NewSparseMultivariatePolynomial(R, VarSet)ΒΆ

newpoly.spad line 1325

A post-facto extension for SMP in order to speed up operations related to pseudo-division and gcd. This domain is based on the NSUP constructor which is itself a post-facto extension of the SUP constructor.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, Fraction Integer) -> % if R has Algebra Fraction Integer
from RightModule Fraction Integer
*: (%, R) -> %
from RightModule R
*: (Fraction Integer, %) -> % if R has Algebra Fraction Integer
from LeftModule Fraction Integer
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
*: (R, %) -> %
from LeftModule R
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
/: (%, R) -> % if R has Field
from AbelianMonoidRing(R, IndexedExponents VarSet)
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associates?: (%, %) -> Boolean if R has EntireRing
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
binomThmExpt: (%, %, NonNegativeInteger) -> % if % has CommutativeRing
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero
from CharacteristicNonZero
coefficient: (%, IndexedExponents VarSet) -> R
from AbelianMonoidRing(R, IndexedExponents VarSet)
coefficient: (%, List VarSet, List NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
coefficient: (%, VarSet, NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
coefficients: % -> List R
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
coerce: % -> % if R has IntegralDomain
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: % -> Polynomial R if VarSet has ConvertibleTo Symbol
from CoercibleTo Polynomial R
coerce: % -> SparseMultivariatePolynomial(R, VarSet)
from CoercibleTo SparseMultivariatePolynomial(R, VarSet)
coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer or R has Algebra Fraction Integer
from Algebra Fraction Integer
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
from Algebra R
coerce: SparseMultivariatePolynomial(R, VarSet) -> %
from RetractableTo SparseMultivariatePolynomial(R, VarSet)
coerce: VarSet -> %
from RetractableTo VarSet
commutator: (%, %) -> %
from NonAssociativeRng
content: % -> R if R has GcdDomain
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
content: (%, VarSet) -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
convert: % -> InputForm if VarSet has ConvertibleTo InputForm and R has ConvertibleTo InputForm
from ConvertibleTo InputForm
convert: % -> Pattern Float if VarSet has ConvertibleTo Pattern Float and R has ConvertibleTo Pattern Float
from ConvertibleTo Pattern Float
convert: % -> Pattern Integer if VarSet has ConvertibleTo Pattern Integer and R has ConvertibleTo Pattern Integer
from ConvertibleTo Pattern Integer
convert: % -> Polynomial R if VarSet has ConvertibleTo Symbol
from ConvertibleTo Polynomial R
convert: % -> String if R has RetractableTo Integer and VarSet has ConvertibleTo Symbol
from ConvertibleTo String
convert: Polynomial Fraction Integer -> % if VarSet has ConvertibleTo Symbol and R has Algebra Fraction Integer
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
convert: Polynomial Integer -> % if VarSet has ConvertibleTo Symbol and R has Algebra Integer
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
convert: Polynomial R -> % if VarSet has ConvertibleTo Symbol
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
D: (%, List VarSet) -> %
from PartialDifferentialRing VarSet
D: (%, List VarSet, List NonNegativeInteger) -> %
from PartialDifferentialRing VarSet
D: (%, VarSet) -> %
from PartialDifferentialRing VarSet
D: (%, VarSet, NonNegativeInteger) -> %
from PartialDifferentialRing VarSet
deepestInitial: % -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
deepestTail: % -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
degree: % -> IndexedExponents VarSet
from AbelianMonoidRing(R, IndexedExponents VarSet)
degree: (%, List VarSet) -> List NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
degree: (%, VarSet) -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
differentiate: (%, List VarSet) -> %
from PartialDifferentialRing VarSet
differentiate: (%, List VarSet, List NonNegativeInteger) -> %
from PartialDifferentialRing VarSet
differentiate: (%, VarSet) -> %
from PartialDifferentialRing VarSet
differentiate: (%, VarSet, NonNegativeInteger) -> %
from PartialDifferentialRing VarSet
discriminant: (%, VarSet) -> % if R has CommutativeRing
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
eval: (%, %, %) -> %
from InnerEvalable(%, %)
eval: (%, Equation %) -> %
from Evalable %
eval: (%, List %, List %) -> %
from InnerEvalable(%, %)
eval: (%, List Equation %) -> %
from Evalable %
eval: (%, List VarSet, List %) -> %
from InnerEvalable(VarSet, %)
eval: (%, List VarSet, List R) -> %
from InnerEvalable(VarSet, R)
eval: (%, VarSet, %) -> %
from InnerEvalable(VarSet, %)
eval: (%, VarSet, R) -> %
from InnerEvalable(VarSet, R)
exactQuotient!: (%, %) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
exactQuotient!: (%, R) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
exactQuotient: (%, %) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
exactQuotient: (%, R) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
exquo: (%, %) -> Union(%, failed) if R has EntireRing
from EntireRing
exquo: (%, R) -> Union(%, failed) if R has EntireRing
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
extendedSubResultantGcd: (%, %) -> Record(gcd: %, coef1: %, coef2: %) if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
factor: % -> Factored % if R has PolynomialFactorizationExplicit
from UniqueFactorizationDomain
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
fmecg: (%, IndexedExponents VarSet, R, %) -> %
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
gcd: (%, %) -> % if R has GcdDomain
from GcdDomain
