| (#1# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #3=(|Fraction| #1#) #2#) |#1|)) (SIGNATURE |retract| (#3# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4=(|Symbol|) #2#) |#1|)) (SIGNATURE |retract| (#4# |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| #2#) |#1|)) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) (|UnivariateLaurentSeriesConstructorCategory| |#2| |#3|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#2|)) (T 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ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePolynomial| (#14=((|Factored| #15=(|SparseUnivariatePolynomial| $)) #15#) 276 (|and| (|has| |#2| . #16=((|PolynomialFactorizationExplicit|))) (|has| |#1| . #5#)) ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #17=((|Field|))) ELT)) (|squareFree| (#18=((|Factored| $) $) 192 (|has| |#1| . #17#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #12#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #19=(|List| #15#) #20="failed") #19# #15#) 273 (|and| (|has| |#2| . #16#) (|has| |#1| . #5#)) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #17#) ELT)) (|sinh| (#11# 163 (|has| |#1| . #12#) ELT)) (|sin| (#13# 148 (|has| |#1| . #12#) ELT)) (|sign| (((|Integer|) $) 285 (|and| (|has| |#2| . #21=((|OrderedIntegralDomain|))) (|has| |#1| . #5#)) ELT)) (|series| (($ (|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|)))) 202 T ELT)) (|sech| (#11# 162 (|has| |#1| . #12#) ELT)) (|sec| (#13# 149 (|has| |#1| . #12#) ELT)) (|sample| (#22=($) 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#36#) (|:| |vec| (|Vector| |#2|))) . #40=(#38# #41=(|Vector| $))) 254 #6# ELT) ((#42=(|Record| (|:| |mat| #43=(|Matrix| #14#)) (|:| |vec| (|Vector| #14#))) . #40#) 253 #44=(|and| (|has| |#2| (|LinearlyExplicitRingOver| #14#)) #6#) ELT) ((#43# . #37#) 252 #44# ELT)) (|recip| ((#45=(|Union| $ #17#) $) 43 T ELT)) (|rationalFunction| ((#46=(|Fraction| (|Polynomial| |#1|)) $ #14#) 200 #11# ELT) ((#46# $ #14# #14#) 199 #11# ELT)) (|random| (#29# 269 #47=(|and| (|has| |#2| (|IntegerNumberSystem|)) #6#) ELT)) (|quo| (#35# 185 #6# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #48=(|List| $)) #49=(|:| |generator| $)) #48#) 180 #6# ELT)) (|prime?| (#3# 193 #6# ELT)) (|positive?| (#3# 283 #28# ELT)) (|pole?| (#3# 95 T ELT)) (|pi| (#29# 174 #18# ELT)) (|patternMatch| ((#50=(|PatternMatchResult| #51=(|Float|) . #52=($)) $ #53=(|Pattern| #51#) #50#) 261 (|and| (|has| |#2| (|PatternMatchable| #51#)) #6#) ELT) ((#54=(|PatternMatchResult| #14# . #52#) $ #55=(|Pattern| #14#) #54#) 260 (|and| (|has| |#2| (|PatternMatchable| #14#)) #6#) ELT)) (|order| (#27# 127 T ELT) ((#14# $ #14#) 126 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|numerator| (#12# 265 #6# ELT)) (|numer| (#4# 263 #6# ELT)) (|nthRoot| (#13# 145 #18# ELT)) (|nextItem| (#56=(#20# $) 297 #57=(|and| (|has| |#2| (|StepThrough|)) #6#) ELT)) (|negative?| (#3# 284 #28# ELT)) (|multiplyExponents| (#58=($ $ #59=(|PositiveInteger|)) 128 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #14#) $) 201 T ELT)) (|multiEuclidean| (((|Union| #48# #17#) #48# $) 189 #6# ELT)) (|monomial?| (#3# 84 T ELT)) (|monomial| (($ |#1| #14#) 83 T ELT) (($ $ #8# #14#) 98 T ELT) (($ $ #7# (|List| #14#)) 97 T ELT)) (|min| (#35# 292 #60=(|and| (|has| |#2| (|OrderedSet|)) #6#) ELT)) (|max| (#35# 291 #60# ELT)) (|map| (($ (|Mapping| |#1| |#1|) . #61=($)) 88 T ELT) (($ #62=(|Mapping| |#2| |#2|) . #61#) 245 #6# ELT)) (|log| (#12# 171 #18# ELT)) (|leftReducedSystem| ((#36# . #63=(#41#)) 257 #6# ELT) ((#39# . #64=(#41# $)) 256 #6# ELT) ((#42# . #64#) 251 #44# ELT) ((#43# . #63#) 250 #44# ELT)) (|leadingMonomial| (#12# 86 T ELT)) (|leadingCoefficient| (#65=(|#1| $) 87 T ELT)) (|lcm| (#66=($ #48#) 178 #6# ELT) (#35# 177 #6# ELT)) (|laurent| (($ #14# |#2|) 304 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#12# 194 #6# ELT)) (|integrate| (#12# 198 #18# ELT) (#67=($ $ #10#) 197 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #14#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) #18#) (AND (|has| |#1| (SIGNATURE |variables| (#68=(|List| #10#) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #10#))) #18#)) ELT)) (|init| (#29# 298 #57# CONST)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#22# #22# #22#) 179 #6# ELT)) (|gcd| (#66# 176 #6# ELT) (#35# 175 #6# ELT)) (|fractionPart| (#12# 268 #5# ELT)) (|floor| (#4# 271 #47# ELT)) (|factorSquareFreePolynomial| (#21# 274 #23# ELT)) (|factorPolynomial| (#21# 275 #23# ELT)) (|factor| (#25# 190 #6# ELT)) 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ELT)) (|differentiate| (#79=($ $ #62# #76#) 247 #6# ELT) (#80=($ $ #62#) 246 #6# ELT) (#12# 112 #81=(OR (|and| (|has| |#2| (|DifferentialSpace|)) #6#) #82=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) (#83=($ $ #76#) 110 #81# ELT) (#67# 120 #84=(OR (|and| (|has| |#2| (|PartialDifferentialSpace| #10#)) #6#) (AND (|has| |#1| (|PartialDifferentialRing| #10#)) #82#)) ELT) (#85=($ $ #68#) 118 #84# ELT) (#86=($ $ #10# #76#) 117 #84# ELT) (#87=($ $ #68# (|List| #76#)) 116 #84# ELT)) (|denominator| (#12# 266 #6# ELT)) (|denom| (#4# 264 #6# ELT)) (|degree| (#27# 85 T ELT)) (|csch| (#12# 161 #18# ELT)) (|csc| (#12# 150 #18# ELT)) (|coth| (#12# 160 #18# ELT)) (|cot| (#12# 151 #18# ELT)) (|cosh| (#12# 159 #18# ELT)) (|cos| (#12# 152 #18# ELT)) (|convert| (((|DoubleFloat|) . #88=($)) 282 #89=(|and| (|has| |#2| (|RealConstant|)) #6#) ELT) ((#51# . #88#) 281 #89# ELT) ((#90=(|InputForm|) . #88#) 280 (|and| (|has| |#2| (|ConvertibleTo| #90#)) #6#) ELT) ((#53# . #88#) 259 (|and| (|has| |#2| (|ConvertibleTo| #53#)) #6#) ELT) ((#55# . #88#) 258 (|and| (|has| |#2| (|ConvertibleTo| #55#)) #6#) ELT)) (|conditionP| (((|Union| #41# #17#) #38#) 272 (|and| #91=(|and| (|has| $ #92=(|CharacteristicNonZero|)) #24#) #6#) ELT)) (|complete| (#12# 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #14#) 42 T ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 305 T ELT) (($ #10#) 279 #33# ELT) (($ #19#) 79 #18# ELT) (#12# 71 #11# ELT)) (|coefficient| (#77# 81 T ELT)) (|charthRoot| (#56# 70 (OR (|and| (OR (|has| |#2| #92#) #91#) #6#) (|has| |#1| #92#)) ELT)) (|characteristic| ((#76#) 41 T CONST)) (|center| (#65# 129 T ELT)) (|ceiling| (#4# 270 #47# ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#12# 170 #18# ELT)) (|atan| (#12# 158 #18# ELT)) (|associates?| (#1# 75 #11# ELT)) (|asinh| (#12# 169 #18# ELT)) (|asin| (#12# 157 #18# ELT)) (|asech| (#12# 168 #18# ELT)) (|asec| (#12# 156 #18# ELT)) (|approximate| (#77# 123 (AND #71# (|has| |#1| (SIGNATURE |coerce| (|#1| #10#)))) ELT)) (|annihilate?| (#1# 34 T ELT)) (|acsch| (#12# 167 #18# ELT)) (|acsc| (#12# 155 #18# ELT)) (|acoth| (#12# 166 #18# ELT)) (|acot| (#12# 154 #18# ELT)) (|acosh| (#12# 165 #18# ELT)) (|acos| (#12# 153 #18# ELT)) (|abs| (#12# 286 #28# ELT)) (|Zero| (#29# 24 T CONST)) (|One| (#29# 46 T CONST)) (D (#79# 249 #6# ELT) (#80# 248 #6# ELT) (#12# 111 #81# ELT) (#83# 109 #81# ELT) (#67# 119 #84# ELT) (#85# 115 #84# ELT) (#86# 114 #84# ELT) (#87# 113 #84# ELT)) (>= (#1# 290 #60# ELT)) (> (#1# 288 #60# ELT)) (= (#1# 8 T ELT)) (<= (#1# 289 #60# ELT)) (< (#1# 287 #60# ELT)) (/ (#93=($ $ |#1|) 80 #6# ELT) (#35# 196 #6# ELT) (($ |#2| |#2|) 262 #6# ELT)) (- (#12# 30 T ELT) (#35# 29 T ELT)) (+ (#35# 18 T ELT)) (** (#58# 36 T ELT) (#83# 44 T ELT) (#13# 195 #6# ELT) (#35# 173 #18# ELT) (#94=($ $ #19#) 144 #18# ELT)) (* (($ #59# $) 17 T ELT) (($ #76# $) 21 T ELT) (#34# 31 T ELT) (#35# 35 T ELT) (#93# 90 T ELT) (($ |#1| . #95=($)) 89 T ELT) (#78# 237 #6# ELT) (($ |#2| . #95#) 236 #6# ELT) (($ #19# . #95#) 78 #18# ELT) (#94# 77 #18# ELT))) (((|UnivariateLaurentSeriesConstructorCategory| |#1| |#2|) (|Category|) (|Ring|) (|UnivariateTaylorSeriesCategory| |t#1|)) (T |UnivariateLaurentSeriesConstructorCategory|)) -((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)) (|isDomain| *2 (|Integer|)))) (|laurent| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *4)))) (|taylorRep| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|removeZeroes| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *2 *3)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *2)))) (|removeZeroes| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateTaylorSeriesCategory| *3)))) (|taylor| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3)))) (|taylorIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateTaylorSeriesCategory| *3))))) -(|Join| (|UnivariateLaurentSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |laurent| ($ (|Integer|) |t#2|)) (SIGNATURE |degree| ((|Integer|) $)) (SIGNATURE |taylorRep| (|t#2| $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ (|Integer|) $)) (SIGNATURE |taylor| (|t#2| $)) (SIGNATURE |taylorIfCan| ((|Union| |t#2| "failed") $)) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|QuotientFieldCategory| |t#2|)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| |#2|) |has| |#1| (|Field|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| |#2| |#2|) |has| |#1| (|Field|)) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicNonZero|))) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicZero|))) (|has| |#1| (|CharacteristicZero|))) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #3=(|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|DoubleFloat|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| (|Float|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialDomain| $) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialExtension| |#2|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialSpace|) OR (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#1| (|Field|)) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| |#2| $) AND (|has| |#1| (|Field|)) (|has| |#2| (|Eltable| |#2| |#2|))) ((|Eltable| $ $) |has| (|Integer|) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Evalable| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|Field|) |has| |#1| (|Field|)) ((|FullyEvalableOver| |#2|) |has| |#1| (|Field|)) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|FullyPatternMatchable| |#2|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|Functorial| |#2|) |has| |#1| (|Field|)) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| (|Symbol|) |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| |#2|) |has| |#1| (|Field|)) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| #4=(|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| |#2|) |has| |#1| (|Field|)) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| |#2|) |has| |#1| (|Field|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| #4#) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#2|) |has| |#1| (|Field|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|OrderedAbelianGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianSemiGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedCancellationAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedIntegralDomain|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedRing|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedSet|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|)))) ((|OrderedType|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|)))) ((|PartialDifferentialDomain| $ #5=(|Symbol|)) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialRing| (|Symbol|)) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PartialDifferentialSpace| #5#) OR (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|))))) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Integer|)))) ((|Patternable| |#2|) |has| |#1| (|Field|)) ((|PolynomialFactorizationExplicit|) AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|QuotientFieldCategory| |#2|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RealConstant|) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|RetractableTo| (|Fraction| (|Integer|))) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| (|Integer|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| #3#) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| |#2|) |has| |#1| (|Field|)) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| |#2|) |has| |#1| (|Field|)) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) AND (|has| |#1| (|Field|)) (|has| |#2| (|StepThrough|))) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariateLaurentSeriesCategory| |#1|) . T) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) +((|degree| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *4)) #3=(|ofCategory| *3 #4=(|Ring|)) #5=(|ofCategory| *4 #6=(|UnivariateTaylorSeriesCategory| *3)) #7=(|isDomain| *2 (|Integer|)))) (|laurent| (*1 *1 *2 *3) (AND #7# (|ofCategory| *4 #4#) (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *4)))) (|taylorRep| #1# #8=(AND #9=(|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *3 *2)) #3# #10=(|ofCategory| *2 #6#))) (|removeZeroes| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateLaurentSeriesConstructorCategory| *2 *3)) (|ofCategory| *2 #4#) (|ofCategory| *3 (|UnivariateTaylorSeriesCategory| *2)))) (|removeZeroes| (*1 *1 *2 *1) (AND #7# #2# #3# #5#)) (|taylor| #1# #8#) (|taylorIfCan| #1# (|partial| AND #9# #3# #10#))) +(|Join| (|UnivariateLaurentSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |laurent| ($ #1=(|Integer|) |t#2|)) (SIGNATURE |degree| (#1# $)) (SIGNATURE |taylorRep| #2=(|t#2| $)) (SIGNATURE |removeZeroes| ($ $)) (SIGNATURE |removeZeroes| ($ #1# $)) (SIGNATURE |taylor| #2#) (SIGNATURE |taylorIfCan| ((|Union| |t#2| "failed") $)) (IF (|has| |t#1| (|Field|)) (ATTRIBUTE (|QuotientFieldCategory| |t#2|)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Integer|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| #1#)) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| |#2|) |has| |#1| (|Field|)) ((|Algebra| $) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| |#2| |#2|) |has| |#1| (|Field|)) ((|BiModule| $ $) OR (|has| |#1| (|CommutativeRing|)) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|)))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|CharacteristicNonZero|)) (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicNonZero|)))) ((|CharacteristicZero|) OR (|has| |#1| (|CharacteristicZero|)) (AND (|has| |#1| (|Field|)) (|has| |#2| (|CharacteristicZero|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|)))) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|))))) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #3=(|Symbol|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|CommutativeRing|)) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|)))) ((|ConvertibleTo| (|DoubleFloat|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| #4=(|Float|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| #4#)) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| #1#)) AND (|has| |#1| (|Field|)) (|has| |#2| (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialDomain| $) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|DifferentialExtension| |#2|) |has| |#1| (|Field|)) ((|DifferentialRing|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|DifferentialSpace|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialRing|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|DifferentialSpace|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|)))) ((|DifferentialSpaceExtension| |#2|) |has| |#1| (|Field|)) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| |#2| $) AND (|has| |#1| (|Field|)) (|has| |#2| (|Eltable| |#2| |#2|))) ((|Eltable| $ $) . T) ((|EntireRing|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Evalable| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|Field|) |has| |#1| (|Field|)) ((|FullyEvalableOver| |#2|) |has| |#1| (|Field|)) ((|FullyLinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|FullyPatternMatchable| |#2|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|Functorial| |#2|) |has| |#1| (|Field|)) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|InnerEvalable| #3# |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|InnerEvalable| (|Symbol|) |#2|))) ((|InnerEvalable| |#2| |#2|) AND (|has| |#1| (|Field|)) (|has| |#2| (|Evalable| |#2|))) ((|IntegralDomain|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| |#2|) |has| |#1| (|Field|)) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #1#) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| |#2|) |has| |#1| (|Field|)) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| |#2|) |has| |#1| (|Field|)) ((|LinearSet| $) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|LinearlyExplicitRingOver| #1#) AND (|has| |#1| (|Field|)) (|has| |#2| (|LinearlyExplicitRingOver| (|Integer|)))) ((|LinearlyExplicitRingOver| |#2|) |has| |#1| (|Field|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#2|) |has| |#1| (|Field|)) ((|Module| $) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) (|has| |#1| (|IntegralDomain|))) ((|Monoid|) . T) ((|OrderedAbelianGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedAbelianSemiGroup|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedCancellationAbelianMonoid|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedIntegralDomain|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedRing|) AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) ((|OrderedSet|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|)))) ((|OrderedType|) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedSet|)))) ((|PartialDifferentialDomain| $ #3#) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) ((|PartialDifferentialRing| #3#) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) ((|PartialDifferentialSpace| #3#) OR (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialRing| (|Symbol|)))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PartialDifferentialSpace| (|Symbol|)))) (AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Integer|) |#1|))))) ((|PatternMatchable| #4#) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Float|)))) ((|PatternMatchable| #1#) AND (|has| |#1| (|Field|)) (|has| |#2| (|PatternMatchable| (|Integer|)))) ((|Patternable| |#2|) |has| |#1| (|Field|)) ((|PolynomialFactorizationExplicit|) AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|QuotientFieldCategory| |#2|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RealConstant|) AND (|has| |#1| (|Field|)) (|has| |#2| (|RealConstant|))) ((|RetractableTo| #2#) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| #1#) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Integer|)))) ((|RetractableTo| #3#) AND (|has| |#1| (|Field|)) (|has| |#2| (|RetractableTo| (|Symbol|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| |#2|) |has| |#1| (|Field|)) ((|RightLinearSet| $) OR (|has| |#1| (|CommutativeRing|)) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|)))) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| |#2|) |has| |#1| (|Field|)) ((|RightModule| $) OR (|has| |#1| (|CommutativeRing|)) (AND (|has| |#1| (|Field|)) (|has| |#2| (|OrderedIntegralDomain|))) (AND (|has| |#1| (|Field|)) (|has| |#2| (|PolynomialFactorizationExplicit|)))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) AND (|has| |#1| (|Field|)) (|has| |#2| (|StepThrough|))) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariateLaurentSeriesCategory| |#1|) . T) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 83 T ELT)) (|wholePart| (#5=(|#2| $) NIL #6=(AND #7=(|has| |#1| (|Field|)) (|has| |#2| (|EuclideanDomain|))) ELT)) (|variables| ((#8=(|List| #9=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| (#10=(#11=(|Symbol|) $) 102 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #13=(#14=($ $) NIL #12# ELT)) (|unit?| (#4# NIL #12# ELT)) (|truncate| (#15=($ $ #16=(|Integer|)) 111 T ELT) (($ $ #16# #16#) 114 T ELT)) (|terms| ((#17=(|Stream| (|Record| (|:| |k| #16#) (|:| |c| |#1|))) $) 51 T ELT)) (|taylorRep| (#5# 11 T ELT)) (|taylorIfCan| (#18=((|Union| |#2| #19="failed") $) 35 T ELT)) (|taylor| (#5# 36 T ELT)) (|tanh| (#14# 208 #20=(|has| |#1| (|Algebra| #21=(|Fraction| #16#))) ELT)) (|tan| (#14# 184 #20# ELT)) (|subtractIfCan| ((#22=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePolynomial| #23=(((|Factored| 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ELT) ((#39# . #71=(#41# $)) 152 #38# ELT) ((#42# . #71#) 147 T ELT) ((#43# . #70#) 146 T ELT)) (|leadingMonomial| (#12# 169 T ELT)) (|leadingCoefficient| (#32# 168 T ELT)) (|lcm| (#72=($ #47#) 109 #18# ELT) (#15# 108 #18# ELT)) (|latex| (((|String|) $) 11 T ELT)) (|karatsubaDivide| ((#65# $ #5#) 266 T ELT)) (|isTimes| (#73=(#61# $) 129 T ELT)) (|isPlus| (#73# 130 T ELT)) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #5#)) #21#) $) 128 T ELT)) (|integrate| (#12# 250 #74=(|has| |#1| (|Algebra| #27#)) ELT)) (|init| (#24# 237 #60# CONST)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|ground?| (#3# 185 T ELT)) (|ground| (#32# 186 T ELT)) (|gcdPolynomial| ((#9# #9# #9#) 110 #18# ELT)) (|gcd| (#72# 107 #18# ELT) (#15# 106 #18# ELT)) (|factorSquareFreePolynomial| (#16# 117 #17# ELT)) (|factorPolynomial| (#16# 116 #17# ELT)) (|factor| (#19# 114 #17# ELT)) (|extendedEuclidean| (((|Union| (|Record| #75=(|:| |coef1| $) #76=(|:| |coef2| $)) #21#) $ $ $) 248 #22# ELT) (((|Record| #75# #76# #48#) $ $) 247 #22# ELT)) (|exquo| ((#44# $ |#1|) 193 #11# ELT) (#77=(#44# $ $) 101 #11# ELT)) (|expressIdealMember| (((|Maybe| #47#) #47# $) 241 #22# ELT)) (|eval| (($ $ (|List| #78=(|Equation| $))) 164 T ELT) (($ $ #78#) 163 T ELT) (($ $ $ $) 162 T ELT) (($ $ #47# #47#) 161 T ELT) (($ $ #7# |#1|) 160 T ELT) (($ $ #6# #79=(|List| |#1|)) 159 T ELT) (($ $ #7# $) 158 T ELT) (($ $ #6# #47#) 157 T ELT)) (|euclideanSize| (#13# 243 #22# ELT)) (|elt| ((|#1| $ |#1|) 282 T ELT) (#15# 281 T ELT) ((#80=(|Fraction| $) #80# #80#) 259 #11# ELT) ((|#1| #80# |#1|) 251 #22# ELT) ((#80# $ #80#) 239 #11# ELT)) (|divideExponents| ((#44# $ #5#) 268 T ELT)) (|divide| (#66# 244 #22# ELT)) (|discriminant| (#49# 122 #34# ELT) (#32# 261 #34# ELT)) (|differentiate| (#63# 53 T ELT) (#62# 52 T ELT) (#81=($ $ #6#) 51 T ELT) (#49# 49 T ELT) (#12# 280 T ELT) (#23# 278 T ELT) (#82=($ $ #69#) 276 T ELT) (#83=($ $ #69# #5#) 275 T ELT) (($ $ #69# $) 262 T ELT) (#84=($ $ #85=(|Symbol|)) 236 #86=(|has| |#1| (|PartialDifferentialSpace| #85#)) ELT) (#87=($ $ #88=(|List| #85#)) 234 #86# ELT) (#89=($ $ #85# #5#) 233 #86# ELT) (#90=($ $ #88# #64#) 232 #86# ELT)) (|degree| (#13# 170 T ELT) (#67# 145 T ELT) (#68# 144 T ELT)) (|convert| ((#54# . #91=($)) 97 (AND (|has| #7# #92=(|ConvertibleTo| #54#)) (|has| |#1| #92#)) ELT) ((#57# . #91#) 96 (AND (|has| #7# #93=(|ConvertibleTo| #57#)) (|has| |#1| #93#)) ELT) ((#94=(|InputForm|) . #91#) 95 (AND (|has| #7# #95=(|ConvertibleTo| #94#)) (|has| |#1| #95#)) ELT)) (|content| (#32# 194 #18# ELT) (#49# 121 #18# ELT)) (|conditionP| (((|Union| #41# #21#) #37#) 119 #96=(|and| (|has| $ #97=(|CharacteristicNonZero|)) #17#) ELT)) (|composite| (#77# 256 #11# ELT) (((|Union| #80# #21#) #80# $) 255 #11# ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #28#) 42 T ELT) (($ |#1|) 184 T ELT) (($ #7#) 154 T ELT) (($ #27#) 93 (OR #29# #74#) ELT) (#12# 100 #11# ELT)) (|coefficients| ((#79# $) 187 T ELT)) (|coefficient| ((|#1| $ #5#) 174 T ELT) (#62# 143 T ELT) (#63# 142 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|integrate| ($ $)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|NonNegativeInteger|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|BasicType|) . T) ((|BiModule| #2# #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #3=(|SingletonAsOrderedSet|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|ConvertibleTo| (|InputForm|)) AND (|has| |#1| (|ConvertibleTo| (|InputForm|))) (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|InputForm|)))) ((|ConvertibleTo| (|Pattern| (|Float|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Float|)))) (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Float|))))) ((|ConvertibleTo| (|Pattern| (|Integer|))) AND (|has| |#1| (|ConvertibleTo| (|Pattern| (|Integer|)))) (|has| (|SingletonAsOrderedSet|) (|ConvertibleTo| (|Pattern| (|Integer|))))) ((|DifferentialDomain| $) . T) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|DifferentialSpaceExtension| |#1|) . T) ((|Eltable| (|Fraction| $) (|Fraction| $)) |has| |#1| (|IntegralDomain|)) ((|Eltable| |#1| |#1|) . T) ((|Eltable| $ $) . T) ((|EntireRing|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| #1#) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|InnerEvalable| #3# |#1|) . T) ((|InnerEvalable| #3# $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #4=(|Integer|)) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|LinearlyExplicitRingOver| #4#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3#) . T) ((|PartialDifferentialDomain| $ #5=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PartialDifferentialRing| #3#) . T) ((|PartialDifferentialRing| (|Symbol|)) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #3#) . T) ((|PartialDifferentialSpace| #5#) OR (|has| |#1| (|PartialDifferentialSpace| (|Symbol|))) (|has| |#1| (|PartialDifferentialRing| (|Symbol|)))) ((|PatternMatchable| (|Float|)) AND (|has| |#1| (|PatternMatchable| (|Float|))) (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Float|)))) ((|PatternMatchable| (|Integer|)) AND (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| (|SingletonAsOrderedSet|) (|PatternMatchable| (|Integer|)))) ((|PolynomialCategory| |#1| #1# #3#) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #3#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) +((|vectorise| #1=(*1 *2 *1 *3) (AND #2=(|isDomain| *3 #3=(|NonNegativeInteger|)) #4=(|ofCategory| *1 (|UnivariatePolynomialCategory| *4)) #5=(|ofCategory| *4 #6=(|Ring|)) (|isDomain| *2 (|Vector| *4)))) (|makeSUP| #7=(*1 *2 *1) (AND #8=(|ofCategory| *1 (|UnivariatePolynomialCategory| *3)) #9=(|ofCategory| *3 #6#) #10=(|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|unmakeSUP| (*1 *1 *2) (AND #10# #9# #8#)) (|multiplyExponents| #11=(*1 *1 *1 *2) #12=(AND #13=(|isDomain| *2 #3#) #8# #9#)) (|divideExponents| #11# (|partial| AND #13# #8# #9#)) (|monicDivide| #14=(*1 *2 *1 *1) (AND #9# #15=(|isDomain| *2 (|Record| #16=(|:| |quotient| *1) #17=(|:| |remainder| *1))) #8#)) (|karatsubaDivide| #1# (AND #2# #5# #15# #4#)) (|shiftRight| #11# #12#) (|shiftLeft| #11# #12#) (|pseudoRemainder| #18=(*1 *1 *1 *1) (AND #19=(|ofCategory| *1 (|UnivariatePolynomialCategory| *2)) #20=(|ofCategory| *2 #6#))) (|differentiate| (*1 *1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 *3)) #8# #9#)) (|discriminant| #7# #21=(AND #19# #20# (|ofCategory| *2 (|CommutativeRing|)))) (|resultant| #14# #21#) (|elt| (*1 *2 *2 *2) (AND #22=(|isDomain| *2 #23=(|Fraction| *1)) #8# #9# #24=(|ofCategory| *3 #25=(|IntegralDomain|)))) (|order| #14# (AND #8# #9# #24# #13#)) (|subResultantGcd| #18# #26=(AND #19# #20# #27=(|ofCategory| *2 #25#))) (|composite| #18# (|partial| AND #19# #20# #27#)) (|composite| (*1 *2 *2 *1) (|partial| AND #22# #8# #9# #24#)) (|pseudoQuotient| #18# #26#) (|pseudoDivide| #14# (AND #24# #9# (|isDomain| *2 (|Record| (|:| |coef| *3) #16# #17#)) #8#)) (|separate| #14# (AND (|ofCategory| *3 (|GcdDomain|)) #9# (|isDomain| *2 (|Record| (|:| |primePart| *1) (|:| |commonPart| *1))) #8#)) (|elt| (*1 *2 *3 *2) (AND (|isDomain| *3 #23#) #19# #20# (|ofCategory| *2 (|Field|)))) (|integrate| (*1 *1 *1) (AND #19# #20# (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|))))))) +(|Join| (|PolynomialCategory| |t#1| #1=(|NonNegativeInteger|) (|SingletonAsOrderedSet|)) (|Eltable| |t#1| |t#1|) (|Eltable| $ $) (|DifferentialRing|) (|DifferentialExtension| |t#1|) (CATEGORY |domain| (SIGNATURE |vectorise| ((|Vector| |t#1|) $ #1#)) (SIGNATURE |makeSUP| (#2=(|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |unmakeSUP| ($ #2#)) (SIGNATURE |multiplyExponents| #3=($ $ #1#)) (SIGNATURE |divideExponents| (#4=(|Union| $ #5="failed") $ #1#)) (SIGNATURE |monicDivide| (#6=(|Record| #7=(|:| |quotient| $) #8=(|:| |remainder| $)) $ $)) (SIGNATURE |karatsubaDivide| (#6# $ #1#)) (SIGNATURE |shiftRight| #3#) (SIGNATURE |shiftLeft| #3#) (SIGNATURE |pseudoRemainder| #9=($ $ $)) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#1| |t#1|) $)) (IF (|has| |t#1| #10=(|StepThrough|)) (ATTRIBUTE #10#) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (PROGN (SIGNATURE |discriminant| (|t#1| $)) (SIGNATURE |resultant| (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|Eltable| #11=(|Fraction| $) #11#)) (SIGNATURE |elt| (#11# #11# #11#)) (SIGNATURE |order| (#1# $ $)) (SIGNATURE |subResultantGcd| #9#) (SIGNATURE |composite| (#4# $ $)) (SIGNATURE |composite| ((|Union| #11# #5#) #11# $)) (SIGNATURE |pseudoQuotient| #9#) (SIGNATURE |pseudoDivide| ((|Record| (|:| |coef| |t#1|) #7# #8#) $ $))) |%noBranch|) (IF (|has| |t#1| (|GcdDomain|)) (SIGNATURE |separate| ((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (|Field|)) (PROGN (ATTRIBUTE (|EuclideanDomain|)) (ATTRIBUTE |additiveValuation|) (SIGNATURE |elt| (|t#1| #11# |t#1|))) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (SIGNATURE |integrate| ($ $)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|NonNegativeInteger|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| #3=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #2# #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Algebra| (|Fraction| (|Integer|)))) (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|))))) ((|CoercibleFrom| #3#) . T) ((|CoercibleFrom| #4=(|SingletonAsOrderedSet|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|DifferentialDomain| $) . T) ((|DifferentialExtension| |#1|) . T) ((|DifferentialRing|) . T) ((|DifferentialSpace|) . T) ((|DifferentialSpaceExtension| |#1|) . T) ((|Eltable| #5=(|Fraction| $) #5#) |has| |#1| (|IntegralDomain|)) ((|Eltable| |#1| |#1|) . T) ((|Eltable| $ $) . T) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Evalable| $) . T) ((|FiniteAbelianMonoidRing| |#1| #1#) . T) ((|FullyLinearlyExplicitRingOver| |#1|) . T) ((|FullyRetractableTo| |#1|) . T) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|GcdDomain|)) ((|InnerEvalable| #4# |#1|) . T) ((|InnerEvalable| #4# $) . T) ((|InnerEvalable| $ $) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #3#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| #3#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|LinearlyExplicitRingOver| #3#) |has| |#1| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#1|) . T) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4#) . T) ((|PartialDifferentialDomain| $ #6=(|Symbol|)) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PartialDifferentialRing| #4#) . T) ((|PartialDifferentialRing| #6#) |has| |#1| (|PartialDifferentialRing| (|Symbol|))) ((|PartialDifferentialSpace| #4#) . T) ((|PartialDifferentialSpace| #6#) OR (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (|PartialDifferentialSpace| (|Symbol|)))) ((|PolynomialCategory| |#1| #1# #4#) . T) ((|PolynomialFactorizationExplicit|) |has| |#1| (|PolynomialFactorizationExplicit|)) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RetractableTo| #2#) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| #3#) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| #4#) . T) ((|RetractableTo| |#1|) . T) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|StepThrough|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|PolynomialFactorizationExplicit|))) ((|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) 22 T ELT))) (((|UnivariatePolynomialCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#4| (|Mapping| |#3| |#1|) |#2|))) #1=(|Ring|) (|UnivariatePolynomialCategory| |#1|) #1# (|UnivariatePolynomialCategory| |#3|)) (T |UnivariatePolynomialCategoryFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|UnivariatePolynomialCategory| *6)) (|isDomain| *1 (|UnivariatePolynomialCategoryFunctions2| *5 *4 *6 *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *5))))) ((|variables| ((#1=(|List| #2=(|SingletonAsOrderedSet|)) $) 34 T ELT)) (|reductum| (#3=($ $) 31 T ELT)) (|monomial| (($ |#2| |#3|) NIL T ELT) (($ $ #2# |#3|) 28 T ELT) (($ $ #1# (|List| |#3|)) 27 T ELT)) (|leadingMonomial| (#3# 14 T ELT)) (|leadingCoefficient| ((|#2| $) 12 T ELT)) (|degree| ((|#3| $) 10 T ELT))) (((|UnivariatePowerSeriesCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |variables| (#1=(|List| #2=(|SingletonAsOrderedSet|)) |#1|)) (SIGNATURE |monomial| (|#1| |#1| #1# (|List| |#3|))) (SIGNATURE |monomial| (|#1| |#1| #2# |#3|)) (SIGNATURE |reductum| #3=(|#1| |#1|)) (SIGNATURE |monomial| (|#1| |#2| |#3|)) (SIGNATURE |degree| (|#3| |#1|)) (SIGNATURE |leadingMonomial| #3#) (SIGNATURE |leadingCoefficient| (|#2| |#1|))) (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Ring|) (|OrderedAbelianMonoid|)) (T |UnivariatePowerSeriesCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| (((|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #4=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #4#) ELT)) (|unit?| ((#5=(|Boolean|) $) 76 (|has| |#1| . #4#) ELT)) (|truncate| (($ $ |#2|) 125 T ELT) (($ $ |#2| |#2|) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 131 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#6=($) 23 T CONST)) (|reductum| (#7=($ $) 82 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|order| ((|#2| $) 127 T ELT) ((|#2| $ |#2|) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|monomial?| (((|Boolean|) $) 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT) (($ $ #3# |#2|) 98 T ELT) (($ $ (|List| #3#) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#7# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (($ $ |#2|) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 72 (|has| |#1| . #4#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) ELT)) (|elt| ((|#1| $ |#2|) 132 T ELT) (($ $ $) 108 (|has| |#2| (|SemiGroup|)) ELT)) (|differentiate| (($ $ #8=(|Symbol|)) 120 (AND (|has| |#1| . #9=((|PartialDifferentialRing| (|Symbol|)))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 118 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10=(#11=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12=((|List| #11#))) 116 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13=($)) 112 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (|degree| ((|#2| $) 85 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ #15=(|Fraction| (|Integer|))) 79 (|has| |#1| . #16=((|Algebra| #15#))) ELT) (($ $) 71 (|has| |#1| . #4#) ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 81 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#5# $ $) 75 (|has| |#1| . #4#) ELT)) (|approximate| ((|#1| $ |#2|) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) (|has| |#1| (SIGNATURE |coerce| (|#1| (|Symbol|))))) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#6# 24 T CONST)) (|One| (($) 46 T CONST)) (D (($ $ #8#) 119 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#)) 115 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ #8# . #10#) 114 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ $ (|List| #8#) . #12#) 113 (AND (|has| |#1| . #9#) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (($ . #13#) 111 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT) (#14# 109 (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 80 (|has| |#1| (|Field|)) ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #17#) 89 T ELT) (($ #15# . #17#) 78 (|has| |#1| . #16#) ELT) (($ $ #15#) 77 (|has| |#1| . #16#) ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|variables| ((#4=(|List| #5=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#6=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 #7=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#8=($ $) 74 #7# ELT)) (|unit?| (#3# 76 #7# ELT)) (|truncate| (#9=($ $ |#2|) 125 T ELT) (($ $ |#2| |#2|) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) 131 T ELT)) (|subtractIfCan| ((#10=(|Maybe| $) $ $) 26 T ELT)) (|sample| (#11=($) 23 T CONST)) (|reductum| (#8# 82 T ELT)) (|recip| ((#12=(|Union| $ "failed") $) 43 T ELT)) (|pole?| (#3# 95 T ELT)) (|order| (#13=(|#2| $) 127 T ELT) ((|#2| $ |#2|) 126 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|multiplyExponents| (#14=($ $ #15=(|PositiveInteger|)) 128 T ELT)) (|monomial?| (#3# 84 T ELT)) (|monomial| (($ |#1| |#2|) 83 T ELT) (($ $ #5# |#2|) 98 T ELT) (($ $ #4# (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|leadingMonomial| (#8# 86 T ELT)) (|leadingCoefficient| (#16=(|#1| $) 87 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (#9# 122 T ELT)) (|exquo| ((#12# $ $) 72 #7# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 #17=(|has| |#1| (SIGNATURE ** (|#1| |#1| |#2|))) ELT)) (|elt| (#18=(|#1| $ |#2|) 132 T ELT) (#19=($ $ $) 108 (|has| |#2| (|SemiGroup|)) ELT)) (|differentiate| (#20=($ $ #6#) 120 #21=(AND (|has| |#1| (|PartialDifferentialRing| #6#)) #22=(|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ELT) (#23=($ $ #24=(|List| #6#)) 118 #21# ELT) (#25=($ $ #6# #26=(|NonNegativeInteger|)) 117 #21# ELT) (#27=($ $ #24# (|List| #26#)) 116 #21# ELT) (#8# 112 #22# ELT) (#28=($ $ #26#) 110 #22# ELT)) (|degree| (#13# 85 T ELT)) (|complete| (#8# 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #29=(|Integer|)) 42 T ELT) (($ #30=(|Fraction| #29#)) 79 #31=(|has| |#1| (|Algebra| #30#)) ELT) (#8# 71 #7# ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| (#18# 81 T ELT)) (|charthRoot| ((#10# $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#26#) 41 T CONST)) (|center| (#16# 129 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 75 #7# ELT)) (|approximate| (#18# 123 (AND #17# (|has| |#1| 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*2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|approximate| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3)) (|ofCategory| *3 (|OrderedAbelianMonoid|)) (|has| *2 (SIGNATURE ** (*2 *2 *3))) (|has| *2 (SIGNATURE |coerce| (*2 (|Symbol|)))) (|ofCategory| *2 (|Ring|)))) (|extend| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|)))) (|eval| (*1 *2 *1 *3) (AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|OrderedAbelianMonoid|)) (|has| *3 (SIGNATURE ** (*3 *3 *4))) (|isDomain| *2 (|Stream| *3))))) -(|Join| (|PowerSeriesCategory| |t#1| |t#2| (|SingletonAsOrderedSet|)) (|Eltable| |t#2| |t#1|) (CATEGORY |domain| (SIGNATURE |terms| ((|Stream| (|Record| (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (SIGNATURE |variable| ((|Symbol|) $)) (SIGNATURE |center| (|t#1| $)) (SIGNATURE |multiplyExponents| ($ $ (|PositiveInteger|))) (SIGNATURE |order| (|t#2| $)) (SIGNATURE |order| (|t#2| $ |t#2|)) (SIGNATURE |truncate| ($ $ |t#2|)) (SIGNATURE |truncate| ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (SIGNATURE |coerce| (|t#1| (|Symbol|)))) (IF (|has| |t#1| (SIGNATURE ** (|t#1| |t#1| |t#2|))) (SIGNATURE |approximate| (|t#1| $ |t#2|)) |%noBranch|) |%noBranch|) (SIGNATURE |extend| ($ $ |t#2|)) (IF (|has| |t#2| (|SemiGroup|)) (ATTRIBUTE (|Eltable| $ $)) |%noBranch|) (IF (|has| |t#1| (SIGNATURE * (|t#1| |t#2| |t#1|))) (PROGN (ATTRIBUTE (|DifferentialRing|)) (IF (|has| |t#1| (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (SIGNATURE ** (|t#1| |t#1| |t#2|))) (SIGNATURE |eval| ((|Stream| |t#1|) $ |t#1|)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|Eltable| |#2| |#1|) . T) ((|Eltable| $ $) |has| |#2| (|SemiGroup|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #2=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PartialDifferentialRing| #2#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PartialDifferentialSpace| #2#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PowerSeriesCategory| |#1| |#2| (|SingletonAsOrderedSet|)) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|terms| #1=(*1 *2 *1) (AND #2=(|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *4)) #3=(|ofCategory| *3 #4=(|Ring|)) #5=(|ofCategory| *4 #6=(|OrderedAbelianMonoid|)) (|isDomain| *2 (|Stream| (|Record| (|:| |k| *4) (|:| |c| *3)))))) (|variable| #1# (AND #2# #3# #5# (|isDomain| *2 #7=(|Symbol|)))) (|center| #1# (AND #8=(|ofCategory| *1 (|UnivariatePowerSeriesCategory| *2 *3)) #9=(|ofCategory| *3 #6#) #10=(|ofCategory| *2 #4#))) (|multiplyExponents| #11=(*1 *1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) #2# #3# #5#)) (|order| #1# #12=(AND (|ofCategory| *1 (|UnivariatePowerSeriesCategory| *3 *2)) #3# (|ofCategory| *2 #6#))) (|order| (*1 *2 *1 *2) #12#) (|truncate| #11# #12#) (|truncate| (*1 *1 *1 *2 *2) #12#) (|approximate| #13=(*1 *2 *1 *3) (AND #8# #9# (|has| *2 (SIGNATURE ** (*2 *2 *3))) (|has| *2 (SIGNATURE |coerce| (*2 #7#))) #10#)) (|extend| #11# #12#) (|eval| #13# (AND #2# #3# #5# (|has| *3 (SIGNATURE ** (*3 *3 *4))) (|isDomain| *2 (|Stream| *3))))) +(|Join| (|PowerSeriesCategory| |t#1| |t#2| (|SingletonAsOrderedSet|)) (|Eltable| |t#2| |t#1|) (CATEGORY |domain| (SIGNATURE |terms| ((|Stream| (|Record| (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (SIGNATURE |variable| (#1=(|Symbol|) $)) (SIGNATURE |center| (|t#1| $)) (SIGNATURE |multiplyExponents| ($ $ (|PositiveInteger|))) (SIGNATURE |order| (|t#2| $)) (SIGNATURE |order| (|t#2| $ |t#2|)) (SIGNATURE |truncate| #2=($ $ |t#2|)) (SIGNATURE |truncate| ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (SIGNATURE |coerce| (|t#1| #1#))) (IF #3=(|has| |t#1| (SIGNATURE ** (|t#1| |t#1| |t#2|))) (SIGNATURE |approximate| (|t#1| $ |t#2|)) |%noBranch|) |%noBranch|) (SIGNATURE |extend| #2#) (IF (|has| |t#2| (|SemiGroup|)) (ATTRIBUTE (|Eltable| $ $)) |%noBranch|) (IF (|has| |t#1| (SIGNATURE * (|t#1| |t#2| |t#1|))) (PROGN (ATTRIBUTE (|DifferentialRing|)) (IF (|has| |t#1| #4=(|PartialDifferentialRing| #1#)) (ATTRIBUTE #4#) |%noBranch|)) |%noBranch|) (IF #3# (SIGNATURE |eval| ((|Stream| |t#1|) $ |t#1|)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| |#2|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| |#2| |#1|))) ((|Eltable| |#2| |#1|) . T) ((|Eltable| $ $) |has| |#2| (|SemiGroup|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| |#2| |#1|)))) ((|PowerSeriesCategory| |#1| |#2| (|SingletonAsOrderedSet|)) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|squareFreePart| ((|#2| |#2|) 12 T ELT)) (|squareFree| (((|Factored| |#2|) |#2|) 14 T ELT)) (|BumInSepFFE| ((#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#) 30 T ELT))) (((|UnivariatePolynomialSquareFree| |#1| |#2|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |squareFreePart| (|#2| |#2|)) (SIGNATURE |BumInSepFFE| (#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#))) #2=(|IntegralDomain|) (|Join| (|UnivariatePolynomialCategory| |#1|) #2# (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) (T |UnivariatePolynomialSquareFree|)) ((|BumInSepFFE| #1=(*1 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (|Integer|)))) (|ofCategory| *4 #2=(|Join| (|UnivariatePolynomialCategory| *3) #3=(|IntegralDomain|) #4=(CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) #5=(|ofCategory| *3 #3#) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *4)))) (|squareFreePart| #1# (AND #5# (|isDomain| *1 (|UnivariatePolynomialSquareFree| *3 *2)) (|ofCategory| *2 #2#))) (|squareFree| (*1 *2 *3) (AND (|ofCategory| *4 #3#) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|UnivariatePolynomialSquareFree| *4 *3)) (|ofCategory| *3 (|Join| (|UnivariatePolynomialCategory| *4) #3# #4#))))) @@ -3885,19 +3885,19 @@ NIL ((|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) 24 T ELT))) (((|UnivariatePuiseuxSeriesFunctions2| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |map| ((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)))) #1=(|Ring|) #1# #2=(|Symbol|) #2# |#1| |#2|) (T |UnivariatePuiseuxSeriesFunctions2|)) ((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|UnivariatePuiseuxSeries| *5 *7 *9)) 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CONST)) (|rem| (#19=($ $ $) 186 #15# ELT)) (|reductum| (#8# 82 T ELT)) (|recip| ((#20=(|Union| $ #21="failed") $) 43 T ELT)) (|quo| (#19# 185 #15# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #22=(|List| $)) #23=(|:| |generator| $)) #22#) 180 #15# ELT)) (|prime?| (#3# 193 #15# ELT)) (|pole?| (#3# 95 T ELT)) (|pi| (#18# 174 #13# ELT)) (|order| (#24=(#10# $) 127 T ELT) ((#10# $ #10#) 126 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|nthRoot| (#25=($ $ #11#) 145 #13# ELT)) (|multiplyExponents| (#26=($ $ #27=(|PositiveInteger|)) 128 T ELT) (#9# 199 T ELT)) (|multiEuclidean| (((|Union| #22# #21#) #22# $) 189 #15# ELT)) (|monomial?