diff options
| author | dos-reis <gdr@axiomatics.org> | 2013-06-24 16:39:32 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2013-06-24 16:39:32 +0000 |
| commit | 36db462d3a02e5df058861589b60d1f9c808e7c3 (patch) | |
| tree | 477a8c3be153d9ca4ba4fc085090e3f6c0a39b03 /src/share/algebra/interp.daase | |
| parent | 0af724597cff0d9235a37223e46e6f9ffb804e0b (diff) | |
| download | open-axiom-36db462d3a02e5df058861589b60d1f9c808e7c3.tar.gz | |
Simplify database construction.
Diffstat (limited to 'src/share/algebra/interp.daase')
| -rw-r--r-- | src/share/algebra/interp.daase | 8126 |
1 files changed, 4063 insertions, 4063 deletions
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 399145ca..5d24f455 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,4065 +1,4065 @@ -(2793524 . 3581069288) -((-1737 (((-82) (-1 (-82) |#2| |#2|) $) 86 T ELT) (((-82) $) NIL T ELT)) (-1735 (($ (-1 (-82) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3791 ((|#2| $ (-485) |#2|) NIL T ELT) ((|#2| $ (-1147 (-485)) |#2|) 44 T ELT)) (-2299 (($ $) 80 T ELT)) (-3845 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3422 (((-485) (-1 (-82) |#2|) $) 27 T ELT) (((-485) |#2| $) NIL T ELT) (((-485) |#2| $ (-485)) 96 T ELT)) (-3521 (($ (-1 (-82) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2611 (((-584 |#2|) $) 13 T ELT)) (-3329 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3846 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2306 (($ |#2| $ (-485)) NIL T ELT) (($ $ $ (-485)) 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T) ((-69) OR (|has| |#2| (-1014)) (|has| |#2| (-962)) (|has| |#2| (-757)) (|has| |#2| (-718)) (|has| |#2| (-664)) (|has| |#2| (-319)) (|has| |#2| (-311)) (|has| |#2| (-145)) (|has| |#2| (-101)) (|has| |#2| (-69)) (|has| |#2| (-22)) (|has| |#2| (-20)) (|has| |#2| (-18))) ((-79 |#2| |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-311)) (|has| |#2| (-145))) ((-101) OR (|has| |#2| (-962)) (|has| |#2| (-718)) (|has| |#2| (-311)) (|has| |#2| (-145)) (|has| |#2| (-101)) (|has| |#2| (-18))) ((-556 (-349 (-485))) -11 (|has| |#2| (-951 (-349 (-485)))) (|has| |#2| (-1014))) ((-556 (-485)) OR (|has| |#2| (-962)) (-11 (|has| |#2| (-951 (-485))) (|has| |#2| (-1014)))) ((-556 |#2|) |has| |#2| (-1014)) ((-553 (-773)) OR (|has| |#2| (-1014)) (|has| |#2| (-962)) (|has| |#2| (-757)) (|has| |#2| (-718)) (|has| |#2| (-664)) (|has| |#2| (-319)) (|has| |#2| (-311)) (|has| |#2| (-145)) (|has| |#2| (-553 (-773))) (|has| |#2| (-101)) (|has| |#2| (-22)) (|has| |#2| (-20)) (|has| |#2| (-18))) ((-553 (-1180 |#2|)) . T) ((-185 $) OR (-11 (|has| |#2| (-188)) (|has| |#2| (-962))) (-11 (|has| |#2| (-189)) (|has| |#2| (-962)))) ((-183 |#2|) |has| |#2| (-962)) ((-189) -11 (|has| |#2| (-189)) (|has| |#2| (-962))) ((-188) OR (-11 (|has| |#2| (-188)) (|has| |#2| (-962))) (-11 (|has| |#2| (-189)) (|has| |#2| (-962)))) ((-224 |#2|) |has| |#2| (-962)) ((-240 (-485) |#2|) . T) ((-242 (-485) |#2|) . T) ((-259 |#2|) -11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ((-319) |has| |#2| (-319)) ((-317 |#2|) . T) ((-328 |#2|) |has| |#2| (-962)) ((-354 |#2|) |has| |#2| (-1014)) ((-380 |#2|) . T) ((-429 |#2|) . T) ((-539 (-485) |#2|) . T) ((-456 |#2| |#2|) -11 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1014))) ((-12) . T) ((-589 (-485)) OR (|has| |#2| (-962)) (|has| |#2| (-311)) (|has| |#2| (-145)) (|has| |#2| (-18))) ((-589 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-664)) (|has| |#2| (-311)) (|has| |#2| (-145))) ((-589 $) |has| |#2| (-962)) ((-591 (-485)) -11 (|has| |#2| (-581 (-485))) (|has| |#2| (-962))) ((-591 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-311)) (|has| |#2| (-145))) ((-591 $) |has| |#2| (-962)) ((-583 |#2|) OR (|has| |#2| (-664)) (|has| |#2| (-311)) (|has| |#2| (-145))) ((-581 (-485)) -11 (|has| |#2| (-581 (-485))) (|has| |#2| (-962))) ((-581 |#2|) |has| |#2| (-962)) ((-655 |#2|) OR (|has| |#2| (-311)) (|has| |#2| (-145))) ((-664) |has| |#2| (-962)) ((-717) |has| |#2| (-718)) ((-718) |has| |#2| (-718)) ((-719) |has| |#2| (-718)) ((-722) |has| |#2| (-718)) ((-757) OR (|has| |#2| (-757)) (|has| |#2| (-718))) ((-760) OR (|has| |#2| (-757)) (|has| |#2| (-718))) ((-807 $ (-1091)) OR (-11 (|has| |#2| (-812 (-1091))) (|has| |#2| (-962))) (-11 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962)))) ((-810 (-1091)) -11 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962))) ((-812 (-1091)) OR (-11 (|has| |#2| (-812 (-1091))) (|has| |#2| (-962))) (-11 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962)))) ((-951 (-349 (-485))) -11 (|has| |#2| (-951 (-349 (-485)))) (|has| |#2| (-1014))) ((-951 (-485)) -11 (|has| |#2| (-951 (-485))) (|has| |#2| (-1014))) ((-951 |#2|) |has| |#2| (-1014)) ((-964 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-664)) (|has| |#2| (-311)) (|has| |#2| (-145))) ((-969 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-311)) (|has| |#2| (-145))) ((-962) |has| |#2| (-962)) ((-971) |has| |#2| (-962)) ((-1026) |has| |#2| (-962)) ((-1062) |has| |#2| (-962)) ((-1014) OR (|has| |#2| (-1014)) (|has| |#2| (-962)) (|has| |#2| (-757)) (|has| |#2| (-718)) (|has| |#2| (-664)) (|has| |#2| (-319)) (|has| |#2| (-311)) (|has| |#2| (-145)) (|has| |#2| (-101)) (|has| |#2| (-22)) (|has| |#2| (-20)) (|has| |#2| (-18))) ((-1130) . 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T) ((-589 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-591 (-485)) |has| |#1| (-581 (-485))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-583 |#1|) |has| |#1| (-145)) ((-583 $) OR (|has| |#1| (-822)) (|has| |#1| (-496)) (|has| |#1| (-392))) ((-581 (-485)) |has| |#1| (-581 (-485))) ((-581 |#1|) . T) ((-655 (-349 (-485))) |has| |#1| (-35 (-349 (-485)))) ((-655 |#1|) |has| |#1| (-145)) ((-655 $) OR (|has| |#1| (-822)) (|has| |#1| (-496)) (|has| |#1| (-392))) ((-664) . T) ((-807 $ (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-807 $ |#3|) . T) ((-810 (-1091)) |has| |#1| (-810 (-1091))) ((-810 |#3|) . T) ((-812 (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-812 |#3|) . 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T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . 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|) $) 17 T ELT))) +(((|AbelianSemiGroup|) (|Category|)) (T |AbelianSemiGroup|)) +((+ (*1 *1 *1 *1) (|ofCategory| *1 (|AbelianSemiGroup|))) (* (*1 *1 *2 *1) (AND (|ofCategory| *1 (|AbelianSemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE + ($ $ $)) (SIGNATURE * ($ (|PositiveInteger|) $)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|zerosOf| (#1=(#2=(|List| $) #3=(|Polynomial| $)) 32 T ELT) (#4=(#2# #5=(|SparseUnivariatePolynomial| $)) 16 T ELT) (#6=(#2# #5# #7=(|Symbol|)) 20 T ELT)) (|zeroOf| (#8=($ #3#) 30 T ELT) (#9=($ #5#) 11 T ELT) (#10=($ #5# #7#) 60 T ELT)) (|rootsOf| (#1# 33 T ELT) (#4# 18 T ELT) (#6# 19 T ELT)) (|rootOf| (#8# 31 T ELT) (#9# 13 T ELT) (#10# NIL T ELT))) +(((|AlgebraicallyClosedField&| |#1|) (CATEGORY |package| (SIGNATURE |zerosOf| #1=(#2=(|List| |#1|) #3=(|SparseUnivariatePolynomial| |#1|) #4=(|Symbol|))) (SIGNATURE |zerosOf| #5=(#2# #3#)) (SIGNATURE |zerosOf| #6=(#2# #7=(|Polynomial| |#1|))) (SIGNATURE |zeroOf| #8=(|#1| #3# #4#)) (SIGNATURE |zeroOf| #9=(|#1| #3#)) (SIGNATURE |zeroOf| #10=(|#1| #7#)) (SIGNATURE |rootsOf| #1#) (SIGNATURE |rootsOf| #5#) (SIGNATURE |rootsOf| #6#) (SIGNATURE |rootOf| #8#) (SIGNATURE |rootOf| #9#) (SIGNATURE |rootOf| #10#)) (|AlgebraicallyClosedField|)) (T |AlgebraicallyClosedField&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zerosOf| (((|List| $) 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(|SparseUnivariatePolynomial| $)) 106 T ELT) (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 105 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #8=(|Integer|)) 109 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 68 T ELT)) (|lcm| (#11=($ $ $) 60 T ELT) (#12=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#13=(|SparseUnivariatePolynomial| $) #13# #13#) 58 T ELT)) (|gcd| (#11# 62 T ELT) (#12# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #14=(|:| |coef1| $) #15=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #14# #15#) #10#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #16=(|Fraction| #17=(|Integer|))) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #17#) 87 T ELT) (($ $ (|Fraction| #8#)) 108 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #18=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #16#) 86 T ELT) (($ #16# . #18#) 85 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| 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|rootOf| ($ (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |rootsOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |rootsOf| ((|List| $) (|SparseUnivariatePolynomial| $))) (SIGNATURE |rootsOf| ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |zeroOf| ($ (|Polynomial| $))) (SIGNATURE |zeroOf| ($ (|SparseUnivariatePolynomial| $))) (SIGNATURE |zeroOf| ($ (|SparseUnivariatePolynomial| $) (|Symbol|))) (SIGNATURE |zerosOf| ((|List| $) (|Polynomial| $))) (SIGNATURE |zerosOf| ((|List| $) (|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|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((|zerosOf| #1=((#2=(|List| $) #3=(|Polynomial| $)) NIL T ELT) #4=((#2# #5=(|SparseUnivariatePolynomial| $)) NIL T ELT) (#6=(#2# #5# #7=(|Symbol|)) 54 T ELT) (#8=(#2# $) 22 T ELT) (#9=(#2# $ #7#) 45 T ELT)) (|zeroOf| #10=(($ #3#) NIL T ELT) #11=(($ #5#) NIL T ELT) (#12=($ #5# #7#) 56 T ELT) (#13=($ $) 20 T ELT) (#14=($ $ #7#) 39 T ELT)) (|rootsOf| #1# #4# (#6# 52 T ELT) (#8# 18 T ELT) (#9# 47 T ELT)) (|rootOf| #10# #11# (#12# NIL T ELT) (#13# 15 T ELT) (#14# 41 T ELT))) +(((|AlgebraicallyClosedFunctionSpace&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zerosOf| #1=(#2=(|List| |#1|) |#1| #3=(|Symbol|))) (SIGNATURE |zeroOf| #4=(|#1| |#1| #3#)) (SIGNATURE |zerosOf| #5=(#2# |#1|)) (SIGNATURE |zeroOf| #6=(|#1| |#1|)) (SIGNATURE |rootsOf| #1#) (SIGNATURE |rootOf| #4#) (SIGNATURE |rootsOf| #5#) (SIGNATURE |rootOf| #6#) (SIGNATURE |zerosOf| #7=(#2# #8=(|SparseUnivariatePolynomial| |#1|) #3#)) (SIGNATURE |zerosOf| #9=(#2# #8#)) (SIGNATURE |zerosOf| #10=(#2# #11=(|Polynomial| |#1|))) (SIGNATURE |zeroOf| #12=(|#1| #8# #3#)) (SIGNATURE |zeroOf| #13=(|#1| #8#)) (SIGNATURE |zeroOf| #14=(|#1| #11#)) (SIGNATURE |rootsOf| #7#) (SIGNATURE |rootsOf| #9#) (SIGNATURE |rootsOf| #10#) (SIGNATURE |rootOf| #12#) (SIGNATURE |rootOf| #13#) (SIGNATURE |rootOf| #14#)) (|AlgebraicallyClosedFunctionSpace| |#2|) (|IntegralDomain|)) (T |AlgebraicallyClosedFunctionSpace&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zerosOf| (#2=(#3=(|List| $) #4=(|Polynomial| $)) 98 T ELT) (#5=(#3# #6=(|SparseUnivariatePolynomial| $)) 97 T ELT) (#7=(#3# #6# #8=(|Symbol|)) 96 T ELT) (((|List| $) $) 148 T ELT) (((|List| $) $ (|Symbol|)) 146 T ELT)) (|zeroOf| (#9=($ #4#) 101 T ELT) (#10=($ #6#) 100 T ELT) (#11=($ #6# #8#) 99 T ELT) (($ $) 149 T ELT) (($ $ (|Symbol|)) 147 T ELT)) (|zero?| ((#12=(|Boolean|) $) 22 T ELT)) (|variables| ((#13=(|List| #14=(|Symbol|)) $) 217 T ELT)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ #15=(|Kernel| $)) 249 (|has| |#1| . #16=((|IntegralDomain|))) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#17=(|Boolean|) $) 52 T ELT)) (|tower| (#18=(#19=(|List| #20=(|Kernel| $)) $) 180 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|subst| (($ $ #19# #21=(|List| $)) 170 T ELT) (($ $ (|List| #22=(|Equation| $))) 169 T ELT) (($ $ #22#) 168 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#23=((|Factored| $) $) 90 T ELT)) (|sqrt| (($ $) 110 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#24=($) 23 T CONST)) (|rootsOf| (#2# 104 T ELT) (#5# 103 T ELT) (#7# 102 T ELT) (((|List| $) $) 152 T ELT) (((|List| $) $ (|Symbol|)) 150 T ELT)) (|rootOf| (#9# 107 T ELT) (#10# 106 T ELT) (#11# 105 T ELT) (($ $) 153 T ELT) (($ $ (|Symbol|)) 151 T ELT)) (|retractIfCan| (((|Union| (|Polynomial| |#1|) . #25=("failed")) . #26=($)) 268 (|has| |#1| . #27=((|Ring|))) ELT) (((|Union| (|Fraction| (|Polynomial| |#1|)) . #25#) . #26#) 251 (|has| |#1| . #16#) ELT) (((|Union| |#1| . #25#) . #26#) 213 T ELT) (((|Union| #28=(|Integer|) . #25#) . #26#) 210 (|has| |#1| . #29=((|RetractableTo| #28#))) ELT) (((|Union| #14# . #25#) . #26#) 204 T ELT) (((|Union| #20# . #25#) . #26#) 155 T ELT) (((|Union| #30=(|Fraction| #28#) . #25#) . #26#) 143 (OR (AND (|has| |#1| . #31=((|RetractableTo| #32=(|Integer|)))) (|has| |#1| . #16#)) (|has| |#1| . #33=((|RetractableTo| #30#)))) ELT)) (|retract| (((|Polynomial| |#1|) . #34=($)) 267 (|has| |#1| . #27#) ELT) (((|Fraction| (|Polynomial| |#1|)) . #34#) 250 (|has| |#1| . #16#) ELT) ((|#1| . #34#) 212 T ELT) ((#28# . #34#) 211 (|has| |#1| . #29#) ELT) ((#14# . #34#) 203 T ELT) ((#20# . #34#) 154 T ELT) ((#30# . #34#) 144 (OR (AND (|has| |#1| . #31#) (|has| |#1| . #16#)) (|has| |#1| . #33#)) ELT)) (|rem| (#35=($ $ $) 71 T ELT)) (|reducedSystem| (((|Matrix| |#1|) . #36=(#37=(|Matrix| $))) 256 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #38=(#37# #39=(|Vector| $))) 255 (|has| |#1| . #27#) ELT) (((|Record| (|:| |mat| (|Matrix| #40=(|Integer|))) (|:| |vec| (|Vector| #40#))) . #38#) 142 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41=((|LinearlyExplicitRingOver| #40#)))) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT) (((|Matrix| #40#) . #36#) 141 (OR (|and| (|has| |#1| . #27#) (|has| |#1| . #41#)) (|and| (|has| |#1| . #41#) (|has| |#1| . #27#))) ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#35# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #42=(|List| $)) (|:| |generator| $)) #42#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|patternMatch| (((|PatternMatchResult| #43=(|Float|) . #44=($)) $ (|Pattern| #43#) (|PatternMatchResult| #43# . #44#)) 209 (|has| |#1| (|PatternMatchable| #43#)) ELT) (((|PatternMatchResult| #45=(|Integer|) . #44#) $ (|Pattern| #45#) (|PatternMatchResult| #45# . #44#)) 208 (|has| |#1| (|PatternMatchable| #45#)) ELT)) (|paren| (#46=($ #21#) 174 T ELT) (#47=($ $) 173 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|key| |#1|) (|:| |entry| |#2|)))) ELT) (($ (|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 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|key| |t#1|) (|:| |entry| |t#2|))) |t#1| $)))) +(((|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|)) (|OrderedSet|)) (|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|)) (|OrderedSet|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|CoercibleTo| (|OutputForm|))) (|has| |#2| (|SetCategory|)) (|has| |#2| (|CoercibleTo| (|OutputForm|)))) ((|Collection| #2=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . T) ((|ConvertibleTo| (|InputForm|)) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|ConvertibleTo| (|InputForm|))) ((|Dictionary| #1#) . T) ((|DictionaryOperations| #1#) . T) ((|Eltable| #3=(|Integer|) #2#) . T) ((|Eltable| (|UniversalSegment| (|Integer|)) $) . T) ((|Eltable| |#1| |#2|) . T) ((|EltableAggregate| #3# #2#) . T) ((|EltableAggregate| |#1| |#2|) . T) ((|Evalable| #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|))) ((|ExtensibleLinearAggregate| #2#) . T) ((|FiniteAggregate| #2#) . T) ((|FiniteLinearAggregate| #2#) . T) ((|Functorial| #2#) . T) ((|Functorial| |#2|) . T) ((|HomogeneousAggregate| #2#) . T) ((|HomogeneousAggregate| |#2|) . T) ((|IndexedAggregate| #3# #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) ((|LinearAggregate| #2#) . T) ((|ListAggregate| #2#) . T) ((|OrderedSet|) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) ((|OrderedType|) |has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) ((|RecursiveAggregate| #2#) . T) ((|SetCategory|) OR (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|SetCategory|)) (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|OrderedSet|)) (|has| |#2| (|SetCategory|))) ((|ShallowlyMutableAggregate| #2#) . T) ((|ShallowlyMutableAggregate| |#2|) . T) ((|StreamAggregate| #2#) . T) ((|TableAggregate| |#1| |#2|) . T) ((|Type|) . T) ((|UnaryRecursiveAggregate| #2#) . T)) +((|coerce| (((|OutputForm|) $) NIL T ELT) (($ (|Integer|)) NIL T ELT) (($ |#2|) 10 T ELT))) +(((|Algebra&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |coerce| (|#1| (|Integer|))) (SIGNATURE |coerce| ((|OutputForm|) |#1|))) (|Algebra| |#2|) (|CommutativeRing|)) (T |Algebra&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 52 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #4=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #4#) 53 T ELT))) +(((|Algebra| |#1|) (|Category|) (|CommutativeRing|)) (T |Algebra|)) +NIL +(|Join| (|Ring|) (|Module| |t#1|) (|CoercibleFrom| |t#1|)) +(((|AbelianGroup|) . 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)) +((|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#))) +((~= #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=(#17=(|Matrix| #10#) #18=(|Vector| $)) NIL T ELT) (#19=(#17#) NIL T ELT)) (|trace| #20=((#10# $) NIL T ELT)) (|tableForDiscreteLogarithm| (((|Table| #21=(|PositiveInteger|) #22=(|NonNegativeInteger|)) #23=(|Integer|)) NIL #24=(|has| #10# (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#25=(#26=(|Union| $ #27="failed") $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #28=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #29=(#2# NIL #9# ELT)) (|size| (#30=(#22#) NIL #31=(|has| #10# #32=(|Finite|)) ELT)) (|singularAtInfinity?| #33=(#34=(#3#) NIL T ELT)) (|singular?| #35=(#36=(#3# |#1|) NIL T ELT) #37=(#38=(#3# |#2|) NIL T ELT)) (|sample| (#39=($) NIL T CONST)) (|retractIfCan| (((|Union| #23# . #40=(#27#)) . #41=($)) NIL #42=(|has| #10# (|RetractableTo| #23#)) ELT) (((|Union| #43=(|Fraction| #23#) . #40#) . #41#) NIL #44=(|has| #10# (|RetractableTo| #43#)) ELT) (((|Union| #10# . #40#) . #41#) NIL T ELT)) (|retract| ((#23# . #45=($)) NIL #42# ELT) ((#43# . #45#) NIL #44# ELT) #20#) (|represents| (($ #46=(|Vector| #10#) #18#) NIL T ELT) (#47=($ #46#) 60 T ELT) (#48=($ #7# |#2|) 130 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #24# ELT)) (|rem| #49=(#50=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#17# $ #18#) NIL T ELT) ((#17# $) NIL T ELT)) (|reducedSystem| ((#51=(|Matrix| #23#) . #52=(#53=(|Matrix| $))) NIL #54=(|has| #10# (|LinearlyExplicitRingOver| #23#)) ELT) ((#55=(|Record| (|:| |mat| #51#) (|:| |vec| (|Vector| #23#))) . #56=(#53# #18#)) NIL #54# ELT) ((#57=(|Record| (|:| |mat| #17#) (|:| |vec| #46#)) . #56#) NIL T ELT) ((#17# . #52#) NIL T ELT)) (|reduceBasisAtInfinity| #58=(#59=(#18# #18#) NIL T ELT)) (|reduce| #60=(($ |#3|) NIL T ELT) ((#26# (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#26# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #32#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#21#) NIL T ELT)) (|random| (#39# NIL #31# ELT)) (|ramifiedAtInfinity?| #33#) (|ramified?| #35# #37#) (|quo| #49#) (|principalIdeal| (((|Record| (|:| |coef| #61=(|List| $)) #62=(|:| |generator| $)) #61#) NIL #9# ELT)) (|primitivePart| #63=(#13# NIL T ELT)) (|primitiveElement| #64=(#39# NIL #24# ELT)) (|primitive?| (#5# NIL #24# ELT)) (|primeFrobenius| (#65=($ $ #22#) NIL #24# ELT) #66=(#13# NIL #24# ELT)) (|prime?| #14#) (|order| (#67=(#21# $) NIL #24# ELT) (((|OnePointCompletion| #21#) $) NIL #24# ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfComponents| #68=(#30# NIL T ELT)) (|normalizeAtInfinity| (#59# 105 T ELT)) (|norm| #20#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #69=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#70=((|Maybe| $) $) NIL #24# ELT)) (|multiEuclidean| (((|Union| #61# #27#) #61# $) NIL #9# ELT)) (|minimalPolynomial| (#71=(|#3| $) NIL #9# ELT)) (|lookup| (#67# NIL #31# ELT)) (|lift| #72=(#71# NIL T ELT)) (|leftReducedSystem| ((#51# #18#) NIL #54# ELT) ((#55# . #73=(#18# $)) NIL #54# ELT) ((#57# . #73#) NIL T ELT) #15#) (|lcm| #74=(($ #61#) NIL #9# ELT) #49#) (|latex| (((|String|) $) NIL T ELT)) (|knownInfBasis| (((|Void|) #22#) 83 T ELT)) (|inverseIntegralMatrixAtInfinity| (#19# 55 T ELT)) (|inverseIntegralMatrix| (#19# 48 T ELT)) (|inv| #12#) (|integralRepresents| (#48# 131 T ELT)) (|integralMatrixAtInfinity| (#19# 49 T ELT)) (|integralMatrix| (#19# 47 T ELT)) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) #8#) #75=(|Mapping| |#2| |#2|)) 129 T ELT)) (|integralCoordinates| (#6# 67 T ELT)) (|integralBasisAtInfinity| (#76=(#18#) 46 T ELT)) (|integralBasis| (#76# 45 T ELT)) (|integralAtInfinity?| #4#) (|integral?| #4# ((#3# $ |#1|) NIL T ELT) ((#3# $ |#2|) NIL T ELT)) (|init| (#39# NIL #24# CONST)) (|index| (($ #21#) NIL #31# ELT)) (|hyperelliptic| #77=(((|Union| |#2| #27#)) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #68#) (|generator| (#39# NIL T ELT)) (|gcdPolynomial| ((#78=(|SparseUnivariatePolynomial| $) #78# #78#) NIL #9# ELT)) (|gcd| #74# #49#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #23#) (|:| |exponent| #23#)))) NIL #24# ELT)) (|factor| #28#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #27#) $ $ $) NIL #9# ELT) (((|Record| #79# #80# #62#) $ $) NIL #9# ELT)) (|exquo| (#25# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #61#) #61# $) NIL #9# ELT)) (|euclideanSize| (#81=(#22# $) NIL #9# ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|elliptic| #77#) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #9# ELT)) (|discriminant| ((#10# #18#) NIL T ELT) ((#10#) 43 T ELT)) (|discreteLog| (#81# NIL #24# ELT) (((|Union| #22# #27#) $ $) NIL #24# ELT)) (|differentiate| #82=(($ $ #83=(|Mapping| #10# #10#)) NIL #9# ELT) #84=(($ $ #83# #22#) NIL #9# ELT) (($ $ #75#) 125 T ELT) #85=(($ $ #86=(|List| #69#) (|List| #22#)) NIL #87=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #69#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #69#)))) ELT) #88=(($ $ #69# #22#) NIL #87# ELT) #89=(($ $ #86#) NIL #87# ELT) #90=(($ $ #69#) NIL #87# ELT) #91=(#65# NIL #92=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #24#) ELT) #93=(#13# NIL #92# ELT)) (|derivationCoordinates| ((#17# #18# #83#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 54 T ELT)) (|createPrimitiveElement| #64#) (|coordinates| ((#46# $ #18#) NIL T ELT) ((#17# #18# #18#) NIL T ELT) (#94=(#46# $) 61 T ELT) (#16# 106 T ELT)) (|convert| (#94# NIL T ELT) (#47# NIL T ELT) #72# #60#) (|conditionP| (((|Union| #18# #27#) #53#) NIL #24# ELT)) (|complementaryBasis| #58#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #23#) NIL T ELT) (($ #10#) NIL T ELT) (($ #43#) NIL (OR #9# #44#) ELT) #12#) (|charthRoot| #66# (#70# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #72#) (|characteristic| (#30# NIL T CONST)) (|branchPointAtInfinity?| (#34# 41 T ELT)) (|branchPoint?| (#36# 53 T ELT) (#38# 137 T ELT)) (|before?| #1#) (|basis| (#76# NIL T ELT)) (|associates?| #29#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #75#) NIL T ELT)) (|absolutelyIrreducible?| #33#) (|Zero| (#39# 17 T CONST)) (|One| (#39# 27 T CONST)) (D #82# #84# #85# #88# #89# #90# #91# #93#) (= #1#) (/ #49#) (- #63# #95=(#50# NIL T ELT)) (+ #95#) (** (($ $ #21#) NIL T ELT) (#65# NIL T ELT) (($ $ #23#) NIL #9# ELT)) (* (($ #21# $) NIL T ELT) (($ #22# $) NIL T ELT) (($ #23# . #96=($)) NIL T ELT) #95# (($ $ #10#) NIL T ELT) (($ #10# . #96#) NIL T ELT) (($ #43# . #96#) NIL #9# ELT) (($ $ #43#) NIL #9# ELT))) +(((|AlgebraicFunctionField| |#1| |#2| |#3| |#4|) (|Join| (|FunctionFieldCategory| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |knownInfBasis| ((|Void|) (|NonNegativeInteger|))))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) |#3|) (T |AlgebraicFunctionField|)) +((|knownInfBasis| (*1 *2 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Field|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|AlgebraicFunctionField| *4 *5 *6 *7)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofType| *7 *6)))) +((|rootSplit| (#1=(|#2| |#2|) 47 T ELT)) (|rootSimp| (#1# 136 #2=(AND (|has| |#2| (|FunctionSpace| |#1|)) (|has| |#1| (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|))))) ELT)) (|rootProduct| (#1# 100 #2# ELT)) (|rootPower| (#1# 101 #2# ELT)) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) 80 #2# ELT)) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) 44 T ELT)) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) 18 T ELT) ((|#2| |#2| (|List| |#2|)) 20 T ELT) ((|#2| |#2| |#2|) 21 T ELT) (#1# 16 T ELT))) +(((|AlgebraicManipulations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootSplit| #1=(|#2| |#2|)) (SIGNATURE |ratDenom| #1#) (SIGNATURE |ratDenom| (|#2| |#2| |#2|)) (SIGNATURE |ratDenom| (|#2| |#2| (|List| |#2|))) (SIGNATURE |ratDenom| (|#2| |#2| (|List| (|Kernel| |#2|)))) (SIGNATURE |ratPoly| ((|SparseUnivariatePolynomial| |#2|) |#2|)) (IF (|has| |#1| (|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)))) (IF (|has| |#2| (|FunctionSpace| |#1|)) (PROGN (SIGNATURE |rootPower| #1#) (SIGNATURE |rootProduct| #1#) (SIGNATURE |rootSimp| #1#) (SIGNATURE |rootKerSimp| (|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)))) |%noBranch|) |%noBranch|)) (|IntegralDomain|) (|Join| (|Field|) (|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| #2=(#3=(|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $)) (SIGNATURE |denom| #2#) (SIGNATURE |coerce| ($ #3#))))) (T |AlgebraicManipulations|)) +((|rootKerSimp| (*1 *2 *3 *2 *4) (AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|NonNegativeInteger|)) (|ofCategory| *5 #1=(|Join| (|GcdDomain|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 #2=(|IntegralDomain|)) (|isDomain| *1 (|AlgebraicManipulations| *5 *2)) (|ofCategory| *2 (|FunctionSpace| *5)) (|ofCategory| *2 (|Join| #3=(|Field|) #4=(|ExpressionSpace|) (CATEGORY |domain| (SIGNATURE |numer| #5=(#6=(|SparseMultivariatePolynomial| *5 #7=(|Kernel| $)) $)) (SIGNATURE |denom| #5#) (SIGNATURE |coerce| ($ #6#))))))) (|rootSimp| #8=(*1 *2 *2) #9=(AND (|ofCategory| *3 #1#) #10=(|ofCategory| *3 #2#) #11=(|isDomain| *1 (|AlgebraicManipulations| *3 *2)) (|ofCategory| *2 (|FunctionSpace| *3)) #12=(|ofCategory| *2 (|Join| #3# #4# (CATEGORY |domain| (SIGNATURE |numer| #13=(#14=(|SparseMultivariatePolynomial| *3 #7#) $)) (SIGNATURE |denom| #13#) (SIGNATURE |coerce| ($ #14#))))))) (|rootProduct| #8# #9#) (|rootPower| #8# #9#) (|ratPoly| (*1 *2 *3) (AND #15=(|ofCategory| *4 #2#) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) (|isDomain| *1 (|AlgebraicManipulations| *4 *3)) (|ofCategory| *3 #16=(|Join| #3# #4# (CATEGORY |domain| (SIGNATURE |numer| #17=(#18=(|SparseMultivariatePolynomial| *4 #7#) $)) (SIGNATURE |denom| #17#) (SIGNATURE |coerce| ($ #18#))))))) (|ratDenom| #19=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| (|Kernel| *2))) #20=(|ofCategory| *2 #16#) #15# #21=(|isDomain| *1 (|AlgebraicManipulations| *4 *2)))) (|ratDenom| #19# (AND (|isDomain| *3 (|List| *2)) #20# #15# #21#)) (|ratDenom| (*1 *2 *2 *2) #22=(AND #10# #11# #12#)) (|ratDenom| #8# #22#) (|rootSplit| #8# #22#)) +((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#3|)) #1# #2=(|List| (|AlgebraicNumber|))) 23 T ELT) (((|Factored| |#3|) |#3| #2#) 19 T ELT))) +(((|AlgebraicMultFact| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#3|) |#3| #1=(|List| #2=(|AlgebraicNumber|)))) (SIGNATURE |factor| ((|Factored| #3=(|SparseUnivariatePolynomial| |#3|)) #3# #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|PolynomialCategory| #2# |#2| |#1|)) (T |AlgebraicMultFact|)) +((|factor| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *4 (|List| #3=(|AlgebraicNumber|))) #4=(|ofCategory| *5 (|OrderedSet|)) #5=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #6=(|PolynomialCategory| #3# *6 *5)) (|isDomain| *2 (|Factored| #7=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *7)) (|isDomain| *3 #7#))) (|factor| #1# (AND #2# #4# #5# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|AlgebraicMultFact| *5 *6 *3)) (|ofCategory| *3 #6#)))) +((|weakBiRank| (#1=((|NonNegativeInteger|) |#2|) 70 T ELT)) (|rightRank| (#1# 74 T ELT)) (|radicalOfLeftTraceForm| (#2=(#3=(|List| |#2|)) 37 T ELT)) (|leftRank| (#1# 73 T ELT)) (|doubleRank| (#1# 69 T ELT)) (|biRank| (#1# 72 T ELT)) (|basisOfRightNucloid| (#4=((|List| (|Matrix| |#1|))) 65 T ELT)) (|basisOfRightNucleus| (#2# 60 T ELT)) (|basisOfRightAnnihilator| (#5=(#3# |#2|) 48 T ELT)) (|basisOfNucleus| (#2# 62 T ELT)) (|basisOfMiddleNucleus| (#2# 61 T ELT)) (|basisOfLeftNucloid| (#4# 53 T ELT)) (|basisOfLeftNucleus| (#2# 59 T ELT)) (|basisOfLeftAnnihilator| (#5# 47 T ELT)) (|basisOfCommutingElements| (#2# 55 T ELT)) (|basisOfCentroid| (#4# 66 T ELT)) (|basisOfCenter| (#2# 64 T ELT)) (|basis| ((#6=(|Vector| |#2|) #6#) 99 (|has| |#1| (|EuclideanDomain|)) ELT))) +(((|AlgebraPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |leftRank| #1=((|NonNegativeInteger|) |#2|)) (SIGNATURE |rightRank| #1#) (SIGNATURE |doubleRank| #1#) (SIGNATURE |weakBiRank| #1#) (SIGNATURE |biRank| #1#) (SIGNATURE |basisOfCommutingElements| #2=(#3=(|List| |#2|))) (SIGNATURE |basisOfLeftAnnihilator| #4=(#3# |#2|)) (SIGNATURE |basisOfRightAnnihilator| #4#) (SIGNATURE |basisOfLeftNucleus| #2#) (SIGNATURE |basisOfRightNucleus| #2#) (SIGNATURE |basisOfMiddleNucleus| #2#) (SIGNATURE |basisOfNucleus| #2#) (SIGNATURE |basisOfCenter| #2#) (SIGNATURE |basisOfLeftNucloid| #5=((|List| (|Matrix| |#1|)))) (SIGNATURE |basisOfRightNucloid| #5#) (SIGNATURE |basisOfCentroid| #5#) (SIGNATURE |radicalOfLeftTraceForm| #2#) (IF (|has| |#1| (|EuclideanDomain|)) (SIGNATURE |basis| (#6=(|Vector| |#2|) #6#)) |%noBranch|)) (|IntegralDomain|) (|FramedNonAssociativeAlgebra| |#1|)) (T |AlgebraPackage|)) +((|basis| (*1 *2 *2) (AND (|isDomain| *2 (|Vector| *4)) #1=(|ofCategory| *4 (|FramedNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|EuclideanDomain|)) #2=(|ofCategory| *3 #3=(|IntegralDomain|)) #4=(|isDomain| *1 (|AlgebraPackage| *3 *4)))) (|radicalOfLeftTraceForm| #5=(*1 *2) #6=(AND #2# (|isDomain| *2 (|List| *4)) #4# #1#)) (|basisOfCentroid| #5# #7=(AND #2# (|isDomain| *2 (|List| (|Matrix| *3))) #4# #1#)) (|basisOfRightNucloid| #5# #7#) (|basisOfLeftNucloid| #5# #7#) (|basisOfCenter| #5# #6#) (|basisOfNucleus| #5# #6#) (|basisOfMiddleNucleus| #5# #6#) (|basisOfRightNucleus| #5# #6#) (|basisOfLeftNucleus| #5# #6#) (|basisOfRightAnnihilator| #8=(*1 *2 *3) #9=(AND #10=(|ofCategory| *4 #3#) (|isDomain| *2 (|List| *3)) #11=(|isDomain| *1 (|AlgebraPackage| *4 *3)) #12=(|ofCategory| *3 (|FramedNonAssociativeAlgebra| *4)))) (|basisOfLeftAnnihilator| #8# #9#) (|basisOfCommutingElements| #5# #6#) (|biRank| #8# #13=(AND #10# (|isDomain| *2 (|NonNegativeInteger|)) #11# #12#)) (|weakBiRank| #8# #13#) (|doubleRank| #8# #13#) (|rightRank| #8# #13#) (|leftRank| #8# #13#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#7=(|Vector| #8=(|Matrix| |#1|)) #9=(|Vector| $)) NIL T ELT) ((#7#) 24 T ELT)) (|someBasis| (#10=(#9#) 52 T ELT)) (|sample| #11=(($) NIL T CONST)) (|rightUnits| #12=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #13=((#8# #9#) NIL T ELT) #14=((#8#) NIL T ELT)) (|rightTrace| #15=((|#1| $) NIL T ELT)) (|rightRegularRepresentation| #16=((#8# $ #9#) NIL T ELT) #17=((#8# $) NIL T ELT)) (|rightRecip| #18=(#19=(#4# $) NIL #6# ELT)) (|rightRankPolynomial| #20=(((|SparseUnivariatePolynomial| #21=(|Polynomial| |#1|))) NIL (|has| |#1| (|Field|)) ELT)) (|rightPower| #22=(($ $ #23=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #15#) (|rightMinimalPolynomial| #24=(#25=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #26=((|#1| #9#) NIL T ELT) #27=((|#1|) NIL T ELT)) (|rightCharacteristicPolynomial| #28=(#25# NIL T ELT)) (|rightAlternative?| (#29=(#2#) 99 T ELT)) (|represents| (($ #30=(|Vector| |#1|) #9#) NIL T ELT) #31=(#32=($ #30#) NIL T ELT)) (|recip| (#19# 14 #6# ELT)) (|rank| ((#23#) 53 T ELT)) (|powerAssociative?| #33=(#29# NIL T ELT)) (|plenaryPower| #22#) (|opposite?| #1#) (|noncommutativeJordanAlgebra?| #33#) (|lieAlgebra?| #33#) (|lieAdmissible?| (#29# 101 T ELT)) (|leftUnits| #12#) (|leftUnit| #3#) (|leftTraceMatrix| #13# #14#) (|leftTrace| #15#) (|leftRegularRepresentation| #16# #17#) (|leftRecip| #18#) (|leftRankPolynomial| #20#) (|leftPower| #22#) (|leftNorm| #15#) (|leftMinimalPolynomial| #24#) (|leftDiscriminant| #26# #27#) (|leftCharacteristicPolynomial| #28#) (|leftAlternative?| (#29# 98 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|jordanAlgebra?| (#29# 106 T ELT)) (|jordanAdmissible?| (#29# 105 T ELT)) (|jacobiIdentity?| (#29# 107 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|flexible?| (#29# 100 T ELT)) (|elt| ((|#1| $ #34=(|Integer|)) 55 T ELT)) (|coordinates| ((#30# $ #9#) 48 T ELT) ((#8# #9# #9#) NIL T ELT) (#35=(#30# $) 28 T ELT) #13#) (|convert| (#35# NIL T ELT) #31#) (|conditionsForIdempotents| ((#36=(|List| #21#) #9#) NIL T ELT) ((#36#) NIL T ELT)) (|commutator| #37=(#38=($ $ $) NIL T ELT)) (|commutative?| (#29# 95 T ELT)) (|coerce| (((|OutputForm|) $) 71 T ELT) (#32# 22 T ELT)) (|before?| #1#) (|basis| (#10# 51 T ELT)) (|associatorDependence| (((|List| #30#)) NIL #6# ELT)) (|associator| (($ $ $ $) NIL T ELT)) (|associative?| (#29# 91 T ELT)) (|apply| (($ #8# $) 18 T ELT)) (|antiCommutator| #37#) (|antiCommutative?| (#29# 97 T ELT)) (|antiAssociative?| (#29# 92 T ELT)) (|alternative?| (#29# 90 T ELT)) (|Zero| #11#) (= #1#) (- (($ $) NIL T ELT) #37#) (+ #37#) (** #22#) (* (($ #23# $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #34# . #39=($)) NIL T ELT) (#38# 80 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #39#) NIL T ELT) (($ (|SquareMatrix| |#2| |#1|) $) 19 T ELT))) +(((|AlgebraGivenByStructuralConstants| |#1| |#2| |#3| |#4|) (|Join| (|FramedNonAssociativeAlgebra| |#1|) (|LeftModule| (|SquareMatrix| |#2| |#1|)) (CATEGORY |domain| (SIGNATURE |coerce| ($ (|Vector| |#1|))))) (|Field|) (|PositiveInteger|) (|List| (|Symbol|)) (|Vector| (|Matrix| |#1|))) (T |AlgebraGivenByStructuralConstants|)) +((|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|Field|)) (|ofType| *6 (|Vector| (|Matrix| *3))) (|isDomain| *1 (|AlgebraGivenByStructuralConstants| *3 *4 *5 *6)) (|ofType| *4 (|PositiveInteger|)) (|ofType| *5 (|List| (|Symbol|)))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL (OR #4=(|has| #5=(|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) #6=(|BasicType|)) #7=(|has| |#2| #6#)) ELT)) (|value| #8=(#9=(#5# $) NIL T ELT)) (|third| #8#) (|tail| #10=(#11=($ $) NIL T ELT)) (|table| (#12=($) NIL T ELT) #13=(#14=($ #15=(|List| #5#)) NIL T ELT)) (|swap!| ((#16=(|Void|) $ |#1| |#1|) NIL #17=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT) ((#16# $ #18=(|Integer|) #18#) NIL #19=(|has| $ (|ShallowlyMutableAggregate| #5#)) ELT)) (|split!| (#20=($ $ #18#) NIL #19# ELT)) (|sorted?| ((#3# #21=(|Mapping| #3# #5# #5#) $) NIL T ELT) (#22=(#3# $) NIL #23=(|has| #5# #24=(|OrderedSet|)) ELT)) (|sort!| (#25=($ #21# $) NIL #19# ELT) (#11# NIL (AND #19# #23#) ELT)) (|sort| (#25# NIL T ELT) (#11# NIL #23# ELT)) (|size?| #26=((#3# $ #27=(|NonNegativeInteger|)) NIL T ELT)) (|setvalue!| #28=(#29=(#5# $ #5#) NIL #19# ELT)) (|setrest!| (#30=($ $ $) 35 #19# ELT)) (|setlast!| #28#) (|setfirst!| (#29# 37 #19# ELT)) (|setelt| (#31=(|#2| $ |#1| |#2|) 60 #17# ELT) #32=(#33=(#5# $ #18# #5#) NIL #19# ELT) ((#5# $ #34=(|UniversalSegment| #18#) #5#) NIL #19# ELT) ((#5# $ #35="last" #5#) NIL #19# ELT) (($ $ #36="rest" $) NIL #19# ELT) ((#5# $ #37="first" #5#) NIL #19# ELT) ((#5# $ #38="value" #5#) NIL #19# ELT)) (|setchildren!| (($ $ #39=(|List| $)) NIL #19# ELT)) (|select!| #40=(#41=($ #42=(|Mapping| #3# #5#) $) NIL #43=(|has| $ (|FiniteAggregate| #5#)) ELT) #44=(#41# NIL T ELT)) (|select| #40# #40#) (|second| #8#) (|search| (#45=((|Union| |#2| #46="failed") |#1| $) 45 T ELT)) (|sample| (#12# NIL T CONST)) (|reverse!| #47=(#11# NIL #19# ELT)) (|reverse| #10#) (|rest| #48=(($ $ #27#) NIL T ELT) (#11# 31 T ELT)) (|removeDuplicates!| (#11# NIL #4# ELT)) (|removeDuplicates| (#11# NIL #49=(AND #43# #4#) ELT)) (|remove!| (#50=($ #5# $) NIL #43# ELT) #40# (#45# 63 T ELT) #44# (#50# NIL #4# ELT)) (|remove| #51=(#50# NIL #49# ELT) #40# #51# #40#) (|reduce| #52=((#5# #53=(|Mapping| #5# #5# #5#) $ #5# #5#) NIL #4# ELT) #54=((#5# #53# $ 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#1=(|isDomain| *1 (|Arity|))) (|zero?| #2=(*1 *2 *1) #3=(AND (|isDomain| *2 (|Boolean|)) #1#)) (|one?| #2# #3#)) +((|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|)) 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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|) . 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(|operator| #8=(*1 *1 *2 *3) (AND #7# (|isDomain| *3 #9=(|NonNegativeInteger|)) #5#)) (|operator| #8# (AND #7# (|isDomain| *3 (|Arity|)) #5#)) (|nullary?| #1# #10=(AND #11=(|isDomain| *2 #12=(|Boolean|)) #5#)) (|unary?| #1# #10#) (|nary?| #1# #10#) (|weight| #1# #13=(AND (|isDomain| *2 #9#) #5#)) (|weight| #14=(*1 *1 *1 *2) #13#) (|equality| #14# #15=(AND (|isDomain| *2 (|Mapping| #12# #6# #6#)) #5#)) (|comparison| #14# #15#) (|display| #1# (AND (|isDomain| *2 (|Maybe| #16=(|Mapping| #17=(|OutputForm|) (|List| #17#)))) #5#)) (|display| #14# (AND (|isDomain| *2 #16#) #5#)) (|display| #14# (AND (|isDomain| *2 (|Mapping| #17# #17#)) #5#)) (|input| #14# (AND (|isDomain| *2 #18=(|Mapping| #19=(|InputForm|) (|List| #19#))) #5#)) (|input| #1# (AND (|isDomain| *2 (|Maybe| #18#)) #5#)) (|has?| #20=(*1 *2 *1 *3) (AND #21=(|isDomain| *3 #22=(|Identifier|)) #11# #5#)) (|assert| #14# #23=(AND #24=(|isDomain| *2 #22#) #5#)) (|deleteProperty!| #14# (AND #25=(|isDomain| *2 #3#) #5#)) 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*2)))) +((|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|) $) 46 T ELT)) (|children| (#4# 32 T ELT)) (= (#5# 38 T ELT))) +(((|BinaryRecursiveAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = #1=(#2=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |setelt| (|#1| |#1| #3="right" |#1|)) (SIGNATURE |setelt| (|#1| |#1| #4="left" |#1|)) (SIGNATURE |elt| (|#1| |#1| #3#)) (SIGNATURE |elt| (|#1| |#1| #4#)) (SIGNATURE |setelt| (|#2| |#1| #5="value" |#2|)) (SIGNATURE |node?| #1#) (SIGNATURE |leaves| ((|List| |#2|) |#1|)) (SIGNATURE |cyclic?| #6=(#2# |#1|)) (SIGNATURE |elt| (|#2| |#1| #5#)) (SIGNATURE |leaf?| #6#) (SIGNATURE 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(SIGNATURE |space| #2=($) |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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|charthRoot| (((|Maybe| $) $) 47 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 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)) +((|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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 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)) +((|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#))) +((|solveLinearPolynomialEquation| (((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#) 35 T ELT))) +(((|ComplexIntegerSolveLinearPolynomialEquation| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| #2=(|SparseUnivariatePolynomial| |#2|)) "failed") #1# #2#))) (|IntegerNumberSystem|) (|ComplexCategory| |#1|)) (T |ComplexIntegerSolveLinearPolynomialEquation|)) +((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| #1=(|SparseUnivariatePolynomial| *5))) (|isDomain| *3 #1#) (|ofCategory| *5 (|ComplexCategory| *4)) (|ofCategory| *4 (|IntegerNumberSystem|)) (|isDomain| *1 (|ComplexIntegerSolveLinearPolynomialEquation| *4 *5))))) +((|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|) $) 16 (|has| |#1| (|CoercibleTo| (|OutputForm|))) ELT)) (|before?| (#1# 19 (|has| |#1| . #2#) ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +(((|Collection| |#1|) (|Category|) (|Type|)) (T |Collection|)) +((|construct| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|Type|)) (|ofCategory| *1 (|Collection| *3)))) (|remove| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|select| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) (|ofCategory| *1 (|FiniteAggregate| *3)) (|ofCategory| *1 (|Collection| *3)) (|ofCategory| *3 (|Type|)))) (|remove| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|)))) (|removeDuplicates| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteAggregate| *2)) (|ofCategory| *1 (|Collection| *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|BasicType|))))) +(|Join| (|HomogeneousAggregate| |t#1|) (CATEGORY |domain| (SIGNATURE |construct| ($ (|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)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| ((#5=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|recip| ((#5# $) 113 T ELT)) (|opposite?| #1#) (|one?| #4#) (|monomial| (($ |#2| #7=(|List| #8=(|PositiveInteger|))) 72 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|e| (($ #8#) 58 T ELT)) (|dimension| (((|CardinalNumber|)) 23 T ELT)) (|coerce| (((|OutputForm|) $) 88 T ELT) (($ #9=(|Integer|)) 54 T ELT) (($ |#2|) 55 T ELT)) (|coefficient| ((|#2| $ #7#) 75 T ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) 20 T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| (#6# 48 T CONST)) (|One| (#6# 52 T CONST)) (= (#2# 34 T ELT)) (/ #11=(($ $ |#2|) NIL T ELT)) (- (($ $) 43 T ELT) (#12=($ $ $) 41 T ELT)) (+ (#12# 39 T ELT)) (** (($ $ #8#) NIL T ELT) (($ $ #10#) NIL T ELT)) (* (($ #8# $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #9# $) 45 T ELT) (#12# 64 T ELT) (($ |#2| $) 47 T 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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|) . 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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|))))) +((|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)))))) +((|macroExpand| ((#1=(|SpadAst|) #1# (|Environment|)) 8 T ELT)) (|elaborateFile| (((|List| #2=(|Maybe| (|Elaboration|))) (|String|)) 81 T ELT)) (|elaborate| ((#2# #1#) 76 T ELT))) +(((|CompilerPackage|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |macroExpand| (#1=(|SpadAst|) #1# (|Environment|))) (SIGNATURE |elaborate| (#2=(|Maybe| (|Elaboration|)) #1#)) (SIGNATURE |elaborateFile| ((|List| #2#) (|String|)))))) (T |CompilerPackage|)) +((|macroExpand| (*1 *2 *2 *3) (AND (|isDomain| *2 #1=(|SpadAst|)) (|isDomain| *3 (|Environment|)) #2=(|isDomain| *1 (|CompilerPackage|)))) (|elaborate| #3=(*1 *2 *3) (AND (|isDomain| *3 #1#) (|isDomain| *2 #4=(|Maybe| (|Elaboration|))) #2#)) (|elaborateFile| #3# (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|List| #4#)) #2#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(OR #6=(AND #7=(|has| |#1| (|EuclideanDomain|)) #8=(|has| |#1| (|PolynomialFactorizationExplicit|))) #9=(|has| |#1| (|IntegralDomain|))) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|traceMatrix| #12=((#13=(|Matrix| |#1|) #14=(|Vector| $)) NIL T ELT) ((#13#) NIL T ELT)) (|trace| #15=(#16=(|#1| $) NIL T ELT)) (|tanh| #17=(#11# NIL #18=(|has| |#1| (|TranscendentalFunctionCategory|)) ELT)) (|tan| #17#) (|tableForDiscreteLogarithm| (((|Table| #19=(|PositiveInteger|) #20=(|NonNegativeInteger|)) #21=(|Integer|)) NIL #22=(|has| |#1| (|FiniteFieldCategory|)) ELT)) (|subtractIfCan| (#23=(#24=(|Union| $ #25="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #26=(((|Factored| #27=(|SparseUnivariatePolynomial| $)) #27#) NIL #6# ELT)) (|squareFreePart| (#11# NIL #28=(OR #6# #29=(|has| |#1| (|Field|))) ELT)) (|squareFree| #30=(((|Factored| $) $) NIL #28# ELT)) (|sqrt| (#11# NIL #31=(AND (|has| |#1| (|RadicalCategory|)) #18#) ELT)) (|solveLinearPolynomialEquation| (((|Union| #32=(|List| #27#) #25#) #32# #27#) NIL #6# ELT)) (|sizeLess?| (#2# NIL #7# ELT)) (|size| (#33=(#20#) NIL #34=(|has| |#1| (|Finite|)) ELT)) (|sinh| #17#) (|sin| #17#) (|sech| #17#) (|sec| #17#) (|sample| (#35=($) NIL T CONST)) (|retractIfCan| (((|Union| #21# . #36=(#25#)) . #37=($)) NIL #38=(|has| |#1| (|RetractableTo| #21#)) ELT) (#39=((|Union| #40=(|Fraction| #21#) . #36#) . #37#) NIL #41=(|has| |#1| (|RetractableTo| #40#)) ELT) (((|Union| |#1| . #36#) . #37#) NIL T ELT)) (|retract| ((#21# . #42=($)) NIL #38# ELT) (#43=(#40# . #42#) NIL #41# ELT) #15#) (|represents| (($ #44=(|Vector| |#1|) #14#) NIL T ELT) #45=(($ #44#) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #22# ELT)) (|rem| #46=(#47=($ $ $) NIL #7# ELT)) (|regularRepresentation| ((#13# $ #14#) NIL T ELT) ((#13# $) NIL T ELT)) (|reducedSystem| ((#48=(|Matrix| #21#) . #49=(#50=(|Matrix| $))) NIL #51=(|has| |#1| (|LinearlyExplicitRingOver| #21#)) ELT) ((#52=(|Record| (|:| |mat| #48#) (|:| |vec| (|Vector| #21#))) . #53=(#50# #14#)) NIL #51# ELT) ((#54=(|Record| (|:| |mat| #13#) (|:| |vec| #44#)) . #53#) NIL T ELT) ((#13# . #49#) NIL T ELT)) (|reduce| #55=(($ #56=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT) ((#24# (|Fraction| #56#)) NIL #29# ELT)) (|recip| ((#24# $) NIL T ELT)) (|real| (#16# 20 T ELT)) (|rationalIfCan| (#39# NIL #57=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#4# NIL #57# ELT)) (|rational| (#43# NIL #57# ELT)) (|rank| ((#19#) NIL T ELT)) (|random| (#35# NIL #34# ELT)) (|quo| #46#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #7# ELT)) (|primitiveElement| #60=(#35# NIL #22# ELT)) (|primitive?| (#4# NIL #22# ELT)) (|primeFrobenius| (#61=($ $ #20#) NIL #22# ELT) #62=(#11# NIL #22# ELT)) (|prime?| (#4# NIL #28# ELT)) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) NIL (AND #63=(|has| |#1| (|RealNumberSystem|)) #18#) ELT)) (|pi| (#35# NIL #18# ELT)) (|patternMatch| ((#64=(|PatternMatchResult| #21# . #65=($)) $ #66=(|Pattern| #21#) #64#) NIL (|has| |#1| (|PatternMatchable| #21#)) ELT) ((#67=(|PatternMatchResult| #68=(|Float|) . #65#) $ #69=(|Pattern| #68#) #67#) NIL (|has| |#1| (|PatternMatchable| #68#)) ELT)) (|order| (#70=(#19# $) NIL #22# ELT) (((|OnePointCompletion| #19#) $) NIL #22# ELT)) (|opposite?| #1#) (|one?| (#4# 17 T ELT)) (|nthRoot| (#71=($ $ #21#) NIL #31# ELT)) (|norm| (#16# 30 T ELT)) (|nextItem| (#72=((|Maybe| $) $) NIL #22# ELT)) (|multiEuclidean| (((|Union| #58# #25#) #58# $) NIL #7# ELT)) (|minimalPolynomial| (#73=(#56# $) NIL #29# ELT)) (|map| (($ #74=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|lookup| (#70# NIL #34# ELT)) (|log| #17#) (|lift| #75=(#73# NIL T ELT)) (|leftReducedSystem| ((#48# #14#) NIL #51# ELT) ((#52# . #76=(#14# $)) NIL #51# ELT) ((#54# . #76#) NIL T ELT) #12#) (|lcm| #77=(($ #58#) NIL #7# ELT) #46#) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#11# NIL #29# ELT)) (|init| (#35# NIL #22# CONST)) (|index| (($ #19#) NIL #34# ELT)) (|imaginary| #78=(#35# NIL T ELT)) (|imag| (#16# 21 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #78#) (|gcdPolynomial| ((#27# #27# #27#) NIL #7# ELT)) (|gcd| #77# #46#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #21#) (|:| |exponent| #21#)))) NIL #22# ELT)) (|factorSquareFreePolynomial| #26#) (|factorPolynomial| #26#) (|factor| #30#) (|extendedEuclidean| (((|Union| (|Record| #79=(|:| |coef1| $) #80=(|:| |coef2| $)) #25#) $ $ $) NIL #7# ELT) (((|Record| #79# #80# #59#) $ $) NIL #7# ELT)) (|exquo| ((#24# $ |#1|) 28 #9# ELT) (#23# 31 #5# ELT)) (|expressIdealMember| (((|Maybe| #58#) #58# $) NIL #7# ELT)) (|exp| #17#) (|eval| (($ $ #81=(|List| |#1|) #81#) NIL #82=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #82# ELT) (($ $ #83=(|Equation| |#1|)) NIL #82# ELT) (($ $ (|List| #83#)) NIL #82# ELT) (($ $ #84=(|List| #85=(|Symbol|)) #81#) NIL #86=(|has| |#1| (|InnerEvalable| #85# |#1|)) ELT) (($ $ #85# |#1|) NIL #86# ELT)) (|euclideanSize| (#87=(#20# $) NIL #7# ELT)) (|elt| (#88=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #7# ELT)) (|discriminant| ((|#1| #14#) NIL T ELT) ((|#1|) NIL T ELT)) (|discreteLog| (#87# NIL #22# ELT) (((|Union| #20# #25#) $ $) NIL #22# ELT)) (|differentiate| #89=(($ $ #74#) NIL T ELT) #90=(($ $ #74# #20#) NIL T ELT) #91=(($ $ #84# (|List| #20#)) NIL #92=(OR (AND #29# (|has| |#1| (|PartialDifferentialRing| #85#))) (|has| |#1| (|PartialDifferentialSpace| #85#))) ELT) #93=(($ $ #85# #20#) NIL #92# ELT) #94=(($ $ #84#) NIL #92# ELT) #95=(($ $ #85#) NIL #92# ELT) #96=(#61# NIL #97=(OR (AND (|has| |#1| (|DifferentialRing|)) #29#) (|has| |#1| (|DifferentialSpace|))) ELT) #98=(#11# NIL #97# ELT)) (|derivationCoordinates| ((#13# #14# #74#) NIL #29# ELT)) (|definingPolynomial| ((#56#) NIL T ELT)) (|csch| #17#) (|csc| #17#) (|createPrimitiveElement| #60#) (|coth| #17#) (|cot| #17#) (|cosh| #17#) (|cos| #17#) (|coordinates| ((#44# $ #14#) NIL T ELT) ((#13# #14# #14#) NIL T ELT) #99=((#44# $) NIL T ELT) #12#) (|convert| #99# #45# #75# #55# ((#66# . #100=($)) NIL (|has| |#1| (|ConvertibleTo| #66#)) ELT) ((#69# . #100#) NIL (|has| |#1| (|ConvertibleTo| #69#)) ELT) (((|Complex| #68#) . #100#) NIL #101=(|has| |#1| (|RealConstant|)) ELT) (((|Complex| (|DoubleFloat|)) . #100#) NIL #101# ELT) ((#102=(|InputForm|) . #100#) NIL (|has| |#1| (|ConvertibleTo| #102#)) ELT)) (|conjugate| (#11# 29 T ELT)) (|conditionP| (((|Union| #14# #25#) #50#) NIL (OR #103=(AND (|has| $ #104=(|CharacteristicNonZero|)) #7# #8#) #22#) ELT)) (|complex| (($ |#1| |#1|) 19 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #21#) NIL T ELT) (($ |#1|) 18 T ELT) (($ #40#) NIL (OR #29# #41#) ELT) #10#) (|charthRoot| #62# (#72# NIL (OR #103# (|has| |#1| #104#)) ELT)) (|characteristicPolynomial| #75#) (|characteristic| (#33# NIL T CONST)) (|before?| #1#) (|basis| ((#14#) NIL T ELT)) (|atanh| #17#) (|atan| #17#) (|associates?| (#2# NIL #5# ELT)) (|asinh| #17#) (|asin| #17#) (|asech| #17#) (|asec| #17#) (|argument| (#16# NIL #18# ELT)) (|annihilate?| #1#) (|acsch| #17#) (|acsc| #17#) (|acoth| #17#) (|acot| #17#) (|acosh| #17#) (|acos| #17#) (|abs| (#11# NIL #63# ELT)) (|Zero| (#35# 8 T CONST)) (|One| (#35# 10 T CONST)) (D #89# #90# #91# #93# #94# #95# #96# #98#) (= #1#) (/ (#47# NIL #29# ELT)) (- (#11# NIL T ELT) (#47# NIL T ELT)) (+ (#47# 23 T ELT)) (** (($ $ #19#) NIL T ELT) (#61# NIL T ELT) (#105=($ $ #40#) NIL #31# ELT) (#47# NIL #18# ELT) (#71# NIL #29# ELT)) (* (($ #19# $) NIL T ELT) (($ #20# $) NIL T ELT) (($ #21# . #106=($)) NIL T ELT) (#47# 26 T ELT) (#88# NIL T ELT) (($ |#1| . #106#) NIL T ELT) (($ #40# . #106#) NIL #29# ELT) (#105# NIL #29# ELT))) +(((|Complex| |#1|) (|ComplexCategory| |#1|) (|CommutativeRing|)) (T |Complex|)) +NIL +((|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) 14 T ELT))) +(((|ComplexFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)))) #1=(|CommutativeRing|) #1#) (T |ComplexFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Complex| *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Complex| *6)) (|isDomain| *1 (|ComplexFunctions2| *5 *6))))) +((|convert| (((|Pattern| |#1|) |#3|) 22 T ELT))) +(((|ComplexPattern| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |convert| (#1=(|Pattern| |#1|) |#3|))) (|SetCategory|) (|Join| (|ConvertibleTo| #1#) (|CommutativeRing|)) (|ComplexCategory| |#2|)) (T |ComplexPattern|)) +((|convert| (*1 *2 *3) (AND (|ofCategory| *5 (|Join| (|ConvertibleTo| *2) (|CommutativeRing|))) (|isDomain| *2 (|Pattern| *4)) (|isDomain| *1 (|ComplexPattern| *4 *5 *3)) (|ofCategory| *4 (|SetCategory|)) (|ofCategory| *3 (|ComplexCategory| *5))))) +((~= #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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 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| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|close!| (($ $) 6 T ELT))) +(((|Conduit|) (|Category|)) (T |Conduit|)) +((|close!| (*1 *1 *1) (|ofCategory| *1 (|Conduit|)))) +(|Join| (CATEGORY |domain| (SIGNATURE |close!| ($ $)))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|wholePart| ((|#1| $) 79 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #7=((#8=(|Union| $ #9="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #10=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|sample| (#11=($) NIL T CONST)) (|rem| #12=(#13=($ $ $) NIL T ELT)) (|reducedForm| (#6# 21 T ELT)) (|reducedContinuedFraction| (($ |#1| #14=(|Stream| |#1|)) 48 T ELT)) (|recip| ((#8# $) 123 T ELT)) (|quo| #12#) (|principalIdeal| (((|Record| (|:| |coef| #15=(|List| $)) #16=(|:| |generator| $)) #15#) NIL T ELT)) (|prime?| #4#) (|partialQuotients| (#17=(#14# $) 86 T ELT)) (|partialNumerators| (#17# 83 T ELT)) (|partialDenominators| (#17# 84 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numerators| (#17# 93 T ELT)) (|multiEuclidean| (((|Union| #15# #9#) #15# $) NIL T ELT)) (|lcm| #18=(($ #15#) NIL T ELT) #12#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#19=(|SparseUnivariatePolynomial| $) #19# #19#) NIL T ELT)) (|gcd| #18# #12#) (|factor| #10#) (|extendedEuclidean| (((|Union| (|Record| #20=(|:| |coef1| $) #21=(|:| |coef2| $)) #9#) $ $ $) NIL T ELT) (((|Record| #20# #21# #16#) $ $) NIL T ELT)) (|extend| (#22=($ $ #23=(|Integer|)) 96 T ELT)) (|exquo| #7#) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|denominators| (#17# 94 T ELT)) (|convergents| (#25=((|Stream| #26=(|Fraction| |#1|)) $) 14 T ELT)) (|continuedFraction| (#27=($ #26#) 17 T ELT) 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#2#))) +((|toroidal| (#1=(#2=(|Mapping| #3=(|Point| |#1|) #3#) |#1|) 38 T ELT)) (|spherical| (#4=(#3# #3#) 22 T ELT)) (|prolateSpheroidal| (#1# 34 T ELT)) (|polar| (#4# 20 T ELT)) (|paraboloidal| (#4# 28 T ELT)) (|parabolicCylindrical| (#4# 27 T ELT)) (|parabolic| (#4# 26 T ELT)) (|oblateSpheroidal| (#1# 35 T ELT)) (|ellipticCylindrical| (#1# 33 T ELT)) (|elliptic| (#1# 32 T ELT)) (|cylindrical| (#4# 21 T ELT)) (|conical| ((#2# |#1| |#1|) 41 T ELT)) (|cartesian| (#4# 8 T ELT)) (|bipolarCylindrical| (#1# 37 T ELT)) (|bipolar| (#1# 36 T ELT))) +(((|CoordinateSystems| |#1|) (CATEGORY |package| (SIGNATURE |cartesian| #1=(#2=(|Point| |#1|) #2#)) (SIGNATURE |polar| #1#) (SIGNATURE |cylindrical| #1#) (SIGNATURE |spherical| #1#) (SIGNATURE |parabolic| #1#) (SIGNATURE |parabolicCylindrical| #1#) (SIGNATURE |paraboloidal| #1#) (SIGNATURE |elliptic| #3=(#4=(|Mapping| #2# #2#) |#1|)) (SIGNATURE |ellipticCylindrical| #3#) (SIGNATURE |prolateSpheroidal| #3#) (SIGNATURE |oblateSpheroidal| #3#) 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T) ((|Type|) . T)) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (#4=($ $ (|NonNegativeInteger|)) 50 T ELT) (($ . #5=($)) 48 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (#4# 51 T ELT) (($ . #5#) 49 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +(((|DifferentialRing|) (|Category|)) (T |DifferentialRing|)) +NIL +(|Join| (|Ring|) (|DifferentialSpace|)) +(((|AbelianGroup|) . 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T)) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 31 T ELT)) (|sample| (#3=($) 30 T CONST)) (|recip| (((|Union| $ "failed") $) 36 T ELT)) (|positive?| (((|Boolean|) $) 28 T ELT)) (|opposite?| ((#2# $ $) 33 T ELT)) (|one?| (((|Boolean|) $) 38 T ELT)) (|min| (#4=($ $ $) 23 T ELT)) (|max| (#4# 22 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 29 T CONST)) (|One| (($) 39 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|)) 40 T ELT) (($ $ (|NonNegativeInteger|)) 37 T ELT)) (* (($ (|PositiveInteger|) $) 26 T ELT) (($ (|NonNegativeInteger|) $) 32 T ELT) (($ $ $) 41 T ELT))) +(((|Dioid|) (|Category|)) (T |Dioid|)) +NIL +(|Join| (|OrderedAbelianMonoid|) (|SemiRing|)) +(((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . 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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|))) ((|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)) +((|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#)) (|Equation| (|Polynomial| (|Integer|)))) 42 T ELT))) +(((|DiophantineSolutionPackage|) (CATEGORY |package| (SIGNATURE |dioSolve| ((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#)) (|Equation| (|Polynomial| (|Integer|))))))) (T |DiophantineSolutionPackage|)) +((|dioSolve| (*1 *2 *3) (AND (|isDomain| *3 (|Equation| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| #1=(|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| #1#))) (|isDomain| *1 (|DiophantineSolutionPackage|))))) +((|size| (#1=(#2=(|NonNegativeInteger|)) 56 T ELT)) (|reducedSystem| (((|Record| (|:| |mat| #3=(|Matrix| |#3|)) (|:| |vec| #4=(|Vector| |#3|))) #5=(|Matrix| $) #6=(|Vector| $)) 53 T ELT) ((#3# #5#) 44 T ELT) (((|Record| (|:| |mat| #7=(|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) #5# #6#) NIL T ELT) ((#7# #5#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) 62 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#3| |#3|)) 18 T ELT) (($ $ #9# #2#) NIL T ELT) (($ $ #10=(|List| #11=(|Symbol|)) (|List| #2#)) NIL T ELT) (($ $ #11# #2#) NIL T ELT) (($ $ #10#) NIL T ELT) (($ $ #11#) NIL T ELT) (($ $ #2#) NIL T ELT) (($ $) NIL T ELT)) (|coerce| ((#4# $) NIL T ELT) (($ |#3|) NIL T ELT) (((|OutputForm|) $) NIL T ELT) (($ #8#) 12 T ELT) (($ (|Fraction| #8#)) NIL T ELT)) (|characteristic| (#1# 15 T CONST)) (/ (($ $ |#3|) 59 T ELT))) +(((|DirectProductCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| (|Fraction| #1=(|Integer|)))) (SIGNATURE |coerce| (|#1| #1#)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|Symbol|))) (SIGNATURE |differentiate| (|#1| |#1| #4=(|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #3# #2#)) (SIGNATURE |differentiate| (|#1| |#1| #4# (|List| #2#))) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |characteristic| #5=(#2#) |constant|) (SIGNATURE |reducedSystem| (#6=(|Matrix| #1#) #7=(|Matrix| |#1|))) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #6#) (|:| |vec| (|Vector| #1#))) #7# #8=(|Vector| |#1|))) (SIGNATURE |coerce| (|#1| |#3|)) (SIGNATURE |differentiate| (|#1| |#1| #9=(|Mapping| |#3| |#3|) #2#)) (SIGNATURE |differentiate| (|#1| |#1| #9#)) (SIGNATURE |reducedSystem| (#10=(|Matrix| |#3|) #7#)) (SIGNATURE |reducedSystem| ((|Record| (|:| |mat| #10#) (|:| |vec| #11=(|Vector| |#3|))) #7# #8#)) (SIGNATURE |size| #5#) (SIGNATURE / (|#1| |#1| |#3|)) (SIGNATURE |dimension| ((|CardinalNumber|))) (SIGNATURE |coerce| (#11# |#1|))) (|DirectProductCategory| |#2| |#3|) #2# (|Type|)) (T |DirectProductCategory&|)) +((|dimension| #1=(*1 *2) (AND (|ofType| *4 #2=(|NonNegativeInteger|)) #3=(|ofCategory| *5 (|Type|)) 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(|has| |#2| . #12=((|RetractableTo| #9#))) (|has| |#2| . #13=((|SetCategory|)))) ELT) (((|Union| #14=(|Fraction| #9#) . #10#) . #11#) 64 (|and| (|has| |#2| . #15=((|RetractableTo| #14#))) (|has| |#2| . #13#)) ELT) (((|Union| |#2| . #10#) . #11#) 61 (|has| |#2| . #13#) ELT)) (|retract| ((#9# . #16=($)) 66 (|and| (|has| |#2| . #12#) (|has| |#2| . #13#)) ELT) ((#14# . #16#) 63 (|and| (|has| |#2| . #15#) (|has| |#2| . #13#)) ELT) ((|#2| . #16#) 62 (|has| |#2| . #13#) ELT)) (|reducedSystem| (((|Matrix| #17=(|Integer|)) . #18=(#19=(|Matrix| $))) 110 (|and| (|has| |#2| . #20=((|LinearlyExplicitRingOver| #17#))) (|has| |#2| . #21=((|Ring|)))) ELT) (((|Record| (|:| |mat| (|Matrix| #17#)) (|:| |vec| (|Vector| #17#))) . #22=(#19# #23=(|Vector| $))) 109 (|and| (|has| |#2| . #20#) (|has| |#2| . #21#)) ELT) (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #22#) 108 (|has| |#2| . #21#) ELT) (((|Matrix| |#2|) . #18#) 107 (|has| |#2| . #21#) ELT)) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) 141 (|has| |#2| . #24=((|BasicType|))) ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) 137 T ELT) ((|#2| (|Mapping| |#2| |#2| |#2|) $) 136 T ELT)) (|recip| (((|Union| $ "failed") $) 87 (|has| |#2| . #25=((|Ring|))) ELT)) (|random| (($) 116 (|has| |#2| . #7#) ELT)) (|qsetelt!| ((|#2| $ #5# |#2|) 48 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ #5#) 46 T ELT)) (|positive?| (((|Boolean|) $) 123 (|has| |#2| . #6#) ELT)) (|opposite?| ((#3# $ $) 74 (|has| |#2| . #4#) ELT)) (|one?| (((|Boolean|) $) 85 (|has| |#2| . #25#) ELT)) (|minIndex| ((#5# . #26=($)) 38 (|has| #5# . #27=((|OrderedSet|))) ELT)) (|min| (#28=($ $ $) 117 (|has| |#2| . #29=((|OrderedSet|))) ELT)) (|members| (((|List| |#2|) $) 135 T ELT)) (|member?| ((#30=(|Boolean|) |#2| $) 140 (|has| |#2| . #24#) ELT)) (|maxIndex| ((#5# . #26#) 39 (|has| #5# . #27#) ELT)) (|max| (#28# 118 (|has| |#2| . #29#) ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 26 T ELT)) (|lookup| ((#31=(|PositiveInteger|) 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|#2|))) 25 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT) (($ $ (|Equation| |#2|)) 24 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT) (($ $ |#2| |#2|) 23 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT) (($ $ (|List| |#2|) (|List| |#2|)) 22 (AND (|has| |#2| (|Evalable| |#2|)) (|has| |#2| . #34#)) ELT)) (|eq?| ((#37=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#35# |#2| $) 40 (AND (|has| $ (|FiniteAggregate| |#2|)) (|has| |#2| (|BasicType|))) ELT)) (|entries| (((|List| |#2|) $) 43 T ELT)) (|empty?| ((#37# $) 7 T ELT)) (|empty| (#8# 8 T ELT)) (|elt| ((|#2| $ #5# |#2|) 45 T ELT) ((|#2| $ #5#) 44 T ELT)) (|dot| ((|#2| $ $) 127 (|has| |#2| (|Ring|)) ELT)) (|directProduct| (($ (|Vector| |#2|)) 129 T ELT)) (|dimension| (((|CardinalNumber|)) 126 (|has| |#2| . #38=((|Field|))) ELT)) (|differentiate| (#39=($ $ (|NonNegativeInteger|)) 103 (|and| (|has| |#2| . #40=((|DifferentialSpace|))) (|has| |#2| . #25#)) ELT) (($ . #41=($)) 101 (|and| (|has| |#2| . #40#) 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(|has| |#2| . #29#) ELT)) (= (#1# 17 (|has| |#2| . #2#) ELT)) (<= (#50# 120 (|has| |#2| . #29#) ELT)) (< (#50# 122 (|has| |#2| . #29#) ELT)) (/ (($ $ |#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# $) 131 T ELT))) +(((|DirectProductCategory| |#1| |#2|) (|Category|) (|NonNegativeInteger|) (|Type|)) (T |DirectProductCategory|)) +((|directProduct| (*1 *1 *2) (AND (|isDomain| *2 (|Vector| *4)) (|ofCategory| *4 (|Type|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)))) (|unitVector| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|DirectProductCategory| *3 *4)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *4 (|Type|)))) (|dot| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|DirectProductCategory| *3 *2)) (|ofCategory| *2 (|Type|)) (|ofCategory| *2 (|Ring|))))) +(|Join| (|IndexedAggregate| (|Integer|) |t#2|) (|FiniteAggregate| |t#2|) (|CoercibleTo| (|Vector| |t#2|)) (CATEGORY |domain| (SIGNATURE |directProduct| ($ (|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| (ATTRIBUTE |unitsKnown|)) (ATTRIBUTE |unitsKnown|) |%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|))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) 63 #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) 69 #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) 54 (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#2| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#2| $ #10# |#2|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#2| (|RetractableTo| #10#)) #25=(|has| |#2| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#2| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#2| . #22#) $) 31 #25# ELT)) (|retract| (#29=(#10# . #30=($)) NIL #24# ELT) ((#26# . #30#) NIL #27# ELT) (#31=(|#2| $) 29 #25# ELT)) (|reducedSystem| ((#32=(|Matrix| #10#) . #33=(#34=(|Matrix| $))) NIL #35=(AND (|has| |#2| (|LinearlyExplicitRingOver| #10#)) #9#) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #10#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#2|)) (|:| |vec| #41=(|Vector| |#2|))) . #37#) NIL #9# ELT) ((#40# . #33#) NIL #9# ELT)) (|reduce| ((|#2| #42=(|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) NIL #4# ELT) ((|#2| #42# $ |#2|) NIL T ELT) ((|#2| #42# $) NIL T ELT)) (|recip| ((#14# $) 59 #9# ELT)) (|random| (#21# NIL #18# ELT)) (|qsetelt!| #19#) (|qelt| (#43=(|#2| $ #10#) 57 T ELT)) (|positive?| (#5# NIL #13# ELT)) (|opposite?| (#2# NIL #6# ELT)) (|one?| (#5# NIL #9# ELT)) (|minIndex| (#29# 20 #44=(|has| #10# #45=(|OrderedSet|)) ELT)) (|min| #46=(#12# NIL #47=(|has| |#2| #45#) ELT)) (|members| (#48=(#49=(|List| |#2|) $) 14 T ELT)) (|member?| (#50=(#3# |#2| $) NIL #4# ELT)) (|maxIndex| (#29# NIL #44# ELT)) (|max| #46#) (|map| (($ #51=(|Mapping| |#2| |#2|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #52=(#38#)) NIL #35# ELT) ((#36# . #53=(#38# $)) NIL #35# ELT) ((#39# . #53#) NIL #9# ELT) ((#40# . #52#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #44# ELT)) (|find| ((#28# #54=(|Mapping| #3# |#2|) $) NIL T ELT)) (|fill!| (#55=($ $ |#2|) NIL #11# ELT)) (|every?| (#56=(#3# #54# $) 24 T ELT)) (|eval| (($ $ (|List| #57=(|Equation| |#2|))) NIL #58=(AND (|has| |#2| (|Evalable| |#2|)) #25#) ELT) (($ $ #57#) NIL #58# ELT) (($ $ |#2| |#2|) NIL #58# ELT) (($ $ #49# #49#) NIL #58# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#50# NIL (AND (|has| $ (|FiniteAggregate| |#2|)) #4#) ELT)) (|entries| (#48# NIL T ELT)) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# 21 T ELT)) (|dot| ((|#2| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) 18 T ELT)) (|dimension| (((|CardinalNumber|)) NIL #59=(|has| |#2| (|Field|)) ELT)) (|differentiate| #60=(#61=($ $ #17#) NIL #62=(AND (|has| |#2| (|DifferentialSpace|)) #9#) ELT) #63=(#64=($ $) NIL #62# ELT) #65=(($ $ #66=(|List| #67=(|Symbol|)) (|List| #17#)) NIL #68=(AND (|has| |#2| (|PartialDifferentialSpace| #67#)) #9#) ELT) #69=(($ $ #67# #17#) NIL #68# ELT) #70=(($ $ #66#) NIL #68# ELT) #71=(($ $ #67#) NIL #68# ELT) #72=(($ $ #51#) NIL #9# ELT) #73=(($ $ #51# #17#) NIL #9# ELT)) (|count| ((#17# |#2| $) NIL #4# ELT) ((#17# #54# $) NIL T ELT)) (|copy| (#64# NIL T ELT)) (|coerce| ((#41# $) 9 T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#2|) 12 #25# ELT) ((#74=(|OutputForm|) $) NIL (|has| |#2| (|CoercibleTo| #74#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| (#56# NIL T ELT)) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# 37 #6# CONST)) (|One| (#21# 41 #9# CONST)) (D #60# #63# #65# #69# #70# #71# #72# #73#) (>= #75=(#2# NIL #47# ELT)) (> #75#) (= (#2# 28 #4# ELT)) (<= #75#) (< (#2# 67 #47# ELT)) (/ (#55# NIL #59# ELT)) (- (#12# NIL #76=(|has| |#2| (|AbelianGroup|)) ELT) (#64# NIL #76# ELT)) (+ (#12# 35 #77=(|has| |#2| (|AbelianSemiGroup|)) ELT)) (** (#61# NIL #9# ELT) (($ $ #8#) NIL #9# ELT)) (* (#12# 47 #9# ELT) (#55# 45 #78=(|has| |#2| (|Monoid|)) ELT) (($ |#2| $) 46 #78# ELT) (($ #10# $) NIL #76# ELT) (($ #17# $) NIL #6# ELT) (($ #8# $) NIL #77# ELT)) (|#| ((#17# $) NIL T ELT))) +(((|DirectProduct| |#1| |#2|) (|DirectProductCategory| |#1| |#2|) (|NonNegativeInteger|) (|Type|)) (T |DirectProduct|)) +NIL +((|scan| ((#1=(|DirectProduct| |#1| |#3|) #2=(|Mapping| |#3| |#2| |#3|) #3=(|DirectProduct| |#1| |#2|) |#3|) 21 T ELT)) (|reduce| ((|#3| #2# #3# |#3|) 23 T ELT)) (|map| ((#1# (|Mapping| |#3| |#2|) #3#) 18 T ELT))) +(((|DirectProductFunctions2| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |scan| (#1=(|DirectProduct| |#1| |#3|) #2=(|Mapping| |#3| |#2| |#3|) #3=(|DirectProduct| |#1| |#2|) |#3|)) (SIGNATURE |reduce| (|#3| #2# #3# |#3|)) (SIGNATURE |map| (#1# (|Mapping| |#3| |#2|) #3#))) (|NonNegativeInteger|) #4=(|Type|) #4#) (T |DirectProductFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *7 *6)) #1=(|isDomain| *4 (|DirectProduct| *5 *6)) #2=(|ofType| *5 #3=(|NonNegativeInteger|)) #4=(|ofCategory| *6 #5=(|Type|)) #6=(|ofCategory| *7 #5#) (|isDomain| *2 (|DirectProduct| *5 *7)) (|isDomain| *1 (|DirectProductFunctions2| *5 *6 *7)))) (|reduce| (*1 *2 *3 *4 *2) (AND (|isDomain| *3 (|Mapping| *2 *6 *2)) #1# #2# #4# (|ofCategory| *2 #5#) (|isDomain| *1 (|DirectProductFunctions2| *5 *6 *2)))) (|scan| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Mapping| *5 *7 *5)) (|isDomain| *4 (|DirectProduct| *6 *7)) (|ofType| *6 #3#) #6# (|ofCategory| *5 #5#) (|isDomain| *2 (|DirectProduct| *6 *5)) (|isDomain| *1 (|DirectProductFunctions2| *6 *7 *5))))) +((|sayLength| ((#1=(|Integer|) #2=(|List| #3=(|String|))) 36 T ELT) ((#1# #3#) 29 T ELT)) (|say| ((#4=(|Void|) #2#) 40 T ELT) ((#4# #3#) 39 T ELT)) (|newLine| ((#3#) 16 T ELT)) (|copies| ((#3# #1# #3#) 23 T ELT)) (|center| ((#2# #2# #1# #3#) 37 T ELT) ((#3# #3# #1# #3#) 35 T ELT)) (|bright| ((#2# #2#) 15 T ELT) ((#2# #3#) 11 T ELT))) +(((|DisplayPackage|) (CATEGORY |package| (SIGNATURE |bright| (#1=(|List| #2=(|String|)) #2#)) (SIGNATURE |bright| (#1# #1#)) (SIGNATURE |newLine| (#2#)) (SIGNATURE |copies| (#2# #3=(|Integer|) #2#)) (SIGNATURE |center| (#2# #2# #3# #2#)) (SIGNATURE |center| (#1# #1# #3# #2#)) (SIGNATURE |say| (#4=(|Void|) #2#)) (SIGNATURE |say| (#4# #1#)) (SIGNATURE |sayLength| (#3# #2#)) (SIGNATURE |sayLength| (#3# #1#)))) (T |DisplayPackage|)) +((|sayLength| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|List| #4=(|String|))) #5=(|isDomain| *2 #6=(|Integer|)) #7=(|isDomain| *1 (|DisplayPackage|)))) (|sayLength| #1# (AND #8=(|isDomain| *3 #4#) #5# #7#)) (|say| #1# (AND #2# #9=(|isDomain| *2 (|Void|)) #7#)) (|say| #1# (AND #8# #9# #7#)) (|center| (*1 *2 *2 *3 *4) (AND #10=(|isDomain| *2 #3#) #11=(|isDomain| *3 #6#) (|isDomain| *4 #4#) #7#)) (|center| (*1 *2 *2 *3 *2) #12=(AND #13=(|isDomain| *2 #4#) #11# #7#)) (|copies| (*1 *2 *3 *2) #12#) (|newLine| (*1 *2) (AND #13# #7#)) (|bright| (*1 *2 *2) (AND #10# #7#)) (|bright| #1# (AND #10# #7# #8#))) +((** (($ $ #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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 55 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #4=(|Fraction| (|Integer|))) 59 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ (|Integer|)) 56 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #5=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ #4# . #5#) 58 T ELT) (($ $ #4#) 57 T ELT))) +(((|DivisionRing|) (|Category|)) (T |DivisionRing|)) +((** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|DivisionRing|)) (|isDomain| *2 (|Integer|)))) (|inv| (*1 *1 *1) (|ofCategory| *1 (|DivisionRing|)))) +(|Join| (|EntireRing|) (|Algebra| (|Fraction| #1=(|Integer|))) (CATEGORY |domain| (SIGNATURE ** ($ $ #1#)) (SIGNATURE |inv| ($ $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| #1=(|Fraction| (|Integer|))) . T) ((|BasicType|) . T) ((|BiModule| #1# #1#) . T) ((|BiModule| $ $) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| #1#) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|EntireRing|) . T) ((|Join|) . T) ((|LeftLinearSet| #1#) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #1#) . T) ((|LeftModule| $) . T) ((|LinearSet| #1#) . T) ((|Module| #1#) . T) ((|Monoid|) . T) ((|RightLinearSet| #1#) . T) ((|RightLinearSet| $) . T) ((|RightModule| #1#) . T) ((|RightModule| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . 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(|SegmentBinding| (|Expression| *4))) (|ofCategory| *4 (|Join| (|OrderedSet|) (|IntegralDomain|) (|ConvertibleTo| #1=(|Float|)))) (|isDomain| *2 (|SegmentBinding| #1#)) (|isDomain| *1 (|DrawNumericHack| *4))))) +((|draw| ((#1=(|ThreeDimensionalViewport|) #2=(|List| #3=(|DoubleFloat|)) #2# #2# #4=(|List| (|DrawOption|))) 23 T ELT) ((#1# #2# #2# #2#) 24 T ELT) ((#5=(|TwoDimensionalViewport|) #6=(|List| (|Point| #3#)) #4#) 16 T ELT) ((#5# #6#) 17 T ELT) ((#5# #2# #2# #4#) 20 T ELT) ((#5# #2# #2#) 21 T ELT))) +(((|TopLevelDrawFunctionsForPoints|) (CATEGORY |package| (SIGNATURE |draw| (#1=(|TwoDimensionalViewport|) #2=(|List| #3=(|DoubleFloat|)) #2#)) (SIGNATURE |draw| (#1# #2# #2# #4=(|List| (|DrawOption|)))) (SIGNATURE |draw| (#1# #5=(|List| (|Point| #3#)))) (SIGNATURE |draw| (#1# #5# #4#)) (SIGNATURE |draw| (#6=(|ThreeDimensionalViewport|) #2# #2# #2#)) (SIGNATURE |draw| (#6# #2# #2# #2# #4#)))) (T |TopLevelDrawFunctionsForPoints|)) +((|draw| (*1 *2 *3 *3 *3 *4) (AND #1=(|isDomain| *3 (|List| #2=(|DoubleFloat|))) #3=(|isDomain| *4 (|List| (|DrawOption|))) #4=(|isDomain| *2 (|ThreeDimensionalViewport|)) #5=(|isDomain| *1 (|TopLevelDrawFunctionsForPoints|)))) (|draw| (*1 *2 *3 *3 *3) (AND #1# #4# #5#)) (|draw| (*1 *2 *3 *4) (AND #6=(|isDomain| *3 (|List| (|Point| #2#))) #3# #7=(|isDomain| *2 (|TwoDimensionalViewport|)) #5#)) (|draw| (*1 *2 *3) (AND #6# #7# #5#)) (|draw| (*1 *2 *3 *3 *4) (AND #1# #3# #7# #5#)) (|draw| (*1 *2 *3 *3) (AND #1# #7# #5#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|viewpoint| (($ (|Record| (|:| |theta| #4=(|DoubleFloat|)) (|:| |phi| #4#) (|:| |scale| #4#) (|:| |scaleX| #4#) (|:| |scaleY| #4#) (|:| |scaleZ| #4#) (|:| |deltaX| #4#) (|:| |deltaY| #4#))) 24 T ELT)) (|var2Steps| (#5=($ (|PositiveInteger|)) 81 T ELT)) (|var1Steps| (#5# 80 T ELT)) (|unit| (($ (|List| #6=(|Float|))) 87 T ELT)) (|tubeRadius| (#7=($ #6#) 66 T ELT)) (|tubePoints| (#5# 82 T ELT)) (|toScale| (#8=($ #3#) 33 T ELT)) (|title| (#9=($ #10=(|String|)) 28 T ELT)) (|style| (#9# 29 T ELT)) (|space| (($ (|ThreeSpace| #4#)) 76 T ELT)) (|ranges| (#11=($ (|List| (|Segment| #6#))) 72 T ELT)) (|range| (#11# 68 T ELT) (($ (|List| (|Segment| (|Fraction| (|Integer|))))) 71 T ELT)) (|pointColor| (#7# 38 T ELT) (#12=($ (|Palette|)) 42 T ELT)) (|option?| ((#3# #13=(|List| $) #14=(|Symbol|)) 100 T ELT)) (|option| (((|Union| (|Any|) "failed") #13# #14#) 102 T ELT)) (|latex| ((#10# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|curveColor| (#7# 43 T ELT) (#12# 44 T ELT)) (|coordinates| (#15=($ (|Mapping| #16=(|Point| #4#) #16#)) 65 T ELT)) (|coord| (#15# 83 T ELT)) (|colorFunction| (($ (|Mapping| #4# #4#)) 48 T ELT) (($ (|Mapping| #4# #4# #4#)) 52 T ELT) (($ (|Mapping| #4# #4# #4# #4#)) 56 T ELT)) (|coerce| (((|OutputForm|) $) 93 T ELT)) (|clip| (#8# 34 T ELT) (#11# 60 T ELT)) (|before?| #1#) (|adaptive| (#8# 35 T ELT)) (= (#2# 97 T ELT))) +(((|DrawOption|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |adaptive| #1=($ #2=(|Boolean|))) (SIGNATURE |clip| #1#) (SIGNATURE |viewpoint| ($ (|Record| (|:| |theta| #3=(|DoubleFloat|)) (|:| |phi| #3#) (|:| |scale| #3#) (|:| |scaleX| #3#) (|:| |scaleY| #3#) (|:| |scaleZ| #3#) (|:| |deltaX| #3#) (|:| |deltaY| #3#)))) (SIGNATURE |title| #4=($ (|String|))) (SIGNATURE |style| #4#) (SIGNATURE |toScale| #1#) (SIGNATURE |clip| #5=($ (|List| (|Segment| #6=(|Float|))))) (SIGNATURE |coordinates| #7=($ (|Mapping| #8=(|Point| #3#) #8#))) (SIGNATURE |pointColor| #9=($ #6#)) (SIGNATURE |pointColor| #10=($ (|Palette|))) (SIGNATURE |curveColor| #9#) (SIGNATURE |curveColor| #10#) (SIGNATURE |colorFunction| ($ (|Mapping| #3# #3#))) (SIGNATURE |colorFunction| ($ (|Mapping| #3# #3# #3#))) (SIGNATURE |colorFunction| ($ (|Mapping| #3# #3# #3# #3#))) (SIGNATURE |tubeRadius| #9#) (SIGNATURE |range| #5#) (SIGNATURE |range| ($ (|List| (|Segment| (|Fraction| (|Integer|)))))) (SIGNATURE |ranges| #5#) (SIGNATURE |space| ($ (|ThreeSpace| #3#))) (SIGNATURE |var1Steps| #11=($ (|PositiveInteger|))) (SIGNATURE |var2Steps| #11#) (SIGNATURE |tubePoints| #11#) (SIGNATURE |coord| #7#) (SIGNATURE |unit| ($ (|List| #6#))) (SIGNATURE |option| ((|Union| (|Any|) "failed") #12=(|List| $) #13=(|Symbol|))) (SIGNATURE |option?| (#2# #12# #13#))))) (T |DrawOption|)) +((|adaptive| #1=(*1 *1 *2) #2=(AND #3=(|isDomain| *2 (|Boolean|)) #4=(|isDomain| *1 #5=(|DrawOption|)))) (|clip| #1# #2#) (|viewpoint| #1# (AND (|isDomain| *2 (|Record| (|:| |theta| #6=(|DoubleFloat|)) (|:| |phi| #6#) (|:| |scale| #6#) (|:| |scaleX| #6#) (|:| |scaleY| #6#) (|:| |scaleZ| #6#) (|:| |deltaX| #6#) (|:| |deltaY| #6#))) #4#)) (|title| #1# #7=(AND (|isDomain| *2 (|String|)) #4#)) (|style| #1# #7#) (|toScale| #1# #2#) (|clip| #1# #8=(AND (|isDomain| *2 (|List| (|Segment| #9=(|Float|)))) #4#)) (|coordinates| #1# #10=(AND (|isDomain| *2 (|Mapping| #11=(|Point| #6#) #11#)) #4#)) (|pointColor| #1# #12=(AND (|isDomain| *2 #9#) #4#)) (|pointColor| #1# #13=(AND (|isDomain| *2 (|Palette|)) #4#)) (|curveColor| #1# #12#) (|curveColor| #1# #13#) (|colorFunction| #1# (AND (|isDomain| *2 (|Mapping| #6# #6#)) #4#)) (|colorFunction| #1# (AND (|isDomain| *2 (|Mapping| #6# #6# #6#)) #4#)) (|colorFunction| #1# (AND (|isDomain| *2 (|Mapping| #6# #6# #6# #6#)) #4#)) (|tubeRadius| #1# #12#) (|range| #1# #8#) (|range| #1# (AND (|isDomain| *2 (|List| (|Segment| (|Fraction| (|Integer|))))) #4#)) (|ranges| #1# #8#) (|space| #1# (AND (|isDomain| *2 (|ThreeSpace| #6#)) #4#)) (|var1Steps| #1# #14=(AND (|isDomain| *2 (|PositiveInteger|)) #4#)) (|var2Steps| #1# #14#) (|tubePoints| #1# #14#) (|coord| #1# #10#) (|unit| #1# (AND (|isDomain| *2 (|List| #9#)) #4#)) (|option| #15=(*1 *2 *3 *4) (|partial| AND #16=(|isDomain| *3 (|List| #5#)) #17=(|isDomain| *4 (|Symbol|)) (|isDomain| *2 (|Any|)) #4#)) (|option?