gcd: (R, %) -> R if R has GcdDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
gcd: List % -> % if R has GcdDomain
from GcdDomain
gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has GcdDomain
from PolynomialFactorizationExplicit
ground: % -> R
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
ground?: % -> Boolean
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
halfExtendedSubResultantGcd1: (%, %) -> Record(gcd: %, coef1: %) if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
halfExtendedSubResultantGcd2: (%, %) -> Record(gcd: %, coef2: %) if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
head: % -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
headReduce: (%, %) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
headReduced?: (%, %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
headReduced?: (%, List %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
iexactQuo: (R, R) -> R if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
infRittWu?: (%, %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
init: % -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
initiallyReduce: (%, %) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
initiallyReduced?: (%, %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
initiallyReduced?: (%, List %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
isExpt: % -> Union(Record(var: VarSet, exponent: NonNegativeInteger), failed)
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
isPlus: % -> Union(List %, failed)
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
isTimes: % -> Union(List %, failed)
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
iteratedInitials: % -> List %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lastSubResultant: (%, %) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
latex: % -> String
from SetCategory
LazardQuotient2: (%, %, %, NonNegativeInteger) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
LazardQuotient: (%, %, NonNegativeInteger) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPquo: (%, %) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPquo: (%, %, VarSet) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPrem: (%, %) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPrem: (%, %, VarSet) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPremWithDefault: (%, %) -> Record(coef: %, gap: NonNegativeInteger, remainder: %)
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPremWithDefault: (%, %, VarSet) -> Record(coef: %, gap: NonNegativeInteger, remainder: %)
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPseudoDivide: (%, %) -> Record(coef: %, gap: NonNegativeInteger, quotient: %, remainder: %)
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyPseudoDivide: (%, %, VarSet) -> Record(coef: %, gap: NonNegativeInteger, quotient: %, remainder: %)
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lazyResidueClass: (%, %) -> Record(polnum: %, polden: %, power: NonNegativeInteger)
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
lcm: (%, %) -> % if R has GcdDomain
from GcdDomain
lcm: List % -> % if R has GcdDomain
from GcdDomain
lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if R has GcdDomain
from LeftOreRing
leadingCoefficient: % -> R
from AbelianMonoidRing(R, IndexedExponents VarSet)
leadingCoefficient: (%, VarSet) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
leadingMonomial: % -> %
from AbelianMonoidRing(R, IndexedExponents VarSet)
leastMonomial: % -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
mainCoefficients: % -> List %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
mainContent: % -> % if R has GcdDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
mainMonomial: % -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
mainMonomials: % -> List %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
mainPrimitivePart: % -> % if R has GcdDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
mainSquareFreePart: % -> % if R has GcdDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
mainVariable: % -> Union(VarSet, failed)
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
map: (R -> R, %) -> %
from AbelianMonoidRing(R, IndexedExponents VarSet)
mapExponents: (IndexedExponents VarSet -> IndexedExponents VarSet, %) -> %
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
mdeg: % -> NonNegativeInteger
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
minimumDegree: % -> IndexedExponents VarSet
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
minimumDegree: (%, List VarSet) -> List NonNegativeInteger
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
minimumDegree: (%, VarSet) -> NonNegativeInteger
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
monic?: % -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
monicDivide: (%, %, VarSet) -> Record(quotient: %, remainder: %)
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
monicModulo: (%, %) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
monomial: (%, List VarSet, List NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
monomial: (%, VarSet, NonNegativeInteger) -> %
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
monomial: (R, IndexedExponents VarSet) -> %
from AbelianMonoidRing(R, IndexedExponents VarSet)
monomial?: % -> Boolean
from AbelianMonoidRing(R, IndexedExponents VarSet)
monomials: % -> List %
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
multivariate: (SparseUnivariatePolynomial %, VarSet) -> %
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
multivariate: (SparseUnivariatePolynomial R, VarSet) -> %
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
mvar: % -> VarSet
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
next_subResultant2: (%, %, %, %) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