| (#3# 84 T ELT)) (|monomial| (($ |#1| #10#) 83 T ELT) (($ $ #5# #10#) 98 T ELT) (($ $ #4# (|List| #10#)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 88 T ELT)) (|log| (#8# 171 #13# ELT)) (|leadingMonomial| (#8# 86 T ELT)) (|leadingCoefficient| (#28=(|#1| $) 87 T ELT)) (|lcm| (#29=($ #22#) 178 #15# ELT) (#19# 177 #15# ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#8# 194 #15# ELT)) (|integrate| (#8# 198 #13# ELT) (#30=($ $ #6#) 197 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #11#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) #13#) (AND (|has| |#1| (SIGNATURE |variables| (#31=(|List| #6#) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #6#))) #13#)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#32=(|SparseUnivariatePolynomial| $) #32# #32#) 179 #15# ELT)) (|gcd| (#29# 176 #15# ELT) (#19# 175 #15# ELT)) (|factor| (#16# 190 #15# ELT)) (|extendedEuclidean| (((|Union| (|Record| #33=(|:| |coef1| $) #34=(|:| |coef2| $)) #21#) $ $ $) 188 #15# ELT) (((|Record| #33# #34# #23#) $ $) 187 #15# ELT)) (|extend| (#9# 122 T ELT)) (|exquo| ((#20# $ $) 72 #7# ELT)) (|expressIdealMember| (((|Maybe| #22#) #22# $) 181 #15# ELT)) (|exp| (#8# 172 #13# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 #35=(|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) 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T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Fraction| (|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|Fraction| (|Integer|)) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) +((|series| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *3 (|Stream| (|Record| (|:| |k| #1=(|Fraction| #2=(|Integer|))) (|:| |c| *4)))) (|ofCategory| *4 #3=(|Ring|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *4)))) (|multiplyExponents| #4=(*1 *1 *1 *2) (AND (|isDomain| *2 #1#) #5=(|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *3)) #6=(|ofCategory| *3 #3#))) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesCategory| *2)) (|ofCategory| *2 #3#) (|ofCategory| *2 #7=(|Algebra| #1#)))) (|integrate| #4# (OR (AND #8=(|isDomain| *2 (|Symbol|)) #5# #6# (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| #2#)) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) #9=(|ofCategory| *3 #7#))) (AND #8# #5# #6# (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3))) (|has| *3 (SIGNATURE |integrate| (*3 *3 *2))) #9#))))) +(|Join| (|UnivariatePowerSeriesCategory| |t#1| #1=(|Fraction| #2=(|Integer|))) (CATEGORY |domain| (SIGNATURE |series| ($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| #1#) (|:| |c| |t#1|))))) (SIGNATURE |multiplyExponents| ($ $ #1#)) (IF (|has| |t#1| (|Algebra| #1#)) (PROGN (SIGNATURE |integrate| ($ $)) (IF (|has| |t#1| (SIGNATURE |integrate| (|t#1| |t#1| #3=(|Symbol|)))) (IF (|has| |t#1| (SIGNATURE |variables| ((|List| #3#) |t#1|))) #4=(SIGNATURE |integrate| ($ $ #3#)) |%noBranch|) |%noBranch|) (IF (|has| |t#1| #5=(|TranscendentalFunctionCategory|)) (IF (|has| |t#1| (|PrimitiveFunctionCategory|)) (IF (|has| |t#1| (|AlgebraicallyClosedFunctionSpace| #2#)) #4# |%noBranch|) |%noBranch|) |%noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE #5#)) |%noBranch|) (IF (|has| |t#1| #6=(|Field|)) (ATTRIBUTE #6#) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Fraction| #2=(|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) . T) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) ((|zero?| (((|Boolean|) $) 12 T ELT)) (|retractIfCan| (((|Union| |#3| "failed") $) 17 T ELT)) (|retract| ((|#3| $) 14 T ELT))) (((|UnivariatePuiseuxSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |retractIfCan| ((|Union| |#3| "failed") |#1|)) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) (|UnivariatePuiseuxSeriesConstructorCategory| |#2| |#3|) (|Ring|) (|UnivariateLaurentSeriesCategory| |#2|)) (T |UnivariatePuiseuxSeriesConstructorCategory&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| #3=(|SingletonAsOrderedSet|)) $) 96 T ELT)) (|variable| ((#4=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 74 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 76 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|Fraction| #8=(|Integer|))) 125 T ELT) (($ $ #7# #7#) 124 T ELT)) (|terms| (((|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#9=($ $) 164 (|has| |#1| . #10=((|Algebra| #7#))) ELT)) (|tan| (#11=($ $) 147 (|has| |#1| . #10#) ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #12=((|Field|))) ELT)) (|squareFree| (#13=((|Factored| $) $) 192 (|has| |#1| . #12#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #10#) ELT)) (|sizeLess?| (((|Boolean|) $ $) 182 (|has| |#1| . #12#) ELT)) (|sinh| (#9# 163 (|has| |#1| . #10#) ELT)) (|sin| (#11# 148 (|has| |#1| . #10#) ELT)) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| #7#) (|:| |c| |#1|)))) 200 T ELT)) (|sech| (#9# 162 (|has| |#1| . #10#) ELT)) (|sec| (#11# 149 (|has| |#1| . #10#) ELT)) (|sample| (#14=($) 23 T CONST)) (|retractIfCan| (((|Union| |#2| "failed") $) 213 T ELT)) (|retract| ((|#2| $) 214 T ELT)) (|rem| (#15=($ $ $) 186 (|has| |#1| . #12#) ELT)) (|reductum| (#16=($ $) 82 T ELT)) (|recip| 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ELT)) (|log| (#21=($ $) 171 (|has| |#1| . #10#) ELT)) (|leadingMonomial| (#16# 86 T ELT)) (|leadingCoefficient| ((|#1| $) 87 T ELT)) (|lcm| (#22=($ (|List| $)) 178 (|has| |#1| . #12#) ELT) (#23=($ $ $) 177 (|has| |#1| . #12#) ELT)) (|laurentRep| ((|#2| $) 209 T ELT)) (|laurentIfCan| (((|Union| |#2| "failed") $) 207 T ELT)) (|laurent| ((|#2| $) 208 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 194 (|has| |#1| . #12#) ELT)) (|integrate| (($ $) 198 (|has| |#1| . #10#) ELT) (($ $ #24=(|Symbol|)) 197 (OR (AND (|has| |#1| (|AlgebraicallyClosedFunctionSpace| #8#)) (|has| |#1| (|PrimitiveFunctionCategory|)) (|has| |#1| (|TranscendentalFunctionCategory|)) (|has| |#1| . #10#)) (AND (|has| |#1| (SIGNATURE |variables| ((|List| #24#) |#1|))) (|has| |#1| (SIGNATURE |integrate| (|#1| |#1| #24#))) (|has| |#1| . #10#))) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#25=(|SparseUnivariatePolynomial| $) #25# #25#) 179 (|has| |#1| . #12#) ELT)) (|gcd| (#22# 176 (|has| |#1| 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. #36=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 71 (|has| |#1| . #5#) ELT)) (|coefficient| ((|#1| $ #7#) 81 T ELT)) (|charthRoot| (((|Maybe| $) $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|center| ((|#1| $) 129 T ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#37=($ $) 170 (|has| |#1| . #10#) ELT)) (|atan| (#38=($ $) 158 (|has| |#1| . #10#) ELT)) (|associates?| ((#6# $ $) 75 (|has| |#1| . #5#) ELT)) (|asinh| (#37# 169 (|has| |#1| . #10#) ELT)) (|asin| (#38# 157 (|has| |#1| . #10#) ELT)) (|asech| (#37# 168 (|has| |#1| . #10#) ELT)) (|asec| (#38# 156 (|has| |#1| . #10#) ELT)) (|approximate| ((|#1| $ #7#) 123 (AND (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) (|has| |#1| (SIGNATURE |coerce| (|#1| #4#)))) ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|acsch| (#37# 167 (|has| |#1| . #10#) ELT)) (|acsc| (#38# 155 (|has| |#1| . #10#) ELT)) (|acoth| (#37# 166 (|has| |#1| . #10#) ELT)) (|acot| (#38# 154 (|has| |#1| . 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$) 26 T ELT)) (|squareFreePart| (#8# 191 #15=(|has| |#1| (|Field|)) ELT)) (|squareFree| (#16=((|Factored| $) $) 192 #15# ELT)) (|sqrt| (#8# 146 #13# ELT)) (|sizeLess?| (#1# 182 #15# ELT)) (|sinh| (#8# 163 #13# ELT)) (|sin| (#8# 148 #13# ELT)) (|series| (($ #17=(|NonNegativeInteger|) #12#) 200 T ELT)) (|sech| (#8# 162 #13# ELT)) (|sec| (#8# 149 #13# ELT)) (|sample| (#18=($) 23 T CONST)) (|retractIfCan| (#19=((|Union| |#2| #20="failed") $) 213 T ELT)) (|retract| (#21=(|#2| $) 214 T ELT)) (|rem| (#22=($ $ $) 186 #15# ELT)) (|reductum| (#8# 82 T ELT)) (|recip| ((#23=(|Union| $ #20#) $) 43 T ELT)) (|rationalPower| (#24=(#10# $) 210 T ELT)) (|quo| (#22# 185 #15# ELT)) (|puiseux| (($ #10# |#2|) 211 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) 180 #15# ELT)) (|prime?| (#3# 193 #15# ELT)) (|pole?| (#3# 95 T ELT)) (|pi| (#18# 174 #13# ELT)) (|order| (#24# 127 T ELT) ((#10# $ #10#) 126 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) 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#6#)))) ELT)) (|annihilate?| (#1# 34 T ELT)) (|acsch| (#8# 167 #13# ELT)) (|acsc| (#8# 155 #13# ELT)) (|acoth| (#8# 166 #13# ELT)) (|acot| (#8# 154 #13# ELT)) (|acosh| (#8# 165 #13# ELT)) (|acos| (#8# 153 #13# ELT)) (|Zero| (#18# 24 T CONST)) (|One| (#18# 46 T CONST)) (D (#32# 119 #39# ELT) (#41# 115 #39# ELT) (#42# 114 #39# ELT) (#43# 113 #39# ELT) (#8# 111 #40# ELT) (#44# 109 #40# ELT)) (= (#1# 8 T ELT)) (/ (#45=($ $ |#1|) 80 #15# ELT) (#22# 196 #15# ELT)) (- (#8# 30 T ELT) (#22# 29 T ELT)) (+ (#22# 18 T ELT)) (** (#28# 36 T ELT) (#44# 44 T ELT) (#27# 195 #15# ELT) (#22# 173 #13# ELT) (#9# 144 #13# ELT)) (* (($ #29# $) 17 T ELT) (($ #17# $) 21 T ELT) (($ #11# . #46=($)) 31 T ELT) (#22# 35 T ELT) (#45# 90 T ELT) (($ |#1| . #46#) 89 T ELT) (($ #10# . #46#) 78 #13# ELT) (#9# 77 #13# ELT))) (((|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|Category|) (|Ring|) (|UnivariateLaurentSeriesCategory| |t#1|)) (T |UnivariatePuiseuxSeriesConstructorCategory|)) -((|degree| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|puiseux| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Fraction| (|Integer|))) (|ofCategory| *4 (|Ring|)) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateLaurentSeriesCategory| *4)))) (|rationalPower| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *4 (|UnivariateLaurentSeriesCategory| *3)) (|isDomain| *2 (|Fraction| (|Integer|))))) (|laurentRep| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))) (|laurent| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3)))) (|laurentIfCan| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|UnivariateLaurentSeriesCategory| *3))))) -(|Join| (|UnivariatePuiseuxSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |puiseux| ($ (|Fraction| (|Integer|)) |t#2|)) (SIGNATURE |rationalPower| ((|Fraction| (|Integer|)) $)) (SIGNATURE |laurentRep| (|t#2| $)) (SIGNATURE |degree| ((|Fraction| (|Integer|)) $)) (SIGNATURE |laurent| (|t#2| $)) (SIGNATURE |laurentIfCan| ((|Union| |t#2| "failed") $)))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Fraction| (|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|Fraction| (|Integer|)) (|SemiGroup|)) ((|EntireRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Join|) . T) ((|LeftLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Module| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|))) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) OR (|has| |#1| (|Field|)) (|has| |#1| (|Algebra| (|Fraction| (|Integer|))))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|Field|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T) ((|UnivariatePuiseuxSeriesCategory| |#1|) . T)) +((|degree| #1=(*1 *2 *1) #2=(AND (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *4)) #3=(|ofCategory| *3 #4=(|Ring|)) (|ofCategory| *4 #5=(|UnivariateLaurentSeriesCategory| *3)) #6=(|isDomain| *2 (|Fraction| (|Integer|))))) (|puiseux| (*1 *1 *2 *3) (AND #6# (|ofCategory| *4 #4#) (|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *4 *3)) (|ofCategory| *3 (|UnivariateLaurentSeriesCategory| *4)))) (|rationalPower| #1# #2#) (|laurentRep| #1# #7=(AND #8=(|ofCategory| *1 (|UnivariatePuiseuxSeriesConstructorCategory| *3 *2)) #3# #9=(|ofCategory| *2 #5#))) (|laurent| #1# #7#) (|laurentIfCan| #1# (|partial| AND #8# #3# #9#))) +(|Join| (|UnivariatePuiseuxSeriesCategory| |t#1|) (|RetractableTo| |t#2|) (|CoercibleFrom| |t#2|) (CATEGORY |domain| (SIGNATURE |puiseux| ($ #1=(|Fraction| (|Integer|)) |t#2|)) (SIGNATURE |rationalPower| #2=(#1# $)) (SIGNATURE |laurentRep| #3=(|t#2| $)) (SIGNATURE |degree| #2#) (SIGNATURE |laurent| #3#) (SIGNATURE |laurentIfCan| ((|Union| |t#2| "failed") $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|Fraction| #2=(|Integer|))) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #1# #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| |#2|) . T) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|))) ((|DivisionRing|) |has| |#1| (|Field|)) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) . T) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|EuclideanDomain|) |has| |#1| (|Field|)) ((|Field|) |has| |#1| (|Field|)) ((|Functorial| |#1|) . T) ((|GcdDomain|) |has| |#1| (|Field|)) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|Fraction| (|Integer|)) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|PrincipalIdealDomain|) |has| |#1| (|Field|)) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RetractableTo| |#2|) . T) ((|RightLinearSet| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #1#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UniqueFactorizationDomain|) |has| |#1| (|Field|)) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T) ((|UnivariatePuiseuxSeriesCategory| |#1|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#8=(|Symbol|) $) 104 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#5# NIL #9# ELT)) (|truncate| (#12=($ $ #13=(|Fraction| #14=(|Integer|))) 116 T ELT) (($ $ #13# #13#) 118 T ELT)) (|terms| ((#15=(|Stream| (|Record| (|:| |k| #13#) (|:| |c| |#1|))) $) 54 T ELT)) (|tanh| (#11# 192 #16=(|has| |#1| (|Algebra| #13#)) ELT)) (|tan| (#11# 168 #16# ELT)) (|subtractIfCan| ((#17=(|Maybe| $) $ $) NIL T ELT)) (|squareFreePart| (#11# NIL #18=(|has| |#1| (|Field|)) ELT)) (|squareFree| #19=(((|Factored| $) $) NIL #18# ELT)) (|sqrt| (#11# NIL #16# ELT)) (|sizeLess?| (#2# NIL #18# ELT)) (|sinh| (#11# 188 #16# ELT)) (|sin| (#11# 164 #16# ELT)) (|series| (($ #20=(|NonNegativeInteger|) #15#) 65 T ELT)) (|sech| (#11# 196 #16# ELT)) (|sec| (#11# 172 #16# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (#22=((|Union| |#2| #23="failed") $) NIL T ELT)) (|retract| (#24=(|#2| $) NIL T ELT)) (|rem| #25=(#26=($ $ $) NIL #18# ELT)) (|reductum| #27=(#11# NIL T ELT)) (|recip| ((#28=(|Union| $ #23#) $) 85 T ELT)) (|rationalPower| (#29=(#13# $) 13 T ELT)) (|quo| #25#) (|puiseux| (($ #13# |#2|) 11 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #30=(|List| $)) #31=(|:| |generator| $)) #30#) NIL #18# ELT)) (|prime?| (#5# NIL #18# ELT)) (|pole?