| #15# (AND #16# #17# #3# #4#))) +((|viewpoint| ((#1=(|Record| (|:| |theta| #2=(|DoubleFloat|)) (|:| |phi| #2#) (|:| |scale| #2#) (|:| |scaleX| #2#) (|:| |scaleY| #2#) (|:| |scaleZ| #2#) (|:| |deltaX| #2#) (|:| |deltaY| #2#)) #3=(|List| (|DrawOption|)) #1#) 25 T ELT)) (|var2Steps| (#4=(#5=(|PositiveInteger|) #3# #5#) 52 T ELT)) (|var1Steps| (#4# 51 T ELT)) (|units| ((#6=(|List| #7=(|Float|)) #3# #6#) 68 T ELT)) (|tubeRadius| ((#7# #3# #7#) 57 T ELT)) (|tubePoints| (#4# 53 T ELT)) (|toScale| (#8=(#9=(|Boolean|) #3# #9#) 27 T ELT)) (|title| (#10=(#11=(|String|) #3# #11#) 19 T ELT)) (|style| (#10# 26 T ELT)) (|space| (((|ThreeSpace| #2#) #3#) 46 T ELT)) (|ranges| ((#12=(|List| (|Segment| #7#)) #3# #12#) 40 T ELT)) (|pointColorPalette| (#13=(#14=(|Palette|) #3# #14#) 32 T ELT)) (|curveColorPalette| (#13# 33 T ELT)) (|coord| ((#15=(|Mapping| #16=(|Point| #2#) #16#) #3# #15#) 63 T ELT)) (|clipBoolean| (#8# 14 T ELT)) (|adaptive| (#8# 13 T ELT))) +(((|DrawOptionFunctions0|) (CATEGORY |package| (SIGNATURE |adaptive| #1=(#2=(|Boolean|) #3=(|List| (|DrawOption|)) #2#)) (SIGNATURE |clipBoolean| #1#) (SIGNATURE |viewpoint| (#4=(|Record| (|:| |theta| #5=(|DoubleFloat|)) (|:| |phi| #5#) (|:| |scale| #5#) (|:| |scaleX| #5#) (|:| |scaleY| #5#) (|:| |scaleZ| #5#) (|:| |deltaX| #5#) (|:| |deltaY| #5#)) #3# #4#)) (SIGNATURE |title| #6=(#7=(|String|) #3# #7#)) (SIGNATURE |style| #6#) (SIGNATURE |toScale| #1#) (SIGNATURE |pointColorPalette| #8=(#9=(|Palette|) #3# #9#)) (SIGNATURE |curveColorPalette| #8#) (SIGNATURE |ranges| (#10=(|List| (|Segment| #11=(|Float|))) #3# #10#)) (SIGNATURE |var1Steps| #12=(#13=(|PositiveInteger|) #3# #13#)) (SIGNATURE |var2Steps| #12#) (SIGNATURE |space| ((|ThreeSpace| #5#) #3#)) (SIGNATURE |tubePoints| #12#) (SIGNATURE |tubeRadius| (#11# #3# #11#)) (SIGNATURE |coord| (#14=(|Mapping| #15=(|Point| #5#) #15#) #3# #14#)) (SIGNATURE |units| (#16=(|List| #11#) #3# #16#)))) (T |DrawOptionFunctions0|)) +((|units| #1=(*1 *2 *3 *2) (AND (|isDomain| *2 (|List| #2=(|Float|))) #3=(|isDomain| *3 (|List| (|DrawOption|))) #4=(|isDomain| *1 (|DrawOptionFunctions0|)))) (|coord| #1# (AND (|isDomain| *2 (|Mapping| #5=(|Point| #6=(|DoubleFloat|)) #5#)) #3# #4#)) (|tubeRadius| #1# (AND (|isDomain| *2 #2#) #3# #4#)) (|tubePoints| #1# #7=(AND (|isDomain| *2 (|PositiveInteger|)) #3# #4#)) (|space| (*1 *2 *3) (AND #3# (|isDomain| *2 (|ThreeSpace| #6#)) #4#)) (|var2Steps| #1# #7#) (|var1Steps| #1# #7#) (|ranges| #1# (AND (|isDomain| *2 (|List| (|Segment| #2#))) #3# #4#)) (|curveColorPalette| #1# #8=(AND (|isDomain| *2 (|Palette|)) #3# #4#)) (|pointColorPalette| #1# #8#) (|toScale| #1# #9=(AND (|isDomain| *2 (|Boolean|)) #3# #4#)) (|style| #1# #10=(AND (|isDomain| *2 (|String|)) #3# #4#)) (|title| #1# #10#) (|viewpoint| #1# (AND (|isDomain| *2 (|Record| (|:| |theta| #6#) (|:| |phi| #6#) (|:| |scale| #6#) (|:| |scaleX| #6#) (|:| |scaleY| #6#) (|:| |scaleZ| #6#) (|:| |deltaX| #6#) (|:| |deltaY| #6#))) #3# #4#)) (|clipBoolean| #1# #9#) (|adaptive| #1# #9#)) +((|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) 17 T ELT))) +(((|DrawOptionFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |option| ((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)))) (|Type|)) (T |DrawOptionFunctions1|)) +((|option| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|List| (|DrawOption|))) (|isDomain| *4 (|Symbol|)) (|isDomain| *1 (|DrawOptionFunctions1| *2)) (|ofCategory| *2 (|Type|))))) +((|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))) +(((|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)) +((~= #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=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #20=(((|Factored| #12#) #12#) NIL #21=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #22=(#16# NIL #23=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#24=((|Factored| $) $) NIL #23# ELT)) 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#19#) $) NIL T ELT)) (|initial| #26#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #36#) (|gcdPolynomial| ((#12# #12# #12#) NIL #23# ELT)) (|gcd| #73# #74#) (|factorSquareFreePolynomial| #20#) (|factorPolynomial| #20#) (|factor| (#24# NIL #21# ELT)) (|exquo| ((#18# $ |#1|) NIL #14# ELT) (#17# 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 #40# 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| 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(|acoth| #2# #3#) (|asech| #2# #3#) (|acsch| #2# #3#)) +((|variable?| (#1=((|Boolean|) $) 20 T ELT)) (|type| (((|Syntax|) $) 9 T ELT)) (|getOperator| (#2=((|Union| (|Identifier|) #3="failed") $) 15 T ELT)) (|getOperands| (((|Union| (|List| $) #3#) $) NIL T ELT)) (|getIdentifier| (#2# 21 T ELT)) (|getConstant| (((|Union| (|SExpression|) #3#) $) 19 T ELT)) (|constant?| (#1# 17 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|callForm?| (#1# 10 T ELT))) +(((|ElaboratedExpression|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |type| ((|Syntax|) $)) (SIGNATURE |constant?| #1=((|Boolean|) $)) (SIGNATURE |getConstant| ((|Union| (|SExpression|) #2="failed") $)) (SIGNATURE |variable?| #1#) (SIGNATURE |getIdentifier| #3=((|Union| (|Identifier|) #2#) $)) (SIGNATURE |callForm?| #1#) (SIGNATURE |getOperator| #3#) (SIGNATURE |getOperands| ((|Union| (|List| $) #2#) $))))) (T |ElaboratedExpression|)) +((|type| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Syntax|)) #2=(|isDomain| *1 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T) ((-20) . T) ((-44 |#1| (-485)) . T) ((-22) . T) ((-35 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-35 |#1|) |has| |#1| (-145)) ((-35 |#2|) |has| |#1| (-311)) ((-35 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-32) |has| |#1| (-35 (-349 (-485)))) ((-63) |has| |#1| (-35 (-349 (-485)))) ((-69) . T) ((-79 (-349 (-485)) (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-79 |#1| |#1|) . T) ((-79 |#2| |#2|) |has| |#1| (-311)) ((-79 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-101) . T) ((-115) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-115))) (|has| |#1| (-115))) ((-117) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-741))) (-11 (|has| |#1| (-311)) (|has| |#2| (-117))) (|has| |#1| (-117))) ((-556 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-556 (-485)) . T) ((-556 (-1091)) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-1091)))) ((-556 |#1|) |has| |#1| (-145)) ((-556 |#2|) . T) ((-556 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-553 (-773)) . T) ((-145) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-554 (-178)) -11 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-554 (-329)) -11 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-554 (-474)) -11 (|has| |#1| (-311)) (|has| |#2| (-554 (-474)))) ((-554 (-801 (-329))) -11 (|has| |#1| (-311)) (|has| |#2| (-554 (-801 (-329))))) ((-554 (-801 (-485))) -11 (|has| |#1| (-311)) (|has| |#2| (-554 (-801 (-485))))) ((-185 $) OR (|has| |#1| (-14 * (|#1| (-485) |#1|))) (-11 (|has| |#1| (-311)) (|has| |#2| (-188))) (-11 (|has| |#1| (-311)) (|has| |#2| (-189)))) ((-183 |#2|) |has| |#1| (-311)) ((-189) OR (|has| |#1| (-14 * (|#1| (-485) |#1|))) (-11 (|has| |#1| (-311)) (|has| |#2| (-189)))) ((-188) OR (|has| |#1| (-14 * (|#1| (-485) |#1|))) (-11 (|has| |#1| (-311)) (|has| |#2| (-188))) (-11 (|has| |#1| (-311)) (|has| |#2| (-189)))) ((-224 |#2|) |has| |#1| (-311)) ((-200) |has| |#1| (-311)) ((-238) |has| |#1| (-35 (-349 (-485)))) ((-240 (-485) |#1|) . T) ((-240 |#2| $) -11 (|has| |#1| (-311)) (|has| |#2| (-240 |#2| |#2|))) ((-240 $ $) |has| (-485) (-1026)) ((-245) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-257) |has| |#1| (-311)) ((-259 |#2|) -11 (|has| |#1| (-311)) (|has| |#2| (-259 |#2|))) ((-311) |has| |#1| (-311)) ((-287 |#2|) |has| |#1| (-311)) ((-328 |#2|) |has| |#1| (-311)) ((-342 |#2|) |has| |#1| (-311)) ((-380 |#1|) . T) ((-380 |#2|) |has| |#1| (-311)) ((-392) |has| |#1| (-311)) ((-433) |has| |#1| (-35 (-349 (-485)))) ((-456 (-1091) |#2|) -11 (|has| |#1| (-311)) (|has| |#2| (-456 (-1091) |#2|))) ((-456 |#2| |#2|) -11 (|has| |#1| (-311)) (|has| |#2| (-259 |#2|))) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-12) . T) ((-589 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-311)) ((-589 $) . T) ((-591 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-591 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-581 (-485)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-311)) ((-591 $) . T) ((-583 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-583 |#1|) |has| |#1| (-145)) ((-583 |#2|) |has| |#1| (-311)) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-581 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-581 (-485)))) ((-581 |#2|) |has| |#1| (-311)) ((-655 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-655 |#1|) |has| |#1| (-145)) ((-655 |#2|) |has| |#1| (-311)) ((-655 $) OR (|has| |#1| (-496)) (|has| |#1| (-311))) ((-664) . T) ((-715) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-717) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-719) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-722) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-741) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-756) -11 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-757) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-757))) (-11 (|has| |#1| (-311)) (|has| |#2| (-741)))) ((-760) OR (-11 (|has| |#1| (-311)) (|has| |#2| (-757))) (-11 (|has| |#1| (-311)) (|has| |#2| (-741)))) ((-807 $ (-1091)) OR (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-485) |#1|)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-812 (-1091)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-810 (-1091))))) ((-810 (-1091)) OR (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-485) |#1|)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-810 (-1091))))) ((-812 (-1091)) OR (-11 (|has| |#1| (-810 (-1091))) (|has| |#1| (-14 * (|#1| (-485) |#1|)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-812 (-1091)))) (-11 (|has| |#1| (-311)) (|has| |#2| (-810 (-1091))))) ((-797 (-329)) -11 (|has| |#1| (-311)) (|has| |#2| (-797 (-329)))) ((-797 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-797 (-485)))) ((-795 |#2|) |has| |#1| (-311)) ((-822) -11 (|has| |#1| (-311)) (|has| |#2| (-822))) ((-887 |#1| (-485) (-995)) . T) ((-833) |has| |#1| (-311)) ((-905 |#2|) |has| |#1| (-311)) ((-916) |has| |#1| (-35 (-349 (-485)))) ((-934) -11 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-951 (-349 (-485))) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-485)))) ((-951 (-485)) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-485)))) ((-951 (-1091)) -11 (|has| |#1| (-311)) (|has| |#2| (-951 (-1091)))) ((-951 |#2|) . T) ((-964 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-964 |#1|) . T) ((-964 |#2|) |has| |#1| (-311)) ((-964 $) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-969 (-349 (-485))) OR (|has| |#1| (-311)) (|has| |#1| (-35 (-349 (-485))))) ((-969 |#1|) . T) ((-969 |#2|) |has| |#1| (-311)) ((-969 $) OR (|has| |#1| (-496)) (|has| |#1| (-311)) (|has| |#1| (-145))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . 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2363995 2365277 2366424 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2358453 2359924 2361235 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2351368 2353432 2355223 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2343537 2351306 2351363 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2338486 2343251 2343366 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2338073 2338156 2338300 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2337224 2337425 2337660 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2336964 2337022 2337115 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2330490 2335167 2335775 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2329666 2329871 2330102 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2328911 2329282 2329429 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2328399 2328641 2328671 "STEP" 2328765 STEP (NIL) -9 NIL 2328836 NIL) (-1066 2320893 2328317 2328394 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2315918 2319673 2319716 "STAGG" 2320143 STAGG (NIL T) -9 NIL 2320317 NIL) (-1064 2314376 2315084 2315913 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2312538 2314203 2314295 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2311818 2312357 2312387 "SRING" 2312392 SRING (NIL) -9 NIL 2312412 NIL) (-1061 2304733 2310356 2310795 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2298507 2299946 2301450 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2291124 2295782 2295812 "SRAGG" 2297111 SRAGG (NIL) -9 NIL 2297715 NIL) (-1058 2290421 2290741 2291119 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2284527 2289743 2290166 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2278456 2281880 2282631 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2274885 2275704 2276341 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2273860 2274165 2274195 "SPFCAT" 2274639 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2272797 2273049 2273313 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2263555 2265829 2265859 "SPADXPT" 2270496 SPADXPT (NIL) -9 NIL 2272620 NIL) (-1051 2263357 2263403 2263472 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2261013 2263321 2263352 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2252687 2254776 2254818 "SPACEC" 2259133 SPACEC (NIL T) -9 NIL 2260938 NIL) (-1048 2250516 2252634 2252682 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2249495 2249684 2249967 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2247899 2248232 2248643 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2247164 2247398 2247659 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2243344 2244304 2245299 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2239702 2240401 2241130 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2233724 2238987 2239083 "SNTSCAT" 2239088 SNTSCAT (NIL T T T T) -9 NIL 2239158 NIL) (-1041 2227545 2232365 2232755 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2221317 2227464 2227540 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2219749 2220080 2220478 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2211363 2216297 2216399 "SMATCAT" 2217742 SMATCAT (NIL NIL T T T) -9 NIL 2218290 NIL) (-1037 2209204 2210188 2211358 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2208806 2208978 2209021 "SMAGG" 2209106 SMAGG (NIL T) -9 NIL 2209163 NIL) (-1035 2206349 2207955 2207998 "SKAGG" 2208259 SKAGG (NIL T) -9 NIL 2208395 NIL) (-1034 2202395 2206169 2206280 "SINT" NIL SINT (NIL) -8 NIL NIL 2206321) (-1033 2202205 2202249 2202315 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2201280 2201512 2201780 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2200284 2200446 2200722 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2199630 2199970 2200093 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2198976 2199283 2199423 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2197087 2197579 2198085 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2190571 2197006 2197082 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2190074 2190311 2190341 "SGROUP" 2190434 SGROUP (NIL) -9 NIL 2190496 NIL) (-1025 2189964 2189996 2190069 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2189602 2189642 2189683 "SGPOPC" 2189688 SGPOPC (NIL T) -9 NIL 2189889 NIL) (-1023 2189136 2189413 2189519 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2186559 2187328 2188050 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2180680 2185943 2186039 "SFRTCAT" 2186044 SFRTCAT (NIL T T T T) -9 NIL 2186082 NIL) (-1020 2175072 2176185 2177312 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2169248 2170409 2171573 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2168220 2169122 2169243 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2163828 2164723 2164818 "SEXCAT" 2167431 SEXCAT (NIL T T T T T) -9 NIL 2167982 NIL) (-1016 2162801 2163755 2163823 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2161192 2161777 2162079 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2160715 2160900 2160930 "SETCAT" 2161047 SETCAT (NIL) -9 NIL 2161131 NIL) (-1013 2160547 2160611 2160710 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2157599 2158983 2159026 "SETAGG" 2159894 SETAGG (NIL T) -9 NIL 2160232 NIL) (-1011 2157205 2157357 2157594 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2154450 2157152 2157200 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2153916 2154226 2154326 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2153043 2153409 2153470 "SEGXCAT" 2153756 SEGXCAT (NIL T T) -9 NIL 2153876 NIL) (-1007 2151968 2152236 2152279 "SEGCAT" 2152801 SEGCAT (NIL T) -9 NIL 2153022 NIL) (-1006 2151648 2151713 2151826 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2150714 2151184 2151392 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2150292 2150571 2150647 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2149657 2149793 2149997 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2148723 2149470 2149652 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2147976 2148671 2148718 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2139461 2147843 2147971 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2138321 2138611 2138928 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2137627 2137839 2138027 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2136977 2137134 2137310 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2136550 2136781 2136809 "SASTCAT" 2136814 SASTCAT (NIL) -9 NIL 2136827 NIL) (-995 2136017 2136442 2136516 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2135620 2135661 2135832 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2135251 2135292 2135449 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2128332 2135168 2135246 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2126982 2127311 2127707 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2125743 2126104 2126404 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-989 2125367 2125588 2125669 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-988 2122827 2123461 2123914 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-987 2122666 2122699 2122767 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-986 2122157 2122460 2122551 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-985 2117785 2118653 2119564 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-984 2106840 2112103 2112197 "RSETCAT" 2116253 RSETCAT (NIL T T T T) -9 NIL 2117341 NIL) (-983 2105378 2106020 2106835 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-982 2099152 2100597 2102104 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-981 2097034 2097591 2097663 "RRCC" 2098736 RRCC (NIL T T) -9 NIL 2099077 NIL) (-980 2096559 2096758 2097029 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-979 2096029 2096339 2096437 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-978 2068562 2079276 2079340 "RPOLCAT" 2089814 RPOLCAT (NIL T T T) -9 NIL 2092959 NIL) (-977 2062661 2065484 2068557 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2058828 2062409 2062547 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2057156 2057895 2058151 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2052799 2055611 2055639 "RNS" 2055901 RNS (NIL) -9 NIL 2056153 NIL) (-973 2051702 2052189 2052726 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2050820 2051221 2051421 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2049958 2050520 2050548 "RNG" 2050608 RNG (NIL) -9 NIL 2050662 NIL) (-970 2049847 2049881 2049953 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2049109 2049614 2049654 "RMODULE" 2049659 RMODULE (NIL T) -9 NIL 2049685 NIL) (-968 2048048 2048154 2048484 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2044945 2047638 2047931 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2037786 2040230 2040342 "RMATCAT" 2043513 RMATCAT (NIL NIL NIL T T T) -9 NIL 2044444 NIL) (-965 2037303 2037482 2037781 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2036871 2037082 2037123 "RLINSET" 2037184 RLINSET (NIL T) -9 NIL 2037228 NIL) (-963 2036516 2036597 2036723 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2035362 2036093 2036121 "RING" 2036176 RING (NIL) -9 NIL 2036268 NIL) (-961 2035207 2035263 2035357 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2034261 2034528 2034784 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2025485 2033889 2034090 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2024710 2025221 2025260 "RGBCSPC" 2025317 RGBCSPC (NIL T) -9 NIL 2025368 NIL) (-957 2023744 2024230 2024269 "RGBCMDL" 2024497 RGBCMDL (NIL T) -9 NIL 2024611 NIL) (-956 2023456 2023525 2023626 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2023219 2023260 2023355 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2021643 2022073 2022453 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2019230 2019898 2020566 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2018780 2018878 2019038 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2018402 2018500 2018541 "RETRACT" 2018672 RETRACT (NIL T) -9 NIL 2018759 NIL) (-950 2018282 2018313 2018397 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2017884 2018156 2018223 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2016364 2017255 2017452 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2016055 2016116 2016212 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2015798 2015839 2015944 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2015533 2015574 2015683 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2010604 2012055 2013270 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2007700 2008458 2009266 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2005669 2006291 2006891 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 1998597 2004220 2004656 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 1997909 1998189 1998338 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 1997394 1997509 1997674 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 1992987 1996797 1997018 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 1992219 1992418 1992631 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 1989509 1990347 1991229 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 1986091 1987127 1988186 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 1985927 1985980 1986008 "REAL" 1986013 REAL (NIL) -9 NIL 1986048 NIL) (-933 1985417 1985721 1985812 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 1984897 1984975 1985180 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 1984130 1984322 1984533 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 1983018 1983315 1983682 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 1981285 1981755 1982288 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1980209 1980486 1980873 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1979038 1979347 1979766 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1972386 1975898 1975926 "RCFIELD" 1977203 RCFIELD (NIL) -9 NIL 1977933 NIL) (-925 1971004 1971616 1972313 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1967758 1969090 1969131 "RCAGG" 1970185 RCAGG (NIL T) -9 NIL 1970647 NIL) (-923 1967485 1967595 1967753 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1966930 1967059 1967220 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1966547 1966626 1966745 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1965962 1966112 1966262 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1965744 1965794 1965865 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1958186 1964862 1965170 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1947888 1958053 1958181 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1947522 1947615 1947643 "RADCAT" 1947800 RADCAT (NIL) -9 NIL NIL NIL) (-915 1947360 1947420 1947517 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1945465 1947191 1947280 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1945146 1945195 1945322 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1937415 1941499 1941539 "QUATCAT" 1942317 QUATCAT (NIL T) -9 NIL 1943081 NIL) (-911 1934665 1935945 1937321 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1930505 1934615 1934660 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1927843 1929502 1929543 "QUAGG" 1929918 QUAGG (NIL T) -9 NIL 1930094 NIL) (-908 1927445 1927717 1927784 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1926451 1927081 1927244 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1926132 1926181 1926308 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1915714 1921883 1921923 "QFCAT" 1922581 QFCAT (NIL T) -9 NIL 1923574 NIL) (-904 1912598 1914037 1915620 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1912144 1912278 1912408 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1906340 1907501 1908663 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1905759 1905939 1906171 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1903581 1904109 1904532 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1902480 1902722 1903039 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1900841 1901039 1901392 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1896597 1897813 1897854 "PTRANFN" 1899738 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1895244 1895589 1895910 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1894937 1895000 1895107 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1889234 1893678 1893718 "PTCAT" 1894010 PTCAT (NIL T) -9 NIL 1894163 NIL) (-893 1888927 1888968 1889092 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1887806 1888122 1888456 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1876685 1879246 1881555 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1869887 1872450 1872544 "PSETCAT" 1875518 PSETCAT (NIL T T T T) -9 NIL 1876327 NIL) (-889 1868337 1869071 1869882 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1867656 1867851 1867879 "PSCURVE" 1868147 PSCURVE (NIL) -9 NIL 1868314 NIL) (-887 1863240 1865060 1865124 "PSCAT" 1865959 PSCAT (NIL T T T) -9 NIL 1866198 NIL) (-886 1862554 1862836 1863235 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1860951 1861866 1862129 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1860442 1860745 1860836 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1851462 1853884 1856072 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1849156 1850725 1850765 "PRQAGG" 1850948 PRQAGG (NIL T) -9 NIL 1851051 NIL) (-881 1848329 1848775 1848803 "PROPLOG" 1848942 PROPLOG (NIL) -9 NIL 1849056 NIL) (-880 1848004 1848067 1848190 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1847440 1847579 1847751 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1845688 1846451 1846748 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1845240 1845372 1845500 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1839681 1844180 1845000 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1839510 1839548 1839607 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1838949 1839089 1839240 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1837417 1837836 1838302 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1837134 1837195 1837223 "PRIMCAT" 1837347 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1836305 1836501 1836729 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1832466 1836255 1836300 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1832165 1832227 1832338 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1829301 1831814 1832047 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1828752 1828909 1828937 "PPCURVE" 1829142 PPCURVE (NIL) -9 NIL 1829278 NIL) (-866 1828365 1828610 1828693 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1826121 1826542 1827134 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1825564 1825628 1825861 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1822284 1822770 1823381 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1807856 1813986 1814050 "POLYCAT" 1817535 POLYCAT (NIL T T T) -9 NIL 1819412 NIL) (-861 1803366 1805513 1807851 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1803023 1803097 1803216 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1802716 1802779 1802886 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1796079 1802449 1802608 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1794966 1795229 1795505 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1793570 1793883 1794213 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1789013 1793520 1793565 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1787501 1787912 1788287 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1786258 1786567 1786963 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1785929 1786013 1786130 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1785508 1785583 1785757 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1784994 1785090 1785250 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1784466 1784586 1784740 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1783361 1783579 1783956 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1782972 1783057 1783209 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1782523 1782605 1782786 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1782215 1782296 1782409 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1781728 1781803 1782011 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1781076 1781204 1781406 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1780438 1780572 1780735 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1779742 1779924 1780105 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1779465 1779539 1779633 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1776033 1777222 1778138 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1775117 1775318 1775553 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1770682 1772066 1773208 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1750603 1755490 1760337 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1750343 1750396 1750499 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1749784 1749918 1750098 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1747793 1749014 1749042 "PID" 1749239 PID (NIL) -9 NIL 1749366 NIL) (-832 1747581 1747624 1747699 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1746768 1747428 1747515 "PI" NIL PI (NIL) -8 NIL NIL 1747555) (-830 1746220 1746371 1746547 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1742548 1743506 1744411 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1740912 1741201 1741567 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1740354 1740469 1740630 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1736895 1739223 1739576 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1735501 1735781 1736106 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1734266 1734520 1734868 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1732976 1733203 1733555 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1729986 1731546 1731574 "PFECAT" 1732167 PFECAT (NIL) -9 NIL 1732544 NIL) (-821 1729609 1729774 1729981 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1728433 1728715 1729016 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1726615 1727002 1727432 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1722585 1726541 1726610 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1718488 1719635 1720502 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1716420 1717509 1717550 "PERMCAT" 1717949 PERMCAT (NIL T) -9 NIL 1718246 NIL) (-815 1716116 1716163 1716286 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1712565 1714246 1714891 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1710591 1712320 1712441 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1709474 1709737 1709776 "PDSPC" 1710297 PDSPC (NIL T) -9 NIL 1710542 NIL) (-811 1708843 1709109 1709469 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1707480 1708473 1708512 "PDRING" 1708517 PDRING (NIL T) -9 NIL 1708544 NIL) (-809 1706192 1706981 1707032 "PDMOD" 1707037 PDMOD (NIL T T) -9 NIL 1707140 NIL) (-808 1705285 1705497 1705746 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1704890 1704957 1705011 "PDDOM" 1705176 PDDOM (NIL T T) -9 NIL 1705256 NIL) (-806 1704742 1704778 1704885 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1704528 1704567 1704656 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1702845 1703599 1703898 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1702534 1702597 1702706 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1700672 1701102 1701553 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1694292 1696121 1697413 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1693923 1693996 1694128 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1691625 1692305 1692786 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1689829 1690257 1690660 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1689275 1689523 1689564 "PATMAB" 1689671 PATMAB (NIL T) -9 NIL 1689754 NIL) (-796 1687922 1688326 1688583 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1687460 1687591 1687632 "PATAB" 1687637 PATAB (NIL T) -9 NIL 1687809 NIL) (-794 1686003 1686440 1686863 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1685681 1685756 1685858 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1685370 1685433 1685542 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1685175 1685221 1685288 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1684853 1684928 1685030 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1684542 1684605 1684714 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1684233 1684303 1684400 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1683922 1683985 1684094 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1683083 1683462 1683641 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1682690 1682788 1682907 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1681658 1682083 1682302 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1680323 1680977 1681337 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1673413 1679727 1679921 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1665834 1672911 1673095 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1662559 1664474 1664514 "PADICCT" 1665095 PADICCT (NIL NIL) -9 NIL 1665377 NIL) (-779 1660549 1662509 1662554 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1659711 1659921 1660187 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1659053 1659196 1659400 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1657434 1658461 1658739 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1656958 1657217 1657314 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1656017 1656695 1656867 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1646439 1649308 1651507 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1645834 1646145 1646271 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1645120 1645312 1645340 "OUTBCON" 1645655 OUTBCON (NIL) -9 NIL 1645818 NIL) (-770 1644830 1644959 1645115 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1644211 1644356 1644517 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1643582 1644009 1644098 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1642997 1643412 1643440 "OSGROUP" 1643445 OSGROUP (NIL) -9 NIL 1643467 NIL) (-766 1641961 1642222 1642507 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1639230 1641836 1641956 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1636371 1638981 1639107 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1634389 1634917 1635477 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1627731 1630271 1630311 "OREPCAT" 1632632 OREPCAT (NIL T) -9 NIL 1633734 NIL) (-761 1625757 1626691 1627726 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1624954 1625225 1625253 "ORDTYPE" 1625558 ORDTYPE (NIL) -9 NIL 1625716 NIL) (-759 1624488 1624699 1624949 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1623950 1624326 1624483 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1623444 1623807 1623835 "ORDSET" 1623840 ORDSET (NIL) -9 NIL 1623862 NIL) (-756 1622009 1623031 1623059 "ORDRING" 1623064 ORDRING (NIL) -9 NIL 1623092 NIL) (-755 1621257 1621814 1621842 "ORDMON" 1621847 ORDMON (NIL) -9 NIL 1621868 NIL) (-754 1620561 1620723 1620915 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1619772 1620280 1620308 "ORDFIN" 1620373 ORDFIN (NIL) -9 NIL 1620447 NIL) (-752 1619166 1619305 1619491 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1615841 1618134 1618540 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1615248 1615603 1615708 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1615056 1615101 1615167 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1614357 1614633 1614674 "OPERCAT" 1614885 OPERCAT (NIL T) -9 NIL 1614981 NIL) (-747 1614169 1614236 1614352 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1611535 1612971 1613467 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1610956 1611083 1611257 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1607857 1610095 1610461 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1604723 1607232 1607272 "OMSAGG" 1607333 OMSAGG (NIL T) -9 NIL 1607397 NIL) (-742 1603135 1604394 1604562 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1601331 1602572 1602600 "OINTDOM" 1602605 OINTDOM (NIL) -9 NIL 1602626 NIL) (-740 1598761 1600333 1600662 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1598015 1598711 1598756 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1595217 1597856 1598010 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1586754 1595088 1595212 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1580209 1586645 1586749 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1579181 1579418 1579691 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1576822 1577492 1578196 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1572599 1573559 1574582 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1572107 1572195 1572389 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1569556 1570138 1570811 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1566951 1567459 1568055 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1563948 1564487 1565133 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1563303 1563411 1563669 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1562461 1562586 1562807 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1558745 1559541 1560454 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1558185 1558280 1558502 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1557866 1557915 1558042 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1554469 1557665 1557784 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1553629 1554251 1554279 "OCAMON" 1554284 OCAMON (NIL) -9 NIL 1554305 NIL) (-721 1547823 1550637 1550677 "OC" 1551772 OC (NIL T) -9 NIL 1552628 NIL) (-720 1545823 1546749 1547729 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1545239 1545657 1545685 "OASGP" 1545690 OASGP (NIL) -9 NIL 1545710 NIL) (-718 1544302 1544951 1544979 "OAMONS" 1545019 OAMONS (NIL) -9 NIL 1545062 NIL) (-717 1543447 1544028 1544056 "OAMON" 1544113 OAMON (NIL) -9 NIL 1544164 NIL) (-716 1543343 1543375 1543442 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1542094 1542868 1542896 "OAGROUP" 1543042 OAGROUP (NIL) -9 NIL 1543134 NIL) (-714 1541885 1541972 1542089 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1541625 1541681 1541769 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1536687 1538250 1539777 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1533382 1534416 1535451 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1532492 1532725 1532943 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1521353 1524381 1526829 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1515476 1520739 1520833 "NTSCAT" 1520838 NTSCAT (NIL T T T T) -9 NIL 1520876 NIL) (-707 1514817 1514996 1515189 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1514510 1514573 1514680 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1502177 1512130 1512940 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1491186 1502042 1502172 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1489906 1490231 1490588 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1488742 1489006 1489364 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1487909 1488042 1488258 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1486227 1486546 1486952 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1485940 1485974 1486098 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1485759 1485794 1485863 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1485535 1485725 1485754 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1485099 1485166 1485343 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1483385 1484462 1484717 "NNI" NIL NNI (NIL) -8 NIL NIL 1485064) (-694 1482113 1482450 1482814 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1481090 1481342 1481644 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1480182 1480742 1480783 "NETCLT" 1480954 NETCLT (NIL T) -9 NIL 1481035 NIL) (-691 1479086 1479353 1479634 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1478885 1478928 1479003 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1477416 1477804 1478224 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1476049 1477015 1477043 "NASRING" 1477153 NASRING (NIL) -9 NIL 1477233 NIL) (-687 1475894 1475950 1476044 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1474823 1475501 1475529 "NARNG" 1475646 NARNG (NIL) -9 NIL 1475737 NIL) (-685 1474599 1474684 1474818 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1473365 1474119 1474159 "NAALG" 1474238 NAALG (NIL T) -9 NIL 1474299 NIL) (-683 1473235 1473270 1473360 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1468214 1469399 1470585 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1467609 1467696 1467880 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1459600 1464095 1464147 "MTSCAT" 1465207 MTSCAT (NIL T T) -9 NIL 1465721 NIL) (-679 1459366 1459426 1459518 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1459192 1459231 1459291 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1456821 1458706 1458747 "MSETAGG" 1458752 MSETAGG (NIL T) -9 NIL 1458786 NIL) (-676 1453191 1455864 1456185 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1449584 1451407 1452126 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1449221 1449294 1449423 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1448874 1448915 1449059 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1446739 1447076 1447507 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1440137 1446638 1446734 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1439662 1439703 1439911 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1439221 1439270 1439453 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1438495 1438588 1438807 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1437112 1437473 1437863 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1436633 1436700 1436739 "MONOPC" 1436799 MONOPC (NIL T) -9 NIL 1437018 NIL) (-665 1436084 1436420 1436548 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1435226 1435605 1435633 "MONOID" 1435851 MONOID (NIL) -9 NIL 1435995 NIL) (-663 1434885 1435035 1435221 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1423823 1430693 1430752 "MONOGEN" 1431426 MONOGEN (NIL T T) -9 NIL 1431882 NIL) (-661 1421835 1422721 1423704 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1420549 1421093 1421121 "MONADWU" 1421512 MONADWU (NIL) -9 NIL 1421747 NIL) (-659 1420097 1420297 1420544 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1419374 1419675 1419703 "MONAD" 1419910 MONAD (NIL) -9 NIL 1420022 NIL) (-657 1419141 1419237 1419369 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1417531 1418301 1418580 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1416665 1417192 1417232 "MODULE" 1417237 MODULE (NIL T) -9 NIL 1417275 NIL) (-654 1416344 1416470 1416660 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1414063 1414949 1415263 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1411242 1412659 1413172 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1409876 1410450 1410726 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1399095 1408541 1408954 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1396059 1398103 1398372 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1395143 1395510 1395700 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1394712 1394761 1394940 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1392537 1393533 1393573 "MLO" 1393990 MLO (NIL T) -9 NIL 1394230 NIL) (-645 1390418 1390945 1391540 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1389886 1389982 1390136 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1389556 1389632 1389755 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1388768 1388954 1389182 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1388261 1388377 1388533 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1387633 1387747 1387932 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1386660 1386933 1387210 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1386093 1386181 1386352 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1383251 1384130 1385009 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1381918 1382266 1382619 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1379342 1381005 1381046 "MDAGG" 1381303 MDAGG (NIL T) -9 NIL 1381448 NIL) (-634 1378616 1378780 1378980 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1377694 1377980 1378210 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1375791 1376368 1376929 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1371535 1375381 1375628 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1367884 1368653 1369387 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1366637 1366806 1367135 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1356082 1359706 1359782 "MATCAT" 1364770 MATCAT (NIL T T T) -9 NIL 1366216 NIL) (-627 1353363 1354669 1356077 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1351764 1352124 1352508 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1350897 1351094 1351316 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1349648 1349974 1350301 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1348810 1349212 1349388 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1348479 1348543 1348666 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1348127 1348200 1348314 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1347662 1347777 1347919 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1345871 1346639 1346940 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1345365 1345667 1345757 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1339686 1343662 1343703 "LZSTAGG" 1344480 LZSTAGG (NIL T) -9 NIL 1344770 NIL) (-616 1337035 1338347 1339681 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1334422 1335388 1335871 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1334003 1334282 1334356 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1326218 1333864 1333998 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1325581 1325726 1325954 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1323065 1323763 1324475 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1321281 1321604 1322038 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1314661 1320313 1320354 "LSAGG" 1320416 LSAGG (NIL T) -9 NIL 1320494 NIL) (-608 1312355 1313454 1314656 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1309835 1311704 1311953 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1309502 1309593 1309716 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1309173 1309252 1309280 "LOGIC" 1309391 LOGIC (NIL) -9 NIL 1309473 NIL) (-604 1309068 1309097 1309168 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1308387 1308545 1308738 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1307172 1307421 1307772 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1302994 1305793 1305833 "LODOCAT" 1306265 LODOCAT (NIL T) -9 NIL 1306476 NIL) (-600 1302787 1302863 1302989 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1299787 1302664 1302782 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1296885 1299737 1299782 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1293972 1296815 1296880 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1293025 1293200 1293502 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1291157 1292287 1292540 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1287072 1289298 1289339 "LNAGG" 1290198 LNAGG (NIL T) -9 NIL 1290636 NIL) (-593 1286459 1286726 1287067 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1283031 1283972 1284609 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1282293 1282798 1282838 "LMODULE" 1282843 LMODULE (NIL T) -9 NIL 1282869 NIL) (-590 1279762 1282029 1282152 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1279330 1279541 1279582 "LLINSET" 1279643 LLINSET (NIL T) -9 NIL 1279687 NIL) (-588 1279006 1279266 1279325 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1278605 1278685 1278824 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1277056 1277404 1277803 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1276227 1276423 1276651 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1269541 1275483 1275737 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1269118 1269351 1269392 "LINSET" 1269397 LINSET (NIL T) -9 NIL 1269430 NIL) (-582 1268019 1268741 1268908 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1266285 1267040 1267080 "LINEXP" 1267566 LINEXP (NIL T) -9 NIL 1267839 NIL) (-580 1264907 1265894 1266075 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1263734 1264006 1264308 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1262947 1263536 1263646 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1260505 1261227 1261977 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1259140 1259437 1259828 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1257933 1258535 1258575 "LIECAT" 1258715 LIECAT (NIL T) -9 NIL 1258866 NIL) (-574 1257807 1257840 1257928 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1252063 1257497 1257725 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1243703 1251739 1251895 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1240155 1241104 1242039 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1238779 1239687 1239715 "LFCAT" 1239922 LFCAT (NIL) -9 NIL 1240061 NIL) (-569 1237018 1237348 1237693 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1234535 1235200 1235881 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1231547 1232525 1233028 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1231038 1231341 1231432 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1229745 1230069 1230469 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1229011 1229096 1229322 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1224014 1227579 1228115 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1223639 1223689 1223849 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1222410 1223183 1223223 "LALG" 1223284 LALG (NIL T) -9 NIL 1223342 NIL) (-560 1222193 1222270 1222405 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1220046 1221461 1221712 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1219875 1219905 1219946 "KVTFROM" 1220008 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1218691 1219406 1219595 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1218520 1218550 1218591 "KRCFROM" 1218653 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1217622 1217819 1218114 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1217451 1217481 1217522 "KONVERT" 1217584 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1217280 1217310 1217351 "KOERCE" 1217413 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1216850 1216943 1217075 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1214903 1215797 1216169 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1207890 1212582 1212636 "KDAGG" 1213012 KDAGG (NIL T T) -9 NIL 1213252 NIL) (-549 1207548 1207683 1207885 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1200852 1207340 1207486 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1200505 1200785 1200847 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1199475 1199974 1200223 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1198601 1199050 1199255 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1197467 1197958 1198257 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1196749 1197148 1197309 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1196462 1196696 1196744 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1190717 1196152 1196380 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1190135 1190468 1190588 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1186863 1188323 1188375 "IXAGG" 1189272 IXAGG (NIL T T) -9 NIL 1189732 NIL) (-538 1186150 1186481 1186858 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1185219 1185494 1185736 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1183881 1184088 1184381 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1182832 1183054 1183337 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1182507 1182570 1182693 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1181769 1182141 1182315 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1179745 1181045 1181319 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1169293 1175062 1176219 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1168538 1168690 1168926 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1168029 1168332 1168423 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1167322 1167413 1167626 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1166454 1166679 1166919 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1164867 1165248 1165676 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1164652 1164696 1164772 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1163502 1163799 1164094 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1162775 1163126 1163277 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1161978 1162109 1162322 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1160140 1160637 1161181 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1157221 1158489 1159178 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1157046 1157086 1157146 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1153044 1156972 1157041 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1151047 1152983 1153039 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1150421 1150719 1150848 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1149874 1150162 1150294 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1148960 1149580 1149706 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1148375 1148864 1148892 "IOBCON" 1148897 IOBCON (NIL) -9 NIL 1148918 NIL) (-512 1147946 1148010 1148192 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1140005 1142376 1144701 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1137116 1137899 1138763 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1136793 1136890 1137007 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1134235 1136729 1136788 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1132347 1132876 1133443 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1131849 1131963 1132103 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1130233 1130639 1131101 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1128012 1128606 1129217 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1125385 1125995 1126715 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1124789 1124947 1125155 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1124308 1124394 1124582 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1122513 1123034 1123491 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1115603 1117256 1118985 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1114969 1115131 1115304 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1112842 1113306 1113850 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1110968 1111918 1111946 "INTDOM" 1112245 INTDOM (NIL) -9 NIL 1112450 NIL) (-495 1110521 1110723 1110963 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1106328 1108800 1108854 "INTCAT" 1109650 INTCAT (NIL T) -9 NIL 1109966 NIL) (-493 1105893 1106013 1106140 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1104733 1104905 1105211 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1104306 1104402 1104559 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1096789 1104213 1104301 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1096087 1096642 1096707 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096741) (-488 1095384 1095939 1096004 "INT64" NIL INT64 (NIL) -8 NIL NIL 1096038) (-487 1094681 1095236 1095301 "INT32" NIL INT32 (NIL) -8 NIL NIL 1095335) (-486 1093978 1094533 1094598 "INT16" NIL INT16 (NIL) -8 NIL NIL 1094632) (-485 1090441 1093897 1093973 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1084498 1087981 1088009 "INS" 1088939 INS (NIL) -9 NIL 1089598 NIL) (-483 1082560 1083478 1084425 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1081619 1081842 1082117 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1080833 1080974 1081171 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1079823 1079964 1080201 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1078975 1079139 1079399 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1078255 1078370 1078558 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1076994 1077263 1077587 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1076274 1076415 1076598 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1075937 1076009 1076107 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1073015 1074501 1075024 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1072614 1072721 1072835 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1071775 1072415 1072516 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1070625 1070893 1071214 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1069615 1070555 1070620 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1069240 1069320 1069437 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1068156 1068699 1068903 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1064251 1065306 1066249 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1063111 1063432 1063460 "INBCON" 1063971 INBCON (NIL) -9 NIL 1064235 NIL) (-465 1062567 1062831 1063106 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1062061 1062363 1062453 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1061518 1061827 1061932 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1060357 1060498 1060815 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-461 1058780 1059049 1059388 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-460 1053623 1058711 1058775 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-459 1053003 1053337 1053452 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-458 1048095 1052441 1052627 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-457 1047125 1048017 1048090 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-456 1046697 1046774 1046828 "IEVALAB" 1047035 IEVALAB (NIL T T) -9 NIL NIL NIL) (-455 1046452 1046532 1046692 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-454 1045837 1046064 1046221 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-453 1044830 1045757 1045832 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-452 1043893 1044750 1044825 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-451 1042976 1043622 1043759 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-450 1041440 1042011 1042062 "IDPC" 1042471 IDPC (NIL T T) -9 NIL 1042762 NIL) (-449 1040728 1041362 1041435 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-448 1039898 1040650 1040723 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-447 1039591 1039804 1039864 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-446 1039295 1039335 1039374 "IDEMOPC" 1039379 IDEMOPC (NIL T) -9 NIL 1039516 NIL) (-445 1036366 1037247 1038139 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-444 1029992 1031269 1032308 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-443 1029254 1029384 1029583 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-442 1028427 1028926 1029064 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-441 1026818 1027149 1027540 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-440 1022855 1026774 1026813 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-439 1020113 1020737 1021432 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1018339 1018819 1019352 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1016154 1018245 1018334 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1012296 1016092 1016149 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1005875 1011260 1011728 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1005443 1005506 1005679 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1004935 1005084 1005112 "HYPCAT" 1005319 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1004591 1004744 1004930 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1004204 1004449 1004532 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1004037 1004086 1004127 "HOMOTOP" 1004132 HOMOTOP (NIL T) -9 NIL 1004165 NIL) (-429 1002540 1003352 1003393 "HOAGG" 1003398 HOAGG (NIL T) -9 NIL 1003698 NIL) (-428 1002167 1002314 1002535 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 995367 1001892 1002040 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 994302 994560 994823 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 993237 994167 994297 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 991436 993070 993158 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 990751 991103 991236 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 984249 990684 990746 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 977388 983985 984136 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 976841 976998 977161 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 969341 976758 976836 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 968832 969135 969226 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 966382 968619 968798 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 962068 966265 966377 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 954545 961965 962063 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 946482 953914 954169 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 945506 946015 946043 "GROUP" 946246 GROUP (NIL) -9 NIL 946380 NIL) (-412 945049 945250 945501 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 943721 944060 944447 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 942543 942900 942951 "GRMOD" 943480 GRMOD (NIL T T) -9 NIL 943646 NIL) (-409 942362 942410 942538 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 938485 939696 940696 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 937207 937531 937846 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 936760 936888 937029 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 935833 936332 936383 "GRALG" 936536 GRALG (NIL T T) -9 NIL 936626 NIL) (-404 935552 935653 935828 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 932571 935243 935410 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 931984 932047 932304 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 927838 928734 929259 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 927013 927215 927453 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 922016 922943 923962 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 921764 921821 921910 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 921246 921335 921500 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 920755 920796 921009 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 919556 919839 920143 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 912831 919246 919407 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 902614 907621 908725 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 900666 901769 901797 "GCDDOM" 902052 GCDDOM (NIL) -9 NIL 902209 NIL) (-391 900289 900446 900661 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 891082 893552 895940 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 889217 889542 889960 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 888158 888347 888614 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 887029 887236 887540 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 886492 886634 886782 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 885104 885452 885765 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 883649 883970 884292 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 881275 881631 882036 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 874527 876188 877766 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 874179 874400 874468 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 873924 873966 874007 "FUNCTOR" 874091 FUNCTOR (NIL T) -9 NIL 874150 NIL) (-379 873548 873769 873850 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-378 871645 872328 872788 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-377 870238 870545 870937 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-376 868893 869252 869576 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-375 868196 868320 868507 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-374 867170 867436 867783 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-373 864828 865358 865840 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-372 864411 864471 864640 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-371 862711 863625 863928 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-370 861859 861993 862216 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-369 861030 861191 861418 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-368 857246 859907 859948 "FSAGG" 860318 FSAGG (NIL T) -9 NIL 860579 NIL) (-367 855600 856359 857151 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-366 853556 853852 854396 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-365 852603 852785 853085 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-364 852284 852333 852460 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-363 832440 841941 841982 "FS" 845852 FS (NIL T) -9 NIL 848130 NIL) (-362 824671 828164 832143 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-361 824205 824332 824484 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-360 818728 821886 821926 "FRNAALG" 823246 FRNAALG (NIL T) -9 NIL 823844 NIL) (-359 815469 816720 817978 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-358 815150 815199 815326 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-357 813637 814194 814488 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-356 812923 813016 813303 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 810757 811523 811839 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-354 809866 810309 810350 "FRETRCT" 810355 FRETRCT (NIL T) -9 NIL 810526 NIL) (-353 809239 809517 809861 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-352 805983 807503 807562 "FRAMALG" 808444 FRAMALG (NIL T T) -9 NIL 808736 NIL) (-351 804579 805130 805760 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-350 804272 804335 804442 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-349 797913 804077 804267 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-348 797606 797669 797776 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-347 790015 794586 795893 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-346 783793 787296 787324 "FPS" 788443 FPS (NIL) -9 NIL 788999 NIL) (-345 783350 783483 783647 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-344 780160 782203 782231 "FPC" 782456 FPC (NIL) -9 NIL 782598 NIL) (-343 780006 780058 780155 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-342 778783 779492 779533 "FPATMAB" 779538 FPATMAB (NIL T) -9 NIL 779690 NIL) (-341 777213 777809 778156 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-340 776788 776846 777019 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-339 775291 776186 776360 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-338 773906 774411 774439 "FNCAT" 774896 FNCAT (NIL) -9 NIL 775153 NIL) (-337 773363 773873 773901 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-336 771950 773312 773358 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-335 768538 769896 769937 "FMONCAT" 771154 FMONCAT (NIL T) -9 NIL 771758 NIL) (-334 765497 766577 766630 "FMCAT" 767712 FMCAT (NIL T T) -9 NIL 768182 NIL) (-333 764197 765320 765419 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-332 763245 764045 764192 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-331 761432 761884 762378 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-330 759367 759903 760481 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-329 752753 757704 758318 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-328 751234 752335 752375 "FLINEXP" 752380 FLINEXP (NIL T) -9 NIL 752473 NIL) (-327 750643 750902 751229 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-326 749892 750051 750265 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-325 746775 747854 747906 "FLALG" 749133 FLALG (NIL T T) -9 NIL 749600 NIL) (-324 745946 746107 746334 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-323 739652 743342 743383 "FLAGG" 744622 FLAGG (NIL T) -9 NIL 745270 NIL) (-322 738760 739164 739647 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-321 735321 736585 736644 "FINRALG" 737772 FINRALG (NIL T T) -9 NIL 738280 NIL) (-320 734712 734977 735316 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-319 734010 734306 734334 "FINITE" 734530 FINITE (NIL) -9 NIL 734637 NIL) (-318 733918 733944 734005 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-317 730688 732014 732055 "FINAGG" 733054 FINAGG (NIL T) -9 NIL 733561 NIL) (-316 729607 730130 730683 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-315 721568 724159 724199 "FINAALG" 727851 FINAALG (NIL T) -9 NIL 729289 NIL) (-314 717835 719080 720203 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-313 716387 716806 716860 "FILECAT" 717544 FILECAT (NIL T T) -9 NIL 717760 NIL) (-312 715738 716212 716315 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-311 712986 714864 714892 "FIELD" 714932 FIELD (NIL) -9 NIL 715012 NIL) (-310 712011 712472 712981 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-309 710015 710961 711307 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-308 709258 709439 709658 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-307 704528 709196 709253 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-306 704190 704257 704392 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-305 703730 703772 703981 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-304 700410 701287 702064 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-303 695694 700342 700405 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-302 690373 695183 695373 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-301 684854 689654 689912 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-300 679061 684305 684516 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-299 678084 678294 678609 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-298 673524 676229 676257 "FFIELDC" 676876 FFIELDC (NIL) -9 NIL 677251 NIL) (-297 672593 673033 673519 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-296 672208 672266 672390 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-295 670352 670875 671392 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-294 665446 670151 670252 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-293 660546 665235 665342 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-292 655212 660337 660445 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-291 654666 654715 654950 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-290 633241 644275 644361 "FFCAT" 649511 FFCAT (NIL T T T) -9 NIL 650947 NIL) (-289 629481 630707 632013 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-288 624324 629412 629476 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-287 623347 623816 623857 "FEVALAB" 623862 FEVALAB (NIL T) -9 NIL 624101 NIL) (-286 622752 623004 623342 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-285 619579 620490 620605 "FDIVCAT" 622172 FDIVCAT (NIL T T T T) -9 NIL 622608 NIL) (-284 619373 619405 619574 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-283 618680 618773 619050 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-282 617166 618164 618367 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-281 616259 616643 616845 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-280 615381 615870 616010 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-279 606968 611611 611651 "FAXF" 613452 FAXF (NIL T) -9 NIL 614142 NIL) (-278 604884 605688 606503 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-277 600033 604406 604580 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-276 594472 596896 596948 "FAMR" 597959 FAMR (NIL T T) -9 NIL 598418 NIL) (-275 593671 594036 594467 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-274 592692 593613 593666 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-273 590286 591165 591218 "FAMONC" 592159 FAMONC (NIL T T) -9 NIL 592544 NIL) (-272 588842 590144 590281 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-271 586922 587283 587685 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-270 586199 586396 586618 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-269 578059 585646 585845 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-268 576078 576648 577234 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-267 572980 573622 574342 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-266 568137 568844 569649 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-265 567826 567889 567998 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-264 552619 566875 567301 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-263 543146 551939 552227 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-262 542640 542942 543032 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-261 542416 542606 542635 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-260 542105 542173 542286 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-259 541622 541764 541805 "EVALAB" 541975 EVALAB (NIL T) -9 NIL 542079 NIL) (-258 541250 541396 541617 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-257 538293 539888 539916 "EUCDOM" 540470 EUCDOM (NIL) -9 NIL 540819 NIL) (-256 537220 537713 538288 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-255 536945 537001 537101 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-254 536633 536697 536806 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-253 530404 532304 532332 "ES" 535074 ES (NIL) -9 NIL 536458 NIL) (-252 526919 528451 530243 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-251 526267 526420 526596 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-250 518773 526197 526262 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-249 518462 518525 518634 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-248 512199 515324 516728 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-247 508502 509598 510691 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-246 507331 507681 507986 