NewSparseMultivariatePolynomial(R, VarSet)

newpoly.spad line 1315 [edit on github]

• R: Ring

• VarSet: OrderedSet

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

*: (%, Integer) -> % if R has LinearlyExplicitOver Integer

from RightModule 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 or % has CharacteristicNonZero and R has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

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 FreeModuleCategory(R, IndexedExponents VarSet)

coerce: % -> % if R has CommutativeRing

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 CoercibleFrom SparseMultivariatePolynomial(R, VarSet)

coerce: VarSet -> %

from CoercibleFrom VarSet

commutator: (%, %) -> %

from NonAssociativeRng

conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and R has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

construct: List Record(k: IndexedExponents VarSet, c: R) -> %

from IndexedProductCategory(R, IndexedExponents VarSet)

constructOrdered: List Record(k: IndexedExponents VarSet, c: R) -> %

from IndexedProductCategory(R, IndexedExponents VarSet)

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 R has Algebra Fraction Integer and VarSet has ConvertibleTo Symbol

from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)

convert: Polynomial Integer -> % if R has Algebra Integer and VarSet has ConvertibleTo Symbol

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?: % -> Boolean

from FiniteAbelianMonoidRing(R, IndexedExponents VarSet)

ground: % -> R

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 if VarSet has Hashable and R has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if VarSet has Hashable and R has Hashable

from Hashable

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 IndexedProductCategory(R, IndexedExponents VarSet)

leadingCoefficient: (%, VarSet) -> %

from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)

leadingMonomial: % -> %

from IndexedProductCategory(R, IndexedExponents VarSet)

leadingSupport: % -> IndexedExponents VarSet

from IndexedProductCategory(R, IndexedExponents VarSet)

leadingTerm: % -> Record(k: IndexedExponents VarSet, c: R)

from IndexedProductCategory(R, IndexedExponents VarSet)

leastMonomial: % -> %

from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

linearExtend: (IndexedExponents VarSet -> R, %) -> R if R has CommutativeRing

from FreeModuleCategory(R, IndexedExponents VarSet)

listOfTerms: % -> List Record(k: IndexedExponents VarSet, c: R)

from IndexedDirectProductCategory(R, IndexedExponents VarSet)

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 IndexedProductCategory(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?: % -> Boolean

from IndexedProductCategory(R, IndexedExponents 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 IndexedProductCategory(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 IndexedDirectProductCategory(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

plenaryPower: (%, PositiveInteger) -> % if R has Algebra Fraction Integer or R has CommutativeRing

from NonAssociativeAlgebra %

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 IndexedProductCategory(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 R has Algebra Fraction Integer and VarSet has ConvertibleTo Symbol

from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)

retract: Polynomial Integer -> % if R has Algebra Integer and VarSet has ConvertibleTo Symbol

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 R has Algebra Fraction Integer and VarSet has ConvertibleTo Symbol

from RecursivePolynomialCategory(R, IndexedExponents VarSet, VarSet)

retractIfCan: Polynomial Integer -> Union(%, failed) if R has Algebra Integer and VarSet has ConvertibleTo Symbol

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

support: % -> List IndexedExponents VarSet

from FreeModuleCategory(R, IndexedExponents VarSet)

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)

AbelianProductCategory R

AbelianSemiGroup

Algebra % if R has CommutativeRing

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

CoercibleFrom Fraction Integer if R has RetractableTo Fraction Integer

CoercibleFrom Integer if R has RetractableTo Integer

CoercibleFrom R

CoercibleFrom SparseMultivariatePolynomial(R, VarSet)

CoercibleFrom VarSet

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)

FreeModuleCategory(R, IndexedExponents VarSet)

FullyLinearlyExplicitOver R

FullyRetractableTo R

GcdDomain if R has GcdDomain

Hashable if VarSet has Hashable and R has Hashable

IndexedDirectProductCategory(R, IndexedExponents VarSet)

IndexedProductCategory(R, IndexedExponents VarSet)

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 CommutativeRing

Module Fraction Integer if R has Algebra Fraction Integer

Module R if R has CommutativeRing

Monoid

NonAssociativeAlgebra % if R has CommutativeRing

NonAssociativeAlgebra Fraction Integer if R has Algebra Fraction Integer

NonAssociativeAlgebra R if R has CommutativeRing

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 Integer if R has LinearlyExplicitOver Integer

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip if R has CommutativeRing

UniqueFactorizationDomain if R has PolynomialFactorizationExplicit

unitsKnown

VariablesCommuteWithCoefficients