| (#5# 74 T ELT)) (|pi| (#21# NIL #16# ELT)) (|order| (#29# 113 T ELT) ((#13# $ #13#) 114 T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#32=($ $ #14#) NIL #16# ELT)) (|multiplyExponents| (#33=($ $ #34=(|PositiveInteger|)) 130 T ELT) (#12# 128 T ELT)) (|multiEuclidean| (((|Union| #30# #23#) #30# $) NIL #18# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #13#) 33 T ELT) (($ $ #7# #13#) NIL T ELT) (($ $ #6# (|List| #13#)) NIL T ELT)) (|map| (($ 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(|extend| (#12# 122 T ELT)) (|exquo| ((#28# $ $) NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #30#) #30# $) NIL #18# ELT)) (|exp| (#11# 160 #16# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 98 #42=(|has| |#1| (SIGNATURE ** (|#1| |#1| #13#))) ELT)) (|euclideanSize| ((#20# $) NIL #18# ELT)) (|elt| (#43=(|#1| $ #13#) 108 T ELT) (#26# 94 (|has| #13# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #18# ELT)) (|differentiate| (#37# 138 #44=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #45=(|has| |#1| (SIGNATURE * (|#1| #13# |#1|)))) ELT) #46=(($ $ #38#) NIL #44# ELT) #47=(($ $ #8# #20#) NIL #44# ELT) #48=(($ $ #38# (|List| #20#)) NIL #44# ELT) (#11# 134 #45# ELT) #49=(#50=($ $ #20#) NIL #45# ELT)) (|degree| (#29# 16 T ELT)) (|csch| (#11# 198 #16# ELT)) (|csc| (#11# 174 #16# ELT)) (|coth| (#11# 194 #16# ELT)) (|cot| (#11# 170 #16# ELT)) (|cosh| (#11# 190 #16# ELT)) (|cos| (#11# 166 #16# ELT)) (|complete| (#11# 120 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) 37 T ELT) (($ |#1|) 27 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 34 T ELT) (($ #13#) 139 #16# ELT) #10#) (|coefficient| (#43# 107 T ELT)) (|charthRoot| ((#17# $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#20#) 127 T CONST)) (|center| (#35# 106 T ELT)) (|before?| #1#) (|atanh| (#11# 204 #16# ELT)) (|atan| (#11# 180 #16# ELT)) (|associates?| (#2# NIL #9# ELT)) (|asinh| (#11# 200 #16# ELT)) (|asin| (#11# 176 #16# ELT)) (|asech| (#11# 208 #16# ELT)) (|asec| (#11# 184 #16# ELT)) (|approximate| (#43# NIL (AND #42# (|has| |#1| (SIGNATURE |coerce| (|#1| #8#)))) ELT)) (|annihilate?| #1#) (|acsch| (#11# 210 #16# ELT)) (|acsc| (#11# 186 #16# ELT)) (|acoth| (#11# 206 #16# ELT)) (|acot| (#11# 182 #16# ELT)) (|acosh| (#11# 202 #16# ELT)) (|acos| (#11# 178 #16# ELT)) (|Zero| (#21# 21 T CONST)) (|One| (#21# 17 T CONST)) (D (#37# NIL #44# ELT) #46# #47# #48# (#11# NIL #45# ELT) #49#) (= (#2# 72 T ELT)) (/ (#51=($ $ |#1|) NIL #18# ELT) (#26# 100 #18# ELT)) (- (#11# 142 T ELT) (#26# 78 T ELT)) (+ (#26# 76 T ELT)) (** (#33# NIL T ELT) (#50# 82 T ELT) (#32# 157 #18# ELT) (#26# NIL #16# ELT) (#12# 158 #16# ELT)) (* (($ #34# $) NIL T ELT) (($ #20# $) NIL T ELT) (($ #14# . #52=($)) NIL T ELT) (#26# 80 T ELT) (#51# NIL T ELT) (($ |#1| . #52#) 137 T ELT) (($ #13# . #52#) NIL #16# ELT) (#12# NIL #16# ELT))) (((|UnivariatePuiseuxSeriesConstructor| |#1| |#2|) (|UnivariatePuiseuxSeriesConstructorCategory| |#1| |#2|) (|Ring|) (|UnivariateLaurentSeriesCategory| |#1|)) (T |UnivariatePuiseuxSeriesConstructor|)) NIL @@ -3907,11 +3907,11 @@ NIL ((|value| (#1=(|#2| $) 34 T ELT)) (|third| (#1# 18 T ELT)) (|tail| (#2=($ $) 43 T ELT)) (|split!| (($ $ (|Integer|)) 78 T ELT)) (|setvalue!| (#3=(|#2| $ |#2|) 75 T ELT)) (|setlast!| (#3# 71 T ELT)) (|setelt| ((|#2| $ #4="value" |#2|) NIL T ELT) ((|#2| $ #5="first" |#2|) 64 T ELT) (($ $ #6="rest" $) 68 T ELT) ((|#2| $ #7="last" |#2|) 66 T ELT)) (|setchildren!| (($ $ #8=(|List| $)) 74 T ELT)) (|second| (#1# 17 T ELT)) (|rest| (#2# NIL T ELT) (#9=($ $ #10=(|NonNegativeInteger|)) 51 T ELT)) (|nodes| (#11=(#8# $) 31 T ELT)) (|node?| (#12=(#13=(|Boolean|) $ $) 62 T ELT)) (|leaf?| (#14=(#13# $) 33 T ELT)) (|last| (#1# 25 T ELT) (#9# 57 T ELT)) (|elt| ((|#2| $ #4#) NIL T ELT) ((|#2| $ #5#) 10 T ELT) (($ $ #6#) 16 T ELT) ((|#2| $ #7#) 13 T ELT)) (|cyclic?| (#14# 23 T ELT)) (|cycleTail| (#2# 46 T ELT)) (|cycleSplit!| (#2# 79 T ELT)) (|cycleLength| ((#10# $) 50 T ELT)) (|cycleEntry| (#2# 49 T ELT)) (|concat| (($ $ $) 70 T ELT) (($ |#2| $) NIL T ELT)) (|children| (#11# 32 T ELT)) (= (#12# 60 T ELT))) (((|UnaryRecursiveAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |split!| (|#1| |#1| (|Integer|))) (SIGNATURE |setelt| (|#2| |#1| #3="last" |#2|)) (SIGNATURE |setlast!| #4=(|#2| |#1| |#2|)) (SIGNATURE |setelt| (|#1| |#1| #5="rest" |#1|)) (SIGNATURE |setelt| (|#2| |#1| #6="first" |#2|)) (SIGNATURE |cycleSplit!| #7=(|#1| |#1|)) (SIGNATURE |cycleTail| #7#) (SIGNATURE |cycleLength| (#8=(|NonNegativeInteger|) |#1|)) (SIGNATURE |cycleEntry| #7#) (SIGNATURE |third| #9=(|#2| |#1|)) (SIGNATURE |second| #9#) (SIGNATURE |tail| #7#) (SIGNATURE |last| #10=(|#1| |#1| #8#)) (SIGNATURE |elt| (|#2| |#1| #3#)) (SIGNATURE |last| #9#) (SIGNATURE |rest| #10#) (SIGNATURE |elt| (|#1| |#1| #5#)) (SIGNATURE |rest| #7#) (SIGNATURE |elt| (|#2| |#1| #6#)) (SIGNATURE |concat| (|#1| |#2| |#1|)) (SIGNATURE |concat| (|#1| |#1| |#1|)) (SIGNATURE |setvalue!| #4#) (SIGNATURE |setelt| (|#2| |#1| #11="value" |#2|)) (SIGNATURE |setchildren!| (|#1| |#1| #12=(|List| |#1|))) (SIGNATURE |node?| #1#) (SIGNATURE |cyclic?| #13=(#2# |#1|)) (SIGNATURE |elt| (|#2| |#1| #11#)) (SIGNATURE |value| #9#) (SIGNATURE |leaf?| #13#) (SIGNATURE |nodes| #14=(#12# |#1|)) (SIGNATURE |children| #14#)) (|UnaryRecursiveAggregate| |#2|) (|Type|)) (T |UnaryRecursiveAggregate&|)) NIL -((~= (#1=((|Boolean|) $ $) 18 (|has| |#1| . #2=((|BasicType|))) ELT)) (|value| ((|#1| $) 43 T ELT)) (|third| ((|#1| $) 62 T ELT)) (|tail| (($ $) 64 T ELT)) (|split!| (($ $ (|Integer|)) 49 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setvalue!| ((|#1| $ |#1|) 34 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setrest!| (($ $ $) 53 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setlast!| ((|#1| $ |#1|) 51 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setfirst!| ((|#1| $ |#1|) 55 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setelt| ((|#1| $ #3="value" |#1|) 35 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ "first" |#1|) 54 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) (($ $ "rest" $) 52 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT) ((|#1| $ "last" |#1|) 50 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|setchildren!| (($ $ #4=(|List| $)) 36 (|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|second| ((|#1| $) 63 T ELT)) (|sample| (#5=($) 6 T CONST)) (|rest| (($ $) 70 T ELT) (($ $ (|NonNegativeInteger|)) 68 T ELT)) (|nodes| 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ELT)) (|variable| ((#6=(|Symbol|) $) 130 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 73 #7=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| (#8=($ $) 74 #7# ELT)) (|unit?| (#3# 76 #7# ELT)) (|truncate| (#9=($ $ #10=(|NonNegativeInteger|)) 125 T ELT) (($ $ #10# #10#) 124 T ELT)) (|terms| ((#11=(|Stream| (|Record| (|:| |k| #10#) (|:| |c| |#1|))) $) 131 T ELT)) (|tanh| (#8# 164 #12=(|has| |#1| (|Algebra| #13=(|Fraction| #14=(|Integer|)))) ELT)) (|tan| (#8# 147 #12# ELT)) (|subtractIfCan| ((#15=(|Maybe| $) $ $) 26 T ELT)) (|sqrt| (#8# 146 #12# ELT)) (|sinh| (#8# 163 #12# ELT)) (|sin| (#8# 148 #12# ELT)) (|series| (($ #11#) 184 T ELT) (($ #16=(|Stream| |#1|)) 182 T ELT)) (|sech| (#8# 162 #12# ELT)) (|sec| (#8# 149 #12# ELT)) (|sample| (#17=($) 23 T CONST)) (|reductum| (#8# 82 T ELT)) (|recip| ((#18=(|Union| $ "failed") $) 43 T ELT)) (|quoByVar| (#8# 181 T ELT)) (|polynomial| ((#19=(|Polynomial| |#1|) $ #10#) 179 T ELT) ((#19# $ #10# 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|#1| #6#))) #12#)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|extend| (#9# 122 T ELT)) (|exquo| ((#18# $ $) 72 #7# ELT)) (|exp| (#8# 172 #12# ELT)) (|eval| ((#16# $ |#1|) 121 #27=(|has| |#1| (SIGNATURE ** (|#1| |#1| #10#))) ELT)) (|elt| (#28=(|#1| $ #10#) 132 T ELT) (#29=($ $ $) 108 (|has| #10# (|SemiGroup|)) ELT)) (|differentiate| (#25# 120 #30=(AND (|has| |#1| (|PartialDifferentialRing| #6#)) #31=(|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (#32=($ $ #26#) 118 #30# ELT) (#33=($ $ #6# #10#) 117 #30# ELT) (#34=($ $ #26# #23#) 116 #30# ELT) (#8# 112 #31# ELT) (#9# 110 #31# ELT)) (|degree| (#20# 85 T ELT)) (|csch| (#8# 161 #12# ELT)) (|csc| (#8# 150 #12# ELT)) (|coth| (#8# 160 #12# ELT)) (|cot| (#8# 151 #12# ELT)) (|cosh| (#8# 159 #12# ELT)) (|cos| (#8# 152 #12# ELT)) (|complete| (#8# 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #14#) 42 T ELT) (($ #13#) 79 #12# ELT) (#8# 71 #7# ELT) (($ |#1|) 69 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficients| ((#16# $) 183 T ELT)) (|coefficient| (#28# 81 T ELT)) (|charthRoot| ((#15# $) 70 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#10#) 41 T CONST)) (|center| (#24# 129 T ELT)) (|before?| (#1# 6 T ELT)) (|atanh| (#8# 170 #12# ELT)) (|atan| (#8# 158 #12# ELT)) (|associates?| (#1# 75 #7# ELT)) (|asinh| (#8# 169 #12# ELT)) (|asin| (#8# 157 #12# ELT)) (|asech| (#8# 168 #12# ELT)) (|asec| (#8# 156 #12# ELT)) (|approximate| (#28# 123 (AND #27# (|has| |#1| (SIGNATURE |coerce| (|#1| #6#)))) ELT)) (|annihilate?| (#1# 34 T ELT)) (|acsch| (#8# 167 #12# ELT)) (|acsc| (#8# 155 #12# ELT)) (|acoth| (#8# 166 #12# ELT)) (|acot| (#8# 154 #12# ELT)) (|acosh| (#8# 165 #12# ELT)) (|acos| (#8# 153 #12# ELT)) (|Zero| (#17# 24 T CONST)) (|One| (#17# 46 T CONST)) (D (#25# 119 #30# ELT) (#32# 115 #30# ELT) (#33# 114 #30# ELT) (#34# 113 #30# ELT) (#8# 111 #31# ELT) (#9# 109 #31# ELT)) (= (#1# 8 T ELT)) (/ (#35=($ $ |#1|) 80 #36=(|has| |#1| (|Field|)) ELT)) (- (#8# 30 T ELT) (#29# 29 T ELT)) (+ (#29# 18 T ELT)) (** (#21# 36 T ELT) (#9# 44 T ELT) (#35# 177 #36# ELT) (#29# 173 #12# ELT) (#37=($ $ #13#) 144 #12# ELT)) (* (($ #22# $) 17 T ELT) (($ #10# $) 21 T ELT) (($ #14# . #38=($)) 31 T ELT) (#29# 35 T ELT) (#35# 90 T ELT) (($ |#1| . #38#) 89 T ELT) (($ #13# . #38#) 78 #12# ELT) (#37# 77 #12# ELT))) (((|UnivariateTaylorSeriesCategory| |#1|) (|Category|) (|Ring|)) (T |UnivariateTaylorSeriesCategory|)) -((|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| *3)))) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)))) (|coefficients| (*1 *2 *1) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)) (|isDomain| *2 (|Stream| *3)))) (|series| (*1 *1 *2) (AND (|isDomain| *2 (|Stream| *3)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)))) (|quoByVar| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)))) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 (|Integer|))) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)) (|ofCategory| *3 (|Ring|)))) (|polynomial| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Polynomial| *4)))) (|polynomial| (*1 *2 *1 *3 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 (|Ring|)) (|isDomain| *2 (|Polynomial| *4)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Field|)))) (|integrate| (*1 *1 *1) (AND (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2)) (|ofCategory| *2 (|Ring|)) (|ofCategory| *2 (|Algebra| (|Fraction| (|Integer|)))))) (|integrate| (*1 *1 *1 *2) (OR (AND #1=(|isDomain| *2 (|Symbol|)) #2=(|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)) #3=(|ofCategory| *3 (|Ring|)) (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))))) (AND #1# #2# #3# (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3))) (|has| *3 (SIGNATURE |integrate| (*3 *3 *2))) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|))))))))) -(|Join| (|UnivariatePowerSeriesCategory| |t#1| (|NonNegativeInteger|)) (CATEGORY |domain| (SIGNATURE |series| ($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |t#1|))))) (SIGNATURE |coefficients| ((|Stream| |t#1|) $)) (SIGNATURE |series| ($ (|Stream| |t#1|))) (SIGNATURE |quoByVar| ($ $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |t#1| (|Integer|)) $)) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|))) (SIGNATURE |polynomial| ((|Polynomial| |t#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|))) (IF (|has| |t#1| (|Field|)) (SIGNATURE ** ($ $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| (|Integer|)))) (PROGN (SIGNATURE |integrate| ($ $)) (IF (|has| |t#1| (SIGNATURE |integrate| (|t#1| |t#1| (|Symbol|)))) (IF (|has| |t#1| (SIGNATURE |variables| ((|List| (|Symbol|)) |t#1|))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (|TranscendentalFunctionCategory|)) (IF (|has| |t#1| (|PrimitiveFunctionCategory|)) (IF (|has| |t#1| (|AlgebraicallyClosedFunctionSpace| (|Integer|))) (SIGNATURE |integrate| ($ $ (|Symbol|))) |%noBranch|) |%noBranch|) |%noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE (|TranscendentalFunctionCategory|))) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|NonNegativeInteger|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| (|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) |has| (|NonNegativeInteger|) (|SemiGroup|)) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|Join|) . T) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #3=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PartialDifferentialRing| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PartialDifferentialSpace| #3#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) +((|series| #1=(*1 *1 *2) (AND (|isDomain| *2 (|Stream| (|Record| (|:| |k| #2=(|NonNegativeInteger|)) (|:| |c| *3)))) #3=(|ofCategory| *3 #4=(|Ring|)) #5=(|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *3)))) (|coefficients| (*1 *2 *1) (AND #5# #3# #6=(|isDomain| *2 (|Stream| *3)))) (|series| #1# (AND #6# #3# #5#)) (|quoByVar| #7=(*1 *1 *1) (AND #8=(|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *2)) #9=(|ofCategory| *2 #4#))) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 #10=(|Integer|))) #5# #3#)) (|polynomial| (*1 *2 *1 *3) #11=(AND (|isDomain| *3 #2#) (|ofCategory| *1 (|UnivariateTaylorSeriesCategory| *4)) (|ofCategory| *4 #4#) (|isDomain| *2 (|Polynomial| *4)))) (|polynomial| (*1 *2 *1 *3 *3) #11#) (** #12=(*1 *1 *1 *2) (AND #8# #9# (|ofCategory| *2 (|Field|)))) (|integrate| #7# (AND #8# #9# (|ofCategory| *2 #13=(|Algebra| (|Fraction| #10#))))) (|integrate| #12# (OR (AND #14=(|isDomain| *2 (|Symbol|)) #5# #3# (AND (|ofCategory| *3 (|AlgebraicallyClosedFunctionSpace| #10#)) (|ofCategory| *3 (|PrimitiveFunctionCategory|)) (|ofCategory| *3 (|TranscendentalFunctionCategory|)) #15=(|ofCategory| *3 #13#))) (AND #14# #5# #3# (AND (|has| *3 (SIGNATURE |variables| ((|List| *2) *3))) (|has| *3 (SIGNATURE |integrate| (*3 *3 *2))) #15#))))) +(|Join| (|UnivariatePowerSeriesCategory| |t#1| #1=(|NonNegativeInteger|)) (CATEGORY |domain| (SIGNATURE |series| ($ (|Stream| (|Record| (|:| |k| #1#) (|:| |c| |t#1|))))) (SIGNATURE |coefficients| (#2=(|Stream| |t#1|) $)) (SIGNATURE |series| ($ #2#)) (SIGNATURE |quoByVar| #3=($ $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |t#1| #4=(|Integer|)) $)) (SIGNATURE |polynomial| (#5=(|Polynomial| |t#1|) $ #1#)) (SIGNATURE |polynomial| (#5# $ #1# #1#)) (IF (|has| |t#1| (|Field|)) (SIGNATURE ** ($ $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (|Algebra| (|Fraction| #4#))) (PROGN (SIGNATURE |integrate| #3#) (IF (|has| |t#1| (SIGNATURE |integrate| (|t#1| |t#1| #6=(|Symbol|)))) (IF (|has| |t#1| (SIGNATURE |variables| ((|List| #6#) |t#1|))) #7=(SIGNATURE |integrate| ($ $ #6#)) |%noBranch|) |%noBranch|) (IF (|has| |t#1| #8=(|TranscendentalFunctionCategory|)) (IF (|has| |t#1| (|PrimitiveFunctionCategory|)) (IF (|has| |t#1| (|AlgebraicallyClosedFunctionSpace| #4#)) #7# |%noBranch|) |%noBranch|) |%noBranch|) (ATTRIBUTE (|RadicalCategory|)) (ATTRIBUTE #8#)) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianMonoidRing| |#1| #1=(|NonNegativeInteger|)) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #2=(|Fraction| #3=(|Integer|))) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|Algebra| $) |has| |#1| (|IntegralDomain|)) ((|ArcHyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|ArcTrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BasicType|) . T) ((|BiModule| #2# #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) |has| |#1| (|CommutativeRing|)) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|CoercibleFrom| #3#) . T) ((|CoercibleFrom| |#1|) |has| |#1| (|CommutativeRing|)) ((|CoercibleFrom| $) |has| |#1| (|IntegralDomain|)) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) |has| |#1| (|CommutativeRing|)) ((|DifferentialDomain| $) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|DifferentialRing|) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|DifferentialSpace|) |has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|))) ((|ElementaryFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Eltable| #1# |#1|) . T) ((|Eltable| $ $) . T) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|Functorial| |#1|) . T) ((|HyperbolicFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|IntegralDomain|) |has| |#1| (|IntegralDomain|)) ((|LeftLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftLinearSet| #3#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|LinearSet| $) |has| |#1| (|IntegralDomain|)) ((|Module| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| $) |has| |#1| (|IntegralDomain|)) ((|Monoid|) . T) ((|PartialDifferentialDomain| $ #4=(|Symbol|)) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PartialDifferentialRing| #4#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PartialDifferentialSpace| #4#) AND (|has| |#1| (|PartialDifferentialRing| (|Symbol|))) (|has| |#1| (SIGNATURE * (|#1| (|NonNegativeInteger|) |#1|)))) ((|PowerSeriesCategory| |#1| #1# (|SingletonAsOrderedSet|)) . T) ((|RadicalCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightLinearSet| |#1|) . T) ((|RightLinearSet| $) |has| |#1| (|CommutativeRing|)) ((|RightModule| #2#) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|RightModule| |#1|) . T) ((|RightModule| $) |has| |#1| (|CommutativeRing|)) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|TranscendentalFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|TrigonometricFunctionCategory|) |has| |#1| (|Algebra| (|Fraction| (|Integer|)))) ((|Type|) . T) ((|UnivariatePowerSeriesCategory| |#1| #1#) . T)) ((|stFuncN| (((|Mapping| #1=(|Stream| |#1|) (|List| #1#)) #2=(|Mapping| |#2| #3=(|List| |#2|))) 24 T ELT)) (|stFunc2| (((|Mapping| #1# #1# #1#) #4=(|Mapping| |#2| |#2| |#2|)) 16 T ELT)) (|stFunc1| (((|Mapping| #1# #1#) #5=(|Mapping| |#2| |#2|)) 13 T ELT)) (|ode2| ((|#2| #4# |#1| |#1|) 48 T ELT)) (|ode1| ((|#2| #5# |#1|) 46 T ELT)) (|ode| ((|#2| #2# #6=(|List| |#1|)) 60 T ELT)) (|mpsode| ((#3# #6# (|List| #2#)) 66 T ELT)) (|fixedPointExquo| ((|#2| |#2| |#2|) 43 T ELT))) (((|UnivariateTaylorSeriesODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |stFunc1| ((|Mapping| #1=(|Stream| |#1|) #1#) #2=(|Mapping| |#2| |#2|))) (SIGNATURE |stFunc2| ((|Mapping| #1# #1# #1#) #3=(|Mapping| |#2| |#2| |#2|))) (SIGNATURE |stFuncN| ((|Mapping| #1# (|List| #1#)) #4=(|Mapping| |#2| #5=(|List| |#2|)))) (SIGNATURE |fixedPointExquo| (|#2| |#2| |#2|)) (SIGNATURE |ode1| (|#2| #2# |#1|)) (SIGNATURE |ode2| (|#2| #3# |#1| |#1|)) (SIGNATURE |ode| (|#2| #4# #6=(|List| |#1|))) (SIGNATURE |mpsode| (#5# #6# 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T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|FiniteLinearAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|LinearAggregate| |#1|) . T) ((|OneDimensionalArrayAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|OrderedSet|))) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) +((+ #1=(*1 *1 *1 *1) (AND #2=(|ofCategory| *1 (|VectorCategory| *2)) #3=(|ofCategory| *2 #4=(|Type|)) (|ofCategory| *2 (|AbelianSemiGroup|)))) (|zero| (*1 *1 *2) (AND (|isDomain| *2 (|NonNegativeInteger|)) #5=(|ofCategory| *1 (|VectorCategory| *3)) (|ofCategory| *3 (|AbelianMonoid|)) #6=(|ofCategory| *3 #4#))) (- (*1 *1 *1) #7=(AND #2# #3# (|ofCategory| *2 #8=(|AbelianGroup|)))) (- #1# #7#) (* #9=(*1 *1 *2 *1) (AND (|isDomain| *2 (|Integer|)) #5# #6# (|ofCategory| *3 #8#))) (* #9# #10=(AND #2# #3# (|ofCategory| *2 (|Monoid|)))) (* (*1 *1 *1 *2) #10#) (|dot| #11=(*1 *2 *1 *1) #12=(AND #2# #3# #13=(|ofCategory| *2 #14=(|Ring|)))) (|outerProduct| #11# (AND #5# #6# (|ofCategory| *3 #14#) (|isDomain| *2 (|Matrix| *3)))) (|cross| #1# #12#) (|length| #15=(*1 *2 *1) #16=(AND #2# #3# (|ofCategory| *2 (|RadicalCategory|)) #13#)) (|magnitude| #15# #16#)) +(|Join| (|OneDimensionalArrayAggregate| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| (|AbelianSemiGroup|)) (SIGNATURE + #1=($ $ $)) |%noBranch|) (IF (|has| |t#1| (|AbelianMonoid|)) (SIGNATURE |zero| ($ (|NonNegativeInteger|))) |%noBranch|) (IF (|has| |t#1| (|AbelianGroup|)) (PROGN (SIGNATURE - ($ $)) (SIGNATURE - #1#) (SIGNATURE * ($ (|Integer|) $))) |%noBranch|) (IF (|has| |t#1| (|Monoid|)) (PROGN (SIGNATURE * ($ |t#1| $)) (SIGNATURE * ($ $ |t#1|))) |%noBranch|) (IF #2=(|has| |t#1| (|Ring|)) (PROGN (SIGNATURE |dot| (|t#1| $ $)) (SIGNATURE |outerProduct| ((|Matrix| |t#1|) $ $)) (SIGNATURE |cross| #1#)) |%noBranch|) (IF (|has| |t#1| (|RadicalCategory|)) (IF #2# (PROGN (SIGNATURE |length| #3=(|t#1| $)) (SIGNATURE |magnitude| #3#)) |%noBranch|) |%noBranch|))) +(((|Aggregate|) . T) ((|BasicType|) |has| |#1| (|BasicType|)) ((|CoercibleTo| (|OutputForm|)) |has| |#1| (|CoercibleTo| (|OutputForm|))) ((|Collection| |#1|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#1| (|ConvertibleTo| (|InputForm|))) ((|Eltable| #1=(|Integer|) |#1|) . T) ((|Eltable| (|UniversalSegment| #1#) $) . T) ((|EltableAggregate| #1# |#1|) . T) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|FiniteAggregate| |#1|) . T) ((|FiniteLinearAggregate| |#1|) . T) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|IndexedAggregate| #1# |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|LinearAggregate| |#1|) . T) ((|OneDimensionalArrayAggregate| |#1|) . T) ((|OrderedSet|) |has| |#1| (|OrderedSet|)) ((|OrderedType|) |has| |#1| (|OrderedSet|)) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|ShallowlyMutableAggregate| |#1|) . T) ((|Type|) . T)) ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|zero| (($ #5=(|NonNegativeInteger|)) NIL (|has| |#1| (|AbelianMonoid|)) ELT)) (|vector| (#6=($ #7=(|List| |#1|)) 9 T ELT)) (|swap!| (((|Void|) $ #8=(|Integer|) #8#) NIL #9=(|has| $ (|ShallowlyMutableAggregate| |#1|)) ELT)) (|sorted?| ((#3# #10=(|Mapping| #3# |#1| |#1|) $) NIL T ELT) (#11=(#3# $) NIL #12=(|has| |#1| #13=(|OrderedSet|)) ELT)) (|sort!| (#14=($ #10# $) NIL #9# ELT) (#15=($ $) NIL (AND #9# #12#) ELT)) (|sort| (#14# NIL T ELT) (#15# NIL #12# ELT)) (|setelt| #16=(#17=(|#1| $ #8# |#1|) NIL #9# ELT) ((|#1| $ #18=(|UniversalSegment| #8#) |#1|) NIL #9# ELT)) (|select| #19=(($ #20=(|Mapping| #3# |#1|) $) NIL #21=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#22=($) NIL T CONST)) (|reverse!| (#15# NIL #9# ELT)) (|reverse| #23=(#15# NIL T ELT)) (|removeDuplicates| (#15# NIL #24=(AND #21# #4#) ELT)) (|remove| (#25=($ |#1| $) NIL #24# ELT) #19#) (|reduce| ((|#1| #26=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #26# $ |#1|) NIL T ELT) ((|#1| #26# $) NIL T ELT)) (|qsetelt!| #16#) (|qelt| #27=((|#1| $ #8#) NIL T ELT)) (|position| ((#8# #20# $) NIL T ELT) ((#8# |#1| $) NIL #4# ELT) ((#8# |#1| $ #8#) NIL #4# ELT)) (|outerProduct| (((|Matrix| |#1|) $ $) NIL #28=(|has| |#1| (|Ring|)) ELT)) (|new| (($ #5# |#1|) NIL T ELT)) (|minIndex| (#29=(#8# $) NIL #30=(|has| #8# #13#) ELT)) (|min| #31=(#32=($ $ $) NIL #12# ELT)) (|merge| (($ #10# $ $) NIL T ELT) #31#) (|members| (#33=(#7# $) 15 T ELT)) (|member?| (#34=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| (#29# 11 #30# ELT)) (|max| #31#) (|map!| #35=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #35# (($ #26# $ $) NIL T ELT)) (|magnitude| #36=(#37=(|#1| $) NIL (AND (|has| |#1| (|RadicalCategory|)) #28#) ELT)) (|length| #36#) (|latex| (((|String|) $) NIL #38=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #8#) NIL T ELT) (#39=($ $ $ #8#) NIL T ELT)) (|indices| (((|List| #8#) $) NIL T ELT)) (|index?| ((#3# #8# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #38# ELT)) (|first| (#37# NIL #30# ELT)) (|find| (((|Union| |#1| "failed") #20# $) NIL T ELT)) (|fill!| (#40=($ $ |#1|) NIL #9# ELT)) (|every?| #41=((#3# #20# $) NIL T ELT)) (|eval| (($ $ (|List| #42=(|Equation| |#1|))) NIL #43=(AND (|has| |#1| (|Evalable| |#1|)) #38#) ELT) (($ $ #42#) NIL #43# ELT) (($ $ |#1| |#1|) NIL #43# ELT) (($ $ #7# #7#) NIL #43# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#34# NIL #24# ELT)) (|entries| (#33# NIL T ELT)) (|empty?| (#11# NIL T ELT)) (|empty| (#22# NIL T ELT)) (|elt| (#17# NIL T ELT) #27# #44=(($ $ #18#) NIL T ELT)) (|dot| ((|#1| $ $) NIL #28# ELT)) (|delete| (($ $ #8#) NIL T ELT) #44#) (|cross| (#32# NIL #28# ELT)) (|count| ((#5# |#1| $) NIL #4# ELT) ((#5# #20# $) NIL T ELT)) (|copyInto!| (#39# NIL #9# ELT)) (|copy| #23#) (|convert| ((#45=(|InputForm|) $) 19 (|has| |#1| (|ConvertibleTo| #45#)) ELT)) (|construct| (#6# 8 T ELT)) (|concat| (#40# NIL T ELT) (#25# NIL T ELT) (#32# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#46=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #46#)) ELT)) (|before?| #1#) (|any?| #41#) (>= #47=(#2# NIL #12# ELT)) (> #47#) (= #1#) (<= #47#) (< #47#) (- (#15# NIL #48=(|has| |#1| (|AbelianGroup|)) ELT) (#32# NIL #48# ELT)) (+ (#32# NIL (|has| |#1| (|AbelianSemiGroup|)) ELT)) (* (($ #8# $) NIL #48# ELT) (#25# NIL #49=(|has| |#1| (|Monoid|)) ELT) (#40# NIL #49# ELT)) (|#| ((#5# $) NIL T ELT))) (((|Vector| |#1|) (|Join| (|VectorCategory| |#1|) (CATEGORY |domain| (SIGNATURE |vector| ($ (|List| |#1|))))) (|Type|)) (T |Vector|)) ((|vector| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|isDomain| *1 (|Vector| *3))))) @@ -3971,11 +3971,11 @@ NIL ((/ (($ $ |#2|) 10 T ELT))) (((|VectorSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE / (|#1| |#1| |#2|))) (|VectorSpace| |#2|) (|Field|)) (T |VectorSpace&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dimension| (((|CardinalNumber|)) 40 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 41 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ |#1| . #4#) 34 T ELT) (($ $ |#1|) 38 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|opposite?| (#1# 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|dimension| (((|CardinalNumber|)) 40 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (/ (#4=($ $ |#1|) 41 T ELT)) (- (($ $) 30 T ELT) (#5=($ $ $) 29 T ELT)) (+ (#5# 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 31 T ELT) (($ |#1| . #6#) 34 T ELT) (#4# 38 T ELT))) (((|VectorSpace| |#1|) (|Category|) (|Field|)) (T |VectorSpace|)) -((/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|VectorSpace| *2)) (|ofCategory| *2 (|Field|)))) (|dimension| (*1 *2) (AND (|ofCategory| *1 (|VectorSpace| *3)) (|ofCategory| *3 (|Field|)) (|isDomain| *2 (|CardinalNumber|))))) +((/ (*1 *1 *1 *2) (AND (|ofCategory| *1 (|VectorSpace| *2)) (|ofCategory| *2 #1=(|Field|)))) (|dimension| (*1 *2) (AND (|ofCategory| *1 (|VectorSpace| *3)) (|ofCategory| *3 #1#) (|isDomain| *2 (|CardinalNumber|))))) (|Join| (|Module| |t#1|) (CATEGORY |domain| (SIGNATURE / ($ $ |t#1|)) (SIGNATURE |dimension| ((|CardinalNumber|))))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftModule| |#1|) . T) ((|LinearSet| |#1|) . T) ((|Module| |#1|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((|weierstrass| (((|List| #1=(|TaylorSeries| |#1|)) #2=(|Symbol|) #1#) 83 T ELT)) (|sts2stst| (((|Stream| #3=(|Stream| #4=(|Polynomial| |#1|))) #2# #3#) 63 T ELT)) (|qqq| (((|Mapping| #5=(|Stream| #1#) #5#) #6=(|NonNegativeInteger|) #1# #5#) 74 T ELT)) (|crest| (#7=((|Mapping| #3# #3#) #6#) 65 T ELT)) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| #4#) #4#) #2#) 32 T ELT)) (|cfirst| (#7# 64 T ELT))) (((|WeierstrassPreparation| |#1|) (CATEGORY |package| (SIGNATURE |crest| #1=((|Mapping| #2=(|Stream| #3=(|Polynomial| |#1|)) #2#) #4=(|NonNegativeInteger|))) (SIGNATURE |cfirst| #1#) (SIGNATURE |sts2stst| ((|Stream| #2#) #5=(|Symbol|) #2#)) (SIGNATURE |clikeUniv| ((|Mapping| (|SparseUnivariatePolynomial| #3#) #3#) #5#)) (SIGNATURE |weierstrass| ((|List| #6=(|TaylorSeries| |#1|)) #5# #6#)) (SIGNATURE |qqq| ((|Mapping| #7=(|Stream| #6#) #7#) #4# #6# #7#))) (|Field|)) (T |WeierstrassPreparation|)) ((|qqq| (*1 *2 *3 *4 *5) (AND #1=(|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *6 #2=(|Field|)) (|isDomain| *4 (|TaylorSeries| *6)) (|isDomain| *2 (|Mapping| #3=(|Stream| *4) #3#)) (|isDomain| *1 (|WeierstrassPreparation| *6)) (|isDomain| *5 #3#))) (|weierstrass| #4=(*1 *2 *3 *4) (AND #5=(|isDomain| *3 (|Symbol|)) #6=(|ofCategory| *5 #2#) (|isDomain| *2 (|List| #7=(|TaylorSeries| *5))) #8=(|isDomain| *1 (|WeierstrassPreparation| *5)) (|isDomain| *4 #7#))) (|clikeUniv| #9=(*1 *2 *3) (AND #5# (|isDomain| *2 (|Mapping| (|SparseUnivariatePolynomial| #10=(|Polynomial| *4)) #10#)) #11=(|isDomain| *1 (|WeierstrassPreparation| *4)) #12=(|ofCategory| *4 #2#))) (|sts2stst| #4# (AND #5# #6# (|isDomain| *2 (|Stream| #13=(|Stream| (|Polynomial| *5)))) #8# (|isDomain| *4 #13#))) (|cfirst| #9# #14=(AND #1# (|isDomain| *2 (|Mapping| #15=(|Stream| #10#) #15#)) #11# #12#)) (|crest| #9# #14#)) @@ -3994,11 +3994,11 @@ NIL ((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| (#6=(#7=(|List| $) #5#) 95 T ELT)) (|variables| #8=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #9=(#10=(#3# $) NIL T ELT)) (|triangular?| #11=(#10# NIL #12=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #13=(#14=(#3# |#4| $) NIL T ELT) #9#) (|stronglyReduce| #15=(#16=(|#4| |#4| $) NIL T ELT)) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) NIL T ELT)) (|select| #17=(($ #18=(|Mapping| #3# |#4|) $) NIL #19=(|has| $ (|FiniteAggregate| |#4|)) ELT) ((#20=(|Union| |#4| #21="failed") $ |#3|) NIL T ELT)) (|sample| (#22=($) NIL T CONST)) (|roughUnitIdeal?| #11#) (|roughSubIdeal?| #23=(#2# NIL #12# ELT)) (|roughEqualIdeals?| #23#) (|roughBase?