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-245 506216 506947 506975 "ENTIRER" 506980 ENTIRER (NIL) -9 NIL 507024 NIL) (-244 506105 506139 506211 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-243 502746 504543 504892 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-242 501847 502062 502114 "ELTAGG" 502480 ELTAGG (NIL T T) -9 NIL 502694 NIL) (-241 501629 501703 501842 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-240 501375 501410 501464 "ELTAB" 501548 ELTAB (NIL T T) -9 NIL 501600 NIL) (-239 500626 500796 500995 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-238 500350 500424 500452 "ELEMFUN" 500557 ELEMFUN (NIL) -9 NIL NIL NIL) (-237 500250 500277 500345 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-236 495567 498257 498298 "ELAGG" 499231 ELAGG (NIL T) -9 NIL 499692 NIL) (-235 494365 494903 495562 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-234 493783 493950 494106 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-233 492696 493015 493294 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-232 486089 488087 488914 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-231 480068 482064 482874 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-230 477882 478288 478759 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-229 468882 470795 472336 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-228 467995 468496 468645 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-227 466693 467367 467407 "DVARCAT" 467690 DVARCAT (NIL T) -9 NIL 467830 NIL) (-226 466112 466376 466688 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-225 458179 465980 466107 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-224 456517 457308 457349 "DSEXT" 457712 DSEXT (NIL T) -9 NIL 458006 NIL) (-223 455322 455846 456512 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-222 455046 455111 455209 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-221 451197 452413 453544 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-220 446843 448198 449262 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-219 445518 445879 446265 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-218 445204 445263 445381 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-217 444179 444477 444767 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-216 443764 443839 443989 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-215 436177 438289 440404 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-214 431694 432713 433792 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-213 428242 430303 430344 "DQAGG" 430973 DQAGG (NIL T) -9 NIL 431246 NIL) (-212 414766 422407 422489 "DPOLCAT" 424326 DPOLCAT (NIL T T T T) -9 NIL 424869 NIL) (-211 411174 412822 414761 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-210 404223 411072 411169 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-209 397181 404052 404218 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-208 396774 397034 397123 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-207 396188 396636 396716 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-206 395474 395799 395950 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-205 388613 395210 395361 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-204 386362 387679 387719 "DMEXT" 387724 DMEXT (NIL T) -9 NIL 387899 NIL) (-203 386018 386080 386224 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-202 379610 385503 385693 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-201 376818 378421 378462 "DLAGG" 379003 DLAGG (NIL T) -9 NIL 379235 NIL) (-200 375169 376040 376068 "DIVRING" 376160 DIVRING (NIL) -9 NIL 376243 NIL) (-199 374620 374864 375164 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-198 373048 373465 373871 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-197 372085 372306 372571 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-196 365603 372017 372080 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-195 353923 360345 360398 "DIRPCAT" 360654 DIRPCAT (NIL NIL T) -9 NIL 361529 NIL) (-194 351929 352699 353586 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-193 351376 351542 351728 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-192 348699 350235 350276 "DIOPS" 350696 DIOPS (NIL T) -9 NIL 350924 NIL) (-191 348359 348503 348694 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-190 347366 348112 348140 "DIOID" 348145 DIOID (NIL) -9 NIL 348167 NIL) (-189 346194 347023 347051 "DIFRING" 347056 DIFRING (NIL) -9 NIL 347077 NIL) (-188 345830 345928 345956 "DIFFSPC" 346075 DIFFSPC (NIL) -9 NIL 346150 NIL) (-187 345571 345673 345825 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-186 344474 345099 345139 "DIFFMOD" 345144 DIFFMOD (NIL T) -9 NIL 345241 NIL) (-185 344158 344215 344256 "DIFFDOM" 344377 DIFFDOM (NIL T) -9 NIL 344445 NIL) (-184 344039 344069 344153 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-183 341712 343233 343273 "DIFEXT" 343278 DIFEXT (NIL T) -9 NIL 343430 NIL) (-182 339640 341176 341217 "DIAGG" 341222 DIAGG (NIL T) -9 NIL 341242 NIL) (-181 339196 339386 339635 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-180 334380 338386 338663 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-179 330838 331891 332901 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-178 325388 329992 330319 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-177 323954 324246 324621 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-176 321236 322488 322856 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-175 318961 321067 321156 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-174 318344 318489 318671 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-173 315662 316386 317186 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-172 313771 314229 314791 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-171 313154 313487 313601 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-170 306354 312879 313027 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-169 304274 304784 305288 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-168 303913 303962 304113 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-167 303172 303734 303825 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-166 301196 301638 301998 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-165 300488 300777 300923 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-164 299939 300085 300237 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-163 297301 298094 298821 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-162 296740 296886 297057 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-161 294812 295123 295490 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-160 294369 294624 294725 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-159 293570 293953 293981 "CTORCAT" 294162 CTORCAT (NIL) -9 NIL 294274 NIL) (-158 293273 293407 293565 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-157 292766 293023 293131 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-156 292182 292613 292686 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-155 291641 291758 291911 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-154 288035 288791 289546 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-153 287526 287829 287920 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-152 286745 286954 287182 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-151 286249 286354 286558 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-150 286002 286036 286142 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-149 282941 283703 284421 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-148 282460 282602 282741 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-147 278353 280923 281415 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-146 278227 278254 278282 "CONDUIT" 278319 CONDUIT (NIL) -9 NIL NIL NIL) (-145 277106 277837 277865 "COMRING" 277870 COMRING (NIL) -9 NIL 277920 NIL) (-144 276271 276638 276816 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-143 275967 276008 276136 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-142 275660 275723 275830 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-141 264502 275610 275655 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-140 263963 264102 264262 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-139 263716 263757 263855 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-138 245129 257379 257419 "COMPCAT" 258420 COMPCAT (NIL T) -9 NIL 259762 NIL) (-137 237667 241180 244773 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-136 237343 237383 237422 "COMOPC" 237427 COMOPC (NIL T) -9 NIL 237592 NIL) (-135 237030 237148 237261 "COMOP" NIL COMOP (NIL T) -8 NIL NIL NIL) (-134 236789 236823 236925 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-133 236619 236658 236716 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-132 236200 236479 236553 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-131 235777 236018 236105 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-130 234972 235220 235248 "COMBOPC" 235586 COMBOPC (NIL) -9 NIL 235761 NIL) (-129 234036 234288 234530 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-128 230968 231652 232275 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-127 229848 230299 230534 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-126 229339 229642 229733 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-125 229026 229079 229204 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-124 228496 228806 228904 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-123 225016 226086 227166 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-122 223311 224296 224534 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-121 220915 222076 222117 "CLAGG" 222586 CLAGG (NIL T) -9 NIL 222913 NIL) (-120 220585 220717 220910 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-119 220214 220305 220445 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-118 218151 218658 219206 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-117 217112 217843 217871 "CHARZ" 217876 CHARZ (NIL) -9 NIL 217890 NIL) (-116 216906 216952 217030 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-115 215745 216508 216536 "CHARNZ" 216597 CHARNZ (NIL) -9 NIL 216645 NIL) (-114 213223 214320 214843 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-113 212931 213010 213038 "CFCAT" 213149 CFCAT (NIL) -9 NIL NIL NIL) (-112 212274 212403 212585 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-111 208542 211687 211967 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-110 207920 208107 208284 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-109 207448 207867 207915 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-108 206921 207230 207327 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-107 206412 206715 206806 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-106 205661 205821 206042 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-105 201761 203018 203726 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-104 200127 201158 201409 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-103 199708 199987 200061 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-102 199142 199395 199423 "CACHSET" 199555 CACHSET (NIL) -9 NIL 199633 NIL) (-101 198494 198909 198937 "CABMON" 198987 CABMON (NIL) -9 NIL 199043 NIL) (-100 198024 198288 198398 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-99 193641 197699 197856 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-98 192617 193321 193454 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193613) (-97 190087 192388 192492 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-96 187524 189841 189949 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-95 184702 186908 186947 "BTCAT" 187014 BTCAT (NIL T) -9 NIL 187095 NIL) (-94 184453 184551 184697 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-93 179770 183626 183652 "BTAGG" 183763 BTAGG (NIL) -9 NIL 183871 NIL) (-92 179401 179562 179765 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-91 176480 178893 179083 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-90 175750 175902 176080 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-89 172826 174447 174486 "BRAGG" 175115 BRAGG (NIL T) -9 NIL 175375 NIL) (-88 171901 172332 172821 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-87 164435 171406 171587 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-86 162427 164387 164430 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-85 162160 162196 162307 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-84 160399 160832 161280 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-83 156365 157781 158671 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-82 155241 156132 156254 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-81 154827 154984 155010 "BOOLE" 155118 BOOLE (NIL) -9 NIL 155199 NIL) (-80 154620 154701 154822 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-79 153758 154285 154335 "BMODULE" 154340 BMODULE (NIL T T) -9 NIL 154404 NIL) (-78 149643 153615 153684 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-77 149456 149496 149535 "BINOPC" 149540 BINOPC (NIL T) -9 NIL 149585 NIL) (-76 148998 149271 149373 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-75 148519 148663 148801 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-74 141725 148249 148394 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-73 139941 140914 140953 "BGAGG" 141209 BGAGG (NIL T) -9 NIL 141349 NIL) (-72 139810 139848 139936 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-71 138661 138862 139147 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-70 135316 137841 138146 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-69 134901 134994 135020 "BASTYPE" 135191 BASTYPE (NIL) -9 NIL 135287 NIL) (-68 134671 134767 134896 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-67 134186 134274 134424 "BALFACT" NIL 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T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| |#1|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . 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| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|size| ((#3# $) NIL T ELT)) (|sample| #5=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #4#) $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|opposite?| #1#) (|nthFactor| ((|#1| $ #6=(|Integer|)) NIL T ELT)) (|nthCoef| ((#3# $ #6#) NIL T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mapCoef| (($ (|Mapping| #3# #3#) $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|highCommonTerms| (#7=($ $ $) NIL (|has| #3# (|OrderedAbelianMonoid|)) ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ |#1|) NIL T ELT)) (|coefficient| ((#3# |#1| $) NIL T ELT)) (|before?| #1#) (|Zero| #5#) (= #1#) (+ (#7# NIL T ELT) (($ |#1| $) NIL T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #3# $) NIL T ELT) (($ 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T) ((|CommutativeRing|) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|EntireRing|) |has| |#1| (|IntegralDomain|)) ((|FullyRetractableTo| |#1|) . T) ((|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) ((|RetractableTo| (|Fraction| (|Integer|))) |has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) ((|RetractableTo| (|Integer|)) |has| |#1| (|RetractableTo| (|Integer|))) ((|RetractableTo| |#1|) . 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)) +((~= #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)) (|shrinkable| ((#3# #3#) NIL T ELT)) (|setelt| #13=(#14=(|#1| $ #5# |#1|) NIL #6# ELT) ((|#1| $ #15=(|UniversalSegment| #5#) |#1|) NIL #6# ELT)) (|select!| #16=(#17=($ #18=(|Mapping| #3# |#1|) $) NIL T ELT)) (|select| #19=(#17# NIL #20=(|has| $ (|FiniteAggregate| |#1|)) ELT)) (|sample| (#21=($) NIL T CONST)) (|reverse!| (#12# NIL #6# ELT)) (|reverse| #22=(#12# NIL T ELT)) (|removeDuplicates!| (#12# NIL #4# ELT)) (|removeDuplicates| (#12# NIL #23=(AND #20# #4#) ELT)) (|remove!| (#24=($ |#1| $) NIL #4# ELT) #16#) (|remove| (#24# NIL #23# ELT) #19#) (|reduce| ((|#1| #25=(|Mapping| 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(|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)) +((~= #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#)) +((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|lookupFunction| (((|Identifier|) $) 20 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|encodingDirectory| (((|PrimitiveArray| #3=(|NonNegativeInteger|)) $) 18 T ELT)) (|domainTemplate| (((|DomainTemplate|) $) 7 T ELT)) (|coerce| (((|OutputForm|) $) 26 T ELT)) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) 16 T ELT)) (|before?| #1#) (|attributeData| (((|List| (|Pair| (|Syntax|) #3#)) $) 12 T ELT)) (= (#2# 22 T ELT))) +(((|FunctorData|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |domainTemplate| ((|DomainTemplate|) $)) (SIGNATURE |attributeData| ((|List| (|Pair| (|Syntax|) #1=(|NonNegativeInteger|))) $)) (SIGNATURE |encodingDirectory| ((|PrimitiveArray| #1#) $)) (SIGNATURE |categories| ((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $)) (SIGNATURE |lookupFunction| ((|Identifier|) $))))) (T |FunctorData|)) +((|domainTemplate| #1=(*1 *2 *1) (AND (|isDomain| *2 (|DomainTemplate|)) #2=(|isDomain| *1 (|FunctorData|)))) (|attributeData| #1# (AND (|isDomain| *2 (|List| (|Pair| (|Syntax|) #3=(|NonNegativeInteger|)))) #2#)) (|encodingDirectory| #1# (AND (|isDomain| *2 (|PrimitiveArray| #3#)) #2#)) (|categories| #1# (AND (|isDomain| *2 (|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|)))) #2#)) (|lookupFunction| #1# (AND (|isDomain| *2 (|Identifier|)) #2#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=((#3# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|reduce| (#7=($ $) 34 T ELT)) (|principal?| #4#) (|opposite?| #1#) (|latex| (((|String|) $) NIL T ELT)) (|lSpaceBasis| (#8=((|Vector| |#4|) $) 133 T ELT)) (|ideal| ((#9=(|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 32 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (((|Union| |#4| #5#) $) 37 T ELT)) (|finiteBasis| (#8# 125 T ELT)) (|divisor| (($ #9#) 42 T ELT) (($ |#4|) 44 T ELT) (($ |#1| |#1|) 46 T ELT) (($ |#1| |#1| #10=(|Integer|)) 48 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 50 T ELT)) (|decompose| (((|Record| (|:| |id| #9#) (|:| |principalPart| |#4|)) $) 40 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT)) (|before?| #1#) (|Zero| (#6# 15 T CONST)) (= (#2# 21 T ELT)) (- (#7# 28 T ELT) (#11=($ $ $) NIL T ELT)) (+ (#11# 26 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ #10# $) 24 T ELT))) +(((|FiniteDivisor| |#1| |#2| |#3| |#4|) (|Join| (|FiniteDivisorCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |finiteBasis| #1=((|Vector| |#4|) $)) (SIGNATURE |lSpaceBasis| #1#))) (|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |FiniteDivisor|)) +((|finiteBasis| #1=(*1 *2 *1) #2=(AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Vector| *6)) (|isDomain| *1 (|FiniteDivisor| *3 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)))) (|lSpaceBasis| #1# #2#)) +((|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) 33 T ELT))) +(((|FiniteDivisorFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| ((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)))) #1=(|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) #1# (|UnivariatePolynomialCategory| |#5|) (|UnivariatePolynomialCategory| (|Fraction| |#6|)) (|FunctionFieldCategory| |#5| |#6| |#7|)) (T |FiniteDivisorFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *9 *5)) (|isDomain| *4 (|FiniteDivisor| *5 *6 *7 *8)) (|ofCategory| *5 #1=(|Field|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|ofCategory| *8 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *9 #1#) (|ofCategory| *10 (|UnivariatePolynomialCategory| *9)) (|ofCategory| *11 (|UnivariatePolynomialCategory| (|Fraction| *10))) (|isDomain| *2 (|FiniteDivisor| *9 *10 *11 *12)) (|isDomain| *1 (|FiniteDivisorFunctions2| *5 *6 *7 *8 *9 *10 *11 *12)) (|ofCategory| *12 (|FunctionFieldCategory| *9 *10 *11))))) +((|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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reduce| (($ $) 35 T ELT)) (|principal?| (((|Boolean|) $) 34 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) 41 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|generator| (((|Union| |#4| "failed") $) 33 T ELT)) (|divisor| (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) 40 T ELT) (($ |#4|) 39 T ELT) (($ |#1| |#1|) 38 T ELT) (($ |#1| |#1| (|Integer|)) 37 T ELT) (($ |#4| |#2| |#2| |#2| |#1|) 32 T ELT)) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) 36 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 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| *4 (|Fraction| *4) *5 *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *6 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|Field|)) (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *6)))) (|divisor| (*1 *1 *2) (AND (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5)))) (|divisor| (*1 *1 *2 *2) (AND (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5)) (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4)))) (|divisor| (*1 *1 *2 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *2 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *1 (|FiniteDivisorCategory| *2 *4 *5 *6)) (|ofCategory| *6 (|FunctionFieldCategory| *2 *4 *5)))) (|decompose| (*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 (|Record| (|:| |id| (|FractionalIdeal| *4 (|Fraction| *4) *5 *6)) (|:| |principalPart| *6))))) (|reduce| (*1 *1 *1) (AND (|ofCategory| *1 (|FiniteDivisorCategory| *2 *3 *4 *5)) (|ofCategory| *2 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *5 (|FunctionFieldCategory| *2 *3 *4)))) (|principal?| (*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 (|Boolean|)))) (|generator| (*1 *2 *1) (|partial| AND (|ofCategory| *1 (|FiniteDivisorCategory| *3 *4 *5 *2)) (|ofCategory| *3 (|Field|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *2 (|FunctionFieldCategory| *3 *4 *5)))) (|divisor| (*1 *1 *2 *3 *3 *3 *4) (AND (|ofCategory| *4 (|Field|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|ofCategory| *1 (|FiniteDivisorCategory| *4 *3 *5 *2)) (|ofCategory| *2 (|FunctionFieldCategory| *4 *3 *5))))) +(|Join| (|AbelianGroup|) (CATEGORY |domain| (SIGNATURE |ideal| ((|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|) $)) (SIGNATURE |divisor| ($ (|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|))) (SIGNATURE |divisor| ($ |t#4|)) (SIGNATURE |divisor| ($ |t#1| |t#1|)) (SIGNATURE |divisor| ($ |t#1| |t#1| (|Integer|))) (SIGNATURE |decompose| ((|Record| (|:| |id| (|FractionalIdeal| |t#2| (|Fraction| |t#2|) |t#3| |t#4|)) (|:| |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) ((|Join|) . 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))) +(((|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)) +((~= #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=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T 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#48#) NIL T ELT))) +(((|FiniteField| |#1| |#2|) (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) #1=(|PositiveInteger|) #1#) (T |FiniteField|)) +NIL +((|yCoordinates| (((|Record| (|:| |num| #1=(|Vector| |#3|)) #2=(|:| |den| |#3|)) $) 39 T ELT)) (|represents| (($ #3=(|Vector| #4=(|Fraction| |#3|)) #5=(|Vector| $)) NIL T ELT) (($ #3#) NIL T ELT) (($ #1# |#3|) 172 T ELT)) (|reduceBasisAtInfinity| (#6=(#5# #5#) 156 T ELT)) (|rationalPoints| (((|List| (|List| |#2|))) 126 T ELT)) (|rationalPoint?| ((#7=(|Boolean|) |#2| |#2|) 76 T ELT)) (|primitivePart| (#8=($ $) 148 T ELT)) (|numberOfComponents| (#9=(#10=(|NonNegativeInteger|)) 171 T ELT)) (|normalizeAtInfinity| (#6# 219 T ELT)) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) #11=(|Symbol|)) 115 T ELT)) (|integralAtInfinity?| (#12=(#7# $) 168 T ELT)) (|integral?| (#12# 27 T ELT) ((#7# $ |#2|) 31 T ELT) ((#7# $ |#3|) 223 T ELT)) (|hyperelliptic| (#13=((|Union| |#3| "failed")) 52 T ELT)) (|genus| (#9# 183 T ELT)) (|elt| ((|#2| $ |#2| 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(SIGNATURE |differentiate| (|#1| |#1| #14=(|Mapping| #15=(|Fraction| |#3|) #15#) #2#)) (SIGNATURE |differentiate| (|#1| |#1| #14#)) (SIGNATURE |represents| (|#1| #16=(|Vector| #15#))) (SIGNATURE |represents| (|#1| #16# #11#))) (|FunctionFieldCategory| |#2| |#3| |#4|) (|UniqueFactorizationDomain|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| #15#)) (T |FunctionFieldCategory&|)) +((|numberOfComponents| #1=(*1 *2) #2=(AND #3=(|ofCategory| *4 #4=(|UniqueFactorizationDomain|)) #5=(|ofCategory| *5 #6=(|UnivariatePolynomialCategory| *4)) #7=(|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|NonNegativeInteger|)) #8=(|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *5 *6)) #9=(|ofCategory| *3 (|FunctionFieldCategory| *4 *5 *6)))) (|genus| #1# #2#) (|absolutelyIrreducible?| #1# (AND #3# #5# #7# #10=(|isDomain| *2 (|Boolean|)) #8# #9#)) (|rationalPoint?| (*1 *2 *3 *3) (AND (|ofCategory| *3 #4#) (|ofCategory| *5 (|UnivariatePolynomialCategory| *3)) #7# #10# (|isDomain| *1 (|FunctionFieldCategory&| *4 *3 *5 *6)) (|ofCategory| *4 (|FunctionFieldCategory| *3 *5 *6)))) (|elliptic| #1# #11=(|partial| AND #3# (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 #6#) (|isDomain| *1 (|FunctionFieldCategory&| *3 *4 *2 *5)) (|ofCategory| *3 (|FunctionFieldCategory| *4 *2 *5)))) (|hyperelliptic| #1# #11#) (|nonSingularModel| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *5 #4#) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *2 (|List| (|Polynomial| *5))) (|isDomain| *1 (|FunctionFieldCategory&| *4 *5 *6 *7)) (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7)))) (|rationalPoints| #1# (AND #3# #5# #7# (|isDomain| *2 (|List| (|List| *4))) #8# #9#))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) 225 T 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| $)) 61 T ELT) (((|Matrix| (|Fraction| |#2|))) 77 T ELT)) (|trace| (((|Fraction| |#2|) . #6=($)) 67 T ELT)) (|tableForDiscreteLogarithm| (((|Table| #7=(|PositiveInteger|) #8=(|NonNegativeInteger|)) #9=(|Integer|)) 167 (|has| (|Fraction| |#2|) . #10=((|FiniteFieldCategory|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 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#) 63 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)) 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(|has| (|Fraction| |#2|) . #12#) ELT)) (|ramifiedAtInfinity?| (((|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|) $) 44 T ELT)) (|numberOfComponents| (((|NonNegativeInteger|)) 249 T ELT)) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) 231 T ELT)) (|norm| (((|Fraction| |#2|) . #6#) 66 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# $) 132 (|has| (|Fraction| |#2|) . #3#) ELT)) (|minimalPolynomial| ((|#3| . #33=($)) 59 (|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)) (|expressIdealMember| (((|Maybe| #28#) #28# $) 124 (|has| (|Fraction| |#2|) . #3#) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 126 (|has| (|Fraction| |#2|) . #3#) ELT)) (|elt| ((|#1| $ |#1| |#1|) 216 T ELT)) (|elliptic| (((|Union| |#2| "failed")) 215 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 127 (|has| (|Fraction| |#2|) . #3#) ELT)) (|discriminant| (((|Fraction| |#2|) #5#) 62 T ELT) (((|Fraction| |#2|)) 76 T ELT)) (|discreteLog| ((#8# $) 171 (|has| (|Fraction| |#2|) . #10#) ELT) (((|Union| #30# "failed") $ $) 159 (|has| (|Fraction| |#2|) . #10#) ELT)) (|differentiate| (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 145 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) . #42=((|NonNegativeInteger|))) 144 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|Mapping| |#2| |#2|)) 218 T ELT) (($ $ (|List| #43=(|Symbol|)) . #44=((|List| #45=(|NonNegativeInteger|)))) 150 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46=((|PartialDifferentialSpace| #43#)))) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47=((|PartialDifferentialRing| (|Symbol|))))) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43# . #48=(#45#)) 149 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ (|List| #43#)) 148 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43#) 146 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (#49=($ $ (|NonNegativeInteger|)) 156 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #50=((|DifferentialSpace|)))) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #51=((|DifferentialRing|)))) (|and| (|has| (|Fraction| |#2|) . #50#) (|has| (|Fraction| |#2|) . #3#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ . #52=($)) 154 (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#)) (|has| (|Fraction| |#2|) . #10#)) 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#) 65 T ELT) (((|Matrix| (|Fraction| |#2|)) #5# #5#) 64 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|)) 41 T ELT) (($ (|Fraction| |#2|)) 52 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| $) $) 58 (|has| (|Fraction| |#2|) (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| ((|#3| . #33#) 60 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 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|) $ $) 33 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| (($) 45 T CONST)) (D (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|))) 143 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|Mapping| (|Fraction| |#2|) (|Fraction| |#2|)) . #42#) 142 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ (|List| #43#) . #44#) 153 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43# . #48#) 152 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ (|List| #43#)) 151 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (($ $ #43#) 147 (OR (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #46#)) (|and| (|has| (|Fraction| |#2|) . #3#) (|has| (|Fraction| |#2|) . #47#)) (|and| (|has| (|Fraction| |#2|) . #46#) (|has| (|Fraction| |#2|) . #3#))) ELT) (#49# 157 (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#)) (|has| (|Fraction| |#2|) . #10#)) ELT) (($ . #52#) 155 (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#)) (|has| (|Fraction| |#2|) . #10#)) ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 141 (|has| (|Fraction| |#2|) . #3#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #56#) 138 (|has| (|Fraction| |#2|) . #3#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #57=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ (|Fraction| |#2|)) 54 T ELT) (($ (|Fraction| |#2|) . #57#) 53 T ELT) (($ #55# . #57#) 140 (|has| (|Fraction| |#2|) . #3#) ELT) (($ $ #55#) 139 (|has| (|Fraction| |#2|) . #3#) 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| (|Fraction| *4))))) (|integralMatrixAtInfinity| (*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))))) (|inverseIntegralMatrixAtInfinity| (*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))))) (|yCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4))))) (|represents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|integralCoordinates| (*1 *2 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|isDomain| *2 (|Record| (|:| |num| (|Vector| *4)) (|:| |den| *4))))) (|integralRepresents| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Vector| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|integralDerivationMatrix| (*1 *2 *3) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Record| (|:| |num| (|Matrix| *5)) (|:| |den| *5))))) (|integral?| (*1 *2 *1 *3) (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 *3) (AND (|ofCategory| *1 (|FunctionFieldCategory| *4 *3 *5)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *3))) (|isDomain| *2 (|Boolean|)))) (|differentiate| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Mapping| *4 *4)) (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))))) (|primitivePart| (*1 *1 *1) (AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4)) (|ofCategory| *2 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|elt| (*1 *2 *1 *2 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *2 *3 *4)) (|ofCategory| *2 (|UniqueFactorizationDomain|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *3))))) (|elliptic| (*1 *2) (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|hyperelliptic| (*1 *2) (|partial| AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *2 *4)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *2))) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|algSplitSimple| (*1 *2 *1 *3) (AND (|isDomain| *3 (|Mapping| *5 *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|isDomain| *2 (|Record| (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) (|:| |gd| *5))) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)))) (|nonSingularModel| (*1 *2 *3) (AND (|isDomain| *3 (|Symbol|)) (|ofCategory| *1 (|FunctionFieldCategory| *4 *5 *6)) (|ofCategory| *4 (|UniqueFactorizationDomain|)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofCategory| *4 (|Field|)) (|isDomain| *2 (|List| (|Polynomial| *4))))) (|rationalPoints| (*1 *2) (AND (|ofCategory| *1 (|FunctionFieldCategory| *3 *4 *5)) (|ofCategory| *3 (|UniqueFactorizationDomain|)) (|ofCategory| *4 (|UnivariatePolynomialCategory| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| (|Fraction| *4))) (|ofCategory| *3 (|Finite|)) (|isDomain| *2 (|List| (|List| *3)))))) +(|Join| (|MonogenicAlgebra| (|Fraction| |t#2|) |t#3|) (CATEGORY |domain| (SIGNATURE |numberOfComponents| ((|NonNegativeInteger|))) (SIGNATURE |genus| ((|NonNegativeInteger|))) (SIGNATURE |absolutelyIrreducible?| ((|Boolean|))) (SIGNATURE |rationalPoint?| ((|Boolean|) |t#1| |t#1|)) (SIGNATURE |branchPointAtInfinity?| ((|Boolean|))) (SIGNATURE |branchPoint?| ((|Boolean|) |t#1|)) (SIGNATURE |branchPoint?| ((|Boolean|) |t#2|)) (SIGNATURE |singularAtInfinity?| ((|Boolean|))) (SIGNATURE |singular?| ((|Boolean|) |t#1|)) (SIGNATURE |singular?| ((|Boolean|) |t#2|)) (SIGNATURE |ramifiedAtInfinity?| ((|Boolean|))) (SIGNATURE |ramified?| ((|Boolean|) |t#1|)) (SIGNATURE |ramified?| ((|Boolean|) |t#2|)) (SIGNATURE |integralBasis| ((|Vector| $))) (SIGNATURE |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|)) (|Mapping| |t#2| |t#2|))) (SIGNATURE |integral?| ((|Boolean|) $ |t#1|)) (SIGNATURE |integral?| ((|Boolean|) $ |t#2|)) (SIGNATURE |differentiate| ($ $ (|Mapping| |t#2| |t#2|))) (SIGNATURE |primitivePart| ($ $)) (SIGNATURE |elt| (|t#1| $ |t#1| |t#1|)) (SIGNATURE |elliptic| ((|Union| |t#2| "failed"))) (SIGNATURE |hyperelliptic| ((|Union| |t#2| "failed"))) (SIGNATURE |algSplitSimple| ((|Record| (|:| |num| $) (|:| |den| |t#2|) (|:| |derivden| |t#2|) (|:| |gd| |t#2|)) $ (|Mapping| |t#2| |t#2|))) (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| (|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|)))) +((|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)))))) +((~= #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=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# #18#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #22=(|Vector| #10#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #8#) NIL #29=(OR (|has| #10# (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #9# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| #10#) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| ((#40=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #40#)) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #41=(|:| |coef1| $) #42=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #41# #42#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#43=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#43# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #44=(#28# NIL #14# ELT) #45=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) (((|Matrix| #10#) #46=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #46# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #47=(|Fraction| #15#)) NIL T ELT) (($ #10#) NIL T ELT)) (|charthRoot| #45# (#34# NIL #29# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#46#) NIL T ELT) ((#46# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #45# #44#) (D #44# #45#) (= #1#) (/ #23# #48=(($ $ #10#) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #15# . #49=($)) NIL T ELT) #23# (($ $ #47#) NIL T ELT) (($ #47# . #49#) NIL T ELT) #48# (($ #10# . #49#) NIL T ELT))) +(((|FiniteFieldCyclicGroup| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| (|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) #1=(|PositiveInteger|) #1#) (T |FiniteFieldCyclicGroup|)) +((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroup| *3 *4)) (|ofType| *3 #1=(|PositiveInteger|)) (|ofType| *4 #1#)))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 58 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|transcendent?| #7#) (|transcendenceDegree| (#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=(#11=(|#1| $) NIL T ELT) #12=(#13=($ $ #14=(|PositiveInteger|)) NIL #15=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #14# #9#) #16=(|Integer|)) 56 #15# ELT)) (|subtractIfCan| #17=((#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #20=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#8# NIL #15# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #19#) $) 139 T ELT)) (|retract| (#11# 111 T ELT)) (|represents| (($ #22=(|Vector| |#1|)) 128 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 119 #15# ELT)) (|rem| #23=(#24=($ $ $) NIL T ELT)) (|recip| ((#18# $) NIL T ELT)) (|random| (#21# 122 #15# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| (#21# 155 #15# ELT)) (|primitive?| (#4# 65 #15# ELT)) (|primeFrobenius| (#27=($ $ #9#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #15#) ELT) (#6# NIL #28# ELT)) (|prime?| #7#) (|order| (#29=(#14# $) 60 #15# ELT) (#30=(#31=(|OnePointCompletion| #14#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| (#4# 62 T ELT)) (|normalElement| (#21# 157 #15# ELT)) (|normal?| (#4# NIL #15# ELT)) (|norm| #10# #12#) (|nextItem| (#32=((|Maybe| $) $) NIL #15# ELT)) (|multiEuclidean| (((|Union| #25# #19#) #25# $) NIL T ELT)) (|minimalPolynomial| (#33=(#34=(|SparseUnivariatePolynomial| |#1|) $) 115 T ELT) ((#35=(|SparseUnivariatePolynomial| $) $ #14#) NIL #15# ELT)) (|lookup| (#29# 165 #15# ELT)) (|linearAssociatedOrder| #36=(#33# NIL #15# ELT)) (|linearAssociatedLog| #36# (((|Union| #34# #19#) $ $) NIL #15# ELT)) (|linearAssociatedExp| (($ $ #34#) NIL #15# ELT)) (|lcm| #23# #37=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 172 T ELT)) (|init| (#21# NIL #15# CONST)) (|index| (($ #14#) 94 #15# ELT)) (|inGroundField?| (#4# 142 T ELT)) (|hash| ((#38=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #38#)) 57 T ELT)) (|generator| (#21# 153 #15# ELT)) (|gcdPolynomial| ((#35# #35# #35#) NIL T ELT)) (|gcd| #23# #37#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) 117 #15# ELT)) (|factor| #20#) (|extensionDegree| ((#31#) 88 T ELT) ((#14#) 89 T ELT)) (|extendedEuclidean| (((|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #39# #40#) #19#) $ $ $) NIL T ELT)) (|exquo| #17#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#41=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#41# 156 #15# ELT) (((|Union| #9# #19#) $ $) 149 #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #42=(#27# NIL #15# ELT) #43=(#6# NIL #15# ELT)) (|degree| (#30# NIL T ELT) (#29# NIL T ELT)) 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(($ #45# $) NIL T ELT) (#46# NIL T ELT) (($ |#1| $) 169 T ELT))) +(((|FiniteFieldCyclicGroupExtensionByPolynomial| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) (|FiniteFieldCategory|) (|SparseUnivariatePolynomial| |#1|)) (T |FiniteFieldCyclicGroupExtensionByPolynomial|)) +((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroupExtensionByPolynomial| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|SparseUnivariatePolynomial| *3))))) +((~= #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=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| #23=(#20# NIL #13# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #17#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #22# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#20# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| ((#39=(|SingleInteger|) $) NIL T ELT)) (|getZechTable| (((|PrimitiveArray| #39#)) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #22# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #18#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #13# ELT) (((|Union| #8# #17#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #43=(#27# NIL #13# ELT) #44=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| |#1|) #45=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #45# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #46=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #44# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#45#) NIL T ELT) ((#45# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| #44# #43#) (D #43# #44#) (= #1#) (/ #22# #47=(($ $ |#1|) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #48=($)) NIL T ELT) #22# (($ $ #46#) NIL T ELT) (($ #46# . #48#) NIL T ELT) #47# (($ |#1| . #48#) NIL T ELT))) +(((|FiniteFieldCyclicGroupExtension| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getZechTable| ((|PrimitiveArray| (|SingleInteger|)))))) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldCyclicGroupExtension|)) +((|getZechTable| (*1 *2) (AND (|isDomain| *2 (|PrimitiveArray| (|SingleInteger|))) (|isDomain| *1 (|FiniteFieldCyclicGroupExtension| *3 *4)) (|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|PositiveInteger|))))) +((|sizeMultiplication| (((|NonNegativeInteger|) #1=(|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #2=(|SingleInteger|)))))) 61 T ELT)) (|createZechTable| (((|PrimitiveArray| #2#) #3=(|SparseUnivariatePolynomial| |#1|)) 112 T ELT)) (|createMultiplicationTable| ((#1# #3#) 103 T ELT)) (|createMultiplicationMatrix| (((|Matrix| |#1|) #1#) 113 T ELT)) (|createLowComplexityTable| (((|Union| #1# "failed") #4=(|PositiveInteger|)) 13 T ELT)) (|createLowComplexityNormalBasis| (((|Union| #3# #1#) #4#) 18 T ELT))) +(((|FiniteFieldFunctions| |#1|) (CATEGORY |package| (SIGNATURE |createZechTable| ((|PrimitiveArray| #1=(|SingleInteger|)) #2=(|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |createMultiplicationTable| (#3=(|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #1#)))) #2#)) (SIGNATURE |createMultiplicationMatrix| ((|Matrix| |#1|) #3#)) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|) #3#)) (SIGNATURE |createLowComplexityTable| ((|Union| #3# "failed") #4=(|PositiveInteger|))) (SIGNATURE |createLowComplexityNormalBasis| ((|Union| #2# #3#) #4#))) (|FiniteFieldCategory|)) (T |FiniteFieldFunctions|)) +((|createLowComplexityNormalBasis| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|Union| #3=(|SparseUnivariatePolynomial| *4) #4=(|Vector| (|List| (|Record| (|:| |value| *4) (|:| |index| #5=(|SingleInteger|))))))) #6=(|isDomain| *1 (|FiniteFieldFunctions| *4)) #7=(|ofCategory| *4 (|FiniteFieldCategory|)))) (|createLowComplexityTable| #1# (|partial| AND #2# #8=(|isDomain| *2 #4#) #6# #7#)) (|sizeMultiplication| #1# (AND #9=(|isDomain| *3 #4#) #7# (|isDomain| *2 (|NonNegativeInteger|)) #6#)) (|createMultiplicationMatrix| #1# (AND #9# #7# (|isDomain| *2 (|Matrix| *4)) #6#)) (|createMultiplicationTable| #1# (AND #10=(|isDomain| *3 #3#) #7# #8# #6#)) (|createZechTable| #1# (AND #10# #7# (|isDomain| *2 (|PrimitiveArray| #5#)) #6#))) +((|coerce| ((|#1| |#3|) 104 T ELT) ((|#3| |#1|) 87 T ELT))) +(((|FiniteFieldHomomorphisms| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |coerce| (|#3| |#1|)) (SIGNATURE |coerce| (|#1| |#3|))) #1=(|FiniteAlgebraicExtensionField| |#2|) (|FiniteFieldCategory|) #1#) (T |FiniteFieldHomomorphisms|)) +((|coerce| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 (|FiniteFieldCategory|)) #3=(|ofCategory| *2 #4=(|FiniteAlgebraicExtensionField| *4)) (|isDomain| *1 (|FiniteFieldHomomorphisms| *2 *4 *3)) #5=(|ofCategory| *3 #4#))) (|coerce| #1# (AND #2# #3# (|isDomain| *1 (|FiniteFieldHomomorphisms| *3 *4 *2)) #5#))) +((|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| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) 113 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|size| (((|NonNegativeInteger|)) 123 T ELT)) (|sample| (#5=($) 23 T CONST)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 107 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|random| (($) 126 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primitiveElement| (($) 111 T ELT)) (|primitive?| (((|Boolean|) $) 110 T ELT)) (|primeFrobenius| (($ $) 97 T ELT) (($ $ #8=(|NonNegativeInteger|)) 96 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 99 T ELT) (((|PositiveInteger|) $) 108 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nextItem| (((|Maybe| $) $) 122 T ELT)) (|multiEuclidean| (((|Union| #9=(|List| $) #10="failed") #9# $) 68 T ELT)) (|lookup| ((#11=(|PositiveInteger|) $) 125 T ELT)) (|lcm| (#12=($ $ $) 60 T ELT) (#13=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|init| (($) 121 T CONST)) (|index| (($ #11#) 124 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#14=(|SparseUnivariatePolynomial| $) #14# #14#) 58 T ELT)) (|gcd| (#12# 62 T ELT) (#13# 61 T ELT)) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) 114 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #15=(|:| |coef1| $) #16=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #15# #16#) #10#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| #8# "failed") $ $) 98 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|)) 41 T ELT) (($ $) 57 T ELT) (($ #19=(|Fraction| #20=(|Integer|))) 84 T ELT)) (|charthRoot| (((|Maybe| $) $) 100 T ELT) (($ $) 116 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ . #17#) 119 T ELT) (#18# 117 T ELT)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #20#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #21=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #19#) 86 T ELT) (($ #19# . #21#) 85 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 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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) ((|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#) . 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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#)) +((~= #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=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=((#11=(|PrimeField| |#1|) $) NIL T ELT) #12=(#13=($ $ #14=(|PositiveInteger|)) NIL #15=(|has| #11# (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #14# #9#) #16=(|Integer|)) NIL #15# ELT)) (|subtractIfCan| #17=((#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #20=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| #7#) (|sizeLess?| #1#) (|size| (#8# NIL #15# ELT)) (|sample| #21=(#22=($) NIL T CONST)) (|retractIfCan| (((|Union| #11# #19#) $) NIL T ELT)) (|retract| #10#) (|represents| (($ #23=(|Vector| #11#)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" 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NIL #15# ELT)) (|linearAssociatedExp| (($ $ #37#) NIL #15# ELT)) (|lcm| #24# #40=(($ #26#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#22# NIL #15# CONST)) (|index| (($ #14#) NIL #15# ELT)) (|inGroundField?| #3#) (|hash| ((#41=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| #11#) (|:| |index| #41#))))) NIL T ELT)) (|getMultiplicationMatrix| ((#42=(|Matrix| #11#)) NIL T ELT)) (|generator| #25#) (|gcdPolynomial| ((#38# #38# #38#) NIL T ELT)) (|gcd| #24# #40#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #16#) (|:| |exponent| #16#)))) NIL #15# ELT)) (|factor| #20#) (|extensionDegree| ((#34#) NIL T ELT) ((#14#) NIL T ELT)) (|extendedEuclidean| (((|Record| #43=(|:| |coef1| $) #44=(|:| |coef2| $) #27#) $ $) NIL T ELT) (((|Union| (|Record| #43# #44#) #19#) $ $ $) NIL T ELT)) (|exquo| #17#) (|expressIdealMember| (((|Maybe| #26#) #26# $) NIL T ELT)) (|euclideanSize| (#45=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#45# NIL #15# ELT) (((|Union| #9# #19#) $ $) NIL #30# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #46=(#29# NIL #15# ELT) #47=(#6# NIL #15# ELT)) (|degree| (#33# NIL T ELT) (#32# NIL T ELT)) (|definingPolynomial| ((#37#) NIL T ELT)) (|createPrimitiveElement| #25#) (|createNormalElement| #25#) (|coordinates| ((#23# $) NIL T ELT) ((#42# #48=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #48# #19#) (|Matrix| $)) NIL #15# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #16#) NIL T ELT) #5# (($ #49=(|Fraction| #16#)) NIL T ELT) (($ #11#) NIL T ELT)) (|charthRoot| #47# (#35# NIL #30# ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#48#) NIL T ELT) ((#48# #14#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #21#) (|One| #21#) (|Frobenius| #47# #46#) (D #46# #47#) (= #1#) (/ #24# #50=(($ $ #11#) NIL T ELT)) (- #5# #24#) (+ #24#) (** (#13# NIL T ELT) (#29# NIL T ELT) (($ $ #16#) NIL T ELT)) (* (($ #14# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #16# . #51=($)) NIL T ELT) #24# (($ $ #49#) NIL T ELT) (($ #49# . #51#) NIL T ELT) #50# (($ #11# . #51#) NIL T ELT))) +(((|FiniteFieldNormalBasis| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| #1=(|PrimeField| |#1|)) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| #1#) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| #1#))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) #2=(|PositiveInteger|) #2#) (T |FiniteFieldNormalBasis|)) +((|getMultiplicationTable| #1=(*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| #2=(|PrimeField| *3)) (|:| |index| (|SingleInteger|)))))) #3=(|isDomain| *1 (|FiniteFieldNormalBasis| *3 *4)) #4=(|ofType| *3 #5=(|PositiveInteger|)) #6=(|ofType| *4 #5#))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| #2#)) #3# #4# #6#)) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4# #6#))) +((~= (#1=(#2=(|Boolean|) $ $) 72 T ELT)) (|zero?| (#3=(#2# $) 87 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #4=(#5=($ $) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|transcendent?| #6#) (|transcendenceDegree| (#7=(#8=(|NonNegativeInteger|)) NIL T ELT)) (|trace| (#9=(|#1| $) 105 T ELT) (#10=($ $ #11=(|PositiveInteger|)) 103 #12=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #11# #8#) #13=(|Integer|)) 168 #12# ELT)) (|subtractIfCan| #14=((#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|squareFreePart| #4#) (|squareFree| #17=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| (#7# 102 T ELT)) (|sizeLess?| #18=(#1# NIL T ELT)) (|size| (#7# 185 #12# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #16#) $) 126 T ELT)) (|retract| (#9# 104 T ELT)) (|represents| (($ #20=(|Vector| |#1|)) 70 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 211 #12# ELT)) (|rem| #21=(#22=($ $ $) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|random| (#19# 180 #12# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #23=(|List| $)) #24=(|:| |generator| $)) #23#) NIL T ELT)) (|primitiveElement| (#19# 169 #12# ELT)) (|primitive?| (#3# NIL #12# ELT)) (|primeFrobenius| (#25=($ $ #8#) NIL #26=(OR (|has| |#1| (|CharacteristicNonZero|)) #12#) ELT) (#5# NIL #26# ELT)) (|prime?| #6#) (|order| (#27=(#11# $) NIL #12# ELT) (#28=(#29=(|OnePointCompletion| #11#) $) NIL #26# ELT)) (|opposite?| #18#) (|one?| #6#) (|normalElement| (#19# 112 #12# ELT)) (|normal?| (#3# 198 #12# ELT)) (|norm| (#9# 107 T ELT) (#10# 106 #12# ELT)) (|nextItem| (#30=((|Maybe| $) $) NIL #12# ELT)) (|multiEuclidean| (((|Union| #23# #16#) #23# $) NIL T ELT)) (|minimalPolynomial| (#31=(#32=(|SparseUnivariatePolynomial| |#1|) $) 212 T ELT) ((#33=(|SparseUnivariatePolynomial| $) $ #11#) NIL #12# ELT)) (|lookup| (#27# 146 #12# ELT)) (|linearAssociatedOrder| (#31# 86 #12# ELT)) (|linearAssociatedLog| (#31# 83 #12# ELT) (((|Union| #32# #16#) $ $) 95 #12# ELT)) (|linearAssociatedExp| (($ $ #32#) 82 #12# ELT)) (|lcm| #21# #34=(($ #23#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#5# 216 T ELT)) (|init| (#19# NIL #12# CONST)) (|index| (($ #11#) 148 #12# ELT)) (|inGroundField?| (#3# 122 T ELT)) (|hash| ((#35=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #35#))))) 96 T ELT)) (|getMultiplicationMatrix| ((#36=(|Matrix| |#1|)) 100 T ELT)) (|generator| (#19# 109 #12# ELT)) (|gcdPolynomial| ((#33# #33# #33#) NIL T ELT)) (|gcd| #21# #34#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #13#) (|:| |exponent| #13#)))) 171 #12# ELT)) (|factor| #17#) (|extensionDegree| ((#29#) NIL T ELT) ((#11#) 172 T ELT)) (|extendedEuclidean| (((|Record| #37=(|:| |coef1| $) #38=(|:| |coef2| $) #24#) $ $) NIL T ELT) (((|Union| (|Record| #37# #38#) #16#) $ $ $) NIL T ELT)) (|exquo| #14#) (|expressIdealMember| (((|Maybe| #23#) #23# $) NIL T ELT)) (|euclideanSize| (#39=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#39# NIL #12# ELT) (((|Union| #8# #16#) $ $) NIL #26# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #40=(#25# NIL #12# ELT) #41=(#5# NIL #12# ELT)) (|degree| (#28# NIL T ELT) (#27# 74 T ELT)) (|definingPolynomial| ((#32#) 173 T ELT)) (|createPrimitiveElement| (#19# 145 #12# ELT)) (|createNormalElement| (#19# NIL #12# ELT)) (|coordinates| ((#20# $) 120 T ELT) ((#36# #42=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #42# #16#) (|Matrix| $)) NIL #12# ELT)) (|coerce| (((|OutputForm|) $) 138 T ELT) (($ #13#) NIL T ELT) #4# (($ #43=(|Fraction| #13#)) NIL T ELT) (($ |#1|) 69 T ELT)) (|charthRoot| #41# (#30# NIL #26# ELT)) (|characteristic| (#7# 178 T CONST)) (|before?| #18#) (|basis| ((#42#) 195 T ELT) ((#42# #11#) 115 T ELT)) (|associates?| #18#) (|annihilate?| #18#) (|algebraic?| #6#) (|Zero| (#19# 184 T CONST)) (|One| (#19# 159 T CONST)) (|Frobenius| (#5# 121 #12# ELT) (#25# 113 #12# ELT)) (D #40# #41#) (= (#1# 206 T ELT)) (/ (#22# 118 T ELT) (#44=($ $ |#1|) 119 T ELT)) (- (#5# 200 T ELT) (#22# 204 T ELT)) (+ (#22# 202 T ELT)) (** (#10# NIL T ELT) (#25# NIL T ELT) (($ $ #13#) 151 T ELT)) (* (($ #11# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #13# $) 209 T ELT) (#22# 162 T ELT) (($ $ #43#) NIL T ELT) (($ #43# $) NIL T ELT) (#44# NIL T ELT) (($ |#1| $) 117 T ELT))) +(((|FiniteFieldNormalBasisExtensionByPolynomial| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| (#1=(|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) (|FiniteFieldCategory|) (|Union| (|SparseUnivariatePolynomial| |#1|) #1#)) (T |FiniteFieldNormalBasisExtensionByPolynomial|)) +((|getMultiplicationTable| #1=(*1 *2) (AND (|isDomain| *2 #2=(|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))) #3=(|isDomain| *1 (|FiniteFieldNormalBasisExtensionByPolynomial| *3 *4)) #4=(|ofCategory| *3 (|FiniteFieldCategory|)) (|ofType| *4 (|Union| #5=(|SparseUnivariatePolynomial| *3) *2)))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| *3)) #3# #4# #6=(|ofType| *4 (|Union| #5# #2#)))) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #3# #4# #6#))) +((~= #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=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #10=((|#1| $) NIL T ELT) #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #13# #9#) #15=(|Integer|)) NIL #14# ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeMultiplication| #7#) (|sizeLess?| #1#) (|size| (#8# NIL #14# ELT)) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #18#) $) NIL T ELT)) (|retract| #10#) (|represents| (($ #22=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #14# ELT)) (|rem| #23=(($ $ $) NIL T ELT)) (|recip| ((#17# $) NIL T ELT)) (|random| #24=(#21# NIL #14# ELT)) (|quo| #23#) (|principalIdeal| (((|Record| (|:| |coef| #25=(|List| $)) #26=(|:| |generator| $)) #25#) NIL T ELT)) (|primitiveElement| #24#) (|primitive?| #27=(#4# NIL #14# ELT)) (|primeFrobenius| (#28=($ $ #9#) NIL #29=(OR (|has| |#1| (|CharacteristicNonZero|)) #14#) ELT) (#6# NIL #29# ELT)) (|prime?| #3#) (|order| #30=(#31=(#13# $) NIL #14# ELT) (#32=(#33=(|OnePointCompletion| #13#) $) NIL #29# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #24#) (|normal?| #27#) (|norm| #10# #11#) (|nextItem| (#34=((|Maybe| $) $) NIL #14# ELT)) (|multiEuclidean| (((|Union| #25# #18#) #25# $) NIL T ELT)) (|minimalPolynomial| (#35=(#36=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#37=(|SparseUnivariatePolynomial| $) $ #13#) NIL #14# ELT)) (|lookup| #30#) (|linearAssociatedOrder| #38=(#35# NIL #14# ELT)) (|linearAssociatedLog| #38# (((|Union| #36# #18#) $ $) NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| ((#40=(|SingleInteger|) $) NIL T ELT)) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| #40#))))) NIL T ELT)) (|getMultiplicationMatrix| ((#41=(|Matrix| |#1|)) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #42=(|:| |coef1| $) #43=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #42# #43#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#44=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#44# NIL #14# ELT) (((|Union| #9# #18#) $ $) NIL #29# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #45=(#28# NIL #14# ELT) #46=(#6# NIL #14# ELT)) (|degree| (#32# NIL T ELT) (#31# NIL T ELT)) (|definingPolynomial| ((#36#) NIL T ELT)) (|createPrimitiveElement| #24#) (|createNormalElement| #24#) (|coordinates| ((#22# $) NIL T ELT) ((#41# #47=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #47# #18#) (|Matrix| $)) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) #5# (($ #48=(|Fraction| #15#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #46# (#34# NIL #29# ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|basis| ((#47#) NIL T ELT) ((#47# #13#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #20#) (|One| #20#) (|Frobenius| #46# #45#) (D #45# #46#) (= #1#) (/ #23# #49=(($ $ |#1|) NIL T ELT)) (- #5# #23#) (+ #23#) (** (#12# NIL T ELT) (#28# NIL T ELT) (($ $ #15#) NIL T ELT)) (* (($ #13# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #15# . #50=($)) NIL T ELT) #23# (($ $ #48#) NIL T ELT) (($ #48# . #50#) NIL T ELT) #49# (($ |#1| . #50#) NIL T ELT))) +(((|FiniteFieldNormalBasisExtension| |#1| |#2|) (|Join| (|FiniteAlgebraicExtensionField| |#1|) (CATEGORY |package| (SIGNATURE |getMultiplicationTable| ((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))))) (SIGNATURE |getMultiplicationMatrix| ((|Matrix| |#1|))) (SIGNATURE |sizeMultiplication| ((|NonNegativeInteger|))))) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldNormalBasisExtension|)) +((|getMultiplicationTable| #1=(*1 *2) (AND (|isDomain| *2 (|Vector| (|List| (|Record| (|:| |value| *3) (|:| |index| (|SingleInteger|)))))) #2=(|isDomain| *1 (|FiniteFieldNormalBasisExtension| *3 *4)) #3=(|ofCategory| *3 (|FiniteFieldCategory|)) #4=(|ofType| *4 (|PositiveInteger|)))) (|getMultiplicationMatrix| #1# (AND (|isDomain| *2 (|Matrix| *3)) #2# #3# #4#)) (|sizeMultiplication| #1# (AND (|isDomain| *2 (|NonNegativeInteger|)) #2# #3# #4#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #6=(#7=($ $) NIL T ELT)) (|unit?| #4#) (|transcendent?| #4#) (|transcendenceDegree| (#8=(#9=(|NonNegativeInteger|)) NIL T ELT)) (|trace| (#10=(|#1| $) NIL T ELT) (#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #9#) #14=(|Integer|)) 130 #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #6#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#8# 156 #13# ELT)) (|sample| (#19=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) 104 T ELT)) (|retract| (#10# 101 T ELT)) (|represents| (($ #20=(|Vector| |#1|)) 96 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 127 #13# ELT)) (|rem| #21=(#22=($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| (#19# 93 #13# ELT)) (|quo| #21#) (|principalIdeal| (((|Record| (|:| |coef| #23=(|List| $)) #24=(|:| |generator| $)) #23#) NIL T ELT)) (|primitiveElement| (#19# 52 #13# ELT)) (|primitive?| (#5# NIL #13# ELT)) (|primeFrobenius| (#25=($ $ #9#) NIL #26=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#7# NIL #26# ELT)) (|prime?| #4#) (|order| (#27=(#12# $) NIL #13# ELT) (#28=(#29=(|OnePointCompletion| #12#) $) NIL #26# ELT)) (|opposite?| #1#) (|one?| #4#) (|normalElement| (#19# 131 #13# ELT)) (|normal?| (#5# 85 #13# ELT)) (|norm| (#10# 48 T ELT) (#11# 53 #13# ELT)) (|nextItem| (#30=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #23# #17#) #23# $) NIL T ELT)) (|minimalPolynomial| (#31=(#32=(|SparseUnivariatePolynomial| |#1|) $) 76 T ELT) ((#33=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| (#27# 108 #13# ELT)) (|linearAssociatedOrder| #34=(#31# NIL #13# ELT)) (|linearAssociatedLog| #34# (((|Union| #32# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #32#) NIL #13# ELT)) (|lcm| #21# #35=(($ #23#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #6#) (|init| (#19# NIL #13# CONST)) (|index| (($ #12#) 106 #13# ELT)) (|inGroundField?| (#5# 158 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| (#19# 45 #13# ELT)) (|gcdPolynomial| ((#33# #33# #33#) NIL T ELT)) (|gcd| #21# #35#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) 125 #13# ELT)) (|factor| #18#) (|extensionDegree| ((#29#) NIL T ELT) ((#12#) 155 T ELT)) (|extendedEuclidean| (((|Record| #36=(|:| |coef1| $) #37=(|:| |coef2| $) #24#) $ $) NIL T ELT) (((|Union| (|Record| #36# #37#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #23#) #23# $) NIL T ELT)) (|euclideanSize| (#38=(#9# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#38# NIL #13# ELT) (((|Union| #9# #17#) $ $) NIL #26# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #39=(#25# NIL #13# ELT) #40=(#7# NIL #13# ELT)) (|degree| (#28# NIL T ELT) (#27# 68 T ELT)) (|definingPolynomial| ((#32#) 99 T ELT)) (|createPrimitiveElement| (#19# 136 #13# ELT)) (|createNormalElement| (#19# NIL #13# ELT)) (|coordinates| ((#20# $) 64 T ELT) (((|Matrix| |#1|) #41=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #41# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) 154 T ELT) (($ #14#) NIL T ELT) #6# (($ #42=(|Fraction| #14#)) NIL T ELT) (($ |#1|) 98 T ELT)) (|charthRoot| #40# (#30# NIL #26# ELT)) (|characteristic| (#8# 160 T CONST)) (|before?| (#2# 162 T ELT)) (|basis| ((#41#) 120 T ELT) ((#41# #12#) 59 T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #4#) (|Zero| (#19# 122 T CONST)) (|One| (#19# 40 T CONST)) (|Frobenius| (#7# 79 #13# ELT) #39#) (D #39# #40#) (= (#2# 118 T ELT)) (/ (#22# 110 T ELT) (#43=($ $ |#1|) 111 T ELT)) (- (#7# 91 T ELT) (#22# 116 T ELT)) (+ (#22# 114 T ELT)) (** (#11# NIL T ELT) (#25# 54 T ELT) (($ $ #14#) 139 T ELT)) (* (($ #12# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #14# $) 89 T ELT) (#22# 66 T ELT) (($ $ #42#) NIL T ELT) (($ #42# $) NIL T ELT) (#43# NIL T ELT) (($ |#1| $) 87 T ELT))) +(((|FiniteFieldExtensionByPolynomial| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|SparseUnivariatePolynomial| |#1|)) (T |FiniteFieldExtensionByPolynomial|)) +NIL +((|reducedQPowers| (((|PrimitiveArray| #1=(|SparseUnivariatePolynomial| |#1|)) #1#) 49 T ELT)) (|random| ((#1# #2=(|PositiveInteger|) #2#) 159 T ELT) (#3=(#1# #2#) 155 T ELT)) (|primitive?| (#4=((|Boolean|) #1#) 110 T ELT)) (|numberOfPrimitivePoly| (#5=(#2# #2#) 85 T ELT)) (|numberOfNormalPoly| (#5# 94 T ELT)) (|numberOfIrreduciblePoly| (#5# 83 T ELT)) (|normal?| (#4# 114 T ELT)) (|nextPrimitivePoly| (#6=((|Union| #1# "failed") #1#) 139 T ELT)) (|nextPrimitiveNormalPoly| (#6# 144 T ELT)) (|nextNormalPrimitivePoly| (#6# 143 T ELT)) (|nextNormalPoly| (#6# 142 T ELT)) (|nextIrreduciblePoly| (#6# 134 T ELT)) (|leastAffineMultiple| ((#1# #1#) 71 T ELT)) (|createPrimitivePoly| (#3# 149 T ELT)) (|createPrimitiveNormalPoly| (#3# 152 T ELT)) (|createNormalPrimitivePoly| (#3# 151 T ELT)) (|createNormalPoly| (#3# 150 T ELT)) (|createIrreduciblePoly| (#3# 147 T ELT))) +(((|FiniteFieldPolynomialPackage| |#1|) (CATEGORY |package| (SIGNATURE |primitive?| #1=((|Boolean|) #2=(|SparseUnivariatePolynomial| |#1|))) (SIGNATURE |normal?| #1#) (SIGNATURE |numberOfIrreduciblePoly| #3=(#4=(|PositiveInteger|) #4#)) (SIGNATURE |numberOfPrimitivePoly| #3#) (SIGNATURE |numberOfNormalPoly| #3#) (SIGNATURE |createIrreduciblePoly| #5=(#2# #4#)) (SIGNATURE |createPrimitivePoly| #5#) (SIGNATURE |createNormalPoly| #5#) (SIGNATURE |createNormalPrimitivePoly| #5#) (SIGNATURE |createPrimitiveNormalPoly| #5#) (SIGNATURE |nextIrreduciblePoly| #6=((|Union| #2# "failed") #2#)) (SIGNATURE |nextPrimitivePoly| #6#) (SIGNATURE |nextNormalPoly| #6#) (SIGNATURE |nextNormalPrimitivePoly| #6#) (SIGNATURE |nextPrimitiveNormalPoly| #6#) (SIGNATURE |random| #5#) (SIGNATURE |random| (#2# #4# #4#)) (SIGNATURE |leastAffineMultiple| (#2# #2#)) (SIGNATURE |reducedQPowers| ((|PrimitiveArray| #2#) #2#))) (|FiniteFieldCategory|)) (T |FiniteFieldPolynomialPackage|)) +((|reducedQPowers| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|FiniteFieldCategory|)) (|isDomain| *2 (|PrimitiveArray| #4=(|SparseUnivariatePolynomial| *4))) #5=(|isDomain| *1 (|FiniteFieldPolynomialPackage| *4)) #6=(|isDomain| *3 #4#))) (|leastAffineMultiple| #7=(*1 *2 *2) (AND #8=(|isDomain| *2 (|SparseUnivariatePolynomial| *3)) #9=(|ofCategory| *3 #3#) #10=(|isDomain| *1 (|FiniteFieldPolynomialPackage| *3)))) (|random| (*1 *2 *3 *3) #11=(AND (|isDomain| *3 #12=(|PositiveInteger|)) (|isDomain| *2 #4#) #5# #2#)) (|random| #1# #11#) (|nextPrimitiveNormalPoly| #7# #13=(|partial| AND #8# #9# #10#)) (|nextNormalPrimitivePoly| #7# #13#) (|nextNormalPoly| #7# #13#) (|nextPrimitivePoly| #7# #13#) (|nextIrreduciblePoly| #7# #13#) (|createPrimitiveNormalPoly| #1# #11#) (|createNormalPrimitivePoly| #1# #11#) (|createNormalPoly| #1# #11#) (|createPrimitivePoly| #1# #11#) (|createIrreduciblePoly| #1# #11#) (|numberOfNormalPoly| #7# #14=(AND (|isDomain| *2 #12#) #10# #9#)) (|numberOfPrimitivePoly| #7# #14#) (|numberOfIrreduciblePoly| #7# #14#) (|normal?| #1# #15=(AND #6# #2# (|isDomain| *2 (|Boolean|)) #5#)) (|primitive?| #1# #15#)) +((|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) 60 T ELT))) +(((|FiniteFieldPolynomialPackage2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rootOfIrreduciblePoly| (|#1| (|SparseUnivariatePolynomial| |#2|)))) (|Join| (|FieldOfPrimeCharacteristic|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| |#2|)) (SIGNATURE |lookup| (#1=(|PositiveInteger|) |#1|)) (SIGNATURE |basis| ((|Vector| |#1|) #1#)) (SIGNATURE |Frobenius| (|#1| |#1|)))) (|FiniteFieldCategory|)) (T |FiniteFieldPolynomialPackage2|)) +((|rootOfIrreduciblePoly| (*1 *2 *3) (AND (|isDomain| *3 (|SparseUnivariatePolynomial| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|ofCategory| *2 (|Join| (|FieldOfPrimeCharacteristic|) (CATEGORY |package| (SIGNATURE |coerce| (*2 *4)) (SIGNATURE |lookup| (#1=(|PositiveInteger|) *2)) (SIGNATURE |basis| ((|Vector| *2) #1#)) (SIGNATURE |Frobenius| (*2 *2))))) (|isDomain| *1 (|FiniteFieldPolynomialPackage2| *2 *4))))) +((|solveLinearPolynomialEquation| (((|Union| #1=(|List| |#3|) "failed") #1# |#3|) 40 T ELT))) +(((|FiniteFieldSolveLinearPolynomialEquation| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solveLinearPolynomialEquation| ((|Union| #1=(|List| |#3|) "failed") #1# |#3|))) (|FiniteFieldCategory|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| |#2|)) (T |FiniteFieldSolveLinearPolynomialEquation|)) +((|solveLinearPolynomialEquation| (*1 *2 *2 *3) (|partial| AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 (|FiniteFieldCategory|)) (|isDomain| *1 (|FiniteFieldSolveLinearPolynomialEquation| *4 *5 *3))))) +((~= #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=((|#1| $) NIL T ELT) #10=(#11=($ $ #12=(|PositiveInteger|)) NIL #13=(|has| |#1| (|Finite|)) ELT)) (|tableForDiscreteLogarithm| (((|Table| #12# #8#) #14=(|Integer|)) NIL #13# ELT)) (|subtractIfCan| #15=((#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #18=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| (#7# NIL #13# ELT)) (|sample| #19=(#20=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #17#) $) NIL T ELT)) (|retract| #9#) (|represents| (($ #21=(|Vector| |#1|)) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #13# ELT)) (|rem| #22=(($ $ $) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|random| #23=(#20# NIL #13# ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL T ELT)) (|primitiveElement| #23#) (|primitive?| #26=(#4# NIL #13# ELT)) (|primeFrobenius| (#27=($ $ #8#) NIL #28=(OR (|has| |#1| (|CharacteristicNonZero|)) #13#) ELT) (#6# NIL #28# ELT)) (|prime?| #3#) (|order| #29=(#30=(#12# $) NIL #13# ELT) (#31=(#32=(|OnePointCompletion| #12#) $) NIL #28# ELT)) (|opposite?| #1#) (|one?| #3#) (|normalElement| #23#) (|normal?| #26#) (|norm| #9# #10#) (|nextItem| (#33=((|Maybe| $) $) NIL #13# ELT)) (|multiEuclidean| (((|Union| #24# #17#) #24# $) NIL T ELT)) (|minimalPolynomial| (#34=(#35=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT) ((#36=(|SparseUnivariatePolynomial| $) $ #12#) NIL #13# ELT)) (|lookup| #29#) (|linearAssociatedOrder| #37=(#34# NIL #13# ELT)) (|linearAssociatedLog| #37# (((|Union| #35# #17#) $ $) NIL #13# ELT)) (|linearAssociatedExp| (($ $ #35#) NIL #13# ELT)) (|lcm| #22# #38=(($ #24#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#20# NIL #13# CONST)) (|index| (($ #12#) NIL #13# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #23#) (|gcdPolynomial| ((#36# #36# #36#) NIL T ELT)) (|gcd| #22# #38#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #14#) (|:| |exponent| #14#)))) NIL #13# ELT)) (|factor| #18#) (|extensionDegree| ((#32#) NIL T ELT) ((#12#) NIL T ELT)) (|extendedEuclidean| (((|Record| #39=(|:| |coef1| $) #40=(|:| |coef2| $) #25#) $ $) NIL T ELT) (((|Union| (|Record| #39# #40#) #17#) $ $ $) NIL T ELT)) (|exquo| #15#) (|expressIdealMember| (((|Maybe| #24#) #24# $) NIL T ELT)) (|euclideanSize| (#41=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#41# NIL #13# ELT) (((|Union| #8# #17#) $ $) NIL #28# ELT)) (|dimension| (((|CardinalNumber|)) NIL T ELT)) (|differentiate| #42=(#27# NIL #13# ELT) #43=(#6# NIL #13# ELT)) (|degree| (#31# NIL T ELT) (#30# NIL T ELT)) (|definingPolynomial| ((#35#) NIL T ELT)) (|createPrimitiveElement| #23#) (|createNormalElement| #23#) (|coordinates| ((#21# $) NIL T ELT) (((|Matrix| |#1|) #44=(|Vector| $)) NIL T ELT)) (|conditionP| (((|Union| #44# #17#) (|Matrix| $)) NIL #13# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #14#) NIL T ELT) #5# (($ #45=(|Fraction| #14#)) NIL T ELT) (($ |#1|) NIL T ELT)) (|charthRoot| #43# (#33# NIL #28# ELT)) (|characteristic| (#7# NIL T CONST)) (|before?| #1#) (|basis| ((#44#) NIL T ELT) ((#44# #12#) NIL T ELT)) (|associates?| #1#) (|annihilate?| #1#) (|algebraic?| #3#) (|Zero| #19#) (|One| #19#) (|Frobenius| #43# #42#) (D #42# #43#) (= #1#) (/ #22# #46=(($ $ |#1|) NIL T ELT)) (- #5# #22#) (+ #22#) (** (#11# NIL T ELT) (#27# NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #12# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #47=($)) NIL T ELT) #22# (($ $ #45#) NIL T ELT) (($ #45# . #47#) NIL T ELT) #46# (($ |#1| . #47#) NIL T ELT))) +(((|FiniteFieldExtension| |#1| |#2|) (|FiniteAlgebraicExtensionField| |#1|) (|FiniteFieldCategory|) (|PositiveInteger|)) (T |FiniteFieldExtension|)) +NIL +((|zeroDimensional?| (((|Boolean|) #1=(|List| (|Polynomial| |#1|))) 41 T ELT)) (|groebner| ((#1# #1#) 53 T ELT)) (|fglmIfCan| (((|Union| #1# "failed") #1#) 48 T ELT))) +(((|FGLMIfCanPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimensional?| ((|Boolean|) #1=(|List| (|Polynomial| |#1|)))) (SIGNATURE |fglmIfCan| ((|Union| #1# "failed") #1#)) (SIGNATURE |groebner| (#1# #1#))) (|GcdDomain|) (|List| (|Symbol|))) (T |FGLMIfCanPackage|)) +((|groebner| #1=(*1 *2 *2) (AND #2=(|isDomain| *2 (|List| (|Polynomial| *3))) #3=(|ofCategory| *3 #4=(|GcdDomain|)) #5=(|isDomain| *1 (|FGLMIfCanPackage| *3 *4)) #6=(|ofType| *4 #7=(|List| (|Symbol|))))) (|fglmIfCan| #1# (|partial| AND #2# #3# #5# #6#)) (|zeroDimensional?| (*1 *2 *3) (AND (|isDomain| *3 (|List| (|Polynomial| *4))) (|ofCategory| *4 #4#) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|FGLMIfCanPackage| *4 *5)) (|ofType| *5 #7#)))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|size| ((#3=(|NonNegativeInteger|) $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| #5="failed") $) NIL T ELT)) (|retract| ((|#1| $) NIL T ELT)) (|recip| (((|Union| $ #5#) $) NIL T ELT)) (|one?| ((#2# $) 17 T ELT)) (|nthFactor| ((|#1| $ #6=(|Integer|)) NIL T ELT)) (|nthExpon| ((#6# $ #6#) NIL T ELT)) (|mapGen| (($ (|Mapping| |#1| |#1|) $) 34 T ELT)) (|mapExpon| (($ (|Mapping| #6# #6#) $) 26 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (($ $) 28 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #6#))) $) 30 T ELT)) (|conjugate| #7=(#8=($ $ $) NIL T ELT)) (|commutator| #7#) (|coerce| (((|OutputForm|) $) 40 T ELT) (($ |#1|) NIL T ELT)) (|before?| #1#) (|One| (#4# 7 T CONST)) (= #1#) (/ #7#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ #3#) NIL T ELT) (($ $ #6#) NIL T ELT) (($ |#1| #6#) 19 T ELT)) (* (#8# 53 T ELT) (($ |#1| $) 23 T ELT) (($ $ |#1|) 21 T ELT))) +(((|FreeGroup| |#1|) (|Join| (|Group|) (|RetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE * ($ |#1| $)) (SIGNATURE * ($ $ |#1|)) (SIGNATURE ** ($ |#1| #1=(|Integer|))) (SIGNATURE |size| ((|NonNegativeInteger|) $)) (SIGNATURE |nthExpon| (#1# $ #1#)) (SIGNATURE |nthFactor| (|#1| $ #1#)) (SIGNATURE |mapExpon| ($ (|Mapping| #1# #1#) $)) (SIGNATURE |mapGen| ($ (|Mapping| |#1| |#1|) $)) (SIGNATURE |factors| ((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| #1#))) $)))) (|SetCategory|)) (T |FreeGroup|)) +((* #1=(*1 *1 *2 *1) #2=(AND #3=(|isDomain| *1 (|FreeGroup| *2)) #4=(|ofCategory| *2 #5=(|SetCategory|)))) (* (*1 *1 *1 *2) #2#) (** (*1 *1 *2 *3) #6=(AND (|isDomain| *3 #7=(|Integer|)) #3# #4#)) (|size| #8=(*1 *2 *1) (AND (|isDomain| *2 (|NonNegativeInteger|)) #9=(|isDomain| *1 (|FreeGroup| *3)) #10=(|ofCategory| *3 #5#))) (|nthExpon| (*1 *2 *1 *2) (AND (|isDomain| *2 #7#) #9# #10#)) (|nthFactor| (*1 *2 *1 *3) #6#) (|mapExpon| #1# (AND (|isDomain| *2 (|Mapping| #7# #7#)) #9# #10#)) (|mapGen| #1# (AND (|isDomain| *2 (|Mapping| *3 *3)) #10# #9#)) (|factors| #8# (AND (|isDomain| *2 (|List| (|Record| (|:| |gen| *3) (|:| |exp| #7#)))) #9# #10#))) +((|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| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 68 T ELT)) (|lcm| (#10=($ $ $) 60 T ELT) (#11=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 58 T ELT)) (|gcd| (#10# 62 T ELT) (#11# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 84 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #16#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #15#) 86 T ELT) (($ #15# . #17#) 85 T ELT))) +(((|Field|) (|Category|)) (T |Field|)) +((/ (*1 *1 *1 *1) (|ofCategory| *1 (|Field|)))) +(|Join| (|EuclideanDomain|) (|UniqueFactorizationDomain|) (|DivisionRing|) (CATEGORY |domain| (SIGNATURE / ($ $ $)) (ATTRIBUTE |canonicalUnitNormal|) (ATTRIBUTE |canonicalsClosed|))) +(((|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)) +((~= #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)) +((|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")) 48 (|has| |#1| (|IntegralDomain|)) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) 89 T ELT)) (|someBasis| (((|Vector| $)) 92 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 51 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightUnit| (((|Union| $ "failed")) 49 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 76 T ELT)) (|rightTrace| ((|#1| $) 85 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 87 T ELT)) (|rightRecip| (((|Union| $ "failed") $) 56 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightPower| (#4=($ $ (|PositiveInteger|)) 37 T ELT)) (|rightNorm| ((|#1| $) 83 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 53 (|has| |#1| (|IntegralDomain|)) ELT)) (|rightDiscriminant| ((|#1| (|Vector| $)) 78 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 74 T ELT)) (|rightAlternative?| (((|Boolean|)) 68 T ELT)) (|represents| (($ (|Vector| |#1|) (|Vector| $)) 80 T ELT)) (|recip| (((|Union| $ "failed") $) 58 (|has| |#1| (|IntegralDomain|)) ELT)) (|rank| (((|PositiveInteger|)) 91 T ELT)) (|powerAssociative?