normalized?: (%, %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
normalized?: (%, List %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
numberOfMonomials: % -> NonNegativeInteger
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if VarSet has PatternMatchable Float and R has PatternMatchable Float
from PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if VarSet has PatternMatchable Integer and R has PatternMatchable Integer
from PatternMatchable Integer
pomopo!: (%, R, IndexedExponents VarSet, %) -> %
from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)
pquo: (%, %) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
pquo: (%, %, VarSet) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
prem: (%, %) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
prem: (%, %, VarSet) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
prime?: % -> Boolean if R has PolynomialFactorizationExplicit
from UniqueFactorizationDomain
primitiveMonomials: % -> List %
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
primitivePart!: % -> % if R has GcdDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
primitivePart: % -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
primitivePart: (%, VarSet) -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
primPartElseUnitCanonical!: % -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
primPartElseUnitCanonical: % -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
pseudoDivide: (%, %) -> Record(quotient: %, remainder: %)
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
quasiMonic?: % -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
recip: % -> Union(%, failed)
from MagmaWithUnit
reduced?: (%, %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
reduced?: (%, List %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if R has LinearlyExplicitOver Integer
from LinearlyExplicitOver Integer
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix R, vec: Vector R)
from LinearlyExplicitOver R
reducedSystem: Matrix % -> Matrix Integer if R has LinearlyExplicitOver Integer
from LinearlyExplicitOver Integer
reducedSystem: Matrix % -> Matrix R
from LinearlyExplicitOver R
reductum: % -> %
from AbelianMonoidRing(R, IndexedExponents VarSet)
reductum: (%, VarSet) -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
resultant: (%, %) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
resultant: (%, %, VarSet) -> % if R has CommutativeRing
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
retract: % -> Fraction Integer if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
retract: % -> Integer if R has RetractableTo Integer
from RetractableTo Integer
retract: % -> R
from RetractableTo R
retract: % -> SparseMultivariatePolynomial(R, VarSet)
from RetractableTo SparseMultivariatePolynomial(R, VarSet)
retract: % -> VarSet
from RetractableTo VarSet
retract: Polynomial Fraction Integer -> % if VarSet has ConvertibleTo Symbol and R has Algebra Fraction Integer
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
retract: Polynomial Integer -> % if VarSet has ConvertibleTo Symbol and R has Algebra Integer
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
retract: Polynomial R -> % if VarSet has ConvertibleTo Symbol
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
retractIfCan: % -> Union(Fraction Integer, failed) if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
retractIfCan: % -> Union(Integer, failed) if R has RetractableTo Integer
from RetractableTo Integer
retractIfCan: % -> Union(R, failed)
from RetractableTo R
retractIfCan: % -> Union(SparseMultivariatePolynomial(R, VarSet), failed)
from RetractableTo SparseMultivariatePolynomial(R, VarSet)
retractIfCan: % -> Union(VarSet, failed)
from RetractableTo VarSet
retractIfCan: Polynomial Fraction Integer -> Union(%, failed) if VarSet has ConvertibleTo Symbol and R has Algebra Fraction Integer
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
retractIfCan: Polynomial Integer -> Union(%, failed) if VarSet has ConvertibleTo Symbol and R has Algebra Integer
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
retractIfCan: Polynomial R -> Union(%, failed) if VarSet has ConvertibleTo Symbol
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
RittWuCompare: (%, %) -> Union(Boolean, failed)
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
sample: %
from AbelianMonoid
smaller?: (%, %) -> Boolean if R has Comparable
from Comparable
solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
squareFree: % -> Factored % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
squareFreePart: % -> % if R has GcdDomain
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
subResultantChain: (%, %) -> List % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
subResultantGcd: (%, %) -> % if R has IntegralDomain
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
supRittWu?: (%, %) -> Boolean
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
tail: % -> %
from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)
totalDegree: % -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
totalDegree: (%, List VarSet) -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
totalDegreeSorted: (%, List VarSet) -> NonNegativeInteger
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
unit?: % -> Boolean if R has EntireRing
from EntireRing
unitCanonical: % -> % if R has EntireRing
from EntireRing
unitNormal: % -> Record(unit: %, canonical: %, associate: %) if R has EntireRing
from EntireRing
univariate: % -> SparseUnivariatePolynomial R
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
univariate: (%, VarSet) -> SparseUnivariatePolynomial %
from PolynomialCategory(R, IndexedExponents VarSet, VarSet)
variables: % -> List VarSet
from MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(R, IndexedExponents VarSet)