| #11#) (|rewriteSetWithReduction| ((#5# #5# $ #24=(|Mapping| |#4| |#4| |#4|) #25=(|Mapping| #3# |#4| |#4|)) 31 T ELT)) (|rewriteIdealWithRemainder| (#26=(#5# #5# $) 28 #12# ELT)) (|rewriteIdealWithHeadRemainder| (#26# NIL #12# ELT)) (|retractIfCan| (#27=(#28=(|Union| $ #21#) #5#) NIL T ELT)) (|retract| #29=(($ #5#) NIL T ELT)) (|rest| ((#28# $) 77 T ELT)) (|removeZero| (#16# 82 T ELT)) (|removeDuplicates| (#30=($ $) NIL #31=(AND #19# #32=(|has| |#4| (|BasicType|))) ELT)) (|remove| (($ |#4| $) NIL #31# ELT) #17#) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) #33=(|:| |den| |#1|)) |#4| $) NIL #12# ELT)) (|reduced?| ((#3# |#4| $ #25#) NIL T ELT)) (|reduceByQuasiMonic| #15#) (|reduce| ((|#4| #24# $ |#4| |#4|) NIL #32# ELT) ((|#4| #24# $ |#4|) NIL T ELT) ((|#4| #24# $) NIL T ELT) ((|#4| |#4| $ #24# #25#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|normalized?| #13# #9#) (|mvar| ((|#3| $) 83 T ELT)) (|members| (#34=(#5# $) 32 T ELT)) (|member?| (#14# NIL #32# ELT)) (|medialSet| (#35=(#28# #5# #25# #24#) 35 T ELT) (#27# 38 T ELT)) (|map!| #36=(($ (|Mapping| |#4| |#4|) $) NIL T ELT)) (|map| #36#) (|mainVariables| #8#) (|mainVariable?| #37=((#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|last| (#38=(#20# $) NIL T ELT)) (|initials| (#34# 53 T ELT)) (|initiallyReduced?| #13# #9#) (|initiallyReduce| (#16# 81 T ELT)) (|infRittWu?| (#2# 92 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#4|) #33#) |#4| $) NIL #12# ELT)) (|headReduced?| #13# #9#) (|headReduce| #15#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#38# 76 T ELT)) (|find| ((#20# #18# $) NIL T ELT)) (|extendIfCan| ((#28# $ |#4|) NIL T ELT)) (|extend| (($ $ |#4|) NIL T ELT)) (|every?| #39=((#3# #18# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #40=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #40# ELT) (($ $ #41=(|Equation| |#4|)) NIL #40# ELT) (($ $ (|List| #41#)) NIL #40# ELT)) (|eq?| #1#) (|empty?| (#10# 74 T ELT)) (|empty| (#22# 45 T ELT)) (|degree| #42=(#43=(#44=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#44# |#4| $) NIL #32# ELT) ((#44# #18# $) NIL T ELT)) (|copy| #45=(#30# NIL T ELT)) (|convert| ((#46=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #46#)) ELT)) (|construct| #29#) (|collectUpper| #47=(($ $ |#3|) NIL T ELT)) (|collectUnder| #47#) (|collectQuasiMonic| #45#) (|collect| #47#) (|coerce| (((|OutputForm|) $) NIL T ELT) (#34# 62 T ELT)) (|coHeight| (#43# NIL (|has| |#3| (|Finite|)) ELT)) (|characteristicSet| (#35# 43 T ELT) (#27# 44 T ELT)) (|characteristicSerie| ((#7# #5# #25# #24#) 72 T ELT) (#6# 73 T ELT)) (|before?| #1#) (|basicSet| ((#48=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #21#) #5# #25#) 27 T ELT) ((#48# #5# #18# #25#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|any?| #39#) (|algebraicVariables| #8#) (|algebraic?| #37#) (= #1#) (|#| #42#)) (((|WuWenTsunTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|TriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |medialSet| #1=(#2=(|Union| $ "failed") #3=(|List| |#4|) #4=(|Mapping| (|Boolean|) |#4| |#4|) #5=(|Mapping| |#4| |#4| |#4|))) (SIGNATURE |medialSet| #6=(#2# #3#)) (SIGNATURE |characteristicSet| #1#) (SIGNATURE |characteristicSet| #6#) (SIGNATURE |characteristicSerie| (#7=(|List| $) #3# #4# #5#)) (SIGNATURE |characteristicSerie| (#7# #3#)))) (|IntegralDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |WuWenTsunTriangularSet|)) ((|medialSet| #1=(*1 *1 *2 *3 *4) #2=(|partial| AND (|isDomain| *2 (|List| *8)) (|isDomain| *3 (|Mapping| #3=(|Boolean|) *8 *8)) (|isDomain| *4 (|Mapping| *8 *8 *8)) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|ofCategory| *5 #4=(|IntegralDomain|)) (|ofCategory| *6 #5=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #6=(|OrderedSet|)) (|isDomain| *1 (|WuWenTsunTriangularSet| *5 *6 *7 *8)))) (|medialSet| #7=(*1 *1 *2) #8=(|partial| AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #5#) (|ofCategory| *5 #6#) (|isDomain| *1 (|WuWenTsunTriangularSet| *3 *4 *5 *6)))) (|characteristicSet| #1# #2#) (|characteristicSet| #7# #8#) (|characteristicSerie| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| *9)) (|isDomain| *4 (|Mapping| #3# *9 *9)) (|isDomain| *5 (|Mapping| *9 *9 *9)) (|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #4#) (|ofCategory| *7 #5#) (|ofCategory| *8 #6#) (|isDomain| *2 (|List| #9=(|WuWenTsunTriangularSet| *6 *7 *8 *9))) (|isDomain| *1 #9#))) (|characteristicSerie| (*1 *2 *3) (AND (|isDomain| *3 (|List| *7)) (|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) (|ofCategory| *4 #4#) (|ofCategory| *5 #5#) (|ofCategory| *6 #6#) (|isDomain| *2 (|List| #10=(|WuWenTsunTriangularSet| *4 *5 *6 *7))) (|isDomain| *1 #10#)))) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#1|) 54 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ |#1|) 56 T ELT) (($ |#1| . #4#) 55 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #5=(|Integer|)) 42 T ELT) (($ |#1|) 54 T ELT)) (|characteristic| ((#6=(|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (#4# 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (#7=($ $ $) 29 T ELT)) (+ (#7# 18 T ELT)) (** (($ $ #8=(|PositiveInteger|)) 36 T ELT) (($ $ #6#) 44 T ELT)) (* (($ #8# $) 17 T ELT) (($ #6# $) 21 T ELT) (($ #5# . #9=($)) 31 T ELT) (#7# 35 T ELT) (($ $ |#1|) 56 T ELT) (($ |#1| . #9#) 55 T ELT))) (((|XAlgebra| |#1|) (|Category|) (|Ring|)) (T |XAlgebra|)) NIL (|Join| (|Ring|) (|BiModule| |t#1| |t#1|) (|CoercibleFrom| |t#1|) (CATEGORY |package| (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|))) -(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#1|) |has| |#1| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#1| |#1|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1=(|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#1|) |has| |#1| (|CommutativeRing|)) ((|Module| |#1|) |has| |#1| (|CommutativeRing|)) ((|Monoid|) . T) ((|RightLinearSet| |#1|) . T) ((|RightModule| |#1|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) ((~= (#1=(#2=(|Boolean|) $ $) 69 T ELT)) (|zero?| #3=(#4=(#2# $) NIL T ELT)) (|varList| (((|List| |#1|) $) 54 T ELT)) (|trunc| (#5=($ $ #6=(|NonNegativeInteger|)) 47 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) NIL T ELT)) (|sh| (#5# 25 #7=(|has| |#2| (|CommutativeRing|)) ELT) (#8=($ $ $) 26 #7# ELT)) (|sample| (#9=($) NIL T CONST)) (|rquo| (#8# 72 T ELT) (#10=($ $ #11=(|OrderedFreeMonoid| |#1|)) 58 T ELT) (#12=($ $ |#1|) 62 T ELT)) (|retractIfCan| (((|Union| #11# #13="failed") $) NIL T ELT)) (|retract| #14=(#15=(#11# $) NIL T ELT)) (|reductum| (#16=($ $) 40 T ELT)) (|recip| (((|Union| $ #13#) $) NIL T ELT)) (|quasiRegular?| #3#) (|quasiRegular| #17=(#16# NIL T ELT)) (|opposite?| #18=(#1# NIL T ELT)) (|one?| #3#) (|numberOfMonomials| (#19=(#6# $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #3#) (|monom| (($ #11# |#2|) 39 T ELT)) (|mirror| (#16# 41 T ELT)) (|mindegTerm| (#20=(#21=(|Record| (|:| |k| #11#) (|:| |c| |#2|)) $) 13 T ELT)) (|mindeg| #14#) (|maxdeg| (#15# 42 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|lquo| (#8# 71 T ELT) (#10# 60 T ELT) (#12# 64 T ELT)) (|leadingTerm| (#20# NIL T ELT)) (|leadingMonomial| (#15# 36 T ELT)) (|leadingCoefficient| (#22=(|#2| $) 38 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|degree| (#19# 44 T ELT)) (|constant?| (#4# 48 T ELT)) (|constant| (#22# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #11#) 31 T ELT) (($ |#1|) 32 T ELT) (($ |#2|) NIL T ELT) (($ #23=(|Integer|)) NIL T ELT)) (|coefficients| (((|List| |#2|) $) NIL T ELT)) (|coefficient| #24=((|#2| $ #11#) NIL T ELT)) (|coef| ((|#2| $ $) 78 T ELT) #24#) (|characteristic| ((#6#) NIL T CONST)) (|before?| #18#) (|annihilate?| #18#) (|Zero| (#9# 14 T CONST)) (|One| (#9# 20 T CONST)) (|ListOfTerms| (((|List| #21#) $) NIL T ELT)) (= (#1# 45 T ELT)) (- #25=(#8# NIL T ELT) #17#) (+ (#8# 29 T ELT)) (** (#5# NIL T ELT) (($ $ #26=(|PositiveInteger|)) NIL T ELT)) (* (($ $ |#2|) 70 T ELT) (($ |#2| . #27=($)) 28 T ELT) (($ #23# . #27#) NIL T ELT) (($ #6# $) NIL T ELT) (($ #26# $) NIL T ELT) (($ |#2| #11#) NIL T ELT) (($ |#1| $) 34 T ELT) #25#)) (((|XDistributedPolynomial| |#1| |#2|) (|Join| (|FreeModuleCat| |#2| (|OrderedFreeMonoid| |#1|)) (|XPolynomialsCat| |#1| |#2|)) (|OrderedSet|) (|Ring|)) (T |XDistributedPolynomial|)) NIL @@ -4008,27 +4008,27 @@ NIL ((|transcendent?| (#1=((|Boolean|) $) 15 T ELT)) (|algebraic?| (#1# 14 T ELT)) (|Frobenius| (($ $) 19 T ELT) (($ $ (|NonNegativeInteger|)) 21 T ELT))) (((|ExtensionField&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |Frobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |Frobenius| (|#1| |#1|)) (SIGNATURE |transcendent?| #1=((|Boolean|) |#1|)) (SIGNATURE |algebraic?| #1#)) (|ExtensionField| |#2|) (|Field|)) (T |ExtensionField&|)) NIL -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (($ $) 55 T ELT)) (|unit?| ((#3=(|Boolean|) $) 53 T ELT)) (|transcendent?| (((|Boolean|) $) 115 T ELT)) (|transcendenceDegree| (((|NonNegativeInteger|)) 111 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (($ $) 92 T ELT)) (|squareFree| (#4=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 76 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 122 T ELT)) (|retract| ((|#1| $) 123 T ELT)) (|rem| (#6=($ $ $) 72 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quo| (#6# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 67 T ELT)) (|primeFrobenius| (($ $ #8=(|NonNegativeInteger|)) 108 (OR (|has| |#1| . #9=((|CharacteristicNonZero|))) (|has| |#1| . #10=((|Finite|)))) ELT) (($ $) 107 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|prime?| (((|Boolean|) $) 90 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 105 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|multiEuclidean| (((|Union| #11=(|List| $) #12="failed") #11# $) 69 T ELT)) (|lcm| (#13=($ $ $) 61 T ELT) (#14=($ (|List| $)) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 89 T ELT)) (|inGroundField?| (((|Boolean|) $) 114 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#15=(|SparseUnivariatePolynomial| $) #15# #15#) 59 T ELT)) (|gcd| (#13# 63 T ELT) (#14# 62 T ELT)) (|factor| (#4# 93 T ELT)) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) 112 T ELT)) (|extendedEuclidean| (((|Record| #16=(|:| |coef1| $) #17=(|:| |coef2| $) (|:| |generator| $)) $ $) 71 T ELT) (((|Union| (|Record| #16# #17#) #12#) $ $ $) 70 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 66 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 106 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|dimension| (((|CardinalNumber|)) 120 T ELT)) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ $) 58 T ELT) (($ #18=(|Fraction| #19=(|Integer|))) 85 T ELT) (($ |#1|) 121 T ELT)) (|charthRoot| (((|Maybe| $) $) 104 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 54 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|algebraic?| (((|Boolean|) $) 116 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 46 T CONST)) (|Frobenius| (($ $) 110 (|has| |#1| (|Finite|)) ELT) (($ $ (|NonNegativeInteger|)) 109 (|has| |#1| (|Finite|)) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 84 T ELT) (($ $ |#1|) 119 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT) (($ $ #19#) 88 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #20=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ $ #18#) 87 T ELT) (($ #18# . #20#) 86 T ELT) (($ $ |#1|) 118 T ELT) (($ |#1| . #20#) 117 T ELT))) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 56 T ELT)) (|unitCanonical| (#4=($ $) 55 T ELT)) (|unit?| (#3# 53 T ELT)) (|transcendent?| (#3# 115 T ELT)) (|transcendenceDegree| (#5=(#6=(|NonNegativeInteger|)) 111 T ELT)) (|subtractIfCan| ((#7=(|Maybe| $) $ $) 26 T ELT)) (|squareFreePart| (#4# 92 T ELT)) (|squareFree| (#8=((|Factored| $) $) 91 T ELT)) (|sizeLess?| (#1# 76 T ELT)) (|sample| (#9=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| #10="failed") $) 122 T ELT)) (|retract| ((|#1| $) 123 T ELT)) (|rem| (#11=($ $ $) 72 T ELT)) (|recip| ((#12=(|Union| $ #10#) $) 43 T ELT)) (|quo| (#11# 73 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #13=(|List| $)) #14=(|:| |generator| $)) #13#) 67 T ELT)) (|primeFrobenius| (#15=($ $ #6#) 108 #16=(OR (|has| |#1| (|CharacteristicNonZero|)) #17=(|has| |#1| (|Finite|))) ELT) (#4# 107 #16# ELT)) (|prime?| (#3# 90 T ELT)) (|order| (#18=(#19=(|OnePointCompletion| #20=(|PositiveInteger|)) $) 105 #16# ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|multiEuclidean| (((|Union| #13# #10#) #13# $) 69 T ELT)) (|lcm| (#11# 61 T ELT) (#21=($ #13#) 60 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (#4# 89 T ELT)) (|inGroundField?| (#3# 114 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#22=(|SparseUnivariatePolynomial| $) #22# #22#) 59 T ELT)) (|gcd| (#11# 63 T ELT) (#21# 62 T ELT)) (|factor| (#8# 93 T ELT)) (|extensionDegree| ((#19#) 112 T ELT)) (|extendedEuclidean| (((|Record| #23=(|:| |coef1| $) #24=(|:| |coef2| $) #14#) $ $) 71 T ELT) (((|Union| (|Record| #23# #24#) #10#) $ $ $) 70 T ELT)) (|exquo| ((#12# $ $) 57 T ELT)) (|expressIdealMember| (((|Maybe| #13#) #13# $) 66 T ELT)) (|euclideanSize| ((#6# $) 75 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 74 T ELT)) (|discreteLog| (((|Union| #6# #10#) $ $) 106 #16# ELT)) (|dimension| (((|CardinalNumber|)) 120 T ELT)) (|degree| (#18# 113 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ #25=(|Integer|)) 42 T ELT) (#4# 58 T ELT) (($ #26=(|Fraction| #25#)) 85 T ELT) (($ |#1|) 121 T ELT)) (|charthRoot| ((#7# $) 104 #16# ELT)) (|characteristic| (#5# 41 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| (#1# 54 T ELT)) (|annihilate?| (#1# 34 T ELT)) (|algebraic?| (#3# 116 T ELT)) (|Zero| (#9# 24 T CONST)) (|One| (#9# 46 T CONST)) (|Frobenius| (#4# 110 #17# ELT) (#15# 109 #17# ELT)) (= (#1# 8 T ELT)) (/ (#11# 84 T ELT) (#27=($ $ |#1|) 119 T ELT)) (- (#4# 30 T ELT) (#11# 29 T ELT)) (+ (#11# 18 T ELT)) (** (($ $ #20#) 36 T ELT) (#15# 44 T ELT) (($ $ #25#) 88 T ELT)) (* (($ #20# $) 17 T ELT) (($ #6# $) 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| |#1| (|Finite|)) (|has| |#1| (|CharacteristicNonZero|))) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . 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T)) -((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 57 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sh| (($ $ $) 59 (|has| |#2| (|CommutativeRing|)) ELT) (($ $ (|NonNegativeInteger|)) 58 (|has| |#2| (|CommutativeRing|)) ELT)) (|sample| (#3=($) 23 T CONST)) (|rquo| (($ $ |#1|) 70 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 69 T ELT) (($ $ $) 68 T ELT)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) 80 T ELT)) (|retract| (((|OrderedFreeMonoid| |#1|) $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 43 T ELT)) (|quasiRegular?| (((|Boolean|) $) 61 T ELT)) (|quasiRegular| (($ $) 60 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 45 T ELT)) (|monomial?