| (((|Boolean|)) 65 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (((|Boolean|)) 61 T ELT)) (|lieAlgebra?| (((|Boolean|)) 59 T ELT)) (|lieAdmissible?| (((|Boolean|)) 63 T ELT)) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) 52 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftUnit| (((|Union| $ "failed")) 50 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) 77 T ELT)) (|leftTrace| ((|#1| $) 86 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) 88 T ELT)) (|leftRecip| (((|Union| $ "failed") $) 57 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftPower| (#4# 38 T ELT)) (|leftNorm| ((|#1| $) 84 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 54 (|has| |#1| (|IntegralDomain|)) ELT)) (|leftDiscriminant| ((|#1| (|Vector| $)) 79 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) 75 T ELT)) (|leftAlternative?| (((|Boolean|)) 69 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (((|Boolean|)) 60 T ELT)) (|jordanAdmissible?| (((|Boolean|)) 62 T ELT)) (|jacobiIdentity?| (((|Boolean|)) 64 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (((|Boolean|)) 67 T ELT)) (|coordinates| (((|Vector| |#1|) $ (|Vector| $)) 82 T ELT) (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) 81 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) 90 T ELT)) (|commutator| (#5=($ $ $) 34 T ELT)) (|commutative?| (((|Boolean|)) 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 55 (|has| |#1| (|IntegralDomain|)) ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|associative?| (((|Boolean|)) 71 T ELT)) (|antiCommutator| (#5# 33 T ELT)) (|antiCommutative?| (((|Boolean|)) 72 T ELT)) (|antiAssociative?| (((|Boolean|)) 70 T ELT)) (|alternative?| (((|Boolean|)) 66 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#4# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #6=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #6#) 45 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))))) (|leftMinimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|rightMinimalPolynomial| (*1 *2 *1) (AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)) (|ofCategory| *3 (|CommutativeRing|)) (|ofCategory| *3 (|IntegralDomain|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *3)))) (|leftUnits| (*1 *2) (|partial| AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1)))) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|rightUnits| (*1 *2) (|partial| AND (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|CommutativeRing|)) (|isDomain| *2 (|Record| (|:| |particular| *1) (|:| |basis| (|List| *1)))) (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *3)))) (|leftUnit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|)))) (|rightUnit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|)))) (|unit| (*1 *1) (|partial| AND (|ofCategory| *1 (|FiniteRankNonAssociativeAlgebra| *2)) (|ofCategory| *2 (|IntegralDomain|)) (|ofCategory| *2 (|CommutativeRing|))))) +(|Join| (|NonAssociativeAlgebra| |t#1|) (CATEGORY |domain| (SIGNATURE |someBasis| ((|Vector| $))) (SIGNATURE |rank| ((|PositiveInteger|))) (SIGNATURE |conditionsForIdempotents| ((|List| (|Polynomial| |t#1|)) (|Vector| $))) (SIGNATURE |structuralConstants| ((|Vector| (|Matrix| |t#1|)) (|Vector| $))) (SIGNATURE |leftRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |rightRegularRepresentation| ((|Matrix| |t#1|) $ (|Vector| $))) (SIGNATURE |leftTrace| (|t#1| $)) (SIGNATURE |rightTrace| (|t#1| $)) (SIGNATURE |leftNorm| (|t#1| $)) (SIGNATURE |rightNorm| (|t#1| $)) (SIGNATURE |coordinates| ((|Vector| |t#1|) $ (|Vector| $))) (SIGNATURE |coordinates| ((|Matrix| |t#1|) (|Vector| $) (|Vector| $))) (SIGNATURE |represents| ($ (|Vector| |t#1|) (|Vector| $))) (SIGNATURE |leftDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |rightDiscriminant| (|t#1| (|Vector| $))) (SIGNATURE |leftTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |rightTraceMatrix| ((|Matrix| |t#1|) (|Vector| $))) (SIGNATURE |leftCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |rightCharacteristicPolynomial| ((|SparseUnivariatePolynomial| |t#1|) $)) (SIGNATURE |commutative?| ((|Boolean|))) (SIGNATURE |antiCommutative?| ((|Boolean|))) (SIGNATURE |associative?| ((|Boolean|))) (SIGNATURE |antiAssociative?| ((|Boolean|))) (SIGNATURE |leftAlternative?| ((|Boolean|))) (SIGNATURE |rightAlternative?| ((|Boolean|))) (SIGNATURE |flexible?| ((|Boolean|))) (SIGNATURE |alternative?| ((|Boolean|))) (SIGNATURE |powerAssociative?| ((|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"))) (ATTRIBUTE |unitsKnown|)) |%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)) +((|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# $) 17 T ELT))) +(((|FiniteAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE = (#1=(|Boolean|) |#1| |#1|)) (SIGNATURE |coerce| ((|OutputForm|) |#1|)) (SIGNATURE |reduce| (|#2| #2=(|Mapping| |#2| |#2| |#2|) |#1| |#2| |#2|)) (SIGNATURE |member?| (#1# |#2| |#1|)) (SIGNATURE |count| (#3=(|NonNegativeInteger|) |#2| |#1|)) (SIGNATURE |find| ((|Union| |#2| "failed") #4=(|Mapping| #1# |#2|) |#1|)) (SIGNATURE |reduce| (|#2| #2# |#1| |#2|)) (SIGNATURE |reduce| (|#2| #2# |#1|)) (SIGNATURE |count| (#3# #4# 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T) ((|BasicType|) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|BasicType|))) ((|CoercibleTo| (|OutputForm|)) OR (|has| |#1| (|SetCategory|)) (|has| |#1| (|CoercibleTo| (|OutputForm|)))) ((|Evalable| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Functorial| |#1|) . T) ((|HomogeneousAggregate| |#1|) . T) ((|InnerEvalable| |#1| |#1|) AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| (|SetCategory|))) ((|Join|) . T) ((|SetCategory|) |has| |#1| (|SetCategory|)) ((|Type|) . T)) +((|random| (($) 15 T ELT))) +(((|Finite&| |#1|) (CATEGORY |package| (SIGNATURE |random| (|#1|))) (|Finite|)) (T |Finite&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|size| (((|NonNegativeInteger|)) 20 T ELT)) (|random| (($) 17 T ELT)) (|lookup| (((|PositiveInteger|) $) 18 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|index| (($ (|PositiveInteger|)) 19 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT))) +(((|Finite|) (|Category|)) (T |Finite|)) +((|size| (*1 *2) (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|index| (*1 *1 *2) (AND (|isDomain| *2 (|PositiveInteger|)) (|ofCategory| *1 (|Finite|)))) (|lookup| (*1 *2 *1) (AND (|ofCategory| *1 (|Finite|)) (|isDomain| *2 (|PositiveInteger|)))) (|random| (*1 *1) (|ofCategory| *1 (|Finite|)))) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |size| ((|NonNegativeInteger|))) (SIGNATURE |index| ($ (|PositiveInteger|))) (SIGNATURE |lookup| ((|PositiveInteger|) $)) (SIGNATURE |random| ($)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . 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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) ((|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)) +((|sorted?| ((#1=(|Boolean|) #2=(|Mapping| #1# |#2| |#2|) $) NIL T ELT) ((#1# $) 18 T ELT)) (|sort!| (#3=($ #2# $) NIL T ELT) (#4=($ $) 28 T ELT)) (|sort| (#3# 27 T ELT) (#4# 22 T ELT)) (|reverse| (#4# 25 T ELT)) (|position| ((#5=(|Integer|) (|Mapping| #1# |#2|) $) NIL T ELT) ((#5# |#2| $) 11 T ELT) ((#5# |#2| $ #5#) NIL T ELT)) (|merge| (($ #2# $ $) NIL T ELT) (($ $ $) 20 T ELT))) +(((|FiniteLinearAggregate&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sort!| #1=(|#1| |#1|)) (SIGNATURE |sort!| #2=(|#1| #3=(|Mapping| #4=(|Boolean|) |#2| |#2|) |#1|)) (SIGNATURE |sorted?| (#4# |#1|)) (SIGNATURE |sort| #1#) (SIGNATURE |merge| (|#1| |#1| |#1|)) (SIGNATURE |position| (#5=(|Integer|) |#2| |#1| #5#)) (SIGNATURE |position| (#5# |#2| |#1|)) (SIGNATURE |position| (#5# (|Mapping| #4# |#2|) |#1|)) (SIGNATURE |sorted?| (#4# #3# |#1|)) (SIGNATURE |sort| #2#) (SIGNATURE |reverse| #1#) (SIGNATURE |merge| (|#1| #3# |#1| |#1|))) (|FiniteLinearAggregate| |#2|) (|Type|)) (T |FiniteLinearAggregate&|)) 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+(|Join| (|LieAlgebra| |t#2|) (CATEGORY |domain| (SIGNATURE |coef| (|t#2| (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |coerce| ($ |t#1|)) (SIGNATURE |coerce| ((|XDistributedPolynomial| |t#1| |t#2|) $)) (SIGNATURE |coerce| ((|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |degree| ((|NonNegativeInteger|) $)) (SIGNATURE |lquo| ((|XRecursivePolynomial| |t#1| |t#2|) (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |rquo| ((|XRecursivePolynomial| |t#1| |t#2|) (|XRecursivePolynomial| |t#1| |t#2|) $)) (SIGNATURE |LiePoly| ($ (|LyndonWord| |t#1|))) (SIGNATURE |mirror| ($ $)) (SIGNATURE |trunc| ($ $ (|NonNegativeInteger|))) (SIGNATURE |varList| ((|List| |t#1|) $)) (SIGNATURE |eval| ($ $ |t#1| $)) (SIGNATURE |eval| ($ $ (|List| |t#1|) (|List| $))))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . 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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|reducedSystem| (((|Matrix| |#1|) . #4=(#5=(|Matrix| $))) 36 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #6=(#5# #7=(|Vector| $))) 35 T ELT) (((|Record| (|:| |mat| (|Matrix| #8=(|Integer|))) (|:| |vec| (|Vector| #8#))) . #6#) 47 (|has| |#1| . #9=((|LinearlyExplicitRingOver| (|Integer|)))) ELT) (((|Matrix| #8#) . #4#) 46 (|has| |#1| . #9#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|leftReducedSystem| (((|Matrix| |#1|) . #10=(#7#)) 38 T ELT) (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #11=(#7# $)) 37 T ELT) (((|Record| (|:| |mat| (|Matrix| #8#)) (|:| |vec| (|Vector| #8#))) . #11#) 45 (|has| |#1| . #9#) ELT) (((|Matrix| #8#) . #10#) 44 (|has| |#1| . #9#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #12=($)) 30 T ELT) (($ |#1| . #12#) 33 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)) +((~= #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| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePart| #7#) (|squareFree| #13=(((|Factored| $) $) NIL T ELT)) (|sqrt| (#8# 28 T ELT)) (|sizeLess?| #1#) (|sinh| (#8# 79 T ELT)) (|sin| (#8# 67 T ELT)) (|sign| (#5# 60 T ELT)) (|shift| (#14=($ $ #6#) 55 T ELT)) (|sech| #7#) (|sec| #7#) (|sample| (#15=($) NIL T CONST)) (|round| (#8# 122 T ELT)) (|retractIfCan| (((|Union| #6# . #16=(#12#)) $) 217 T ELT) (((|Union| #17=(|Fraction| #6#) . #16#) $) 213 T ELT)) (|retract| (#5# 215 T ELT) ((#17# $) 211 T ELT)) (|rem| #18=(#19=($ $ $) NIL T ELT)) (|relerror| ((#6# $ $) 110 T ELT)) (|recip| ((#11# $) 125 T ELT)) (|rationalApproximation| ((#17# $ #20=(|NonNegativeInteger|)) 218 T ELT) ((#17# $ #20# #20#) 210 T ELT)) (|quo| #18#) (|principalIdeal| (((|Record| (|:| |coef| #21=(|List| $)) #22=(|:| |generator| $)) #21#) NIL T ELT)) (|prime?| #9#) (|precision| (#23=(#24=(|PositiveInteger|)) 106 T ELT) (#25=(#24# #24#) 107 #26=(|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|positive?| (#4# 38 T ELT)) (|pi| (#15# 22 T ELT)) (|patternMatch| ((#27=(|PatternMatchResult| #28=(|Float|) $) $ #29=(|Pattern| #28#) #27#) NIL T ELT)) (|outputSpacing| (#30=(#31=(|Void|) #20#) 177 T ELT)) (|outputGeneral| (#32=(#31#) 182 T ELT) (#30# 183 T ELT)) (|outputFloating| (#32# 184 T ELT) (#30# 185 T ELT)) (|outputFixed| (#32# 180 T ELT) (#30# 181 T ELT)) (|order| (#5# 50 T ELT)) (|opposite?| #1#) (|one?| (#4# 21 T ELT)) (|nthRoot| (#14# NIL T ELT)) (|normalize| (#8# 32 T ELT)) (|norm| #7#) (|negative?| (#4# 18 T ELT)) (|multiEuclidean| (((|Union| #21# #12#) #21# $) NIL T ELT)) (|min| #18# #33=(#15# NIL (AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|))) (|not| #26#)) ELT)) (|max| #18# #33#) (|mantissa| (#5# 112 T ELT)) (|log2| (#15# 90 T ELT) (#8# 97 T ELT)) (|log10| (#15# 96 T ELT) (#8# 98 T ELT)) (|log| (#8# 84 T ELT)) (|lcm| #18# #34=(($ #21#) NIL T ELT)) (|latex| (#35=((|String|) $) NIL T ELT)) (|inv| (#8# 127 T ELT)) (|increasePrecision| (#36=(#24# #6#) 27 #26# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#37=(|SparseUnivariatePolynomial| $) #37# #37#) NIL T ELT)) (|gcd| #18# #34#) (|fractionPart| (#8# 41 T ELT)) (|floor| (#8# 119 T ELT)) (|float| (($ #6# #6#) 115 T ELT) (($ #6# #6# #24#) 116 T ELT)) (|factor| #13#) (|extendedEuclidean| (((|Record| #38=(|:| |coef1| $) #39=(|:| |coef2| $) #22#) $ $) NIL T ELT) (((|Union| (|Record| #38# #39#) #12#) $ $ $) NIL T ELT)) (|exquo| #10#) (|expressIdealMember| (((|Maybe| #21#) #21# $) NIL T ELT)) (|exponent| (#5# 113 T ELT)) (|exp1| (#15# 99 T ELT)) (|exp| (#8# 78 T ELT)) (|euclideanSize| ((#20# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|digits| (#23# 108 T ELT) (#25# 109 #26# ELT)) (|differentiate| (#8# 126 T ELT) #40=(($ $ #20#) NIL T ELT)) (|decreasePrecision| (#36# 31 #26# ELT)) (|csch| #7#) (|csc| #7#) (|coth| #7#) (|cot| #7#) (|cosh| (#8# 80 T ELT)) (|cos| (#8# 71 T ELT)) (|convert| ((#28# $) 202 T ELT) (#41=(#42=(|DoubleFloat|) $) 204 T ELT) ((#29# $) NIL T ELT) (#35# 188 T ELT) (((|InputForm|) $) 200 T ELT) (($ #42#) 209 T ELT)) (|coerce| (((|OutputForm|) $) 192 T ELT) #43=(($ #6#) 214 T ELT) #7# #44=(($ #17#) NIL T ELT) #43# #44# (#41# 205 T ELT)) (|characteristic| ((#20#) NIL T CONST)) (|ceiling| (#8# 121 T ELT)) (|bits| (#23# 42 T ELT) (#25# 62 #26# ELT)) (|before?| #1#) (|base| (#23# 111 T ELT)) (|atanh| (#8# 87 T ELT)) (|atan| (#8# 30 T ELT) (#19# 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| (#15# 17 T CONST)) (|One| (#15# 24 T CONST)) (D #7# #40#) (>= (#2# 189 T ELT)) (> (#2# 26 T ELT)) (= (#2# 37 T ELT)) (<= #1#) (< (#2# 43 T ELT)) (/ (#19# 29 T ELT) (#14# 23 T ELT)) (- (#8# 19 T ELT) (#19# 34 T ELT)) (+ (#19# 54 T ELT)) (** (($ $ #24#) 65 T ELT) #40# (#14# 91 T ELT) (#45=($ $ #17#) 137 T ELT) (#19# 129 T ELT)) (* (($ #24# $) 61 T ELT) (($ #20# $) NIL T ELT) (($ #6# $) 66 T ELT) (#19# 53 T ELT) (#45# NIL T ELT) (($ #17# $) NIL T ELT))) +(((|Float|) (|Join| (|FloatingPointSystem|) (|DifferentialRing|) (|ConvertibleTo| (|String|)) (|CoercibleTo| #1=(|DoubleFloat|)) (|TranscendentalFunctionCategory|) (|ConvertibleTo| (|InputForm|)) (|ConvertibleFrom| #1#) (CATEGORY |domain| (SIGNATURE / #2=($ $ #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#)) +((|complexSolve| ((#1=(|List| (|Equation| (|Polynomial| #2=(|Complex| |#1|)))) #3=(|Equation| #4=(|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) 52 T ELT) ((#1# #4# |#1|) 51 T ELT) ((#5=(|List| #1#) (|List| #3#) |#1|) 48 T ELT) ((#5# #6=(|List| #4#) |#1|) 42 T ELT)) (|complexRoots| (((|List| #7=(|List| #2#)) #6# (|List| (|Symbol|)) |#1|) 30 T ELT) ((#7# #4# |#1|) 18 T ELT))) +(((|FloatingComplexPackage| |#1|) (CATEGORY |package| (SIGNATURE |complexSolve| (#1=(|List| #2=(|List| (|Equation| (|Polynomial| #3=(|Complex| |#1|))))) #4=(|List| #5=(|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|)) (SIGNATURE |complexSolve| (#1# (|List| #6=(|Equation| #5#)) |#1|)) (SIGNATURE |complexSolve| (#2# #5# |#1|)) (SIGNATURE |complexSolve| (#2# #6# |#1|)) (SIGNATURE |complexRoots| (#7=(|List| #3#) #5# |#1|)) (SIGNATURE |complexRoots| ((|List| #7#) #4# (|List| (|Symbol|)) |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |FloatingComplexPackage|)) +((|complexRoots| (*1 *2 *3 *4 *5) (AND #1=(|isDomain| *3 (|List| #2=(|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| (|Complex| *5)))) (|isDomain| *1 (|FloatingComplexPackage| *5)) (|ofCategory| *5 #3=(|Join| (|Field|) (|OrderedRing|))))) (|complexRoots| #4=(*1 *2 *3 *4) (AND #5=(|isDomain| *3 #2#) (|isDomain| *2 (|List| #6=(|Complex| *4))) #7=(|isDomain| *1 (|FloatingComplexPackage| *4)) #8=(|ofCategory| *4 #3#))) (|complexSolve| #4# (AND (|isDomain| *3 #9=(|Equation| #2#)) #10=(|isDomain| *2 #11=(|List| (|Equation| (|Polynomial| #6#)))) #7# #8#)) (|complexSolve| #4# (AND #5# #10# #7# #8#)) (|complexSolve| #4# (AND (|isDomain| *3 (|List| #9#)) #12=(|isDomain| *2 (|List| #11#)) #7# #8#)) (|complexSolve| #4# (AND #1# #12# #7# #8#))) +((|solve| ((#1=(|List| (|Equation| (|Polynomial| |#1|))) #2=(|Equation| #3=(|Fraction| (|Polynomial| (|Integer|)))) |#1|) 47 T ELT) ((#1# #3# |#1|) 46 T ELT) ((#4=(|List| #1#) (|List| #2#) |#1|) 43 T ELT) ((#4# #5=(|List| #3#) |#1|) 37 T ELT)) (|realRoots| ((#6=(|List| |#1|) #3# |#1|) 20 T ELT) (((|List| #6#) #5# (|List| (|Symbol|)) |#1|) 30 T ELT))) +(((|FloatingRealPackage| |#1|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|List| (|Equation| (|Polynomial| |#1|)))) #3=(|List| #4=(|Fraction| (|Polynomial| (|Integer|)))) |#1|)) (SIGNATURE |solve| (#1# (|List| #5=(|Equation| #4#)) |#1|)) (SIGNATURE |solve| (#2# #4# |#1|)) (SIGNATURE |solve| (#2# #5# |#1|)) (SIGNATURE |realRoots| ((|List| #6=(|List| |#1|)) #3# (|List| (|Symbol|)) |#1|)) (SIGNATURE |realRoots| (#6# #4# |#1|))) (|Join| (|OrderedRing|) (|Field|))) (T |FloatingRealPackage|)) +((|realRoots| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 #3=(|Fraction| (|Polynomial| (|Integer|)))) (|isDomain| *2 (|List| *4)) #4=(|isDomain| *1 (|FloatingRealPackage| *4)) #5=(|ofCategory| *4 #6=(|Join| (|OrderedRing|) (|Field|))))) (|realRoots| (*1 *2 *3 *4 *5) (AND #7=(|isDomain| *3 (|List| #3#)) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| *2 (|List| (|List| *5))) (|isDomain| *1 (|FloatingRealPackage| *5)) (|ofCategory| *5 #6#))) (|solve| #1# (AND (|isDomain| *3 #8=(|Equation| #3#)) #9=(|isDomain| *2 #10=(|List| (|Equation| (|Polynomial| *4)))) #4# #5#)) (|solve| #1# (AND #2# #9# #4# #5#)) (|solve| #1# (AND (|isDomain| *3 (|List| #8#)) #11=(|isDomain| *2 (|List| #10#)) #4# #5#)) (|solve| #1# (AND #7# #11# #4# #5#))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|terms| ((#3=(|List| (|IndexedProductTerm| |#1| |#2|)) $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#4=($) NIL T CONST)) (|reductum| #5=(($ $) NIL T ELT)) (|opposite?| #1#) (|monomial| (($ |#1| |#2|) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingSupport| ((|#2| $) NIL T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|convert| (($ #3#) NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT)) (|before?| #1#) (|Zero| (#4# 12 T CONST)) (= #1#) (- #5# #6=(($ $ $) NIL T ELT)) (+ #6#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT) (($ |#1| $) 15 T ELT) (($ $ |#1|) 18 T ELT))) +(((|FreeModule| |#1| |#2|) (|Join| (|BiModule| |#1| |#1|) (|IndexedDirectProductCategory| |#1| |#2|) (CATEGORY |package| (IF (|has| |#1| (|CommutativeRing|)) (ATTRIBUTE (|Module| |#1|)) |%noBranch|))) (|Ring|) (|OrderedType|)) (T |FreeModule|)) +NIL +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ #4="failed") $ $) NIL T ELT)) (|sample| (#5=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| #4#) $) 29 T ELT)) (|retract| (#6=(|#2| $) 31 T ELT)) (|reductum| #7=(($ $) NIL T ELT)) (|opposite?| #1#) (|numberOfMonomials| ((#8=(|NonNegativeInteger|) $) 13 T ELT)) (|monomials| (((|List| $) $) 23 T ELT)) (|monomial?| #3#) (|monom| (#9=($ |#2| |#1|) 21 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingTerm| ((#10=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) 17 T ELT)) (|leadingMonomial| (#6# 18 T ELT)) (|leadingCoefficient| ((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 50 T ELT) (($ |#2|) 30 T ELT)) (|coefficients| (((|List| |#1|) $) 20 T ELT)) (|coefficient| ((|#1| $ |#2|) 54 T ELT)) (|before?| #1#) (|Zero| (#5# 32 T CONST)) (|ListOfTerms| (((|List| #10#) $) 14 T ELT)) (= #1#) (- #11=(($ $ $) NIL T ELT) #7#) (+ #11#) (* (($ $ |#1|) 36 T ELT) (($ |#1| $) 35 T ELT) (($ (|Integer|) $) NIL T ELT) (($ #8# $) NIL T ELT) (($ (|PositiveInteger|) $) NIL T ELT) (($ |#1| |#2|) 38 T ELT) 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(|FunctionFieldCategory| |#1| |#2| |#3|)) (T |FindOrderFinite|)) +((|order| (*1 *2 *3) (AND (|isDomain| *3 (|FiniteDivisor| *4 *5 *6 *7)) (|ofCategory| *4 (|Join| (|Finite|) (|Field|))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *6 (|UnivariatePolynomialCategory| (|Fraction| *5))) (|ofCategory| *7 (|FunctionFieldCategory| *4 *5 *6)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|FindOrderFinite| *4 *5 *6 *7))))) +((~= #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|))) $) 39 T ELT)) (|differentiate| (#5=($ $ #4#) 36 T ELT) (#6=($ $) 34 T ELT)) (|convert| ((#2# $) 49 T ELT)) (|construct| (($ #3#) 33 T ELT)) (|coerce| (((|OutputForm|) $) 131 T ELT)) (|before?| #1#) (D (#5# 37 T ELT) (#6# 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T) ((|PatternMatchable| (|Float|)) |has| |#1| (|PatternMatchable| (|Float|))) ((|PatternMatchable| (|Integer|)) |has| |#1| (|PatternMatchable| (|Integer|))) ((|SetCategory|) OR (|has| |#1| (|PatternMatchable| (|Integer|))) (|has| |#1| (|PatternMatchable| (|Float|)))) ((|Type|) . T)) +((|primeFrobenius| (($ $) 10 T ELT) (($ $ (|NonNegativeInteger|)) 12 T ELT))) +(((|FieldOfPrimeCharacteristic&| |#1|) (CATEGORY |package| (SIGNATURE |primeFrobenius| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |primeFrobenius| (|#1| |#1|))) (|FieldOfPrimeCharacteristic|)) (T |FieldOfPrimeCharacteristic&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primeFrobenius| (($ $) 97 T ELT) (($ $ (|NonNegativeInteger|)) 96 T ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 99 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #8=(|List| $) #9="failed") #8# $) 68 T ELT)) (|lcm| (#10=($ $ $) 60 T ELT) (#11=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#12=(|SparseUnivariatePolynomial| $) #12# #12#) 58 T ELT)) (|gcd| (#10# 62 T ELT) (#11# 61 T ELT)) (|factor| (#4# 92 T ELT)) (|extendedEuclidean| (((|Record| #13=(|:| |coef1| $) #14=(|:| |coef2| $) (|:| |generator| $)) $ $) 70 T ELT) (((|Union| (|Record| #13# #14#) #9#) $ $ $) 69 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| #7#) #7# $) 65 T ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 74 T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 73 T ELT)) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) 98 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT) (($ #15=(|Fraction| #16=(|Integer|))) 84 T ELT)) (|charthRoot| (((|Maybe| $) $) 100 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #16#) 87 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #17=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #15#) 86 T ELT) (($ #15# . #17#) 85 T ELT))) +(((|FieldOfPrimeCharacteristic|) (|Category|)) (T |FieldOfPrimeCharacteristic|)) +((|order| (*1 *2 *1) (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|OnePointCompletion| (|PositiveInteger|))))) (|discreteLog| (*1 *2 *1 *1) (|partial| AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|primeFrobenius| (*1 *1 *1) (|ofCategory| *1 (|FieldOfPrimeCharacteristic|))) (|primeFrobenius| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|FieldOfPrimeCharacteristic|)) (|isDomain| *2 (|NonNegativeInteger|))))) +(|Join| (|Field|) (|CharacteristicNonZero|) (CATEGORY |domain| (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) $)) (SIGNATURE |discreteLog| ((|Union| (|NonNegativeInteger|) "failed") $ $)) (SIGNATURE |primeFrobenius| ($ $)) (SIGNATURE |primeFrobenius| ($ $ (|NonNegativeInteger|))))) +(((|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) ((|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| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|UniqueFactorizationDomain|) . T)) +((|float| (($ #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|) $) 108 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#4=(|Boolean|) $) 52 T ELT)) (|truncate| (#5=($ $) 106 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| 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155 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #16=(|Integer|)) 115 T ELT)) (|norm| (#5# 111 T ELT)) (|negative?| (((|Boolean|) $) 132 T ELT)) (|multiEuclidean| (((|Union| #17=(|List| $) #18="failed") #17# $) 68 T ELT)) (|min| (#19=($ $ $) 125 T ELT) (($) 143 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|max| (#19# 126 T ELT) (($) 142 (AND (|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))) (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))) ELT)) (|mantissa| (((|Integer|) $) 152 T ELT)) (|lcm| (#20=($ $ $) 60 T ELT) (#21=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 88 T ELT)) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) 145 (|has| $ (ATTRIBUTE |arbitraryPrecision|)) ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#22=(|SparseUnivariatePolynomial| $) #22# #22#) 58 T ELT)) (|gcd| (#20# 62 T ELT) (#21# 61 T 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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) ((|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|) . 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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| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|squareFreePart| (#5# NIL #11=(|has| |#1| (|UniqueFactorizationDomain|)) ELT)) (|squareFree| #12=(((|Factored| $) $) NIL #11# ELT)) (|sqfrFactor| (#13=($ |#1| #14=(|Integer|)) 42 T ELT)) (|sample| (#15=($) NIL T CONST)) (|retractIfCan| (((|Union| #14# . #16=(#10#)) $) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (#18=((|Union| #19=(|Fraction| #14#) #10#) $) NIL #20=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| |#1| . #16#) $) 147 T ELT)) (|retract| (#21=(#14# $) NIL #17# ELT) (#22=(#19# $) NIL #20# ELT) (#7# 73 T ELT)) (|recip| ((#9# $) 163 T ELT)) (|rationalIfCan| (#18# 84 #23=(|has| |#1| 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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|) 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(|partial| AND #18# #8# #17# #9#))) +((|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) 20 T ELT))) +(((|FactoredFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)))) #1=(|IntegralDomain|) #1#) (T |FactoredFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Factored| *5)) (|ofCategory| *5 #1=(|IntegralDomain|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Factored| *6)) (|isDomain| *1 (|FactoredFunctions2| *5 *6))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 13 T ELT)) (|wholePart| (#5=(|#1| $) 21 #6=(|has| |#1| (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #7=(#8=($ $) NIL T ELT)) (|unit?| #9=(#4# NIL T ELT)) (|subtractIfCan| #10=((#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|squareFreePolynomial| (#13=((|Factored| #14=(|SparseUnivariatePolynomial| $)) #14#) NIL #15=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #7#) (|squareFree| #16=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #17=(|List| #14#) #12#) #17# #14#) NIL #15# ELT)) (|sizeLess?| #1#) (|sign| (#18=(#19=(|Integer|) $) NIL #20=(|has| |#1| (|OrderedIntegralDomain|)) ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #22=(#12#)) $) 17 T ELT) (((|Union| #23=(|Symbol|) . #22#) . #24=($)) NIL #25=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| #26=(|Fraction| #19#) . #22#) $) 54 #27=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #19# . #22#) . #24#) NIL #27# ELT)) (|retract| (#5# 15 T ELT) ((#23# $) NIL #25# ELT) ((#26# $) 51 #27# ELT) (#18# NIL #27# ELT)) (|rem| #28=(#29=($ $ $) NIL T ELT)) (|reducedSystem| ((#30=(|Matrix| #19#) . #31=(#32=(|Matrix| $))) NIL #33=(|has| |#1| (|LinearlyExplicitRingOver| #19#)) ELT) ((#34=(|Record| (|:| |mat| #30#) (|:| |vec| (|Vector| #19#))) . #35=(#32# #36=(|Vector| $))) NIL #33# ELT) ((#37=(|Record| (|:| |mat| #38=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #35#) NIL T ELT) ((#38# . #31#) NIL T ELT)) (|recip| ((#11# $) 32 T ELT)) (|random| (#21# NIL #39=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|quo| #28#) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) #41=(|:| |generator| $)) #40#) NIL T ELT)) (|prime?| #9#) (|positive?| (#4# NIL #20# ELT)) (|patternMatch| ((#42=(|PatternMatchResult| #19# . #43=($)) $ #44=(|Pattern| #19#) #42#) NIL (|has| |#1| (|PatternMatchable| #19#)) ELT) ((#45=(|PatternMatchResult| #46=(|Float|) . #43#) $ #47=(|Pattern| #46#) #45#) NIL (|has| |#1| (|PatternMatchable| #46#)) ELT)) (|opposite?| #1#) (|one?| (#4# 38 T ELT)) (|numerator| #7#) (|numer| (#5# 55 T ELT)) (|nextItem| (#48=((|Maybe| $) $) NIL #49=(|has| |#1| (|StepThrough|)) ELT)) (|negative?| (#4# 22 #20# ELT)) (|multiEuclidean| (((|Union| #40# #12#) #40# $) NIL T ELT)) (|min| #50=(#29# NIL #51=(|has| 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(((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 83 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 54 T ELT) (($ |#1| . #7#) 53 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 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*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)) +((|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))) +(((|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)) +((~= #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| $) 53 T ELT)) (|minimize| (#8=($ $) 156 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 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(|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))))) +((|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) 35 T ELT))) +(((|FractionalIdealFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (CATEGORY |package| (SIGNATURE |map| ((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)))) #1=(|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|Join| (|FramedAlgebra| |#2| |#3|) (|RetractableTo| |#2|)) #1# (|QuotientFieldCategory| |#5|) (|UnivariatePolynomialCategory| |#6|) (|Join| (|FramedAlgebra| |#6| |#7|) (|RetractableTo| |#6|))) (T |FractionalIdealFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *9 *5)) (|isDomain| *4 (|FractionalIdeal| *5 *6 *7 *8)) (|ofCategory| *5 #1=(|EuclideanDomain|)) (|ofCategory| *6 (|QuotientFieldCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *8 (|Join| (|FramedAlgebra| *6 *7) (|RetractableTo| *6))) (|ofCategory| *9 #1#) (|ofCategory| *10 (|QuotientFieldCategory| *9)) (|ofCategory| *11 (|UnivariatePolynomialCategory| *10)) (|isDomain| *2 (|FractionalIdeal| *9 *10 *11 *12)) (|isDomain| *1 (|FractionalIdealFunctions2| *5 *6 *7 *8 *9 *10 *11 *12)) (|ofCategory| *12 (|Join| (|FramedAlgebra| *10 *11) (|RetractableTo| *10)))))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#2# $) NIL T ELT)) (|norm| ((|#2| $) 69 T ELT)) (|module| (($ #4=(|Vector| |#4|)) 27 T ELT) (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) 83 (|has| |#4| (|RetractableTo| |#2|)) ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 37 T ELT)) (|before?| #1#) (|basis| ((#4# $) 28 T ELT)) (|One| (#3# 26 T CONST)) (= #1#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT)) (* (($ $ $) 80 T ELT))) +(((|FramedModule| |#1| |#2| |#3| |#4| |#5|) (|Join| (|Monoid|) (CATEGORY |domain| (SIGNATURE |basis| (#1=(|Vector| |#4|) $)) (SIGNATURE |norm| (|#2| $)) (SIGNATURE |module| ($ #1#)) (IF (|has| |#4| (|RetractableTo| |#2|)) (SIGNATURE |module| ($ (|FractionalIdeal| |#1| |#2| |#3| |#4|))) |%noBranch|))) (|EuclideanDomain|) (|QuotientFieldCategory| |#1|) (|UnivariatePolynomialCategory| |#2|) (|FramedAlgebra| |#2| |#3|) #1#) (T |FramedModule|)) +((|basis| #1=(*1 *2 *1) (AND #2=(|ofCategory| *3 (|EuclideanDomain|)) #3=(|ofCategory| *4 #4=(|QuotientFieldCategory| *3)) #5=(|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) #6=(|isDomain| *2 #7=(|Vector| *6)) #8=(|isDomain| *1 (|FramedModule| *3 *4 *5 *6 *7)) #9=(|ofCategory| *6 (|FramedAlgebra| *4 *5)) #10=(|ofType| *7 *2))) (|norm| #1# (AND (|ofCategory| *4 (|UnivariatePolynomialCategory| *2)) (|ofCategory| *2 #4#) (|isDomain| *1 (|FramedModule| *3 *2 *4 *5 *6)) #2# (|ofCategory| *5 (|FramedAlgebra| *2 *4)) (|ofType| *6 (|Vector| *5)))) (|module| #11=(*1 *1 *2) (AND #6# #9# #3# #5# #2# #8# #10#)) (|module| #11# (AND (|isDomain| *2 (|FractionalIdeal| *3 *4 *5 *6)) (|ofCategory| *6 (|RetractableTo| *4)) #2# #3# #5# #9# (|ofType| *7 #7#) #8#))) +((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 29 T ELT))) +(((|FramedNonAssociativeAlgebraFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|FramedNonAssociativeAlgebra| |#2|) #1=(|CommutativeRing|) (|FramedNonAssociativeAlgebra| |#4|) #1#) (T |FramedNonAssociativeAlgebraFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|FramedNonAssociativeAlgebra| *6)) (|isDomain| *1 (|FramedNonAssociativeAlgebraFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|FramedNonAssociativeAlgebra| *5))))) +((|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")) 48 (|has| |#1| . #6=((|IntegralDomain|))) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) #7=(|Vector| $)) 89 T ELT) (((|Vector| (|Matrix| |#1|))) 115 T ELT)) (|someBasis| ((#7#) 92 T ELT)) (|sample| (#8=($) 23 T CONST)) (|rightUnits| (#9=((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) 51 (|has| |#1| . #6#) ELT)) (|rightUnit| (#3# 49 (|has| |#1| . #6#) ELT)) (|rightTraceMatrix| (((|Matrix| |#1|) . #10=(#7#)) 76 T ELT) (((|Matrix| |#1|)) 107 T ELT)) (|rightTrace| ((|#1| . #11=($)) 85 T ELT)) (|rightRegularRepresentation| (((|Matrix| |#1|) . #12=($ #7#)) 87 T ELT) (((|Matrix| |#1|) $) 105 T ELT)) (|rightRecip| (#13=(#4# $) 56 (|has| |#1| . #6#) ELT)) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 103 (|has| |#1| (|Field|)) ELT)) (|rightPower| (#14=($ $ (|PositiveInteger|)) 37 T ELT)) (|rightNorm| ((|#1| . #11#) 83 T ELT)) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15=($)) 53 (|has| |#1| . #6#) ELT)) (|rightDiscriminant| ((|#1| . #16=(#7#)) 78 T ELT) ((|#1|) 109 T ELT)) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 74 T ELT)) (|rightAlternative?| (#17=((|Boolean|)) 68 T ELT)) (|represents| (($ (|Vector| |#1|) #7#) 80 T ELT) (($ (|Vector| |#1|)) 113 T ELT)) (|recip| (#13# 58 (|has| |#1| . #6#) ELT)) (|rank| (((|PositiveInteger|)) 91 T ELT)) (|powerAssociative?| (#17# 65 T ELT)) (|plenaryPower| (($ $ (|PositiveInteger|)) 44 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|noncommutativeJordanAlgebra?| (#17# 61 T ELT)) (|lieAlgebra?| (#17# 59 T ELT)) (|lieAdmissible?| (#17# 63 T ELT)) (|leftUnits| (#9# 52 (|has| |#1| . #6#) ELT)) (|leftUnit| (#3# 50 (|has| |#1| . #6#) ELT)) (|leftTraceMatrix| (((|Matrix| |#1|) . #10#) 77 T ELT) (((|Matrix| |#1|)) 108 T ELT)) (|leftTrace| ((|#1| . #11#) 86 T ELT)) (|leftRegularRepresentation| (((|Matrix| |#1|) . #12#) 88 T ELT) (((|Matrix| |#1|) $) 106 T ELT)) (|leftRecip| (#13# 57 (|has| |#1| . #6#) ELT)) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) 104 (|has| |#1| (|Field|)) ELT)) (|leftPower| (#14# 38 T ELT)) (|leftNorm| ((|#1| . #11#) 84 T ELT)) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 54 (|has| |#1| . #6#) ELT)) (|leftDiscriminant| ((|#1| . #16#) 79 T ELT) ((|#1|) 110 T ELT)) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) . #15#) 75 T ELT)) (|leftAlternative?| (#17# 69 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|jordanAlgebra?| (#17# 60 T ELT)) (|jordanAdmissible?| (#17# 62 T ELT)) (|jacobiIdentity?| (#17# 64 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|flexible?| (#17# 67 T ELT)) (|elt| ((|#1| $ (|Integer|)) 119 T ELT)) (|coordinates| (((|Vector| |#1|) $ #7#) 82 T ELT) (((|Matrix| |#1|) #7# #7#) 81 T ELT) (((|Vector| |#1|) $) 117 T ELT) (((|Matrix| |#1|) (|Vector| $)) 116 T ELT)) (|convert| (((|Vector| |#1|) $) 112 T ELT) (($ (|Vector| |#1|)) 111 T ELT)) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) #7#) 90 T ELT) (((|List| (|Polynomial| |#1|))) 114 T ELT)) (|commutator| (#18=($ $ $) 34 T ELT)) (|commutative?| (#17# 73 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|basis| (((|Vector| $)) 118 T ELT)) (|associatorDependence| (((|List| (|Vector| |#1|))) 55 (|has| |#1| . #6#) ELT)) (|associator| (($ $ $ $) 35 T ELT)) (|associative?| (#17# 71 T ELT)) (|apply| (($ (|Matrix| |#1|) $) 102 T ELT)) (|antiCommutator| (#18# 33 T ELT)) (|antiCommutative?| (#17# 72 T ELT)) (|antiAssociative?| (#17# 70 T ELT)) (|alternative?| (#17# 66 T ELT)) (|Zero| (#8# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (#14# 39 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #19=($)) 30 T ELT) (($ $ $) 36 T ELT) (($ $ |#1|) 46 T ELT) (($ |#1| . #19#) 45 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)) +((|refine| ((#1=(|Factored| |#1|) #1# (|Mapping| #1# |#1|)) 28 T ELT)) (|mergeFactors| ((#1# #1# #1#) 17 T ELT))) +(((|FactoredFunctionUtilities| |#1|) (CATEGORY |package| (SIGNATURE |refine| (#1=(|Factored| |#1|) #1# (|Mapping| #1# |#1|))) (SIGNATURE |mergeFactors| (#1# #1# #1#))) (|IntegralDomain|)) (T |FactoredFunctionUtilities|)) +((|mergeFactors| (*1 *2 *2 *2) (AND (|isDomain| *2 (|Factored| *3)) (|ofCategory| *3 #1=(|IntegralDomain|)) (|isDomain| *1 (|FactoredFunctionUtilities| *3)))) (|refine| (*1 *2 *2 *3) (AND (|isDomain| *3 (|Mapping| #2=(|Factored| *4) *4)) (|ofCategory| *4 #1#) (|isDomain| *2 #2#) (|isDomain| *1 (|FactoredFunctionUtilities| *4))))) +((|variables| ((#1=(|List| #2=(|Symbol|)) $) 81 T ELT)) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ #3=(|Kernel| $)) 313 T ELT)) (|subst| #4=(($ $ #5=(|Equation| $)) NIL T ELT) #6=(($ $ (|List| #5#)) NIL T ELT) (#7=($ $ #8=(|List| #3#) #9=(|List| $)) 277 T ELT)) (|retractIfCan| (#10=((|Union| #3# 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(ATTRIBUTE (|Ring|)) (ATTRIBUTE (|RetractableTo| (|Polynomial| |t#1|))) (ATTRIBUTE (|PartialDifferentialRing| (|Symbol|))) (ATTRIBUTE (|FullyLinearlyExplicitRingOver| |t#1|)) (SIGNATURE |coerce| ($ (|SparseMultivariatePolynomial| |t#1| (|Kernel| $)))) (SIGNATURE |numer| ((|SparseMultivariatePolynomial| |t#1| (|Kernel| $)) $)) (SIGNATURE |numerator| ($ $)) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|))) (SIGNATURE |isExpt| ((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|))) (SIGNATURE |isPower| ((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $)) (SIGNATURE |eval| ($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $)))) (SIGNATURE |eval| ($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $))))) (SIGNATURE |eval| ($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $)))) (SIGNATURE |eval| ($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)))) |%noBranch|) (IF (|has| |t#1| (|CharacteristicZero|)) (ATTRIBUTE (|CharacteristicZero|)) |%noBranch|) (IF (|has| |t#1| (|CharacteristicNonZero|)) (ATTRIBUTE (|CharacteristicNonZero|)) |%noBranch|) (IF (|has| |t#1| (|CommutativeRing|)) (ATTRIBUTE (|Algebra| |t#1|)) |%noBranch|) (IF (|has| |t#1| (|IntegralDomain|)) (PROGN (ATTRIBUTE (|Field|)) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Polynomial| |t#1|)))) (SIGNATURE |convert| ($ (|Factored| $))) (SIGNATURE |denom| ((|SparseMultivariatePolynomial| |t#1| (|Kernel| $)) $)) (SIGNATURE |denominator| ($ $)) (SIGNATURE / ($ (|SparseMultivariatePolynomial| |t#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |t#1| (|Kernel| $)))) (SIGNATURE |coerce| ($ (|Fraction| |t#1|))) (SIGNATURE |coerce| ($ (|Polynomial| (|Fraction| |t#1|)))) (SIGNATURE |coerce| ($ (|Fraction| (|Polynomial| (|Fraction| |t#1|))))) (SIGNATURE |univariate| ((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $))) (IF (|has| |t#1| (|RetractableTo| (|Integer|))) (ATTRIBUTE (|RetractableTo| (|Fraction| (|Integer|)))) |%noBranch|)) |%noBranch|))) +(((|AbelianGroup|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianGroup|))) ((|AbelianMonoid|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianSemiGroup|)) (|has| |#1| (|AbelianGroup|))) ((|AbelianSemiGroup|) OR (|has| |#1| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianSemiGroup|)) (|has| |#1| (|AbelianGroup|))) ((|Algebra| #1=(|Fraction| (|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| (|Ring|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|)) (|has| |#1| (|AbelianGroup|))) ((|CharacteristicNonZero|) |has| |#1| (|CharacteristicNonZero|)) ((|CharacteristicZero|) |has| |#1| (|CharacteristicZero|)) ((|CoercibleFrom| #1#) OR (|has| |#1| (|RetractableTo| (|Fraction| (|Integer|)))) (|has| |#1| (|IntegralDomain|))) ((|CoercibleFrom| #2=(|Fraction| (|Polynomial| |#1|))) |has| |#1| (|IntegralDomain|)) ((|CoercibleFrom| (|Integer|)) OR (|has| |#1| (|Ring|)) (|has| |#1| (|RetractableTo| (|Integer|))) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|)) (|has| |#1| (|CharacteristicZero|)) (|has| |#1| (|CharacteristicNonZero|))) ((|CoercibleFrom| #3=(|Kernel| $)) . 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|))) +((|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))))) +((|localAbs| ((|#2| |#2|) 182 T ELT)) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| #1=(|String|)) (|:| |prob| #1#)))) |#2| (|Boolean|)) 60 T ELT))) +(((|FunctionSpaceToExponentialExpansion| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |exprToXXP| ((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| #1=(|String|)) (|:| |prob| #1#)))) |#2| (|Boolean|))) (SIGNATURE |localAbs| (|#2| |#2|))) (|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|)) (|Symbol|) |#2|) (T |FunctionSpaceToExponentialExpansion|)) +((|localAbs| (*1 *2 *2) (AND (|ofCategory| *3 #1=(|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#))) (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *3 *2 *4 *5)) (|ofCategory| *2 (|Join| #3=(|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| *3))) (|ofType| *4 #5=(|Symbol|)) (|ofType| *5 *2))) (|exprToXXP| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *5 #1#) (|isDomain| *2 (|Union| (|:| |%expansion| (|ExponentialExpansion| *5 *3 *6 *7)) (|:| |%problem| (|Record| (|:| |func| #6=(|String|)) (|:| |prob| #6#))))) (|isDomain| *1 (|FunctionSpaceToExponentialExpansion| *5 *3 *6 *7)) (|ofCategory| *3 (|Join| #3# #4# (|FunctionSpace| *5))) (|ofType| *6 #5#) (|ofType| *7 *3)))) +((|localAbs| ((|#2| |#2|) 105 T ELT)) (|exprToUPS| (#1=((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| #2=(|String|)) (|:| |prob| #2#)))) |#2| (|Boolean|) #2#) 52 T ELT)) (|exprToGenUPS| (#1# 169 T ELT))) +(((|FunctionSpaceToUnivariatePowerSeries| |#1| |#2| |#3| |#4| |#5| |#6|) (CATEGORY |package| (SIGNATURE |exprToUPS| #1=((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| #2=(|String|)) (|:| |prob| #2#)))) |#2| (|Boolean|) #2#)) (SIGNATURE |exprToGenUPS| #1#) (SIGNATURE |localAbs| (|#2| |#2|))) (|Join| (|GcdDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#)) (|Join| (|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#3|)))) (|OrderedRing|) (|Join| (|UnivariatePowerSeriesCategory| |#2| |#3|) (|Field|) #4# (CATEGORY |domain| (SIGNATURE |differentiate| #5=($ $)) (SIGNATURE |integrate| #5#))) (|PartialTranscendentalFunctions| |#4|) (|Symbol|)) (T |FunctionSpaceToUnivariatePowerSeries|)) +((|localAbs| (*1 *2 *2) (AND (|ofCategory| *3 #1=(|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#))) (|ofCategory| *2 (|Join| #3=(|AlgebraicallyClosedField|) #4=(|TranscendentalFunctionCategory|) (|FunctionSpace| *3) (CATEGORY |domain| (SIGNATURE |coerce| ($ *4))))) (|ofCategory| *4 #5=(|OrderedRing|)) (|ofCategory| *5 (|Join| (|UnivariatePowerSeriesCategory| *2 *4) #6=(|Field|) #4# #7=(CATEGORY |domain| (SIGNATURE |differentiate| #8=($ $)) (SIGNATURE |integrate| #8#)))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *3 *2 *4 *5 *6 *7)) (|ofCategory| *6 (|PartialTranscendentalFunctions| *5)) (|ofType| *7 #9=(|Symbol|)))) (|exprToGenUPS| #10=(*1 *2 *3 *4 *5) #11=(AND (|isDomain| *4 (|Boolean|)) (|ofCategory| *6 #1#) (|ofCategory| *3 (|Join| #3# #4# (|FunctionSpace| *6) (CATEGORY |domain| (SIGNATURE |coerce| ($ *7))))) (|ofCategory| *7 #5#) (|ofCategory| *8 (|Join| (|UnivariatePowerSeriesCategory| *3 *7) #6# #4# #7#)) (|isDomain| *2 (|Union| (|:| |%series| *8) (|:| |%problem| (|Record| (|:| |func| #12=(|String|)) (|:| |prob| #12#))))) (|isDomain| *1 (|FunctionSpaceToUnivariatePowerSeries| *6 *3 *7 *8 *9 *10)) (|isDomain| *5 #12#) (|ofCategory| *9 (|PartialTranscendentalFunctions| *8)) (|ofType| *10 #9#))) (|exprToUPS| #10# #11#)) +((|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# 66 T ELT)) (|part?| (#4# 15 T ELT)) (|min| (#9=(|#2| $) 77 T ELT)) (|max| (#9# 75 T ELT)) (|lookup| ((#10=(|PositiveInteger|) $) 70 T ELT)) (|intersect| (#3# 42 T ELT)) (|index| (($ #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|)) 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$ $) NIL T ELT)) (|scalarTypeOf| ((#3=(|Union| (|:| |fst| #4=(|FortranScalarType|)) (|:| |void| "void")) $) 11 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|fortranReal| (#5=($) 35 T ELT)) (|fortranLogical| (#5# 41 T ELT)) (|fortranInteger| (#5# 37 T ELT)) (|fortranDoubleComplex| (#5# 39 T ELT)) (|fortranDouble| (#5# 36 T ELT)) (|fortranComplex| (#5# 38 T ELT)) (|fortranCharacter| (#5# 40 T ELT)) (|external?| ((#2# $) 8 T ELT)) (|dimensionsOf| ((#6=(|List| (|Polynomial| (|Integer|))) $) 19 T ELT)) (|construct| (($ #3# (|List| (|Symbol|)) #2#) 29 T ELT) (($ #3# #6# #2#) 30 T ELT)) (|coerce| (((|OutputForm|) $) 24 T ELT) (($ #4#) 32 T ELT)) (|before?| #1#) (= #1#)) +(((|FortranType|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |coerce| ($ #1=(|FortranScalarType|))) (SIGNATURE |scalarTypeOf| (#2=(|Union| (|:| |fst| #1#) (|:| |void| "void")) $)) (SIGNATURE |dimensionsOf| (#3=(|List| (|Polynomial| (|Integer|))) $)) (SIGNATURE |external?| 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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|))))) +((|useSingleFactorBound?| (#1=(#2=(|Boolean|)) 18 T ELT)) (|useSingleFactorBound| (#3=(#2# #2#) 19 T ELT)) (|useEisensteinCriterion?| (#1# 14 T ELT)) (|useEisensteinCriterion| (#3# 15 T ELT)) (|tryFunctionalDecomposition?| (#1# 16 T ELT)) (|tryFunctionalDecomposition| (#3# 17 T ELT)) (|stopMusserTrials| (#4=(#5=(|PositiveInteger|) #5#) 22 T ELT) (#6=(#5#) 21 T ELT)) (|numberOfFactors| ((#7=(|NonNegativeInteger|) #8=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #9=(|Integer|))))) 52 T ELT)) (|musserTrials| (#4# 24 T ELT) (#6# 23 T ELT)) (|modularFactor| (((|Record| (|:| |prime| #9#) (|:| |factors| (|List| |#1|))) |#1|) 94 T ELT)) (|makeFR| ((#10=(|Factored| |#1|) #11=(|Record| (|:| |contp| #9#) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #9#)))))) 176 T ELT)) (|henselFact| ((#11# |#1| #2#) 209 T ELT)) (|factorSquareFree| (#12=(#10# |#1| #7# #7#) 224 T ELT) (#13=(#10# |#1| #14=(|List| #7#) #7#) 221 T ELT) (#15=(#10# |#1| #14#) 223 T ELT) (#16=(#10# |#1| #7#) 222 T ELT) (#17=(#10# |#1|) 220 T ELT)) (|factorOfDegree| ((#18=(|Union| |#1| "failed") #5# |#1| #14# #7# #2#) 226 T ELT) ((#18# #5# |#1| #14# #7#) 227 T ELT) ((#18# #5# |#1| #14#) 229 T ELT) ((#18# #5# |#1| #7#) 228 T ELT) ((#18# #5# |#1|) 230 T ELT)) (|factor| (#12# 219 T ELT) (#13# 215 T ELT) (#15# 217 T ELT) (#16# 216 T ELT) (#17# 214 T ELT)) (|eisensteinIrreducible?| ((#2# |#1|) 43 T ELT)) (|degreePartition| (((|Multiset| #7#) #8#) 99 T ELT)) (|btwFact| ((#11# |#1| #2# (|Set| #7#) #7#) 213 T ELT))) +(((|GaloisGroupFactorizer| |#1|) (CATEGORY |package| (SIGNATURE |makeFR| (#1=(|Factored| |#1|) #2=(|Record| (|:| |contp| #3=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| #3#))))))) (SIGNATURE |degreePartition| ((|Multiset| #4=(|NonNegativeInteger|)) #5=(|List| (|Record| (|:| |factor| |#1|) (|:| |degree| #3#))))) (SIGNATURE |musserTrials| #6=(#7=(|PositiveInteger|))) (SIGNATURE |musserTrials| #8=(#7# #7#)) (SIGNATURE |stopMusserTrials| #6#) (SIGNATURE |stopMusserTrials| #8#) (SIGNATURE |numberOfFactors| (#4# #5#)) (SIGNATURE |modularFactor| ((|Record| (|:| |prime| #3#) (|:| |factors| (|List| |#1|))) |#1|)) (SIGNATURE |useSingleFactorBound?| #9=(#10=(|Boolean|))) (SIGNATURE |useSingleFactorBound| #11=(#10# #10#)) (SIGNATURE |useEisensteinCriterion?| #9#) (SIGNATURE |useEisensteinCriterion| #11#) (SIGNATURE |eisensteinIrreducible?| (#10# |#1|)) (SIGNATURE |tryFunctionalDecomposition?| #9#) (SIGNATURE |tryFunctionalDecomposition| #11#) (SIGNATURE 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#5=(|:| |contp| #6=(|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| *3) #7=(|:| |pow| #6#)))))) #8=(|isDomain| *1 (|GaloisGroupFactorizer| *3)) #9=(|ofCategory| *3 #10=(|UnivariatePolynomialCategory| #6#)))) (|henselFact| #11=(*1 *2 *3 *4) (AND #1# #4# #8# #9#)) (|factorOfDegree| (*1 *2 *3 *2 *4 *5 *6) (|partial| AND #12=(|isDomain| *3 #13=(|PositiveInteger|)) #14=(|isDomain| *4 (|List| #3#)) #15=(|isDomain| *5 #3#) (|isDomain| *6 #2#) #16=(|isDomain| *1 (|GaloisGroupFactorizer| *2)) #17=(|ofCategory| *2 #10#))) (|factorOfDegree| (*1 *2 *3 *2 *4 *5) (|partial| AND #12# #14# #15# #16# #17#)) (|factorOfDegree| #18=(*1 *2 *3 *2 *4) (|partial| AND #12# #14# #16# #17#)) (|factorOfDegree| #18# (|partial| AND #12# #19=(|isDomain| *4 #3#) #16# #17#)) (|factorOfDegree| (*1 *2 *3 *2) (|partial| AND #12# #16# #17#)) (|factorSquareFree| #20=(*1 *2 *3 *4 *4) #21=(AND #19# #22=(|isDomain| *2 (|Factored| *3)) #8# #9#)) (|factorSquareFree| #23=(*1 *2 *3 *4 *5) #24=(AND #14# #15# #22# #8# #9#)) (|factorSquareFree| #11# #25=(AND #14# #22# #8# #9#)) (|factorSquareFree| #11# #21#) (|factorSquareFree| #26=(*1 *2 *3) #27=(AND #22# #8# #9#)) (|factor| #20# #21#) (|factor| #23# #24#) (|factor| #11# #25#) (|factor| #11# #21#) (|factor| #26# #27#) (|tryFunctionalDecomposition| #28=(*1 *2 *2) #29=(AND (|isDomain| *2 #2#) #8# #9#)) (|tryFunctionalDecomposition?| #30=(*1 *2) #29#) (|eisensteinIrreducible?| #26# #29#) (|useEisensteinCriterion| #28# #29#) (|useEisensteinCriterion?| #30# #29#) (|useSingleFactorBound| #28# #29#) (|useSingleFactorBound?| #30# #29#) (|modularFactor| #26# (AND (|isDomain| *2 (|Record| (|:| |prime| #6#) (|:| |factors| (|List| *3)))) #8# #9#)) (|numberOfFactors| #26# (AND #31=(|isDomain| *3 (|List| (|Record| (|:| |factor| *4) (|:| |degree| #6#)))) #32=(|ofCategory| *4 #10#) (|isDomain| *2 #3#) #33=(|isDomain| *1 (|GaloisGroupFactorizer| *4)))) (|stopMusserTrials| #28# #34=(AND (|isDomain| *2 #13#) #8# #9#)) (|stopMusserTrials| #30# #34#) (|musserTrials| #28# #34#) (|musserTrials| #30# #34#) (|degreePartition| #26# (AND #31# #32# (|isDomain| *2 (|Multiset| #3#)) #33#)) (|makeFR| #26# (AND (|isDomain| *3 (|Record| #5# (|:| |factors| (|List| (|Record| (|:| |irr| *4) #7#))))) #32# (|isDomain| *2 (|Factored| *4)) #33#))) +((|singleFactorBound| (#1=(#2=(|Integer|) |#2|) 52 T ELT) ((#2# |#2| (|NonNegativeInteger|)) 51 T ELT)) (|rootBound| (#1# 64 T ELT)) (|quadraticNorm| (#3=(|#3| |#2|) 26 T ELT)) (|norm| (#4=(|#3| |#2| (|PositiveInteger|)) 15 T ELT)) (|length| (#3# 16 T ELT)) (|infinityNorm| (#3# 9 T ELT)) (|height| (#3# 10 T ELT)) (|bombieriNorm| (#4# 71 T ELT) (#3# 34 T ELT)) (|beauzamyBound| (#1# 66 T ELT))) +(((|GaloisGroupFactorizationUtilities| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |beauzamyBound| #1=(#2=(|Integer|) |#2|)) (SIGNATURE |bombieriNorm| #3=(|#3| |#2|)) (SIGNATURE |bombieriNorm| #4=(|#3| |#2| (|PositiveInteger|))) (SIGNATURE |rootBound| #1#) (SIGNATURE |singleFactorBound| (#2# |#2| (|NonNegativeInteger|))) (SIGNATURE 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(|GaloisGroupFactorizationUtilities| *5 *3 *2)) #15=(|ofCategory| *3 (|UnivariatePolynomialCategory| *5)))) (|singleFactorBound| #1# #16=(AND #3# #17=(|isDomain| *2 (|Integer|)) (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *4 *3 *5)) #10# (|ofCategory| *5 #5#))) (|singleFactorBound| #11# (AND (|isDomain| *4 (|NonNegativeInteger|)) #13# #17# (|isDomain| *1 (|GaloisGroupFactorizationUtilities| *5 *3 *6)) #15# (|ofCategory| *6 #14#))) (|rootBound| #1# #16#) (|bombieriNorm| #11# #12#) (|bombieriNorm| #1# #2#) (|beauzamyBound| #1# #16#)) +((|unvectorise| ((|#2| (|Vector| |#1|)) 42 T ELT)) (|shiftRoots| (#1=(|#2| |#2| |#1|) 58 T ELT)) (|scaleRoots| (#1# 49 T ELT)) (|reverse| ((|#2| |#2|) 44 T ELT)) (|monic?| (((|Boolean|) |#2|) 32 T ELT)) (|factorsOfDegree| (((|List| |#2|) #2=(|PositiveInteger|) #3=(|Factored| |#2|)) 21 T ELT)) (|factorOfDegree| ((|#2| #2# #3#) 25 T ELT)) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) #3#) 29 T ELT))) +(((|GaloisGroupPolynomialUtilities| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monic?| ((|Boolean|) |#2|)) (SIGNATURE |unvectorise| (|#2| (|Vector| |#1|))) (SIGNATURE |reverse| (|#2| |#2|)) (SIGNATURE |scaleRoots| #1=(|#2| |#2| |#1|)) (SIGNATURE |shiftRoots| #1#) (SIGNATURE |degreePartition| ((|Multiset| (|NonNegativeInteger|)) #2=(|Factored| |#2|))) (SIGNATURE |factorOfDegree| (|#2| #3=(|PositiveInteger|) #2#)) (SIGNATURE |factorsOfDegree| ((|List| |#2|) #3# #2#))) (|Ring|) (|UnivariatePolynomialCategory| |#1|)) (T |GaloisGroupPolynomialUtilities|)) +((|factorsOfDegree| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|PositiveInteger|)) (|isDomain| *4 (|Factored| *6)) (|ofCategory| *6 #3=(|UnivariatePolynomialCategory| *5)) #4=(|ofCategory| *5 #5=(|Ring|)) (|isDomain| *2 (|List| *6)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *6)))) (|factorOfDegree| #1# (AND #2# (|isDomain| *4 (|Factored| *2)) (|ofCategory| *2 #3#) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *5 *2)) #4#)) (|degreePartition| #6=(*1 *2 *3) (AND (|isDomain| *3 (|Factored| *5)) (|ofCategory| *5 #7=(|UnivariatePolynomialCategory| *4)) #8=(|ofCategory| *4 #5#) (|isDomain| *2 (|Multiset| (|NonNegativeInteger|))) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *5)))) (|shiftRoots| #9=(*1 *2 *2 *3) #10=(AND (|ofCategory| *3 #5#) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|scaleRoots| #9# #10#) (|reverse| (*1 *2 *2) #10#) (|unvectorise| #6# (AND (|isDomain| *3 (|Vector| *4)) #8# (|ofCategory| *2 #7#) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *2)))) (|monic?| #6# (AND #8# (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GaloisGroupPolynomialUtilities| *4 *3)) (|ofCategory| *3 #7#)))) +((|sizePascalTriangle| (#1=(#2=(|NonNegativeInteger|)) 59 T ELT)) (|safetyMargin| (#1# 29 #3=(|has| |#1| (|FloatingPointSystem|)) ELT) (#4=(#2# #2#) 28 #3# ELT)) (|safeFloor| (#5=(#6=(|Integer|) |#1|) 25 #3# ELT)) (|safeCeiling| (#5# 27 #3# ELT)) (|rangePascalTriangle| (#1# 58 T ELT) (#4# 57 T ELT)) (|pascalTriangle| ((|#1| #2# #6#) 37 T ELT)) (|fillPascalTriangle| (((|Void|)) 61 T ELT))) +(((|GaloisGroupUtilities| |#1|) (CATEGORY |package| (SIGNATURE |pascalTriangle| (|#1| #1=(|NonNegativeInteger|) #2=(|Integer|))) (SIGNATURE |rangePascalTriangle| #3=(#1# #1#)) (SIGNATURE |rangePascalTriangle| #4=(#1#)) (SIGNATURE |sizePascalTriangle| #4#) (SIGNATURE |fillPascalTriangle| ((|Void|))) (IF (|has| |#1| (|FloatingPointSystem|)) (PROGN (SIGNATURE |safeCeiling| #5=(#2# |#1|)) (SIGNATURE |safeFloor| #5#) (SIGNATURE |safetyMargin| #3#) (SIGNATURE |safetyMargin| #4#)) |%noBranch|)) (|Ring|)) (T |GaloisGroupUtilities|)) +((|safetyMargin| #1=(*1 *2) #2=(AND #3=(|isDomain| *2 #4=(|NonNegativeInteger|)) #5=(|isDomain| *1 (|GaloisGroupUtilities| *3)) #6=(|ofCategory| *3 (|FloatingPointSystem|)) #7=(|ofCategory| *3 #8=(|Ring|)))) (|safetyMargin| #9=(*1 *2 *2) #2#) (|safeFloor| #10=(*1 *2 *3) #11=(AND (|isDomain| *2 #12=(|Integer|)) #5# #6# #7#)) (|safeCeiling| #10# #11#) (|fillPascalTriangle| #1# (AND (|isDomain| *2 (|Void|)) #5# #7#)) (|sizePascalTriangle| #1# #13=(AND #3# #5# #7#)) (|rangePascalTriangle| #1# #13#) (|rangePascalTriangle| #9# #13#) (|pascalTriangle| (*1 *2 *3 *4) (AND (|isDomain| *3 #4#) (|isDomain| *4 #12#) (|isDomain| *1 (|GaloisGroupUtilities| *2)) (|ofCategory| *2 #8#)))) +((|sumSquares| (((|List| #1=(|Integer|)) #1#) 76 T ELT)) (|prime?| (((|Boolean|) #2=(|Complex| #1#)) 84 T ELT)) (|factor| (((|Factored| #2#) #2#) 75 T ELT))) +(((|GaussianFactorizationPackage|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| #1=(|Complex| #2=(|Integer|))) #1#)) (SIGNATURE |sumSquares| ((|List| #2#) #2#)) (SIGNATURE |prime?| ((|Boolean|) #1#)))) (T |GaussianFactorizationPackage|)) +((|prime?| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Complex| #4=(|Integer|))) (|isDomain| *2 (|Boolean|)) #5=(|isDomain| *1 (|GaussianFactorizationPackage|)))) (|sumSquares| #1# (AND (|isDomain| *2 (|List| #4#)) #5# (|isDomain| *3 #4#))) (|factor| #1# (AND (|isDomain| *2 (|Factored| #3#)) #5# #2#))) +((|normalForm| ((|#4| |#4| #1=(|List| |#4|)) 20 (|has| |#1| (|Field|)) ELT)) (|groebner| ((#1# #1# #2=(|String|) #2#) 46 T ELT) ((#1# #1# #2#) 45 T ELT) ((#1# #1#) 34 T ELT))) +(((|GroebnerPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |groebner| (#1=(|List| |#4|) #1#)) (SIGNATURE |groebner| (#1# #1# #2=(|String|))) (SIGNATURE |groebner| (#1# #1# #2# #2#)) (IF (|has| |#1| (|Field|)) (SIGNATURE |normalForm| (|#4| |#4| #1#)) |%noBranch|)) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |GroebnerPackage|)) +((|normalForm| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #2=(|PolynomialCategory| *4 *5 *6)) (|ofCategory| *4 (|Field|)) #3=(|ofCategory| *4 #4=(|GcdDomain|)) #5=(|ofCategory| *5 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *6 #8=(|OrderedSet|)) (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *2)))) (|groebner| (*1 *2 *2 *3 *3) #9=(AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 #2#) #3# #5# #7# (|isDomain| *1 (|GroebnerPackage| *4 *5 *6 *7)))) (|groebner| #1# #9#) (|groebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|isDomain| *1 (|GroebnerPackage| *3 *4 *5 *6))))) +((|euclideanNormalForm| ((|#4| |#4| #1=(|List| |#4|)) 82 T ELT)) (|euclideanGroebner| ((#1# #1# #2=(|String|) #2#) 22 T ELT) ((#1# #1# #2#) 21 T ELT) ((#1# #1#) 13 T ELT))) +(((|EuclideanGroebnerBasisPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |euclideanNormalForm| (|#4| |#4| #1=(|List| |#4|))) (SIGNATURE |euclideanGroebner| (#1# #1#)) (SIGNATURE |euclideanGroebner| (#1# #1# #2=(|String|))) (SIGNATURE |euclideanGroebner| (#1# #1# #2# #2#))) (|EuclideanDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialCategory| |#1| |#2| |#3|)) (T |EuclideanGroebnerBasisPackage|)) +((|euclideanGroebner| (*1 *2 *2 *3 *3) #1=(AND (|isDomain| *2 (|List| *7)) (|isDomain| *3 (|String|)) (|ofCategory| *7 #2=(|PolynomialCategory| *4 *5 *6)) #3=(|ofCategory| *4 #4=(|EuclideanDomain|)) #5=(|ofCategory| *5 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *6 #8=(|OrderedSet|)) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *7)))) (|euclideanGroebner| #9=(*1 *2 *2 *3) #1#) (|euclideanGroebner| (*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) (|ofCategory| *6 (|PolynomialCategory| *3 *4 *5)) (|ofCategory| *3 #4#) (|ofCategory| *4 #6#) (|ofCategory| *5 #8#) (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *3 *4 *5 *6)))) (|euclideanNormalForm| #9# (AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #2#) #3# #5# #7# (|isDomain| *1 (|EuclideanGroebnerBasisPackage| *4 *5 *6 *2))))) +((|groebnerFactorize| (#1=(#2=(|List| #3=(|List| |#4|)) #3# #4=(|Boolean|)) 90 T ELT) (#5=(#2# #3#) 89 T ELT) ((#2# #3# #3# #4#) 83 T ELT) ((#2# #3# #3#) 84 T ELT)) (|factorGroebnerBasis| (#1# 56 T ELT) (#5# 78 T ELT))) 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(|ofCategory| *4 #3#) (|ofCategory| *5 #4#) (|ofCategory| *6 #5#) (|ofCategory| *7 (|PolynomialCategory| *4 *5 *6)) (|isDomain| *2 (|List| #9=(|List| *7))) (|isDomain| *1 (|GroebnerFactorizationPackage| *4 *5 *6 *7)) (|isDomain| *3 #9#))) (|groebnerFactorize| (*1 *2 *3 *3 *4) #2#) (|groebnerFactorize| (*1 *2 *3 *3) #8#) (|factorGroebnerBasis| #1# #2#) (|factorGroebnerBasis| #7# #8#)) +((|virtualDegree| ((#1=(|NonNegativeInteger|) |#4|) 12 T ELT)) (|updatF| ((#2=(|List| #3=(|Record| #4=(|:| |totdeg| #1#) (|:| |pol| |#4|))) |#4| #1# #2#) 39 T ELT)) (|updatD| ((#5=(|List| #6=(|Record| (|:| |lcmfij| |#2|) #4# (|:| |poli| |#4|) (|:| |polj| |#4|))) #5# #5#) 49 T ELT)) (|sPol| ((|#4| #6#) 52 T ELT)) (|redPol| (#7=(|#4| |#4| #8=(|List| |#4|)) 54 T ELT)) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| #8#) 96 T ELT)) (|prinshINFO| ((#9=(|Void|) |#4|) 59 T ELT)) (|prinpolINFO| ((#9# #8#) 69 T ELT)) (|prindINFO| ((#10=(|Integer|) #6# |#4| |#4| #10# #10# #10#) 66 T ELT)) (|prinb| ((#9# #10#) 110 T ELT)) (|minGbasis| ((#8# #8#) 104 T ELT)) (|makeCrit| ((#6# #3# |#4| #1#) 31 T ELT)) (|lepol| ((#10# |#4|) 109 T ELT)) (|hMonic| ((|#4| |#4|) 37 T ELT)) (|gbasis| ((#8# #8# #10# #10#) 74 T ELT)) (|fprindINFO| ((#10# #6# |#4| |#4| #10# #10# #10# #10#) 123 T ELT)) (|critpOrder| ((#11=(|Boolean|) #6# #6#) 20 T ELT)) (|critT| ((#11# #6#) 78 T ELT)) (|critMonD1| ((#5# |#2| #5#) 76 T ELT)) (|critMTonD1| ((#5# #5#) 47 T ELT)) (|critM| ((#11# |#2| |#2|) 75 T ELT)) (|critBonD| ((#5# |#4| #5#) 48 T ELT)) (|critB| ((#11# |#2| |#2| |#2| |#2|) 80 T ELT)) (|credPol| (#7# 97 T ELT))) +(((|GroebnerInternalPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |credPol| #1=(|#4| |#4| #2=(|List| |#4|))) (SIGNATURE |redPol| #1#) (SIGNATURE |gbasis| (#2# #2# #3=(|Integer|) #3#)) (SIGNATURE |critT| (#4=(|Boolean|) #5=(|Record| (|:| |lcmfij| |#2|) #6=(|:| |totdeg| #7=(|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) (SIGNATURE |critM| (#4# |#2| |#2|)) (SIGNATURE |critB| 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#2=(|ofCategory| *4 #3=(|GcdDomain|)) #4=(|ofCategory| *5 #5=(|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *6 #7=(|OrderedSet|)) (|isDomain| *2 #8=(|NonNegativeInteger|)) #9=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *3)) #10=(|ofCategory| *3 #11=(|PolynomialCategory| *4 *5 *6)))) (|makeCrit| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Record| #12=(|:| |totdeg| #8#) (|:| |pol| *4))) (|isDomain| *5 #8#) (|ofCategory| *4 (|PolynomialCategory| *6 *7 *8)) (|ofCategory| *6 #3#) (|ofCategory| *7 #5#) (|ofCategory| *8 #7#) (|isDomain| *2 (|Record| (|:| |lcmfij| *7) (|:| |totdeg| *5) #13=(|:| |poli| *4) #14=(|:| |polj| *4))) (|isDomain| *1 (|GroebnerInternalPackage| *6 *7 *8 *4)))) (|critpOrder| #15=(*1 *2 *3 *3) #16=(AND (|isDomain| *3 (|Record| #17=(|:| |lcmfij| *5) #12# (|:| |poli| *7) (|:| |polj| *7))) #4# #18=(|ofCategory| *7 #11#) #2# #6# #19=(|isDomain| *2 (|Boolean|)) #20=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *7)))) (|prinb| #1# (AND #21=(|isDomain| *3 #22=(|Integer|)) #2# #4# #6# #23=(|isDomain| *2 (|Void|)) #20# #18#)) (|prinpolINFO| #1# (AND (|isDomain| *3 #24=(|List| *7)) #18# #2# #4# #6# #23# #20#)) (|fprindINFO| (*1 *2 *3 *4 *4 *2 *2 *2 *2) #25=(AND #26=(|isDomain| *2 #22#) (|isDomain| *3 (|Record| (|:| |lcmfij| *6) #12# #13# #14#)) #27=(|ofCategory| *6 #5#) (|ofCategory| *4 #28=(|PolynomialCategory| *5 *6 *7)) #29=(|ofCategory| *5 #3#) #30=(|ofCategory| *7 #7#) (|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *4)))) (|prindINFO| (*1 *2 *3 *4 *4 *2 *2 *2) #25#) (|prinshINFO| #1# (AND #2# #4# #6# #23# #9# #10#)) (|lepol| #1# (AND #2# #4# #6# #26# #9# #10#)) (|minGbasis| #31=(*1 *2 *2) (AND (|isDomain| *2 (|List| *6)) #32=(|ofCategory| *6 #33=(|PolynomialCategory| *3 *4 *5)) #34=(|ofCategory| *3 #3#) #35=(|ofCategory| *4 #5#) #36=(|ofCategory| *5 #7#) #37=(|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *6)))) (|updatD| (*1 *2 *2 *2) #38=(AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *4) #12# #39=(|:| |poli| *6) #40=(|:| |polj| *6)))) #35# #32# #34# #36# #37#)) (|sPol| #1# (AND (|isDomain| *3 (|Record| #17# #12# (|:| |poli| *2) (|:| |polj| *2))) #4# #41=(|ofCategory| *2 #11#) #42=(|isDomain| *1 (|GroebnerInternalPackage| *4 *5 *6 *2)) #2# #6#)) (|updatF| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|List| (|Record| #12# (|:| |pol| *3)))) (|isDomain| *4 #8#) #43=(|ofCategory| *3 #28#) #29# #27# #30# #44=(|isDomain| *1 (|GroebnerInternalPackage| *5 *6 *7 *3)))) (|hMonic| #31# (AND #34# #35# #36# (|isDomain| *1 (|GroebnerInternalPackage| *3 *4 *5 *2)) (|ofCategory| *2 #33#))) (|redPo| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) #43# #29# #27# #30# (|isDomain| *2 (|Record| (|:| |poly| *3) (|:| |mult| *5))) #44#)) (|critMonD1| #45=(*1 *2 *3 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |lcmfij| *3) #12# #39# #40#))) #46=(|ofCategory| *3 #5#) #47=(|ofCategory| *6 (|PolynomialCategory| *4 *3 *5)) #2# #36# #48=(|isDomain| *1 (|GroebnerInternalPackage| *4 *3 *5 *6)))) (|critMTonD1| #31# #38#) (|critBonD| #45# (AND (|isDomain| *2 (|List| (|Record| #17# #12# (|:| |poli| *3) (|:| |polj| *3)))) #4# #10# #2# #6# #9#)) (|critB| (*1 *2 *3 *3 *3 *3) #49=(AND #2# #46# #36# #19# #48# #47#)) (|critM| #15# #49#) (|critT| #1# #16#) (|gbasis| (*1 *2 *2 *3 *3) (AND (|isDomain| *2 #24#) #21# #18# #2# #4# #6# #20#)) (|redPol| #50=(*1 *2 *2 *3) #51=(AND (|isDomain| *3 (|List| *2)) #41# #2# #4# #6# #42#)) (|credPol| #50# #51#)) +((|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| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (($ $ $) 60 T ELT) (($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) 58 T ELT)) (|gcd| (($ $ $) 62 T ELT) (($ (|List| $)) 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +(((|GcdDomain|) (|Category|)) (T |GcdDomain|)) +((|gcd| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|gcd| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|lcm| (*1 *1 *1 *1) (|ofCategory| *1 (|GcdDomain|))) (|lcm| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|GcdDomain|)))) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *1)) (|ofCategory| *1 (|GcdDomain|))))) +(|Join| (|IntegralDomain|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (SIGNATURE |gcd| ($ (|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)) +((~= #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| ((#4# $ $) 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#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 19 T ELT)) (|variables| ((#5=(|List| #6=(|OrderedVariableList| |#1|)) $) 88 T ELT)) (|univariate| ((#7=(|SparseUnivariatePolynomial| $) $ #6#) 53 T ELT) ((#8=(|SparseUnivariatePolynomial| |#2|) $) 140 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #9=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #10=(#11=($ $) NIL #9# ELT)) (|unit?| (#4# NIL #9# ELT)) (|totalDegree| (#12=(#13=(|NonNegativeInteger|) $) 28 T ELT) ((#13# $ #5#) NIL T ELT)) (|subtractIfCan| (#14=(#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #17=(((|Factored| #7#) #7#) NIL #18=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #19=(#11# NIL #20=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#21=((|Factored| $) $) NIL #20# ELT)) (|solveLinearPolynomialEquation| (((|Union| #22=(|List| #7#) #16#) #22# #7#) NIL #18# ELT)) (|sample| (#23=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #24=(#16#)) $) 51 T ELT) (((|Union| #25=(|Fraction| #26=(|Integer|)) . #24#) . #27=($)) NIL #28=(|has| |#2| (|RetractableTo| #25#)) ELT) (((|Union| #26# . #24#) . #27#) NIL #29=(|has| |#2| (|RetractableTo| #26#)) ELT) (#30=((|Union| #6# . #24#) . #27#) NIL T ELT)) (|retract| (#31=(|#2| $) 49 T ELT) ((#25# . #32=($)) NIL #28# ELT) ((#26# . #32#) NIL #29# ELT) ((#6# . #32#) NIL T ELT)) (|resultant| (($ $ $ #6#) NIL #33=(|has| |#2| (|CommutativeRing|)) ELT)) (|reorder| (($ $ (|List| #26#)) 95 T ELT)) (|reductum| (#11# 81 T ELT)) (|reducedSystem| ((#34=(|Matrix| #26#) . #35=(#36=(|Matrix| $))) NIL #37=(|has| |#2| (|LinearlyExplicitRingOver| #26#)) ELT) ((#38=(|Record| (|:| |mat| #34#) (|:| |vec| (|Vector| #26#))) . #39=(#36# #40=(|Vector| $))) NIL #37# ELT) ((#41=(|Record| (|:| |mat| #42=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #39#) NIL T ELT) ((#42# . #35#) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|primitivePart| #19# #43=(#44=($ $ #6#) NIL #20# ELT)) (|primitiveMonomials| #45=((#46=(|List| $) $) NIL T ELT)) (|prime?| (#4# NIL #18# ELT)) (|pomopo!| (($ $ |#2| |#3| $) NIL T ELT)) (|patternMatch| ((#47=(|PatternMatchResult| #48=(|Float|) . #49=($)) $ #50=(|Pattern| #48#) #47#) NIL (AND (|has| #6# #51=(|PatternMatchable| #48#)) (|has| |#2| #51#)) ELT) ((#52=(|PatternMatchResult| #26# . #49#) $ #53=(|Pattern| #26#) #52#) NIL (AND (|has| #6# #54=(|PatternMatchable| #26#)) (|has| |#2| #54#)) ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|numberOfMonomials| (#12# 66 T ELT)) (|multivariate| (($ #8# #6#) 145 T ELT) (($ #7# #6#) 59 T ELT)) (|monomials| #45#) (|monomial?| (#4# 69 T ELT)) (|monomial| (($ |#2| |#3|) 36 T ELT) (#55=($ $ #6# #13#) 38 T ELT) #56=(($ $ #5# #57=(|List| #13#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #6#) NIL T ELT)) (|minimumDegree| (#58=(|#3| $) NIL T ELT) (#59=(#13# $ #6#) 57 T ELT) (#60=(#57# $ #5#) 64 T ELT)) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| (#30# 46 T ELT)) (|leftReducedSystem| ((#34# . #61=(#40#)) NIL #37# ELT) ((#38# . #62=(#40# $)) NIL #37# ELT) ((#41# . #62#) NIL T ELT) ((#42# . #61#) NIL T ELT)) (|leadingMonomial| #63=(#11# NIL T ELT)) (|leadingCoefficient| (#31# 48 T ELT)) (|lcm| #64=(($ #46#) NIL #20# ELT) (#65=($ $ $) NIL #20# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #66=(((|Union| #46# #16#) $) NIL T ELT)) (|isPlus| #66#) (|isExpt| (((|Union| (|Record| (|:| |var| #6#) (|:| |exponent| #13#)) #16#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#4# 47 T ELT)) (|ground| (#31# 138 T ELT)) (|gcdPolynomial| ((#7# #7# #7#) NIL #20# ELT)) (|gcd| #64# (#65# 151 #20# ELT)) (|factorSquareFreePolynomial| #17#) (|factorPolynomial| #17#) (|factor| (#21# NIL #18# ELT)) (|exquo| ((#15# $ |#2|) NIL #9# ELT) (#14# NIL #9# ELT)) (|eval| (($ $ (|List| #67=(|Equation| $))) NIL T ELT) (($ $ #67#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #46# #46#) NIL T ELT) (($ $ #6# |#2|) 102 T ELT) (($ $ #5# #68=(|List| |#2|)) 108 T ELT) (($ $ #6# $) 100 T ELT) (($ $ #5# #46#) 126 T ELT)) (|discriminant| (#44# NIL #33# ELT)) (|differentiate| #56# #69=(#55# NIL T ELT) #70=(($ $ #5#) NIL T ELT) (#44# 60 T ELT)) (|degree| (#58# 80 T ELT) (#59# 43 T ELT) (#60# 63 T ELT)) (|convert| ((#50# . #71=($)) NIL (AND (|has| #6# #72=(|ConvertibleTo| #50#)) (|has| |#2| #72#)) ELT) ((#53# . #71#) NIL (AND (|has| #6# #73=(|ConvertibleTo| #53#)) (|has| |#2| #73#)) ELT) ((#74=(|InputForm|) . #71#) NIL (AND (|has| #6# #75=(|ConvertibleTo| #74#)) (|has| |#2| #75#)) ELT)) (|content| (#31# 147 #20# ELT) #43#) (|conditionP| (((|Union| #40# #16#) #36#) NIL #76=(AND (|has| $ #77=(|CharacteristicNonZero|)) #18#) ELT)) (|coerce| (((|OutputForm|) $) 175 T ELT) (($ #26#) NIL T ELT) (($ |#2|) 101 T ELT) (($ #6#) 40 T ELT) (($ #25#) NIL (OR #78=(|has| |#2| (|Algebra| #25#)) #28#) ELT) #10#) (|coefficients| ((#68# $) NIL T ELT)) (|coefficient| ((|#2| $ |#3|) NIL T ELT) #69# #56#) (|charthRoot| (((|Maybe| $) $) NIL (OR #76# (|has| |#2| #77#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (($ $ $ #13#) NIL #33# ELT)) (|before?| #1#) (|associates?| (#2# NIL #9# ELT)) (|annihilate?| #1#) (|Zero| (#23# 24 T CONST)) (|One| (#23# 32 T CONST)) (D #56# #69# #70# (#44# NIL T ELT)) (= #1#) (/ (#79=($ $ |#2|) 77 (|has| |#2| (|Field|)) ELT)) (- #63# (#65# NIL T ELT)) (+ (#65# 133 T ELT)) (** (($ $ #80=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 131 T ELT)) (* (($ #80# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #26# . #81=($)) NIL T ELT) (#65# 37 T ELT) (($ $ #25#) NIL #78# ELT) (($ #25# . #81#) NIL #78# ELT) (($ |#2| . #81#) 76 T ELT) (#79# NIL T ELT))) +(((|GeneralDistributedMultivariatePolynomial| |#1| |#2| |#3|) (|Join| (|PolynomialCategory| |#2| |#3| (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|) (|DirectProductCategory| (|#| |#1|) (|NonNegativeInteger|))) (T |GeneralDistributedMultivariatePolynomial|)) +((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|ofType| *3 (|List| (|Symbol|))) (|isDomain| *1 (|GeneralDistributedMultivariatePolynomial| *3 *4 *5)) (|ofCategory| *4 (|Ring|)) (|ofCategory| *5 (|DirectProductCategory| (|#| *3) (|NonNegativeInteger|)))))) +((|testModulus| (((|Boolean|) |#1| #1=(|List| |#2|)) 90 T ELT)) (|tablePow| (((|Union| #2=(|Vector| #1#) #3="failed") #4=(|NonNegativeInteger|) |#1| #1#) 99 T ELT)) (|solveid| (((|Union| #1# #3#) |#2| |#1| #2#) 101 T ELT)) (|reduction| ((|#2| |#2| |#1|) 35 T ELT)) (|compBound| ((#4# |#2| #1#) 26 T ELT))) +(((|GenExEuclid| |#1| |#2|) (CATEGORY |package| (SIGNATURE |reduction| (|#2| |#2| |#1|)) (SIGNATURE |compBound| (#1=(|NonNegativeInteger|) |#2| #2=(|List| |#2|))) (SIGNATURE |tablePow| ((|Union| #3=(|Vector| #2#) #4="failed") #1# |#1| #2#)) (SIGNATURE |solveid| ((|Union| #2# #4#) |#2| |#1| #3#)) (SIGNATURE |testModulus| ((|Boolean|) |#1| #2#))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |GenExEuclid|)) +((|testModulus| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *5)) (|ofCategory| *5 #2=(|UnivariatePolynomialCategory| *3)) #3=(|ofCategory| *3 #4=(|EuclideanDomain|)) (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|GenExEuclid| *3 *5)))) (|solveid| #5=(*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 (|Vector| #6=(|List| *3))) #7=(|ofCategory| *4 #4#) (|isDomain| *2 #6#) (|isDomain| *1 (|GenExEuclid| *4 *3)) (|ofCategory| *3 #8=(|UnivariatePolynomialCategory| *4)))) (|tablePow| #5# (|partial| AND (|isDomain| *3 #9=(|NonNegativeInteger|)) #7# (|ofCategory| *6 #8#) (|isDomain| *2 (|Vector| #10=(|List| *6))) (|isDomain| *1 (|GenExEuclid| *4 *6)) (|isDomain| *5 #10#))) (|compBound| #1# (AND (|isDomain| *4 #6#) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #4#) (|isDomain| *2 #9#) (|isDomain| *1 (|GenExEuclid| *5 *3)))) (|reduction| (*1 *2 *2 *3) (AND #3# (|isDomain| *1 (|GenExEuclid| *3 *2)) (|ofCategory| *2 #2#)))) +((|factor| (((|Factored| |#5|) |#5|) 24 T ELT))) +(((|GeneralizedMultivariateFactorize| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#5|) |#5|))) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#)))) (|OrderedAbelianMonoidSup|) #2=(|IntegralDomain|) #2# (|PolynomialCategory| |#4| |#2| |#1|)) (T |GeneralizedMultivariateFactorize|)) +((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#))))) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #2=(|IntegralDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|GeneralizedMultivariateFactorize| *4 *5 *6 *7 *3)) (|ofCategory| *6 #2#) (|ofCategory| *3 (|PolynomialCategory| *7 *5 *4))))) +((|randomR| ((|#3|) 43 T ELT)) (|gcdPolynomial| ((#1=(|SparseUnivariatePolynomial| |#4|) #1# #1#) 34 T ELT))) +(((|GeneralPolynomialGcdPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcdPolynomial| (#1=(|SparseUnivariatePolynomial| |#4|) #1# #1#)) (SIGNATURE |randomR| (|#3|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|PolynomialFactorizationExplicit|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |GeneralPolynomialGcdPackage|)) +((|randomR| (*1 *2) (AND #1=(|ofCategory| *3 (|OrderedAbelianMonoidSup|)) #2=(|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *2 #3=(|PolynomialFactorizationExplicit|)) (|isDomain| *1 (|GeneralPolynomialGcdPackage| *3 *4 *2 *5)) (|ofCategory| *5 (|PolynomialCategory| *2 *3 *4)))) (|gcdPolynomial| (*1 *2 *2 *2) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *6 (|PolynomialCategory| *5 *3 *4)) #1# #2# (|ofCategory| *5 #3#) (|isDomain| *1 (|GeneralPolynomialGcdPackage| *3 *4 *5 *6))))) +((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#1|)) #1#) 43 T ELT))) +(((|GenUFactorize| |#1|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| #1=(|SparseUnivariatePolynomial| |#1|)) #1#))) (|EuclideanDomain|)) (T |GenUFactorize|)) +((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| #1=(|SparseUnivariatePolynomial| *4))) (|isDomain| *1 (|GenUFactorize| *4)) (|isDomain| *3 #1#)))) +((|taylor| ((#1=(|Any|) |#2| #2=(|Symbol|) #3=(|Equation| |#2|) #4=(|UniversalSegment| (|NonNegativeInteger|))) 44 T ELT) ((#1# #5=(|Mapping| |#2| #6=(|Integer|)) #3# #4#) 43 T ELT) (#7=(#1# |#2| #2# #3#) 36 T ELT) (#8=(#1# #5# #3#) 29 T ELT)) (|series| (#9=(#1# |#2| #2# #3# #10=(|UniversalSegment| #11=(|Fraction| #6#)) #11#) 88 T ELT) (#12=(#1# (|Mapping| |#2| #11#) #3# #10# #11#) 87 T ELT) (#13=(#1# |#2| #2# #3# #14=(|UniversalSegment| #6#)) 86 T ELT) (#15=(#1# #5# #3# #14#) 85 T ELT) (#7# 80 T ELT) (#8# 79 T ELT)) (|puiseux| (#9# 74 T ELT) (#12# 72 T ELT)) (|laurent| (#13# 51 T ELT) (#15# 50 T ELT))) +(((|GenerateUnivariatePowerSeries| |#1| |#2|) (CATEGORY |package| (SIGNATURE |taylor| #1=(#2=(|Any|) #3=(|Mapping| |#2| #4=(|Integer|)) #5=(|Equation| |#2|))) (SIGNATURE |taylor| #6=(#2# |#2| #7=(|Symbol|) #5#)) (SIGNATURE |taylor| (#2# #3# #5# #8=(|UniversalSegment| (|NonNegativeInteger|)))) (SIGNATURE |taylor| (#2# |#2| #7# #5# #8#)) (SIGNATURE |laurent| #9=(#2# #3# #5# #10=(|UniversalSegment| #4#))) (SIGNATURE |laurent| #11=(#2# |#2| #7# #5# #10#)) (SIGNATURE |puiseux| #12=(#2# (|Mapping| |#2| #13=(|Fraction| #4#)) #5# #14=(|UniversalSegment| #13#) #13#)) (SIGNATURE |puiseux| #15=(#2# |#2| #7# #5# #14# #13#)) (SIGNATURE |series| #1#) (SIGNATURE |series| #6#) (SIGNATURE |series| #9#) (SIGNATURE |series| #11#) (SIGNATURE |series| #12#) (SIGNATURE |series| #15#)) (|Join| (|IntegralDomain|) (|RetractableTo| #4#) (|LinearlyExplicitRingOver| #4#)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |GenerateUnivariatePowerSeries|)) +((|series| #1=(*1 *2 *3 *4 *5 *6 *7) #2=(AND #3=(|isDomain| *4 (|Symbol|)) #4=(|isDomain| *5 (|Equation| *3)) (|isDomain| *6 #5=(|UniversalSegment| #6=(|Fraction| #7=(|Integer|)))) (|isDomain| *7 #6#) (|ofCategory| *3 (|Join| #8=(|AlgebraicallyClosedField|) #9=(|TranscendentalFunctionCategory|) (|FunctionSpace| *8))) (|ofCategory| *8 #10=(|Join| (|IntegralDomain|) (|RetractableTo| #7#) (|LinearlyExplicitRingOver| #7#))) #11=(|isDomain| *2 (|Any|)) (|isDomain| *1 (|GenerateUnivariatePowerSeries| *8 *3)))) (|series| #12=(*1 *2 *3 *4 *5 *6) #13=(AND (|isDomain| *3 (|Mapping| *8 #6#)) (|isDomain| *4 (|Equation| *8)) (|isDomain| *5 #5#) (|isDomain| *6 #6#) (|ofCategory| *8 #14=(|Join| #8# #9# (|FunctionSpace| *7))) #15=(|ofCategory| *7 #10#) #11# (|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *8)))) (|series| #12# #16=(AND #3# #4# (|isDomain| *6 #17=(|UniversalSegment| #7#)) #18=(|ofCategory| *3 #14#) #15# #11# #19=(|isDomain| *1 (|GenerateUnivariatePowerSeries| *7 *3)))) (|series| #20=(*1 *2 *3 *4 *5) #21=(AND #22=(|isDomain| *3 (|Mapping| *7 #7#)) #23=(|isDomain| *4 (|Equation| *7)) (|isDomain| *5 #17#) #24=(|ofCategory| *7 #25=(|Join| #8# #9# (|FunctionSpace| *6))) #26=(|ofCategory| *6 #10#) #11# #27=(|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *7)))) (|series| #20# #28=(AND #3# #4# (|ofCategory| *3 #25#) #26# #11# (|isDomain| *1 (|GenerateUnivariatePowerSeries| *6 *3)))) (|series| #29=(*1 *2 *3 *4) #30=(AND (|isDomain| *3 (|Mapping| *6 #7#)) (|isDomain| *4 (|Equation| *6)) (|ofCategory| *6 (|Join| #8# #9# (|FunctionSpace| *5))) (|ofCategory| *5 #10#) #11# (|isDomain| *1 (|GenerateUnivariatePowerSeries| *5 *6)))) (|puiseux| #1# #2#) (|puiseux| #12# #13#) (|laurent| #12# #16#) (|laurent| #20# #21#) (|taylor| #12# (AND #3# #4# (|isDomain| *6 #31=(|UniversalSegment| (|NonNegativeInteger|))) #18# #15# #11# #19#)) (|taylor| #20# (AND #22# #23# (|isDomain| *5 #31#) #24# #26# #11# #27#)) (|taylor| #20# #28#) (|taylor| #29# #30#)) +((|reduction| ((|#2| |#2| |#1|) 15 T ELT)) (|completeHensel| ((#1=(|List| |#2|) |#2| #1# |#1| #2=(|PositiveInteger|)) 82 T ELT)) (|HenselLift| (((|Record| (|:| |plist| #1#) (|:| |modulo| |#1|)) |#2| #1# |#1| #2#) 71 T ELT))) +(((|GeneralHenselPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |HenselLift| ((|Record| (|:| |plist| #1=(|List| |#2|)) (|:| |modulo| |#1|)) |#2| #1# |#1| #2=(|PositiveInteger|))) (SIGNATURE |completeHensel| (#1# |#2| #1# |#1| #2#)) (SIGNATURE |reduction| (|#2| |#2| |#1|))) (|EuclideanDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |GeneralHenselPackage|)) +((|reduction| (*1 *2 *2 *3) (AND (|ofCategory| *3 #1=(|EuclideanDomain|)) (|isDomain| *1 (|GeneralHenselPackage| *3 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3)))) (|completeHensel| (*1 *2 *3 *2 *4 *5) (AND (|isDomain| *2 #2=(|List| *3)) (|isDomain| *5 #3=(|PositiveInteger|)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4)) (|ofCategory| *4 #1#) (|isDomain| *1 (|GeneralHenselPackage| *4 *3)))) (|HenselLift| (*1 *2 *3 *4 *5 *6) (AND (|isDomain| *6 #3#) (|ofCategory| *5 #1#) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |plist| #2#) (|:| |modulo| *5))) (|isDomain| *1 (|GeneralHenselPackage| *5 *3)) (|isDomain| *4 #2#)))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) 28 T ELT)) (|unitVector| (($ |#3|) 25 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#3=($) NIL T CONST)) (|reductum| (#4=($ $) 32 T ELT)) (|opposite?