AbelianSemiGroup

Algebra % if R has IntegralDomain

Algebra Fraction Integer if R has Algebra Fraction Integer

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer) if R has Algebra Fraction Integer

BiModule(R, R)

CancellationAbelianMonoid

canonicalUnitNormal if R has canonicalUnitNormal

CharacteristicNonZero if R has CharacteristicNonZero

CharacteristicZero if R has CharacteristicZero

CoercibleTo OutputForm

CoercibleTo Polynomial R if VarSet has ConvertibleTo Symbol

CoercibleTo SparseMultivariatePolynomial(R, VarSet)

CommutativeRing if R has CommutativeRing

CommutativeStar if R has CommutativeRing

Comparable if R has Comparable

ConvertibleTo InputForm if VarSet has ConvertibleTo InputForm and R has ConvertibleTo InputForm

ConvertibleTo Pattern Float if VarSet has ConvertibleTo Pattern Float and R has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if VarSet has ConvertibleTo Pattern Integer and R has ConvertibleTo Pattern Integer

ConvertibleTo Polynomial R if VarSet has ConvertibleTo Symbol

ConvertibleTo String if R has RetractableTo Integer and VarSet has ConvertibleTo Symbol

EntireRing if R has EntireRing

Evalable %

FiniteAbelianMonoidRing(R, IndexedExponents VarSet)

FullyLinearlyExplicitOver R

FullyRetractableTo R

GcdDomain if R has GcdDomain

InnerEvalable(%, %)

InnerEvalable(VarSet, %)

InnerEvalable(VarSet, R)

IntegralDomain if R has IntegralDomain

LeftModule %

LeftModule Fraction Integer if R has Algebra Fraction Integer

LeftModule R

LeftOreRing if R has GcdDomain

LinearlyExplicitOver Integer if R has LinearlyExplicitOver Integer

LinearlyExplicitOver R

Magma

MagmaWithUnit

MaybeSkewPolynomialCategory(R, IndexedExponents VarSet, VarSet)

Module % if R has IntegralDomain

Module Fraction Integer if R has Algebra Fraction Integer

Module R if R has CommutativeRing

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has EntireRing

PartialDifferentialRing VarSet

PatternMatchable Float if VarSet has PatternMatchable Float and R has PatternMatchable Float

PatternMatchable Integer if VarSet has PatternMatchable Integer and R has PatternMatchable Integer

PolynomialCategory(R, IndexedExponents VarSet, VarSet)

PolynomialFactorizationExplicit if R has PolynomialFactorizationExplicit

RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer

RetractableTo Integer if R has RetractableTo Integer

RetractableTo R

RetractableTo SparseMultivariatePolynomial(R, VarSet)

RetractableTo VarSet

RightModule %

RightModule Fraction Integer if R has Algebra Fraction Integer

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

UniqueFactorizationDomain if R has PolynomialFactorizationExplicit

unitsKnown

VariablesCommuteWithCoefficients