| (((|Boolean|) $) 66 T ELT)) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) 67 T ELT)) (|mirror| (($ $) 65 T ELT)) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) 76 T ELT)) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) 77 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 82 T ELT)) (|lquo| (($ $ |#1|) 73 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 72 T ELT) (($ $ $) 71 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|constant?| (((|Boolean|) $) 63 T ELT)) (|constant| ((|#2| $) 62 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 42 T ELT) (($ |#2|) 85 T ELT) (($ (|OrderedFreeMonoid| |#1|)) 79 T ELT) (($ |#1|) 64 T ELT)) (|coef| ((|#2| $ (|OrderedFreeMonoid| |#1|)) 75 T ELT) ((|#2| $ $) 74 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 41 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 34 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 46 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 30 T ELT) (($ $ $) 29 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 36 T ELT) (($ $ (|NonNegativeInteger|)) 44 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 31 T ELT) (($ $ $) 35 T ELT) (($ |#2| . #4#) 84 T ELT) (($ $ |#2|) 83 T ELT) (($ |#1| $) 78 T ELT))) +((|algebraic?| #1=(*1 *2 *1) #2=(AND #3=(|ofCategory| *1 (|ExtensionField| *3)) #4=(|ofCategory| *3 #5=(|Field|)) (|isDomain| *2 (|Boolean|)))) (|transcendent?| #1# #2#) (|inGroundField?| #1# #2#) (|degree| #1# #6=(AND #3# #4# (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|extensionDegree| #7=(*1 *2) #6#) (|transcendenceDegree| #7# (AND #3# #4# #8=(|isDomain| *2 (|NonNegativeInteger|)))) (|Frobenius| (*1 *1 *1) (AND (|ofCategory| *1 (|ExtensionField| *2)) (|ofCategory| *2 #5#) (|ofCategory| *2 #9=(|Finite|)))) (|Frobenius| (*1 *1 *1 *2) (AND #8# #3# #4# (|ofCategory| *3 #9#)))) +(|Join| (|Field|) (|RetractableTo| |t#1|) (|VectorSpace| |t#1|) (CATEGORY |domain| (IF (|has| |t#1| #1=(|CharacteristicZero|)) (ATTRIBUTE #1#) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) #2=(ATTRIBUTE (|FieldOfPrimeCharacteristic|)) |%noBranch|) (SIGNATURE |algebraic?| #3=((|Boolean|) $)) (SIGNATURE |transcendent?| #3#) (SIGNATURE |inGroundField?| #3#) (SIGNATURE |degree| (#4=(|OnePointCompletion| (|PositiveInteger|)) $)) (SIGNATURE |extensionDegree| (#4#)) (SIGNATURE |transcendenceDegree| (#5=(|NonNegativeInteger|))) (IF (|has| |t#1| (|Finite|)) (PROGN #2# (SIGNATURE |Frobenius| ($ $)) (SIGNATURE |Frobenius| ($ $ #5#))) |%noBranch|))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| #2=(|Integer|))) . T) ((|Algebra| $) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| |#1| |#1|) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CharacteristicNonZero|) OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| #2#) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleFrom| $) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|CommutativeRing|) . T) ((|DivisionRing|) . T) ((|EntireRing|) . T) ((|EuclideanDomain|) . T) ((|Field|) . T) ((|FieldOfPrimeCharacteristic|) OR (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|Finite|))) ((|GcdDomain|) . T) ((|IntegralDomain|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| #2#) . T) ((|LeftLinearSet| |#1|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| |#1|) . T) ((|LeftModule| $) . 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T)) +((~= (#1=(#2=(|Boolean|) $ $) 7 T ELT)) (|zero?| (#3=(#2# $) 22 T ELT)) (|varList| (((|List| |#1|) $) 57 T ELT)) (|subtractIfCan| (((|Maybe| $) $ $) 26 T ELT)) (|sh| (#4=($ $ $) 59 #5=(|has| |#2| (|CommutativeRing|)) ELT) (#6=($ $ #7=(|NonNegativeInteger|)) 58 #5# ELT)) (|sample| (#8=($) 23 T CONST)) (|rquo| (#9=($ $ |#1|) 70 T ELT) (#10=($ $ #11=(|OrderedFreeMonoid| |#1|)) 69 T ELT) (#4# 68 T ELT)) (|retractIfCan| (((|Union| #11# #12="failed") $) 80 T ELT)) (|retract| (#13=(#11# $) 81 T ELT)) (|recip| (((|Union| $ #12#) $) 43 T ELT)) (|quasiRegular?| (#3# 61 T ELT)) (|quasiRegular| (#14=($ $) 60 T ELT)) (|opposite?| (#1# 20 T ELT)) (|one?| (#3# 45 T ELT)) (|monomial?| (#3# 66 T ELT)) (|monom| (($ #11# |#2|) 67 T ELT)) (|mirror| (#14# 65 T ELT)) (|mindegTerm| (((|Record| (|:| |k| #11#) (|:| |c| |#2|)) $) 76 T ELT)) (|mindeg| (#13# 77 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 82 T ELT)) (|lquo| (#9# 73 T ELT) (#10# 72 T ELT) (#4# 71 T ELT)) (|latex| (((|String|) $) 11 T ELT)) 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1738241 1738293 "ORDRING" 1738298 ORDRING (NIL) |category| NIL 1738366 NIL) (|OrderedMonoid| 1736144 1736737 1736793 "ORDMON" 1736798 ORDMON (NIL) |category| NIL 1736840 NIL) (|OrderingFunctions| 1735505 1735629 1735877 "ORDFUNS" NIL ORDFUNS (NIL NIL T) |package| NIL NIL NIL) (|OrderedFinite| 1734515 1735048 1735104 "ORDFIN" 1735211 ORDFIN (NIL) |category| NIL 1735333 NIL) (|OrderedCompletionFunctions2| 1733767 1733909 1734179 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) |package| NIL NIL NIL) (|OrderedCompletion| 1730753 1732530 1733181 "ORDCOMP" NIL ORDCOMP (NIL T) |domain| NIL NIL NIL) (|OperatorSignature| 1729963 1730356 1730556 "OPSIG" NIL OPSIG (NIL) |domain| NIL NIL NIL) (|OperationsQuery| 1729618 1729687 1729821 "OPQUERY" NIL OPQUERY (NIL) |package| NIL NIL NIL) (|OperatorCategory| 1728602 1728908 1728991 "OPERCAT" 1729357 OPERCAT (NIL T) |category| NIL 1729506 NIL) (|OperatorCategory&| 1728304 1728388 1728597 "OPERCAT-" NIL OPERCAT- (NIL T T) |package| NIL NIL NIL) (|Operator| 1725419 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NIL NIL NIL) (|CombinatorialFunctionCategory| 187166 187263 187351 "CFCAT" 187492 CFCAT (NIL) |category| NIL NIL NIL) (|CommonDenominator| 185997 186172 186510 "CDEN" NIL CDEN (NIL T T T) |package| NIL NIL NIL) (|CharacterClass| 182743 185194 185690 "CCLASS" NIL CCLASS (NIL) |domain| NIL NIL NIL) (|Category| 181851 182121 182437 "CATEGORY" NIL CATEGORY (NIL) |domain| NIL NIL NIL) (|CategoryConstructor| 181247 181726 181846 "CATCTOR" NIL CATCTOR (NIL) |domain| NIL NIL NIL) (|CategoryAst| 180581 180906 181084 "CATAST" NIL CATAST (NIL) |domain| NIL NIL NIL) (|CaseAst| 180036 180333 180475 "CASEAST" NIL CASEAST (NIL) |domain| NIL NIL NIL) (|CartesianTensorFunctions2| 179092 179261 179595 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) |package| NIL NIL NIL) (|CartesianTensor| 175573 176870 177838 "CARTEN" NIL CARTEN (NIL NIL NIL T) |domain| NIL NIL NIL) (|CardinalNumber| 173662 174717 175197 "CARD" NIL CARD (NIL) |domain| NIL NIL NIL) (|CapsuleAst| 173151 173432 173565 "CAPSLAST" NIL CAPSLAST (NIL) |domain| NIL NIL NIL) (|CachableSet| 172363 172663 172715 "CACHSET" 172912 CACHSET (NIL) |category| NIL 173054 NIL) (|CancellationAbelianMonoid| 171452 171923 172003 "CABMON" 172121 CABMON (NIL) |category| NIL 172215 NIL) (|ByteOrder| 170833 171133 171340 "BYTEORD" NIL BYTEORD (NIL) |domain| NIL NIL NIL) (|ByteBuffer| 167343 170364 170664 "BYTEBUF" NIL BYTEBUF (NIL) |domain| NIL NIL NIL) (|Byte| 166221 166908 167129 "BYTE" NIL BYTE (NIL) |domain| NIL NIL 167299) (|BinaryTree| 163960 165892 166079 "BTREE" NIL BTREE (NIL T) |domain| NIL NIL NIL) (|BinaryTournament| 161580 163513 163721 "BTOURN" NIL BTOURN (NIL T) |domain| NIL NIL NIL) (|BinaryTreeCategory| 158716 160635 160722 "BTCAT" 160835 BTCAT (NIL T) |category| NIL 160995 NIL) (|BinaryTreeCategory&| 158330 158451 158711 "BTCAT-" NIL BTCAT- (NIL T T) |package| NIL NIL NIL) (|BitAggregate| 154310 157322 157376 "BTAGG" 157475 BTAGG (NIL) |category| NIL 157666 NIL) (|BitAggregate&| 153913 154063 154305 "BTAGG-" NIL BTAGG- (NIL T) |package| NIL NIL NIL) (|BinarySearchTree| 151176 153219 153533 "BSTREE" NIL BSTREE (NIL T) |domain| NIL NIL NIL) (|BrillhartTests| 150232 150438 150798 "BRILL" NIL BRILL (NIL T) |package| NIL NIL NIL) (|BinaryRecursiveAggregate| 147280 148691 148783 "BRAGG" 149380 BRAGG (NIL T) |category| NIL 149759 NIL) (|BinaryRecursiveAggregate&| 146146 146602 147275 "BRAGG-" NIL BRAGG- (NIL T T) |package| NIL NIL NIL) (|BalancedPAdicRational| 139798 145306 145656 "BPADICRT" NIL BPADICRT (NIL NIL) |domain| NIL NIL NIL) (|BalancedPAdicInteger| 137794 139689 139793 "BPADIC" NIL BPADIC (NIL NIL) |domain| NIL NIL NIL) (|BoundIntegerRoots| 137287 137337 137560 "BOUNDZRO" NIL BOUNDZRO (NIL T T) |package| NIL NIL NIL) (|BasicOperatorFunctions1| 135445 135854 136425 "BOP1" NIL BOP1 (NIL T) |package| NIL NIL NIL) (|BasicOperator| 131271 132672 133916 "BOP" NIL BOP (NIL) |domain| NIL NIL NIL) (|Boolean| 130154 130972 131179 "BOOLEAN" NIL BOOLEAN (NIL) |domain| NIL NIL NIL) (|BooleanLogic| 129704 129848 129902 "BOOLE" 130006 BOOLE (NIL) |category| NIL 130120 NIL) (|BooleanLogic&| 129445 129524 129699 "BOOLE-" NIL BOOLE- (NIL T) |package| NIL NIL NIL) (|BiModule| 128366 128960 129032 "BMODULE" 129037 BMODULE (NIL T T) |category| NIL 129090 NIL) (|Bits| 125335 128113 128242 "BITS" NIL BITS (NIL) |domain| NIL NIL NIL) (|BinaryOperatorCategory| 125110 125150 125238 "BINOPC" 125243 BINOPC (NIL T) |category| NIL 125291 NIL) (|BinaryOperation| 124483 124768 124967 "BINOP" NIL BINOP (NIL T) |domain| NIL NIL NIL) (|Binding| 123860 124036 124256 "BINDING" NIL BINDING (NIL) |domain| NIL NIL NIL) (|BinaryExpansion| 118240 123463 123717 "BINARY" NIL BINARY (NIL) |domain| NIL NIL NIL) (|BagAggregate| 116362 117192 117260 "BGAGG" 117530 BGAGG (NIL T) |category| NIL 117760 NIL) (|BagAggregate&| 116173 116213 116357 "BGAGG-" NIL BGAGG- (NIL T T) |package| NIL NIL NIL) (|BezoutMatrix| 114816 115044 115493 "BEZOUT" NIL BEZOUT (NIL T T T T T) |package| NIL NIL NIL) (|BalancedBinaryTree| 111625 113745 114218 "BBTREE" NIL BBTREE (NIL T) |domain| NIL NIL NIL) (|BasicType| 111231 111314 111362 "BASTYPE" 111488 BASTYPE (NIL) |category| NIL 111607 NIL) (|BasicType&| 110977 111063 111226 "BASTYPE-" NIL BASTYPE- (NIL T) |package| NIL NIL NIL) (|BalancedFactorisation| 110109 110218 110522 "BALFACT" NIL BALFACT (NIL T T) |package| NIL NIL NIL) (|Automorphism| 108884 109595 109859 "AUTOMOR" NIL AUTOMOR (NIL T) |domain| NIL NIL NIL) (|AttributeRegistry| 108556 108561 108625 "ATTREG" 108630 ATTREG (NIL) |category| NIL NIL NIL) (|AttributeAst| 108066 108338 108466 "ATTRAST" NIL ATTRAST (NIL) |domain| NIL NIL NIL) (|ArcTrigonometricFunctionCategory| 107482 107630 107724 "ATRIG" 107893 ATRIG (NIL) |category| NIL NIL NIL) (|ArcTrigonometricFunctionCategory&| 107218 107274 107477 "ATRIG-" NIL ATRIG- (NIL T) |package| NIL NIL NIL) (|AbstractSyntaxCategory| 106638 106899 106973 "ASTCAT" 106978 ASTCAT (NIL) |category| NIL 107031 NIL) (|AbstractSyntaxCategory&| 106310 106400 106633 "ASTCAT-" NIL ASTCAT- (NIL T) |package| NIL NIL NIL) (|ArrayStack| 104607 106025 106179 "ASTACK" NIL ASTACK (NIL T) |domain| NIL NIL NIL) (|AssociatedEquations| 102930 103297 103834 "ASSOCEQ" NIL ASSOCEQ (NIL T T) |package| NIL NIL NIL) (|TwoDimensionalArray| 101099 102783 102925 "ARRAY2" NIL ARRAY2 (NIL T) |domain| NIL NIL NIL) (|OneDimensionalArrayFunctions2| 99945 100162 100495 "ARRAY12" NIL ARRAY12 (NIL T T) |package| NIL NIL NIL) (|OneDimensionalArray| 96544 99452 99706 "ARRAY1" NIL ARRAY1 (NIL T) |domain| NIL NIL NIL) (|TwoDimensionalArrayCategory| 91696 93474 93621 "ARR2CAT" 95258 ARR2CAT (NIL T T T) |category| NIL 96033 NIL) (|TwoDimensionalArrayCategory&| 90433 90935 91691 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) |package| NIL NIL NIL) (|Arity| 89666 90083 90297 "ARITY" NIL ARITY (NIL) |domain| NIL NIL NIL) (|ApplyRules| 88299 88490 88904 "APPRULE" NIL APPRULE (NIL T T T) |package| NIL NIL NIL) (|ApplyUnivariateSkewPolynomial| 87745 87808 88049 "APPLYORE" NIL APPLYORE (NIL T T T) |package| NIL NIL NIL) (|AnyFunctions1| 86907 87088 87340 "ANY1" NIL ANY1 (NIL T) |package| NIL NIL NIL) (|Any| 86228 86535 86708 "ANY" NIL ANY (NIL) |domain| NIL NIL NIL) (|AntiSymm| 83815 85087 85601 "ANTISYM" NIL ANTISYM (NIL T NIL) |domain| NIL NIL NIL) (|AnonymousFunction| 83189 83463 83646 "ANON" NIL ANON (NIL) |domain| NIL NIL NIL) (|AlgebraicNumber| 77419 82033 82720 "AN" NIL AN (NIL) |domain| NIL NIL NIL) (|AbelianMonoidRing| 72089 73815 73923 "AMR" 74548 AMR (NIL T T) |category| NIL 75374 NIL) (|AbelianMonoidRing&| 71197 71529 72084 "AMR-" NIL AMR- (NIL T T T) |package| NIL NIL NIL) (|AssociationList| 65507 71073 71192 "ALIST" NIL ALIST (NIL T T) |domain| NIL NIL NIL) (|AlgebraGivenByStructuralConstants| 61835 64916 65245 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) |domain| NIL NIL NIL) (|AlgebraPackage| 59084 59857 60760 "ALGPKG" NIL ALGPKG (NIL T T) |package| NIL NIL NIL) (|AlgebraicMultFact| 58104 58259 58590 "ALGMFACT" NIL ALGMFACT (NIL T T T) |package| NIL NIL NIL) (|AlgebraicManipulations| 55068 55604 56496 "ALGMANIP" NIL ALGMANIP (NIL T T) |package| NIL NIL NIL) (|AlgebraicFunctionField| 47408 54427 54745 "ALGFF" NIL ALGFF (NIL T T T NIL) |domain| NIL NIL NIL) (|AlgFactor| 46592 46776 47065 "ALGFACT" NIL ALGFACT (NIL T) |package| NIL NIL NIL) (|Algebra| 44962 45833 45902 "ALGEBRA" 45907 ALGEBRA (NIL T) |category| NIL 45967 NIL) (|Algebra&| 44647 44740 44957 "ALGEBRA-" NIL ALGEBRA- (NIL T T) |package| NIL NIL NIL) (|AssociationListAggregate| 36087 42592 42703 "ALAGG" 42917 ALAGG (NIL T T) |category| |AssociationList| 43128 NIL) (|ArcHyperbolicFunctionCategory| 35494 35648 35736 "AHYP" 35908 AHYP (NIL) |category| NIL NIL NIL) (|Aggregate| 34891 35042 35090 "AGG" 35281 AGG (NIL) |category| NIL 35476 NIL) (|Aggregate&| 34661 34728 34886 "AGG-" NIL AGG- (NIL T) |package| NIL NIL NIL) (|AlgebraicFunction| 32229 32724 33346 "AF" NIL AF (NIL T T) |package| NIL NIL NIL) (|AddAst| 31681 31980 32122 "ADDAST" NIL ADDAST (NIL) |domain| NIL NIL NIL) (|PlaneAlgebraicCurvePlot| 30788 31122 31402 "ACPLOT" NIL ACPLOT (NIL) |domain| NIL NIL NIL) (|AlgebraicallyClosedFunctionSpace| 18418 26293 26411 "ACFS" 27001 ACFS (NIL T) |category| |Expression| 27340 NIL) (|AlgebraicallyClosedFunctionSpace&| 17050 17526 18413 "ACFS-" NIL ACFS- (NIL T T) |package| NIL NIL NIL) (|AlgebraicallyClosedField| 12305 14780 14858 "ACF" 15493 ACF (NIL) |category| NIL 15985 NIL) (|AlgebraicallyClosedField&| 11372 11728 12300 "ACF-" NIL ACF- (NIL T) |package| NIL NIL NIL) (|AbelianSemiGroup| 10712 10978 11040 "ABELSG" 11167 ABELSG (NIL) |category| NIL 11275 NIL) (|AbelianSemiGroup&| 10519 10563 10707 "ABELSG-" NIL ABELSG- (NIL T) |package| NIL NIL NIL) (|AbelianMonoid| 9433 9857 9913 "ABELMON" 10155 ABELMON (NIL) |category| NIL 10395 NIL) (|AbelianMonoid&| 8936 9123 9428 "ABELMON-" NIL ABELMON- (NIL T) |package| NIL NIL NIL) (|AbelianGroup| 7913 8452 8506 "ABELGRP" 8584 ABELGRP (NIL) |category| NIL 8716 NIL) (|AbelianGroup&| 7285 7529 7908 "ABELGRP-" NIL ABELGRP- (NIL T) |package| NIL NIL NIL) (|OneDimensionalArrayAggregate| 3204 6178 6278 "A1AGG" 6283 A1AGG (NIL T) |category| NIL 6361 NIL) (|OneDimensionalArrayAggregate&| 30 1394 3199 "A1AGG-" NIL A1AGG- (NIL T T) |package| NIL NIL NIL))
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