| #1#) (|multMonom| (($ |#2| |#4| $) 33 T ELT)) (|monomial| (($ |#2| #5=(|ModuleMonomial| |#3| |#4| |#5|)) 24 T ELT)) (|leadingMonomial| ((#5# $) 15 T ELT)) (|leadingIndex| ((|#3| $) 19 T ELT)) (|leadingExponent| ((|#4| $) 17 T ELT)) (|leadingCoefficient| ((|#2| $) 29 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|build| (($ |#2| |#3| |#4|) 26 T ELT)) (|before?| #1#) (|Zero| (#3# 36 T CONST)) (= #1#) (- (#4# NIL T ELT) (#6=($ $ $) NIL T ELT)) (+ (#6# 34 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) . #7=($)) NIL T ELT) (($ |#6| $) 40 T ELT) (($ $ |#6|) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #7#) NIL T ELT))) +(((|GeneralModulePolynomial| |#1| |#2| |#3| |#4| |#5| |#6|) (|Join| (|Module| |#6|) (|Module| |#2|) (CATEGORY |domain| (SIGNATURE |leadingCoefficient| (|#2| $)) (SIGNATURE |leadingMonomial| (#1=(|ModuleMonomial| |#3| |#4| |#5|) $)) (SIGNATURE |leadingExponent| (|#4| $)) (SIGNATURE |leadingIndex| (|#3| $)) (SIGNATURE |reductum| ($ $)) (SIGNATURE |monomial| ($ |#2| #1#)) (SIGNATURE |unitVector| ($ |#3|)) (SIGNATURE |build| ($ |#2| |#3| |#4|)) (SIGNATURE |multMonom| ($ |#2| |#4| $)) (SIGNATURE * ($ |#6| $)))) (|List| (|Symbol|)) (|CommutativeRing|) (|OrderedSet|) (|DirectProductCategory| (|#| |#1|) (|NonNegativeInteger|)) (|Mapping| (|Boolean|) #2=(|Record| (|:| |index| |#3|) (|:| |exponent| |#4|)) #2#) (|PolynomialCategory| |#2| |#4| (|OrderedVariableList| |#1|))) (T |GeneralModulePolynomial|)) +((* (*1 *1 *2 *1) (AND #1=(|ofType| *3 #2=(|List| (|Symbol|))) #3=(|ofCategory| *4 #4=(|CommutativeRing|)) #5=(|ofCategory| *6 #6=(|DirectProductCategory| (|#| *3) #7=(|NonNegativeInteger|))) #8=(|ofType| *7 (|Mapping| #9=(|Boolean|) #10=(|Record| #11=(|:| |index| *5) (|:| |exponent| *6)) #10#)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *2)) #12=(|ofCategory| *5 #13=(|OrderedSet|)) (|ofCategory| *2 #14=(|PolynomialCategory| *4 *6 #15=(|OrderedVariableList| *3))))) (|leadingCoefficient| #16=(*1 *2 *1) (AND #1# #17=(|ofCategory| *5 #6#) #18=(|ofType| *6 (|Mapping| #9# #19=(|Record| (|:| |index| *4) #20=(|:| |exponent| *5)) #19#)) #21=(|ofCategory| *2 #4#) (|isDomain| *1 (|GeneralModulePolynomial| *3 *2 *4 *5 *6 *7)) #22=(|ofCategory| *4 #13#) (|ofCategory| *7 (|PolynomialCategory| *2 *5 #15#)))) (|leadingMonomial| #16# (AND #1# #3# #5# #8# (|isDomain| *2 #23=(|ModuleMonomial| *5 *6 *7)) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *6 *7 *8)) #12# (|ofCategory| *8 #14#))) (|leadingExponent| #16# (AND #1# #3# (|ofType| *6 (|Mapping| #9# #24=(|Record| #11# (|:| |exponent| *2)) #24#)) (|ofCategory| *2 #6#) (|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *5 *2 *6 *7)) #12# (|ofCategory| *7 (|PolynomialCategory| *4 *2 #15#)))) (|leadingIndex| #16# (AND #1# #3# #17# #25=(|ofType| *6 (|Mapping| #9# #26=(|Record| (|:| |index| *2) #20#) #26#)) #27=(|ofCategory| *2 #13#) #28=(|isDomain| *1 (|GeneralModulePolynomial| *3 *4 *2 *5 *6 *7)) #29=(|ofCategory| *7 (|PolynomialCategory| *4 *5 #15#)))) (|reductum| (*1 *1 *1) (AND (|ofType| *2 #2#) (|ofCategory| *3 #4#) (|ofCategory| *5 (|DirectProductCategory| (|#| *2) #7#)) #18# (|isDomain| *1 (|GeneralModulePolynomial| *2 *3 *4 *5 *6 *7)) #22# (|ofCategory| *7 (|PolynomialCategory| *3 *5 (|OrderedVariableList| *2))))) (|monomial| (*1 *1 *2 *3) (AND (|isDomain| *3 #23#) #12# (|ofCategory| *6 #30=(|DirectProductCategory| (|#| *4) #7#)) #8# #31=(|ofType| *4 #2#) #21# (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *6 *7 *8)) (|ofCategory| *8 (|PolynomialCategory| *2 *6 #32=(|OrderedVariableList| *4))))) (|unitVector| (*1 *1 *2) (AND #1# #3# #17# #25# #28# #27# #29#)) (|build| (*1 *1 *2 *3 *4) (AND (|ofType| *5 #2#) #21# (|ofCategory| *4 (|DirectProductCategory| (|#| *5) #7#)) (|ofType| *6 (|Mapping| #9# #33=(|Record| (|:| |index| *3) (|:| |exponent| *4)) #33#)) (|isDomain| *1 (|GeneralModulePolynomial| *5 *2 *3 *4 *6 *7)) (|ofCategory| *3 #13#) (|ofCategory| *7 (|PolynomialCategory| *2 *4 (|OrderedVariableList| *5))))) (|multMonom| (*1 *1 *2 *3 *1) (AND #31# #21# (|ofCategory| *3 #30#) (|ofType| *6 (|Mapping| #9# #34=(|Record| #11# (|:| |exponent| *3)) #34#)) (|isDomain| *1 (|GeneralModulePolynomial| *4 *2 *5 *3 *6 *7)) #12# (|ofCategory| *7 (|PolynomialCategory| *2 *3 #32#))))) +((|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) 39 T ELT))) +(((|GosperSummationMethod| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |GospersMethod| ((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|RetractableTo| (|Fraction| (|Integer|))) (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |numer| #1=(|#4| $)) (SIGNATURE |denom| #1#)))) (T |GosperSummationMethod|)) +((|GospersMethod| (*1 *2 *2 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *3)) (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *5 (|OrderedAbelianMonoidSup|)) (|ofCategory| *6 (|IntegralDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *5 *3)) (|isDomain| *1 (|GosperSummationMethod| *5 *3 *6 *7 *2)) 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T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . 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NIL T ELT) (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT) #11#) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) +(((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Join| (|PolynomialCategory| |#2| (|HomogeneousDirectProduct| (|#| |#1|) (|NonNegativeInteger|)) (|OrderedVariableList| |#1|)) (CATEGORY |domain| (SIGNATURE |reorder| ($ $ (|List| (|Integer|)))))) (|List| (|Symbol|)) (|Ring|)) (T |HomogeneousDistributedMultivariatePolynomial|)) +((|reorder| (*1 *1 *1 *2) (AND (|isDomain| *2 (|List| (|Integer|))) (|isDomain| *1 (|HomogeneousDistributedMultivariatePolynomial| *3 *4)) (|ofType| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|Ring|))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#2| (|BasicType|)) ELT)) (|zero?| (#5=(#3# $) NIL #6=(|has| |#2| (|AbelianMonoid|)) ELT)) (|unitVector| (#7=($ #8=(|PositiveInteger|)) NIL #9=(|has| |#2| (|Ring|)) ELT)) (|swap!| (((|Void|) $ #10=(|Integer|) #10#) NIL #11=(|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|sup| (#12=($ $ $) NIL #13=(|has| |#2| (|OrderedAbelianMonoidSup|)) ELT)) (|subtractIfCan| ((#14=(|Union| $ #15="failed") $ $) NIL (|has| |#2| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#2| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#2| $ #10# |#2|) NIL #11# ELT)) 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NIL #14# ELT)) (|linearAssociatedExp| (($ $ #36#) NIL #14# ELT)) (|lcm| #23# #39=(($ #25#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #5#) (|init| (#21# NIL #14# CONST)) (|index| (($ #13#) NIL #14# ELT)) (|inGroundField?| #3#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|generator| #24#) (|gcdPolynomial| ((#37# #37# #37#) NIL T ELT)) (|gcd| #23# #39#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #15#) (|:| |exponent| #15#)))) NIL #14# ELT)) (|factor| #19#) (|extensionDegree| ((#33#) NIL T ELT) ((#13#) NIL T ELT)) (|extendedEuclidean| (((|Record| #40=(|:| |coef1| $) #41=(|:| |coef2| $) #26#) $ $) NIL T ELT) (((|Union| (|Record| #40# #41#) #18#) $ $ $) NIL T ELT)) (|exquo| #16#) (|expressIdealMember| (((|Maybe| #25#) #25# $) NIL T ELT)) (|euclideanSize| (#42=(#8# $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|discreteLog| (#42# NIL #14# ELT) (((|Union| #8# #18#) $ $) NIL #29# ELT)) (|dimension| 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(SIGNATURE |makeEq| ((|List| (|Equation| (|Polynomial| |#2|))) #1# #4#))) (|GcdDomain|) #5=(|Field|) (|Join| #5# (|OrderedRing|))) (T |InnerNumericFloatSolvePackage|)) +((|makeEq| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 #2=(|List| *6)) #3=(|isDomain| *4 (|List| (|Symbol|))) #4=(|ofCategory| *6 #5=(|Field|)) (|isDomain| *2 (|List| (|Equation| #6=(|Polynomial| *6)))) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *7)) #7=(|ofCategory| *5 #8=(|GcdDomain|)) (|ofCategory| *7 #9=(|Join| #5# (|OrderedRing|))))) (|innerSolve| (*1 *2 *3 *3 *4 *5) (AND (|isDomain| *3 (|List| #6#)) #3# (|ofCategory| *6 #8#) (|isDomain| *2 (|List| (|List| *7))) (|isDomain| *1 (|InnerNumericFloatSolvePackage| *6 *7 *5)) (|ofCategory| *7 #5#) (|ofCategory| *5 #9#))) (|innerSolve1| #1# (AND (|isDomain| *3 (|Polynomial| *5)) #7# #10=(|isDomain| *2 #2#) #11=(|isDomain| *1 (|InnerNumericFloatSolvePackage| *5 *6 *4)) #4# #12=(|ofCategory| *4 #9#))) (|innerSolve1| #1# (AND (|isDomain| *3 (|SparseUnivariatePolynomial| 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(|modularGcdPrimitive| #3# #4#)) +((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1# #2=(|Mapping| (|Factored| #3=(|SparseUnivariatePolynomial| |#3|)) #3#)) 90 T ELT) (((|Factored| |#4|) |#4| #2#) 213 T ELT))) +(((|InnerMultFact| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4| #1=(|Mapping| (|Factored| #2=(|SparseUnivariatePolynomial| |#3|)) #2#))) (SIGNATURE |factor| ((|Factored| #3=(|SparseUnivariatePolynomial| |#4|)) #3# #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|PolynomialCategory| |#3| |#2| |#1|)) (T |InnerMultFact|)) +((|factor| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *4 (|Mapping| (|Factored| #3=(|SparseUnivariatePolynomial| *7)) #3#)) #4=(|ofCategory| *7 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #5=(|ofCategory| *5 (|OrderedSet|)) #6=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) (|ofCategory| *8 #7=(|PolynomialCategory| *7 *6 *5)) (|isDomain| *2 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$) 30 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #5=(#6=($ $) NIL T ELT)) (|unit?| #7=(#4# NIL T ELT)) (|transcendent?| #7#) (|transcendenceDegree| #8=(#9=(#10=(|NonNegativeInteger|)) NIL T ELT)) (|trace| #11=(#12=($ $ #13=(|PositiveInteger|)) NIL #14=(|has| $ (|Finite|)) ELT) #5#) (|tableForDiscreteLogarithm| (((|Table| #13# #10#) #15=(|Integer|)) 59 T ELT)) (|subtractIfCan| #16=((#17=(|Union| $ #18="failed") $ $) NIL T ELT)) (|squareFreePart| #5#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|sizeLess?| #1#) (|size| #8#) (|sample| #20=(#21=($) NIL T CONST)) (|retractIfCan| (#22=(#17# $) 95 T ELT)) (|retract| (#6# 94 T ELT)) (|represents| (($ #23=(|Vector| $)) 93 T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) 56 T ELT)) (|rem| #24=(#25=($ $ $) NIL T ELT)) (|recip| (#22# 47 T ELT)) (|random| (#21# NIL T ELT)) (|quo| #24#) (|principalIdeal| (((|Record| (|:| |coef| 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(|List| (|Record| #8=(|:| |coeff| *6) (|:| |logand| *6)))))) #9=(|isDomain| *1 (|IntegrationResultFunctions2| *5 *6)))) (|map| #1# (|partial| AND (|isDomain| *3 (|Mapping| *2 *5)) (|isDomain| *4 (|Union| *5 #4#)) #5# (|ofCategory| *2 #6#) (|isDomain| *1 (|IntegrationResultFunctions2| *5 *2)))) (|map| #1# (|partial| AND #2# (|isDomain| *4 (|Union| (|Record| (|:| |ratpart| *5) #3#) #4#)) #5# #7# (|isDomain| *2 (|Record| (|:| |ratpart| *6) #8#)) #9#)) (|map| #1# (AND #2# (|isDomain| *4 (|IntegrationResult| *5)) #5# #7# (|isDomain| *2 (|IntegrationResult| *6)) #9#))) +((|split| ((#1=(|IntegrationResult| |#2|) #1#) 42 T ELT)) (|expand| (((|List| |#2|) #1#) 44 T ELT)) (|complexExpand| ((|#2| #1#) 50 T ELT))) +(((|IntegrationResultToFunction| |#1| |#2|) (CATEGORY |package| (SIGNATURE |split| (#1=(|IntegrationResult| |#2|) #1#)) (SIGNATURE |expand| ((|List| |#2|) #1#)) (SIGNATURE |complexExpand| (|#2| #1#))) (|Join| (|GcdDomain|) (|RetractableTo| #2=(|Integer|)) (|LinearlyExplicitRingOver| #2#)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|))) (T |IntegrationResultToFunction|)) +((|complexExpand| #1=(*1 *2 *3) (AND (|isDomain| *3 (|IntegrationResult| *2)) (|ofCategory| *2 #2=(|Join| (|AlgebraicallyClosedFunctionSpace| *4) #3=(|TranscendentalFunctionCategory|))) (|isDomain| *1 (|IntegrationResultToFunction| *4 *2)) #4=(|ofCategory| *4 #5=(|Join| (|GcdDomain|) (|RetractableTo| #6=(|Integer|)) (|LinearlyExplicitRingOver| #6#))))) (|expand| #1# (AND (|isDomain| *3 (|IntegrationResult| *5)) (|ofCategory| *5 #2#) #4# (|isDomain| *2 (|List| *5)) (|isDomain| *1 (|IntegrationResultToFunction| *4 *5)))) (|split| (*1 *2 *2) (AND (|isDomain| *2 (|IntegrationResult| *4)) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedFunctionSpace| *3) #3#)) (|ofCategory| *3 #5#) (|isDomain| *1 (|IntegrationResultToFunction| *3 *4))))) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|irVar| (#2=($ #3=(|Identifier|) #4=(|InternalTypeForm|)) 14 T ELT)) (|irDef| (($ #3# #4# $) 16 T ELT)) (|irCtor| (#2# 15 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #5=(|Syntax|)) 7 T ELT) ((#5# $) 6 T ELT)) (|before?| #1#) (= #1#)) +(((|InternalRepresentationForm|) (|Join| (|SetCategory|) (|HomotopicTo| (|Syntax|)) (CATEGORY |domain| (SIGNATURE |irVar| #1=($ #2=(|Identifier|) #3=(|InternalTypeForm|))) (SIGNATURE |irCtor| #1#) (SIGNATURE |irDef| ($ #2# #3# $))))) (T |InternalRepresentationForm|)) +((|irVar| #1=(*1 *1 *2 *3) #2=(AND (|isDomain| *2 (|Identifier|)) (|isDomain| *3 (|InternalTypeForm|)) (|isDomain| *1 (|InternalRepresentationForm|)))) (|irCtor| #1# #2#) (|irDef| (*1 *1 *2 *3 *1) #2#)) +((|perfectSquare?| ((#1=(|Boolean|) |#1|) 16 T ELT)) (|perfectSqrt| ((#2=(|Union| |#1| "failed") |#1|) 14 T ELT)) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| #3=(|NonNegativeInteger|))) |#1|) 37 T ELT) ((#2# |#1| #3#) 18 T ELT)) (|perfectNthPower?| ((#1# |#1| #3#) 19 T ELT)) (|approxSqrt| ((|#1| |#1|) 41 T ELT)) (|approxNthRoot| ((|#1| |#1| #3#) 44 T ELT))) +(((|IntegerRoots| |#1|) (CATEGORY |package| (SIGNATURE |perfectNthPower?| (#1=(|Boolean|) |#1| #2=(|NonNegativeInteger|))) (SIGNATURE |perfectNthRoot| (#3=(|Union| |#1| "failed") |#1| #2#)) (SIGNATURE |perfectNthRoot| ((|Record| (|:| |base| |#1|) (|:| |exponent| #2#)) |#1|)) (SIGNATURE |approxNthRoot| (|#1| |#1| #2#)) (SIGNATURE |perfectSquare?| (#1# |#1|)) (SIGNATURE |perfectSqrt| (#3# |#1|)) (SIGNATURE |approxSqrt| (|#1| |#1|))) (|IntegerNumberSystem|)) (T |IntegerRoots|)) +((|approxSqrt| #1=(*1 *2 *2) (AND #2=(|isDomain| *1 (|IntegerRoots| *2)) #3=(|ofCategory| *2 #4=(|IntegerNumberSystem|)))) (|perfectSqrt| #1# (|partial| AND #2# #3#)) (|perfectSquare?| #5=(*1 *2 *3) (AND #6=(|isDomain| *2 (|Boolean|)) #7=(|isDomain| *1 (|IntegerRoots| *3)) #8=(|ofCategory| *3 #4#))) (|approxNthRoot| #9=(*1 *2 *2 *3) (AND #10=(|isDomain| *3 #11=(|NonNegativeInteger|)) #2# #3#)) (|perfectNthRoot| #5# (AND (|isDomain| *2 (|Record| (|:| |base| *3) (|:| |exponent| #11#))) #7# #8#)) (|perfectNthRoot| #9# (|partial| AND #10# #2# #3#)) (|perfectNthPower?| (*1 *2 *3 *4) (AND (|isDomain| *4 #11#) #6# #7# #8#))) +((|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) 44 T ELT))) +(((|IrredPolyOverFiniteField| |#1|) (CATEGORY |package| (SIGNATURE |generateIrredPoly| ((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)))) (|FiniteFieldCategory|)) (T |IrredPolyOverFiniteField|)) +((|generateIrredPoly| (*1 *2 *3) (AND (|isDomain| *3 (|PositiveInteger|)) (|isDomain| *2 (|SparseUnivariatePolynomial| *4)) (|isDomain| *1 (|IrredPolyOverFiniteField| *4)) (|ofCategory| *4 (|FiniteFieldCategory|))))) +((|split| ((#1=(|IntegrationResult| #2=(|Fraction| (|Polynomial| |#1|))) #1#) 27 T ELT)) (|integrate| (((|Union| #3=(|Expression| |#1|) #4=(|List| #3#)) #2# #5=(|Symbol|)) 33 #6=(|has| |#1| (|CharacteristicZero|)) ELT)) (|expand| ((#4# #1#) 19 T ELT)) (|complexIntegrate| ((#3# #2# #5#) 31 #6# ELT)) (|complexExpand| ((#3# #1#) 21 T ELT))) +(((|IntegrationResultRFToFunction| |#1|) (CATEGORY |package| (SIGNATURE |split| (#1=(|IntegrationResult| #2=(|Fraction| (|Polynomial| |#1|))) #1#)) (SIGNATURE |expand| (#3=(|List| #4=(|Expression| |#1|)) #1#)) (SIGNATURE |complexExpand| (#4# #1#)) (IF (|has| |#1| (|CharacteristicZero|)) (PROGN (SIGNATURE |integrate| ((|Union| #4# #3#) #2# #5=(|Symbol|))) (SIGNATURE |complexIntegrate| (#4# #2# #5#))) |%noBranch|)) (|Join| (|GcdDomain|) (|RetractableTo| #6=(|Integer|)) (|LinearlyExplicitRingOver| #6#))) (T |IntegrationResultRFToFunction|)) +((|complexIntegrate| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Fraction| (|Polynomial| *5))) #3=(|isDomain| *4 (|Symbol|)) #4=(|ofCategory| *5 (|CharacteristicZero|)) #5=(|ofCategory| *5 #6=(|Join| (|GcdDomain|) (|RetractableTo| #7=(|Integer|)) (|LinearlyExplicitRingOver| #7#))) (|isDomain| *2 #8=(|Expression| *5)) #9=(|isDomain| *1 (|IntegrationResultRFToFunction| *5)))) (|integrate| #1# (AND #2# #3# #4# #5# (|isDomain| *2 (|Union| #8# (|List| #8#))) #9#)) (|complexExpand| #10=(*1 *2 *3) (AND #11=(|isDomain| *3 (|IntegrationResult| (|Fraction| (|Polynomial| *4)))) #12=(|ofCategory| *4 #6#) (|isDomain| *2 #13=(|Expression| *4)) #14=(|isDomain| *1 (|IntegrationResultRFToFunction| *4)))) (|expand| #10# (AND #11# #12# (|isDomain| *2 (|List| #13#)) #14#)) (|split| (*1 *2 *2) (AND (|isDomain| *2 (|IntegrationResult| (|Fraction| (|Polynomial| *3)))) (|ofCategory| *3 #6#) (|isDomain| *1 (|IntegrationResultRFToFunction| *3))))) +((|irreducibleRepresentation| ((#1=(|List| #2=(|Matrix| #3=(|Integer|))) #4=(|List| (|PositiveInteger|)) (|List| #5=(|Permutation| #3#))) 80 T ELT) ((#1# #4#) 81 T ELT) ((#2# #4# #5#) 74 T ELT)) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) #4#) 71 T ELT))) +(((|IrrRepSymNatPackage|) (CATEGORY |package| (SIGNATURE |dimensionOfIrreducibleRepresentation| ((|NonNegativeInteger|) #1=(|List| (|PositiveInteger|)))) (SIGNATURE |irreducibleRepresentation| (#2=(|Matrix| #3=(|Integer|)) #1# #4=(|Permutation| #3#))) (SIGNATURE |irreducibleRepresentation| (#5=(|List| #2#) #1#)) (SIGNATURE |irreducibleRepresentation| (#5# #1# (|List| #4#))))) (T |IrrRepSymNatPackage|)) +((|irreducibleRepresentation| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|List| (|PositiveInteger|))) (|isDomain| *4 (|List| #3=(|Permutation| #4=(|Integer|)))) #5=(|isDomain| *2 (|List| #6=(|Matrix| #4#))) #7=(|isDomain| *1 (|IrrRepSymNatPackage|)))) (|irreducibleRepresentation| #8=(*1 *2 *3) (AND #2# #5# #7#)) (|irreducibleRepresentation| #1# (AND #2# (|isDomain| *4 #3#) (|isDomain| *2 #6#) #7#)) (|dimensionOfIrreducibleRepresentation| #8# (AND #2# (|isDomain| *2 (|NonNegativeInteger|)) #7#))) +((|rur| ((#1=(|List| |#5|) |#5| #2=(|Boolean|)) 97 T ELT)) (|checkRur| ((#2# |#5| #1#) 34 T ELT))) +(((|InternalRationalUnivariateRepresentationPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |rur| (#1=(|List| |#5|) |#5| #2=(|Boolean|))) (SIGNATURE |checkRur| (#2# |#5| #1#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|SquareFreeRegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |InternalRationalUnivariateRepresentationPackage|)) +((|checkRur| #1=(*1 *2 *3 *4) (AND (|isDomain| *4 #2=(|List| *3)) #3=(|ofCategory| *3 (|SquareFreeRegularTriangularSetCategory| *5 *6 *7 *8)) #4=(|ofCategory| *5 (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #5=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *7 (|OrderedSet|)) #7=(|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) (|isDomain| *2 #8=(|Boolean|)) #9=(|isDomain| *1 (|InternalRationalUnivariateRepresentationPackage| *5 *6 *7 *8 *3)))) (|rur| #1# (AND (|isDomain| *4 #8#) #4# #5# #6# #7# (|isDomain| *2 #2#) #9# #3#))) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|rhs| (#2=((|SpadAst|) $) 12 T ELT)) (|lhs| (#2# 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #3=(|Syntax|)) NIL T ELT) ((#3# $) NIL T ELT)) (|before?| #1#) (= #1#)) +(((|IsAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |lhs| #1=((|SpadAst|) $)) (SIGNATURE |rhs| #1#)))) (T |IsAst|)) +((|lhs| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|IsAst|)))) (|rhs| #1# #2#)) +((|sum| ((#1=(|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) 23 T ELT) ((#1# |#4| |#2| (|Segment| |#4|)) 32 T ELT))) +(((|InnerPolySum| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |sum| (#1=(|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|))) (SIGNATURE |sum| (#1# |#4| |#2|))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |InnerPolySum|)) +((|sum| (*1 *2 *3 *4) (AND (|ofCategory| *5 #1=(|OrderedAbelianMonoidSup|)) #2=(|ofCategory| *4 (|OrderedSet|)) (|ofCategory| *6 #3=(|IntegralDomain|)) #4=(|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| (|Integer|)))) (|isDomain| *1 (|InnerPolySum| *5 *4 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| *6 *5 *4)))) (|sum| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Segment| *3)) (|ofCategory| *3 (|PolynomialCategory| *7 *6 *4)) (|ofCategory| *6 #1#) #2# (|ofCategory| *7 #3#) #4# (|isDomain| *1 (|InnerPolySum| *6 *4 *7 *3))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 71 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|truncate| (#11=($ $ #12=(|Integer|)) 58 T ELT) (($ $ #12# #12#) 59 T ELT)) (|terms| (#13=(#14=(|Stream| (|Record| (|:| |k| #12#) (|:| |c| |#1|))) $) 65 T ELT)) (|taylorQuoByVar| (#10# 109 T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ "failed") $ $) NIL T ELT)) (|seriesToOutputForm| ((#17=(|OutputForm|) #14# #18=(|Reference| (|OrderedCompletion| #12#)) #7# |#1| #19=(|Fraction| #12#)) 232 T ELT)) (|series| (($ #14#) 36 T ELT)) (|sample| (#20=($) NIL T CONST)) (|reductum| #21=(#10# NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|pole?| #22=(#4# NIL T ELT)) (|order| (#23=(#12# $) 63 T ELT) ((#12# $ #12#) 64 T ELT)) (|opposite?| #1#) (|one?| #22#) (|multiplyExponents| (#24=($ $ #25=(|PositiveInteger|)) 83 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #12#) $) 80 T ELT)) (|monomial?| (#4# 26 T ELT)) (|monomial| (($ |#1| #12#) 22 T ELT) (($ $ #6# #12#) NIL T ELT) (($ $ #5# (|List| #12#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 75 T ELT)) (|makeSeries| (($ #18# #14#) 13 T ELT)) (|leadingMonomial| #21#) (|leadingCoefficient| #26=((|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#10# 120 #27=(|has| |#1| (|Algebra| #19#)) ELT)) (|iExquo| ((#16# $ $ #3#) 108 T ELT)) (|iCompose| (#28=($ $ $) 116 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|getStream| (#13# 15 T ELT)) (|getRef| ((#18# $) 14 T ELT)) (|extend| (#11# 47 T ELT)) (|exquo| (#15# NIL #8# ELT)) (|eval| (((|Stream| |#1|) $ |#1|) NIL #29=(|has| |#1| (SIGNATURE ** (|#1| |#1| #12#))) ELT)) (|elt| (#30=(|#1| $ #12#) 62 T ELT) (#28# NIL (|has| #12# (|SemiGroup|)) ELT)) (|differentiate| #31=(($ $ #7#) NIL #32=(AND (|has| |#1| (|PartialDifferentialRing| #7#)) #33=(|has| |#1| (SIGNATURE * (|#1| #12# |#1|)))) ELT) #34=(($ $ #35=(|List| #7#)) NIL #32# ELT) #36=(($ $ #7# #37=(|NonNegativeInteger|)) NIL #32# ELT) #38=(($ $ #35# (|List| #37#)) NIL #32# ELT) (#10# 77 #33# ELT) #39=(#40=($ $ #37#) NIL #33# ELT)) (|degree| (#23# NIL T ELT)) (|complete| (#10# 48 T ELT)) (|coerce| ((#17# $) NIL T ELT) (($ #12#) 29 T ELT) (($ #19#) NIL #27# ELT) #9# (($ |#1|) 28 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| (#30# 61 T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#37#) 39 T CONST)) (|center| #26#) (|cTanh| (#10# 192 #27# ELT)) (|cTan| (#10# 167 #27# ELT)) (|cSinh| (#10# 189 #27# ELT)) (|cSin| (#10# 164 #27# ELT)) (|cSech| (#10# 194 #27# ELT)) (|cSec| (#10# 170 #27# ELT)) (|cRationalPower| (#41=($ $ #19#) 157 #27# ELT)) (|cPower| (#42=($ $ |#1|) 128 #27# ELT)) (|cLog| (#10# 161 #27# ELT)) (|cExp| (#10# 159 #27# ELT)) (|cCsch| (#10# 195 #27# ELT)) (|cCsc| (#10# 171 #27# ELT)) (|cCoth| (#10# 193 #27# ELT)) (|cCot| (#10# 169 #27# ELT)) (|cCosh| (#10# 190 #27# ELT)) (|cCos| (#10# 165 #27# ELT)) (|cAtanh| (#10# 200 #27# ELT)) (|cAtan| (#10# 180 #27# ELT)) (|cAsinh| (#10# 197 #27# ELT)) (|cAsin| (#10# 176 #27# ELT)) (|cAsech| (#10# 204 #27# ELT)) (|cAsec| (#10# 184 #27# ELT)) (|cAcsch| (#10# 206 #27# ELT)) (|cAcsc| (#10# 186 #27# ELT)) (|cAcoth| (#10# 202 #27# ELT)) (|cAcot| (#10# 182 #27# ELT)) (|cAcosh| (#10# 199 #27# ELT)) (|cAcos| (#10# 178 #27# ELT)) (|before?| #1#) (|associates?| (#2# NIL #8# ELT)) (|approximate| (#30# NIL (AND #29# (|has| |#1| (SIGNATURE |coerce| (|#1| #7#)))) ELT)) (|annihilate?| #1#) (|Zero| (#20# 30 T CONST)) (|One| (#20# 40 T CONST)) (D #31# #34# #36# #38# (#10# NIL #33# ELT) #39#) (= (#2# 73 T ELT)) (/ (#42# NIL (|has| |#1| (|Field|)) ELT)) (- (#10# 91 T ELT) (#28# 72 T ELT)) (+ (#28# 88 T ELT)) (** (#24# NIL T ELT) (#40# 111 T ELT)) (* (($ #25# $) 98 T ELT) (($ #37# $) 96 T ELT) (($ #12# $) 93 T ELT) (#28# 104 T ELT) (#42# NIL T ELT) (($ |#1| . #43=($)) 123 T ELT) (($ #19# . #43#) NIL #27# ELT) (#41# NIL #27# ELT))) +(((|InnerSparseUnivariatePowerSeries| |#1|) (|Join| (|UnivariatePowerSeriesCategory| |#1| #1=(|Integer|)) (CATEGORY |domain| (SIGNATURE |makeSeries| ($ #2=(|Reference| (|OrderedCompletion| #1#)) #3=(|Stream| (|Record| (|:| |k| #1#) (|:| |c| |#1|))))) (SIGNATURE |getRef| (#2# $)) (SIGNATURE |getStream| (#3# $)) (SIGNATURE |series| ($ #3#)) (SIGNATURE |monomial?| (#4=(|Boolean|) $)) (SIGNATURE |multiplyCoefficients| ($ (|Mapping| |#1| #1#) $)) (SIGNATURE |iExquo| ((|Union| $ "failed") $ $ #4#)) (SIGNATURE |taylorQuoByVar| #5=($ $)) (SIGNATURE |iCompose| ($ $ $)) (SIGNATURE |seriesToOutputForm| ((|OutputForm|) #3# #2# (|Symbol|) |#1| #6=(|Fraction| #1#))) (IF (|has| |#1| (|Algebra| #6#)) (PROGN (SIGNATURE |integrate| #5#) (SIGNATURE |cPower| ($ $ |#1|)) (SIGNATURE |cRationalPower| ($ $ #6#)) (SIGNATURE |cExp| #5#) (SIGNATURE |cLog| #5#) (SIGNATURE |cSin| #5#) (SIGNATURE |cCos| #5#) (SIGNATURE |cTan| #5#) (SIGNATURE |cCot| #5#) (SIGNATURE |cSec| #5#) (SIGNATURE |cCsc| #5#) (SIGNATURE |cAsin| #5#) (SIGNATURE |cAcos| #5#) (SIGNATURE |cAtan| #5#) (SIGNATURE |cAcot| #5#) (SIGNATURE |cAsec| #5#) (SIGNATURE |cAcsc| #5#) (SIGNATURE |cSinh| #5#) (SIGNATURE |cCosh| #5#) (SIGNATURE |cTanh| #5#) (SIGNATURE |cCoth| #5#) (SIGNATURE |cSech| #5#) (SIGNATURE |cCsch| #5#) (SIGNATURE |cAsinh| #5#) (SIGNATURE |cAcosh| #5#) (SIGNATURE |cAtanh| #5#) (SIGNATURE |cAcoth| #5#) (SIGNATURE |cAsech| #5#) (SIGNATURE |cAcsch| #5#)) |%noBranch|))) (|Ring|)) (T |InnerSparseUnivariatePowerSeries|)) +((|monomial?| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Boolean|)) #3=(|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *3)) #4=(|ofCategory| *3 #5=(|Ring|)))) (|makeSeries| (*1 *1 *2 *3) (AND #6=(|isDomain| *2 #7=(|Reference| (|OrderedCompletion| #8=(|Integer|)))) (|isDomain| *3 (|Stream| (|Record| #9=(|:| |k| #8#) (|:| |c| *4)))) (|ofCategory| *4 #5#) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *4)))) (|getRef| #1# (AND #6# #3# #4#)) (|getStream| #1# (AND #10=(|isDomain| *2 (|Stream| (|Record| #9# (|:| |c| *3)))) #3# #4#)) (|series| (*1 *1 *2) (AND #10# #4# #3#)) (|multiplyCoefficients| (*1 *1 *2 *1) (AND (|isDomain| *2 (|Mapping| *3 #8#)) #4# #3#)) (|iExquo| (*1 *1 *1 *1 *2) (|partial| AND #2# #3# #4#)) (|taylorQuoByVar| #11=(*1 *1 *1) #12=(AND #13=(|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *2)) #14=(|ofCategory| *2 #5#))) (|iCompose| (*1 *1 *1 *1) #12#) (|seriesToOutputForm| (*1 *2 *3 *4 *5 *6 *7) (AND (|isDomain| *3 (|Stream| (|Record| #9# (|:| |c| *6)))) (|isDomain| *4 #7#) (|isDomain| *5 (|Symbol|)) (|isDomain| *7 #15=(|Fraction| #8#)) (|ofCategory| *6 #5#) (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|InnerSparseUnivariatePowerSeries| *6)))) (|integrate| #11# #16=(AND #13# (|ofCategory| *2 (|Algebra| #15#)) #14#)) (|cPower| #17=(*1 *1 *1 *2) #16#) (|cRationalPower| #17# (AND (|isDomain| *2 #15#) #3# (|ofCategory| *3 (|Algebra| *2)) #4#)) (|cExp| #11# #16#) (|cLog| #11# #16#) (|cSin| #11# #16#) (|cCos| #11# #16#) (|cTan| #11# #16#) (|cCot| #11# #16#) (|cSec| #11# #16#) (|cCsc| #11# #16#) (|cAsin| #11# #16#) (|cAcos| #11# #16#) (|cAtan| #11# #16#) (|cAcot| #11# #16#) (|cAsec| #11# #16#) (|cAcsc| #11# #16#) (|cSinh| #11# #16#) (|cCosh| #11# #16#) (|cTanh| #11# #16#) (|cCoth| #11# #16#) (|cSech| #11# #16#) (|cCsch| #11# #16#) (|cAsinh| #11# #16#) (|cAcosh| #11# #16#) (|cAtanh| #11# #16#) (|cAcoth| #11# #16#) (|cAsech| #11# #16#) (|cAcsch| #11# #16#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 62 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #6=(#7=($ $) NIL #5# ELT)) (|unit?| (#4# NIL #5# ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ "failed") $ $) NIL T ELT)) (|series| (($ #10=(|Stream| |#1|)) 9 T ELT)) (|sample| (#11=($) NIL T CONST)) (|recip| ((#9# $) 44 T ELT)) (|pole?| (#4# 56 T ELT)) (|order| ((#12=(|NonNegativeInteger|) $) 61 T ELT) ((#12# $ #12#) 60 T ELT)) (|opposite?| #1#) (|one?| (#4# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| (#8# 46 #5# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13=(|Integer|)) NIL T ELT) #6#) (|coefficients| ((#10# $) 25 T ELT)) (|characteristic| ((#12#) 55 T CONST)) (|before?| #1#) (|associates?| (#2# NIL #5# ELT)) (|annihilate?| #1#) (|Zero| (#11# 10 T CONST)) (|One| (#11# 14 T CONST)) (= (#2# 24 T ELT)) (- (#7# 32 T ELT) (#14=($ $ $) 16 T ELT)) (+ (#14# 27 T ELT)) (** (($ $ #15=(|PositiveInteger|)) NIL T ELT) (($ $ #12#) 53 T ELT)) (* (($ #15# $) NIL T ELT) (($ #12# $) NIL T ELT) (($ #13# $) 36 T ELT) (#14# 30 T ELT) (($ $ |#1|) 40 T ELT) (($ |#1| $) 39 T ELT) (($ $ #13#) 38 T ELT))) +(((|InnerTaylorSeries| |#1|) (|Join| #1=(|Ring|) (|BiModule| |#1| |#1|) (CATEGORY |domain| (SIGNATURE |coefficients| (#2=(|Stream| |#1|) $)) (SIGNATURE |series| ($ #2#)) (SIGNATURE |pole?| ((|Boolean|) $)) (SIGNATURE |order| (#3=(|NonNegativeInteger|) $)) (SIGNATURE |order| (#3# $ #3#)) (SIGNATURE * ($ $ (|Integer|))) (IF (|has| |#1| #4=(|IntegralDomain|)) (ATTRIBUTE #4#) |%noBranch|))) #1#) (T |InnerTaylorSeries|)) +((|coefficients| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Stream| *3)) #3=(|isDomain| *1 (|InnerTaylorSeries| *3)) #4=(|ofCategory| *3 (|Ring|)))) (|series| (*1 *1 *2) (AND #2# #4# #3#)) (|pole?| #1# (AND (|isDomain| *2 (|Boolean|)) #3# #4#)) (|order| #1# #5=(AND (|isDomain| 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$)) (SIGNATURE |filterUntil| #1#) (SIGNATURE |select| #1#) (SIGNATURE |generate| ($ (|Mapping| |#1| |#1|) |#1|)) (SIGNATURE |construct| ((|Stream| |#1|) $)))) (|Type|)) (T |InfiniteTuple|)) +((|filterWhile| #1=(*1 *1 *2 *1) #2=(AND (|isDomain| *2 (|Mapping| (|Boolean|) *3)) #3=(|ofCategory| *3 (|Type|)) #4=(|isDomain| *1 (|InfiniteTuple| *3)))) (|filterUntil| #1# #2#) (|select| #1# #2#) (|generate| (*1 *1 *2 *3) (AND (|isDomain| *2 (|Mapping| *3 *3)) #3# #4#)) (|construct| (*1 *2 *1) (AND (|isDomain| *2 (|Stream| *3)) #4# #3#))) +((|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| 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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 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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)) +((~= #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#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| #14=(($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) 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|#2|)))) ELT) (($ (|Mapping| #3# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #4#) 43 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT) (((|Union| |#2| "failed") |#1| $) 60 T ELT)) (|remove| (($ (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) $) 50 (AND (|has| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) . #8#) (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))))) ELT) (($ (|Mapping| #5# (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #6#) 48 (|has| $ (|FiniteAggregate| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) ELT)) (|qsetelt!| ((|#2| $ |#1| |#2|) 69 (|has| $ (|ShallowlyMutableAggregate| |#2|)) ELT)) (|qelt| ((|#2| $ |#1|) 71 T ELT)) (|minIndex| ((|#1| . #9=($)) 79 (|has| |#1| . #10=((|OrderedSet|))) ELT)) (|maxIndex| ((|#1| . #9#) 78 (|has| |#1| . #10#) ELT)) (|map!| (($ (|Mapping| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) . #11=($)) 39 T ELT) (($ (|Mapping| 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$) NIL T ELT)) (|unit?| #6=(#3# NIL T ELT)) (|trailingCoefficient| (#7=(|#1| $) 55 T ELT)) (|subtractIfCan| (#8=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|sizeLess?| (#1# NIL #11=(|has| |#1| (|Field|)) ELT)) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| #12=(|Fraction| |#2|))) #12#) 111 #11# ELT)) (|sample| (#13=($) NIL T CONST)) (|retractIfCan| (((|Union| #14=(|Integer|) . #15=(#10#)) . #16=($)) NIL #17=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| #18=(|Fraction| #14#) . #15#) . #16#) NIL #19=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| |#1| . #15#) $) 99 T ELT) (((|Union| |#2| . #15#) $) 95 T ELT)) (|retract| (#20=(#14# $) NIL #17# ELT) ((#18# . #21=($)) NIL #19# ELT) (#7# NIL T ELT) ((|#2| . #21#) NIL T ELT)) (|rem| #22=(#23=($ $ $) NIL #11# ELT)) (|reductum| (#5# 27 T ELT)) (|recip| ((#9# $) 88 T ELT)) (|quo| #22#) (|principalIdeal| (((|Record| (|:| |coef| #24=(|List| $)) #25=(|:| |generator| $)) #24#) NIL #11# ELT)) (|order| (#20# 22 T ELT)) 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T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#6# 81 T ELT)) (|identification| (((|List| (|Equation| |#2|)) $ $) 42 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exp| (($ #7#) 56 T ELT)) (|conjugate| #8=(#9=($ $ $) NIL T ELT)) (|commutator| #8#) (|coerce| (((|OutputForm|) $) 66 T ELT) (((|XDistributedPolynomial| |#1| |#2|) $) NIL T ELT) (((|XPBWPolynomial| |#1| |#2|) $) 74 T ELT)) (|before?| #1#) (|One| (#5# 61 T CONST)) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) #10=(|:| |c| |#2|))) $) 41 T ELT)) (|LyndonBasis| (((|List| #7#) #4#) 73 T ELT)) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) #10#)) $) 46 T ELT)) (= (#2# 62 T ELT)) (/ #8#) (** (($ $ (|PositiveInteger|)) NIL T ELT) (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ (|Integer|)) NIL T ELT)) (* (#9# 52 T ELT))) +(((|LieExponentials| |#1| |#2| |#3|) (|Join| (|Group|) (CATEGORY |domain| (SIGNATURE |exp| ($ #1=(|LiePolynomial| |#1| |#2|))) (SIGNATURE |log| (#1# $)) (SIGNATURE |ListOfTerms| ((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) #2=(|:| |c| |#2|))) $)) (SIGNATURE |coerce| ((|XDistributedPolynomial| |#1| |#2|) $)) (SIGNATURE |coerce| ((|XPBWPolynomial| |#1| |#2|) $)) (SIGNATURE |mirror| ($ $)) (SIGNATURE |varList| (#3=(|List| |#1|) $)) (SIGNATURE |LyndonBasis| ((|List| #1#) #3#)) (SIGNATURE |LyndonCoordinates| ((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) #2#)) $)) (SIGNATURE |identification| ((|List| (|Equation| |#2|)) $ $)))) (|OrderedSet|) (|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|)))) (|PositiveInteger|)) (T |LieExponentials|)) +((|exp| (*1 *1 *2) (AND #1=(|isDomain| *2 (|LiePolynomial| *3 *4)) #2=(|ofCategory| *3 #3=(|OrderedSet|)) #4=(|ofCategory| *4 #5=(|Join| (|CommutativeRing|) (|Module| (|Fraction| (|Integer|))))) #6=(|isDomain| *1 (|LieExponentials| *3 *4 *5)) #7=(|ofType| *5 #8=(|PositiveInteger|)))) (|log| #9=(*1 *2 *1) (AND #1# #6# #2# #4# #7#)) (|ListOfTerms| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| *3)) #10=(|:| |c| *4)))) #6# #2# #4# #7#)) (|coerce| #9# (AND (|isDomain| *2 (|XDistributedPolynomial| *3 *4)) #6# #2# #4# #7#)) (|coerce| #9# (AND (|isDomain| *2 (|XPBWPolynomial| *3 *4)) #6# #2# #4# #7#)) (|mirror| (*1 *1 *1) (AND (|isDomain| *1 (|LieExponentials| *2 *3 *4)) (|ofCategory| *2 #3#) (|ofCategory| *3 #5#) (|ofType| *4 #8#))) (|varList| #9# (AND (|isDomain| *2 (|List| *3)) #6# #2# #4# #7#)) (|LyndonBasis| (*1 *2 *3) (AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #3#) (|isDomain| *2 (|List| (|LiePolynomial| *4 *5))) (|isDomain| *1 (|LieExponentials| *4 *5 *6)) (|ofCategory| *5 #5#) (|ofType| *6 #8#))) (|LyndonCoordinates| #9# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| (|LyndonWord| *3)) #10#))) #6# #2# #4# #7#)) (|identification| (*1 *2 *1 *1) (AND (|isDomain| *2 (|List| (|Equation| *4))) #6# #2# #4# #7#))) +((|zeroSetSplit| (#1=((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #2=(|OrderedVariableList| |#2|)) #2# #3=(|NewSparseMultivariatePolynomial| |#1| #2#))) #4=(|List| #3#) #5=(|Boolean|)) 103 T ELT) (#6=((|List| (|RegularChain| |#1| |#2|)) #4# #5#) 77 T ELT)) (|zeroDimensional?| ((#5# #4#) 26 T ELT)) (|squareFreeLexTriangular| (#1# 102 T ELT)) (|lexTriangular| (#6# 76 T ELT)) (|groebner| ((#4# #4#) 30 T ELT)) (|fglmIfCan| (((|Union| #4# "failed") #4#) 29 T ELT))) +(((|LexTriangularPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |zeroDimensional?| (#1=(|Boolean|) #2=(|List| #3=(|NewSparseMultivariatePolynomial| |#1| #4=(|OrderedVariableList| |#2|))))) (SIGNATURE |fglmIfCan| ((|Union| #2# "failed") #2#)) (SIGNATURE |groebner| (#2# #2#)) (SIGNATURE |lexTriangular| #5=((|List| (|RegularChain| |#1| |#2|)) #2# #1#)) (SIGNATURE |squareFreeLexTriangular| #6=((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| #4#) #4# #3#)) #2# #1#)) (SIGNATURE |zeroSetSplit| #5#) (SIGNATURE |zeroSetSplit| #6#)) (|GcdDomain|) (|List| 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T) ((|ArcTrigonometricFunctionCategory|) . T) ((|ElementaryFunctionCategory|) . T) ((|HyperbolicFunctionCategory|) . T) ((|PrimitiveFunctionCategory|) . T) ((|TranscendentalFunctionCategory|) . T) ((|TrigonometricFunctionCategory|) . 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#8#) NIL T ELT) ((#8# #26# $) NIL T ELT)) (|qsetelt!| #15#) (|qelt| #27=((#5# $ #9#) NIL T ELT)) (|pack!| #28=(#23# NIL T ELT)) (|minIndex| #29=(#30=(#9# $) NIL #31=(|has| #9# (|OrderedSet|)) ELT)) (|members| ((#13# $) NIL T ELT)) (|member?| ((#3# #8# $) NIL #7# ELT)) (|maxIndex| #29#) (|map!| #32=(($ (|Mapping| #8# #8#) . #33=($)) NIL T ELT) #34=(($ (|Mapping| #5# #5#) . #33#) NIL T ELT)) (|map| #32# #34# #32# (($ (|Mapping| #5# #5# #5#) $ $) NIL T ELT)) (|library| (($ (|FileName|)) 8 T ELT)) (|latex| (#30# NIL #35=(OR #36=(|has| #5# #37=(|SetCategory|)) #38=(|has| #8# #37#)) ELT)) (|keys| #39=(((|List| #9#) $) NIL T ELT)) (|key?| #40=((#3# #9# $) NIL T ELT)) (|inspect| #41=((#8# $) NIL T ELT)) (|insert!| (#25# NIL T ELT)) (|indices| #39#) (|index?| #40#) (|hash| (((|SingleInteger|) $) NIL #35# ELT)) (|first| ((#5# $) NIL #31# ELT)) (|find| (((|Union| #8# #22#) #19# $) NIL T ELT)) (|fill!| (($ $ #5#) NIL #14# ELT)) (|extract!| #41#) (|every?| #42=((#3# #19# $) NIL T ELT)) (|eval| 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#42#) (= #1#) (|#| ((#52# $) NIL T ELT))) +(((|Library|) (|Join| (|TableAggregate| (|String|) #1=(|Any|)) (|Eltable| #2=(|Symbol|) #1#) (CATEGORY |domain| (SIGNATURE |library| ($ (|FileName|))) (SIGNATURE |pack!| ($ $)) (SIGNATURE |setelt| (#1# $ #2# #1#))))) (T |Library|)) +((|library| (*1 *1 *2) (AND (|isDomain| *2 (|FileName|)) #1=(|isDomain| *1 (|Library|)))) (|pack!| (*1 *1 *1) #1#) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *2 (|Any|)) (|isDomain| *3 (|Symbol|)) #1#))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|unit| #3=((#4=(|Union| $ #5="failed")) NIL #6=(OR (AND #7=(|has| |#2| (|FiniteRankNonAssociativeAlgebra| |#1|)) #8=(|has| |#1| (|IntegralDomain|))) (AND #9=(|has| |#2| (|FramedNonAssociativeAlgebra| |#1|)) #8#)) ELT)) (|subtractIfCan| ((#4# $ $) NIL T ELT)) (|structuralConstants| ((#10=(|Vector| #11=(|Matrix| |#1|))) NIL #9# ELT) ((#10# #12=(|Vector| $)) NIL #7# ELT)) (|someBasis| (#13=(#12#) NIL #7# ELT)) (|sample| (#14=($) NIL T CONST)) (|rightUnits| #15=(((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) #5#)) NIL #6# ELT)) (|rightUnit| #3#) (|rightTraceMatrix| #16=((#11#) NIL #9# ELT) #17=(#18=(#11# #12#) NIL #7# ELT)) (|rightTrace| #19=((|#1| $) NIL #7# ELT)) (|rightRegularRepresentation| #20=((#11# $) NIL #9# ELT) #21=((#11# $ #12#) NIL #7# ELT)) (|rightRecip| #22=((#4# $) NIL #6# ELT)) (|rightRankPolynomial| #23=(((|SparseUnivariatePolynomial| #24=(|Polynomial| |#1|))) NIL (AND #9# (|has| |#1| (|Field|))) ELT)) (|rightPower| #25=(#26=($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|rightNorm| #19#) (|rightMinimalPolynomial| #28=(#29=((|SparseUnivariatePolynomial| |#1|) $) NIL #6# ELT)) (|rightDiscriminant| #30=((|#1|) NIL #9# ELT) #31=((|#1| #12#) NIL #7# ELT)) (|rightCharacteristicPolynomial| #32=(#29# NIL #7# ELT)) (|rightAlternative?| #33=((#2#) NIL #7# ELT)) (|represents| #34=(($ #35=(|Vector| |#1|)) NIL #9# ELT) (($ #35# #12#) NIL #7# ELT)) (|recip| #22#) (|rank| ((#27#) NIL #7# ELT)) 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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)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| (#3=($) 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#))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (= (#1# 8 T ELT)) (* (($ |#1| $) 17 T ELT) (($ $ |#1|) 20 T ELT))) +(((|LinearSet| |#1|) (|Category|) (|SemiGroup|)) (T |LinearSet|)) +NIL +(|Join| (|LeftLinearSet| |t#1|) (|RightLinearSet| |t#1|)) +(((|BasicType|) . 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#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| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT) (($ $ (|List| |#1|) (|List| |#1|)) 22 (AND (|has| |#1| (|Evalable| |#1|)) (|has| |#1| . #10#)) ELT)) (|eq?| ((#12=(|Boolean|) $ $) 10 T ELT)) (|entry?| ((#11# |#1| $) 40 (AND (|has| $ (|FiniteAggregate| |#1|)) (|has| |#1| (|BasicType|))) ELT)) (|entries| (((|List| |#1|) $) 43 T ELT)) (|empty?| ((#12# $) 7 T ELT)) (|empty| (#6# 8 T ELT)) (|elt| ((|#1| $ #3# |#1|) 45 T ELT) ((|#1| $ #3#) 44 T ELT) (($ $ (|UniversalSegment| (|Integer|))) 66 T ELT)) (|delete| (($ $ (|Integer|)) 59 T ELT) (($ $ (|UniversalSegment| (|Integer|))) 58 T ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#13=(|InputForm|) $) 72 (|has| |#1| (|ConvertibleTo| #13#)) ELT)) (|construct| (($ (|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)) (= (#1# 17 (|has| |#1| . #2#) ELT))) +(((|LinearAggregate| |#1|) (|Category|) (|Type|)) (T |LinearAggregate|)) +((|new| (*1 *1 *2 *3) (AND (|isDomain| *2 (|NonNegativeInteger|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|concat| (*1 *1 *1 *2) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2 *1) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *1 *1) (AND (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|concat| (*1 *1 *2) (AND (|isDomain| *2 (|List| *1)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|map| (*1 *1 *2 *1 *1) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete| (*1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|delete| (*1 *1 *1 *2) (AND (|isDomain| *2 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|insert| (*1 *1 *2 *1 *3) (AND (|isDomain| *3 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|insert| (*1 *1 *1 *1 *2) (AND (|isDomain| *2 (|Integer|)) (|ofCategory| *1 (|LinearAggregate| *3)) (|ofCategory| *3 (|Type|)))) (|setelt| (*1 *2 *1 *3 *2) (AND (|isDomain| *3 (|UniversalSegment| (|Integer|))) (|ofCategory| *1 (|ShallowlyMutableAggregate| *2)) (|ofCategory| *1 (|LinearAggregate| *2)) (|ofCategory| *2 (|Type|))))) +(|Join| (|IndexedAggregate| (|Integer|) |t#1|) (|Collection| |t#1|) (|Eltable| (|UniversalSegment| (|Integer|)) $) (CATEGORY |domain| (SIGNATURE |new| ($ (|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|) $ $)) (SIGNATURE |delete| ($ $ (|Integer|))) (SIGNATURE |delete| ($ $ (|UniversalSegment| (|Integer|)))) (SIGNATURE |insert| ($ |t#1| $ (|Integer|))) (SIGNATURE |insert| ($ $ $ (|Integer|))) (IF (|has| $ (|ShallowlyMutableAggregate| |t#1|)) (SIGNATURE |setelt| (|t#1| $ (|UniversalSegment| (|Integer|)) |t#1|)) |%noBranch|))) +(((|Aggregate|) . 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)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 15 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 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#))) +((|solve| (((|Union| |#2| #1="failed") |#3| |#2| #2=(|Symbol|) |#2| #3=(|List| |#2|)) 174 T ELT) (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #3#)) #1#) |#3| |#2| #2#) 44 T ELT))) +(((|ElementaryFunctionLODESolver| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #1=(|List| |#2|))) #2="failed") |#3| |#2| #3=(|Symbol|))) (SIGNATURE |solve| ((|Union| |#2| #2#) |#3| |#2| #3# |#2| #1#))) (|Join| (|EuclideanDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)) (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (T |ElementaryFunctionLODESolver|)) +((|solve| (*1 *2 *3 *2 *4 *2 *5) (|partial| AND (|isDomain| *4 #1=(|Symbol|)) (|isDomain| *5 (|List| *2)) (|ofCategory| *2 #2=(|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) #3=(|ofCategory| *6 (|Join| (|EuclideanDomain|) (|RetractableTo| #4=(|Integer|)) (|LinearlyExplicitRingOver| #4#) (|CharacteristicZero|))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *2 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)))) (|solve| (*1 *2 *3 *4 *5) (|partial| AND (|isDomain| *5 #1#) #3# (|ofCategory| *4 #2#) (|isDomain| *2 (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|ElementaryFunctionLODESolver| *6 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (#6=($ $ $) 28 #5# ELT)) (|symmetricPower| (#7=($ $ #8=(|NonNegativeInteger|)) 31 #5# ELT)) (|subtractIfCan| (#9=(#10=(|Union| $ #11="failed") $ $) NIL T ELT)) (|sample| (#12=($) NIL T CONST)) (|rightRemainder| #13=(#6# NIL #5# ELT)) (|rightQuotient| #13#) (|rightLcm| #13#) (|rightGcd| #13#) (|rightExtendedGcd| #14=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #15=(#9# NIL #5# ELT)) (|rightDivide| #16=(#17=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #18=(|Integer|) . #19=(#11#)) . #20=($)) NIL #21=(|has| |#1| (|RetractableTo| #18#)) ELT) (((|Union| #22=(|Fraction| #18#) . #19#) . #20#) NIL #23=(|has| |#1| (|RetractableTo| #22#)) ELT) (((|Union| |#1| . #19#) . #20#) NIL T ELT)) (|retract| ((#18# . #24=($)) NIL #21# ELT) ((#22# . #24#) NIL #23# ELT) #25=(#26=(|#1| . #24#) NIL T ELT)) (|reductum| #27=(#4# NIL T ELT)) (|recip| ((#10# $) NIL T ELT)) (|primitivePart| (#4# NIL #28=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #8#) NIL T ELT)) (|monicRightDivide| #29=(#17# NIL #30=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #29#) (|minimumDegree| #31=((#8# $) NIL T ELT)) (|leftRemainder| #13#) (|leftQuotient| #13#) (|leftLcm| #13#) (|leftGcd| #13#) (|leftExtendedGcd| #14#) (|leftExactQuotient| #15#) (|leftDivide| #16#) (|leadingCoefficient| #25#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#10# $ |#1|) NIL #30# ELT)) (|elt| ((|#1| $ |#1|) 24 T ELT)) (|directSum| (#6# 33 #5# ELT)) (|degree| #31#) (|content| (#26# NIL #28# ELT)) (|coerce| (((|OutputForm|) $) 20 T ELT) (($ #18#) NIL T ELT) (($ #22#) NIL #23# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #8#) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 23 T ELT)) (|annihilate?| #1#) (|adjoint| #27#) (|Zero| (#12# 21 T CONST)) (|One| (#12# 8 T CONST)) (D (#12# NIL T ELT)) (= #1#) (- #27# #32=(#6# NIL T ELT)) (+ #32#) (** (($ $ #33=(|PositiveInteger|)) NIL T ELT) (#7# NIL T ELT)) (* (($ #33# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #18# . #34=($)) NIL T ELT) #32# (($ $ |#1|) NIL T ELT) (($ |#1| . #34#) NIL T ELT))) +(((|LinearOrdinaryDifferentialOperator| |#1| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Ring|) (|Mapping| |#1| |#1|)) (T |LinearOrdinaryDifferentialOperator|)) +NIL +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|sample| #13=(#14=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #15=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #16=(#10# NIL #5# ELT)) (|rightDivide| #17=(#18=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #19=(|Integer|) . #20=(#12#)) . #21=($)) NIL #22=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #23=(|Fraction| #19#) . #20#) . #21#) NIL #24=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| |#1| . #20#) . #21#) NIL T ELT)) (|retract| ((#19# . #25=($)) NIL #22# ELT) ((#23# . #25#) NIL #24# ELT) #26=(#27=(|#1| . #25#) NIL T ELT)) (|reductum| #28=(#4# NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#4# NIL #29=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #30=(#18# NIL #31=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #30#) (|minimumDegree| #32=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #15#) (|leftExactQuotient| #16#) (|leftDivide| #17#) (|leadingCoefficient| #26#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#1|) NIL #31# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|directSum| #6#) (|degree| #32#) (|content| (#27# NIL #29# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) (($ #23#) NIL #24# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #28#) (|Zero| #13#) (|One| #13#) (D (#14# NIL T ELT)) (= #1#) (- #28# #33=(#7# NIL T ELT)) (+ #33#) (** (($ $ #34=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #34# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #19# . #35=($)) NIL T ELT) #33# (($ $ |#1|) NIL T ELT) (($ |#1| . #35#) NIL T ELT))) +(((|LinearOrdinaryDifferentialOperator1| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|DifferentialRing|)) (T |LinearOrdinaryDifferentialOperator1|)) +NIL +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetricSquare| (#4=($ $) NIL #5=(|has| |#1| (|Field|)) ELT)) (|symmetricProduct| #6=(#7=($ $ $) NIL #5# ELT)) (|symmetricPower| (#8=($ $ #9=(|NonNegativeInteger|)) NIL #5# ELT)) (|subtractIfCan| (#10=(#11=(|Union| $ #12="failed") $ $) NIL T ELT)) (|sample| #13=(#14=($) NIL T CONST)) (|rightRemainder| #6#) (|rightQuotient| #6#) (|rightLcm| #6#) (|rightGcd| #6#) (|rightExtendedGcd| #15=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #5# ELT)) (|rightExactQuotient| #16=(#10# NIL #5# ELT)) (|rightDivide| #17=(#18=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #5# ELT)) (|retractIfCan| (((|Union| #19=(|Integer|) . #20=(#12#)) . #21=($)) NIL #22=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| #23=(|Fraction| #19#) . #20#) . #21#) NIL #24=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| |#1| . #20#) . #21#) NIL T ELT)) (|retract| ((#19# . #25=($)) NIL #22# ELT) ((#23# . #25#) NIL #24# ELT) #26=(#27=(|#1| . #25#) NIL T ELT)) (|reductum| #28=(#4# NIL T ELT)) (|recip| ((#11# $) NIL T ELT)) (|primitivePart| (#4# NIL #29=(|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #9#) NIL T ELT)) (|monicRightDivide| #30=(#18# NIL #31=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| #30#) (|minimumDegree| #32=((#9# $) NIL T ELT)) (|leftRemainder| #6#) (|leftQuotient| #6#) (|leftLcm| #6#) (|leftGcd| #6#) (|leftExtendedGcd| #15#) (|leftExactQuotient| #16#) (|leftDivide| #17#) (|leadingCoefficient| #26#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#11# $ |#1|) NIL #31# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) ((|#2| $ |#2|) 13 T ELT)) (|directSum| #6#) (|degree| #32#) (|content| (#27# NIL #29# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #19#) NIL T ELT) (($ #23#) NIL #24# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #9#) NIL T ELT)) (|characteristic| ((#9#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) NIL T ELT)) (|annihilate?| #1#) (|adjoint| #28#) (|Zero| #13#) (|One| #13#) (D (#14# NIL T ELT)) (= #1#) (- #28# #33=(#7# NIL T ELT)) (+ #33#) (** (($ $ #34=(|PositiveInteger|)) NIL T ELT) (#8# NIL T ELT)) (* (($ #34# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #19# . #35=($)) NIL T ELT) #33# (($ $ |#1|) NIL T ELT) (($ |#1| . #35#) NIL T ELT))) +(((|LinearOrdinaryDifferentialOperator2| |#1| |#2|) (|Join| (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|Eltable| |#2| |#2|)) (|DifferentialRing|) (|Join| (|LeftModule| |#1|) (CATEGORY |domain| (SIGNATURE |differentiate| ($ $))))) (T |LinearOrdinaryDifferentialOperator2|)) +NIL +((|symmetricSquare| (#1=($ $) 29 T ELT)) (|adjoint| (#1# 27 T ELT)) (D (($) 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|) $) 22 T ELT)) (|symmetricSquare| (($ $) 96 (|has| |#1| (|Field|)) ELT)) (|symmetricProduct| (($ $ $) 98 (|has| |#1| (|Field|)) ELT)) (|symmetricPower| (($ $ (|NonNegativeInteger|)) 97 (|has| |#1| (|Field|)) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (#4=($ $ $) 58 (|has| |#1| . #5=((|Field|))) ELT)) (|rightQuotient| (#4# 59 (|has| |#1| . #5#) ELT)) (|rightLcm| (#4# 61 (|has| |#1| . #5#) ELT)) (|rightGcd| (#4# 56 (|has| |#1| . #5#) ELT)) (|rightExtendedGcd| (#6=((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 55 (|has| |#1| . #5#) ELT)) (|rightExactQuotient| (#7=(#8=(|Union| $ "failed") $ $) 57 (|has| |#1| . #5#) ELT)) (|rightDivide| (#9=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 60 (|has| |#1| . #5#) ELT)) (|retractIfCan| (((|Union| #10=(|Integer|) . #11=("failed")) . #12=($)) 88 (|has| |#1| . #13=((|RetractableTo| #10#))) ELT) (((|Union| #14=(|Fraction| #10#) . #11#) . #12#) 85 (|has| |#1| . #15=((|RetractableTo| #14#))) ELT) (((|Union| |#1| . #11#) . #12#) 82 T ELT)) (|retract| ((#10# . #16=($)) 87 (|has| |#1| . #13#) ELT) ((#14# . #16#) 84 (|has| |#1| . #15#) ELT) ((|#1| . #16#) 83 T ELT)) (|reductum| (#17=($ $) 77 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (#17# 68 (|has| |#1| . #18=((|GcdDomain|))) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| #19=(|NonNegativeInteger|)) 75 T ELT)) (|monicRightDivide| (#9# 70 (|has| |#1| . #20=((|IntegralDomain|))) ELT)) (|monicLeftDivide| (#9# 71 (|has| |#1| . #20#) ELT)) (|minimumDegree| (#21=(#19# $) 79 T ELT)) (|leftRemainder| (#4# 65 (|has| |#1| . #5#) ELT)) (|leftQuotient| (#4# 66 (|has| |#1| . #5#) ELT)) (|leftLcm| (#4# 54 (|has| |#1| . #5#) ELT)) (|leftGcd| (#4# 63 (|has| |#1| . #5#) ELT)) (|leftExtendedGcd| (#6# 62 (|has| |#1| . #5#) ELT)) (|leftExactQuotient| (#7# 64 (|has| |#1| . #5#) ELT)) (|leftDivide| (#9# 67 (|has| |#1| . #5#) ELT)) (|leadingCoefficient| ((|#1| . #22=($)) 78 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| ((#8# $ |#1|) 72 (|has| |#1| . #20#) ELT)) (|elt| ((|#1| $ |#1|) 101 T ELT)) (|directSum| (($ $ $) 95 (|has| |#1| (|Field|)) ELT)) (|degree| (#21# 80 T ELT)) (|content| ((|#1| . #22#) 69 (|has| |#1| . #18#) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #14#) 86 (|has| |#1| . #15#) ELT) (($ |#1|) 81 T ELT)) (|coefficients| (((|List| |#1|) $) 74 T ELT)) (|coefficient| ((|#1| $ #19#) 76 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|apply| ((|#1| $ |#1| |#1|) 73 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|adjoint| (($ $) 99 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($) 100 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #23=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 90 T ELT) (($ |#1| . #23#) 89 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)) +((|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#)))) +((|symmetricProduct| (#1=(|#2| |#2| |#2| #2=(|Mapping| |#1| |#1|)) 65 T ELT)) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) #2#) 45 T ELT)) (|directSum| (#1# 67 T ELT))) +(((|LinearOrdinaryDifferentialOperatorsOps| |#1| |#2|) (CATEGORY |package| (SIGNATURE |symmetricProduct| #1=(|#2| |#2| |#2| #2=(|Mapping| |#1| |#1|))) (SIGNATURE |symmetricPower| (|#2| |#2| (|NonNegativeInteger|) #2#)) (SIGNATURE |directSum| #1#)) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |LinearOrdinaryDifferentialOperatorsOps|)) +((|directSum| #1=(*1 *2 *2 *2 *3) #2=(AND (|isDomain| *3 (|Mapping| *4 *4)) (|ofCategory| *4 #3=(|Field|)) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *4 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *4)))) (|symmetricPower| (*1 *2 *2 *3 *4) (AND (|isDomain| *3 (|NonNegativeInteger|)) (|isDomain| *4 (|Mapping| *5 *5)) (|ofCategory| *5 #3#) (|isDomain| *1 (|LinearOrdinaryDifferentialOperatorsOps| *5 *2)) (|ofCategory| *2 (|LinearOrdinaryDifferentialOperatorCategory| *5)))) (|symmetricProduct| #1# #2#)) +((|\\/| (($ $ $) 9 T ELT))) +(((|Logic&| |#1|) (CATEGORY |package| (SIGNATURE |\\/| (|#1| |#1| |#1|))) (|Logic|)) (T |Logic&|)) +NIL +((~ (($ $) 8 T ELT)) (|\\/| (($ $ $) 6 T ELT)) (|/\\| (($ $ $) 7 T ELT))) +(((|Logic|) (|Category|)) (T |Logic|)) +((~ (*1 *1 *1) (|ofCategory| *1 (|Logic|))) (|/\\| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|))) (|\\/| (*1 *1 *1 *1) (|ofCategory| *1 (|Logic|)))) +(|Join| (|Type|) (CATEGORY |domain| (SIGNATURE ~ ($ $)) (SIGNATURE |/\\| ($ $ $)) (SIGNATURE |\\/| ($ $ $)))) +(((|Join|) . T) ((|Type|) . 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*3 *3 *4 *5 *6) (AND (|isDomain| *3 (|Expression| (|Integer|))) (|isDomain| *4 (|Mapping| #2# #2#)) #6=(|isDomain| *5 #7=(|Segment| #2#)) #8=(|isDomain| *6 #9=(|List| (|DrawOption|))) #10=(|isDomain| *2 (|ThreeSpace| #2#)) #5#)) (|meshFun2Var| (*1 *2 *3 *4 *5 *5 *6) #11=(AND #1# (|isDomain| *4 (|Union| #3# "undefined")) #6# #8# #10# #5#)) (|meshPar2Var| (*1 *2 *2 *3 *4 *4 *5) (AND #10# #12=(|isDomain| *3 #4#) #13=(|isDomain| *4 #7#) #14=(|isDomain| *5 #9#) #5#)) (|meshPar2Var| (*1 *2 *3 *4 *4 *5) (AND #12# #13# #14# #10# #5#)) (|meshPar2Var| (*1 *2 *3 *3 *3 *4 *5 *5 *6) #11#)) +((|factor| (((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#) 87 T ELT) (((|Factored| |#4|) |#4|) 270 T ELT))) +(((|MultFiniteFactorize| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|)) (SIGNATURE |factor| ((|Factored| #1=(|SparseUnivariatePolynomial| |#4|)) #1#))) (|OrderedSet|) (|OrderedAbelianMonoidSup|) (|FiniteFieldCategory|) (|PolynomialCategory| |#3| |#2| |#1|)) (T |MultFiniteFactorize|)) +((|factor| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 (|OrderedSet|)) #3=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *6 (|FiniteFieldCategory|)) (|ofCategory| *7 #5=(|PolynomialCategory| *6 *5 *4)) (|isDomain| *2 (|Factored| #6=(|SparseUnivariatePolynomial| *7))) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *7)) (|isDomain| *3 #6#))) (|factor| #1# (AND #2# #3# #4# (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MultFiniteFactorize| *4 *5 *6 *3)) (|ofCategory| *3 #5#)))) +((|rowEchelonLocal| ((#1=(|Matrix| |#1|) #1# |#1| |#1|) 85 T ELT)) (|rowEchelon| (#2=(#1# #1# |#1|) 66 T ELT)) (|rowEchLocal| (#2# 86 T ELT)) (|rowEch| ((#1# #1#) 67 T ELT)) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) 84 T ELT))) +(((|ModularHermitianRowReduction| |#1|) (CATEGORY |package| (SIGNATURE |rowEch| (#1=(|Matrix| |#1|) #1#)) (SIGNATURE |rowEchelon| #2=(#1# #1# |#1|)) (SIGNATURE |rowEchLocal| #2#) (SIGNATURE 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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)) +((|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))))) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| ((#2=(|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exprex| (#3=(#2# #4=(|OutputForm|)) 36 T ELT)) 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+((|modulus| #1=(*1 *2 *1) (AND (|ofCategory| *2 #2=(|AbelianMonoid|)) (|isDomain| *1 (|ModularField| *3 *2 *4 *5 *6)) (|ofCategory| *3 #3=(|CommutativeRing|)) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #4=(|Union| *2 #5="failed") *2 *2)) (|ofType| *6 (|Mapping| #6=(|Union| *3 #5#) *3 *3 *2)))) (|coerce| #1# (AND #7=(|ofCategory| *2 #3#) #8=(|isDomain| *1 (|ModularField| *2 *3 *4 *5 *6)) #9=(|ofCategory| *3 #2#) #10=(|ofType| *4 (|Mapping| *2 *2 *3)) #11=(|ofType| *5 (|Mapping| #6# *3 *3)) #12=(|ofType| *6 (|Mapping| #4# *2 *2 *3)))) (|reduce| (*1 *1 *2 *3) (AND #8# #7# #9# #10# #11# #12#)) (|exQuo| (*1 *1 *1 *1) (|partial| AND #8# #7# #9# #10# #11# #12#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 37 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #9=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| 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*3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *2))))) +((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|min| #3=(($ $ $) NIL T ELT)) (|max| #3#) (|latex| (((|String|) $) NIL T ELT)) (|index| ((|#1| $) 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exponent| ((|#2| $) 12 T ELT)) (|construct| (($ |#1| |#2|) 16 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #4=(|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) 15 T ELT) ((#4# $) 14 T ELT)) (|before?| #1#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< (#2# 11 T ELT))) +(((|ModuleMonomial| |#1| |#2| |#3|) (|Join| #1=(|OrderedSet|) (|HomotopicTo| #2=(|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) (CATEGORY |domain| (SIGNATURE |exponent| (|#2| $)) (SIGNATURE |index| (|#1| $)) (SIGNATURE |construct| ($ |#1| |#2|)))) #1# (|SetCategory|) (|Mapping| (|Boolean|) #2# #2#)) (T |ModuleMonomial|)) +((|exponent| #1=(*1 *2 *1) (AND (|ofCategory| *2 #2=(|SetCategory|)) (|isDomain| *1 (|ModuleMonomial| *3 *2 *4)) (|ofCategory| *3 #3=(|OrderedSet|)) (|ofType| *4 (|Mapping| #4=(|Boolean|) #5=(|Record| (|:| |index| *3) (|:| |exponent| *2)) #5#)))) (|index| #1# (AND #6=(|ofCategory| *2 #3#) #7=(|isDomain| *1 (|ModuleMonomial| *2 *3 *4)) #8=(|ofCategory| *3 #2#) #9=(|ofType| *4 (|Mapping| #4# #10=(|Record| (|:| |index| *2) (|:| |exponent| *3)) #10#)))) (|construct| (*1 *1 *2 *3) (AND #7# #6# #8# #9#))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) 66 T ELT)) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| (#6=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #7=(#5#)) $) 101 T ELT) (((|Union| #8=(|BasicOperator|) . #7#) $) 107 T ELT)) (|retract| ((|#1| . #9=($)) NIL T ELT) ((#8# . #9#) 39 T ELT)) (|recip| ((#4# $) 102 T ELT)) (|opposite?| #1#) (|opeval| ((|#2| #8# |#2|) 93 T ELT)) (|one?| (#3# NIL T ELT)) (|makeop| (($ |#1| (|FreeGroup| #8#)) 14 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|evaluateInverse| (#10=($ $ (|Mapping| 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+((|recip| #1=(*1 *1 *1) #2=(|partial| AND #3=(|isDomain| *1 (|ModularRing| *2 *3 *4 *5 *6)) #4=(|ofCategory| *2 #5=(|CommutativeRing|)) #6=(|ofCategory| *3 #7=(|AbelianMonoid|)) #8=(|ofType| *4 (|Mapping| *2 *2 *3)) #9=(|ofType| *5 (|Mapping| #10=(|Union| *3 #11="failed") *3 *3)) #12=(|ofType| *6 (|Mapping| #13=(|Union| *2 #11#) *2 *2 *3)))) (|modulus| #14=(*1 *2 *1) (AND (|ofCategory| *2 #7#) (|isDomain| *1 (|ModularRing| *3 *2 *4 *5 *6)) (|ofCategory| *3 #5#) (|ofType| *4 (|Mapping| *3 *3 *2)) (|ofType| *5 (|Mapping| #13# *2 *2)) (|ofType| *6 (|Mapping| #10# *3 *3 *2)))) (|coerce| #14# (AND #4# #3# #6# #8# #9# #12#)) (|reduce| (*1 *1 *2 *3) #15=(AND #3# #4# #6# #8# #9# #12#)) (|exQuo| (*1 *1 *1 *1) #2#) (|inv| #1# #15#)) +((* (($ (|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|)) 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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|) . 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T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . 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T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|Monad|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|size| ((#1=(|NonNegativeInteger|)) 39 T ELT)) (|retractIfCan| (((|Union| #2=(|Integer|) #3="failed") $) NIL T ELT) (((|Union| #4=(|Fraction| #2#) #3#) $) NIL T ELT) (((|Union| |#2| #3#) $) 26 T ELT)) (|retract| ((#2# $) NIL T ELT) ((#4# $) NIL T ELT) (#5=(|#2| $) 23 T ELT)) (|reduce| (#6=($ |#3|) NIL T ELT) ((#7=(|Union| $ #3#) (|Fraction| |#3|)) 49 T ELT)) (|recip| ((#7# $) 69 T ELT)) (|random| (#8=($) 43 T ELT)) (|norm| (#5# 21 T ELT)) (|generator| (#8# 18 T ELT)) (|differentiate| (($ $ #9=(|Mapping| |#2| |#2|)) 57 T ELT) (($ $ #9# #1#) NIL T ELT) (($ $ #10=(|List| #11=(|Symbol|)) (|List| #1#)) NIL T ELT) (($ $ #11# #1#) NIL T ELT) (($ $ #10#) NIL T ELT) (($ $ #11#) NIL T ELT) (($ $ #1#) NIL T ELT) (($ $) NIL T ELT)) (|derivationCoordinates| (((|Matrix| |#2|) #12=(|Vector| $) #9#) 64 T ELT)) (|convert| ((#13=(|Vector| |#2|) $) NIL T ELT) (($ #13#) NIL T ELT) (#14=(|#3| $) 10 T ELT) (#6# 12 T ELT)) (|characteristicPolynomial| (#14# 36 T ELT)) (|basis| ((#12#) 33 T ELT))) 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(|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 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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| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|StepThrough|) |has| |#1| (|FiniteFieldCategory|)) ((|Type|) . T) ((|UniqueFactorizationDomain|) OR (|has| |#1| (|FiniteFieldCategory|)) (|has| |#1| (|Field|)))) +((|sample| (($) 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)) (* (($ $ $) 18 T ELT))) +(((|Monoid|) (|Category|)) (T |Monoid|)) +((|One| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|sample| (*1 *1) (|ofCategory| *1 (|Monoid|))) (|one?| (*1 *2 *1) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|Boolean|)))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|Monoid|)) (|isDomain| *2 (|NonNegativeInteger|)))) (|recip| (*1 *1 *1) (|partial| |ofCategory| *1 (|Monoid|)))) +(|Join| (|SemiGroup|) (CATEGORY |domain| (SIGNATURE |One| ($) |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)) +((~= #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)) +((|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#))) +((|reshape| ((|#7| (|List| |#5|) |#6|) NIL T ELT)) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) 27 T ELT))) +(((|MPolyCatFunctions2| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#5| |#4|) |#6|)) (SIGNATURE |reshape| (|#7| (|List| |#5|) |#6|))) (|OrderedSet|) #1=(|OrderedAbelianMonoidSup|) #1# #2=(|Ring|) #2# (|PolynomialCategory| |#4| |#2| |#1|) (|PolynomialCategory| |#5| |#3| |#1|)) (T |MPolyCatFunctions2|)) +((|reshape| #1=(*1 *2 *3 *4) (AND (|isDomain| *3 (|List| *9)) #2=(|ofCategory| *9 #3=(|Ring|)) #4=(|ofCategory| *5 (|OrderedSet|)) #5=(|ofCategory| *6 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *8 #3#) #8=(|ofCategory| *2 (|PolynomialCategory| *9 *7 *5)) #9=(|isDomain| *1 (|MPolyCatFunctions2| *5 *6 *7 *8 *9 *4 *2)) #10=(|ofCategory| *7 #6#) #11=(|ofCategory| *4 (|PolynomialCategory| *8 *6 *5)))) (|map| #1# (AND (|isDomain| *3 (|Mapping| *9 *8)) #7# #2# #4# #5# #8# #9# #10# #11#))) +((|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) 28 T ELT))) +(((|MPolyCatFunctions3| |#1| |#2| |#3| |#4| |#5| |#6| |#7|) (CATEGORY |package| (SIGNATURE |map| (|#7| (|Mapping| |#2| |#1|) |#6|))) #1=(|OrderedSet|) #1# #2=(|OrderedAbelianMonoidSup|) #2# (|Ring|) (|PolynomialCategory| |#5| |#3| |#1|) (|PolynomialCategory| |#5| |#4| |#2|)) (T |MPolyCatFunctions3|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|OrderedSet|)) (|ofCategory| *6 #1#) (|ofCategory| *7 #2=(|OrderedAbelianMonoidSup|)) (|ofCategory| *9 (|Ring|)) (|ofCategory| *2 (|PolynomialCategory| *9 *8 *6)) (|isDomain| *1 (|MPolyCatFunctions3| *5 *6 *7 *8 *9 *4 *2)) (|ofCategory| *8 #2#) (|ofCategory| *4 (|PolynomialCategory| *9 *7 *5))))) +((|factor| (((|Factored| |#4|) |#4|) 42 T ELT))) +(((|MPolyCatPolyFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#)))) (|EuclideanDomain|) (|PolynomialCategory| (|Polynomial| |#3|) |#1| |#2|)) (T |MPolyCatPolyFactorizer|)) +((|factor| (*1 *2 *3) (AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| (#1=(|Symbol|) $)) (SIGNATURE |variable| ((|Union| $ "failed") #1#))))) (|ofCategory| *6 (|EuclideanDomain|)) (|isDomain| *2 (|Factored| *3)) (|isDomain| *1 (|MPolyCatPolyFactorizer| *4 *5 *6 *3)) (|ofCategory| *3 (|PolynomialCategory| (|Polynomial| *6) *4 *5))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|variables| ((#6=(|List| #7=(|OrderedVariableList| |#1|)) $) NIL T ELT)) (|univariate| ((#8=(|SparseUnivariatePolynomial| $) $ #7#) NIL T ELT) ((#9=(|SparseUnivariatePolynomial| |#2|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#5# NIL #10# ELT)) (|totalDegree| #13=((#14=(|NonNegativeInteger|) $) NIL T ELT) ((#14# $ #6#) NIL T ELT)) (|subtractIfCan| (#15=(#16=(|Union| $ #17="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #18=(((|Factored| #8#) #8#) NIL #19=(|has| |#2| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #20=(#12# NIL #21=(|has| |#2| (|GcdDomain|)) ELT)) (|squareFree| (#22=((|Factored| $) $) NIL #21# ELT)) (|solveLinearPolynomialEquation| (((|Union| #23=(|List| #8#) #17#) #23# #8#) NIL #19# ELT)) (|sample| #24=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| . #25=(#17#)) . #26=($)) NIL T ELT) (((|Union| #27=(|Fraction| #28=(|Integer|)) . #25#) . #26#) NIL #29=(|has| |#2| (|RetractableTo| #27#)) ELT) (((|Union| #28# . #25#) . #26#) NIL #30=(|has| |#2| (|RetractableTo| #28#)) ELT) #31=(((|Union| #7# . #25#) . #26#) NIL T ELT)) (|retract| #32=(#33=(|#2| . #34=($)) NIL T ELT) ((#27# . #34#) NIL #29# ELT) ((#28# . #34#) NIL #30# ELT) ((#7# . #34#) NIL T ELT)) (|resultant| (($ $ $ #7#) NIL #35=(|has| |#2| (|CommutativeRing|)) ELT)) (|reductum| #36=(#12# NIL T ELT)) (|reducedSystem| ((#37=(|Matrix| #28#) . #38=(#39=(|Matrix| $))) NIL #40=(|has| |#2| (|LinearlyExplicitRingOver| #28#)) ELT) ((#41=(|Record| (|:| |mat| #37#) (|:| |vec| (|Vector| #28#))) . #42=(#39# #43=(|Vector| $))) NIL #40# ELT) ((#44=(|Record| (|:| |mat| #45=(|Matrix| |#2|)) (|:| |vec| (|Vector| |#2|))) . #42#) NIL T ELT) ((#45# . #38#) NIL T ELT)) (|recip| ((#16# $) NIL T ELT)) (|primitivePart| #20# #46=(#47=($ $ #7#) NIL #21# ELT)) (|primitiveMonomials| #48=((#49=(|List| $) $) NIL T ELT)) (|prime?| (#5# NIL #19# ELT)) (|pomopo!| (($ $ |#2| #50=(|IndexedExponents| #7#) $) NIL T ELT)) (|patternMatch| ((#51=(|PatternMatchResult| #52=(|Float|) . #53=($)) $ #54=(|Pattern| #52#) #51#) NIL (AND (|has| #7# #55=(|PatternMatchable| #52#)) (|has| |#2| #55#)) ELT) ((#56=(|PatternMatchResult| #28# . #53#) $ #57=(|Pattern| #28#) #56#) NIL (AND (|has| #7# #58=(|PatternMatchable| #28#)) (|has| |#2| #58#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| #13#) (|multivariate| (($ #9# #7#) NIL T ELT) (($ #8# #7#) NIL T ELT)) (|monomials| #48#) (|monomial?| #4#) (|monomial| (($ |#2| #50#) NIL T ELT) #59=(($ $ #7# #14#) NIL T ELT) #60=(($ $ #6# #61=(|List| #14#)) NIL T ELT)) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ #7#) NIL T ELT)) (|minimumDegree| #62=((#50# $) NIL T ELT) #63=((#14# $ #7#) NIL T ELT) #64=((#61# $ #6#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #50# #50#) $) NIL T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) NIL T ELT)) (|mainVariable| #31#) (|leftReducedSystem| ((#37# . #65=(#43#)) NIL #40# ELT) ((#41# . #66=(#43# $)) NIL #40# ELT) ((#44# . #66#) NIL T ELT) ((#45# . #65#) NIL T ELT)) (|leadingMonomial| #36#) (|leadingCoefficient| #32#) (|lcm| #67=(($ #49#) NIL #21# ELT) #68=(#69=($ $ $) NIL #21# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #70=(((|Union| #49# #17#) $) NIL T ELT)) (|isPlus| #70#) (|isExpt| (((|Union| (|Record| (|:| |var| #7#) (|:| |exponent| #14#)) #17#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #32#) (|gcdPolynomial| ((#8# #8# #8#) NIL #21# ELT)) (|gcd| #67# #68#) (|factorSquareFreePolynomial| #18#) (|factorPolynomial| #18#) (|factor| (#22# NIL #19# ELT)) (|exquo| ((#16# $ |#2|) NIL #10# ELT) (#15# 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 #35# 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| (#33# NIL #21# ELT) #46#) (|conditionP| (((|Union| #43# #17#) #39#) NIL #80=(AND (|has| $ #81=(|CharacteristicNonZero|)) #19#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #28#) NIL T ELT) (($ |#2|) NIL T ELT) (($ #7#) NIL T ELT) #11# (($ #27#) NIL (OR #82=(|has| |#2| (|Algebra| #27#)) #29#) ELT)) (|coefficients| ((#72# $) NIL T ELT)) (|coefficient| ((|#2| $ #50#) NIL T ELT) #59# #60#) (|charthRoot| (((|Maybe| $) $) NIL (OR #80# (|has| |#2| #81#)) ELT)) (|characteristic| ((#14#) NIL T CONST)) (|binomThmExpt| (($ $ $ #14#) NIL #35# ELT)) (|before?| #1#) (|associates?| (#2# NIL #10# ELT)) (|annihilate?| #1#) (|Zero| #24#) (|One| #24#) (D #60# #59# #73# #74#) (= #1#) (/ (#83=($ $ |#2|) NIL (|has| |#2| (|Field|)) ELT)) (- #36# #84=(#69# NIL T ELT)) (+ #84#) (** (($ $ #85=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT)) (* (($ #85# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #28# . #86=($)) NIL T ELT) #84# (($ $ #27#) NIL #82# ELT) (($ #27# . #86#) NIL #82# ELT) (($ |#2| . #86#) NIL T ELT) (#83# NIL T ELT))) +(((|MultivariatePolynomial| |#1| |#2|) (|PolynomialCategory| |#2| (|IndexedExponents| #1=(|OrderedVariableList| |#1|)) #1#) (|List| (|Symbol|)) (|Ring|)) (T |MultivariatePolynomial|)) +NIL +((|totalfract| (((|Record| (|:| |sup| #1=(|Polynomial| |#3|)) (|:| |inf| #1#)) |#4|) 14 T ELT)) (|pushup| (#2=(|#4| |#4| |#2|) 33 T ELT)) (|pushuconst| ((|#4| (|Fraction| #1#) |#2|) 62 T ELT)) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| #1#) |#2|) 74 T ELT)) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) 49 T ELT)) (|pushdown| (#2# 52 T ELT)) (|factor| (((|Factored| |#4|) |#4|) 40 T ELT))) +(((|MPolyCatRationalFunctionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |totalfract| ((|Record| (|:| |sup| #1=(|Polynomial| |#3|)) (|:| |inf| #1#)) |#4|)) (SIGNATURE |pushdown| #2=(|#4| |#4| |#2|)) (SIGNATURE |pushdterm| (|#4| (|SparseUnivariatePolynomial| |#4|) |#2|)) (SIGNATURE |pushup| #2#) (SIGNATURE |pushucoef| (|#4| (|SparseUnivariatePolynomial| #1#) |#2|)) (SIGNATURE |pushuconst| (|#4| #3=(|Fraction| #1#) |#2|)) (SIGNATURE |factor| ((|Factored| |#4|) |#4|))) (|OrderedAbelianMonoidSup|) (|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $)))) (|IntegralDomain|) (|PolynomialCategory| #3# |#1| |#2|)) (T |MPolyCatRationalFunctionFactorizer|)) +((|factor| #1=(*1 *2 *3) (AND #2=(|ofCategory| *4 #3=(|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *5 #5=(|Join| (|OrderedSet|) (CATEGORY |domain| (SIGNATURE |convert| ((|Symbol|) $))))) #6=(|ofCategory| *6 #7=(|IntegralDomain|)) (|isDomain| *2 (|Factored| *3)) #8=(|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *4 *5 *6 *3)) #9=(|ofCategory| *3 (|PolynomialCategory| #10=(|Fraction| #11=(|Polynomial| *6)) *4 *5)))) (|pushuconst| #12=(*1 *2 *3 *4) (AND #6# (|ofCategory| *2 (|PolynomialCategory| *3 *5 *4)) #13=(|isDomain| *1 (|MPolyCatRationalFunctionFactorizer| *5 *4 *6 *2)) (|isDomain| *3 #10#) #14=(|ofCategory| *5 #3#) #15=(|ofCategory| *4 #5#))) (|pushucoef| #12# (AND (|isDomain| *3 (|SparseUnivariatePolynomial| #11#)) #6# #16=(|ofCategory| *2 (|PolynomialCategory| #10# *5 *4)) #13# #14# #15#)) (|pushup| #17=(*1 *2 *2 *3) #18=(AND #2# 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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)) +((|systemCommand| (((|Void|) (|String|)) 8 T ELT))) +(((|MoreSystemCommands|) (CATEGORY |package| (SIGNATURE |systemCommand| ((|Void|) (|String|))))) (T |MoreSystemCommands|)) +((|systemCommand| (*1 *2 *3) (AND (|isDomain| *3 (|String|)) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|MoreSystemCommands|))))) +((|mergeDifference| ((#1=(|List| |#1|) #1# #1#) 15 T ELT))) +(((|MergeThing| |#1|) (CATEGORY |package| (SIGNATURE |mergeDifference| (#1=(|List| |#1|) #1# #1#))) (|OrderedSet|)) (T |MergeThing|)) +((|mergeDifference| (*1 *2 *2 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|OrderedSet|)) (|isDomain| *1 (|MergeThing| *3))))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|variables| (((|List| |#2|) $) 160 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 153 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 152 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 150 (|has| |#1| . 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|Monad|) . T) ((|SetCategory|) . T) ((|Type|) . 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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|) . 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T) ((|InputByteConduit|) . T) ((|InputOutputByteConduit|) . T) ((|OutputByteConduit|) . 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*2) (AND (|isDomain| *2 (|Integer|)) #2#)) (|random| (*1 *1 *1) #2#)) +((|Integer|) (|%not| (|%ilt| |#1| 0))) +((|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) 37 T ELT))) +(((|NonLinearFirstOrderODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| ((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)))) (|Join| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |NonLinearFirstOrderODESolver|)) +((|solve| (*1 *2 *2 *2 *3 *4) (|partial| AND (|isDomain| *3 (|BasicOperator|)) (|isDomain| *4 (|Symbol|)) (|ofCategory| *5 (|Join| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|CharacteristicZero|))) (|isDomain| *1 (|NonLinearFirstOrderODESolver| *5 *2)) (|ofCategory| *2 (|Join| (|AlgebraicallyClosedFunctionSpace| *5) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)))))) +((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 7 T ELT)) (|before?| #1#) (= (#2# 9 T ELT))) +(((|None|) (|SetCategory|)) (T |None|)) +NIL +((|coerce| (((|None|) |#1|) 8 T ELT))) +(((|NoneFunctions1| |#1|) (CATEGORY |package| (SIGNATURE |coerce| ((|None|) |#1|))) (|Type|)) (T |NoneFunctions1|)) +((|coerce| (*1 *2 *3) (AND (|isDomain| *2 (|None|)) (|isDomain| *1 (|NoneFunctions1| *3)) (|ofCategory| *3 (|Type|))))) +((|norm| ((|#2| |#4|) 35 T ELT))) +(((|NormInMonogenicAlgebra| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |norm| (|#2| |#4|))) (|GcdDomain|) (|UnivariatePolynomialCategory| |#1|) (|MonogenicAlgebra| |#1| |#2|) (|UnivariatePolynomialCategory| |#3|)) (T |NormInMonogenicAlgebra|)) +((|norm| (*1 *2 *3) (AND (|ofCategory| *4 (|GcdDomain|)) (|ofCategory| *5 (|MonogenicAlgebra| *4 *2)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|NormInMonogenicAlgebra| *4 *2 *5 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *5))))) +((|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) 57 T ELT)) (|outputArgs| (((|Void|) #1=(|String|) #1# |#4| |#5|) 33 T ELT)) (|normalizedAssociate| ((|#4| |#4| |#5|) 74 T ELT)) (|normalize| (((|List| (|Record| (|:| |val| |#4|) #2=(|:| |tower| |#5|))) |#4| |#5|) 79 T ELT)) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) #2#)) |#4| |#5|) 16 T ELT))) +(((|NormalizationPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |recip| ((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|)) (SIGNATURE |normalizedAssociate| (|#4| |#4| |#5|)) (SIGNATURE |normalize| ((|List| (|Record| (|:| |val| |#4|) #1=(|:| |tower| |#5|))) |#4| |#5|)) (SIGNATURE |outputArgs| ((|Void|) #2=(|String|) #2# |#4| |#5|)) (SIGNATURE |normInvertible?| ((|List| (|Record| (|:| |val| (|Boolean|)) #1#)) |#4| |#5|))) (|GcdDomain|) 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(|isDomain| *2 (|List| (|Record| (|:| |val| *3) #9#))) #10# #11#)) (|normalizedAssociate| (*1 *2 *2 *3) (AND (|ofCategory| *4 #3#) (|ofCategory| *5 #5#) (|ofCategory| *6 #7#) (|ofCategory| *2 (|RecursivePolynomialCategory| *4 *5 *6)) (|isDomain| *1 (|NormalizationPackage| *4 *5 *6 *2 *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *4 *5 *6 *2)))) (|recip| #1# (AND #2# #4# #6# #8# (|isDomain| *2 (|Record| (|:| |num| *3) (|:| |den| *3))) #10# #11#))) +((|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) 53 T ELT)) (|normFactors| (((|List| |#4|) |#4|) 22 T ELT)) (|Frobenius| ((|#4| |#4|) 17 T ELT))) +(((|NormRetractPackage| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |normFactors| ((|List| |#4|) |#4|)) (SIGNATURE |retractIfCan| ((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|)) (SIGNATURE |Frobenius| (|#4| |#4|))) (|FiniteFieldCategory|) (|FiniteAlgebraicExtensionField| |#1|) (|UnivariatePolynomialCategory| |#2|) (|UnivariatePolynomialCategory| |#3|) (|PositiveInteger|)) (T |NormRetractPackage|)) +((|Frobenius| (*1 *2 *2) (AND (|ofCategory| *3 #1=(|FiniteFieldCategory|)) (|ofCategory| *4 (|FiniteAlgebraicExtensionField| *3)) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|NormRetractPackage| *3 *4 *5 *2 *6)) (|ofCategory| *2 #2=(|UnivariatePolynomialCategory| *5)) (|ofType| *6 #3=(|PositiveInteger|)))) (|retractIfCan| #4=(*1 *2 *3) (|partial| AND #5=(|ofCategory| *4 #1#) #6=(|ofCategory| *5 (|FiniteAlgebraicExtensionField| *4)) #7=(|ofCategory| *6 #2#) (|isDomain| *2 (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4))) #8=(|isDomain| *1 (|NormRetractPackage| *4 *5 *6 *3 *7)) #9=(|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) #10=(|ofType| *7 #3#))) (|normFactors| #4# (AND #5# #6# #7# (|isDomain| *2 (|List| *3)) #8# #9# #10#))) +((|npcoef| (((|Record| (|:| |deter| (|List| #1=(|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| #2=(|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| #3=(|List| |#1|)) (|:| |nlead| #4=(|List| |#5|))) #1# #3# #4#) 72 T ELT)) (|listexp| (((|List| #2#) |#1|) 20 T ELT))) +(((|NPCoef| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |npcoef| ((|Record| (|:| |deter| (|List| #1=(|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| #2=(|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| #3=(|List| |#1|)) (|:| |nlead| #4=(|List| |#5|))) #1# #3# #4#)) (SIGNATURE |listexp| ((|List| #2#) |#1|))) (|UnivariatePolynomialCategory| |#4|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#4| |#2| |#3|)) (T |NPCoef|)) +((|listexp| (*1 *2 *3) (AND (|ofCategory| *4 #1=(|OrderedAbelianMonoidSup|)) (|ofCategory| *5 #2=(|OrderedSet|)) (|ofCategory| *6 #3=(|EuclideanDomain|)) (|isDomain| *2 (|List| #4=(|NonNegativeInteger|))) (|isDomain| *1 (|NPCoef| *3 *4 *5 *6 *7)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)))) (|npcoef| (*1 *2 *3 *4 *5) (AND (|ofCategory| *6 (|UnivariatePolynomialCategory| *9)) (|ofCategory| *7 #1#) (|ofCategory| *8 #2#) (|ofCategory| *9 #3#) (|ofCategory| *10 (|PolynomialCategory| *9 *7 *8)) (|isDomain| *2 (|Record| (|:| |deter| (|List| #5=(|SparseUnivariatePolynomial| *10))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| #4#) (|:| |pcoef| *10))))) (|:| |nfacts| #6=(|List| *6)) (|:| |nlead| #7=(|List| *10)))) (|isDomain| *1 (|NPCoef| *6 *7 *8 *9 *10)) (|isDomain| *3 #5#) (|isDomain| *4 #6#) (|isDomain| *5 #7#)))) +((|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| #1=(|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) #2=(|Matrix| #3=(|Fraction| #1#)) |#1|) 31 T ELT)) (|realEigenvalues| (((|List| |#1|) #2# |#1|) 21 T ELT)) (|characteristicPolynomial| ((#4=(|Polynomial| #3#) #2# (|Symbol|)) 18 T ELT) ((#4# #2#) 17 T ELT))) +(((|NumericRealEigenPackage| |#1|) (CATEGORY |package| (SIGNATURE |characteristicPolynomial| (#1=(|Polynomial| #2=(|Fraction| #3=(|Integer|))) #4=(|Matrix| #2#))) (SIGNATURE |characteristicPolynomial| (#1# #4# (|Symbol|))) (SIGNATURE |realEigenvalues| ((|List| |#1|) #4# |#1|)) (SIGNATURE |realEigenvectors| ((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| #3#) (|:| |outvect| (|List| (|Matrix| |#1|))))) #4# |#1|))) (|Join| (|Field|) (|OrderedRing|))) (T |NumericRealEigenPackage|)) +((|realEigenvectors| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Matrix| #3=(|Fraction| #4=(|Integer|)))) (|isDomain| *2 (|List| (|Record| (|:| |outval| *4) (|:| |outmult| #4#) (|:| |outvect| (|List| (|Matrix| *4)))))) #5=(|isDomain| *1 (|NumericRealEigenPackage| *4)) #6=(|ofCategory| *4 #7=(|Join| (|Field|) (|OrderedRing|))))) (|realEigenvalues| #1# (AND #2# (|isDomain| *2 (|List| *4)) #5# #6#)) (|characteristicPolynomial| #1# (AND #2# (|isDomain| *4 (|Symbol|)) #8=(|isDomain| *2 (|Polynomial| #3#)) (|isDomain| *1 (|NumericRealEigenPackage| *5)) (|ofCategory| *5 #7#))) (|characteristicPolynomial| (*1 *2 *3) (AND #2# #8# #5# #6#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 36 T ELT)) (|variables| ((#5=(|List| |#2|) $) NIL T ELT)) (|univariate| ((#6=(|SparseUnivariatePolynomial| $) $ |#2|) NIL T ELT) ((#7=(|SparseUnivariatePolynomial| |#1|) $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #8=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #9=(#10=($ $) NIL #8# ELT)) (|unit?| (#4# NIL #8# ELT)) (|totalDegree| #11=(#12=(#13=(|NonNegativeInteger|) $) NIL T ELT) ((#13# $ #5#) NIL T ELT)) (|tail| (#10# 30 T ELT)) (|supRittWu?| #1#) (|subtractIfCan| (#14=(#15=(|Union| $ #16="failed") $ $) NIL T ELT)) (|subResultantGcd| (#17=($ $ $) 110 #8# ELT)) (|subResultantChain| ((#18=(|List| $) $ $) 123 #8# ELT)) (|squareFreePolynomial| #19=(((|Factored| #6#) #6#) NIL #20=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #21=(#10# NIL #22=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#23=((|Factored| $) $) NIL #22# ELT)) (|solveLinearPolynomialEquation| (((|Union| #24=(|List| #6#) #16#) #24# #6#) NIL #20# ELT)) (|sample| (#25=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #26=(#16#)) . #27=($)) NIL T ELT) (((|Union| #28=(|Fraction| #29=(|Integer|)) . #26#) . #27#) NIL #30=(|has| |#1| (|RetractableTo| #28#)) ELT) (((|Union| #29# . #26#) . #27#) NIL #31=(|has| |#1| (|RetractableTo| #29#)) ELT) #32=(((|Union| |#2| . #26#) . #27#) NIL T ELT) ((#15# #33=(|Polynomial| #28#)) NIL #34=(AND #35=(|has| |#1| (|Algebra| #28#)) #36=(|has| |#2| (|ConvertibleTo| (|Symbol|)))) ELT) ((#15# #37=(|Polynomial| #29#)) NIL #38=(OR (AND #39=(|has| |#1| (|Algebra| #29#)) #36# #40=(|not| #35#)) #34#) ELT) ((#15# #41=(|Polynomial| |#1|)) NIL #42=(OR (AND #36# #40# (|not| #39#)) (AND #39# #36# #40# (|not| (|has| |#1| (|IntegerNumberSystem|)))) (AND #35# #36# (|not| (|has| |#1| (|QuotientFieldCategory| #29#))))) ELT) (((|Union| #43=(|SparseMultivariatePolynomial| |#1| |#2|) . #26#) $) 21 T ELT)) (|retract| #44=(#45=(|#1| . #46=($)) NIL T ELT) ((#28# . #46#) NIL #30# ELT) ((#29# . #46#) NIL #31# ELT) (#47=(|#2| . #46#) NIL T ELT) #48=(($ #33#) NIL #34# ELT) #49=(($ #37#) NIL #38# ELT) (#50=($ #41#) NIL #42# ELT) (#51=(#43# . #46#) NIL T ELT)) (|resultant| (#52=($ $ $ |#2|) NIL #53=(|has| |#1| (|CommutativeRing|)) ELT) (#17# 121 #8# ELT)) (|reductum| #54=(#10# NIL T ELT) #55=(#56=($ $ |#2|) NIL T ELT)) (|reducedSystem| ((#57=(|Matrix| #29#) . #58=(#59=(|Matrix| $))) NIL #60=(|has| |#1| (|LinearlyExplicitRingOver| #29#)) ELT) ((#61=(|Record| (|:| |mat| #57#) (|:| |vec| (|Vector| #29#))) . #62=(#59# #63=(|Vector| $))) NIL #60# ELT) ((#64=(|Record| (|:| |mat| #65=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #62#) NIL T ELT) ((#65# . #58#) NIL T ELT)) (|reduced?| #1# #66=((#3# $ #18#) NIL T ELT)) (|recip| ((#15# $) NIL T ELT)) (|quasiMonic?| #67=(#4# NIL T ELT)) (|pseudoDivide| ((#68=(|Record| #69=(|:| |quotient| $) #70=(|:| |remainder| $)) $ $) 81 T ELT)) (|primitivePart!| (#10# 136 #22# ELT)) (|primitivePart| #21# #71=(#56# NIL #22# ELT)) (|primitiveMonomials| #72=(#73=(#18# $) NIL T ELT)) (|prime?| (#4# NIL #20# ELT)) (|primPartElseUnitCanonical!| #9#) (|primPartElseUnitCanonical| #9#) (|prem| (#17# 76 T ELT) #74=(#52# NIL T ELT)) (|pquo| (#17# 79 T ELT) #74#) (|pomopo!| (($ $ |#1| #75=(|IndexedExponents| |#2|) $) NIL T ELT)) (|patternMatch| ((#76=(|PatternMatchResult| #77=(|Float|) . #78=($)) $ #79=(|Pattern| #77#) #76#) NIL (AND (|has| |#1| #80=(|PatternMatchable| #77#)) (|has| |#2| #80#)) ELT) ((#81=(|PatternMatchResult| #29# . #78#) $ #82=(|Pattern| #29#) #81#) NIL (AND (|has| |#1| #83=(|PatternMatchable| #29#)) (|has| |#2| #83#)) ELT)) (|opposite?| #1#) (|one?| (#4# 57 T ELT)) (|numberOfMonomials| #11#) (|normalized?| #1# #66#) (|nextsubResultant2| (($ $ $ $ $) 107 #8# ELT)) (|mvar| (#47# 22 T ELT)) (|multivariate| (($ #7# |#2|) NIL T ELT) (($ #6# |#2|) NIL T ELT)) (|monomials| #72#) (|monomial?| #67#) (|monomial| (($ |#1| #75#) NIL T ELT) (#84=($ $ |#2| #13#) 38 T ELT) #85=(($ $ #5# #86=(|List| #13#)) NIL T ELT)) (|monicModulo| (#17# 63 T ELT)) (|monicDivide| ((#68# $ $ |#2|) NIL T ELT)) (|monic?| #67#) (|minimumDegree| #87=((#75# $) NIL T ELT) (#88=(#13# $ |#2|) NIL T ELT) #89=((#86# $ #5#) NIL T ELT)) (|mdeg| (#12# 23 T ELT)) (|mapExponents| (($ (|Mapping| #75# #75#) $) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|mainVariable| #32#) (|mainSquareFreePart| #21#) (|mainPrimitivePart| #21#) (|mainMonomials| #72#) (|mainMonomial| (#10# 39 T ELT)) (|mainContent| #21#) (|mainCoefficients| (#73# 43 T ELT)) (|leftReducedSystem| ((#57# . #90=(#63#)) NIL #60# ELT) ((#61# . #91=(#63# $)) NIL #60# ELT) ((#64# . #91#) NIL T ELT) ((#65# . #90#) NIL T ELT)) (|leastMonomial| (#10# 41 T ELT)) (|leadingMonomial| #54#) (|leadingCoefficient| #44# (#56# 48 T ELT)) (|lcm| #92=(($ #18#) NIL #22# ELT) #93=(#17# NIL #22# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| #13#)) $ $) 96 T ELT)) (|lazyPseudoDivide| ((#94=(|Record| #95=(|:| |coef| $) #96=(|:| |gap| #13#) #69# #70#) $ $) 78 T ELT) ((#94# $ $ |#2|) NIL T ELT)) (|lazyPremWithDefault| ((#97=(|Record| #95# #96# #70#) $ $) NIL T ELT) ((#97# $ $ |#2|) NIL T ELT)) (|lazyPrem| (#17# 83 T ELT) #74#) (|lazyPquo| (#17# 86 T ELT) #74#) (|latex| (#98=((|String|) $) NIL T ELT)) (|lastSubResultant| (#17# 125 #8# ELT)) (|iteratedInitials| (#73# 32 T ELT)) (|isTimes| #99=(((|Union| #18# #16#) $) NIL T ELT)) (|isPlus| #99#) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| #13#)) #16#) $) NIL T ELT)) (|initiallyReduced?| #1# #66#) (|initiallyReduce| #100=(#17# NIL T ELT)) (|init| (#10# 24 T ELT)) (|infRittWu?| #1#) (|headReduced?| #1# #66#) (|headReduce| #100#) (|head| (#10# 26 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #101=(|:| |gcd| $) #102=(|:| |coef2| $)) $ $) 116 #8# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #101# #103=(|:| |coef1| $)) $ $) 113 #8# ELT)) (|ground?| (#4# 56 T ELT)) (|ground| (#45# 58 T ELT)) (|gcdPolynomial| ((#6# #6# #6#) NIL #22# ELT)) (|gcd| ((|#1| |#1| $) 133 #22# ELT) #92# #93#) (|factorSquareFreePolynomial| #19#) (|factorPolynomial| #19#) (|factor| (#23# NIL #20# ELT)) (|extendedSubResultantGcd| (((|Record| #101# #103# #102#) $ $) 119 #8# ELT)) (|exquo| ((#15# $ |#1|) NIL #8# ELT) (#14# 98 #8# ELT)) (|exactQuotient!| (#104=($ $ |#1|) 129 #8# ELT) #105=(#17# NIL #8# ELT)) (|exactQuotient| (#104# 128 #8# ELT) #105#) (|eval| (($ $ (|List| #106=(|Equation| $))) NIL T ELT) (($ $ #106#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #18# #18#) NIL T ELT) (($ $ |#2| |#1|) NIL T ELT) (($ $ #5# #107=(|List| |#1|)) NIL T ELT) (($ $ |#2| $) NIL T ELT) (($ $ #5# #18#) NIL T ELT)) (|discriminant| (#56# NIL #53# ELT)) (|differentiate| #85# #108=(#84# NIL T ELT) #109=(($ $ #5#) NIL T ELT) #55#) (|degree| #87# (#88# 45 T ELT) #89#) (|deepestTail| #54#) (|deepestInitial| (#10# 35 T ELT)) (|convert| ((#79# . #110=($)) NIL (AND (|has| |#1| #111=(|ConvertibleTo| #79#)) (|has| |#2| #111#)) ELT) ((#82# . #110#) NIL (AND (|has| |#1| #112=(|ConvertibleTo| #82#)) (|has| |#2| #112#)) ELT) ((#113=(|InputForm|) . #110#) NIL (AND (|has| |#1| #114=(|ConvertibleTo| #113#)) (|has| |#2| #114#)) ELT) #48# #49# (#50# NIL #36# ELT) (#98# NIL (AND #31# #36#) ELT) #115=((#41# . #110#) NIL #36# ELT)) (|content| (#45# 132 #22# ELT) #71#) (|conditionP| (((|Union| #63# #16#) #59#) NIL #116=(AND (|has| $ #117=(|CharacteristicNonZero|)) #20#) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #29#) NIL T ELT) (($ |#1|) NIL T ELT) (($ |#2|) NIL T ELT) #115# (#51# 18 T ELT) (($ #43#) 19 T ELT) (($ #28#) NIL (OR #35# #30#) ELT) #9#) (|coefficients| ((#107# $) NIL T ELT)) (|coefficient| ((|#1| $ #75#) NIL T ELT) (#84# 47 T ELT) #85#) (|charthRoot| (((|Maybe| $) $) NIL (OR #116# (|has| |#1| #117#)) ELT)) (|characteristic| ((#13#) NIL T CONST)) (|binomThmExpt| (#118=($ $ $ #13#) NIL #53# ELT)) (|before?| #1#) (|associates?| (#2# NIL #8# ELT)) (|annihilate?| #1#) (|Zero| (#25# 13 T CONST)) (|RittWuCompare| (((|Union| #3# #16#) $ $) NIL T ELT)) (|One| (#25# 37 T CONST)) (|LazardQuotient2| (($ $ $ $ #13#) 105 #8# ELT)) (|LazardQuotient| (#118# 104 #8# ELT)) (D #85# #108# #109# #55#) (= #1#) (/ (#104# NIL (|has| |#1| (|Field|)) ELT)) (- #54# (#17# 75 T ELT)) (+ (#17# 85 T ELT)) (** (($ $ #119=(|PositiveInteger|)) NIL T ELT) (($ $ #13#) 70 T ELT)) (* (($ #119# $) NIL T ELT) (($ #13# $) NIL T ELT) (($ #29# . #120=($)) NIL T ELT) (#17# 62 T ELT) (($ $ #28#) NIL #35# ELT) (($ #28# . #120#) NIL #35# ELT) (($ |#1| . #120#) 61 T ELT) (#104# NIL T ELT))) +(((|NewSparseMultivariatePolynomial| |#1| |#2|) (|Join| (|RecursivePolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|CoercibleTo| #1=(|SparseMultivariatePolynomial| |#1| |#2|)) (|RetractableTo| #1#)) (|Ring|) (|OrderedSet|)) (T |NewSparseMultivariatePolynomial|)) +NIL +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 12 T ELT)) (|vectorise| ((#5=(|Vector| |#1|) $ #6=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#7=(|List| #8=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (#9=($ #10=(|SparseUnivariatePolynomial| |#1|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #8#) NIL T ELT) #12=(#13=(#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #14=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #15=(#16=($ $) NIL #14# ELT)) (|unit?| (#4# NIL #14# ELT)) (|totalDegree| #17=(#18=(#6# $) NIL T ELT) ((#6# $ #7#) NIL T ELT)) (|subtractIfCan| (#19=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|subResultantsChain| ((#22=(|List| $) $ $) 54 #14# ELT)) (|subResultantGcd| (#23=($ $ $) 50 #14# ELT)) (|squareFreePolynomial| #24=(((|Factored| #11#) #11#) NIL #25=(|has| |#1| (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #26=(#16# NIL #27=(|has| |#1| (|GcdDomain|)) ELT)) (|squareFree| (#28=((|Factored| $) $) NIL #27# ELT)) (|solveLinearPolynomialEquation| (((|Union| #29=(|List| #11#) #21#) #29# #11#) NIL #25# ELT)) (|sizeLess?| (#2# NIL #30=(|has| |#1| (|Field|)) ELT)) (|shiftRight| #31=(($ $ #6#) NIL T ELT)) (|shiftLeft| #31#) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) NIL #27# ELT)) (|sample| (#32=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #33=(#21#)) . #34=($)) NIL T ELT) (((|Union| #35=(|Fraction| #36=(|Integer|)) . #33#) . #34#) NIL #37=(|has| |#1| (|RetractableTo| #35#)) ELT) (((|Union| #36# . #33#) . #34#) NIL #38=(|has| |#1| (|RetractableTo| #36#)) ELT) #39=(((|Union| #8# . #33#) . #34#) NIL T ELT) (((|Union| #10# . #33#) $) 10 T ELT)) (|retract| #40=(#41=(|#1| . #42=($)) NIL T ELT) ((#35# . #42#) NIL #37# ELT) ((#36# . #42#) NIL #38# ELT) ((#8# . #42#) NIL T ELT) #12#) (|resultant| (($ $ $ #8#) NIL #43=(|has| |#1| (|CommutativeRing|)) ELT) ((|#1| $ $) 58 #43# ELT)) (|rem| #44=(#23# NIL #30# ELT)) (|reductum| #45=(#16# NIL T ELT)) (|reducedSystem| ((#46=(|Matrix| #36#) . #47=(#48=(|Matrix| $))) NIL #49=(|has| |#1| (|LinearlyExplicitRingOver| #36#)) ELT) ((#50=(|Record| (|:| |mat| #46#) (|:| |vec| (|Vector| #36#))) . #51=(#48# #52=(|Vector| $))) NIL #49# ELT) ((#53=(|Record| (|:| |mat| #54=(|Matrix| |#1|)) (|:| |vec| #5#)) . #51#) NIL T ELT) ((#54# . #47#) NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|quo| #44#) (|pseudoRemainder| #55=(#23# NIL T ELT)) (|pseudoQuotient| (#23# 87 #14# ELT)) (|pseudoDivide| (((|Record| #56=(|:| |coef| |#1|) #57=(|:| |quotient| $) #58=(|:| |remainder| $)) $ $) 86 #14# ELT)) (|principalIdeal| (((|Record| (|:| |coef| #22#) #59=(|:| |generator| $)) #22#) NIL #30# ELT)) (|primitivePart| #26# #60=(#61=($ $ #8#) NIL #27# ELT)) (|primitiveMonomials| #62=((#22# $) NIL T ELT)) (|prime?| (#4# NIL #25# ELT)) (|pomopo!| (($ $ |#1| #6# $) NIL T ELT)) (|patternMatch| ((#63=(|PatternMatchResult| #64=(|Float|) . #65=($)) $ #66=(|Pattern| #64#) #63#) NIL (AND (|has| #8# #67=(|PatternMatchable| #64#)) (|has| |#1| #67#)) ELT) ((#68=(|PatternMatchResult| #36# . #65#) $ #69=(|Pattern| #36#) #68#) NIL (AND (|has| #8# #70=(|PatternMatchable| #36#)) (|has| |#1| #70#)) ELT)) (|order| ((#6# $ $) NIL #14# ELT)) (|opposite?| #1#) (|one?| #71=(#4# NIL T ELT)) (|numberOfMonomials| #17#) (|nextItem| (#72=((|Maybe| $) $) NIL #73=(|has| |#1| (|StepThrough|)) ELT)) (|multivariate| (($ #10# #8#) NIL T ELT) (($ #11# #8#) NIL T ELT)) (|multiplyExponents| #31#) (|multiEuclidean| ((#74=(|Union| #22# #21#) #22# $) NIL #30# ELT)) (|monomials| #62#) (|monomial?| #71#) (|monomial| (($ |#1| #6#) NIL T ELT) #75=(($ $ #8# #6#) NIL T ELT) #76=(($ $ #7# #77=(|List| #6#)) NIL T ELT)) (|monicModulo| (#23# 27 T ELT)) (|monicDivide| ((#78=(|Record| #57# #58#) $ $ #8#) NIL T ELT) (#79=(#78# $ $) NIL T ELT)) (|minimumDegree| #17# #80=((#6# $ #8#) NIL T ELT) #81=((#77# $ #7#) NIL T ELT)) (|mapExponents| (($ (|Mapping| #6# #6#) $) NIL T ELT)) (|map| (($ #82=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|makeSUP| #12#) (|mainVariable| #39#) (|leftReducedSystem| ((#46# . #83=(#52#)) NIL #49# ELT) ((#50# . #84=(#52# $)) NIL #49# ELT) ((#53# . #84#) NIL T ELT) ((#54# . #83#) NIL T ELT)) (|leadingMonomial| #45#) (|leadingCoefficient| #40#) (|lcm| #85=(($ #22#) NIL #27# ELT) #86=(#23# NIL #27# ELT)) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| #6#)) $ $) 37 T ELT)) (|lazyPseudoRemainder| (#23# 41 T ELT)) (|lazyPseudoQuotient| (#23# 47 T ELT)) (|lazyPseudoDivide| (((|Record| #56# (|:| |gap| #6#) #57# #58#) $ $) 46 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultant| (#23# 56 #14# ELT)) (|karatsubaDivide| ((#78# $ #6#) NIL T ELT)) (|isTimes| #87=((#74# $) NIL T ELT)) (|isPlus| #87#) (|isExpt| (((|Union| (|Record| (|:| |var| #8#) (|:| |exponent| #6#)) #21#) $) NIL T ELT)) (|integrate| (#16# NIL #88=(|has| |#1| (|Algebra| #35#)) ELT)) (|init| (#32# NIL #73# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| #89=(|:| |gcd| $) #90=(|:| |coef2| $)) $ $) 82 #14# ELT)) (|halfExtendedSubResultantGcd1| (((|Record| #89# #91=(|:| |coef1| $)) $ $) 78 #14# ELT)) (|halfExtendedResultant2| (((|Record| #92=(|:| |resultant| |#1|) #90#) $ $) 70 #14# ELT)) (|halfExtendedResultant1| (((|Record| #92# #91#) $ $) 66 #14# ELT)) (|ground?| (#4# 13 T ELT)) (|ground| #40#) (|gcdPolynomial| ((#11# #11# #11#) NIL #27# ELT)) (|gcd| #85# #86#) (|fmecg| (($ $ #6# |#1| $) 26 T ELT)) (|factorSquareFreePolynomial| #24#) (|factorPolynomial| #24#) (|factor| (#28# NIL #25# ELT)) (|extendedSubResultantGcd| (((|Record| #89# #91# #90#) $ $) 74 #14# ELT)) (|extendedResultant| (((|Record| #92# #91# #90#) $ $) 62 #14# ELT)) (|extendedEuclidean| (((|Union| (|Record| #91# #90#) #21#) $ $ $) NIL #30# ELT) (((|Record| #91# #90# #59#) $ $) NIL #30# ELT)) (|exquo| ((#20# $ |#1|) NIL #14# ELT) #93=(#19# NIL #14# ELT)) (|expressIdealMember| (((|Maybe| #22#) #22# $) NIL #30# ELT)) (|eval| (($ $ (|List| #94=(|Equation| $))) NIL T ELT) (($ $ #94#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #22# #22#) NIL T ELT) (($ $ #8# |#1|) NIL T ELT) (($ $ #7# #95=(|List| |#1|)) NIL T ELT) (($ $ #8# $) NIL T ELT) (($ $ #7# #22#) NIL T ELT)) (|euclideanSize| (#18# NIL #30# ELT)) (|elt| ((|#1| $ |#1|) NIL T ELT) #55# ((#96=(|Fraction| $) #96# #96#) NIL #14# ELT) ((|#1| #96# |#1|) NIL #30# ELT) ((#96# $ #96#) NIL #14# ELT)) (|divideExponents| ((#20# $ #6#) NIL T ELT)) (|divide| (#79# NIL #30# ELT)) (|discriminant| (#61# NIL #43# ELT) (#41# NIL #43# ELT)) (|differentiate| #76# #75# #97=(($ $ #7#) NIL T ELT) #98=(#61# NIL T ELT) #45# #31# #99=(($ $ #82#) NIL T ELT) #100=(($ $ #82# #6#) NIL T ELT) (($ $ #82# $) NIL T ELT) #101=(($ $ #102=(|Symbol|)) NIL #103=(|has| |#1| (|PartialDifferentialSpace| #102#)) ELT) #104=(($ $ #105=(|List| #102#)) NIL #103# ELT) #106=(($ $ #102# #6#) NIL #103# ELT) #107=(($ $ #105# #77#) NIL #103# ELT)) (|degree| #17# #80# #81#) (|convert| ((#66# . #108=($)) NIL (AND (|has| #8# #109=(|ConvertibleTo| #66#)) (|has| |#1| #109#)) ELT) ((#69# . #108#) NIL (AND (|has| #8# #110=(|ConvertibleTo| #69#)) (|has| |#1| #110#)) ELT) ((#111=(|InputForm|) . #108#) NIL (AND (|has| #8# #112=(|ConvertibleTo| #111#)) (|has| |#1| #112#)) ELT)) (|content| (#41# NIL #27# ELT) #60#) (|conditionP| (((|Union| #52# #21#) #48#) NIL #113=(AND (|has| $ #114=(|CharacteristicNonZero|)) #25#) ELT)) (|composite| #93# (((|Union| #96# #21#) #96# $) NIL #14# ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #36#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #8#) NIL T ELT) (#13# 7 T ELT) (#9# 8 T ELT) (($ #35#) NIL (OR #88# #37#) ELT) #15#) (|coefficients| ((#95# $) NIL T ELT)) (|coefficient| ((|#1| $ #6#) NIL T ELT) #75# #76#) (|charthRoot| (#72# NIL (OR #113# (|has| |#1| #114#)) ELT)) (|characteristic| ((#6#) NIL T CONST)) (|binomThmExpt| (($ $ $ #6#) NIL #43# ELT)) (|before?| #1#) (|associates?| (#2# NIL #14# ELT)) (|annihilate?| #1#) (|Zero| (#32# 28 T CONST)) (|One| (#32# 32 T CONST)) (D #76# #75# #97# #98# #45# #31# #99# #100# #101# #104# #106# #107#) (= #1#) (/ (#115=($ $ |#1|) NIL #30# ELT)) (- (#16# 40 T ELT) #55#) (+ #55#) (** (($ $ #116=(|PositiveInteger|)) NIL T ELT) #31#) (* (($ #116# $) NIL T ELT) (($ #6# $) NIL T ELT) (($ #36# . #117=($)) NIL T ELT) #55# (($ $ #35#) NIL #88# ELT) (($ #35# . #117#) NIL #88# ELT) (($ |#1| . #117#) 31 T ELT) (#115# NIL T ELT))) +(((|NewSparseUnivariatePolynomial| |#1|) (|Join| (|UnivariatePolynomialCategory| |#1|) (|CoercibleTo| #1=(|SparseUnivariatePolynomial| |#1|)) (|RetractableTo| #1#) (CATEGORY |domain| (SIGNATURE |fmecg| ($ $ #2=(|NonNegativeInteger|) |#1| $)) (SIGNATURE |monicModulo| #3=($ $ $)) (SIGNATURE |lazyResidueClass| ((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| #2#)) $ $)) (SIGNATURE |lazyPseudoRemainder| #3#) (SIGNATURE |lazyPseudoDivide| ((|Record| (|:| |coef| |#1|) (|:| |gap| #2#) (|:| |quotient| $) (|:| |remainder| $)) $ $)) (SIGNATURE |lazyPseudoQuotient| #3#) (IF (|has| |#1| (|IntegralDomain|)) (PROGN (SIGNATURE |subResultantsChain| ((|List| $) $ $)) (SIGNATURE |lastSubResultant| #3#) (SIGNATURE |extendedSubResultantGcd| ((|Record| #4=(|:| |gcd| $) #5=(|:| |coef1| $) #6=(|:| |coef2| $)) $ $)) (SIGNATURE |halfExtendedSubResultantGcd1| ((|Record| #4# #5#) $ $)) (SIGNATURE |halfExtendedSubResultantGcd2| ((|Record| #4# #6#) $ $)) (SIGNATURE |extendedResultant| ((|Record| #7=(|:| |resultant| |#1|) #5# #6#) $ $)) (SIGNATURE |halfExtendedResultant1| ((|Record| #7# #5#) $ $)) (SIGNATURE |halfExtendedResultant2| ((|Record| #7# #6#) $ $))) |%noBranch|))) (|Ring|)) (T |NewSparseUnivariatePolynomial|)) +((|fmecg| (*1 *1 *1 *2 *3 *1) (AND (|isDomain| *2 #1=(|NonNegativeInteger|)) #2=(|isDomain| *1 #3=(|NewSparseUnivariatePolynomial| *3)) #4=(|ofCategory| *3 #5=(|Ring|)))) (|monicModulo| #6=(*1 *1 *1 *1) #7=(AND #8=(|isDomain| *1 (|NewSparseUnivariatePolynomial| *2)) #9=(|ofCategory| *2 #5#))) (|lazyResidueClass| #10=(*1 *2 *1 *1) (AND (|isDomain| *2 (|Record| (|:| |polnum| #3#) (|:| |polden| *3) (|:| |power| #1#))) #2# #4#)) (|lazyPseudoRemainder| #6# #7#) (|lazyPseudoDivide| #10# (AND (|isDomain| *2 (|Record| (|:| |coef| *3) (|:| |gap| #1#) (|:| |quotient| #3#) (|:| |remainder| #3#))) #2# #4#)) (|lazyPseudoQuotient| #6# #7#) (|subResultantsChain| #10# (AND (|isDomain| *2 (|List| #3#)) #2# #11=(|ofCategory| *3 #12=(|IntegralDomain|)) #4#)) (|lastSubResultant| #6# (AND #8# (|ofCategory| *2 #12#) #9#)) (|extendedSubResultantGcd| #10# (AND (|isDomain| *2 (|Record| #13=(|:| |gcd| #3#) #14=(|:| |coef1| #3#) #15=(|:| |coef2| #3#))) #2# #11# #4#)) (|halfExtendedSubResultantGcd1| #10# (AND (|isDomain| *2 (|Record| #13# #14#)) #2# #11# #4#)) (|halfExtendedSubResultantGcd2| #10# (AND (|isDomain| *2 (|Record| #13# #15#)) #2# #11# #4#)) (|extendedResultant| #10# (AND (|isDomain| *2 (|Record| #16=(|:| |resultant| *3) #14# #15#)) #2# #11# #4#)) (|halfExtendedResultant1| #10# (AND 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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| 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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# 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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) ((|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#))) 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#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#))) +((|ScanRoman| (#1=(#2=(|PositiveInteger|) #3=(|String|)) 90 T ELT)) (|ScanFloatIgnoreSpacesIfCan| (((|Union| #4=(|Float|) "failed") #3#) 36 T ELT)) (|ScanFloatIgnoreSpaces| ((#4# #3#) 34 T ELT)) (|ScanArabic| (#1# 64 T ELT)) (|FormatRoman| (#5=(#3# #2#) 74 T ELT)) (|FormatArabic| (#5# 63 T ELT))) +(((|NumberFormats|) (CATEGORY |package| (SIGNATURE |FormatArabic| #1=(#2=(|String|) #3=(|PositiveInteger|))) (SIGNATURE |ScanArabic| #4=(#3# 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((#1# #2# #4# #3# #3# #6# #2# #2# #2# #2#) 63 T ELT) ((#1# #2# #4# #3# #3# #6#) 62 T ELT))) +(((|NumericalOrdinaryDifferentialEquations|) (CATEGORY |package| (SIGNATURE |rk4| (#1=(|Void|) #2=(|Vector| #3=(|Float|)) #4=(|Integer|) #3# #3# #5=(|Mapping| #1# #2# #2# #3#))) (SIGNATURE |rk4| (#1# #2# #4# #3# #3# #5# #2# #2# #2# #2#)) (SIGNATURE |rk4a| (#1# #2# #4# #3# #3# #3# #3# #4# #5#)) (SIGNATURE |rk4qc| (#1# #2# #4# #3# #6=(|Record| (|:| |tryValue| #3#) (|:| |did| #3#) (|:| |next| #3#)) #3# #2# #5#)) (SIGNATURE |rk4qc| (#1# #2# #4# #3# #6# #3# #2# #5# #2# #2# #2# #2# #2# #2# #2#)) (SIGNATURE |rk4f| (#1# #2# #4# #3# #3# #4# #5#)))) (T |NumericalOrdinaryDifferentialEquations|)) +((|rk4f| (*1 *2 *3 *4 *5 *5 *4 *6) #1=(AND #2=(|isDomain| *4 (|Integer|)) (|isDomain| *6 #3=(|Mapping| #4=(|Void|) #5=(|Vector| *5) #5# #6=(|Float|))) #7=(|isDomain| *3 (|Vector| #6#)) #8=(|isDomain| *5 #6#) #9=(|isDomain| *2 #4#) #10=(|isDomain| *1 (|NumericalOrdinaryDifferentialEquations|)))) (|rk4qc| (*1 *2 *3 *4 *5 *6 *5 *3 *7 *3 *3 *3 *3 *3 *3 *3) #11=(AND #2# (|isDomain| *6 (|Record| (|:| |tryValue| #6#) (|:| |did| #6#) (|:| |next| #6#))) (|isDomain| *7 #3#) #7# #8# #9# #10#)) (|rk4qc| (*1 *2 *3 *4 *5 *6 *5 *3 *7) #11#) (|rk4a| (*1 *2 *3 *4 *5 *5 *5 *5 *4 *6) #1#) (|rk4| (*1 *2 *3 *4 *5 *5 *6 *3 *3 *3 *3) #1#) (|rk4| (*1 *2 *3 *4 *5 *5 *6) #1#)) +((|trapezoidalo| (#1=(#2=(|Record| (|:| |value| #3=(|Float|)) (|:| |error| #3#) (|:| |totalpts| #4=(|Integer|)) (|:| |success| (|Boolean|))) #5=(|Mapping| #3# #3#) #3# #3# #3# #3# #4# #4#) 65 T ELT)) (|trapezoidal| (#1# 40 T ELT)) (|simpsono| (#1# 64 T ELT)) (|simpson| (#1# 38 T ELT)) (|rombergo| (#1# 63 T ELT)) (|romberg| (#1# 24 T ELT)) (|atrapezoidal| (#6=(#2# #5# #3# #3# #3# #3# #4# #4# #4#) 41 T ELT)) (|asimpson| (#6# 39 T ELT)) (|aromberg| (#6# 37 T ELT))) +(((|NumericalQuadrature|) (CATEGORY |package| (SIGNATURE |aromberg| #1=(#2=(|Record| (|:| |value| #3=(|Float|)) (|:| |error| #3#) (|:| |totalpts| #4=(|Integer|)) (|:| |success| 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$)) (SIGNATURE |abs| ($ $)))) +(((|AbelianGroup|) . T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|OrderedAbelianMonoid|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedCancellationAbelianMonoid|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . 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T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|OrderedAbelianSemiGroup|) . T) ((|OrderedSet|) . T) ((|OrderedType|) . T) ((|SetCategory|) . T) ((|Type|) . 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T)) +((|zero?| (#1=(#2=(|Boolean|) $) 42 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) NIL T ELT) (#5=((|Union| #6=(|Fraction| #3#) #4#) $) NIL T ELT) (((|Union| |#2| #4#) $) 45 T ELT)) (|retract| ((#3# $) NIL T ELT) (#7=(#6# $) NIL T ELT) (#8=(|#2| $) 43 T ELT)) (|rationalIfCan| (#5# 78 T ELT)) (|rational?| (#1# 72 T ELT)) (|rational| (#7# 76 T ELT)) (|norm| (#8# 26 T ELT)) (|map| (($ (|Mapping| |#2| |#2|) $) 23 T ELT)) (|inv| (#9=($ $) 58 T ELT)) (|convert| (((|InputForm|) $) 67 T ELT)) (|conjugate| (#9# 21 T ELT)) (|coerce| (((|OutputForm|) $) 53 T ELT) (($ #3#) 40 T ELT) (($ |#2|) 38 T ELT) (($ #6#) NIL T ELT)) (|characteristic| ((#10=(|NonNegativeInteger|)) 10 T CONST)) (|abs| (#8# 71 T ELT)) (= (#11=(#2# $ $) 30 T ELT)) (< (#11# 69 T ELT)) (- (#9# 32 T ELT) #12=(#13=($ $ $) NIL T ELT)) (+ (#13# 31 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #10# $) NIL T ELT) (($ #3# $) 36 T ELT) #12# (($ $ |#2|) NIL T ELT) (($ |#2| $) 33 T ELT))) 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#11=($)) 108 (|has| |#1| . #8#) ELT) ((#9# . #11#) 105 (|has| |#1| . #10#) ELT) ((|#1| . #11#) 104 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|real| ((|#1| $) 93 T ELT)) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) 80 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (((|Boolean|) $) 82 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational| (((|Fraction| (|Integer|)) $) 81 (|has| |#1| (|IntegerNumberSystem|)) ELT)) (|random| (($) 70 (|has| |#1| . #3#) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) 84 T ELT)) (|norm| ((|#1| $) 85 T ELT)) (|min| (#12=($ $ $) 71 (|has| |#1| . #13=((|OrderedSet|))) ELT)) (|max| (#12# 72 (|has| |#1| . #13#) ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 95 T ELT)) (|lookup| ((#14=(|PositiveInteger|) $) 69 (|has| |#1| . #3#) ELT)) (|latex| (((|String|) $) 11 T ELT)) (|inv| (($ $) 79 (|has| |#1| (|Field|)) ELT)) (|index| (($ #14#) 68 (|has| 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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| (((|Union| $ "failed") $ $) 35 T ELT)) (|sample| (#3=($) 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))) +(((|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)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|size| (#8=(#9=(|NonNegativeInteger|)) NIL #10=(|has| |#1| (|Finite|)) ELT)) (|sample| (#11=($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #12=(#7#)) . #13=($)) NIL T ELT) (((|Union| #14=(|Quaternion| |#1|) . #12#) $) 35 T ELT) (((|Union| #15=(|Integer|) . #12#) . #13#) NIL #16=(OR (|has| #14# #17=(|RetractableTo| #15#)) (|has| |#1| #17#)) ELT) (#18=((|Union| #19=(|Fraction| #15#) . #12#) . #13#) NIL #20=(OR (|has| #14# #21=(|RetractableTo| #19#)) (|has| |#1| #21#)) ELT)) (|retract| #22=(#23=(|#1| . #24=($)) NIL T ELT) ((#14# $) 33 T ELT) ((#15# . #24#) NIL #16# ELT) (#25=(#19# . #24#) NIL #20# ELT)) (|recip| ((#6# $) NIL T ELT)) (|real| (#23# 16 T ELT)) (|rationalIfCan| (#18# NIL #26=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#5# NIL #26# ELT)) (|rational| (#25# NIL #26# ELT)) (|random| (#11# NIL #10# ELT)) 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NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|convert| ((#38=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #38#)) ELT)) (|conjugate| #39=(#31# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #15#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #14#) 30 T ELT) (($ #19#) NIL #20# ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (#8# NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#23# NIL (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#11# 8 T CONST)) (|One| (#11# 12 T CONST)) (>= #40=(#2# NIL #29# ELT)) (> #40#) (= #1#) (<= #40#) (< #40#) (- #39# #41=(#28# NIL T ELT)) (+ #41#) (** (($ $ #30#) NIL T ELT) (($ $ #9#) NIL T ELT)) (* (($ #30# $) NIL T ELT) (($ #9# $) NIL T ELT) (($ #15# . #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))))) +((|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) 20 T ELT))) +(((|OctonionCategoryFunctions2| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |map| (|#3| (|Mapping| |#4| |#2|) |#1|))) (|OctonionCategory| |#2|) #1=(|CommutativeRing|) (|OctonionCategory| |#4|) #1#) (T |OctonionCategoryFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|ofCategory| *5 #1=(|CommutativeRing|)) (|ofCategory| *6 #1#) (|ofCategory| *2 (|OctonionCategory| *6)) (|isDomain| *1 (|OctonionCategoryFunctions2| *4 *5 *2 *6)) (|ofCategory| *4 (|OctonionCategory| *5))))) +((|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) 19 T ELT))) +(((|ConstantLODE| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |constDsolve| ((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)))) (|Join| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|)) (|LinearOrdinaryDifferentialOperatorCategory| |#2|)) (T |ConstantLODE|)) +((|constDsolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 (|Symbol|)) (|ofCategory| *6 (|Join| (|EuclideanDomain|) (|RetractableTo| #1=(|Integer|)) (|LinearlyExplicitRingOver| #1#) (|CharacteristicZero|))) (|ofCategory| *4 (|Join| (|AlgebraicallyClosedFunctionSpace| *6) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (|isDomain| *2 (|Record| (|:| |particular| *4) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|ConstantLODE| *6 *4 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *4))))) +((|solve| ((#1=(|Union| |#2| #2="failed") |#2| #3=(|BasicOperator|) #4=(|Equation| |#2|) #5=(|List| |#2|)) 28 T ELT) ((#1# #4# #3# #4# #5#) 29 T ELT) ((#6=(|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #5#)) |#2| #2#) |#2| #3# #7=(|Symbol|)) 17 T ELT) ((#6# #4# #3# #7#) 18 T ELT) ((#8=(|Union| (|Record| (|:| |particular| #9=(|Vector| |#2|)) (|:| |basis| #10=(|List| #9#))) #2#) #5# #11=(|List| #3#) #7#) 24 T ELT) ((#8# (|List| #4#) #11# #7#) 26 T ELT) (((|Union| #10# #2#) #12=(|Matrix| |#2|) #7#) 37 T ELT) ((#8# #12# #9# #7#) 35 T ELT))) +(((|ElementaryFunctionODESolver| |#1| |#2|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|Union| (|Record| (|:| |particular| #2=(|Vector| |#2|)) (|:| |basis| #3=(|List| #2#))) #4="failed") #5=(|Matrix| |#2|) #2# #6=(|Symbol|))) (SIGNATURE |solve| ((|Union| #3# #4#) #5# #6#)) (SIGNATURE |solve| (#1# (|List| #7=(|Equation| |#2|)) #8=(|List| #9=(|BasicOperator|)) #6#)) (SIGNATURE |solve| (#1# #10=(|List| |#2|) #8# #6#)) (SIGNATURE |solve| (#11=(|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| #10#)) |#2| #4#) #7# #9# #6#)) (SIGNATURE |solve| (#11# |#2| #9# #6#)) (SIGNATURE |solve| (#12=(|Union| |#2| #4#) #7# #9# #7# #10#)) (SIGNATURE |solve| (#12# |#2| #9# #7# #10#))) (|Join| (|EuclideanDomain|) (|RetractableTo| #13=(|Integer|)) (|LinearlyExplicitRingOver| #13#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |ElementaryFunctionODESolver|)) +((|solve| (*1 *2 *2 *3 *4 *5) (|partial| AND (|isDomain| *3 #1=(|BasicOperator|)) (|isDomain| *4 #2=(|Equation| *2)) #3=(|isDomain| *5 (|List| *2)) #4=(|ofCategory| *2 #5=(|Join| (|AlgebraicallyClosedFunctionSpace| *6) #6=(|TranscendentalFunctionCategory|) #7=(|PrimitiveFunctionCategory|))) #8=(|ofCategory| *6 #9=(|Join| (|EuclideanDomain|) (|RetractableTo| #10=(|Integer|)) (|LinearlyExplicitRingOver| #10#) (|CharacteristicZero|))) #11=(|isDomain| *1 (|ElementaryFunctionODESolver| *6 *2)))) (|solve| (*1 *2 *3 *4 *3 *5) (|partial| AND (|isDomain| *3 #2#) #12=(|isDomain| *4 #1#) #3# #4# #11# #8#)) (|solve| #13=(*1 *2 *3 *4 *5) (AND #12# #14=(|isDomain| *5 #15=(|Symbol|)) #8# (|isDomain| *2 (|Union| (|Record| (|:| |particular| *3) (|:| |basis| (|List| *3))) *3 #16="failed")) (|isDomain| *1 (|ElementaryFunctionODESolver| *6 *3)) (|ofCategory| *3 #5#))) (|solve| #13# (AND (|isDomain| *3 #17=(|Equation| *7)) #12# #14# #18=(|ofCategory| *7 #5#) #8# (|isDomain| *2 (|Union| (|Record| (|:| |particular| *7) (|:| |basis| #19=(|List| *7))) *7 #16#)) #20=(|isDomain| *1 (|ElementaryFunctionODESolver| *6 *7)))) (|solve| #13# (|partial| AND (|isDomain| *3 #19#) #21=(|isDomain| *4 (|List| #1#)) #14# #18# #8# #22=(|isDomain| *2 (|Record| (|:| |particular| #23=(|Vector| *7)) (|:| |basis| (|List| #23#)))) #20#)) (|solve| #13# (|partial| AND (|isDomain| *3 (|List| #17#)) #21# #14# #18# #8# #22# #20#)) (|solve| (*1 *2 *3 *4) (|partial| AND (|isDomain| *3 (|Matrix| *6)) (|isDomain| *4 #15#) (|ofCategory| *6 (|Join| (|AlgebraicallyClosedFunctionSpace| *5) #6# #7#)) (|ofCategory| *5 #9#) (|isDomain| *2 (|List| (|Vector| *6))) (|isDomain| *1 (|ElementaryFunctionODESolver| *5 *6)))) (|solve| #13# (|partial| AND (|isDomain| *3 (|Matrix| *7)) #14# #18# #8# #22# #20# (|isDomain| *4 #23#)))) +((|int| (#1=(|#2| |#2| #2=(|Symbol|)) 17 T ELT)) (|expint| (#1# 56 T ELT)) (|diff| (((|Mapping| |#2| |#2|) #2#) 11 T ELT))) +(((|ODEIntegration| |#1| |#2|) (CATEGORY |package| (SIGNATURE |int| #1=(|#2| |#2| #2=(|Symbol|))) (SIGNATURE |expint| #1#) (SIGNATURE |diff| ((|Mapping| |#2| |#2|) #2#))) (|Join| (|EuclideanDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#) (|CharacteristicZero|)) (|Join| (|AlgebraicallyClosedFunctionSpace| |#1|) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))) (T |ODEIntegration|)) +((|diff| (*1 *2 *3) (AND #1=(|isDomain| *3 (|Symbol|)) #2=(|ofCategory| *4 (|Join| (|EuclideanDomain|) (|RetractableTo| #3=(|Integer|)) (|LinearlyExplicitRingOver| #3#) (|CharacteristicZero|))) (|isDomain| *2 (|Mapping| *5 *5)) (|isDomain| *1 (|ODEIntegration| *4 *5)) (|ofCategory| *5 #4=(|Join| (|AlgebraicallyClosedFunctionSpace| *4) (|TranscendentalFunctionCategory|) (|PrimitiveFunctionCategory|))))) (|expint| #5=(*1 *2 *2 *3) #6=(AND #1# #2# (|isDomain| *1 (|ODEIntegration| *4 *2)) (|ofCategory| *2 #4#))) (|int| #5# #6#)) +((|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) 33 T ELT))) +(((|PureAlgebraicLODE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |algDsolve| ((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#))) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|)) (T |PureAlgebraicLODE|)) +((|algDsolve| (*1 *2 *3 *4) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| *4)) (|ofCategory| *4 (|FunctionFieldCategory| *5 *6 *7)) (|ofCategory| *5 (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #1=(|Integer|)) (|RetractableTo| (|Fraction| #1#)))) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *7 (|UnivariatePolynomialCategory| (|Fraction| *6))) (|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) (|isDomain| *1 (|PureAlgebraicLODE| *5 *6 *7 *4))))) +((|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| #1=(|List| #2=(|Fraction| |#2|)))) |#4| #1#) 53 T ELT)) (|indicialEquations| ((#3=(|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) 62 T ELT) ((#3# |#4|) 61 T ELT) ((#3# |#3| |#2|) 20 T ELT) ((#3# |#3|) 21 T ELT)) (|indicialEquation| ((|#2| |#4| |#1|) 63 T ELT) ((|#2| |#3| |#1|) 28 T ELT)) (|denomLODE| ((|#2| |#3| #1#) 109 T ELT) (((|Union| |#2| "failed") |#3| #2#) 105 T ELT))) +(((|PrimitiveRatDE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |denomLODE| ((|Union| |#2| "failed") |#3| #1=(|Fraction| |#2|))) (SIGNATURE |denomLODE| (|#2| |#3| #2=(|List| #1#))) (SIGNATURE |indicialEquations| (#3=(|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|)) (SIGNATURE |indicialEquations| (#3# |#3| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#3| |#1|)) (SIGNATURE |indicialEquations| (#3# |#4|)) (SIGNATURE |indicialEquations| (#3# |#4| |#2|)) (SIGNATURE |indicialEquation| (|#2| |#4| |#1|)) (SIGNATURE |splitDenominator| ((|Record| (|:| |eq| |#3|) (|:| |rh| #2#)) |#4| #2#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| #1#)) (T |PrimitiveRatDE|)) +((|splitDenominator| #1=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 #3=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) (|ofCategory| *6 #4=(|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|Record| (|:| |eq| *7) (|:| |rh| #5=(|List| #6=(|Fraction| *6))))) (|isDomain| *1 (|PrimitiveRatDE| *5 *6 *7 *3)) (|isDomain| *4 #5#) (|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| *6)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| #6#)))) (|indicialEquation| #1# (AND #7=(|ofCategory| *2 #8=(|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *5 *3)) #9=(|ofCategory| *4 #3#) (|ofCategory| *5 #10=(|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *3 #11=(|LinearOrdinaryDifferentialOperatorCategory| #12=(|Fraction| *2))))) (|indicialEquations| #1# (AND #2# #13=(|ofCategory| *4 #4#) #14=(|isDomain| *2 (|List| (|Record| (|:| |center| *4) (|:| |equation| *4)))) (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *6 *3)) #15=(|ofCategory| *6 #16=(|LinearOrdinaryDifferentialOperatorCategory| *4)) (|ofCategory| *3 #17=(|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *4))))) (|indicialEquations| #18=(*1 *2 *3) (AND #9# #19=(|ofCategory| *5 #8#) #20=(|isDomain| *2 (|List| (|Record| (|:| |center| *5) (|:| |equation| *5)))) (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *6 *3)) (|ofCategory| *6 #21=(|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *3 #22=(|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *5))))) (|indicialEquation| #1# (AND #7# (|isDomain| *1 (|PrimitiveRatDE| *4 *2 *3 *5)) #9# #23=(|ofCategory| *3 #10#) (|ofCategory| *5 #11#))) (|indicialEquations| #1# (AND #2# #13# #14# (|isDomain| *1 (|PrimitiveRatDE| *5 *4 *3 *6)) (|ofCategory| *3 #16#) (|ofCategory| *6 #17#))) (|indicialEquations| #18# (AND #9# #19# #20# (|isDomain| *1 (|PrimitiveRatDE| *4 *5 *3 *6)) (|ofCategory| *3 #21#) (|ofCategory| *6 #22#))) (|denomLODE| #1# (AND (|isDomain| *4 (|List| #12#)) #24=(|ofCategory| *2 #4#) #25=(|isDomain| *1 (|PrimitiveRatDE| *5 *2 *3 *6)) #2# #23# (|ofCategory| *6 #11#))) (|denomLODE| #1# (|partial| AND (|isDomain| *4 #12#) #24# #25# #2# #23# #15#))) +((|singRicDE| (((|List| (|Record| (|:| |frac| #1=(|Fraction| |#2|)) #2=(|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) 156 T ELT)) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) #2#)) |#3| #3=(|Mapping| (|List| |#1|) |#2|)) 52 T ELT)) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) 123 T ELT)) (|denomRicDE| ((|#2| |#3|) 42 T ELT)) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) #2#)) |#3| #3#) 100 T ELT)) (|changeVar| ((|#3| |#3| #1#) 71 T ELT) ((|#3| |#3| |#2|) 97 T ELT))) +(((|PrimitiveRatRicDE| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |denomRicDE| (|#2| |#3|)) (SIGNATURE |leadingCoefficientRicDE| ((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|)) (SIGNATURE |constantCoefficientRicDE| ((|List| (|Record| (|:| |constant| |#1|) #1=(|:| |eq| |#3|))) |#3| #2=(|Mapping| (|List| |#1|) |#2|))) (SIGNATURE |polyRicDE| ((|List| (|Record| (|:| |poly| |#2|) #1#)) |#3| #2#)) (SIGNATURE |singRicDE| ((|List| (|Record| (|:| |frac| #3=(|Fraction| |#2|)) #1#)) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|))) (SIGNATURE |changeVar| (|#3| |#3| |#2|)) (SIGNATURE |changeVar| (|#3| |#3| #3#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|)))) (|UnivariatePolynomialCategory| |#1|) (|LinearOrdinaryDifferentialOperatorCategory| |#2|) (|LinearOrdinaryDifferentialOperatorCategory| #3#)) (T |PrimitiveRatRicDE|)) +((|changeVar| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 #2=(|Fraction| *5)) #3=(|ofCategory| *4 #4=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Fraction| (|Integer|))))) #5=(|ofCategory| *5 #6=(|UnivariatePolynomialCategory| *4)) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *2 *6)) (|ofCategory| *2 #7=(|LinearOrdinaryDifferentialOperatorCategory| *5)) (|ofCategory| *6 #8=(|LinearOrdinaryDifferentialOperatorCategory| *3)))) (|changeVar| #1# (AND #3# (|ofCategory| *3 #6#) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *3 *2 *5)) (|ofCategory| *2 #8#) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *3))))) (|singRicDE| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Mapping| (|List| *7) *7 (|SparseUnivariatePolynomial| *7))) (|isDomain| *5 (|Mapping| (|Factored| *7) *7)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 #4#) (|isDomain| *2 (|List| (|Record| (|:| |frac| #9=(|Fraction| *7)) #10=(|:| |eq| *3)))) (|isDomain| *1 (|PrimitiveRatRicDE| *6 *7 *3 *8)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *7)) (|ofCategory| *8 (|LinearOrdinaryDifferentialOperatorCategory| #9#)))) (|polyRicDE| #11=(*1 *2 *3 *4) (AND #12=(|isDomain| *4 (|Mapping| (|List| *5) *6)) #13=(|ofCategory| *5 #4#) #14=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|isDomain| *2 (|List| (|Record| (|:| |poly| *6) #10#))) #15=(|isDomain| *1 (|PrimitiveRatRicDE| *5 *6 *3 *7)) #16=(|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *6)) #17=(|ofCategory| *7 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *6))))) (|constantCoefficientRicDE| #11# (AND #12# #13# #14# (|isDomain| *2 (|List| (|Record| (|:| |constant| *5) #10#))) #15# #16# #17#)) (|leadingCoefficientRicDE| #18=(*1 *2 *3) (AND #3# #5# (|isDomain| *2 (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| *5)))) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *5 *3 *6)) (|ofCategory| *3 #7#) (|ofCategory| *6 (|LinearOrdinaryDifferentialOperatorCategory| #2#)))) (|denomRicDE| #18# (AND (|ofCategory| *2 #6#) (|isDomain| *1 (|PrimitiveRatRicDE| *4 *2 *3 *5)) #3# (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *2)) (|ofCategory| *5 (|LinearOrdinaryDifferentialOperatorCategory| (|Fraction| *2)))))) +((|ratDsolve| ((#1=(|Record| #2=(|:| |basis| #3=(|List| #4=(|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) #5=(|LinearOrdinaryDifferentialOperator2| |#2| #4#) #3#) 146 T ELT) ((#6=(|Record| (|:| |particular| (|Union| #4# "failed")) #2#) #5# #4#) 145 T ELT) ((#1# #7=(|LinearOrdinaryDifferentialOperator1| #4#) #3#) 140 T ELT) ((#6# #7# #4#) 138 T ELT)) (|indicialEquationAtInfinity| ((|#2| #5#) 86 T ELT) ((|#2| #7#) 89 T ELT))) +(((|RationalLODE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ratDsolve| (#1=(|Record| (|:| |particular| (|Union| #2=(|Fraction| |#2|) "failed")) #3=(|:| |basis| #4=(|List| #2#))) #5=(|LinearOrdinaryDifferentialOperator1| #2#) #2#)) (SIGNATURE |ratDsolve| (#6=(|Record| #3# (|:| |mat| (|Matrix| |#1|))) #5# #4#)) (SIGNATURE |ratDsolve| (#1# #7=(|LinearOrdinaryDifferentialOperator2| |#2| #2#) #2#)) (SIGNATURE |ratDsolve| (#6# #7# #4#)) (SIGNATURE |indicialEquationAtInfinity| (|#2| #5#)) (SIGNATURE |indicialEquationAtInfinity| (|#2| #7#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #8=(|Integer|)) (|RetractableTo| (|Fraction| #8#))) (|UnivariatePolynomialCategory| |#1|)) (T |RationalLODE|)) +((|indicialEquationAtInfinity| #1=(*1 *2 *3) (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *2 #2=(|Fraction| *2))) #3=(|ofCategory| *2 (|UnivariatePolynomialCategory| *4)) #4=(|isDomain| *1 (|RationalLODE| *4 *2)) #5=(|ofCategory| *4 #6=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #7=(|Integer|)) (|RetractableTo| (|Fraction| #7#)))))) (|indicialEquationAtInfinity| #1# (AND (|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| #2#)) #3# #4# #5#)) (|ratDsolve| #8=(*1 *2 *3 *4) (AND #9=(|isDomain| *3 (|LinearOrdinaryDifferentialOperator2| *6 #10=(|Fraction| *6))) #11=(|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) #12=(|ofCategory| *5 #6#) #13=(|isDomain| *2 (|Record| (|:| |basis| #14=(|List| #10#)) (|:| |mat| (|Matrix| *5)))) #15=(|isDomain| *1 (|RationalLODE| *5 *6)) #16=(|isDomain| *4 #14#))) (|ratDsolve| #8# (AND #9# #17=(|isDomain| *4 #10#) #11# #12# #18=(|isDomain| *2 (|Record| (|:| |particular| (|Union| *4 "failed")) (|:| |basis| (|List| *4)))) #15#)) (|ratDsolve| #8# (AND #19=(|isDomain| *3 (|LinearOrdinaryDifferentialOperator1| #10#)) #11# #12# #13# #15# #16#)) (|ratDsolve| #8# (AND #19# #17# #11# #12# #18# #15#))) +((|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) 49 T ELT))) +(((|ReduceLODE| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |reduceLODE| ((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|))) (|Field|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|) (|UnivariatePolynomialCategory| |#1|) (|MonogenicAlgebra| |#1| |#3|) (|LinearOrdinaryDifferentialOperatorCategory| |#4|)) (T |ReduceLODE|)) +((|reduceLODE| (*1 *2 *3 *4) (AND (|ofCategory| *5 (|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *4 (|MonogenicAlgebra| *5 *7)) (|isDomain| *2 (|Record| (|:| |mat| (|Matrix| *6)) (|:| |vec| (|Vector| *5)))) (|isDomain| *1 (|ReduceLODE| *5 *6 *7 *4 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T)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ "failed") $ $) NIL T ELT)) (|sample| #5=(($) NIL T CONST)) (|reductum| #6=(#7=($ $) NIL T ELT)) (|recip| ((#4# $) NIL T ELT)) (|po| ((|#1| $) 10 T ELT)) (|opposite?| #1#) (|op| (($ |#1|) 9 T ELT)) (|one?| #3#) (|monomial| (($ |#2| #8=(|NonNegativeInteger|)) NIL T ELT)) (|minimumDegree| #9=((#8# $) NIL T ELT)) (|leadingCoefficient| ((|#2| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|differentiate| #10=(#7# NIL #11=(|has| |#1| (|DifferentialRing|)) ELT) #12=(#13=($ $ #8#) NIL #11# ELT)) (|degree| #9#) (|coerce| (((|OutputForm|) $) 17 T ELT) (($ #14=(|Integer|)) NIL T ELT) (($ |#2|) NIL (|has| |#2| (|CommutativeRing|)) ELT)) (|coefficient| ((|#2| $ #8#) NIL T ELT)) (|characteristic| ((#8#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|Zero| #5#) (|One| #5#) (D #10# #12#) (= #1#) (- #6# #15=(#16=($ $ $) NIL T ELT)) (+ #15#) (** (($ $ #17=(|PositiveInteger|)) NIL T ELT) (#13# NIL T ELT)) (* (($ #17# $) NIL T ELT) (($ #8# $) NIL T ELT) (($ #14# . #18=($)) NIL T ELT) (#16# 12 T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| . #18#) NIL T ELT))) +(((|OppositeMonogenicLinearOperator| |#1| |#2|) (|Join| #1=(|MonogenicLinearOperator| |#2|) (CATEGORY |domain| (IF (|has| |#1| #2=(|DifferentialRing|)) (ATTRIBUTE #2#) |%noBranch|) (SIGNATURE |op| ($ |#1|)) (SIGNATURE |po| (|#1| $)))) #1# (|Ring|)) (T |OppositeMonogenicLinearOperator|)) +((|op| (*1 *1 *2) (AND #1=(|ofCategory| *3 (|Ring|)) #2=(|isDomain| *1 (|OppositeMonogenicLinearOperator| *2 *3)) #3=(|ofCategory| *2 (|MonogenicLinearOperator| *3)))) (|po| (*1 *2 *1) (AND #3# #2# #1#))) +((~= (#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)) (|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| |#1|) $) 81 T ELT)) (|member?| ((#13=(|Boolean|) |#1| $) 76 (|has| |#1| . #11#) ELT)) (|max| ((|#1| $) 86 T ELT)) (|map!| (($ (|Mapping| |#1| |#1|) $) 39 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 26 T ELT)) (|latex| (((|String|) $) 21 T ELT)) (|intersect| (#2# 64 T ELT)) (|inspect| ((|#1| . #14=($)) 35 T ELT)) (|insert!| (($ |#1| $) 36 T ELT) (($ |#1| $ #15=(|NonNegativeInteger|)) 56 T ELT)) (|hash| (((|SingleInteger|) $) 20 T ELT)) (|find| (((|Union| |#1| "failed") (|Mapping| #13# |#1|) $) 78 T ELT)) (|extract!| ((|#1| . #14#) 37 T ELT)) (|every?| ((#13# (|Mapping| #13# |#1|) . #16=($)) 83 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| (#9# 8 T ELT)) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| #15#))) $) 54 T ELT)) (|difference| (($ $ |#1|) 66 T ELT) (#2# 65 T ELT)) (|dictionary| (($) 46 T ELT) (($ (|List| |#1|)) 45 T ELT)) (|count| ((#19=(|NonNegativeInteger|) (|Mapping| #13# |#1|) $) 82 T ELT) ((#19# |#1| $) 77 (|has| |#1| . #11#) ELT)) (|copy| (($ $) 9 T ELT)) (|convert| ((#20=(|InputForm|) $) 52 (|has| |#1| (|ConvertibleTo| #20#)) ELT)) (|construct| (($ (|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)) (|any?| ((#13# (|Mapping| #13# |#1|) . #16#) 84 T ELT)) (= (#1# 17 T ELT)) (|#| ((#19# $) 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)) +((~= (#1=(#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#3=(#2# $) NIL #4=(|has| |#1| (|AbelianGroup|)) ELT)) (|subtractIfCan| ((#5=(|Union| $ #6="failed") $ $) NIL #4# ELT)) (|sign| (#7=(#8=(|Integer|) $) NIL #9=(|has| |#1| (|OrderedRing|)) ELT)) (|sample| (#10=($) NIL #4# CONST)) (|retractIfCan| (((|Union| #8# . #11=(#6#)) $) NIL #12=(|has| |#1| (|RetractableTo| #8#)) ELT) (#13=((|Union| #14=(|Fraction| #8#) #6#) $) NIL #15=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| |#1| . #11#) $) 15 T ELT)) (|retract| (#7# NIL #12# ELT) (#16=(#14# $) NIL #15# ELT) ((|#1| $) 9 T ELT)) (|recip| ((#5# $) 42 #9# ELT)) (|rationalIfCan| (#13# 51 #17=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#3# 46 #17# ELT)) (|rational| (#16# 48 #17# ELT)) (|positive?| #18=(#3# NIL #9# ELT)) (|opposite?| (#1# NIL #4# ELT)) (|one?| #18#) (|negative?| #18#) (|min| #19=(#20=($ $ $) NIL #9# ELT)) (|max| #19#) (|latex| (((|String|) $) NIL T ELT)) (|infinity| (#10# 13 T ELT)) (|infinite?| (#3# 12 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|finite?| (#3# 11 T ELT)) (|coerce| (((|OutputForm|) $) 18 T ELT) (($ #14#) NIL #15# ELT) (($ |#1|) 8 T ELT) (($ #8#) NIL (OR #9# #12#) ELT)) (|characteristic| ((#21=(|NonNegativeInteger|)) 36 #9# CONST)) (|before?| (#1# 53 T ELT)) (|annihilate?| #22=(#1# NIL #9# ELT)) (|abs| (#23=($ $) NIL #9# ELT)) (|Zero| (#10# 23 #4# CONST)) (|One| (#10# 33 #9# CONST)) (>= #22#) (> #22#) (= (#1# 21 T ELT)) (<= #22#) (< (#1# 45 #9# ELT)) (- (#20# NIL #4# ELT) (#23# 29 #4# ELT)) (+ (#20# 31 #4# ELT)) (** (($ $ #24=(|PositiveInteger|)) NIL #9# ELT) (($ $ #21#) NIL #9# ELT)) (* (#20# 39 #9# ELT) (($ #8# $) 27 #4# ELT) (($ #21# $) NIL #4# ELT) (($ #24# $) NIL #4# ELT))) +(((|OnePointCompletion| |#1|) (|Join| #1=(|SetCategory|) (|FullyRetractableTo| |#1|) (CATEGORY |domain| (SIGNATURE |infinity| ($)) (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#))) +((|map| ((#1=(|OnePointCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OnePointCompletion| |#1|) #1#) 12 T ELT) ((#1# #2# #3#) 13 T ELT))) +(((|OnePointCompletionFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| (#1=(|OnePointCompletion| |#2|) #2=(|Mapping| |#2| |#1|) #3=(|OnePointCompletion| |#1|))) (SIGNATURE |map| (#1# #2# #3# #1#))) #4=(|SetCategory|) #4#) (T |OnePointCompletionFunctions2|)) +((|map| (*1 *2 *3 *4 *2) (AND #1=(|isDomain| *2 (|OnePointCompletion| *6)) #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|OnePointCompletion| *5)) #4=(|ofCategory| *5 #5=(|SetCategory|)) #6=(|ofCategory| *6 #5#) #7=(|isDomain| *1 (|OnePointCompletionFunctions2| *5 *6)))) (|map| (*1 *2 *3 *4) (AND #2# #3# #4# #6# #1# #7#))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|sample| #6=(($) NIL T CONST)) (|retractIfCan| (((|Union| |#1| . #7=(#5#)) . #8=($)) NIL T ELT) (((|Union| #9=(|BasicOperator|) . #7#) . #8#) NIL T ELT)) (|retract| ((|#1| . #10=($)) NIL T ELT) ((#9# . #10#) NIL T ELT)) (|recip| ((#4# $) NIL T ELT)) (|opposite?| #1#) (|opeval| ((|#1| #9# |#1|) NIL T ELT)) (|one?| #3#) (|makeop| (($ |#1| (|FreeGroup| #9#)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|evaluateInverse| #11=(($ $ (|Mapping| |#1| |#1|)) NIL T ELT)) (|evaluate| #11#) (|elt| ((|#1| $ |#1|) NIL T ELT)) (|conjug| ((|#1| |#1|) NIL #12=(|has| |#1| (|CommutativeRing|)) ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #13=(|Integer|)) NIL T ELT) (($ |#1|) NIL T ELT) (($ #9#) NIL T ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#14=(|NonNegativeInteger|)) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|adjoint| (#15=($ $) NIL #12# ELT) (#16=($ $ $) NIL #12# ELT)) (|Zero| #6#) (|One| #6#) (= #1#) (- (#15# NIL T ELT) #17=(#16# NIL T ELT)) (+ #17#) (** (($ $ #18=(|PositiveInteger|)) NIL T ELT) (($ $ #14#) NIL T ELT) (($ #9# #13#) NIL T ELT) (($ $ #13#) NIL T ELT)) (* (($ #18# $) NIL T ELT) (($ #14# $) NIL T ELT) (($ #13# . #19=($)) NIL T ELT) #17# (($ |#1| . #19#) NIL #12# ELT) (($ $ |#1|) NIL #12# ELT))) +(((|Operator| |#1|) (|Join| #1=(|Ring|) (|RetractableTo| |#1|) (|RetractableTo| #2=(|BasicOperator|)) (|Eltable| |#1| |#1|) (CATEGORY |domain| (IF (|has| |#1| #3=(|CharacteristicZero|)) (ATTRIBUTE #3#) |%noBranch|) (IF (|has| |#1| #4=(|CharacteristicNonZero|)) (ATTRIBUTE #4#) |%noBranch|) (IF (|has| |#1| (|CommutativeRing|)) (PROGN (ATTRIBUTE (|Algebra| |#1|)) (SIGNATURE |adjoint| ($ $)) (SIGNATURE |adjoint| ($ $ $)) (SIGNATURE |conjug| (|#1| |#1|))) |%noBranch|) (SIGNATURE |evaluate| #5=($ $ (|Mapping| |#1| |#1|))) (SIGNATURE |evaluateInverse| #5#) (SIGNATURE ** ($ #2# #6=(|Integer|))) (SIGNATURE ** ($ $ #6#)) (SIGNATURE |opeval| (|#1| #2# |#1|)) (SIGNATURE |makeop| ($ |#1| (|FreeGroup| #2#))))) #1#) (T |Operator|)) +((|adjoint| (*1 *1 *1) #1=(AND #2=(|isDomain| *1 (|Operator| *2)) (|ofCategory| *2 (|CommutativeRing|)) #3=(|ofCategory| *2 #4=(|Ring|)))) (|adjoint| (*1 *1 *1 *1) #1#) (|conjug| (*1 *2 *2) #1#) (|evaluate| #5=(*1 *1 *1 *2) #6=(AND (|isDomain| *2 (|Mapping| *3 *3)) #7=(|ofCategory| *3 #4#) #8=(|isDomain| *1 (|Operator| *3)))) (|evaluateInverse| #5# #6#) (** #9=(*1 *1 *2 *3) (AND (|isDomain| *2 #10=(|BasicOperator|)) (|isDomain| *3 #11=(|Integer|)) (|isDomain| *1 (|Operator| *4)) (|ofCategory| *4 #4#))) (** #5# (AND (|isDomain| *2 #11#) #8# #7#)) (|opeval| (*1 *2 *3 *2) (AND (|isDomain| *3 #10#) #2# #3#)) (|makeop| #9# (AND (|isDomain| *3 (|FreeGroup| #10#)) #2# #3#))) +((|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))) +(((|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|))))) +(|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|) . 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T) ((|Join|) . 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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|rightRemainder| (($ $ $) 58 (|has| |#1| (|Field|)) ELT)) (|rightQuotient| (($ $ $) 59 (|has| |#1| (|Field|)) ELT)) (|rightLcm| (($ $ $) 61 (|has| |#1| (|Field|)) ELT)) (|rightGcd| (($ $ $) 56 (|has| |#1| (|Field|)) ELT)) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 55 (|has| |#1| (|Field|)) ELT)) (|rightExactQuotient| (((|Union| $ "failed") $ $) 57 (|has| |#1| (|Field|)) ELT)) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 60 (|has| |#1| (|Field|)) ELT)) (|retractIfCan| (((|Union| #4=(|Integer|) . #5=("failed")) . #6=($)) 88 (|has| |#1| . #7=((|RetractableTo| #4#))) ELT) (((|Union| #8=(|Fraction| #4#) . #5#) . #6#) 85 (|has| |#1| . #9=((|RetractableTo| #8#))) ELT) (((|Union| |#1| . #5#) . #6#) 82 T ELT)) (|retract| ((#4# . #10=($)) 87 (|has| |#1| . #7#) ELT) ((#8# . #10#) 84 (|has| |#1| . #9#) ELT) ((|#1| . #10#) 83 T ELT)) (|reductum| (($ $) 77 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|primitivePart| (($ $) 68 (|has| |#1| (|GcdDomain|)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial| (($ |#1| (|NonNegativeInteger|)) 75 T ELT)) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 70 (|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 71 (|has| |#1| (|IntegralDomain|)) ELT)) (|minimumDegree| (((|NonNegativeInteger|) $) 79 T ELT)) (|leftRemainder| (($ $ $) 65 (|has| |#1| (|Field|)) ELT)) (|leftQuotient| (($ $ $) 66 (|has| |#1| (|Field|)) ELT)) (|leftLcm| (($ $ $) 54 (|has| |#1| (|Field|)) ELT)) (|leftGcd| (($ $ $) 63 (|has| |#1| (|Field|)) ELT)) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) 62 (|has| |#1| (|Field|)) ELT)) (|leftExactQuotient| (((|Union| $ "failed") $ $) 64 (|has| |#1| (|Field|)) ELT)) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 67 (|has| |#1| (|Field|)) ELT)) (|leadingCoefficient| ((|#1| $) 78 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ |#1|) 72 (|has| |#1| (|IntegralDomain|)) ELT)) (|degree| (((|NonNegativeInteger|) $) 80 T ELT)) (|content| ((|#1| $) 69 (|has| |#1| (|GcdDomain|)) ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #8#) 86 (|has| 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(|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| 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|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)) +((|times| ((|#2| |#2| |#2| #1=(|Automorphism| |#1|) #2=(|Mapping| |#1| |#1|)) 20 T ELT)) (|rightDivide| (#3=((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| #1#) 46 #4=(|has| |#1| (|Field|)) ELT)) (|monicRightDivide| (#3# 43 #5=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#3# 42 #5# ELT)) (|leftDivide| (#3# 45 #4# ELT)) (|apply| ((|#1| |#2| |#1| |#1| #1# #2#) 33 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#)))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ #6="failed") $ $) NIL T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rightRemainder| #9=(#10=($ $ $) NIL #11=(|has| |#1| (|Field|)) ELT)) (|rightQuotient| #9#) (|rightLcm| #9#) (|rightGcd| #9#) (|rightExtendedGcd| #12=(((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) NIL #11# ELT)) (|rightExactQuotient| #13=(#4# NIL #11# ELT)) (|rightDivide| (#14=((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 34 #11# ELT)) (|retractIfCan| (((|Union| #15=(|Integer|) . #16=(#6#)) . #17=($)) NIL #18=(|has| |#1| (|RetractableTo| #15#)) ELT) (((|Union| #19=(|Fraction| #15#) . #16#) . #17#) NIL #20=(|has| |#1| (|RetractableTo| #19#)) ELT) (((|Union| |#1| . #16#) . #17#) NIL T ELT)) (|retract| ((#15# . #21=($)) NIL #18# ELT) ((#19# . #21#) NIL #20# ELT) #22=(#23=(|#1| . #21#) NIL T ELT)) (|reductum| #24=(#25=($ $) NIL T ELT)) (|recip| ((#5# $) NIL T ELT)) (|primitivePart| (#25# NIL #26=(|has| |#1| (|GcdDomain|)) ELT)) (|outputForm| ((#27=(|OutputForm|) $ #27#) NIL T ELT)) (|opposite?| #1#) (|one?| #3#) (|monomial| (($ |#1| #28=(|NonNegativeInteger|)) NIL T ELT)) (|monicRightDivide| (#14# 30 #29=(|has| |#1| (|IntegralDomain|)) ELT)) (|monicLeftDivide| (#14# 28 #29# ELT)) (|minimumDegree| #30=((#28# $) NIL T ELT)) (|leftRemainder| #9#) (|leftQuotient| #9#) (|leftLcm| #9#) (|leftGcd| #9#) (|leftExtendedGcd| #12#) (|leftExactQuotient| #13#) (|leftDivide| (#14# 32 #11# ELT)) (|leadingCoefficient| #22#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|exquo| ((#5# $ |#1|) NIL #29# ELT)) (|degree| #30#) (|content| (#23# NIL #26# ELT)) (|coerce| ((#27# $) NIL T ELT) (($ #15#) NIL T ELT) (($ #19#) NIL #20# ELT) (($ |#1|) NIL T ELT)) (|coefficients| (((|List| |#1|) $) NIL T ELT)) (|coefficient| ((|#1| $ #28#) NIL T ELT)) (|characteristic| ((#28#) NIL T CONST)) (|before?| #1#) (|apply| ((|#1| $ |#1| |#1|) 15 T ELT)) (|annihilate?| #1#) (|Zero| #7#) (|One| (#8# 23 T CONST)) (= #1#) (- #24# #31=(#10# NIL T ELT)) (+ #31#) (** (($ $ #32=(|PositiveInteger|)) 19 T ELT) (($ $ #28#) 24 T ELT)) (* (($ #32# $) NIL T ELT) (($ #28# $) NIL T ELT) (($ #15# . #33=($)) NIL T ELT) (#10# 13 T ELT) (($ $ |#1|) NIL T ELT) (($ |#1| . #33#) NIL T ELT))) +(((|SparseUnivariateSkewPolynomial| |#1| |#2| |#3|) (|Join| (|UnivariateSkewPolynomialCategory| |#1|) (CATEGORY |domain| (SIGNATURE |outputForm| (#1=(|OutputForm|) $ #1#)))) (|Ring|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) (T |SparseUnivariateSkewPolynomial|)) +((|outputForm| (*1 *2 *1 *2) (AND (|isDomain| *2 (|OutputForm|)) (|isDomain| *1 (|SparseUnivariateSkewPolynomial| *3 *4 *5)) (|ofCategory| *3 (|Ring|)) (|ofType| *4 (|Automorphism| *3)) (|ofType| *5 (|Mapping| *3 *3))))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|subtractIfCan| (#4=(#5=(|Union| $ #6="failed") $ $) NIL T ELT)) (|sample| #7=(#8=($) NIL T CONST)) (|rightRemainder| #9=(#10=($ $ $) NIL #11=(|has| 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#1=(|Type|) #1#) (T |ParametricSpaceCurveFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|ParametricSpaceCurve| *5)) (|ofCategory| *5 #1=(|Type|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|ParametricSpaceCurve| *6)) (|isDomain| *1 (|ParametricSpaceCurveFunctions2| *5 *6))))) +((|curve| (($ |#1| |#1| |#1|) 8 T ELT)) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) 15 T ELT))) +(((|ParametricSpaceCurve| |#1|) (CATEGORY |domain| (SIGNATURE |curve| ($ |#1| |#1| |#1|)) (SIGNATURE |coordinate| (|#1| $ (|NonNegativeInteger|)))) (|Type|)) (T |ParametricSpaceCurve|)) +((|coordinate| (*1 *2 *1 *3) (AND (|isDomain| *3 (|NonNegativeInteger|)) #1=(|isDomain| *1 (|ParametricSpaceCurve| *2)) #2=(|ofCategory| *2 (|Type|)))) (|curve| (*1 *1 *2 *2 *2) (AND #1# #2#))) +((|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) 9 T ELT))) +(((|Parser|) (CATEGORY |package| (SIGNATURE |getSyntaxFormsFromFile| ((|List| (|Syntax|)) (|String|))))) (T |Parser|)) 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T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|SetCategory|) . T) ((|Type|) . 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#17# (|:| |exponent| #19=(|NonNegativeInteger|))) #12#) $) 45 T ELT)) (|inR?| (#10# 34 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|hasTopPredicate?| (#10# 28 T ELT)) (|hasPredicate?| (#10# 52 T ELT)) (|getBadValues| (#14# 130 T ELT)) (|generic?| (#10# 56 T ELT)) (|elt| (($ #18# #7#) 104 T ELT)) (|depth| ((#19# $) 33 T ELT)) (|copy| (#13# 72 T ELT)) (|convert| (($ #7#) 69 T ELT)) (|constant?| (#10# 32 T ELT)) (|coerce| (((|OutputForm|) $) 63 T ELT) (($ |#1|) 23 T ELT) (($ #9#) 76 T ELT)) (|before?| #1#) (|addBadValue| (($ $ #6#) 129 T ELT)) (|Zero| (#20=($) 103 T CONST)) (|One| (#20# 83 T CONST)) (= (#2# 93 T ELT)) (/ (#21=($ $ $) 117 T ELT)) (+ (#21# 121 T ELT)) (** (($ $ #19#) 115 T ELT) (#21# 64 T ELT)) (* (#21# 122 T ELT))) +(((|Pattern| |#1|) (|Join| #1=(|SetCategory|) (|RetractableTo| |#1|) (|RetractableTo| #2=(|Symbol|)) (CATEGORY |domain| (SIGNATURE |Zero| #3=($) |constant|) (SIGNATURE |One| #3# |constant|) (SIGNATURE |isPlus| #4=(#5=(|Union| #6=(|List| $) #7="failed") 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(|:| |arg| #7#))) #9# #10#)) (|isExpt| #4# (|partial| AND (|isDomain| *2 (|Record| #16=(|:| |val| #8#) (|:| |exponent| #17=(|NonNegativeInteger|)))) #9# #10#)) (|isQuotient| #4# (|partial| AND (|isDomain| *2 (|Record| (|:| |num| #8#) (|:| |den| #8#))) #9# #10#)) (|isList| #4# #5#) (|isPower| #4# (|partial| AND (|isDomain| *2 (|Record| #16# (|:| |exponent| #8#))) #9# #10#)) (|elt| (*1 *1 *2 *3) (AND (|isDomain| *2 #11#) (|isDomain| *3 #12#) #14# #15#)) (+ #18=(*1 *1 *1 *1) #2#) (* #18# #2#) (** #19=(*1 *1 *1 *2) #20=(AND (|isDomain| *2 #17#) #9# #10#)) (** #18# #2#) (/ #18# #2#) (|depth| #4# #20#) (|convert| (*1 *1 *2) #21=(AND #6# #9# #10#)) (|copy| #22=(*1 *1 *1) #2#) (|inR?| #4# #23=(AND (|isDomain| *2 #24=(|Boolean|)) #9# #10#)) (|quoted?| #4# #23#) (|symbol?| #4# #23#) (|constant?| #4# #23#) (|generic?| #4# #23#) (|multiple?| #4# #23#) (|optional?| #4# #23#) (|hasPredicate?| #4# #23#) (|predicates| #4# #25=(AND (|isDomain| *2 (|List| #26=(|Any|))) #9# #10#)) (|setPredicates| #19# 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(#1=(|Pattern| |#1|) #1# #2=(|Mapping| #3=(|Boolean|) |#2|))) (SIGNATURE |suchThat| (#1# #1# (|List| #2#))) (SIGNATURE |suchThat| (#1# #1# (|List| (|Symbol|)) (|Mapping| #3# #4=(|List| |#2|)))) (SIGNATURE |predicate| (#2# #1#)) (SIGNATURE |satisfy?| (#3# |#2| #1#)) (SIGNATURE |satisfy?| (#3# #4# #1#)) (SIGNATURE |addBadValue| (#1# #1# |#2|)) (SIGNATURE |badValues| (#4# #1#))) (|SetCategory|) (|Type|)) (T |PatternFunctions1|)) +((|badValues| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Pattern| *4)) #4=(|ofCategory| *4 #5=(|SetCategory|)) (|isDomain| *2 (|List| *5)) #6=(|isDomain| *1 (|PatternFunctions1| *4 *5)) #7=(|ofCategory| *5 #8=(|Type|)))) (|addBadValue| #9=(*1 *2 *2 *3) (AND #10=(|isDomain| *2 #3#) #4# (|isDomain| *1 (|PatternFunctions1| *4 *3)) #11=(|ofCategory| *3 #8#))) (|satisfy?| #12=(*1 *2 *3 *4) (AND (|isDomain| *3 #13=(|List| *6)) #14=(|isDomain| *4 #15=(|Pattern| *5)) #16=(|ofCategory| *5 #5#) #17=(|ofCategory| *6 #8#) #18=(|isDomain| *2 #19=(|Boolean|)) #20=(|isDomain| *1 (|PatternFunctions1| *5 *6)))) (|satisfy?| #12# (AND #14# #16# #18# (|isDomain| *1 (|PatternFunctions1| *5 *3)) #11#)) (|predicate| #1# (AND #2# #4# (|isDomain| *2 #21=(|Mapping| #19# *5)) #6# #7#)) (|suchThat| (*1 *2 *2 *3 *4) (AND (|isDomain| *2 #15#) (|isDomain| *3 (|List| (|Symbol|))) (|isDomain| *4 (|Mapping| #19# #13#)) #16# #17# #20#)) (|suchThat| #9# (AND #10# (|isDomain| *3 (|List| #21#)) #4# #7# #6#)) (|suchThat| #9# (AND #10# (|isDomain| *3 #21#) #4# #7# #6#))) +((|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) 19 T ELT))) +(((|PatternFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |map| ((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)))) #1=(|SetCategory|) #1#) (T |PatternFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|Pattern| *6)) (|isDomain| *1 (|PatternFunctions2| *5 *6))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|varList| (((|List| |#1|) $) 20 T ELT)) (|retractable?| ((#3# $) 49 T ELT)) (|retractIfCan| (((|Union| #4=(|LyndonWord| |#1|) "failed") $) 55 T ELT)) (|retract| (#5=(#4# $) 53 T ELT)) (|rest| (($ $) 24 T ELT)) (|min| #6=(($ $ $) NIL T ELT)) (|max| #6#) (|length| (((|NonNegativeInteger|) $) 60 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#5# 22 T ELT)) (|coerce| (((|OutputForm|) $) 47 T ELT) (($ #4#) 27 T ELT) (((|OrderedFreeMonoid| |#1|) $) 36 T ELT) (($ |#1|) 26 T ELT)) (|before?| #1#) (|One| (($) 11 T CONST)) (|ListOfTerms| (((|List| #4#) $) 28 T ELT)) (>= #1#) (> #1#) (= (#2# 14 T ELT)) (<= #1#) (< (#2# 66 T ELT))) +(((|PoincareBirkhoffWittLyndonBasis| |#1|) (|Join| #1=(|OrderedSet|) (|RetractableTo| #2=(|LyndonWord| |#1|)) (CATEGORY |domain| (SIGNATURE |One| ($) |constant|) (SIGNATURE |coerce| ((|OrderedFreeMonoid| |#1|) $)) (SIGNATURE |coerce| ($ |#1|)) (SIGNATURE |first| (#2# $)) (SIGNATURE |length| ((|NonNegativeInteger|) $)) (SIGNATURE |ListOfTerms| ((|List| #2#) $)) (SIGNATURE |rest| ($ $)) (SIGNATURE |retractable?| ((|Boolean|) $)) (SIGNATURE |varList| ((|List| |#1|) $)))) #1#) (T |PoincareBirkhoffWittLyndonBasis|)) +((|One| (*1 *1) #1=(AND (|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *2)) (|ofCategory| *2 #2=(|OrderedSet|)))) (|coerce| #3=(*1 *2 *1) (AND (|isDomain| *2 (|OrderedFreeMonoid| *3)) #4=(|isDomain| *1 (|PoincareBirkhoffWittLyndonBasis| *3)) #5=(|ofCategory| *3 #2#))) (|coerce| (*1 *1 *2) #1#) (|first| #3# (AND (|isDomain| *2 #6=(|LyndonWord| *3)) #4# #5#)) (|length| #3# (AND (|isDomain| *2 (|NonNegativeInteger|)) #4# #5#)) (|ListOfTerms| #3# (AND (|isDomain| *2 (|List| #6#)) #4# #5#)) (|rest| (*1 *1 *1) #1#) (|retractable?| #3# (AND (|isDomain| *2 (|Boolean|)) #4# #5#)) (|varList| #3# (AND (|isDomain| *2 (|List| *3)) #4# #5#))) +((|compose| ((|#1| |#1| |#1|) 19 T ELT))) +(((|PolynomialComposition| |#1| |#2|) (CATEGORY |package| (SIGNATURE |compose| (|#1| |#1| |#1|))) (|UnivariatePolynomialCategory| |#2|) (|Ring|)) (T |PolynomialComposition|)) +((|compose| (*1 *2 *2 *2) (AND (|ofCategory| *3 (|Ring|)) (|isDomain| *1 (|PolynomialComposition| *2 *3)) (|ofCategory| *2 (|UnivariatePolynomialCategory| *3))))) +((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)) +((|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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 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|)))) 45 T ELT) (($ $ |#2| . #6=(#5#)) 44 T ELT) (($ $ (|List| |#2|)) 43 T ELT) (($ $ |#2|) 41 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) (|Zero| (#3# 24 T CONST)) (D (($ $ (|List| |#2|) . #4#) 48 T ELT) (($ $ |#2| . #6#) 47 T ELT) (($ $ (|List| |#2|)) 46 T ELT) (($ $ |#2|) 42 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #7=($)) 30 T ELT) (($ |#1| . #7#) 33 T ELT) (($ $ |#1|) 37 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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|differentiate| (($ $ (|List| |#1|) . #4=((|List| #5=(|NonNegativeInteger|)))) 52 T ELT) (($ $ |#1| . #6=(#5#)) 51 T ELT) (($ $ (|List| |#1|)) 50 T ELT) (($ $ |#1|) 48 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ (|List| |#1|) . #4#) 55 T ELT) (($ $ |#1| . #6#) 54 T ELT) (($ $ (|List| |#1|)) 53 T ELT) (($ $ |#1|) 49 T ELT)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +(((|PartialDifferentialRing| |#1|) (|Category|) (|BasicType|)) (T |PartialDifferentialRing|)) +NIL +(|Join| (|Ring|) (|PartialDifferentialSpace| |t#1|)) +(((|AbelianGroup|) . 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T) ((|PartialDifferentialDomain| $ |#1|) . T) ((|Type|) . 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#2#))) (|PolynomialFactorizationExplicit|)) (T |PolynomialFactorizationExplicit&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 75 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (#4=((|Factored| $) $) 67 T ELT)) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) 72 T ELT)) (|sample| (#5=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#6=($ $ $) 60 T ELT) (#7=($ 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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) ((|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)) +((|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 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#2=(|Record| (|:| |den| #1#) (|:| |gcdnum| #1#)))) 15 T ELT)) (|getGoodPrime| (((|PositiveInteger|) #1#) 38 T ELT)) (|doubleDisc| (#3=(#1# |#2|) 45 T ELT)) (|badNum| (#3# 21 T ELT) ((#2# |#1|) 20 T ELT))) +(((|PointsOfFiniteOrderTools| |#1| |#2|) (CATEGORY |package| (SIGNATURE |getGoodPrime| ((|PositiveInteger|) #1=(|Integer|))) (SIGNATURE |badNum| (#2=(|Record| (|:| |den| #1#) (|:| |gcdnum| #1#)) |#1|)) (SIGNATURE |badNum| #3=(#1# |#2|)) (SIGNATURE |mix| (#1# (|List| #2#))) (SIGNATURE |doubleDisc| #3#) (SIGNATURE |polyred| (|#2| |#2|))) (|UnivariatePolynomialCategory| (|Fraction| #1#)) (|UnivariatePolynomialCategory| (|Fraction| |#1|))) (T |PointsOfFiniteOrderTools|)) +((|polyred| (*1 *2 *2) (AND #1=(|ofCategory| *3 (|UnivariatePolynomialCategory| (|Fraction| #2=(|Integer|)))) (|isDomain| *1 (|PointsOfFiniteOrderTools| *3 *2)) (|ofCategory| *2 #3=(|UnivariatePolynomialCategory| (|Fraction| *3))))) (|doubleDisc| #4=(*1 *2 *3) #5=(AND #6=(|ofCategory| *4 (|UnivariatePolynomialCategory| 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#16#) $ $) NIL T ELT) (((|Union| (|Record| #22# #23#) #10#) $ $ $) NIL T ELT)) (|exquo| (#8# 92 T ELT)) (|expressIdealMember| (((|Maybe| #15#) #15# $) NIL T ELT)) (|euclideanSize| ((#24=(|NonNegativeInteger|) $) NIL T ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|compactFraction| (#7# 49 T ELT)) (|coerce| (((|OutputForm|) $) 123 T ELT) (($ #18#) 72 T ELT) #6# (($ #25=(|Fraction| #18#)) NIL T ELT) (($ |#1|) 40 T ELT) (((|Fraction| |#1|) $) 77 T ELT) (($ (|Fraction| #17#)) 85 T ELT)) (|characteristic| ((#24#) 70 T CONST)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|Zero| (#12# 24 T CONST)) (|One| (#12# 12 T CONST)) (= (#2# 86 T ELT)) (/ #13#) (- (#7# 107 T ELT) #13#) (+ (#14# 48 T ELT)) (** (($ $ #26=(|PositiveInteger|)) NIL T ELT) (($ $ #24#) NIL T ELT) (#19# NIL T ELT)) (* (($ #26# $) NIL T ELT) (($ #24# $) NIL T ELT) (($ #18# $) 109 T ELT) (#14# 47 T ELT) (($ $ #25#) NIL T ELT) (($ #25# $) NIL T ELT) (($ |#1| $) 108 T ELT) (($ $ |#1|) NIL T ELT))) +(((|PartialFraction| |#1|) (|Join| (|Field|) (|Algebra| |#1|) (CATEGORY |domain| (SIGNATURE |coerce| ((|Fraction| |#1|) $)) (SIGNATURE |coerce| ($ (|Fraction| #1=(|Factored| |#1|)))) (SIGNATURE |compactFraction| #2=($ $)) (SIGNATURE |firstDenom| (#1# $)) (SIGNATURE |firstNumer| #3=(|#1| $)) (SIGNATURE |nthFractionalTerm| ($ $ #4=(|Integer|))) (SIGNATURE |numberOfFractionalTerms| (#4# $)) (SIGNATURE |padicallyExpand| ((|SparseUnivariatePolynomial| |#1|) |#1| |#1|)) (SIGNATURE |padicFraction| #2#) (SIGNATURE |partialFraction| ($ |#1| #1#)) (SIGNATURE |wholePart| #3#))) (|EuclideanDomain|)) (T |PartialFraction|)) +((|coerce| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Fraction| *3)) #2=(|isDomain| *1 (|PartialFraction| *3)) #3=(|ofCategory| *3 #4=(|EuclideanDomain|)))) (|coerce| (*1 *1 *2) (AND (|isDomain| *2 (|Fraction| #5=(|Factored| *3))) #3# #2#)) (|compactFraction| #6=(*1 *1 *1) #7=(AND #8=(|isDomain| *1 (|PartialFraction| *2)) #9=(|ofCategory| *2 #4#))) (|firstDenom| #1# (AND (|isDomain| *2 #5#) #2# #3#)) (|firstNumer| #1# #7#) (|nthFractionalTerm| (*1 *1 *1 *2) #10=(AND (|isDomain| *2 (|Integer|)) #2# #3#)) (|numberOfFractionalTerms| #1# #10#) (|padicallyExpand| (*1 *2 *3 *3) (AND (|isDomain| *2 (|SparseUnivariatePolynomial| *3)) #2# #3#)) (|padicFraction| #6# #7#) (|partialFraction| (*1 *1 *2 *3) (AND (|isDomain| *3 (|Factored| *2)) #9# #8#)) (|wholePart| #1# #7#)) +((|partialFraction| ((#1=(|Any|) #2=(|Polynomial| |#1|) (|Factored| #2#) #3=(|Symbol|)) 17 T ELT) ((#1# (|Fraction| #2#) #3#) 18 T ELT))) +(((|PartialFractionPackage| |#1|) (CATEGORY |package| (SIGNATURE |partialFraction| (#1=(|Any|) (|Fraction| #2=(|Polynomial| |#1|)) #3=(|Symbol|))) (SIGNATURE |partialFraction| (#1# #2# (|Factored| #2#) #3#))) (|Join| (|EuclideanDomain|) (|CharacteristicZero|))) (T |PartialFractionPackage|)) +((|partialFraction| (*1 *2 *3 *4 *5) (AND (|isDomain| *4 (|Factored| #1=(|Polynomial| *6))) (|isDomain| *5 #2=(|Symbol|)) (|isDomain| *3 #1#) (|ofCategory| *6 #3=(|Join| (|EuclideanDomain|) (|CharacteristicZero|))) #4=(|isDomain| *2 (|Any|)) (|isDomain| *1 (|PartialFractionPackage| *6)))) (|partialFraction| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Fraction| (|Polynomial| *5))) (|isDomain| *4 #2#) (|ofCategory| *5 #3#) #4# (|isDomain| *1 (|PartialFractionPackage| *5))))) +((|gcdPrimitive| (#1=(|#4| (|List| |#4|)) 148 T ELT) (#2=(#3=(|SparseUnivariatePolynomial| |#4|) #3# #3#) 85 T ELT) (#4=(|#4| |#4| |#4|) 147 T ELT)) (|gcd| ((#3# (|List| #3#)) 141 T ELT) (#2# 61 T ELT) (#1# 70 T ELT) (#4# 108 T ELT))) +(((|PolynomialGcdPackage| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |gcd| #1=(|#4| |#4| |#4|)) (SIGNATURE |gcd| #2=(|#4| (|List| |#4|))) (SIGNATURE |gcd| #3=(#4=(|SparseUnivariatePolynomial| |#4|) #4# #4#)) (SIGNATURE |gcd| (#4# (|List| #4#))) (SIGNATURE |gcdPrimitive| #1#) (SIGNATURE |gcdPrimitive| #3#) (SIGNATURE |gcdPrimitive| #2#)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|EuclideanDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |PolynomialGcdPackage|)) +((|gcdPrimitive| #1=(*1 *2 *3) #2=(AND (|isDomain| *3 (|List| *2)) (|ofCategory| *2 #3=(|PolynomialCategory| *6 *4 *5)) (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *2)) #4=(|ofCategory| *4 #5=(|OrderedAbelianMonoidSup|)) #6=(|ofCategory| *5 #7=(|OrderedSet|)) #8=(|ofCategory| *6 #9=(|EuclideanDomain|)))) (|gcdPrimitive| #10=(*1 *2 *2 *2) #11=(AND (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|ofCategory| *6 #12=(|PolynomialCategory| *5 *3 *4)) #13=(|ofCategory| *3 #5#) #14=(|ofCategory| *4 #7#) #15=(|ofCategory| *5 #9#) (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *6)))) (|gcdPrimitive| #10# #16=(AND #13# #14# #15# (|isDomain| *1 (|PolynomialGcdPackage| *3 *4 *5 *2)) (|ofCategory| *2 #12#))) (|gcd| #1# (AND (|isDomain| *3 (|List| #17=(|SparseUnivariatePolynomial| *7))) #4# #6# #8# (|isDomain| *2 #17#) (|isDomain| *1 (|PolynomialGcdPackage| *4 *5 *6 *7)) (|ofCategory| *7 #3#))) (|gcd| #10# #11#) (|gcd| #1# #2#) (|gcd| #10# #16#)) +((|youngGroup| ((#1=(|PermutationGroup| #2=(|Integer|)) (|Partition|)) 38 T ELT) (#3=(#1# (|List| #2#)) 34 T ELT)) (|symmetricGroup| (#3# 66 T ELT) (#4=(#1# #5=(|PositiveInteger|)) 67 T ELT)) (|rubiksGroup| (#6=(#1#) 39 T ELT)) (|mathieu24| (#6# 53 T ELT) (#3# 52 T ELT)) (|mathieu23| (#6# 51 T ELT) (#3# 50 T ELT)) (|mathieu22| (#6# 49 T ELT) (#3# 48 T ELT)) (|mathieu12| (#6# 47 T ELT) (#3# 46 T ELT)) (|mathieu11| (#6# 45 T ELT) (#3# 44 T ELT)) (|janko2| (#6# 55 T ELT) (#3# 54 T ELT)) (|dihedralGroup| (#3# 71 T ELT) (#4# 73 T ELT)) (|cyclicGroup| (#3# 68 T ELT) (#4# 69 T ELT)) (|alternatingGroup| (#3# 64 T ELT) (#4# 65 T ELT)) (|abelianGroup| ((#1# (|List| #5#)) 57 T ELT))) +(((|PermutationGroupExamples|) (CATEGORY |package| (SIGNATURE |symmetricGroup| #1=(#2=(|PermutationGroup| #3=(|Integer|)) #4=(|PositiveInteger|))) (SIGNATURE |symmetricGroup| #5=(#2# (|List| #3#))) (SIGNATURE |alternatingGroup| #1#) (SIGNATURE |alternatingGroup| #5#) (SIGNATURE |abelianGroup| (#2# (|List| #4#))) (SIGNATURE 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(|mathieu22| #6# #7#) (|mathieu22| #1# #5#) (|mathieu12| #6# #7#) (|mathieu12| #1# #5#) (|mathieu11| #6# #7#) (|mathieu11| #1# #5#) (|dihedralGroup| #1# #5#) (|dihedralGroup| #1# #8=(AND (|isDomain| *3 #9=(|PositiveInteger|)) #2# #4#)) (|cyclicGroup| #1# #5#) (|cyclicGroup| #1# #8#) (|abelianGroup| #1# (AND (|isDomain| *3 (|List| #9#)) #2# #4#)) (|alternatingGroup| #1# #5#) (|alternatingGroup| #1# #8#) (|symmetricGroup| #1# #5#) (|symmetricGroup| #1# #8#)) +((|totalGroebner| (#1=(#2=(|List| (|Polynomial| |#1|)) #2# (|List| (|Symbol|))) 14 T ELT)) (|lexGroebner| (#1# 13 T ELT))) +(((|PolyGroebner| |#1|) (CATEGORY |package| (SIGNATURE |lexGroebner| #1=(#2=(|List| (|Polynomial| |#1|)) #2# (|List| (|Symbol|)))) (SIGNATURE |totalGroebner| #1#)) (|GcdDomain|)) (T |PolyGroebner|)) +((|totalGroebner| #1=(*1 *2 *2 *3) #2=(AND (|isDomain| *2 (|List| (|Polynomial| *4))) (|isDomain| *3 (|List| (|Symbol|))) (|ofCategory| *4 (|GcdDomain|)) (|isDomain| *1 (|PolyGroebner| *4)))) (|lexGroebner| #1# #2#)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|sample| #3=(($) NIL T CONST)) (|recip| (((|Union| $ "failed") $) NIL T ELT)) (|one?| ((#2# $) NIL T ELT)) (|min| #4=(($ $ $) NIL T ELT)) (|max| #4#) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcd| #4#) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|One| #3#) (>= #1#) (> #1#) (= #1#) (<= #1#) (< #1#) (+ #4#) (** (($ $ (|NonNegativeInteger|)) NIL T ELT) (($ $ #5=(|PositiveInteger|)) NIL T ELT)) (* (($ #5# $) NIL T ELT) #4#)) +(((|PositiveInteger|) (|Join| (|OrderedAbelianSemiGroup|) (|Monoid|) (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $)) (ATTRIBUTE (|commutative| "*"))))) (T |PositiveInteger|)) +((|gcd| (*1 *1 *1 *1) (|isDomain| *1 (|PositiveInteger|)))) +((|NonNegativeInteger|) (|%ilt| 0 |#1|)) +((|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| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) 66 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#5=($ $ $) 60 T ELT) (#6=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 58 T ELT)) (|gcd| (#5# 62 T ELT) (#6# 61 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) 65 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 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 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#1#)) (|isDomain| *1 (|PatternMatchFunctionSpace| *5 *6 *3))))) +((|patternMatch| ((#1=(|PatternMatchResult| #2=(|Integer|) |#1|) |#1| (|Pattern| #2#) #1#) 13 T ELT))) +(((|PatternMatchIntegerNumberSystem| |#1|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| #2=(|Integer|) |#1|) |#1| (|Pattern| #2#) #1#))) (|IntegerNumberSystem|)) (T |PatternMatchIntegerNumberSystem|)) +((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| #1=(|Integer|) *3)) (|isDomain| *4 (|Pattern| #1#)) (|ofCategory| *3 (|IntegerNumberSystem|)) (|isDomain| *1 (|PatternMatchIntegerNumberSystem| *3))))) +((|patternMatch| ((#1=(|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) #1#) 57 T ELT))) +(((|PatternMatchKernel| |#1| |#2|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) #2=(|Pattern| |#1|) #1#))) #3=(|SetCategory|) (|Join| #3# (|RetractableTo| (|Kernel| $)) (|ConvertibleTo| #2#) (|PatternMatchable| |#1|))) (T |PatternMatchKernel|)) +((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchResult| *5 *6)) (|isDomain| *3 (|Kernel| *6)) (|ofCategory| *5 #1=(|SetCategory|)) (|ofCategory| *6 (|Join| #1# (|RetractableTo| (|Kernel| $)) (|ConvertibleTo| *4) (|PatternMatchable| *5))) (|isDomain| *4 (|Pattern| *5)) (|isDomain| *1 (|PatternMatchKernel| *5 *6))))) +((|patternMatch| ((#1=(|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) #1#) 17 T ELT))) +(((|PatternMatchListAggregate| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |patternMatch| (#1=(|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) #1#))) (|SetCategory|) (|PatternMatchable| |#1|) (|ListAggregate| |#2|)) (T |PatternMatchListAggregate|)) +((|patternMatch| (*1 *2 *3 *4 *2) (AND (|isDomain| *2 (|PatternMatchListResult| *5 *6 *3)) (|isDomain| *4 (|Pattern| *5)) (|ofCategory| *5 (|SetCategory|)) (|ofCategory| *6 (|PatternMatchable| *5)) (|ofCategory| *3 (|ListAggregate| *6)) (|isDomain| *1 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#3=(|PatternMatchable| *5)) (|ofCategory| *6 #4=(|OrderedAbelianMonoidSup|)) (|ofCategory| *7 #5=(|OrderedSet|)) (|ofCategory| *8 (|Join| #6=(|Ring|) #3#)) (|isDomain| *1 (|PatternMatchPolynomialCategory| *5 *6 *7 *8 *3)))) (|patternMatch| (*1 *2 *3 *4 *2 *5) (AND (|isDomain| *5 (|Mapping| #7=(|PatternMatchResult| *6 *3) *8 #8=(|Pattern| *6) #7#)) (|ofCategory| *8 #5#) (|isDomain| *2 #7#) (|isDomain| *4 #8#) (|ofCategory| *6 #1#) (|ofCategory| *3 (|Join| (|PolynomialCategory| *9 *7 *8) #2#)) (|ofCategory| *7 #4#) (|ofCategory| *9 (|Join| #6# (|PatternMatchable| *6))) (|isDomain| *1 (|PatternMatchPolynomialCategory| *6 *7 *8 *9 *3))))) +((|suchThat| ((#1=(|Expression| (|Integer|)) #2=(|Symbol|) (|List| #3=(|Mapping| (|Boolean|) |#1|))) 18 T ELT) ((#1# #2# #3#) 15 T ELT))) +(((|AttachPredicates| |#1|) (CATEGORY |package| (SIGNATURE |suchThat| (#1=(|Expression| (|Integer|)) #2=(|Symbol|) #3=(|Mapping| (|Boolean|) |#1|))) (SIGNATURE |suchThat| (#1# #2# (|List| #3#)))) (|Type|)) (T |AttachPredicates|)) +((|suchThat| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Symbol|)) (|isDomain| *4 (|List| #3=(|Mapping| (|Boolean|) *5))) #4=(|ofCategory| *5 (|Type|)) #5=(|isDomain| *2 (|Expression| (|Integer|))) #6=(|isDomain| *1 (|AttachPredicates| *5)))) (|suchThat| #1# (AND #2# (|isDomain| *4 #3#) #4# #5# #6#))) +((|suchThat| ((|#2| |#2| (|List| #1=(|Mapping| (|Boolean|) |#3|))) 12 T ELT) ((|#2| |#2| #1#) 13 T ELT))) +(((|FunctionSpaceAttachPredicates| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |suchThat| (|#2| |#2| #1=(|Mapping| (|Boolean|) |#3|))) (SIGNATURE |suchThat| (|#2| |#2| (|List| #1#)))) (|SetCategory|) (|FunctionSpace| |#1|) (|Type|)) (T |FunctionSpaceAttachPredicates|)) +((|suchThat| #1=(*1 *2 *2 *3) (AND (|isDomain| *3 (|List| #2=(|Mapping| (|Boolean|) *5))) #3=(|ofCategory| *5 (|Type|)) #4=(|ofCategory| *4 (|SetCategory|)) #5=(|isDomain| *1 (|FunctionSpaceAttachPredicates| *4 *2 *5)) #6=(|ofCategory| *2 (|FunctionSpace| *4)))) (|suchThat| #1# (AND (|isDomain| 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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| $) . 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T) ((|RightModule| $) OR (|has| |#1| (|PolynomialFactorizationExplicit|)) (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|GcdDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . 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|#4|))) |#4| #3#))) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|IntegralDomain|) (|PolynomialCategory| |#3| |#1| |#2|) (|Join| (|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ |#4|)) (SIGNATURE |numer| #4=(|#4| $)) (SIGNATURE |denom| #4#)))) (T |PolynomialRoots|)) +((|nthr| #1=(*1 *2 *3 *4) (AND #2=(|ofCategory| *5 (|OrderedAbelianMonoidSup|)) #3=(|ofCategory| *6 (|OrderedSet|)) #4=(|ofCategory| *7 #5=(|IntegralDomain|)) (|ofCategory| *3 #6=(|PolynomialCategory| *7 *5 *6)) (|isDomain| *2 (|Record| #7=(|:| |exponent| #8=(|NonNegativeInteger|)) #9=(|:| |coef| *3) (|:| |radicand| (|List| *3)))) (|isDomain| *1 (|PolynomialRoots| *5 *6 *7 *3 *8)) #10=(|isDomain| *4 #8#) (|ofCategory| *8 (|Join| #11=(|Field|) (CATEGORY |domain| (SIGNATURE |coerce| ($ *3)) (SIGNATURE |numer| #12=(*3 $)) (SIGNATURE |denom| #12#)))))) (|froot| #1# (AND (|ofCategory| *7 (|GcdDomain|)) #2# #3# #4# #13=(|ofCategory| *8 #6#) (|isDomain| *2 (|Record| #7# #9# (|:| |radicand| *3))) (|isDomain| *1 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(CATEGORY |domain| (SIGNATURE |listBranches| ((|List| (|List| (|Point| (|DoubleFloat|)))) $)) (SIGNATURE |xRange| ((|Segment| (|DoubleFloat|)) $)) (SIGNATURE |yRange| ((|Segment| (|DoubleFloat|)) $)))) +(((|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=(#9=(|Union| $ #10="failed") $ $) NIL T ELT)) (|sample| (#11=($) NIL T CONST)) (|retractIfCan| (((|Union| #12=(|Integer|) . #13=(#10#)) . #14=($)) NIL #15=(|has| |#1| (|RetractableTo| #12#)) ELT) (((|Union| #16=(|Fraction| #12#) . #13#) . #14#) NIL #17=(|has| |#1| (|RetractableTo| #16#)) ELT) (((|Union| |#1| . #13#) $) 35 T ELT)) (|retract| ((#12# . #18=($)) NIL #15# ELT) ((#16# . #18#) NIL #17# ELT) #19=(#20=(|#1| . #18#) NIL T ELT)) (|reductum| (#7# 32 T ELT)) (|recip| ((#9# $) 43 T ELT)) (|primitivePart| (#7# NIL #21=(|has| |#1| (|GcdDomain|)) ELT)) (|pomopo!| (($ $ |#1| |#2| $) 64 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| ((#22=(|NonNegativeInteger|) $) 18 T ELT)) 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(|PolynomialRing| *3 *2)) (|ofCategory| *2 (|CancellationAbelianMonoid|)) (|ofCategory| *3 (|IntegralDomain|)) (|ofCategory| *3 (|Ring|)) (|ofCategory| *2 (|OrderedAbelianMonoid|))))) +((|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) 18 T ELT))) +(((|PrecomputedAssociatedEquations| |#1| |#2|) (CATEGORY |package| (SIGNATURE |firstUncouplingMatrix| ((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)))) (|IntegralDomain|) (|LinearOrdinaryDifferentialOperatorCategory| |#1|)) (T |PrecomputedAssociatedEquations|)) +((|firstUncouplingMatrix| (*1 *2 *3 *4) (|partial| AND (|isDomain| *4 (|PositiveInteger|)) (|ofCategory| *5 (|IntegralDomain|)) (|isDomain| *2 (|Matrix| *5)) (|isDomain| *1 (|PrecomputedAssociatedEquations| *5 *3)) (|ofCategory| *3 (|LinearOrdinaryDifferentialOperatorCategory| *5))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|swap!| (((|Void|) $ #5=(|Integer|) #5#) NIL #6=(|has| $ 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#23=(|NonNegativeInteger|) |#1|) 14 T ELT)) (|minIndex| (#24=(#5# $) 10 #25=(|has| #5# #10#) ELT)) (|min| #26=(#27=($ $ $) NIL #9# ELT)) (|merge| (($ #7# $ $) NIL T ELT) #26#) (|members| (#28=(#29=(|List| |#1|) $) 23 T ELT)) (|member?| (#30=(#3# |#1| $) NIL #4# ELT)) (|maxIndex| (#24# 22 #25# ELT)) (|max| #26#) (|map!| #31=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #31# (($ #21# $ $) NIL T ELT)) (|latex| (((|String|) $) NIL #32=(|has| |#1| (|SetCategory|)) ELT)) (|insert| (($ |#1| $ #5#) NIL T ELT) (#33=($ $ $ #5#) NIL T ELT)) (|indices| (((|List| #5#) $) NIL T ELT)) (|index?| ((#3# #5# $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL #32# ELT)) (|first| ((|#1| $) NIL #25# ELT)) (|find| (((|Union| |#1| "failed") #16# $) NIL T ELT)) (|fill!| (#34=($ $ |#1|) 19 #6# ELT)) (|every?| #35=((#3# #16# $) NIL T ELT)) (|eval| (($ $ (|List| #36=(|Equation| |#1|))) NIL #37=(AND (|has| |#1| (|Evalable| |#1|)) #32#) ELT) (($ $ #36#) NIL #37# ELT) (($ $ |#1| |#1|) NIL #37# ELT) (($ $ #29# #29#) NIL #37# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#30# NIL #19# ELT)) (|entries| (#28# NIL T ELT)) (|empty?| (#8# NIL T ELT)) (|empty| (#18# 11 T ELT)) (|elt| (#13# NIL T ELT) (#22# 16 T ELT) #38=(($ $ #14#) NIL T ELT)) (|delete| (($ $ #5#) NIL T ELT) #38#) (|count| ((#23# |#1| $) NIL #4# ELT) ((#23# #16# $) NIL T ELT)) (|copyInto!| (#33# NIL #6# ELT)) (|copy| (#12# 20 T ELT)) (|convert| ((#39=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #39#)) ELT)) (|construct| (($ #29#) 13 T ELT)) (|concat| (#34# NIL T ELT) (#20# NIL T ELT) (#27# NIL T ELT) (($ (|List| $)) NIL T ELT)) (|coerce| ((#40=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #40#)) ELT)) (|before?| #1#) (|any?| #35#) (>= #41=(#2# NIL #9# ELT)) (> #41#) (= #1#) (<= #41#) (< #41#) (|#| ((#23# $) 8 T ELT))) +(((|PrimitiveArray| |#1|) (|OneDimensionalArrayAggregate| |#1|) (|Type|)) (T |PrimitiveArray|)) +NIL +((|scan| ((#1=(|PrimitiveArray| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|PrimitiveArray| |#1|) |#2|) 16 T ELT)) (|reduce| ((|#2| #2# #3# |#2|) 18 T ELT)) (|map| ((#1# (|Mapping| |#2| |#1|) #3#) 13 T ELT))) +(((|PrimitiveArrayFunctions2| |#1| |#2|) (CATEGORY |package| (SIGNATURE |scan| (#1=(|PrimitiveArray| |#2|) #2=(|Mapping| |#2| |#1| |#2|) #3=(|PrimitiveArray| |#1|) |#2|)) (SIGNATURE |reduce| (|#2| #2# #3# |#2|)) (SIGNATURE |map| (#1# (|Mapping| |#2| |#1|) #3#))) #4=(|Type|) #4#) (T |PrimitiveArrayFunctions2|)) +((|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| 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|selectfirst| (|#1| $)) (SIGNATURE |selectsecond| (|#2| $)))) #1# #1#) (T |Product|)) +((|makeprod| (*1 *1 *2 *3) (AND #1=(|isDomain| *1 (|Product| *2 *3)) #2=(|ofCategory| *2 #3=(|SetCategory|)) #4=(|ofCategory| *3 #3#))) (|selectfirst| #5=(*1 *2 *1) (AND #2# #1# #4#)) (|selectsecond| #5# (AND #2# (|isDomain| *1 (|Product| *3 *2)) #4#))) +((|value| ((#1=(|SExpression|) $) 13 T ELT)) (|property| (($ #2=(|Identifier|) #1#) 15 T ELT)) (|name| ((#2# $) 11 T ELT)) (|coerce| (((|OutputForm|) $) 25 T ELT))) +(((|Property|) (|Join| (|CoercibleTo| (|OutputForm|)) (CATEGORY |domain| (SIGNATURE |name| (#1=(|Identifier|) $)) (SIGNATURE |value| (#2=(|SExpression|) $)) (SIGNATURE |property| ($ #1# #2#))))) (T |Property|)) +((|name| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|Identifier|)) #3=(|isDomain| *1 (|Property|)))) (|value| #1# (AND (|isDomain| *2 #4=(|SExpression|)) #3#)) (|property| (*1 *1 *2 *3) (AND #2# (|isDomain| *3 #4#) #3#))) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (~ (#2=($ $) 29 T ELT)) (|true| (#3=($) 17 T CONST)) (|or| #4=(#5=($ $ $) NIL T ELT)) (|not| (#2# NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isOr| (#6=((|Maybe| (|Pair| $ $)) $) 62 T ELT)) (|isNot| (((|Maybe| $) $) 52 T ELT)) (|isImplies| (#6# 63 T ELT)) (|isEquiv| (#6# 64 T ELT)) (|isAtom| (((|Maybe| |#1|) $) 43 T ELT)) (|isAnd| (#6# 61 T ELT)) (|implies| (#5# 38 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|false| (#3# 16 T CONST)) (|equiv| (#5# 39 T ELT)) (|disjunction| (#5# 36 T ELT)) (|conjunction| (#5# 34 T ELT)) (|coerce| (((|OutputForm|) $) 66 T ELT) (($ |#1|) 12 T ELT)) (|before?| #1#) (|and| #4#) (|\\/| (#5# 37 T ELT)) (= #1#) (|/\\| (#5# 35 T ELT))) +(((|PropositionalFormula| |#1|) (|Join| (|PropositionalLogic|) (|CoercibleFrom| |#1|) (CATEGORY |domain| (SIGNATURE |isAtom| ((|Maybe| |#1|) $)) (SIGNATURE |isNot| ((|Maybe| $) $)) (SIGNATURE |isAnd| #1=((|Maybe| (|Pair| $ $)) $)) (SIGNATURE |isOr| #1#) (SIGNATURE |isImplies| #1#) (SIGNATURE |isEquiv| #1#) (SIGNATURE |conjunction| #2=($ $ $)) (SIGNATURE |disjunction| #2#))) (|SetCategory|)) (T |PropositionalFormula|)) +((|isAtom| #1=(*1 *2 *1) (AND (|isDomain| *2 (|Maybe| *3)) #2=(|isDomain| *1 #3=(|PropositionalFormula| *3)) #4=(|ofCategory| *3 #5=(|SetCategory|)))) (|isNot| #1# (AND (|isDomain| *2 (|Maybe| #3#)) #2# #4#)) (|isAnd| #1# #6=(AND (|isDomain| *2 (|Maybe| (|Pair| #3# #3#))) #2# #4#)) (|isOr| #1# #6#) (|isImplies| #1# #6#) (|isEquiv| #1# #6#) (|conjunction| #7=(*1 *1 *1 *1) #8=(AND (|isDomain| *1 (|PropositionalFormula| *2)) (|ofCategory| *2 #5#))) (|disjunction| #7# #8#)) +((|simplify| (#1=(#2=(|PropositionalFormula| |#1|) #2#) 46 T ELT)) (|dual| (#1# 22 T ELT)) (|atoms| (((|Set| |#1|) #2#) 41 T ELT))) +(((|PropositionalFormulaFunctions1| |#1|) (|Join| (|Type|) (CATEGORY |package| (SIGNATURE |dual| #1=(#2=(|PropositionalFormula| |#1|) #2#)) (SIGNATURE |atoms| ((|Set| |#1|) #2#)) (SIGNATURE |simplify| #1#))) (|SetCategory|)) (T |PropositionalFormulaFunctions1|)) +((|dual| #1=(*1 *2 *2) #2=(AND (|isDomain| 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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))) +(((|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)) +((|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)) 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*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 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(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| $)) $) 72 (|has| |#1| . #3=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #3#) ELT)) (|unit?| ((#4=(|Boolean|) $) 75 (|has| |#1| . #3#) ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#5=($) 23 T CONST)) (|reductum| (#6=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| |#2|) 82 T ELT) (($ $ |#3| |#2|) 98 T ELT) (($ $ (|List| |#3|) (|List| |#2|)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|leadingMonomial| (#6# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #3#) ELT)) (|degree| ((|#2| $) 84 T ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ #7=(|Fraction| (|Integer|))) 78 (|has| |#1| . #8=((|Algebra| #7#))) ELT) (($ $) 70 (|has| |#1| . #3#) ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT)) (|coefficient| ((|#1| $ |#2|) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#4# $ $) 74 (|has| |#1| . #3#) ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #9=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #9#) 88 T ELT) (($ #7# . #9#) 77 (|has| |#1| . #8#) ELT) (($ $ #7#) 76 (|has| |#1| . #8#) 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))) +(((|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|)) $)))) +(((|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# $) 98 T ELT)) (|rewriteIdealWithHeadRemainder| (#5# 95 T ELT)) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) #7=(|:| |den| |#2|)) |#5| $) 88 T ELT)) (|mainVariables| (#1# 27 T ELT)) (|mainVariable?| ((#3# |#4| $) 34 T ELT)) (|headRemainder| (((|Record| (|:| |num| |#5|) #7#) |#5| $) 81 T ELT)) (|collectUpper| (#8=($ $ |#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))) +(((|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 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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)) +((|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| 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#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#)) +((|normalForm| (((|Record| (|:| R #1=(|Matrix| |#1|)) (|:| A #1#) (|:| |Ainv| #1#)) #1# #2=(|Automorphism| |#1|) #3=(|Mapping| |#1| |#1|)) 19 T ELT)) (|companionBlocks| (((|List| (|Record| (|:| C #1#) (|:| |g| #4=(|Vector| |#1|)))) #1# #4#) 45 T ELT)) (|changeBase| ((#1# #1# #1# #2# #3#) 16 T ELT))) +(((|PseudoLinearNormalForm| |#1|) (CATEGORY |package| (SIGNATURE |normalForm| ((|Record| (|:| R #1=(|Matrix| |#1|)) (|:| A #1#) (|:| 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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)) +((|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))))) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| ((#2# $) NIL T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) NIL T ELT)) (|sample| #3=(($) NIL T CONST)) (|quadraticForm| (($ #4=(|SquareMatrix| |#1| |#2|)) 11 T ELT)) (|opposite?| #1#) (|matrix| ((#4# $) 12 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) 16 T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (|Zero| #3#) (= #1#) (- (($ $) NIL T ELT) #5=(($ $ $) NIL T ELT)) (+ #5#) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ (|NonNegativeInteger|) $) NIL T ELT) (($ (|Integer|) $) NIL T ELT))) +(((|QuadraticForm| |#1| |#2|) (|Join| (|AbelianGroup|) (|Eltable| (|DirectProduct| |#1| |#2|) |#2|) (CATEGORY |domain| (SIGNATURE |quadraticForm| ($ #1=(|SquareMatrix| |#1| |#2|))) (SIGNATURE |matrix| (#1# $)))) (|PositiveInteger|) (|Field|)) (T |QuadraticForm|)) +((|quadraticForm| (*1 *1 *2) (AND #1=(|isDomain| *2 (|SquareMatrix| *3 *4)) #2=(|ofType| *3 (|PositiveInteger|)) #3=(|ofCategory| *4 (|Field|)) #4=(|isDomain| *1 (|QuadraticForm| *3 *4)))) (|matrix| (*1 *2 *1) (AND #1# #4# #2# #3#))) +((~= #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?| ((#5# (|Mapping| #5# |#1|) . #8#) 48 T ELT)) (= (#1# 17 (|has| |#1| . #2#) ELT)) (|#| ((#10# $) 47 T ELT))) +(((|QueueAggregate| |#1|) (|Category|) (|Type|)) (T |QueueAggregate|)) +((|enqueue!| (*1 *2 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|dequeue!| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|rotate!| (*1 *1 *1) (AND (|ofCategory| *1 (|QueueAggregate| *2)) (|ofCategory| *2 (|Type|)))) (|length| (*1 *2 *1) (AND (|ofCategory| *1 (|QueueAggregate| *3)) (|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)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sample| (#8=($) NIL T CONST)) (|retractIfCan| (((|Union| #9=(|Integer|) . #10=(#7#)) . #11=($)) NIL #12=(|has| |#1| (|RetractableTo| #9#)) ELT) (#13=((|Union| #14=(|Fraction| #9#) . #10#) . #11#) NIL #15=(|has| |#1| (|RetractableTo| #14#)) ELT) (((|Union| |#1| . #10#) . #11#) NIL T ELT)) (|retract| ((#9# . #16=($)) NIL #12# ELT) (#17=(#14# . #16#) NIL #15# ELT) #18=(#19=(|#1| . #16#) NIL T ELT)) (|reducedSystem| ((#20=(|Matrix| #9#) . #21=(#22=(|Matrix| $))) NIL #23=(|has| |#1| (|LinearlyExplicitRingOver| #9#)) ELT) ((#24=(|Record| (|:| |mat| #20#) (|:| |vec| (|Vector| #9#))) . #25=(#22# #26=(|Vector| $))) NIL #23# ELT) ((#27=(|Record| (|:| |mat| #28=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #25#) NIL T ELT) ((#28# . #21#) NIL T ELT)) (|recip| ((#6# $) NIL T ELT)) (|real| (#19# 12 T ELT)) (|rationalIfCan| (#13# NIL #29=(|has| |#1| (|IntegerNumberSystem|)) ELT)) (|rational?| (#5# NIL #29# ELT)) (|rational| (#17# NIL #29# ELT)) (|quatern| (($ |#1| |#1| |#1| |#1|) 16 T ELT)) (|opposite?| #1#) (|one?| #4#) (|norm| #18#) (|min| #30=(#31=($ $ $) NIL #32=(|has| |#1| (|OrderedSet|)) ELT)) (|max| #30#) (|map| (($ #33=(|Mapping| |#1| |#1|) $) NIL T ELT)) (|leftReducedSystem| ((#20# . #34=(#26#)) NIL #23# ELT) ((#24# . #35=(#26# $)) NIL #23# ELT) ((#27# . #35#) NIL T ELT) ((#28# . #34#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| (#36=($ $) NIL #37=(|has| |#1| (|Field|)) ELT)) (|imagK| (#19# 15 T ELT)) (|imagJ| (#19# 14 T ELT)) (|imagI| (#19# 13 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|eval| (($ $ #38=(|List| |#1|) #38#) NIL #39=(|has| |#1| (|Evalable| |#1|)) ELT) (($ $ |#1| |#1|) NIL #39# ELT) (($ $ #40=(|Equation| |#1|)) NIL #39# ELT) (($ $ (|List| #40#)) NIL #39# ELT) (($ $ #41=(|List| #42=(|Symbol|)) #38#) NIL #43=(|has| |#1| (|InnerEvalable| #42# |#1|)) ELT) (($ $ #42# |#1|) NIL #43# ELT)) (|elt| (#44=($ $ |#1|) NIL (|has| |#1| (|Eltable| |#1| |#1|)) ELT)) (|differentiate| #45=(($ $ #33#) NIL T ELT) #46=(($ $ #33# #47=(|NonNegativeInteger|)) NIL T ELT) #48=(#36# NIL #49=(|has| |#1| (|DifferentialSpace|)) ELT) #50=(#51=($ $ #47#) NIL #49# ELT) #52=(($ $ #42#) NIL #53=(|has| |#1| (|PartialDifferentialSpace| #42#)) ELT) #54=(($ $ #41#) NIL #53# ELT) #55=(($ $ #42# #47#) NIL #53# ELT) #56=(($ $ #41# (|List| #47#)) NIL #53# ELT)) (|convert| ((#57=(|InputForm|) $) NIL (|has| |#1| (|ConvertibleTo| #57#)) ELT)) (|conjugate| #58=(#36# NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #9#) NIL T ELT) (($ |#1|) NIL T ELT) (($ #14#) NIL (OR #37# #15#) ELT)) (|charthRoot| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#47#) NIL T CONST)) (|before?| #1#) (|annihilate?| #1#) (|abs| (#19# NIL (|has| |#1| (|RealNumberSystem|)) ELT)) (|Zero| (#8# 8 T CONST)) (|One| (#8# 10 T CONST)) (D #45# #46# #48# #50# #52# #54# #55# #56#) (>= #59=(#2# NIL #32# ELT)) (> #59#) (= #1#) (<= #59#) (< #59#) (- #58# #60=(#31# NIL T ELT)) (+ #60#) (** (($ $ #61=(|PositiveInteger|)) NIL T ELT) (#51# NIL T ELT) (($ $ #9#) NIL #37# ELT)) (* (($ #61# $) NIL T ELT) (($ #47# $) NIL T ELT) (($ #9# . #62=($)) NIL T ELT) (#31# 20 T ELT) (#44# NIL T ELT) (($ |#1| . #62#) NIL T ELT) (($ $ #14#) NIL #37# ELT) (($ #14# . #62#) NIL #37# ELT))) +(((|Quaternion| |#1|) (|QuaternionCategory| |#1|) (|CommutativeRing|)) (T |Quaternion|)) +NIL +((|zero?| (#1=(#2=(|Boolean|) $) 43 T ELT)) (|retractIfCan| (((|Union| #3=(|Integer|) #4="failed") $) NIL T ELT) (#5=((|Union| #6=(|Fraction| #3#) #4#) $) NIL T ELT) (((|Union| |#2| #4#) $) 46 T ELT)) (|retract| ((#3# $) NIL T ELT) (#7=(#6# $) NIL T ELT) (#8=(|#2| $) 44 T ELT)) (|rationalIfCan| (#5# 78 T ELT)) (|rational?| (#1# 72 T ELT)) (|rational| (#7# 76 T ELT)) (|one?| (#1# 42 T ELT)) (|norm| (#8# 22 T ELT)) (|map| (($ #9=(|Mapping| |#2| |#2|) $) 19 T ELT)) (|inv| (#10=($ $) 58 T ELT)) (|differentiate| (($ $ #9#) 35 T ELT) (($ $ #9# #11=(|NonNegativeInteger|)) NIL T ELT) (($ $ #12=(|Symbol|)) NIL T ELT) (($ $ #13=(|List| #12#)) NIL T ELT) (($ $ #12# #11#) NIL T ELT) (($ $ #13# (|List| #11#)) NIL T ELT) (#10# NIL T ELT) (($ $ #11#) NIL T ELT)) (|convert| (((|InputForm|) $) 67 T ELT)) (|conjugate| (#10# 17 T ELT)) (|coerce| (((|OutputForm|) $) 53 T ELT) (($ #3#) 39 T ELT) (($ |#2|) 37 T ELT) (($ #6#) NIL T ELT)) (|characteristic| ((#11#) 10 T CONST)) (|abs| (#8# 71 T ELT)) (= (#14=(#2# $ $) 26 T ELT)) (< (#14# 69 T ELT)) (- (#10# 30 T ELT) (#15=($ $ $) 29 T ELT)) (+ (#15# 27 T ELT)) (* (($ (|PositiveInteger|) $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #3# $) 34 T ELT) (#15# NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) 31 T ELT) (($ $ #6#) NIL T ELT) (($ #6# $) NIL T ELT))) +(((|QuaternionCategory&| |#1| |#2|) (CATEGORY |package| (SIGNATURE |coerce| (|#1| #1=(|Fraction| #2=(|Integer|)))) (SIGNATURE |differentiate| (|#1| |#1| #3=(|NonNegativeInteger|))) (SIGNATURE |differentiate| #4=(|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #5=(|List| #6=(|Symbol|)) (|List| #3#))) (SIGNATURE |differentiate| (|#1| |#1| #6# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #5#)) (SIGNATURE |differentiate| (|#1| |#1| #6#)) (SIGNATURE < #7=(#8=(|Boolean|) |#1| |#1|)) (SIGNATURE * (|#1| #1# |#1|)) (SIGNATURE * (|#1| |#1| #1#)) (SIGNATURE |inv| #4#) (SIGNATURE |convert| ((|InputForm|) |#1|)) (SIGNATURE |rationalIfCan| #9=((|Union| #1# #10="failed") |#1|)) (SIGNATURE |rational| #11=(#1# |#1|)) (SIGNATURE |rational?| #12=(#8# |#1|)) (SIGNATURE |abs| #13=(|#2| |#1|)) (SIGNATURE |norm| #13#) (SIGNATURE |conjugate| #4#) (SIGNATURE |map| (|#1| #14=(|Mapping| |#2| |#2|) |#1|)) (SIGNATURE |differentiate| (|#1| |#1| #14# #3#)) (SIGNATURE |differentiate| (|#1| |#1| #14#)) (SIGNATURE |retractIfCan| ((|Union| |#2| #10#) |#1|)) (SIGNATURE |retract| #13#) (SIGNATURE |retract| #11#) (SIGNATURE |retractIfCan| #9#) (SIGNATURE |retract| (#2# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #2# #10#) |#1|)) (SIGNATURE 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(|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|) 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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)) +((|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))))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL #4=(|has| |#1| (|BasicType|)) ELT)) (|sample| (#5=($) NIL T CONST)) (|rotate!| (#6=($ $) 24 T ELT)) (|reduce| ((|#1| #7=(|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) NIL #4# ELT) ((|#1| #7# $ |#1|) NIL T ELT) ((|#1| #7# $) NIL T ELT)) (|queue| (#8=($ #9=(|List| |#1|)) 34 T ELT)) (|members| ((#9# $) NIL T ELT)) (|member?| ((#3# |#1| $) NIL #4# ELT)) (|map!| #10=(($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|map| #10#) (|length| (#11=(#12=(|NonNegativeInteger|) $) 27 T ELT)) (|latex| (((|String|) $) NIL #13=(|has| |#1| (|SetCategory|)) ELT)) (|inspect| (#14=(|#1| $) 29 T ELT)) (|insert!| (($ |#1| $) 18 T ELT)) (|hash| (((|SingleInteger|) $) NIL #13# ELT)) (|front| (#14# 28 T ELT)) (|find| (((|Union| |#1| "failed") #15=(|Mapping| #3# |#1|) $) NIL T ELT)) (|extract!| (#14# 23 T ELT)) (|every?| #16=((#3# #15# $) NIL T ELT)) (|eval| (($ $ (|List| #17=(|Equation| |#1|))) NIL #18=(AND (|has| |#1| (|Evalable| |#1|)) #13#) ELT) (($ $ #17#) NIL #18# ELT) (($ $ |#1| |#1|) NIL #18# ELT) (($ $ #9# #9#) NIL #18# ELT)) (|eq?| (#2# NIL T ELT)) (|enqueue!| ((|#1| |#1| $) 17 T ELT)) (|empty?| ((#3# $) 19 T ELT)) (|empty| (#5# NIL T ELT)) (|dequeue!| (#14# 22 T ELT)) (|count| ((#12# |#1| $) NIL #4# ELT) ((#12# #15# $) NIL T ELT)) (|copy| (#6# NIL T ELT)) (|coerce| ((#19=(|OutputForm|) $) NIL (|has| |#1| (|CoercibleTo| #19#)) ELT)) (|before?| #1#) (|bag| (#8# NIL T ELT)) (|back| (#14# 31 T ELT)) (|any?| #16#) (= #1#) (|#| (#11# NIL T ELT))) +(((|Queue| |#1|) (|Join| (|QueueAggregate| |#1|) (CATEGORY |domain| (SIGNATURE |queue| ($ (|List| |#1|))))) (|SetCategory|)) (T |Queue|)) +((|queue| (*1 *1 *2) (AND (|isDomain| *2 (|List| *3)) (|ofCategory| *3 (|SetCategory|)) (|isDomain| *1 (|Queue| *3))))) +((|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))) +(((|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=(#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=(#25=(|Union| $ #26="failed") $ $) NIL T ELT)) (|squareFreePart| #12#) (|squareFree| #27=(((|Factored| $) $) NIL #9# ELT)) (|sizeLess?| #28=(#2# NIL #9# ELT)) (|size| (#29=(#21#) NIL #30=(|has| #10# #31=(|Finite|)) ELT)) (|singularAtInfinity?| #32=(#33=(#3#) NIL T ELT)) (|singular?| (#34=(#3# |#1|) 162 T ELT) (#35=(#3# |#2|) 166 T ELT)) (|sample| #36=(#37=($) NIL T CONST)) (|retractIfCan| (((|Union| #22# . #38=(#26#)) . #39=($)) NIL #40=(|has| #10# (|RetractableTo| #22#)) ELT) (((|Union| #41=(|Fraction| #22#) . #38#) . #39#) NIL #42=(|has| #10# (|RetractableTo| #41#)) ELT) (((|Union| #10# . #38#) . #39#) NIL T ELT)) (|retract| ((#22# . #43=($)) NIL #40# ELT) ((#41# . #43#) NIL #42# ELT) #19#) (|represents| (($ #44=(|Vector| #10#) #17#) NIL T ELT) (#45=($ #44#) 79 T ELT) (#46=($ #7# |#2|) NIL T ELT)) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) NIL #23# ELT)) (|rem| #47=(#48=($ $ $) NIL #9# ELT)) (|regularRepresentation| ((#16# $ #17#) NIL T ELT) ((#16# $) NIL T ELT)) (|reducedSystem| ((#49=(|Matrix| #22#) . #50=(#51=(|Matrix| $))) NIL #52=(|has| #10# (|LinearlyExplicitRingOver| #22#)) ELT) ((#53=(|Record| (|:| |mat| #49#) (|:| |vec| (|Vector| #22#))) . #54=(#51# #17#)) NIL #52# ELT) ((#55=(|Record| (|:| |mat| #16#) (|:| |vec| #44#)) . #54#) NIL T ELT) ((#16# . #50#) NIL T ELT)) (|reduceBasisAtInfinity| #56=((#17# #17#) NIL T ELT)) (|reduce| (#57=($ |#3|) 73 T ELT) ((#25# (|Fraction| |#3|)) NIL #9# ELT)) (|recip| ((#25# $) NIL T ELT)) (|rationalPoints| (((|List| (|List| |#1|))) NIL (|has| |#1| #31#) ELT)) (|rationalPoint?| ((#3# |#1| |#1|) NIL T ELT)) (|rank| ((#20#) NIL T ELT)) (|random| (#37# NIL #30# ELT)) (|ramifiedAtInfinity?| #32#) (|ramified?| (#34# 61 T ELT) (#35# 164 T ELT)) (|quo| #47#) (|principalIdeal| (((|Record| (|:| |coef| #58=(|List| $)) #59=(|:| |generator| $)) #58#) NIL #9# ELT)) (|primitivePart| #60=(#13# NIL T ELT)) (|primitiveElement| #61=(#37# NIL #23# ELT)) (|primitive?| (#5# NIL #23# ELT)) (|primeFrobenius| (#62=($ $ #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=(#29# NIL T ELT)) (|normalizeAtInfinity| #56#) (|norm| #19#) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) #66=(|Symbol|)) NIL (|has| |#1| #11#) ELT)) (|nextItem| (#67=((|Maybe| $) $) NIL #23# ELT)) (|multiEuclidean| (((|Union| #58# #26#) #58# $) NIL #9# ELT)) (|minimalPolynomial| (#68=(|#3| $) NIL #9# ELT)) (|lookup| (#64# NIL #30# ELT)) (|lift| #69=(#68# NIL T ELT)) (|leftReducedSystem| ((#49# #17#) NIL #52# ELT) ((#53# . #70=(#17# $)) NIL #52# ELT) ((#55# . #70#) NIL T ELT) #15#) (|lcm| #71=(($ #58#) NIL #9# ELT) #47#) (|latex| (((|String|) $) NIL T ELT)) (|inverseIntegralMatrixAtInfinity| (#18# 57 T ELT)) (|inverseIntegralMatrix| (#18# 56 T ELT)) (|inv| #12#) (|integralRepresents| (#46# 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| (#37# NIL #23# CONST)) (|index| (($ #20#) NIL #30# ELT)) (|hyperelliptic| (#74=((|Union| |#2| #26#)) 70 T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|genus| #65#) (|generator| (#37# NIL T ELT)) (|gcdPolynomial| ((#75=(|SparseUnivariatePolynomial| $) #75# #75#) NIL #9# ELT)) (|gcd| #71# #47#) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| #22#) (|:| |exponent| #22#)))) NIL #23# ELT)) (|factor| #27#) (|extendedEuclidean| (((|Union| (|Record| #76=(|:| |coef1| $) #77=(|:| |coef2| $)) #26#) $ $ $) NIL #9# ELT) (((|Record| #76# #77# #59#) $ $) NIL #9# ELT)) (|exquo| (#24# 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# #26#) $ $) NIL #23# ELT)) (|differentiate| #79=(($ $ #80=(|Mapping| #10# #10#)) NIL #9# ELT) #81=(($ $ #80# #21#) NIL #9# ELT) (($ $ #72#) NIL T ELT) #82=(($ $ #83=(|List| #66#) (|List| #21#)) NIL #84=(OR (AND #9# (|has| #10# (|PartialDifferentialRing| #66#))) (AND #9# (|has| #10# (|PartialDifferentialSpace| #66#)))) ELT) #85=(($ $ #66# #21#) NIL #84# ELT) #86=(($ $ #83#) NIL #84# ELT) #87=(($ $ #66#) NIL #84# ELT) #88=(#62# NIL #89=(OR (AND (|has| #10# (|DifferentialRing|)) #9#) (AND (|has| #10# (|DifferentialSpace|)) #9#) #23#) ELT) #90=(#13# NIL #89# ELT)) (|derivationCoordinates| ((#16# #17# #80#) NIL #9# ELT)) (|definingPolynomial| ((|#3|) 58 T ELT)) (|createPrimitiveElement| #61#) (|coordinates| ((#44# $ #17#) NIL T ELT) ((#16# #17# #17#) NIL T ELT) (#91=(#44# $) 81 T ELT) #15#) (|convert| (#91# NIL T ELT) (#45# NIL T ELT) #69# (#57# NIL T ELT)) (|conditionP| (((|Union| #17# #26#) #51#) NIL #23# ELT)) (|complementaryBasis| #56#) (|coerce| (((|OutputForm|) $) NIL T ELT) (($ #22#) NIL T ELT) (($ #10#) NIL T ELT) (($ #41#) NIL (OR #9# #42#) ELT) #12#) (|charthRoot| #63# (#67# NIL (|has| #10# (|CharacteristicNonZero|)) ELT)) (|characteristicPolynomial| #69#) (|characteristic| (#29# NIL T CONST)) (|branchPointAtInfinity?| (#33# 65 T ELT)) (|branchPoint?| (#34# 167 T ELT) (#35# 168 T ELT)) (|before?| #1#) (|basis| (#73# NIL T ELT)) (|associates?| #28#) (|annihilate?| #1#) (|algSplitSimple| (((|Record| (|:| |num| $) #8# (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ #72#) NIL T ELT)) (|absolutelyIrreducible?| #32#) (|Zero| #36#) (|One| #36#) (D #79# #81# #82# #85# #86# #87# #88# #90#) (= #1#) (/ #47#) (- #60# #92=(#48# 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) (($ #41# . #93#) NIL #9# ELT) (($ $ #41#) 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 +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|wholeRagits| (#6=(#7=(|List| #8=(|Integer|)) $) 73 T ELT)) (|wholeRadix| (($ #7#) 81 T ELT)) (|wholePart| (#9=(#8# $) 48 #10=(|has| #8# (|EuclideanDomain|)) ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL T ELT)) (|unitCanonical| #11=(#12=($ $) NIL T ELT)) (|unit?| #4#) (|subtractIfCan| #13=((#14=(|Union| $ #15="failed") $ $) NIL T ELT)) (|squareFreePolynomial| #16=(((|Factored| #17=(|SparseUnivariatePolynomial| $)) #17#) NIL #18=(|has| #8# (|PolynomialFactorizationExplicit|)) ELT)) (|squareFreePart| #11#) (|squareFree| #19=(((|Factored| $) $) NIL T ELT)) (|solveLinearPolynomialEquation| (((|Union| #20=(|List| #17#) #15#) #20# #17#) NIL #18# ELT)) (|sizeLess?| #1#) (|sign| (#9# NIL #21=(|has| #8# (|OrderedIntegralDomain|)) ELT)) (|sample| (#22=($) NIL T CONST)) (|retractIfCan| (#23=((|Union| #8# . #24=(#15#)) $) 60 T ELT) (((|Union| #25=(|Symbol|) . #24#) $) NIL #26=(|has| #8# (|RetractableTo| #25#)) ELT) (((|Union| #27=(|Fraction| #8#) . #24#) $) 57 #28=(|has| #8# (|RetractableTo| #8#)) ELT) (#23# 60 #28# ELT)) (|retract| (#9# NIL T ELT) ((#25# $) NIL #26# ELT) (#29=(#27# $) NIL #28# ELT) (#9# NIL #28# ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|reducedSystem| (#32=(#33=(|Matrix| #8#) #34=(|Matrix| $)) NIL #35=(|has| #8# (|LinearlyExplicitRingOver| #8#)) ELT) (#36=(#37=(|Record| (|:| |mat| #33#) (|:| |vec| (|Vector| #8#))) #34# #38=(|Vector| $)) NIL #35# ELT) (#36# NIL T ELT) (#32# NIL T ELT)) (|recip| ((#14# $) NIL T ELT)) (|random| (#22# NIL #39=(|has| #8# (|IntegerNumberSystem|)) ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #40=(|List| $)) #41=(|:| |generator| $)) #40#) NIL T ELT)) (|prime?| #4#) (|prefixRagits| (#6# 79 T ELT)) (|positive?| #42=(#5# NIL #21# ELT)) (|patternMatch| ((#43=(|PatternMatchResult| #8# . #44=($)) $ #45=(|Pattern| #8#) #43#) NIL (|has| #8# (|PatternMatchable| #8#)) ELT) ((#46=(|PatternMatchResult| #47=(|Float|) . #44#) $ #48=(|Pattern| #47#) #46#) NIL (|has| #8# (|PatternMatchable| #47#)) ELT)) (|opposite?| #1#) (|one?| #4#) (|numerator| #11#) (|numer| (#9# 45 T ELT)) (|nextItem| (#49=((|Maybe| $) $) NIL #50=(|has| #8# (|StepThrough|)) ELT)) (|negative?| #42#) (|multiEuclidean| (((|Union| #40# #15#) #40# $) NIL T ELT)) (|min| #51=(#31# NIL #52=(|has| #8# (|OrderedSet|)) ELT)) (|max| #51#) (|map| (($ #53=(|Mapping| #8# #8#) $) NIL T ELT)) (|leftReducedSystem| (#54=(#33# #38#) NIL #35# ELT) (#55=(#37# #38# $) NIL #35# ELT) (#55# NIL T ELT) (#54# NIL T ELT)) (|lcm| #30# #56=(($ #40#) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|inv| #11#) (|init| (#22# NIL #50# CONST)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#17# #17# #17#) NIL T ELT)) (|gcd| #30# #56#) (|fractionPart| (#12# NIL #10# ELT) (#29# 50 T ELT)) (|fractRagits| (((|Stream| #8#) $) 78 T ELT)) (|fractRadix| (($ #7# #7#) 82 T ELT)) (|floor| (#9# 64 #39# ELT)) (|factorSquareFreePolynomial| #16#) (|factorPolynomial| #16#) (|factor| #19#) (|extendedEuclidean| (((|Record| #57=(|:| |coef1| $) #58=(|:| |coef2| $) #41#) $ $) NIL T ELT) (((|Union| (|Record| #57# #58#) #15#) $ $ $) NIL T ELT)) (|exquo| #13#) (|expressIdealMember| (((|Maybe| #40#) #40# $) NIL T ELT)) (|eval| (($ $ #7# #7#) NIL #59=(|has| #8# (|Evalable| #8#)) ELT) (($ $ #8# #8#) NIL #59# ELT) (($ $ #60=(|Equation| #8#)) NIL #59# ELT) (($ $ (|List| #60#)) NIL #59# ELT) (($ $ #61=(|List| #25#) #7#) NIL #62=(|has| #8# (|InnerEvalable| #25# #8#)) ELT) (($ $ #25# #8#) NIL #62# ELT)) (|euclideanSize| ((#63=(|NonNegativeInteger|) $) NIL T ELT)) (|elt| (#64=($ $ #8#) NIL (|has| #8# (|Eltable| #8# #8#)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL T ELT)) (|differentiate| #65=(($ $ #53#) NIL T ELT) #66=(($ $ #53# #63#) NIL T ELT) #67=(($ $ #25#) NIL #68=(|has| #8# (|PartialDifferentialSpace| #25#)) ELT) #69=(($ $ #61#) NIL #68# ELT) #70=(($ $ #25# #63#) NIL #68# ELT) #71=(($ $ #61# (|List| #63#)) NIL #68# ELT) (#12# 15 #72=(|has| #8# (|DifferentialSpace|)) ELT) #73=(#74=($ $ #63#) NIL #72# ELT)) (|denominator| #11#) (|denom| (#9# 47 T ELT)) (|cycleRagits| (#6# 80 T ELT)) (|convert| ((#45# . #75=($)) NIL (|has| #8# (|ConvertibleTo| #45#)) ELT) ((#48# . #75#) NIL (|has| #8# (|ConvertibleTo| #48#)) ELT) ((#76=(|InputForm|) . #75#) NIL (|has| #8# (|ConvertibleTo| #76#)) ELT) ((#47# . #75#) NIL #77=(|has| #8# (|RealConstant|)) ELT) (((|DoubleFloat|) . #75#) NIL #77# ELT)) (|conditionP| (((|Union| #38# #15#) #34#) NIL #78=(AND (|has| $ #79=(|CharacteristicNonZero|)) #18#) ELT)) (|coerce| (((|OutputForm|) $) 108 T ELT) #80=(($ #8#) 51 T ELT) #11# (($ #27#) 27 T ELT) #80# (($ #25#) NIL #26# ELT) (#29# 25 T ELT)) (|charthRoot| (#49# NIL (OR #78# (|has| #8# #79#)) ELT)) (|characteristic| ((#63#) 13 T CONST)) (|ceiling| (#9# 62 #39# ELT)) (|before?| #1#) (|associates?| #1#) (|annihilate?| #1#) (|abs| (#12# NIL #21# ELT)) (|Zero| (#22# 14 T CONST)) (|One| (#22# 17 T CONST)) (D #65# #66# #67# #69# #70# #71# (#12# NIL #72# ELT) #73#) (>= #81=(#2# NIL #52# ELT)) (> #81#) (= (#2# 21 T ELT)) (<= #81#) (< (#2# 40 #52# ELT)) (/ (#31# 36 T ELT) (($ #8# #8#) 38 T ELT)) (- (#12# 23 T ELT) (#31# 30 T ELT)) (+ (#31# 28 T ELT)) (** (($ $ #82=(|PositiveInteger|)) NIL T ELT) (#74# NIL T ELT) #83=(#64# NIL T ELT)) (* (($ #82# $) NIL T ELT) (($ #63# $) NIL T ELT) #84=(($ #8# $) 32 T ELT) (#31# 34 T ELT) (($ $ #27#) NIL T ELT) (($ #27# $) NIL T ELT) #84# #83#)) +(((|RadixExpansion| |#1|) (|Join| (|QuotientFieldCategory| #1=(|Integer|)) 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(|isDomain| *4 #1#) (|isDomain| *2 (|Any|)) (|isDomain| *1 (|RadixUtilities|))))) +((|size| (#1=(#2=(|Integer|)) 21 T ELT)) (|seed| (#1# 26 T ELT)) (|reseed| (((|Void|) #2#) 24 T ELT)) (|randnum| ((#2# #2#) 27 T ELT) (#1# 20 T ELT))) +(((|RandomNumberSource|) (CATEGORY |package| (SIGNATURE |randnum| #1=(#2=(|Integer|))) (SIGNATURE |size| #1#) (SIGNATURE |randnum| (#2# #2#)) (SIGNATURE |reseed| ((|Void|) #2#)) (SIGNATURE |seed| #1#))) (T |RandomNumberSource|)) +((|seed| #1=(*1 *2) #2=(AND (|isDomain| *2 #3=(|Integer|)) #4=(|isDomain| *1 (|RandomNumberSource|)))) (|reseed| (*1 *2 *3) (AND (|isDomain| *3 #3#) (|isDomain| *2 (|Void|)) #4#)) (|randnum| (*1 *2 *2) #2#) (|size| #1# #2#) (|randnum| #1# #2#)) +((|factorSquareFree| (#1=((|Factored| |#1|) |#1|) 43 T ELT)) (|factor| (#1# 41 T ELT))) +(((|RationalFactorize| |#1|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| |#1|) |#1|)) (SIGNATURE |factorSquareFree| #1#)) (|UnivariatePolynomialCategory| (|Fraction| (|Integer|)))) (T 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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)) +((|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))))) +((|rischDEsys| (((|Union| #1=(|List| |#2|) #2="failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #3=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2#) |#2| #1#) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #3#) #2#) |#2| |#2|)) 55 T ELT))) +(((|ElementaryRischDESystem| |#1| |#2|) (CATEGORY |package| (SIGNATURE |rischDEsys| ((|Union| #1=(|List| |#2|) #2="failed") #3=(|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| #4=(|:| |coeff| |#2|) (|:| |logand| |#2|))))) #2#) |#2| #1#) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) #4#) #2#) |#2| |#2|)))) (|Join| (|GcdDomain|) (|CharacteristicZero|) (|RetractableTo| #3#) (|LinearlyExplicitRingOver| #3#)) (|Join| (|TranscendentalFunctionCategory|) (|AlgebraicallyClosedField|) (|FunctionSpace| |#1|))) (T |ElementaryRischDESystem|)) +((|rischDEsys| (*1 *2 *3 *4 *4 *4 *5 *6 *7) (|partial| AND (|isDomain| *5 (|Symbol|)) (|isDomain| *6 (|Mapping| (|Union| (|Record| (|:| |mainpart| *4) (|:| |limitedlogs| (|List| (|Record| #1=(|:| |coeff| *4) (|:| |logand| *4))))) #2="failed") *4 #3=(|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 #3#) (|isDomain| *1 (|ElementaryRischDESystem| *8 *4))))) +((|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) #1=(|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| #2=(|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| #2# #3=(|Mapping| |#2| |#2|)) 39 T ELT)) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #4=(|Fraction| |#2|)) (|:| |c| #4#) (|:| |t| |#2|)) "failed") #4# #4# #3#) 71 T ELT)) (|baseRDE| (((|Record| (|:| |ans| #4#) #1#) #4# #4#) 76 T ELT))) +(((|TranscendentalRischDE| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monomRDE| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #1=(|Fraction| |#2|)) (|:| |c| #1#) (|:| |t| |#2|)) "failed") #1# #1# #2=(|Mapping| |#2| |#2|))) (SIGNATURE |baseRDE| ((|Record| (|:| |ans| #1#) #3=(|:| |nosol| (|Boolean|))) #1# #1#)) (SIGNATURE |polyRDE| ((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) #3#)) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| #4=(|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| #4# #2#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| #4#)) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalRischDE|)) +((|polyRDE| (*1 *2 *3 *3 *3 *4 *5) (AND (|isDomain| *5 (|Mapping| *3 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *6 (|Join| #1=(|Field|) #2=(|CharacteristicZero|) (|RetractableTo| *4))) (|isDomain| *4 #3=(|Integer|)) (|isDomain| *2 (|Union| (|:| |ans| (|Record| (|:| |ans| *3) #4=(|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) (|:| |beta| *3))))) (|isDomain| *1 (|TranscendentalRischDE| *6 *3)))) (|baseRDE| (*1 *2 *3 *3) (AND (|ofCategory| *4 #5=(|Join| #1# #2# (|RetractableTo| #3#))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|Record| (|:| |ans| #6=(|Fraction| *5)) #4#)) (|isDomain| *1 (|TranscendentalRischDE| *4 *5)) (|isDomain| *3 #6#))) (|monomRDE| (*1 *2 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #5#) (|isDomain| *2 (|Record| (|:| |a| *6) (|:| |b| #7=(|Fraction| *6)) (|:| |c| #7#) (|:| |t| *6))) (|isDomain| *1 (|TranscendentalRischDE| *5 *6)) (|isDomain| *3 #7#)))) +((|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #1=(|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| #1#) (|:| |c2| #1#) (|:| |t| |#2|)) #2="failed") #1# #1# #1# (|Mapping| |#2| |#2|)) 22 T ELT)) (|baseRDEsys| (((|Union| (|List| #1#) #2#) #1# #1# #1#) 34 T ELT))) +(((|TranscendentalRischDESystem| |#1| |#2|) (CATEGORY |package| (SIGNATURE |monomRDEsys| ((|Union| (|Record| (|:| |a| |#2|) (|:| |b| #1=(|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| #1#) (|:| |c2| #1#) (|:| |t| |#2|)) #2="failed") #1# #1# #1# (|Mapping| |#2| |#2|))) (SIGNATURE |baseRDEsys| ((|Union| (|List| #1#) #2#) #1# #1# #1#))) (|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|))) (|UnivariatePolynomialCategory| |#1|)) (T |TranscendentalRischDESystem|)) +((|baseRDEsys| (*1 *2 *3 *3 *3) (|partial| AND (|ofCategory| *4 #1=(|Join| (|Field|) (|CharacteristicZero|) (|RetractableTo| (|Integer|)))) (|ofCategory| *5 (|UnivariatePolynomialCategory| *4)) (|isDomain| *2 (|List| #2=(|Fraction| *5))) (|isDomain| *1 (|TranscendentalRischDESystem| *4 *5)) (|isDomain| *3 #2#))) (|monomRDEsys| (*1 *2 *3 *3 *3 *4) (|partial| AND (|isDomain| *4 (|Mapping| *6 *6)) (|ofCategory| *6 (|UnivariatePolynomialCategory| *5)) (|ofCategory| *5 #1#) (|isDomain| *2 (|Record| (|:| |a| *6) (|:| |b| #3=(|Fraction| *6)) (|:| |h| *6) (|:| |c1| #3#) (|:| |c2| #3#) (|:| |t| *6))) (|isDomain| *1 (|TranscendentalRischDESystem| *5 *6)) (|isDomain| *3 #3#)))) +((|weighted| ((#1=(|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| #2=(|Integer|))))) 34 T ELT)) (|uniform| ((#1# (|Set| |#1|)) 42 T ELT)) (|rdHack1| ((#1# (|Vector| |#1|) (|Vector| #2#) #2#) 31 T ELT))) +(((|RandomDistributions| |#1|) (CATEGORY |package| (SIGNATURE |uniform| (#1=(|Mapping| |#1|) (|Set| |#1|))) (SIGNATURE |weighted| (#1# (|List| (|Record| (|:| |value| |#1|) (|:| |weight| #2=(|Integer|)))))) (SIGNATURE |rdHack1| (#1# (|Vector| |#1|) (|Vector| #2#) #2#))) (|SetCategory|)) (T |RandomDistributions|)) +((|rdHack1| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|Vector| *6)) (|isDomain| *4 (|Vector| #1=(|Integer|))) (|isDomain| *5 #1#) (|ofCategory| *6 #2=(|SetCategory|)) (|isDomain| *2 (|Mapping| *6)) (|isDomain| *1 (|RandomDistributions| *6)))) (|weighted| #3=(*1 *2 *3) (AND (|isDomain| *3 (|List| (|Record| (|:| |value| *4) (|:| |weight| #1#)))) #4=(|ofCategory| *4 #2#) #5=(|isDomain| *2 (|Mapping| *4)) #6=(|isDomain| *1 (|RandomDistributions| *4)))) (|uniform| #3# (AND (|isDomain| *3 (|Set| *4)) #4# #5# #6#))) +((|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) 23 T ELT))) +(((|ReducedDivisor| |#1| |#2| |#3| |#4| |#5|) (CATEGORY |package| (SIGNATURE |order| ((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)))) #1=(|Field|) (|UnivariatePolynomialCategory| |#1|) (|UnivariatePolynomialCategory| (|Fraction| |#2|)) (|FunctionFieldCategory| |#1| |#2| |#3|) (|Join| (|Finite|) #1#)) (T |ReducedDivisor|)) +((|order| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|FiniteDivisor| *6 *7 *4 *8)) (|isDomain| *5 (|Mapping| *9 *6)) (|ofCategory| *6 #1=(|Field|)) (|ofCategory| *7 (|UnivariatePolynomialCategory| *6)) (|ofCategory| *4 (|UnivariatePolynomialCategory| (|Fraction| *7))) (|ofCategory| *8 (|FunctionFieldCategory| *6 *7 *4)) (|ofCategory| *9 (|Join| (|Finite|) #1#)) (|isDomain| *2 (|NonNegativeInteger|)) (|isDomain| *1 (|ReducedDivisor| *6 *7 *4 *8 *9))))) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|operator| (#2=((|SpadAst|) $) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) . #3=($)) NIL T ELT) (($ #4=(|Syntax|)) NIL T ELT) ((#4# . #3#) NIL T ELT)) (|body| (#2# 12 T ELT)) (|before?| #1#) (= #1#)) +(((|ReduceAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |operator| #1=((|SpadAst|) $)) (SIGNATURE |body| #1#)))) (T |ReduceAst|)) +((|operator| #1=(*1 *2 *1) #2=(AND (|isDomain| *2 (|SpadAst|)) (|isDomain| *1 (|ReduceAst|)))) (|body| #1# #2#)) +((|convert| (((|DoubleFloat|) . #1=($)) 6 T ELT) (((|Float|) . #1#) 9 T ELT))) +(((|RealConstant|) (|Category|)) (T |RealConstant|)) +NIL +(|Join| (|ConvertibleTo| (|DoubleFloat|)) (|ConvertibleTo| (|Float|))) +(((|ConvertibleTo| (|DoubleFloat|)) . T) ((|ConvertibleTo| (|Float|)) . T)) +((|refine| (((|Union| #1=(|Record| (|:| |left| #2=(|Fraction| (|Integer|))) (|:| |right| #2#)) "failed") |#1| #1# #1#) 32 T ELT) ((#1# |#1| #1# #2#) 29 T ELT)) (|realZeros| ((#3=(|List| #1#) |#1| #1# #2#) 34 T ELT) ((#3# |#1| #2#) 30 T ELT) ((#3# |#1| #1#) 33 T ELT) ((#3# |#1|) 28 T ELT)) (|midpoints| (((|List| #2#) #3#) 20 T ELT)) (|midpoint| ((#2# #1#) 17 T ELT))) +(((|RealZeroPackage| |#1|) (CATEGORY |package| (SIGNATURE |realZeros| (#1=(|List| #2=(|Record| (|:| |left| #3=(|Fraction| #4=(|Integer|))) (|:| |right| #3#))) |#1|)) (SIGNATURE |realZeros| (#1# |#1| #2#)) (SIGNATURE |realZeros| (#1# |#1| #3#)) (SIGNATURE |realZeros| (#1# |#1| #2# #3#)) (SIGNATURE |refine| (#2# |#1| #2# #3#)) (SIGNATURE |refine| ((|Union| #2# "failed") |#1| #2# #2#)) (SIGNATURE |midpoint| (#3# #2#)) (SIGNATURE |midpoints| ((|List| #3#) #1#))) (|UnivariatePolynomialCategory| #4#)) (T |RealZeroPackage|)) +((|midpoints| #1=(*1 *2 *3) (AND (|isDomain| *3 #2=(|List| #3=(|Record| (|:| |left| #4=(|Fraction| #5=(|Integer|))) (|:| |right| #4#)))) (|isDomain| *2 (|List| #4#)) #6=(|isDomain| *1 (|RealZeroPackage| *4)) #7=(|ofCategory| *4 #8=(|UnivariatePolynomialCategory| #5#)))) (|midpoint| #1# (AND (|isDomain| *3 #3#) (|isDomain| *2 #4#) #6# #7#)) (|refine| (*1 *2 *3 *2 *2) (|partial| AND #9=(|isDomain| *2 #3#) #10=(|isDomain| *1 (|RealZeroPackage| *3)) #11=(|ofCategory| *3 #8#))) (|refine| (*1 *2 *3 *2 *4) (AND #9# #12=(|isDomain| *4 #4#) #10# #11#)) (|realZeros| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 #4#) (|isDomain| *2 (|List| #13=(|Record| (|:| |left| *5) (|:| |right| *5)))) #10# #11# (|isDomain| *4 #13#))) (|realZeros| #14=(*1 *2 *3 *4) (AND #15=(|isDomain| *2 #2#) #10# #11# #12#)) (|realZeros| #14# (AND #15# #10# #11# (|isDomain| *4 #3#))) (|realZeros| #1# (AND #15# #10# #11#))) +((|refine| (((|Union| #1=(|Record| (|:| |left| #2=(|Fraction| (|Integer|))) (|:| |right| #2#)) "failed") |#1| #1# #1#) 35 T ELT) ((#1# |#1| #1# #2#) 32 T ELT)) (|realZeros| ((#3=(|List| #1#) |#1| #1# #2#) 30 T ELT) ((#3# |#1| #2#) 26 T ELT) ((#3# |#1| #1#) 28 T ELT) ((#3# |#1|) 24 T ELT))) +(((|RealZeroPackageQ| |#1|) (CATEGORY |package| (SIGNATURE |realZeros| (#1=(|List| #2=(|Record| (|:| |left| #3=(|Fraction| (|Integer|))) (|:| |right| #3#))) |#1|)) (SIGNATURE |realZeros| (#1# |#1| #2#)) (SIGNATURE |realZeros| (#1# |#1| #3#)) (SIGNATURE |realZeros| (#1# |#1| #2# #3#)) (SIGNATURE |refine| (#2# |#1| #2# #3#)) (SIGNATURE |refine| ((|Union| #2# "failed") |#1| #2# #2#))) (|UnivariatePolynomialCategory| #3#)) (T |RealZeroPackageQ|)) +((|refine| (*1 *2 *3 *2 *2) (|partial| AND #1=(|isDomain| *2 #2=(|Record| (|:| |left| #3=(|Fraction| (|Integer|))) (|:| |right| #3#))) #4=(|isDomain| *1 (|RealZeroPackageQ| *3)) #5=(|ofCategory| *3 (|UnivariatePolynomialCategory| #3#)))) (|refine| (*1 *2 *3 *2 *4) (AND #1# #6=(|isDomain| *4 #3#) #4# #7=(|ofCategory| *3 (|UnivariatePolynomialCategory| *4)))) (|realZeros| (*1 *2 *3 *4 *5) (AND (|isDomain| *5 #3#) (|isDomain| *2 (|List| #8=(|Record| (|:| |left| *5) (|:| |right| *5)))) #4# (|ofCategory| *3 (|UnivariatePolynomialCategory| *5)) (|isDomain| *4 #8#))) (|realZeros| #9=(*1 *2 *3 *4) (AND #6# (|isDomain| *2 (|List| (|Record| (|:| |left| *4) (|:| |right| *4)))) #4# #7#)) (|realZeros| #9# (AND #10=(|isDomain| *2 (|List| #2#)) #4# #5# (|isDomain| *4 #2#))) (|realZeros| (*1 *2 *3) (AND #10# #4# #5#))) +((|solve| ((#1=(|List| #2=(|Float|)) #3=(|Polynomial| #4=(|Integer|)) #2#) 28 T ELT) ((#1# (|Polynomial| (|Fraction| #4#)) #2#) 27 T ELT)) (|realSolve| (((|List| #1#) (|List| #3#) (|List| (|Symbol|)) #2#) 37 T ELT))) +(((|RealSolvePackage|) (CATEGORY |package| (SIGNATURE |solve| (#1=(|List| #2=(|Float|)) (|Polynomial| (|Fraction| #3=(|Integer|))) #2#)) (SIGNATURE |solve| (#1# #4=(|Polynomial| #3#) #2#)) (SIGNATURE |realSolve| ((|List| #1#) (|List| #4#) (|List| (|Symbol|)) #2#)))) (T |RealSolvePackage|)) +((|realSolve| (*1 *2 *3 *4 *5) (AND (|isDomain| *3 (|List| #1=(|Polynomial| #2=(|Integer|)))) (|isDomain| *4 (|List| (|Symbol|))) (|isDomain| 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T ELT)) (|retractIfCan| (#22=((|Union| #15# . #23=(#10#)) . #24=($)) NIL #25=(|has| #15# (|RetractableTo| #15#)) ELT) (#22# NIL T ELT) (((|Union| |#1| . #23#) $) 115 T ELT) (((|Union| #16# . #23#) . #24#) NIL #26=(OR (|has| #15# #27=(|RetractableTo| #16#)) (|has| |#1| #27#)) ELT)) (|retract| (#28=(#15# $) 17 #25# ELT) (#28# 17 T ELT) ((|#1| $) 116 T ELT) (#18# NIL #26# ELT)) (|rename!| (#29=($ $ #21#) 47 T ELT)) (|rename| (#29# 48 T ELT)) (|rem| #30=(#31=($ $ $) NIL T ELT)) (|relativeApprox| (#32=(#15# $ $) 21 T ELT)) (|recip| ((#9# $) 88 T ELT)) (|quo| #30#) (|principalIdeal| (((|Record| (|:| |coef| #33=(|List| $)) #34=(|:| |generator| $)) #33#) NIL T ELT)) (|prime?| #7#) (|positive?| (#4# 66 T ELT)) (|opposite?| #1#) (|one?| #7#) (|nthRoot| #35=(($ $ #16#) NIL T ELT)) (|negative?| (#4# 69 T ELT)) (|multiEuclidean| (((|Union| #33# #10#) #33# $) NIL T ELT)) (|min| #30#) (|max| #30#) (|mainValue| (#36=((|Union| #20# #10#) $) 83 T ELT)) (|mainForm| (((|Union| #21# #10#) $) 82 T ELT)) 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|mainCharacterization| ((|Union| #1# "failed") $)) (SIGNATURE |relativeApprox| ((|Fraction| (|Integer|)) $ $)))) (|Join| (|OrderedRing|) (|Field|) (|RealConstant|))) (T |RealClosure|)) +((|algebraicOf| (*1 *1 *2 *3) (AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| #1=(|RealClosure| *4) (|SparseUnivariatePolynomial| #1#))) (|isDomain| *3 (|OutputForm|)) (|isDomain| *1 #1#) (|ofCategory| *4 #2=(|Join| (|OrderedRing|) (|Field|) (|RealConstant|))))) (|mainCharacterization| (*1 *2 *1) (|partial| AND (|isDomain| *2 (|RightOpenIntervalRootCharacterization| #3=(|RealClosure| *3) (|SparseUnivariatePolynomial| #3#))) #4=(|isDomain| *1 #3#) #5=(|ofCategory| *3 #2#))) (|relativeApprox| (*1 *2 *1 *1) (AND (|isDomain| *2 (|Fraction| (|Integer|))) #4# #5#))) +((|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| #1=(|List| |#1|))) |#2| #1#) 32 T ELT) ((|#2| |#2| |#1|) 27 T ELT))) +(((|ReductionOfOrder| |#1| |#2|) (CATEGORY |package| (SIGNATURE |ReduceOrder| (|#2| |#2| |#1|)) (SIGNATURE 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(SIGNATURE |deref| (|#1| $)) (SIGNATURE |setref| (|#1| $ |#1|)) (SIGNATURE = ((|Boolean|) $ $)))) (|Type|)) (T |Reference|)) +((= (*1 *2 *1 *1) (AND (|isDomain| *2 (|Boolean|)) (|isDomain| *1 (|Reference| *3)) (|ofCategory| *3 #1=(|Type|)))) (|ref| (*1 *1 *2) #2=(AND (|isDomain| *1 (|Reference| *2)) (|ofCategory| *2 #1#))) (|deref| (*1 *2 *1) #2#) (|setref| (*1 *2 *1 *2) #2#)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) #4=(|:| |open| #5=(|List| |#4|)))) #5#) NIL T ELT)) (|zeroSetSplit| ((#6=(|List| $) #5#) 113 T ELT) ((#6# #5# #3#) 114 T ELT) ((#6# #5# #3# #3#) 112 T ELT) ((#6# #5# #3# #3# #3# #3#) 115 T ELT)) (|variables| #7=(((|List| |#3|) $) NIL T ELT)) (|trivialIdeal?| #8=(#9=(#3# $) NIL T ELT)) (|triangular?| #10=(#9# NIL #11=(|has| |#1| (|IntegralDomain|)) ELT)) (|stronglyReduced?| #12=(#13=(#3# |#4| $) NIL T ELT) #8#) (|stronglyReduce| #14=(#15=(|#4| |#4| $) NIL T ELT)) (|squareFreePart| ((#16=(|List| 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|#1|) (|:| |polnum| |#4|) #34=(|:| |den| |#1|)) |#4| $) 80 #11# ELT)) (|reduced?| ((#3# |#4| $ #26#) NIL T ELT)) (|reduceByQuasiMonic| #14#) (|reduce| ((|#4| #25# $ |#4| |#4|) NIL #32# ELT) ((|#4| #25# $ |#4|) NIL T ELT) ((|#4| #25# $) NIL T ELT) ((|#4| |#4| $ #25# #26#) NIL T ELT)) (|quasiComponent| (((|Record| (|:| |close| #5#) #4#) $) NIL T ELT)) (|purelyTranscendental?| #12#) (|purelyAlgebraicLeadingMonomial?| #12#) (|purelyAlgebraic?| #12# #8#) (|preprocess| (((|Record| (|:| |val| #5#) (|:| |towers| #6#)) #5# #3# #3#) 128 T ELT)) (|normalized?| #12# #8#) (|mvar| ((|#3| $) 37 T ELT)) (|members| (#35=(#5# $) 18 T ELT)) (|member?| (#13# 26 #32# ELT)) (|map!| (#36=($ (|Mapping| |#4| |#4|) $) 24 T ELT)) (|map| (#36# 22 T ELT)) (|mainVariables| #7#) (|mainVariable?| (#37=(#3# |#3| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|lastSubResultantElseSplit| (((|Union| |#4| #6#) |#4| |#4| $) NIL T ELT)) (|lastSubResultant| ((#16# |#4| |#4| $) 105 T ELT)) (|last| (#38=(#21# $) 41 T ELT)) (|invertibleSet| (#39=(#6# |#4| $) 88 T ELT)) (|invertibleElseSplit?| (((|Union| #3# #6#) |#4| $) NIL T ELT)) (|invertible?| (((|List| (|Record| (|:| |val| #3#) #17#)) |#4| $) 98 T ELT) (#13# 60 T ELT)) (|intersect| (#39# 110 T ELT) #40=((#6# #5# $) NIL T ELT) (#41=(#6# #5# #6#) 111 T ELT) #42=((#6# |#4| #6#) NIL T ELT)) (|internalZeroSetSplit| ((#6# #5# #3# #3# #3#) 123 T ELT)) (|internalAugment| (#33# 77 T ELT) (($ #5# $) 78 T ELT) ((#6# |#4| $ #3# #3# #3# #3# #3#) 74 T ELT)) (|initials| (#35# NIL T ELT)) (|initiallyReduced?| #12# #8#) (|initiallyReduce| #14#) (|infRittWu?| #1#) (|headRemainder| (((|Record| (|:| |num| |#4|) #34#) |#4| $) NIL #11# ELT)) (|headReduced?| #12# #8#) (|headReduce| #14#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|first| (#38# 39 T ELT)) (|find| ((#21# #19# $) NIL T ELT)) (|extendIfCan| ((#28# $ |#4|) 55 T ELT)) (|extend| (($ $ |#4|) NIL T ELT) (#39# 90 T ELT) #42# #40# (#41# 84 T ELT)) (|every?| #43=((#3# #19# $) NIL T ELT)) (|eval| (($ $ #5# #5#) NIL #44=(AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ELT) (($ $ |#4| |#4|) NIL #44# ELT) (($ $ #45=(|Equation| |#4|)) NIL #44# ELT) (($ $ (|List| #45#)) NIL #44# ELT)) (|eq?| #1#) (|empty?| (#9# 17 T ELT)) (|empty| (#23# 14 T ELT)) (|degree| #46=(#47=(#48=(|NonNegativeInteger|) $) NIL T ELT)) (|count| ((#48# |#4| $) NIL #32# ELT) ((#48# #19# $) NIL T ELT)) (|copy| (#30# 13 T ELT)) (|convert| ((#49=(|InputForm|) $) NIL (|has| |#4| (|ConvertibleTo| #49#)) ELT)) (|construct| (#29# 21 T ELT)) (|collectUpper| (#50=($ $ |#3|) 48 T ELT)) (|collectUnder| (#50# 50 T ELT)) (|collectQuasiMonic| (#30# NIL T ELT)) (|collect| (#50# NIL T ELT)) (|coerce| (((|OutputForm|) $) 34 T ELT) (#35# 45 T ELT)) (|coHeight| (#47# NIL (|has| |#3| (|Finite|)) ELT)) (|before?| #1#) (|basicSet| ((#51=(|Union| (|Record| (|:| |bas| $) (|:| |top| #5#)) #22#) #5# #26#) NIL T ELT) ((#51# #5# #19# #26#) NIL T ELT)) (|autoReduced?| ((#3# $ (|Mapping| #3# |#4| #5#)) NIL T ELT)) (|augment| (#39# 87 T ELT) #42# #40# (#41# NIL T ELT)) (|any?| #43#) (|algebraicVariables| #7#) (|algebraicCoefficients?| #12#) (|algebraic?| (#37# 61 T ELT)) (= #1#) (|#| #46#)) +(((|RegularTriangularSet| |#1| |#2| |#3| |#4|) (|Join| (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|) (CATEGORY |domain| (SIGNATURE |internalAugment| (#1=(|List| $) |#4| $ #2=(|Boolean|) #2# #2# #2# #2#)) (SIGNATURE |zeroSetSplit| (#1# #3=(|List| |#4|) #2# #2#)) (SIGNATURE |zeroSetSplit| (#1# #3# #2# #2# #2# #2#)) (SIGNATURE |internalZeroSetSplit| (#1# #3# #2# #2# #2#)) (SIGNATURE |preprocess| ((|Record| (|:| |val| #3#) (|:| |towers| #1#)) #3# #2# #2#)))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|)) (T |RegularTriangularSet|)) +((|internalAugment| (*1 *2 *3 *1 *4 *4 *4 *4 *4) (AND #1=(|isDomain| *4 (|Boolean|)) #2=(|ofCategory| *5 (|GcdDomain|)) #3=(|ofCategory| *6 (|OrderedAbelianMonoidSup|)) #4=(|ofCategory| *7 (|OrderedSet|)) (|isDomain| *2 (|List| #5=(|RegularTriangularSet| *5 *6 *7 *3))) (|isDomain| *1 #5#) (|ofCategory| *3 #6=(|RecursivePolynomialCategory| *5 *6 *7)))) (|zeroSetSplit| #7=(*1 *2 *3 *4 *4) #8=(AND #9=(|isDomain| *3 #10=(|List| *8)) #1# #11=(|ofCategory| *8 #6#) #2# #3# #4# (|isDomain| *2 #12=(|List| #13=(|RegularTriangularSet| *5 *6 *7 *8))) #14=(|isDomain| *1 #13#))) (|zeroSetSplit| (*1 *2 *3 *4 *4 *4 *4) #8#) (|internalZeroSetSplit| (*1 *2 *3 *4 *4 *4) #8#) (|preprocess| #7# (AND #1# #2# #3# #4# #11# (|isDomain| *2 (|Record| (|:| |val| #10#) (|:| |towers| #12#))) #14# #9#))) +((|radicalEigenvectors| (((|List| (|Record| (|:| |radval| #1=(|Expression| #2=(|Integer|))) (|:| |radmult| #2#) (|:| |radvect| #3=(|List| #4=(|Matrix| #1#))))) #5=(|Matrix| (|Fraction| (|Polynomial| #2#)))) 67 T ELT)) (|radicalEigenvector| ((#3# #1# #5#) 52 T ELT)) (|radicalEigenvalues| (((|List| #1#) #5#) 45 T ELT)) (|orthonormalBasis| ((#3# #5#) 85 T ELT)) (|normalise| ((#4# #4#) 38 T ELT)) (|gramschmidt| ((#3# #3#) 74 T ELT)) (|eigenMatrix| (((|Union| #4# "failed") #5#) 82 T ELT))) +(((|RadicalEigenPackage|) (CATEGORY |package| (SIGNATURE |radicalEigenvectors| ((|List| (|Record| (|:| |radval| #1=(|Expression| #2=(|Integer|))) (|:| |radmult| #2#) (|:| |radvect| #3=(|List| #4=(|Matrix| #1#))))) #5=(|Matrix| (|Fraction| (|Polynomial| #2#))))) (SIGNATURE |radicalEigenvector| (#3# #1# #5#)) (SIGNATURE |radicalEigenvalues| ((|List| #1#) #5#)) (SIGNATURE |eigenMatrix| ((|Union| #4# "failed") #5#)) (SIGNATURE |normalise| (#4# #4#)) (SIGNATURE |gramschmidt| (#3# #3#)) (SIGNATURE |orthonormalBasis| (#3# #5#)))) (T |RadicalEigenPackage|)) +((|orthonormalBasis| #1=(*1 *2 *3) (AND #2=(|isDomain| *3 #3=(|Matrix| (|Fraction| (|Polynomial| #4=(|Integer|))))) #5=(|isDomain| *2 #6=(|List| #7=(|Matrix| #8=(|Expression| #4#)))) #9=(|isDomain| *1 (|RadicalEigenPackage|)))) (|gramschmidt| #10=(*1 *2 *2) (AND #5# #9#)) (|normalise| #10# (AND #11=(|isDomain| *2 #7#) #9#)) (|eigenMatrix| #1# (|partial| AND #2# #11# #9#)) 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Aggregate|) . T) ((|BasicType|) . T) ((|BiModule| |#3| |#3|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Evalable| |#3|) AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ((|FiniteAggregate| |#3|) . T) ((|Functorial| |#3|) . T) ((|HomogeneousAggregate| |#3|) . T) ((|InnerEvalable| |#3| |#3|) AND (|has| |#3| (|Evalable| |#3|)) (|has| |#3| (|SetCategory|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#3|) . T) ((|LeftModule| |#3|) . T) ((|LinearSet| |#3|) |has| |#3| (|CommutativeRing|)) ((|Module| |#3|) |has| |#3| (|CommutativeRing|)) ((|RightLinearSet| |#3|) . T) ((|RightModule| |#3|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((~= #1=((#2=(|Boolean|) $ $) NIL T ELT)) (|zero?| #3=((#2# $) NIL T ELT)) (|symmetric?| #3#) (|subtractIfCan| ((#4=(|Union| $ #5="failed") $ $) NIL T ELT)) (|square?| #3#) (|sample| (#6=($) NIL T CONST)) (|rowEchelon| (#7=($ $) 46 (|has| |#3| (|EuclideanDomain|)) ELT)) (|row| (((|DirectProduct| |#2| |#3|) $ #8=(|Integer|)) 35 T ELT)) (|reduce| ((|#3| #9=(|Mapping| |#3| |#3| |#3|) $ |#3| |#3|) NIL #10=(|has| |#3| (|BasicType|)) ELT) ((|#3| #9# $ |#3|) NIL T ELT) ((|#3| #9# $) NIL T ELT)) (|rectangularMatrix| (($ #11=(|Matrix| |#3|)) 44 T ELT)) (|rank| (#12=(#13=(|NonNegativeInteger|) $) 48 #14=(|has| |#3| (|IntegralDomain|)) ELT)) (|qelt| #15=((|#3| $ #8# #8#) NIL T ELT)) (|opposite?| #1#) (|nullity| (#12# 50 #14# ELT)) (|nullSpace| (((|List| #16=(|DirectProduct| |#1| |#3|)) $) 54 #14# ELT)) (|nrows| #17=(#12# NIL T ELT)) (|ncols| #17#) (|minRowIndex| #18=((#8# $) NIL T ELT)) (|minColIndex| #18#) (|members| ((#19=(|List| |#3|) $) NIL T ELT)) (|member?| ((#2# |#3| $) NIL #10# ELT)) 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|BasicType|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|RightLinearSet| |#1|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|annihilate?| (((|Boolean|) $ $) 10 T ELT))) +(((|Rng&| |#1|) (CATEGORY |package| (SIGNATURE |annihilate?| ((|Boolean|) |#1| |#1|))) (|Rng|)) (T |Rng&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 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)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 T ELT))) +(((|Rng|) (|Category|)) (T |Rng|)) +((|annihilate?| (*1 *2 *1 *1) (AND (|ofCategory| *1 (|Rng|)) (|isDomain| *2 (|Boolean|))))) +(|Join| (|AbelianGroup|) (|SemiGroup|) (CATEGORY |domain| (SIGNATURE |annihilate?| ((|Boolean|) $ $)))) +(((|AbelianGroup|) . 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#26=(|Integer|))) 84 T ELT) (($ #6#) 120 T ELT) (($ #9#) 117 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|ceiling| (($ $) 110 T ELT)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|abs| (($ $) 134 T ELT)) (|Zero| (#5# 24 T CONST)) (|One| (($) 45 T CONST)) (>= (#27=((|Boolean|) $ $) 127 T ELT)) (> (#27# 129 T ELT)) (= (#1# 8 T ELT)) (<= (#27# 128 T ELT)) (< (#27# 130 T ELT)) (/ (($ $ $) 83 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #26#) 87 T ELT) (($ $ (|Fraction| #15#)) 114 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #28=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ #25#) 86 T ELT) (($ #25# . #28#) 85 T ELT))) +(((|RealNumberSystem|) (|Category|)) (T |RealNumberSystem|)) +((|norm| (*1 *1 *1) (|ofCategory| *1 (|RealNumberSystem|))) 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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| $)) (SIGNATURE |right| #1#) (SIGNATURE 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$)) 276 T ELT)) (|headReduce| (($ $ $) 256 T ELT)) (|head| (($ $) 295 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) 236 (|has| |#1| (|IntegralDomain|)) ELT)) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) 237 (|has| |#1| (|IntegralDomain|)) ELT)) (|ground?| (((|Boolean|) $) 184 T ELT)) (|ground| ((|#1| . #48=($)) 185 T ELT)) (|gcdPolynomial| ((#49=(|SparseUnivariatePolynomial| $) #49# #49#) 109 (|has| |#1| . #10#) ELT)) (|gcd| ((|#1| |#1| $) 229 (|has| |#1| (|GcdDomain|)) ELT) (#45# 106 (|has| |#1| . #10#) ELT) (#46# 105 (|has| |#1| . #10#) ELT)) (|factorSquareFreePolynomial| (#7# 116 (|has| |#1| . #9#) ELT)) (|factorPolynomial| (#7# 115 (|has| |#1| . #9#) ELT)) (|factor| (#11# 113 (|has| |#1| . #9#) ELT)) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) 238 (|has| |#1| (|IntegralDomain|)) ELT)) (|exquo| (((|Union| $ "failed") $ 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(|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 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(|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|))) +((~= #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|) (CATEGORY |package| (SIGNATURE |rootOf| ((|Union| |#1| #1="failed") |#3| (|PositiveInteger|))) (SIGNATURE |recip| ((|Union| |#3| #1#) |#3| |#1|)) (SIGNATURE |positive?| #2=((|Boolean|) |#3| |#1|)) (SIGNATURE |negative?| #2#) (SIGNATURE |zero?| #2#)) (|RealRootCharacterizationCategory| |#2| |#3|) (|Join| (|OrderedRing|) (|Field|)) (|UnivariatePolynomialCategory| |#2|)) (T |RealRootCharacterizationCategory&|)) +NIL +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| (((|Boolean|) |#2| $) 25 T ELT)) (|sign| (((|Integer|) |#2| $) 26 T ELT)) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) 19 T ELT)) (|relativeApprox| ((|#1| |#2| $ |#1|) 17 T ELT)) (|recip| (((|Union| |#2| "failed") |#2| $) 22 T ELT)) (|positive?| (((|Boolean|) |#2| $) 23 T ELT)) (|negative?| (((|Boolean|) |#2| $) 24 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|definingPolynomial| ((|#2| $) 21 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT)) (|before?| (#1# 6 T ELT)) 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(SIGNATURE |relativeApprox| (|t#1| |t#2| $ |t#1|)))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . 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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(|ofCategory| *10 #17=(|RecursivePolynomialCategory| *7 *8 *9)) (|ofCategory| *11 (|RegularTriangularSetCategory| *7 *8 *9 *10)) #18=(|ofCategory| *7 #8#) #19=(|ofCategory| *8 #10#) #20=(|ofCategory| *9 #12#) (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *10 *11)))) (|decompose| (*1 *2 *3 *2 *4 *4 *4 *4 *4) #21=(AND (|isDomain| *2 #22=(|List| *9)) #23=(|isDomain| *3 #2#) (|isDomain| *4 #24=(|Boolean|)) #4# #6# #7# #9# #11# #13#)) (|decompose| (*1 *2 *3 *2 *4 *4) #21#) (|internalDecompose| #1# #25=(AND #7# #9# #11# (|ofCategory| *3 #5#) #26=(|isDomain| *2 (|Record| (|:| |done| (|List| *4)) (|:| |todo| (|List| (|Record| (|:| |val| (|List| *3)) (|:| |tower| *4)))))) (|isDomain| *1 (|RegularSetDecompositionPackage| *5 *6 *7 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|internalDecompose| #27=(*1 *2 *3 *4 *5) #28=(AND #29=(|isDomain| *5 #3#) #30=(|ofCategory| *6 #8#) #31=(|ofCategory| *7 #10#) #32=(|ofCategory| *8 #12#) #33=(|ofCategory| *3 (|RecursivePolynomialCategory| *6 *7 *8)) #26# #34=(|isDomain| *1 (|RegularSetDecompositionPackage| *6 *7 *8 *3 *4)) #35=(|ofCategory| *4 (|RegularTriangularSetCategory| *6 *7 *8 *3)))) (|internalDecompose| (*1 *2 *3 *4 *5 *6) (AND #29# (|isDomain| *6 #24#) #18# #19# #20# (|ofCategory| *3 #17#) #26# (|isDomain| *1 (|RegularSetDecompositionPackage| *7 *8 *9 *3 *4)) (|ofCategory| *4 (|RegularTriangularSetCategory| *7 *8 *9 *3)))) (|transcendentalDecompose| #1# #25#) (|transcendentalDecompose| #27# #28#) (|algebraicDecompose| #27# (AND (|isDomain| *5 #24#) #30# #31# #32# #33# #26# #34# #35#)) (|numberOfVariables| #1# #36=(AND #23# (|isDomain| *4 #22#) #4# #6# #7# #9# #11# (|isDomain| *2 #3#) #13#)) (|KrullNumber| #1# #36#)) +((|purelyTranscendental?| (#1=(#2=(|Boolean|) |#5| $) 26 T ELT)) (|purelyAlgebraicLeadingMonomial?| (#1# 29 T ELT)) (|purelyAlgebraic?| (#1# 18 T ELT) ((#2# $) 52 T ELT)) (|intersect| #3=((#4=(|List| $) |#5| $) NIL T ELT) (#5=(#4# #6=(|List| |#5|) $) 94 T ELT) (#7=(#4# #6# #4#) 92 T ELT) (#8=(#4# |#5| #4#) 95 T ELT)) (|extend| (($ $ |#5|) NIL T ELT) #3# (#8# 73 T ELT) (#5# 75 T ELT) (#7# 77 T ELT)) (|augment| #3# (#8# 64 T ELT) (#5# 69 T ELT) (#7# 71 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))) +(((|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|) $)) (SIGNATURE |purelyAlgebraicLeadingMonomial?| ((|Boolean|) 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((#50# . #72#) NIL T ELT)) (|leadingMonomial| #27#) (|leadingCoefficient| #37#) (|leader| #40#) (|lcm| #74=(($ #54#) NIL #24# ELT) #75=(#76=($ $ $) NIL #24# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isobaric?| #4#) (|isTimes| #77=(((|Union| #54# #20#) $) NIL T ELT)) (|isPlus| #77#) (|isExpt| (((|Union| (|Record| (|:| |var| #12#) (|:| |exponent| #7#)) #20#) $) NIL T ELT)) (|initial| #27#) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| #4#) (|ground| #37#) (|gcdPolynomial| ((#13# #13# #13#) NIL #24# ELT)) (|gcd| #74# #75#) (|factorSquareFreePolynomial| #21#) (|factorPolynomial| #21#) (|factor| (#25# NIL #22# ELT)) (|exquo| ((#19# $ |#1|) NIL #15# ELT) (#18# NIL #15# ELT)) (|eval| (($ $ (|List| #78=(|Equation| $))) NIL T ELT) (($ $ #78#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #54# #54#) NIL T ELT) (($ $ #12# |#1|) NIL T ELT) (($ $ #11# #79=(|List| |#1|)) NIL T ELT) (($ $ #12# $) NIL T ELT) (($ $ #11# #54#) NIL T ELT) (($ $ #8# $) NIL #71# ELT) (($ $ #80=(|List| #8#) #54#) NIL 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#8#) #11# (|:| |ineq| #8#))) #8# #6# #4# #4#)) (SIGNATURE |branchIfCan| ((|Union| #13# #9#) #8# |#5| #8# #4# #4# #4# #4# #4#))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |SquareFreeQuasiComponentPackage|)) +((|branchIfCan| (*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) (|partial| AND #1=(|isDomain| *5 #2=(|Boolean|)) #3=(|ofCategory| *6 #4=(|GcdDomain|)) #5=(|ofCategory| *7 #6=(|OrderedAbelianMonoidSup|)) #7=(|ofCategory| *8 #8=(|OrderedSet|)) #9=(|ofCategory| *9 (|RecursivePolynomialCategory| *6 *7 *8)) (|isDomain| *2 (|Record| #10=(|:| |eq| #11=(|List| *9)) (|:| |tower| *4) #12=(|:| |ineq| #11#))) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *4)) #13=(|isDomain| *3 #11#) (|ofCategory| *4 #14=(|RegularTriangularSetCategory| *6 *7 *8 *9)))) (|prepareDecompose| (*1 *2 *3 *4 *5 *5) (AND (|isDomain| *4 (|List| *10)) #1# (|ofCategory| *10 #14#) #3# #5# #7# #9# (|isDomain| *2 (|List| (|Record| #10# (|:| |tower| *10) #12#))) (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *6 *7 *8 *9 *10)) #13#)) (|removeSuperfluousCases| #15=(*1 *2 *2) (AND (|isDomain| *2 (|List| (|Record| (|:| |val| (|List| *6)) (|:| |tower| *7)))) #16=(|ofCategory| *6 (|RecursivePolynomialCategory| *3 *4 *5)) #17=(|ofCategory| *7 (|RegularTriangularSetCategory| *3 *4 *5 *6)) #18=(|ofCategory| *3 #4#) #19=(|ofCategory| *4 #6#) #20=(|ofCategory| *5 #8#) #21=(|isDomain| *1 (|SquareFreeQuasiComponentPackage| *3 *4 *5 *6 *7)))) (|subCase?| #22=(*1 *2 *3 *3) (AND (|isDomain| *3 (|Record| (|:| |val| #23=(|List| *7)) (|:| |tower| *8))) #24=(|ofCategory| *7 (|RecursivePolynomialCategory| *4 *5 *6)) #25=(|ofCategory| *8 #26=(|RegularTriangularSetCategory| *4 *5 *6 *7)) #27=(|ofCategory| *4 #4#) #28=(|ofCategory| *5 #6#) #29=(|ofCategory| *6 #8#) #30=(|isDomain| *2 #2#) #31=(|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *8)))) (|removeSuperfluousQuasiComponents| #15# #32=(AND (|isDomain| *2 #23#) #17# #18# #19# #20# #16# #21#)) (|subQuasiComponent?| (*1 *2 *3 *4) (AND (|isDomain| *4 (|List| *3)) (|ofCategory| *3 (|RegularTriangularSetCategory| *5 *6 *7 *8)) (|ofCategory| *5 #4#) (|ofCategory| *6 #6#) (|ofCategory| *7 #8#) (|ofCategory| *8 (|RecursivePolynomialCategory| *5 *6 *7)) #30# (|isDomain| *1 (|SquareFreeQuasiComponentPackage| *5 *6 *7 *8 *3)))) (|subQuasiComponent?| #22# #33=(AND #27# #28# #29# #24# #30# #34=(|isDomain| *1 (|SquareFreeQuasiComponentPackage| *4 *5 *6 *7 *3)) #35=(|ofCategory| *3 #26#))) (|internalSubQuasiComponent?| #22# (|partial| AND #27# #28# #29# #24# #30# #34# #35#)) (|infRittWu?| #22# #36=(AND (|isDomain| *3 #23#) #24# #27# #28# #29# #30# #31# #25#)) (|internalInfRittWu?| #22# #36#) (|internalSubPolSet?| #22# #36#) (|subPolSet?| #22# #36#) (|subTriSet?| #22# #33#) (|moreAlgebraic?| #22# #33#) (|algebraicSort| #15# #32#) (|supDimElseRittWu?| #22# #33#) (|stopTable!| (*1 *2) (AND #18# #19# #20# #16# #37=(|isDomain| *2 (|Void|)) #21# #17#)) (|startTable!| (*1 *2 *3 *3 *3) (AND (|isDomain| *3 (|String|)) #27# #28# #29# #24# #37# #31# #25#))) +((|stoseSquareFreePart| ((#1=(|List| (|Record| (|:| |val| |#4|) #2=(|:| |tower| |#5|))) |#4| |#5|) 106 T ELT)) (|stosePrepareSubResAlgo| ((#3=(|List| (|Record| (|:| |val| (|List| |#4|)) #2#)) |#4| |#4| |#5|) 79 T ELT)) (|stoseLastSubResultant| (#4=(#1# |#4| |#4| |#5|) 100 T ELT)) (|stoseInvertibleSetsqfreg| (#5=((|List| |#5|) |#4| |#5|) 122 T ELT)) (|stoseInvertibleSetreg| (#5# 129 T ELT)) (|stoseInvertibleSet| (#5# 130 T ELT)) (|stoseInvertible?sqfreg| (#6=((|List| (|Record| (|:| |val| #7=(|Boolean|)) #2#)) |#4| |#5|) 107 T ELT)) (|stoseInvertible?reg| (#6# 128 T ELT)) (|stoseInvertible?| (#6# 47 T ELT) ((#7# |#4| |#5|) 55 T ELT)) (|stoseInternalLastSubResultant| ((#1# #3# |#3| #7#) 91 T ELT) ((#1# |#4| |#4| |#5| #7# #7#) 52 T ELT)) (|stoseIntegralLastSubResultant| (#4# 86 T ELT)) (|stopTableInvSet!| (#8=(#9=(|Void|)) 36 T ELT)) (|stopTableGcd!| (#8# 25 T ELT)) (|startTableInvSet!| (#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 |stoseInvertible?reg| #10#) (SIGNATURE |stoseInvertibleSetreg| #11#) (SIGNATURE |stoseInvertible?| #10#) (SIGNATURE |stoseInvertibleSet| #11#) (SIGNATURE |stoseSquareFreePart| (#7# |#4| |#5|))) (|GcdDomain|) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|RecursivePolynomialCategory| |#1| |#2| |#3|) (|RegularTriangularSetCategory| |#1| |#2| |#3| |#4|)) (T |SquareFreeRegularTriangularSetGcdPackage|)) +((|stoseSquareFreePart| #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 (|SquareFreeRegularTriangularSetGcdPackage| *5 *6 *7 *3 *4)) #13=(|ofCategory| *4 (|RegularTriangularSetCategory| *5 *6 *7 *3)))) (|stoseInvertibleSet| #1# #14=(AND #3# #5# #7# #9# (|isDomain| *2 (|List| *4)) #12# #13#)) (|stoseInvertible?| #1# #15=(AND #3# #5# #7# #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)) (|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))) +(((|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)) +((|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#))) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|elt| ((|#1| $ |#1| |#1|) NIL T ELT)) (|coerce| (((|OutputForm|) $) NIL T ELT)) (|before?| #1#) (= #1#)) +(((|SemiGroupOperation| |#1|) (|Join| (|SemiGroupOperatorCategory| |#1|) (|SetCategory|) (CATEGORY |domain| (SIGNATURE |semiGroupOperation| ($ (|Mapping| |#1| |#1| |#1|))))) (|BasicType|)) (T |SemiGroupOperation|)) +((|semiGroupOperation| (*1 *1 *2) (AND (|isDomain| *2 (|Mapping| *3 *3 *3)) (|ofCategory| *3 (|BasicType|)) (|isDomain| *1 (|SemiGroupOperation| *3))))) +((|elt| ((|#1| $ |#1| |#1|) 6 T ELT))) +(((|SemiGroupOperatorCategory| |#1|) (|Category|) (|BasicType|)) (T |SemiGroupOperatorCategory|)) +NIL +(|Join| (|BinaryOperatorCategory| |t#1|) (CATEGORY |domain| (ATTRIBUTE (|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |t#1|) (|:| |y| |t#1|) (|:| |z| |t#1|)) (= (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|)))))))) +(((|BinaryOperatorCategory| |#1|) . T) ((|MappingCategory| |#1| |#1| |#1|) . T) ((|Type|) . T)) +((** (($ $ (|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)) (* (($ $ $) 18 T ELT))) +(((|SemiGroup|) (|Category|)) (T |SemiGroup|)) +((* (*1 *1 *1 *1) (|ofCategory| *1 (|SemiGroup|))) (** (*1 *1 *1 *2) (AND (|ofCategory| *1 (|SemiGroup|)) (|isDomain| *2 (|PositiveInteger|))))) +(|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE * ($ $ $)) (SIGNATURE ** ($ $ (|PositiveInteger|))))) +(((|BasicType|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Join|) . 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| ((#14=(|Union| $ #15="failed") $ $) NIL (|has| |#3| (|CancellationAbelianMonoid|)) ELT)) (|size| (#16=(#17=(|NonNegativeInteger|)) NIL #18=(|has| |#3| (|Finite|)) ELT)) (|setelt| #19=(#20=(|#3| $ #10# |#3|) NIL #11# ELT)) (|sample| (#21=($) NIL T CONST)) (|retractIfCan| (((|Union| #10# . #22=(#15#)) . #23=($)) NIL #24=(AND (|has| |#3| (|RetractableTo| #10#)) #25=(|has| |#3| (|SetCategory|))) ELT) (((|Union| #26=(|Fraction| #10#) . #22#) . #23#) NIL #27=(AND (|has| |#3| (|RetractableTo| #26#)) #25#) ELT) ((#28=(|Union| |#3| . #22#) . #23#) NIL #25# ELT)) (|retract| (#29=(#10# 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NIL #4# ELT)) (|maxIndex| #44#) (|max| #47#) (|map| (($ #52=(|Mapping| |#3| |#3|) $) NIL T ELT)) (|lookup| ((#8# $) NIL #18# ELT)) (|leftReducedSystem| ((#32# . #53=(#38#)) NIL #35# ELT) ((#36# . #54=(#38# $)) NIL #35# ELT) ((#39# . #54#) NIL #9# ELT) ((#40# . #53#) NIL #9# ELT)) (|latex| (((|String|) $) NIL #25# ELT)) (|indices| (((|List| #10#) $) NIL T ELT)) (|index?| ((#3# #10# $) NIL T ELT)) (|index| (#7# NIL #18# ELT)) (|hash| (((|SingleInteger|) $) NIL #25# ELT)) (|first| (#31# NIL #45# ELT)) (|find| ((#28# #55=(|Mapping| #3# |#3|) $) NIL T ELT)) (|fill!| (#56=($ $ |#3|) NIL #11# ELT)) (|every?| #57=((#3# #55# $) NIL T ELT)) (|eval| (($ $ (|List| #58=(|Equation| |#3|))) NIL #59=(AND (|has| |#3| (|Evalable| |#3|)) #25#) ELT) (($ $ #58#) NIL #59# ELT) (($ $ |#3| |#3|) NIL #59# ELT) (($ $ #50# #50#) NIL #59# ELT)) (|eq?| (#2# NIL T ELT)) (|entry?| (#51# NIL (AND (|has| $ (|FiniteAggregate| |#3|)) #4#) ELT)) (|entries| #49#) (|empty?| (#5# NIL T ELT)) (|empty| (#21# NIL T ELT)) (|elt| (#20# NIL T ELT) (#43# NIL T ELT)) (|dot| ((|#3| $ $) NIL #9# ELT)) (|directProduct| (($ #41#) NIL T ELT)) (|dimension| (((|CardinalNumber|)) NIL #60=(|has| |#3| (|Field|)) ELT)) (|differentiate| #61=(#62=($ $ #17#) NIL #63=(AND (|has| |#3| (|DifferentialSpace|)) #9#) ELT) #64=(#65=($ $) NIL #63# ELT) #66=(($ $ #67=(|List| #68=(|Symbol|)) (|List| #17#)) NIL #69=(AND (|has| |#3| (|PartialDifferentialSpace| #68#)) #9#) ELT) #70=(($ $ #68# #17#) NIL #69# ELT) #71=(($ $ #67#) NIL #69# ELT) #72=(($ $ #68#) NIL #69# ELT) #73=(($ $ #52#) NIL #9# ELT) #74=(($ $ #52# #17#) NIL #9# ELT)) (|count| ((#17# |#3| $) NIL #4# ELT) ((#17# #55# $) NIL T ELT)) (|copy| (#65# NIL T ELT)) (|coerce| ((#41# . #75=($)) NIL T ELT) (($ #10#) NIL (OR #24# #9#) ELT) (($ #26#) NIL #27# ELT) (($ |#3|) NIL #25# ELT) ((#76=(|OutputForm|) . #75#) NIL (|has| |#3| (|CoercibleTo| #76#)) ELT)) (|characteristic| (#16# NIL #9# CONST)) (|before?| #1#) (|any?| #57#) (|annihilate?| (#2# NIL #9# ELT)) (|Zero| (#21# NIL #6# 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(|SturmHabichtSequence| (#1# 58 T ELT)) (|SturmHabichtMultiple| (#6=(#4# #2# #2#) 81 #5# ELT)) (|SturmHabichtCoefficients| (((|List| |#1|) #2# #2#) 61 T ELT)) (|SturmHabicht| (#6# 78 T ELT))) +(((|SturmHabichtPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |subresultantSequence| #1=((|List| #2=(|UnivariatePolynomial| |#2| |#1|)) #2# #2#)) (SIGNATURE |SturmHabichtSequence| #1#) (SIGNATURE |SturmHabichtCoefficients| ((|List| |#1|) #2# #2#)) (SIGNATURE |SturmHabicht| #3=(#4=(|Integer|) #2# #2#)) (SIGNATURE |countRealRoots| #5=(#4# #2#)) (IF (|has| |#1| (|GcdDomain|)) (PROGN (SIGNATURE |SturmHabichtMultiple| #3#) (SIGNATURE |countRealRootsMultiple| #5#)) |%noBranch|)) (|OrderedIntegralDomain|) (|Symbol|)) (T |SturmHabichtPackage|)) +((|countRealRootsMultiple| #1=(*1 *2 *3) #2=(AND #3=(|isDomain| *3 #4=(|UnivariatePolynomial| *5 *4)) (|ofCategory| *4 (|GcdDomain|)) #5=(|ofCategory| *4 (|OrderedIntegralDomain|)) #6=(|ofType| *5 (|Symbol|)) #7=(|isDomain| *2 (|Integer|)) #8=(|isDomain| *1 (|SturmHabichtPackage| *4 *5)))) (|SturmHabichtMultiple| #9=(*1 *2 *3 *3) #2#) (|countRealRoots| #1# #10=(AND #3# #5# #6# #7# #8#)) (|SturmHabicht| #9# #10#) (|SturmHabichtCoefficients| #9# (AND #3# #5# #6# (|isDomain| *2 (|List| *4)) #8#)) (|SturmHabichtSequence| #9# #11=(AND #5# #6# (|isDomain| *2 (|List| #4#)) #8# #3#)) (|subresultantSequence| #9# #11#)) +((~= #1=(#2=((|Boolean|) $ $) NIL T ELT)) (|target| ((#3=(|Syntax|) $) 12 T ELT)) (|source| ((#4=(|List| #3#) $) 14 T ELT)) (|signature| (($ #4# #3#) 10 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 29 T ELT)) (|before?| #1#) (= (#2# 17 T ELT))) +(((|Signature|) (|Join| (|SetCategory|) (CATEGORY |domain| (SIGNATURE |signature| ($ #1=(|List| #2=(|Syntax|)) #2#)) (SIGNATURE |target| (#2# $)) (SIGNATURE |source| (#1# $))))) (T |Signature|)) +((|signature| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|List| #2=(|Syntax|))) (|isDomain| *3 #2#) #3=(|isDomain| *1 (|Signature|)))) (|target| #4=(*1 *2 *1) (AND (|isDomain| *2 #2#) #3#)) (|source| #4# (AND #1# #3#))) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|signatureAst| (($ #2=(|Identifier|) #3=(|Signature|)) 14 T ELT)) (|signature| ((#3# $) 20 T ELT)) (|name| ((#2# $) 17 T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 27 T ELT) (($ #4=(|Syntax|)) NIL T ELT) ((#4# $) NIL T ELT)) (|before?| #1#) (= #1#)) +(((|SignatureAst|) (|Join| (|SpadSyntaxCategory|) (CATEGORY |domain| (SIGNATURE |signatureAst| ($ #1=(|Identifier|) #2=(|Signature|))) (SIGNATURE |name| (#1# $)) (SIGNATURE |signature| (#2# $))))) (T |SignatureAst|)) +((|signatureAst| (*1 *1 *2 *3) (AND #1=(|isDomain| *2 (|Identifier|)) (|isDomain| *3 #2=(|Signature|)) #3=(|isDomain| *1 (|SignatureAst|)))) (|name| #4=(*1 *2 *1) (AND #1# #3#)) (|signature| #4# (AND (|isDomain| *2 #2#) #3#))) +((|sign| ((#1=(|Union| (|Integer|) "failed") |#2| #2=(|Symbol|) |#2| (|String|)) 19 T ELT) ((#1# |#2| #2# (|OrderedCompletion| |#2|)) 17 T ELT) ((#1# |#2|) 60 T ELT))) +(((|ElementaryFunctionSign| |#1| |#2|) (CATEGORY |package| (SIGNATURE |sign| (#1=(|Union| #2=(|Integer|) "failed") |#2|)) (SIGNATURE |sign| (#1# |#2| #3=(|Symbol|) (|OrderedCompletion| |#2|))) (SIGNATURE |sign| (#1# |#2| #3# |#2| (|String|)))) (|Join| (|IntegralDomain|) (|RetractableTo| #2#) (|LinearlyExplicitRingOver| #2#) (|GcdDomain|)) (|Join| (|AlgebraicallyClosedField|) (|TranscendentalFunctionCategory|) (|FunctionSpace| |#1|))) (T |ElementaryFunctionSign|)) +((|sign| (*1 *2 *3 *4 *3 *5) (|partial| AND #1=(|isDomain| *4 (|Symbol|)) (|isDomain| *5 (|String|)) #2=(|ofCategory| *6 #3=(|Join| (|IntegralDomain|) (|RetractableTo| *2) (|LinearlyExplicitRingOver| *2) (|GcdDomain|))) #4=(|isDomain| *2 (|Integer|)) #5=(|isDomain| *1 (|ElementaryFunctionSign| *6 *3)) #6=(|ofCategory| *3 (|Join| #7=(|AlgebraicallyClosedField|) #8=(|TranscendentalFunctionCategory|) (|FunctionSpace| *6))))) (|sign| (*1 *2 *3 *4 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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| (|Integer|))) |has| |#2| (|RetractableTo| (|Fraction| (|Integer|)))) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|DifferentialDomain| $) OR (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|DifferentialRing|))) ((|DifferentialExtension| |#2|) . T) ((|DifferentialRing|) |has| |#2| (|DifferentialRing|)) ((|DifferentialSpace|) OR (|has| |#2| (|DifferentialSpace|)) (|has| |#2| (|DifferentialRing|))) ((|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|))) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| #3=(|Integer|)) |has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#2|) OR (|has| |#2| (|CommutativeRing|)) (|has| |#2| (ATTRIBUTE (|commutative| #1#)))) ((|LinearlyExplicitRingOver| #3#) |has| |#2| (|LinearlyExplicitRingOver| (|Integer|))) ((|LinearlyExplicitRingOver| |#2|) . T) ((|Module| |#2|) OR (|has| |#2| (|CommutativeRing|)) (|has| |#2| (ATTRIBUTE (|commutative| #1#)))) ((|Monoid|) . 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#22=(#14#)) $) 167 T ELT) (((|Union| #23=(|Fraction| #24=(|Integer|)) . #22#) . #25=($)) NIL #26=(|has| |#1| (|RetractableTo| #23#)) ELT) (((|Union| #24# . #22#) . #25#) NIL #27=(|has| |#1| (|RetractableTo| #24#)) ELT) (#28=((|Union| |#2| . #22#) . #25#) NIL T ELT)) (|retract| (#29=(|#1| $) 165 T ELT) ((#23# . #30=($)) NIL #26# ELT) ((#24# . #30#) NIL #27# ELT) ((|#2| . #30#) NIL T ELT)) (|resultant| (($ $ $ |#2|) NIL #31=(|has| |#1| (|CommutativeRing|)) ELT)) (|reductum| (#9# 218 T ELT)) (|reducedSystem| ((#32=(|Matrix| #24#) . #33=(#34=(|Matrix| $))) NIL #35=(|has| |#1| (|LinearlyExplicitRingOver| #24#)) ELT) ((#36=(|Record| (|:| |mat| #32#) (|:| |vec| (|Vector| #24#))) . #37=(#34# #38=(|Vector| $))) NIL #35# ELT) ((#39=(|Record| (|:| |mat| #40=(|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) . #37#) NIL T ELT) ((#40# . #33#) NIL T ELT)) (|recip| ((#13# $) 90 T ELT)) (|primitivePart| #17# (#41=($ $ |#2|) NIL #18# ELT)) (|primitiveMonomials| #42=((#43=(|List| $) $) NIL T ELT)) (|prime?| 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128 T ELT)) (|mainVariable| (#28# 177 T ELT)) (|leftReducedSystem| ((#32# . #59=(#38#)) NIL #35# ELT) ((#36# . #60=(#38# $)) NIL #35# ELT) ((#39# . #60#) NIL T ELT) ((#40# . #59#) NIL T ELT)) (|leadingMonomial| (#9# 217 T ELT)) (|leadingCoefficient| (#29# 43 T ELT)) (|lcm| (#61=($ #43#) NIL #18# ELT) (#62=($ $ $) NIL #18# ELT)) (|latex| (((|String|) $) NIL T ELT)) (|isTimes| #63=(((|Union| #43# #14#) $) NIL T ELT)) (|isPlus| #63#) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| #11#)) #14#) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|ground?| (#4# 39 T ELT)) (|ground| (#29# NIL T ELT)) (|gcdPolynomial| ((#6# #6# #6#) 148 #18# ELT)) (|gcd| (#61# 153 #18# ELT) (#62# 138 #18# ELT)) (|factorSquareFreePolynomial| #15#) (|factorPolynomial| #15#) (|factor| (#19# NIL #16# ELT)) (|exquo| ((#13# $ |#1|) NIL #8# ELT) (#12# 126 #8# ELT)) (|eval| (($ $ (|List| #64=(|Equation| $))) NIL T ELT) (($ $ #64#) NIL T ELT) (($ $ $ $) NIL T ELT) (($ $ #43# #43#) NIL T ELT) (($ 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#44#) 80 T ELT) #66# #54#) (|charthRoot| (((|Maybe| $) $) NIL (OR #73# (|has| |#1| #74#)) ELT)) (|characteristic| ((#11#) 87 T CONST)) (|binomThmExpt| (($ $ $ #11#) NIL #31# ELT)) (|before?| #1#) (|associates?| (#2# 123 #8# ELT)) (|annihilate?| #1#) (|Zero| (#21# 12 T CONST)) (|One| (#21# 14 T CONST)) (D #54# #66# #67# (#41# NIL T ELT)) (= (#2# 106 T ELT)) (/ (#76=($ $ |#1|) 132 (|has| |#1| (|Field|)) ELT)) (- (#9# 93 T ELT) (#62# 104 T ELT)) (+ (#62# 55 T ELT)) (** (($ $ #77=(|PositiveInteger|)) 110 T ELT) (($ $ #11#) 109 T ELT)) (* (($ #77# $) NIL T ELT) (($ #11# $) NIL T ELT) (($ #24# $) 96 T ELT) (#62# 72 T ELT) (($ $ #23#) NIL #75# ELT) (($ #23# $) NIL #75# ELT) (($ |#1| $) 99 T ELT) (#76# NIL T ELT))) +(((|SparseMultivariatePolynomial| |#1| |#2|) (|PolynomialCategory| |#1| (|IndexedExponents| |#2|) |#2|) (|Ring|) (|OrderedSet|)) (T |SparseMultivariatePolynomial|)) +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=(#14=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| (#9# NIL #10# ELT)) (|sinh| (#9# 145 #10# ELT)) (|sin| (#9# 121 #10# ELT)) (|sech| (#9# 153 #10# ELT)) (|sec| (#9# 129 #10# ELT)) (|sample| (#15=($) NIL T CONST)) (|reductum| #16=(#9# NIL T ELT)) (|recip| ((#14# $) NIL T ELT)) (|polynomial| ((#17=(|Polynomial| |#1|) $ #18=(|NonNegativeInteger|)) NIL T ELT) ((#17# $ #18# #18#) NIL T ELT)) (|pole?| #4#) (|pi| (#15# 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| #16#) (|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| (#13# 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| (((|Maybe| $) $) NIL (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| ((#18#) NIL T CONST)) (|before?| #1#) (|atanh| (#9# 161 #10# ELT)) (|atan| (#9# 137 #10# ELT)) (|associates?| (#2# NIL #7# ELT)) (|asinh| (#9# 157 #10# ELT)) (|asin| (#9# 133 #10# ELT)) (|asech| (#9# 165 #10# ELT)) (|asec| (#9# 141 #10# ELT)) (|annihilate?| #1#) (|acsch| (#9# 167 #10# ELT)) (|acsc| (#9# 143 #10# ELT)) (|acoth| (#9# 163 #10# ELT)) (|acot| (#9# 139 #10# ELT)) (|acosh| (#9# 159 #10# ELT)) (|acos| (#9# 135 #10# ELT)) (|Zero| (#15# 52 T CONST)) (|One| (#15# 62 T CONST)) (D #21# #26# #27# (#22# NIL T ELT)) (= #1#) (/ (#29=($ $ |#1|) 196 (|has| |#1| (|Field|)) ELT)) (- #16# (#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))) +(((|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|) . 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#16#)))) +((|insertionSort!| (#1=(|#2| |#2|) 28 #2=(|has| |#1| (|OrderedSet|)) ELT) (#3=(|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) 25 T ELT)) (|bubbleSort!| (#1# 27 #2# ELT) (#3# 22 T ELT))) +(((|SortPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |bubbleSort!| #1=(|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|))) (SIGNATURE |insertionSort!| #1#) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |bubbleSort!| #2=(|#2| |#2|)) (SIGNATURE |insertionSort!| #2#)) |%noBranch|)) (|Type|) (|Join| (|IndexedAggregate| (|Integer|) |#1|) (|FiniteAggregate| |#1|) (|ShallowlyMutableAggregate| |#1|))) (T |SortPackage|)) +((|insertionSort!| #1=(*1 *2 *2) #2=(AND (|ofCategory| *3 (|OrderedSet|)) (|ofCategory| *3 #3=(|Type|)) (|isDomain| *1 (|SortPackage| *3 *2)) (|ofCategory| *2 (|Join| (|IndexedAggregate| #4=(|Integer|) *3) (|FiniteAggregate| *3) (|ShallowlyMutableAggregate| *3))))) (|bubbleSort!| #1# #2#) (|insertionSort!| #5=(*1 *2 *2 *3) #6=(AND (|isDomain| *3 (|Mapping| (|Boolean|) *4 *4)) 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#4=(|ofCategory| *2 #5=(|Join| (|SetCategory|) (|Aggregate|))) #6=(|ofCategory| *3 #5#))) (|updateStatus!| #1# (AND #2# #4# #6#)) (|construct| (*1 *1 *2) #7=(AND (|isDomain| *2 #8=(|SplittingNode| *3 *4)) #6# #9=(|ofCategory| *4 #5#) #10=(|isDomain| *1 (|SplittingTree| *3 *4)))) (|construct| #11=(*1 *1 *2 *3 *4) (AND (|isDomain| *4 (|List| #3#)) #2# #4# #6#)) (|construct| #11# (AND (|isDomain| *4 (|List| (|SplittingNode| *2 *3))) #4# #6# #2#)) (|construct| (*1 *1 *2 *3 *2 *4) (AND (|isDomain| *4 (|List| *3)) #6# #2# #4#)) (|conditions| #12=(*1 *2 *1) (AND (|isDomain| *2 (|List| *4)) #10# #6# #9#)) (|result| #12# (AND (|isDomain| *2 (|List| (|Record| (|:| |val| *3) (|:| |tower| *4)))) #10# #6# #9#)) (|nodeOf?| (*1 *2 *3 *1) (AND (|isDomain| *3 #13=(|SplittingNode| *4 *5)) #9# #14=(|ofCategory| *5 #5#) #15=(|isDomain| *2 #16=(|Boolean|)) #17=(|isDomain| *1 (|SplittingTree| *4 *5)))) (|subNodeOf?| (*1 *2 *3 *1 *4) (AND (|isDomain| *3 (|SplittingNode| *5 *6)) (|isDomain| *4 (|Mapping| #16# 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(|content| (#35# 164 #21# ELT) #52#) (|conditionP| (((|Union| #45# #17#) #41#) NIL #104=(AND (|has| $ #105=(|CharacteristicNonZero|)) #20#) ELT)) (|composite| (#15# NIL #11# ELT) (((|Union| #86# #17#) #86# $) NIL #11# ELT)) (|coerce| ((#63# $) 151 T ELT) (($ #30#) NIL T ELT) (($ |#1|) 78 T ELT) (($ #7#) NIL T ELT) (($ #29#) NIL (OR #81# #31#) ELT) (#12# NIL #11# ELT)) (|coefficients| ((#85# $) NIL T ELT)) (|coefficient| ((|#1| $ #5#) NIL T ELT) #68# #69#) (|charthRoot| (#65# NIL (OR #104# (|has| |#1| #105#)) ELT)) (|characteristic| ((#5#) NIL T CONST)) (|binomThmExpt| (($ $ $ #5#) 42 #37# ELT)) (|before?| #64#) (|associates?| (#1# NIL #11# ELT)) (|annihilate?| #64#) (|Zero| (#26# 18 T CONST)) (|One| (#26# 20 T CONST)) (D #69# #68# #87# #88# #78# #89# #90# #91# #92# #95# #97# #98#) (= (#1# 122 T ELT)) (/ (#106=($ $ |#1|) 174 #24# ELT)) (- #78# (#18# NIL T ELT)) (+ (#18# 92 T ELT)) (** (($ $ #107=(|PositiveInteger|)) 14 T ELT) (#25# 12 T ELT)) (* (($ #107# $) NIL T ELT) (($ #5# $) NIL T 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|SparseUnivariatePolynomialFunctions2|)) +((|map| (*1 *2 *3 *4) (AND (|isDomain| *3 (|Mapping| *6 *5)) (|isDomain| *4 (|SparseUnivariatePolynomial| *5)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|isDomain| *2 (|SparseUnivariatePolynomial| *6)) (|isDomain| *1 (|SparseUnivariatePolynomialFunctions2| *5 *6))))) +((|squareFree| (#1=((|Factored| #2=(|SparseUnivariatePolynomial| (|Fraction| |#4|))) #2#) 51 T ELT)) (|factor| (#1# 52 T ELT))) +(((|SupFractionFactorizer| |#1| |#2| |#3| |#4|) (CATEGORY |package| (SIGNATURE |factor| #1=((|Factored| #2=(|SparseUnivariatePolynomial| (|Fraction| |#4|))) #2#)) (SIGNATURE |squareFree| #1#)) (|OrderedAbelianMonoidSup|) (|OrderedSet|) (|GcdDomain|) (|PolynomialCategory| |#3| |#1| |#2|)) (T |SupFractionFactorizer|)) +((|squareFree| #1=(*1 *2 *3) #2=(AND (|ofCategory| *4 (|OrderedAbelianMonoidSup|)) (|ofCategory| *5 (|OrderedSet|)) (|ofCategory| *6 (|GcdDomain|)) (|ofCategory| *7 (|PolynomialCategory| *6 *4 *5)) (|isDomain| *2 (|Factored| #3=(|SparseUnivariatePolynomial| (|Fraction| *7)))) (|isDomain| *1 (|SupFractionFactorizer| *4 *5 *6 *7)) (|isDomain| *3 #3#))) (|factor| #1# #2#)) +((~= #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|) $) 11 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=(#20=(|Union| $ #21="failed") $ $) NIL T ELT)) (|squareFreePart| #22=(#11# NIL #23=(|has| |#1| (|Field|)) ELT)) (|squareFree| #24=(((|Factored| $) $) NIL #23# ELT)) (|sqrt| #17#) (|sizeLess?| (#2# NIL #23# ELT)) (|sinh| #17#) (|sin| #17#) (|series| (($ #25=(|NonNegativeInteger|) #16#) NIL T ELT)) (|sech| #17#) (|sec| #17#) (|sample| (#26=($) NIL T CONST)) (|retractIfCan| (#27=((|Union| #28=(|SparseUnivariateLaurentSeries| |#1| |#2| |#3|) . #29=(#21#)) $) 33 T ELT) (((|Union| #30=(|SparseUnivariateTaylorSeries| |#1| |#2| |#3|) . #29#) $) 36 T ELT)) (|retract| #31=(#32=(#28# . #33=($)) NIL T ELT) ((#30# . #33#) NIL T ELT)) (|rem| #34=(#35=($ $ $) NIL #23# ELT)) (|reductum| #36=(#11# NIL T ELT)) (|recip| ((#20# $) NIL T ELT)) (|rationalPower| (#37=(#14# $) 59 T ELT)) (|quo| #34#) (|puiseux| (($ #14# #28#) NIL T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #38=(|List| $)) #39=(|:| |generator| $)) #38#) NIL #23# ELT)) (|prime?| (#5# NIL #23# ELT)) (|pole?| #4#) (|pi| (#26# NIL #18# ELT)) (|order| #40=(#37# NIL T ELT) ((#14# $ #14#) NIL T ELT)) (|opposite?| #1#) (|one?| #4#) (|nthRoot| (#41=($ $ #15#) NIL #18# ELT)) (|multiplyExponents| #42=(($ $ #43=(|PositiveInteger|)) NIL T ELT) #12#) (|multiEuclidean| (((|Union| #38# #21#) #38# $) NIL #23# ELT)) (|monomial?| #4#) (|monomial| (($ |#1| #14#) 20 T ELT) (($ $ #7# #14#) NIL T ELT) (($ $ #6# (|List| #14#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| #17#) (|leadingMonomial| #36#) (|leadingCoefficient| (#44=(|#1| $) NIL T ELT)) (|lcm| #45=(($ #38#) NIL #23# ELT) #34#) (|laurentRep| (#32# 41 T ELT)) (|laurentIfCan| (#27# NIL T ELT)) (|laurent| #31#) (|latex| (((|String|) $) NIL T ELT)) (|inv| #22#) (|integrate| (#11# 39 #18# ELT) (#46=($ $ #8#) NIL (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| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #23# ELT)) (|gcd| #45# #34#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #51# #52# #39#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#35# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| (SIGNATURE * (|#1| #14# |#1|)))) ELT) #59=(($ $ #47#) NIL #57# ELT) #60=(($ $ #8# #25#) NIL #57# ELT) #61=(($ $ #47# (|List| #25#)) NIL #57# ELT) (#11# 37 #58# ELT) #62=(#63=($ $ #25#) NIL #58# ELT) (#48# 38 T ELT)) 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(|Ring|)) (|ofType| *5 *3)))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| (#4=(#3# $) 129 T ELT)) (|variables| ((#5=(|List| #6=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|variable| ((#7=(|Symbol|) $) 119 T ELT)) (|univariatePolynomial| ((#8=(|UnivariatePolynomial| |#2| |#1|) $ #9=(|NonNegativeInteger|)) 69 T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #10=(|has| |#1| (|IntegralDomain|)) ELT)) (|unitCanonical| #11=(#12=($ $) NIL #10# ELT)) (|unit?| (#4# NIL #10# ELT)) (|truncate| (#13=($ $ #9#) 85 T ELT) (($ $ #9# #9#) 82 T ELT)) (|terms| ((#14=(|Stream| (|Record| (|:| |k| #9#) (|:| |c| |#1|))) $) 105 T ELT)) (|tanh| (#12# 173 #15=(|has| |#1| (|Algebra| #16=(|Fraction| #17=(|Integer|)))) ELT)) (|tan| (#12# 149 #15# ELT)) (|subtractIfCan| (#18=(#19=(|Union| $ "failed") $ $) NIL T ELT)) (|sqrt| (#12# NIL #15# ELT)) (|sinh| (#12# 169 #15# ELT)) (|sin| (#12# 145 #15# ELT)) (|series| (($ #14#) 118 T ELT) (($ #20=(|Stream| |#1|)) 113 T ELT)) (|sech| (#12# 177 #15# ELT)) (|sec| (#12# 153 #15# ELT)) (|sample| (#21=($) NIL T CONST)) (|reductum| #22=(#12# NIL T ELT)) (|recip| ((#19# $) 25 T ELT)) (|quoByVar| (#12# 28 T ELT)) (|polynomial| ((#23=(|Polynomial| |#1|) $ #9#) 81 T ELT) ((#23# $ #9# #9#) 83 T ELT)) (|pole?| (#4# 124 T ELT)) (|pi| (#21# NIL #15# ELT)) (|order| (#24=(#9# $) 126 T ELT) ((#9# $ #9#) 128 T ELT)) (|opposite?| #1#) (|one?| #25=(#4# NIL T ELT)) (|nthRoot| (($ $ #17#) NIL #15# ELT)) (|multiplyExponents| #26=(($ $ #27=(|PositiveInteger|)) NIL T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| #17#) $) NIL T ELT)) (|monomial?| #25#) (|monomial| (($ |#1| #9#) 13 T ELT) (($ $ #6# #9#) NIL T ELT) (($ $ #5# #28=(|List| #9#)) NIL T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|log| (#12# 135 #15# ELT)) (|leadingMonomial| #22#) (|leadingCoefficient| (#29=(|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|integrate| (#12# 133 #15# ELT) (#30=($ $ #7#) NIL (OR (AND #15# (|has| |#1| 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(((|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))) +(((|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| $)) (SIGNATURE 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T) ((|BasicType|) . T) ((|CoercibleTo| (|List| |#4|)) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Collection| |#4|) . T) ((|ConvertibleTo| (|InputForm|)) |has| |#4| (|ConvertibleTo| (|InputForm|))) ((|Evalable| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|FiniteAggregate| |#4|) . T) ((|Functorial| |#4|) . T) ((|HomogeneousAggregate| |#4|) . T) ((|InnerEvalable| |#4| |#4|) AND (|has| |#4| (|Evalable| |#4|)) (|has| |#4| (|SetCategory|))) ((|Join|) . T) ((|PolynomialSetCategory| |#1| |#2| |#3| |#4|) . T) ((|SetCategory|) . T) ((|ShallowlyMutableAggregate| |#4|) . T) ((|Type|) . T)) +((|tube| (($ |#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#))) +((|unitVector| ((#1=(|Point| #2=(|DoubleFloat|)) #1#) 31 T ELT)) (|point| ((#1# #2# #2# #2# #2#) 10 T ELT)) (|loopPoints| (((|List| #1#) #1# #1# #1# #2# #3=(|List| (|List| #2#))) 57 T ELT)) (|dot| ((#2# #1# #1#) 27 T ELT)) (|cross| (#4=(#1# #1# #1#) 28 T ELT)) (|cosSinInfo| ((#3# (|Integer|)) 45 T ELT)) (- (#4# 26 T ELT)) (+ (#4# 24 T ELT)) (* ((#1# #2# #1#) 22 T ELT))) +(((|TubePlotTools|) (CATEGORY |package| (SIGNATURE |point| (#1=(|Point| #2=(|DoubleFloat|)) #2# #2# #2# #2#)) (SIGNATURE * (#1# #2# #1#)) (SIGNATURE + #3=(#1# #1# #1#)) (SIGNATURE - #3#) (SIGNATURE |dot| (#2# #1# #1#)) (SIGNATURE |cross| #3#) (SIGNATURE |unitVector| (#1# #1#)) (SIGNATURE |cosSinInfo| (#4=(|List| (|List| #2#)) (|Integer|))) (SIGNATURE |loopPoints| ((|List| #1#) #1# #1# #1# #2# #4#)))) (T |TubePlotTools|)) +((|loopPoints| (*1 *2 *3 *3 *3 *4 *5) (AND (|isDomain| *5 #1=(|List| (|List| #2=(|DoubleFloat|)))) (|isDomain| *4 #2#) (|isDomain| *2 (|List| #3=(|Point| *4))) #4=(|isDomain| *1 (|TubePlotTools|)) (|isDomain| *3 #3#))) (|cosSinInfo| (*1 *2 *3) (AND (|isDomain| *3 (|Integer|)) (|isDomain| *2 #1#) #4#)) (|unitVector| (*1 *2 *2) #5=(AND #6=(|isDomain| *2 #7=(|Point| #2#)) #4#)) (|cross| #8=(*1 *2 *2 *2) #5#) (|dot| (*1 *2 *3 *3) (AND (|isDomain| *3 #7#) (|isDomain| *2 #2#) #4#)) (- #8# #5#) (+ #8# #5#) (* (*1 *2 *3 *2) (AND #6# #9=(|isDomain| *3 #2#) #4#)) (|point| (*1 *2 *3 *3 *3 *3) (AND #6# #4# #9#))) +((~= #1=(#2=((|Boolean|) $ $) NIL #3=(|has| |#1| (|SetCategory|)) ELT)) (|select| ((|#1| $ #4=(|NonNegativeInteger|)) 18 T ELT)) (|length| ((#4# $) 13 T ELT)) (|latex| (((|String|) $) NIL #3# ELT)) (|hash| (((|SingleInteger|) $) NIL #3# ELT)) (|coerce| ((#5=(|PrimitiveArray| |#1|) $) 12 T ELT) (($ #5#) 11 T ELT) ((#6=(|OutputForm|) $) 29 (|has| |#1| (|CoercibleTo| #6#)) ELT)) (|before?| #1#) (= (#2# 22 #3# ELT))) +(((|Tuple| |#1|) (|Join| (|HomotopicTo| (|PrimitiveArray| |#1|)) (CATEGORY |domain| (SIGNATURE |select| (|#1| $ #1=(|NonNegativeInteger|))) (SIGNATURE |length| (#1# $)) (IF (|has| |#1| #2=(|CoercibleTo| (|OutputForm|))) (ATTRIBUTE #2#) |%noBranch|) (IF (|has| |#1| #3=(|SetCategory|)) (ATTRIBUTE #3#) |%noBranch|))) (|Type|)) (T |Tuple|)) +((|select| (*1 *2 *1 *3) (AND (|isDomain| *3 #1=(|NonNegativeInteger|)) (|isDomain| *1 (|Tuple| *2)) (|ofCategory| *2 #2=(|Type|)))) (|length| (*1 *2 *1) (AND (|isDomain| *2 #1#) (|isDomain| *1 (|Tuple| *3)) (|ofCategory| *3 #2#)))) +((|twoFactor| ((#1=(|Factored| #2=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) #2# (|Integer|)) 92 T ELT)) (|generalTwoFactor| (#3=(#1# #2#) 84 T ELT)) (|generalSqFr| (#3# 68 T ELT))) +(((|TwoFactorize| |#1|) (CATEGORY |package| (SIGNATURE |generalTwoFactor| #1=(#2=(|Factored| #3=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) #3#)) (SIGNATURE |generalSqFr| #1#) (SIGNATURE |twoFactor| (#2# #3# (|Integer|)))) (|FiniteFieldCategory|)) (T |TwoFactorize|)) +((|twoFactor| (*1 *2 *3 *4) (AND (|isDomain| *4 (|Integer|)) (|ofCategory| *5 #1=(|FiniteFieldCategory|)) (|isDomain| *2 (|Factored| #2=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *5)))) (|isDomain| *1 (|TwoFactorize| *5)) (|isDomain| *3 #2#))) (|generalSqFr| #3=(*1 *2 *3) #4=(AND (|ofCategory| *4 #1#) (|isDomain| *2 (|Factored| #5=(|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| *4)))) (|isDomain| *1 (|TwoFactorize| *4)) (|isDomain| *3 #5#))) (|generalTwoFactor| #3# #4#)) +NIL +(((|Type|) (|Category|)) (T |Type|)) +NIL +(|Join|) +(((|Join|) . T)) +((~= #1=(((|Boolean|) $ $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|coerce| (((|OutputForm|) $) 9 T ELT) (($ #2=(|Syntax|)) NIL T ELT) ((#2# $) NIL T ELT)) (|before?| #1#) (= #1#)) +(((|TypeAst|) (|SpadSyntaxCategory|)) (T |TypeAst|)) +NIL +((|userOrdered?| ((#1=(|Boolean|)) 18 T ELT)) (|setOrder| ((#2=(|Void|) #3=(|List| |#1|) #3#) 22 T ELT) ((#2# #3#) 23 T ELT)) (|more?| ((#1# |#1| |#1|) 37 #4=(|has| |#1| (|OrderedSet|)) ELT)) (|less?| ((#1# |#1| |#1| #5=(|Mapping| #1# |#1| |#1|)) 29 T ELT) (((|Union| #1# "failed") |#1| |#1|) 27 T ELT)) (|largest| ((|#1| #3#) 38 #4# ELT) ((|#1| #3# #5#) 32 T ELT)) (|getOrder| (((|Record| (|:| |low| #3#) (|:| |high| #3#))) 20 T ELT))) +(((|UserDefinedPartialOrdering| |#1|) (CATEGORY |package| (SIGNATURE |setOrder| (#1=(|Void|) #2=(|List| |#1|))) (SIGNATURE |setOrder| (#1# #2# #2#)) (SIGNATURE |getOrder| ((|Record| (|:| |low| #2#) (|:| |high| #2#)))) (SIGNATURE |less?| ((|Union| #3=(|Boolean|) "failed") |#1| |#1|)) (SIGNATURE |less?| (#3# |#1| |#1| #4=(|Mapping| #3# |#1| |#1|))) (SIGNATURE |largest| (|#1| #2# #4#)) (SIGNATURE |userOrdered?| (#3#)) (IF (|has| |#1| (|OrderedSet|)) (PROGN (SIGNATURE |largest| (|#1| #2#)) (SIGNATURE |more?| (#3# |#1| |#1|))) |%noBranch|)) (|SetCategory|)) (T |UserDefinedPartialOrdering|)) +((|more?| #1=(*1 *2 *3 *3) (AND #2=(|isDomain| *2 #3=(|Boolean|)) #4=(|isDomain| *1 (|UserDefinedPartialOrdering| *3)) (|ofCategory| *3 #5=(|OrderedSet|)) #6=(|ofCategory| *3 #7=(|SetCategory|)))) (|largest| #8=(*1 *2 *3) (AND #9=(|isDomain| *3 (|List| *2)) #10=(|ofCategory| *2 #7#) (|ofCategory| *2 #5#) #11=(|isDomain| *1 (|UserDefinedPartialOrdering| *2)))) (|userOrdered?| #12=(*1 *2) (AND #2# #4# #6#)) (|largest| (*1 *2 *3 *4) (AND #9# (|isDomain| *4 (|Mapping| #3# *2 *2)) #11# #10#)) (|less?| (*1 *2 *3 *3 *4) (AND (|isDomain| *4 (|Mapping| #3# *3 *3)) #6# #2# #4#)) (|less?| #1# (|partial| AND #2# #4# #6#)) (|getOrder| #12# (AND (|isDomain| *2 (|Record| (|:| |low| #13=(|List| *3)) (|:| |high| #13#))) #4# #6#)) (|setOrder| #1# #14=(AND (|isDomain| *3 (|List| *4)) (|ofCategory| *4 #7#) (|isDomain| *2 (|Void|)) (|isDomain| *1 (|UserDefinedPartialOrdering| *4)))) (|setOrder| #8# #14#)) +((|setVariableOrder| ((#1=(|Void|) #2=(|List| (|Symbol|)) #2#) 14 T ELT) ((#1# #2#) 12 T ELT)) (|resetVariableOrder| ((#1#) 16 T ELT)) (|getVariableOrder| (((|Record| (|:| |high| #2#) (|:| |low| #2#))) 20 T ELT))) +(((|UserDefinedVariableOrdering|) (CATEGORY |package| (SIGNATURE |setVariableOrder| (#1=(|Void|) #2=(|List| (|Symbol|)))) (SIGNATURE |setVariableOrder| (#1# #2# #2#)) (SIGNATURE |getVariableOrder| ((|Record| (|:| |high| #2#) (|:| |low| #2#)))) (SIGNATURE |resetVariableOrder| (#1#)))) (T |UserDefinedVariableOrdering|)) +((|resetVariableOrder| #1=(*1 *2) (AND #2=(|isDomain| *2 (|Void|)) #3=(|isDomain| *1 (|UserDefinedVariableOrdering|)))) (|getVariableOrder| #1# (AND (|isDomain| *2 (|Record| (|:| |high| #4=(|List| (|Symbol|))) (|:| |low| #4#))) #3#)) (|setVariableOrder| (*1 *2 *3 *3) #5=(AND (|isDomain| *3 #4#) #2# #3#)) (|setVariableOrder| (*1 *2 *3) #5#)) +((|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| $)) $) 55 T ELT)) (|unitCanonical| (($ $) 54 T ELT)) (|unit?| ((#3=(|Boolean|) $) 52 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 66 T ELT)) (|squareFree| (((|Factored| $) $) 67 T ELT)) (|sample| (#4=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|prime?| (((|Boolean|) $) 68 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|lcm| (#5=($ $ $) 60 T ELT) (#6=($ (|List| $)) 59 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|gcdPolynomial| ((#7=(|SparseUnivariatePolynomial| $) #7# #7#) 58 T ELT)) (|gcd| (#5# 62 T ELT) (#6# 61 T ELT)) (|factor| (((|Factored| $) $) 65 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 56 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ $) 57 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|associates?| ((#3# $ $) 53 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#4# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) $) 30 T ELT) (($ $ $) 34 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| $) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . 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. #11#) ELT)) (|reductum| (#16=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) 200 (|has| |#1| (|IntegralDomain|)) ELT) (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) 199 (|has| |#1| (|IntegralDomain|)) ELT)) (|quo| (#15# 185 (|has| |#1| . #11#) ELT)) (|principalIdeal| (((|Record| (|:| |coef| #17=(|List| $)) (|:| |generator| $)) #17#) 180 (|has| |#1| . #11#) ELT)) (|prime?| (((|Boolean|) $) 193 (|has| |#1| . #11#) ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #9#) ELT)) (|order| ((#7# $) 127 T ELT) ((#7# $ #7#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #18=(|Integer|)) 145 (|has| |#1| . #13#) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT)) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) 201 T ELT)) (|multiEuclidean| (((|Union| #19=(|List| $) #20="failed") #19# $) 189 (|has| 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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|)) . 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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# $) NIL T ELT))) +(((|UnivariateLaurentSeriesConstructorCategory&| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |retractIfCan| ((|Union| #1=(|Integer|) #2="failed") |#1|)) (SIGNATURE |retract| (#1# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #3=(|Fraction| #1#) #2#) |#1|)) (SIGNATURE |retract| (#3# |#1|)) (SIGNATURE |retractIfCan| ((|Union| #4=(|Symbol|) #2#) |#1|)) (SIGNATURE |retract| (#4# |#1|)) (SIGNATURE |retractIfCan| ((|Union| |#3| #2#) |#1|)) (SIGNATURE |retract| (|#3| |#1|)) (SIGNATURE |zero?| ((|Boolean|) |#1|))) (|UnivariateLaurentSeriesConstructorCategory| |#2| |#3|) (|Ring|) (|UnivariateTaylorSeriesCategory| |#2|)) (T 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#10# |#1|)))) ELT) (#66# 109 (OR (|and| (|has| |#2| . #65#) (|has| |#1| . #5#)) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|)))) ELT) (($ $ #7#) 119 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#)) 115 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ #7# . #69#) 114 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT) (($ $ (|List| #7#) . #71#) 113 (OR (|and| (|has| |#2| . #67#) (|has| |#1| . #5#)) (AND (|has| |#1| . #68#) (|has| |#1| (SIGNATURE * (|#1| #10# |#1|))))) ELT)) (>= (#83=((|Boolean|) $ $) 290 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (> (#83# 288 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (= (#1# 8 T ELT)) (<= (#83# 289 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (< (#83# 287 (|and| (|has| |#2| . #51#) (|has| |#1| . #5#)) ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT) (($ $ $) 196 (|has| |#1| . #17#) ELT) (($ |#2| |#2|) 262 (|has| |#1| . #5#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #79#) 195 (|has| |#1| . #17#) ELT) (($ $ $) 173 (|has| |#1| . #12#) ELT) (($ $ (|Fraction| #46#)) 144 (|has| |#1| . #12#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #84=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #84#) 88 T ELT) (($ $ |#2|) 237 (|has| |#1| . #5#) ELT) (($ |#2| . #84#) 236 (|has| |#1| . #5#) ELT) (($ #78# . #84#) 77 (|has| |#1| . #80#) ELT) (($ $ #78#) 76 (|has| |#1| . #80#) 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)) +((~= #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=(#23=(|Union| $ #19#) $ $) NIL T ELT)) (|squareFreePolynomial| #24=(((|Factored| #25=(|SparseUnivariatePolynomial| $)) #25#) NIL #26=(AND #7# #27=(|has| |#2| (|PolynomialFactorizationExplicit|))) ELT)) (|squareFreePart| #28=(#14# NIL #7# ELT)) (|squareFree| #29=(((|Factored| $) $) NIL #7# ELT)) (|sqrt| (#14# NIL #20# ELT)) (|solveLinearPolynomialEquation| (((|Union| #30=(|List| #25#) #19#) #30# #25#) NIL #26# ELT)) (|sizeLess?| (#2# NIL #7# ELT)) (|sinh| (#14# 204 #20# ELT)) (|sin| (#14# 180 #20# ELT)) (|sign| (#31=(#16# $) NIL #32=(AND #7# (|has| |#2| (|OrderedIntegralDomain|))) ELT)) (|series| (($ #17#) 59 T ELT)) (|sech| (#14# 212 #20# ELT)) (|sec| (#14# 188 #20# ELT)) (|sample| (#33=($) NIL T CONST)) (|retractIfCan| (#18# 159 T ELT) (((|Union| #16# . #34=(#19#)) . #35=($)) NIL #36=(AND #7# (|has| |#2| (|RetractableTo| #16#))) ELT) (((|Union| #21# . #34#) . #35#) NIL #36# ELT) (((|Union| #11# . #34#) . #35#) NIL #37=(AND #7# (|has| |#2| (|RetractableTo| #11#))) ELT)) (|retract| (#5# 158 T ELT) (#31# NIL #36# ELT) ((#21# $) NIL #36# ELT) (#10# NIL #37# ELT)) 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#3=(|Type|) #3#) (T |UniversalSegmentFunctions2|)) +((|map| #1=(*1 *2 *3 *4) (AND #2=(|isDomain| *3 (|Mapping| *6 *5)) #3=(|isDomain| *4 (|UniversalSegment| *5)) (|ofCategory| *5 (|OrderedRing|)) #4=(|ofCategory| *5 #5=(|Type|)) #6=(|ofCategory| *6 #5#) (|isDomain| *2 (|Stream| *6)) #7=(|isDomain| *1 (|UniversalSegmentFunctions2| *5 *6)))) (|map| #1# (AND #2# #3# #4# #6# (|isDomain| *2 (|UniversalSegment| *6)) #7#))) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|vectorise| ((#6=(|Vector| |#2|) $ #7=(|NonNegativeInteger|)) NIL T ELT)) (|variables| ((#8=(|List| #9=(|SingletonAsOrderedSet|)) $) NIL T ELT)) (|unmakeSUP| (($ #10=(|SparseUnivariatePolynomial| |#2|)) NIL T ELT)) (|univariate| ((#11=(|SparseUnivariatePolynomial| $) $ #9#) NIL T ELT) #12=((#10# $) NIL T ELT)) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) NIL #13=(|has| |#2| (|IntegralDomain|)) ELT)) (|unitCanonical| #14=(#15=($ $) NIL #13# ELT)) 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(|ofCategory| *2 #6#))) (|monicRightFactorIfCan| (*1 *2 *2 *3) #7#)) +((|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) 30 T ELT))) +(((|UnivariatePolynomialDivisionPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE |divideIfCan| ((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|))) (|IntegralDomain|) (|UnivariatePolynomialCategory| |#1|)) (T |UnivariatePolynomialDivisionPackage|)) +((|divideIfCan| (*1 *2 *3 *3) (|partial| AND (|ofCategory| *4 (|IntegralDomain|)) (|isDomain| *2 (|Record| (|:| |quotient| *3) (|:| |remainder| *3))) (|isDomain| *1 (|UnivariatePolynomialDivisionPackage| *4 *3)) (|ofCategory| *3 (|UnivariatePolynomialCategory| *4))))) +((|noKaratsuba| (#1=(|#2| |#2| |#2|) 22 T ELT)) (|karatsubaOnce| (#1# 36 T ELT)) (|karatsuba| ((|#2| |#2| |#2| #2=(|NonNegativeInteger|) #2#) 44 T ELT))) +(((|UnivariatePolynomialMultiplicationPackage| |#1| |#2|) (CATEGORY |package| (SIGNATURE 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#8=(|SparseUnivariatePolynomial| $)) #8#) 217 T ELT)) (|squareFreePart| (#9=($ $) 207 T ELT)) (|squareFree| (#10=((|Factored| $) $) 205 T ELT)) (|solveLinearPolynomialEquation| (((|Union| #11=(|List| #8#) #12="failed") #11# #8#) 95 T ELT)) (|shiftRight| (#13=($ $ #1#) 84 T ELT)) (|shiftLeft| (#13# 86 T ELT)) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) 157 T ELT)) (|retractIfCan| (((|Union| |#2| #12#) $) 132 T ELT) (((|Union| #14=(|Fraction| #15=(|Integer|)) #12#) $) NIL T ELT) (((|Union| #15# #12#) $) NIL T ELT) (#16=((|Union| #3# #12#) $) NIL T ELT)) (|retract| (#17=(|#2| $) 130 T ELT) ((#14# $) NIL T ELT) ((#15# $) NIL T ELT) ((#3# $) NIL T ELT)) (|pseudoQuotient| (#18=($ $ $) 182 T ELT)) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) #19=(|:| |quotient| $) #20=(|:| |remainder| $)) $ $) 185 T ELT)) (|order| ((#1# $ $) 202 T ELT)) (|nextItem| (((|Maybe| $) $) 149 T ELT)) (|monomial| (($ |#2| #1#) NIL T ELT) (#21=($ $ #3# #1#) 59 T ELT) #22=(($ $ #2# 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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|))) +((|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)) 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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| $) |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|)) . 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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| $) OR (|has| |#1| (|IntegralDomain|)) (|has| |#1| (|CommutativeRing|))) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T)) +((|squareFreePart| ((|#2| |#2|) 12 T ELT)) (|squareFree| (((|Factored| |#2|) |#2|) 14 T ELT)) (|BumInSepFFE| ((#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#) 30 T ELT))) +(((|UnivariatePolynomialSquareFree| |#1| |#2|) (CATEGORY |package| (SIGNATURE |squareFree| ((|Factored| |#2|) |#2|)) (SIGNATURE |squareFreePart| (|#2| |#2|)) (SIGNATURE |BumInSepFFE| (#1=(|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) #1#))) #2=(|IntegralDomain|) (|Join| (|UnivariatePolynomialCategory| |#1|) #2# (CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) (T |UnivariatePolynomialSquareFree|)) +((|BumInSepFFE| #1=(*1 *2 *2) (AND (|isDomain| *2 (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (|Integer|)))) (|ofCategory| *4 #2=(|Join| (|UnivariatePolynomialCategory| *3) #3=(|IntegralDomain|) #4=(CATEGORY |domain| (SIGNATURE |gcd| ($ $ $))))) 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|#1| (SIGNATURE |integrate| (|#1| |#1| #8#))) (|has| |#1| (SIGNATURE |variables| (#47=(|List| #8#) |#1|))))) ELT) (#48=($ $ #49=(|Variable| |#2|)) 40 #18# ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|gcdPolynomial| ((#50=(|SparseUnivariatePolynomial| $) #50# #50#) NIL #23# ELT)) (|gcd| #45# #34#) (|factor| #24#) (|extendedEuclidean| (((|Union| (|Record| #51=(|:| |coef1| $) #52=(|:| |coef2| $)) #21#) $ $ $) NIL #23# ELT) (((|Record| #51# #52# #39#) $ $) NIL #23# ELT)) (|extend| #12#) (|exquo| (#19# NIL #9# ELT)) (|expressIdealMember| (((|Maybe| #38#) #38# $) NIL #23# ELT)) (|exp| #17#) (|eval| (((|Stream| |#1|) $ |#1|) NIL #53=(|has| |#1| (SIGNATURE ** (|#1| |#1| #14#))) ELT)) (|euclideanSize| ((#25# $) NIL #23# ELT)) (|elt| #54=(#55=(|#1| $ #14#) NIL T ELT) (#35# NIL (|has| #14# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) NIL #23# ELT)) (|differentiate| #56=(#46# NIL #57=(AND (|has| |#1| (|PartialDifferentialRing| #8#)) #58=(|has| |#1| 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*2) (AND (|isDomain| *2 (|Variable| *4)) (|ofType| *4 (|Symbol|)) (|isDomain| *1 (|UnivariatePuiseuxSeries| *3 *4 *5)) (|ofCategory| *3 (|Algebra| (|Fraction| (|Integer|)))) (|ofCategory| *3 (|Ring|)) (|ofType| *5 *3)))) +((|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)) (|ofCategory| *5 #1=(|Ring|)) (|ofCategory| *6 #1#) (|ofType| *7 #2=(|Symbol|)) (|ofType| *9 *5) (|ofType| *10 *6) (|isDomain| *2 (|UnivariatePuiseuxSeries| *6 *8 *10)) (|isDomain| *1 (|UnivariatePuiseuxSeriesFunctions2| *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| $)) $) 72 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 75 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #7=(|Fraction| (|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| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 191 (|has| |#1| . #11=((|Field|))) ELT)) (|squareFree| (#12=((|Factored| $) $) 192 (|has| |#1| . #11#) ELT)) (|sqrt| (($ $) 146 (|has| |#1| . #13=((|Algebra| 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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)) +((|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| $)) $) 72 (|has| |#1| . #5=((|IntegralDomain|))) ELT)) (|unitCanonical| (($ $) 73 (|has| |#1| . #5#) ELT)) (|unit?| ((#6=(|Boolean|) $) 75 (|has| |#1| . #5#) ELT)) (|truncate| (($ $ #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| (((|Union| $ "failed") $ $) 26 T ELT)) (|squareFreePart| (($ $) 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| $) 214 T ELT)) (|rem| (#15=($ $ $) 186 (|has| |#1| . #12#) ELT)) (|reductum| (#16=($ $) 81 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|rationalPower| (((|Fraction| (|Integer|)) $) 210 T ELT)) (|quo| (#15# 185 (|has| |#1| . #12#) ELT)) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) 211 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #17=(|List| $)) (|:| |generator| $)) #17#) 180 (|has| |#1| . #12#) ELT)) (|prime?| (((|Boolean|) $) 193 (|has| |#1| . #12#) ELT)) (|pole?| (((|Boolean|) $) 95 T ELT)) (|pi| (($) 174 (|has| |#1| . #10#) ELT)) (|order| ((#7# $) 127 T ELT) ((#7# $ #7#) 126 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|nthRoot| (($ $ #18=(|Integer|)) 145 (|has| |#1| . #10#) ELT)) (|multiplyExponents| (($ $ (|PositiveInteger|)) 128 T ELT) (($ $ #7#) 199 T ELT)) (|multiEuclidean| (((|Union| #19=(|List| $) #20="failed") #19# $) 189 (|has| |#1| . #12#) ELT)) (|monomial?| (((|Boolean|) $) 83 T ELT)) (|monomial| (($ |#1| #7#) 82 T ELT) (($ $ #3# #7#) 98 T ELT) (($ $ (|List| #3#) (|List| #7#)) 97 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) 87 T ELT)) (|log| (#21=($ $) 171 (|has| |#1| . #10#) ELT)) (|leadingMonomial| (#16# 85 T ELT)) (|leadingCoefficient| ((|#1| $) 86 T ELT)) (|lcm| (#22=($ (|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| . #12#) ELT) (#23# 175 (|has| |#1| . #12#) ELT)) (|factor| (#13# 190 (|has| |#1| . #12#) ELT)) (|extendedEuclidean| (((|Union| (|Record| #26=(|:| |coef1| $) #27=(|:| |coef2| $)) #20#) $ $ $) 188 (|has| |#1| . #12#) ELT) (((|Record| #26# #27# (|:| |generator| $)) $ $) 187 (|has| |#1| . #12#) ELT)) (|extend| (($ $ #7#) 122 T ELT)) (|exquo| (((|Union| $ "failed") $ $) 71 (|has| |#1| . #5#) ELT)) (|expressIdealMember| (((|Maybe| #17#) #17# $) 181 (|has| |#1| . #12#) ELT)) (|exp| (#21# 172 (|has| |#1| . #10#) ELT)) (|eval| (((|Stream| |#1|) $ |#1|) 121 (|has| |#1| (SIGNATURE ** (|#1| |#1| #7#))) ELT)) (|euclideanSize| (((|NonNegativeInteger|) $) 183 (|has| |#1| . #12#) ELT)) (|elt| ((|#1| $ #7#) 132 T ELT) (($ $ $) 108 (|has| #7# (|SemiGroup|)) ELT)) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) 184 (|has| |#1| . #12#) ELT)) (|differentiate| (($ $ #4#) 120 (AND (|has| |#1| . #28=((|PartialDifferentialRing| #4#))) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 118 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #29=(#30=(|NonNegativeInteger|))) 117 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #31=((|List| #30#))) 116 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #32=($)) 112 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#33=($ $ (|NonNegativeInteger|)) 110 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (|degree| ((#7# $) 84 T ELT)) (|csch| (#9# 161 (|has| |#1| . #10#) ELT)) (|csc| (#11# 150 (|has| |#1| . #10#) ELT)) (|coth| (#9# 160 (|has| |#1| . #10#) ELT)) (|cot| (#11# 151 (|has| |#1| . #10#) ELT)) (|cosh| (#9# 159 (|has| |#1| . #10#) ELT)) (|cos| (#11# 152 (|has| |#1| . #10#) ELT)) (|complete| (($ $) 94 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 68 (|has| |#1| (|CommutativeRing|)) ELT) (($ |#2|) 212 T ELT) (($ #34=(|Fraction| #35=(|Integer|))) 78 (|has| |#1| . #36=((|Algebra| (|Fraction| (|Integer|))))) ELT) (($ $) 70 (|has| |#1| . #5#) ELT)) (|coefficient| ((|#1| $ #7#) 80 T ELT)) (|charthRoot| (((|Maybe| $) $) 69 (|has| |#1| (|CharacteristicNonZero|)) ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 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# $ $) 74 (|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|) $ $) 33 T ELT)) (|acsch| (#37# 167 (|has| |#1| . #10#) ELT)) (|acsc| (#38# 155 (|has| |#1| . #10#) ELT)) (|acoth| (#37# 166 (|has| |#1| . #10#) ELT)) (|acot| (#38# 154 (|has| |#1| . #10#) ELT)) (|acosh| (#37# 165 (|has| |#1| . #10#) ELT)) (|acos| (#38# 153 (|has| |#1| . #10#) ELT)) (|Zero| (#14# 24 T CONST)) (|One| (($) 45 T CONST)) (D (($ $ #4#) 119 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#)) 115 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ #4# . #29#) 114 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ $ (|List| #4#) . #31#) 113 (AND (|has| |#1| . #28#) (|has| |#1| (SIGNATURE * (|#1| #7# |#1|)))) ELT) (($ . #32#) 111 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT) (#33# 109 (|has| |#1| (SIGNATURE * (|#1| #7# |#1|))) ELT)) (= (#1# 8 T ELT)) (/ (($ $ |#1|) 79 (|has| |#1| (|Field|)) ELT) (($ $ $) 196 (|has| |#1| . #12#) ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ $ (|PositiveInteger|)) 35 T ELT) (($ $ (|NonNegativeInteger|)) 43 T ELT) (($ $ #35#) 195 (|has| |#1| . #12#) ELT) (($ $ $) 173 (|has| |#1| . #10#) ELT) (($ $ (|Fraction| #18#)) 144 (|has| |#1| . #10#) ELT)) (* (($ (|PositiveInteger|) $) 17 T ELT) (($ (|NonNegativeInteger|) $) 21 T ELT) (($ (|Integer|) . #39=($)) 30 T ELT) (($ $ $) 34 T ELT) (($ $ |#1|) 89 T ELT) (($ |#1| . #39#) 88 T ELT) (($ #34# . #39#) 77 (|has| |#1| . #36#) ELT) (($ $ #34#) 76 (|has| |#1| . #36#) 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)) +((~= #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=(#18=(|Union| $ #19="failed") $ $) NIL T ELT)) (|squareFreePart| (#11# NIL #20=(|has| |#1| (|Field|)) ELT)) (|squareFree| #21=(((|Factored| $) $) NIL #20# ELT)) (|sqrt| (#11# NIL #16# ELT)) (|sizeLess?| (#2# NIL #20# ELT)) (|sinh| (#11# 188 #16# ELT)) (|sin| (#11# 164 #16# ELT)) (|series| (($ 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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|))) ((|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#) . 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(|:| |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)) 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(|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| (((|Union| $ "failed") $ $) 26 T ELT)) (|sample| (#3=($) 23 T CONST)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|latex| (((|String|) $) 11 T ELT)) (|hash| (((|SingleInteger|) $) 12 T ELT)) (|coerce| (((|OutputForm|) $) 13 T ELT) (($ (|Integer|)) 41 T ELT) (($ |#1|) 53 T ELT)) (|characteristic| (((|NonNegativeInteger|)) 40 T CONST)) (|before?| (#1# 6 T ELT)) (|annihilate?| (((|Boolean|) $ $) 33 T ELT)) (|Zero| (#3# 24 T CONST)) (|One| (($) 45 T CONST)) (= (#1# 8 T ELT)) (- (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (+ (($ $ $) 18 T ELT)) (** (($ 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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)) +((~= (#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| ((#7=(|Union| $ #8="failed") $ $) NIL T ELT)) (|sh| (#5# 25 #9=(|has| |#2| (|CommutativeRing|)) ELT) (#10=($ $ $) 26 #9# ELT)) (|sample| (#11=($) NIL T CONST)) (|rquo| (#10# 72 T ELT) (#12=($ $ #13=(|OrderedFreeMonoid| |#1|)) 58 T ELT) (#14=($ $ |#1|) 62 T ELT)) (|retractIfCan| (((|Union| #13# #8#) $) NIL T ELT)) (|retract| #15=(#16=(#13# $) NIL T ELT)) (|reductum| (#17=($ $) 40 T ELT)) (|recip| ((#7# $) NIL T ELT)) (|quasiRegular?| #3#) (|quasiRegular| #18=(#17# NIL T ELT)) (|opposite?| #19=(#1# NIL T ELT)) (|one?| #3#) (|numberOfMonomials| (#20=(#6# $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #3#) (|monom| (($ #13# |#2|) 39 T ELT)) (|mirror| (#17# 41 T ELT)) (|mindegTerm| (#21=(#22=(|Record| (|:| |k| #13#) (|:| |c| |#2|)) $) 13 T ELT)) (|mindeg| #15#) (|maxdeg| (#16# 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|#2| . #28=($)) 28 T ELT) (($ #24# . #28#) NIL T ELT) (($ #6# $) NIL T ELT) (($ #27# $) NIL T ELT) (($ |#2| #13#) NIL T ELT) (($ |#1| $) 34 T ELT) #26#)) +(((|XDistributedPolynomial| |#1| |#2|) (|Join| (|FreeModuleCat| |#2| (|OrderedFreeMonoid| |#1|)) (|XPolynomialsCat| |#1| |#2|)) (|OrderedSet|) (|Ring|)) (T |XDistributedPolynomial|)) +NIL +((|log| (#1=(|#3| |#3| #2=(|NonNegativeInteger|)) 28 T ELT)) (|exp| (#1# 34 T ELT)) (|Hausdorff| ((|#3| |#3| |#3| #2#) 35 T ELT))) +(((|XExponentialPackage| |#1| |#2| |#3|) (CATEGORY |package| (SIGNATURE |exp| #1=(|#3| |#3| #2=(|NonNegativeInteger|))) (SIGNATURE |log| #1#) (SIGNATURE |Hausdorff| (|#3| |#3| |#3| #2#))) (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|)))) (|OrderedSet|) (|XPolynomialsCat| |#2| |#1|)) (T |XExponentialPackage|)) +((|Hausdorff| (*1 *2 *2 *2 *3) #1=(AND (|isDomain| *3 (|NonNegativeInteger|)) (|ofCategory| *4 (|Join| (|Ring|) (|Module| (|Fraction| (|Integer|))))) (|ofCategory| *5 (|OrderedSet|)) (|isDomain| *1 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(($ $) 91 T ELT)) (|squareFree| (#4=((|Factored| $) $) 90 T ELT)) (|sizeLess?| (((|Boolean|) $ $) 75 T ELT)) (|sample| (#5=($) 23 T CONST)) (|retractIfCan| (((|Union| |#1| "failed") $) 121 T ELT)) (|retract| ((|#1| $) 122 T ELT)) (|rem| (#6=($ $ $) 71 T ELT)) (|recip| (((|Union| $ "failed") $) 42 T ELT)) (|quo| (#6# 72 T ELT)) (|principalIdeal| (((|Record| (|:| |coef| #7=(|List| $)) (|:| |generator| $)) #7#) 66 T ELT)) (|primeFrobenius| (($ $ #8=(|NonNegativeInteger|)) 107 (OR (|has| |#1| . #9=((|CharacteristicNonZero|))) (|has| |#1| . #10=((|Finite|)))) ELT) (($ $) 106 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|prime?| (((|Boolean|) $) 89 T ELT)) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) 104 (OR (|has| |#1| . #9#) (|has| |#1| . #10#)) ELT)) (|opposite?| ((#2# $ $) 20 T ELT)) (|one?| (((|Boolean|) $) 44 T ELT)) (|multiEuclidean| (((|Union| #11=(|List| $) #12="failed") #11# $) 68 T ELT)) (|lcm| (#13=($ $ $) 60 T ELT) (#14=($ (|List| $)) 59 T ELT)) (|latex| 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(|Record| (|:| |k| #1#) (|:| |c| $))) $)))) (|Ring|)) (T |XPolynomial|)) +((|expand| #1=(*1 *2 *1) (AND #2=(|isDomain| *2 (|XDistributedPolynomial| #3=(|Symbol|) *3)) #4=(|isDomain| *1 #5=(|XPolynomial| *3)) #6=(|ofCategory| *3 (|Ring|)))) (|unexpand| (*1 *1 *2) (AND #2# #6# #4#)) (|RemainderList| #1# (AND (|isDomain| *2 (|List| (|Record| (|:| |k| #3#) (|:| |c| #5#)))) #4# #6#))) +((~= (#1=((|Boolean|) $ $) 7 T ELT)) (|zero?| ((#2=(|Boolean|) $) 22 T ELT)) (|varList| (((|List| |#1|) $) 56 T ELT)) (|trunc| (($ $ (|NonNegativeInteger|)) 90 T ELT)) (|subtractIfCan| (((|Union| $ "failed") $ $) 26 T ELT)) (|sh| (#3=($ $ $) 58 (|has| |#2| . #4=((|CommutativeRing|))) ELT) (($ $ (|NonNegativeInteger|)) 57 (|has| |#2| . #4#) ELT)) (|sample| (#5=($) 23 T CONST)) (|rquo| (($ $ |#1|) 69 T ELT) (($ $ (|OrderedFreeMonoid| |#1|)) 68 T ELT) (#3# 67 T ELT)) (|retractIfCan| (((|Union| (|OrderedFreeMonoid| |#1|) "failed") $) 79 T ELT)) (|retract| (((|OrderedFreeMonoid| |#1|) $) 80 T ELT)) (|recip| 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T) ((|AbelianMonoid|) . T) ((|AbelianSemiGroup|) . T) ((|Algebra| |#2|) |has| |#2| (|CommutativeRing|)) ((|BasicType|) . T) ((|BiModule| |#2| |#2|) . T) ((|CancellationAbelianMonoid|) . T) ((|CoercibleFrom| (|Integer|)) . T) ((|CoercibleFrom| #1=(|OrderedFreeMonoid| |#1|)) . T) ((|CoercibleFrom| |#2|) . T) ((|CoercibleTo| (|OutputForm|)) . T) ((|Functorial| |#2|) . T) ((|Join|) . T) ((|LeftLinearSet| (|Integer|)) . T) ((|LeftLinearSet| |#2|) . T) ((|LeftLinearSet| $) . T) ((|LeftModule| |#2|) . T) ((|LeftModule| $) . T) ((|LinearSet| |#2|) |has| |#2| (|CommutativeRing|)) ((|Module| |#2|) |has| |#2| (|CommutativeRing|)) ((|Monoid|) . T) ((|RetractableTo| #1#) . T) ((|RightLinearSet| |#2|) . T) ((|RightModule| |#2|) . T) ((|Ring|) . T) ((|Rng|) . T) ((|SemiGroup|) . T) ((|SemiRing|) . T) ((|SetCategory|) . T) ((|Type|) . T) ((|XAlgebra| |#2|) . T) ((|XFreeAlgebra| |#1| |#2|) . T)) +((~= #1=(#2=(#3=(|Boolean|) $ $) NIL T ELT)) (|zero?| #4=(#5=(#3# $) NIL T ELT)) (|subtractIfCan| ((#6=(|Union| $ #7="failed") $ $) NIL T ELT)) (|sample| (#8=($) NIL T CONST)) (|retractIfCan| (((|Union| |#2| #7#) $) NIL T ELT)) (|retract| #9=(#10=(|#2| $) NIL T ELT)) (|reductum| #11=(#12=($ $) NIL T ELT)) (|recip| ((#6# $) 43 T ELT)) (|quasiRegular?| (#5# 37 T ELT)) (|quasiRegular| (#12# 38 T ELT)) (|opposite?| #1#) (|one?| #4#) (|numberOfMonomials| (#13=(#14=(|NonNegativeInteger|) $) NIL T ELT)) (|monomials| (((|List| $) $) NIL T ELT)) (|monomial?| #4#) (|monom| (($ |#2| |#1|) NIL T ELT)) (|mindeg| (#10# 25 T ELT)) (|maxdeg| (#10# 23 T ELT)) (|map| (($ (|Mapping| |#1| |#1|) $) NIL T ELT)) (|leadingTerm| ((#15=(|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) NIL T ELT)) (|leadingMonomial| #9#) (|leadingCoefficient| (#16=(|#1| $) NIL T ELT)) (|latex| (((|String|) $) NIL T ELT)) (|hash| (((|SingleInteger|) $) NIL T ELT)) (|constant?| (#5# 33 T ELT)) (|constant| (#16# 34 T ELT)) (|coerce| 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2402523 2404123 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) |package| NIL NIL NIL) (|ShallowlyMutableAggregate| 2400879 2401078 2401172 "SMAGG" 2401316 SMAGG (NIL T) |category| NIL 2401409 NIL) (|StackAggregate| 2397653 2399548 2399620 "SKAGG" 2400038 SKAGG (NIL T) |category| NIL 2400257 NIL) (|SingleInteger| 2393665 2397324 2397561 "SINT" NIL SINT (NIL) |domain| NIL NIL 2397620) (|SimplifyAlgebraicNumberConvertPackage| 2393235 2393311 2393495 "SIMPAN" NIL SIMPAN (NIL) |package| NIL NIL NIL) (|RationalFunctionSign| 2392203 2392399 2392704 "SIGNRF" NIL SIGNRF (NIL T) |package| NIL NIL NIL) (|ElementaryFunctionSign| 2390867 2391036 2391505 "SIGNEF" NIL SIGNEF (NIL T T) |package| NIL NIL NIL) (|SignatureAst| 2390057 2390421 2390639 "SIGAST" NIL SIGAST (NIL) |domain| NIL NIL NIL) (|Signature| 2389326 2389645 2389841 "SIG" NIL SIG (NIL) |domain| NIL NIL NIL) (|SturmHabichtPackage| 2387744 2388158 2388707 "SHP" NIL SHP (NIL T NIL) |package| NIL NIL NIL) (|SplitHomogeneousDirectProduct| 2382993 2387555 2387739 "SHDP" NIL SHDP (NIL NIL NIL T) |domain| NIL NIL NIL) (|SemiGroup| 2382311 2382578 2382626 "SGROUP" 2382772 SGROUP (NIL) |category| NIL 2382881 NIL) (|SemiGroup&| 2382137 2382182 2382306 "SGROUP-" NIL SGROUP- (NIL T) |package| NIL NIL NIL) (|SemiGroupOperatorCategory| 2381657 2381697 2381796 "SGPOPC" 2381801 SGPOPC (NIL T) |category| NIL 2382040 NIL) (|SemiGroupOperation| 2380995 2381287 2381503 "SGPOP" NIL SGPOP (NIL T) |domain| NIL NIL NIL) (|SymmetricGroupCombinatoricFunctions| 2378636 2379279 2380033 "SGCF" NIL SGCF (NIL) |package| NIL NIL NIL) (|SquareFreeRegularTriangularSetCategory| 2370968 2377585 2377818 "SFRTCAT" 2377823 SFRTCAT (NIL T T T T) |category| |SquareFreeRegularTriangularSet| 2377890 NIL) (|SquareFreeRegularTriangularSetGcdPackage| 2366012 2366992 2368301 "SFRGCD" NIL SFRGCD (NIL T T T T T) |package| NIL NIL NIL) (|SquareFreeQuasiComponentPackage| 2360975 2361959 2363225 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) |package| NIL NIL NIL) (|SExpressionOf| 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SEGXCAT (NIL T T) |category| NIL 2341222 NIL) (|SegmentCategory| 2338454 2338739 2338813 "SEGCAT" 2339628 SEGCAT (NIL T) |category| NIL 2339937 NIL) (|SegmentBindingFunctions2| 2337914 2338008 2338210 "SEGBIND2" NIL SEGBIND2 (NIL T T) |package| NIL NIL NIL) (|SegmentBinding| 2336954 2337304 2337585 "SEGBIND" NIL SEGBIND (NIL T) |domain| NIL NIL NIL) (|SegmentAst| 2336437 2336720 2336855 "SEGAST" NIL SEGAST (NIL) |domain| NIL NIL NIL) (|SegmentFunctions2| 2335680 2335828 2336096 "SEG2" NIL SEG2 (NIL T T) |package| NIL NIL NIL) (|Segment| 2334751 2335404 2335675 "SEG" NIL SEG (NIL T) |domain| NIL NIL NIL) (|SequentialDifferentialVariable| 2333994 2334611 2334746 "SDVAR" NIL SDVAR (NIL T) |domain| NIL NIL NIL) (|SequentialDifferentialPolynomial| 2327055 2333704 2333989 "SDPOL" NIL SDPOL (NIL T) |domain| NIL NIL NIL) (|StructuralConstantsPackage| 2325633 2325923 2326359 "SCPKG" NIL SCPKG (NIL T) |package| NIL NIL NIL) (|Scope| 2324632 2324935 2325276 "SCOPE" NIL SCOPE (NIL) |domain| NIL NIL NIL) (|SortedCache| 2323714 2323917 2324211 "SCACHE" NIL SCACHE (NIL T) |package| NIL NIL NIL) (|SpadSyntaxCategory| 2323110 2323371 2323437 "SASTCAT" 2323442 SASTCAT (NIL) |category| NIL 2323479 NIL) (|SingletonAsOrderedSet| 2322529 2322889 2323046 "SAOS" NIL SAOS (NIL) |domain| NIL NIL NIL) (|SAERationalFunctionAlgFactor| 2321781 2321831 2322172 "SAERFFC" NIL SAERFFC (NIL T T T) |package| NIL NIL NIL) (|SimpleAlgebraicExtensionAlgFactor| 2321048 2321098 2321434 "SAEFACT" NIL SAEFACT (NIL T T T) |package| NIL NIL NIL) (|SimpleAlgebraicExtension| 2315644 2320869 2321043 "SAE" NIL SAE (NIL T T NIL) |domain| NIL NIL NIL) (|RationalUnivariateRepresentationPackage| 2314266 2314491 2314924 "RURPK" NIL RURPK (NIL T NIL) |package| NIL NIL NIL) (|Ruleset| 2312839 2313216 2313610 "RULESET" NIL RULESET (NIL T T T) |domain| NIL NIL NIL) (|RuleCalled| 2312371 2312604 2312732 "RULECOLD" NIL RULECOLD (NIL NIL) |domain| NIL NIL NIL) (|RewriteRule| 2309854 2310541 2311165 "RULE" NIL RULE (NIL T T T) |domain| NIL NIL NIL) (|RuntimeValue| 2309611 2309649 2309763 "RTVALUE" NIL RTVALUE (NIL) |domain| NIL NIL NIL) (|RestrictAst| 2308972 2309288 2309457 "RSTRCAST" NIL RSTRCAST (NIL) |domain| NIL NIL NIL) (|RegularTriangularSetGcdPackage| 2304659 2305440 2306530 "RSETGCD" NIL RSETGCD (NIL T T T T T) |package| NIL NIL NIL) (|RegularTriangularSetCategory| 2286900 2293624 2293837 "RSETCAT" 2302271 RSETCAT (NIL T T T T) |category| NIL 2303972 NIL) (|RegularTriangularSetCategory&| 2285440 2285947 2286895 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) |package| NIL NIL NIL) (|RegularSetDecompositionPackage| 2280734 2281453 2282514 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) |package| NIL NIL NIL) (|RealRootCharacterizationCategory| 2277009 2277692 2277870 "RRCC" 2280090 RRCC (NIL T T) |category| |RightOpenIntervalRootCharacterization| 2280622 NIL) (|RealRootCharacterizationCategory&| 2276308 2276536 2277004 "RRCC-" NIL RRCC- (NIL T T T) |package| NIL NIL NIL) (|RepeatAst| 2275672 2275989 2276155 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NIL NIL NIL) (|CombinatorialFunctionCategory| 223089 223187 223275 "CFCAT" 223516 CFCAT (NIL) |category| NIL NIL NIL) (|CommonDenominator| 221920 222095 222433 "CDEN" NIL CDEN (NIL T T T) |package| NIL NIL NIL) (|CharacterClass| 218666 221117 221613 "CCLASS" NIL CCLASS (NIL) |domain| NIL NIL NIL) (|Category| 217774 218044 218360 "CATEGORY" NIL CATEGORY (NIL) |domain| NIL NIL NIL) (|CategoryConstructor| 217170 217649 217769 "CATCTOR" NIL CATCTOR (NIL) |domain| NIL NIL NIL) (|CategoryAst| 216504 216829 217007 "CATAST" NIL CATAST (NIL) |domain| NIL NIL NIL) (|CaseAst| 215959 216256 216398 "CASEAST" NIL CASEAST (NIL) |domain| NIL NIL NIL) (|CartesianTensorFunctions2| 215015 215184 215518 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) |package| NIL NIL NIL) (|CartesianTensor| 211496 212793 213761 "CARTEN" NIL CARTEN (NIL NIL NIL T) |domain| NIL NIL NIL) (|CardinalNumber| 209585 210640 211120 "CARD" NIL CARD (NIL) |domain| NIL NIL NIL) (|CapsuleAst| 209074 209355 209488 "CAPSLAST" NIL CAPSLAST (NIL) |domain| NIL NIL NIL) (|CachableSet| 208196 208512 208564 "CACHSET" 208804 CACHSET (NIL) |category| NIL 208962 NIL) (|CancellationAbelianMonoid| 207263 207757 207837 "CABMON" 207930 CABMON (NIL) |category| NIL 208033 NIL) (|ByteOrder| 206644 206944 207151 "BYTEORD" NIL BYTEORD (NIL) |domain| NIL NIL NIL) (|ByteBuffer| 203154 206175 206475 "BYTEBUF" NIL BYTEBUF (NIL) |domain| NIL NIL NIL) (|Byte| 202032 202719 202940 "BYTE" NIL BYTE (NIL) |domain| NIL NIL 203110) (|BinaryTree| 199771 201703 201890 "BTREE" NIL BTREE (NIL T) |domain| NIL NIL NIL) (|BinaryTournament| 197391 199324 199532 "BTOURN" NIL BTOURN (NIL T) |domain| NIL NIL NIL) (|BinaryTreeCategory| 193655 196363 196450 "BTCAT" 196563 BTCAT (NIL T) |category| NIL 196723 NIL) (|BinaryTreeCategory&| 193269 193390 193650 "BTCAT-" NIL BTCAT- (NIL T T) |package| NIL NIL NIL) (|BitAggregate| 187496 191894 191948 "BTAGG" 192123 BTAGG (NIL) |category| NIL 192319 NIL) (|BitAggregate&| 187099 187249 187491 "BTAGG-" NIL BTAGG- (NIL T) |package| NIL NIL NIL) (|BinarySearchTree| 184362 186405 186719 "BSTREE" NIL BSTREE (NIL T) |domain| NIL NIL NIL) (|BrillhartTests| 183418 183624 183984 "BRILL" NIL BRILL (NIL T) |package| NIL NIL NIL) (|BinaryRecursiveAggregate| 179246 181229 181321 "BRAGG" 182482 BRAGG (NIL T) |category| NIL 182862 NIL) (|BinaryRecursiveAggregate&| 178112 178568 179241 "BRAGG-" NIL BRAGG- (NIL T T) |package| NIL NIL NIL) (|BalancedPAdicRational| 171782 177272 177622 "BPADICRT" NIL BPADICRT (NIL NIL) |domain| NIL NIL NIL) (|BalancedPAdicInteger| 169794 171673 171777 "BPADIC" NIL BPADIC (NIL NIL) |domain| NIL NIL NIL) (|BoundIntegerRoots| 169287 169337 169560 "BOUNDZRO" NIL BOUNDZRO (NIL T T) |package| NIL NIL NIL) (|BasicOperatorFunctions1| 167445 167854 168425 "BOP1" NIL BOP1 (NIL T) |package| NIL NIL NIL) (|BasicOperator| 163271 164672 165916 "BOP" NIL BOP (NIL) |domain| NIL NIL NIL) (|Boolean| 162154 162972 163179 "BOOLEAN" NIL BOOLEAN (NIL) |domain| NIL NIL NIL) (|BooleanLogic| 161615 161766 161820 "BOOLE" 161990 BOOLE (NIL) |category| NIL 162105 NIL) (|BooleanLogic&| 161356 161435 161610 "BOOLE-" NIL BOOLE- (NIL T) |package| NIL NIL NIL) (|BiModule| 160162 160780 160854 "BMODULE" 160859 BMODULE (NIL T T) |category| NIL 160986 NIL) (|Bits| 157131 159909 160038 "BITS" NIL BITS (NIL) |domain| NIL NIL NIL) (|BinaryOperatorCategory| 156891 156931 157019 "BINOPC" 157024 BINOPC (NIL T) |category| NIL 157072 NIL) (|BinaryOperation| 156264 156549 156748 "BINOP" NIL BINOP (NIL T) |domain| NIL NIL NIL) (|Binding| 155641 155817 156037 "BINDING" NIL BINDING (NIL) |domain| NIL NIL NIL) (|BinaryExpansion| 150039 155244 155498 "BINARY" NIL BINARY (NIL) |domain| NIL NIL NIL) (|BagAggregate| 147649 148768 148836 "BGAGG" 149243 BGAGG (NIL T) |category| NIL 149476 NIL) (|BagAggregate&| 147460 147500 147644 "BGAGG-" NIL BGAGG- (NIL T T) |package| NIL NIL NIL) (|BezoutMatrix| 146103 146331 146780 "BEZOUT" NIL BEZOUT (NIL T T T T T) |package| NIL NIL NIL) (|BalancedBinaryTree| 142912 145032 145505 "BBTREE" NIL BBTREE (NIL T) |domain| NIL NIL NIL) (|BasicType| 142503 142586 142634 "BASTYPE" 142760 BASTYPE (NIL) |category| NIL 142879 NIL) (|BasicType&| 142249 142335 142498 "BASTYPE-" NIL BASTYPE- (NIL T) |package| NIL NIL NIL) (|BalancedFactorisation| 141381 141490 141794 "BALFACT" NIL BALFACT (NIL T T) |package| NIL NIL NIL) (|Automorphism| 140156 140867 141131 "AUTOMOR" NIL AUTOMOR (NIL T) |domain| NIL NIL NIL) (|AttributeRegistry| 139585 139590 139654 "ATTREG" 139659 ATTREG (NIL) |category| NIL NIL NIL) (|AttributeAst| 139095 139367 139495 "ATTRAST" NIL ATTRAST (NIL) |domain| NIL NIL NIL) (|ArcTrigonometricFunctionCategory| 138213 138368 138462 "ATRIG" 138915 ATRIG (NIL) |category| NIL NIL NIL) (|ArcTrigonometricFunctionCategory&| 137949 138005 138208 "ATRIG-" NIL ATRIG- (NIL T) |package| NIL NIL NIL) (|AbstractSyntaxCategory| 137354 137615 137689 "ASTCAT" 137694 ASTCAT (NIL) |category| NIL 137747 NIL) (|AbstractSyntaxCategory&| 137026 137116 137349 "ASTCAT-" NIL ASTCAT- (NIL T) |package| NIL NIL NIL) (|ArrayStack| 135323 136741 136895 "ASTACK" NIL ASTACK (NIL T) |domain| NIL NIL NIL) (|AssociatedEquations| 133646 134013 134550 "ASSOCEQ" NIL ASSOCEQ (NIL T T) |package| NIL NIL NIL) (|TwoDimensionalArray| 131815 133499 133641 "ARRAY2" NIL ARRAY2 (NIL T) |domain| NIL NIL NIL) (|OneDimensionalArrayFunctions2| 130661 130878 131211 "ARRAY12" NIL ARRAY12 (NIL T T) |package| NIL NIL NIL) (|OneDimensionalArray| 127260 130168 130422 "ARRAY1" NIL ARRAY1 (NIL T) |domain| NIL NIL NIL) (|TwoDimensionalArrayCategory| 118326 120856 121028 "ARR2CAT" 125623 ARR2CAT (NIL T T T) |category| NIL 126666 NIL) (|TwoDimensionalArrayCategory&| 117063 117565 118321 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) |package| NIL NIL NIL) (|Arity| 116296 116713 116927 "ARITY" NIL ARITY (NIL) |domain| NIL NIL NIL) (|ApplyRules| 114929 115120 115534 "APPRULE" NIL APPRULE (NIL T T T) |package| NIL NIL NIL) (|ApplyUnivariateSkewPolynomial| 114375 114438 114679 "APPLYORE" NIL APPLYORE (NIL T T T) |package| NIL NIL NIL) (|AnyFunctions1| 113537 113718 113970 "ANY1" NIL ANY1 (NIL T) |package| NIL NIL NIL) (|Any| 112858 113165 113338 "ANY" NIL ANY (NIL) |domain| NIL NIL NIL) (|AntiSymm| 110447 111717 112231 "ANTISYM" NIL ANTISYM (NIL T NIL) |domain| NIL NIL NIL) (|AnonymousFunction| 109821 110095 110278 "ANON" NIL ANON (NIL) |domain| NIL NIL NIL) (|AlgebraicNumber| 104072 108665 109352 "AN" NIL AN (NIL) |domain| NIL NIL NIL) (|AbelianMonoidRing| 97569 99582 99690 "AMR" 100936 AMR (NIL T T) |category| NIL 101851 NIL) (|AbelianMonoidRing&| 96677 97009 97564 "AMR-" NIL AMR- (NIL T T T) |package| NIL NIL NIL) (|AssociationList| 90987 96553 96672 "ALIST" NIL ALIST (NIL T T) |domain| NIL NIL NIL) (|AlgebraGivenByStructuralConstants| 87323 90396 90725 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) |domain| NIL NIL NIL) (|AlgebraPackage| 84572 85345 86248 "ALGPKG" NIL ALGPKG (NIL T T) |package| NIL NIL NIL) (|AlgebraicMultFact| 83592 83747 84078 "ALGMFACT" NIL ALGMFACT (NIL T T T) |package| NIL NIL NIL) (|AlgebraicManipulations| 80556 81092 81984 "ALGMANIP" NIL ALGMANIP (NIL T T) |package| NIL NIL NIL) (|AlgebraicFunctionField| 72902 79915 80233 "ALGFF" NIL ALGFF (NIL T T T NIL) |domain| NIL NIL NIL) (|AlgFactor| 72086 72270 72559 "ALGFACT" NIL ALGFACT (NIL T) |package| NIL NIL NIL) (|Algebra| 70332 71307 71376 "ALGEBRA" 71381 ALGEBRA (NIL T) |category| NIL 71441 NIL) (|Algebra&| 70017 70110 70327 "ALGEBRA-" NIL ALGEBRA- (NIL T T) |package| NIL NIL NIL) (|AssociationListAggregate| 44166 66656 66776 "ALAGG" 66999 ALAGG (NIL T T) |category| |AssociationList| 67252 NIL) (|ArcHyperbolicFunctionCategory| 43290 43451 43539 "AHYP" 43980 AHYP (NIL) |category| NIL NIL NIL) (|Aggregate| 42527 42680 42728 "AGG" 43060 AGG (NIL) |category| NIL 43257 NIL) (|Aggregate&| 42297 42364 42522 "AGG-" NIL AGG- (NIL T) |package| NIL NIL NIL) (|AlgebraicFunction| 39865 40360 40982 "AF" NIL AF (NIL T T) |package| NIL NIL NIL) (|AddAst| 39317 39616 39758 "ADDAST" NIL ADDAST (NIL) |domain| NIL NIL NIL) (|PlaneAlgebraicCurvePlot| 38424 38758 39038 "ACPLOT" NIL ACPLOT (NIL) |domain| NIL NIL NIL) (|AlgebraicallyClosedFunctionSpace| 22471 33054 33172 "ACFS" 34395 ACFS (NIL T) |category| |Expression| 34778 NIL) (|AlgebraicallyClosedFunctionSpace&| 21103 21579 22466 "ACFS-" NIL ACFS- (NIL T T) |package| NIL NIL NIL) (|AlgebraicallyClosedField| 14337 17403 17481 "ACF" 19214 ACF (NIL) |category| NIL 20010 NIL) (|AlgebraicallyClosedField&| 13404 13760 14332 "ACF-" NIL ACF- (NIL T) |package| NIL NIL NIL) (|AbelianSemiGroup| 12697 12963 13025 "ABELSG" 13184 ABELSG (NIL) |category| NIL 13292 NIL) (|AbelianSemiGroup&| 12504 12548 12692 "ABELSG-" NIL ABELSG- (NIL T) |package| NIL NIL NIL) (|AbelianMonoid| 11228 11668 11724 "ABELMON" 12123 ABELMON (NIL) |category| NIL 12365 NIL) (|AbelianMonoid&| 10731 10918 11223 "ABELMON-" NIL ABELMON- (NIL T) |package| NIL NIL NIL) (|AbelianGroup| 9641 10204 10258 "ABELGRP" 10364 ABELGRP (NIL) |category| NIL 10496 NIL) (|AbelianGroup&| 8995 9248 9636 "ABELGRP-" NIL ABELGRP- (NIL T) |package| NIL NIL NIL) (|OneDimensionalArrayAggregate| 3204 7708 7808 "A1AGG" 7813 A1AGG (NIL T) |category| NIL 7891 NIL) (|OneDimensionalArrayAggregate&| 30 1394 3199 "A1AGG-" NIL A1AGG- (NIL T T) |package| NIL NIL NIL))
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