QEtaPolynomialAlgebra(C, P)ΒΆ

qetapolyalg.spad line 105 [edit on github]

QEtaPolynomialAlgebra(C, P) turns a univariate polynomial algebra P inte a QEtaAlgebra.

0: %

from QEtaAlgebra C

1: %

from QEtaAlgebra C

*: (%, %) -> %

from QEtaAlgebra C

*: (%, C) -> %

from RightModule C

*: (%, Fraction Integer) -> % if C has Algebra Fraction Integer

from RightModule Fraction Integer

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

from RightModule Integer

*: (C, %) -> %

from QEtaAlgebra C

*: (Fraction Integer, %) -> % if C has Algebra Fraction Integer

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from QEtaAlgebra C

-: % -> %

from QEtaAlgebra C

-: (%, %) -> %

from QEtaAlgebra C

/: (%, C) -> % if C has Field

from AbelianMonoidRing(C, NonNegativeInteger)

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from QEtaAlgebra C

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean if C has EntireRing

from EntireRing

associator: (%, %, %) -> %

from NonAssociativeRng

binomThmExpt: (%, %, NonNegativeInteger) -> %

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

charthRoot: % -> Union(%, failed) if C has CharacteristicNonZero or % has CharacteristicNonZero and C has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

coefficient: (%, List SingletonAsOrderedSet, List NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

coefficient: (%, NonNegativeInteger) -> C

from FreeModuleCategory(C, NonNegativeInteger)

coefficient: (%, SingletonAsOrderedSet, NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

coefficients: % -> List C

from FreeModuleCategory(C, NonNegativeInteger)

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: % -> P

coerce(x) returns the element x as a univariate polynomial.

coerce: C -> %

from CoercibleFrom C

coerce: Fraction Integer -> % if C has Algebra Fraction Integer or C has RetractableTo Fraction Integer

from CoercibleFrom Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: P -> %

coerce(x) turns a univariate polynomial into this domain. No check is made.

coerce: SingletonAsOrderedSet -> %

from CoercibleFrom SingletonAsOrderedSet

commutator: (%, %) -> %

from NonAssociativeRng

composite: (%, %) -> Union(%, failed) if C has IntegralDomain

from UnivariatePolynomialCategory C

composite: (Fraction %, %) -> Union(Fraction %, failed) if C has IntegralDomain

from UnivariatePolynomialCategory C

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

from PolynomialFactorizationExplicit

construct: List Record(k: NonNegativeInteger, c: C) -> %

from IndexedProductCategory(C, NonNegativeInteger)

constructOrdered: List Record(k: NonNegativeInteger, c: C) -> %

from IndexedProductCategory(C, NonNegativeInteger)

content: % -> C if C has GcdDomain

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

content: (%, SingletonAsOrderedSet) -> % if C has GcdDomain

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

convert: % -> InputForm if C has ConvertibleTo InputForm and SingletonAsOrderedSet has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float if C has ConvertibleTo Pattern Float and SingletonAsOrderedSet has ConvertibleTo Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer if C has ConvertibleTo Pattern Integer and SingletonAsOrderedSet has ConvertibleTo Pattern Integer

from ConvertibleTo Pattern Integer

D: % -> %

from DifferentialRing

D: (%, C -> C) -> %

from DifferentialExtension C

D: (%, C -> C, NonNegativeInteger) -> %

from DifferentialExtension C

D: (%, List SingletonAsOrderedSet) -> %

from PartialDifferentialRing SingletonAsOrderedSet

D: (%, List SingletonAsOrderedSet, List NonNegativeInteger) -> %

from PartialDifferentialRing SingletonAsOrderedSet

D: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, SingletonAsOrderedSet) -> %

from PartialDifferentialRing SingletonAsOrderedSet

D: (%, SingletonAsOrderedSet, NonNegativeInteger) -> %

from PartialDifferentialRing SingletonAsOrderedSet

D: (%, Symbol) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

degree: % -> NonNegativeInteger

from AbelianMonoidRing(C, NonNegativeInteger)

degree: (%, List SingletonAsOrderedSet) -> List NonNegativeInteger

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

degree: (%, SingletonAsOrderedSet) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

differentiate: % -> %

from DifferentialRing

differentiate: (%, C -> C) -> %

from DifferentialExtension C

differentiate: (%, C -> C, %) -> %

from UnivariatePolynomialCategory C

differentiate: (%, C -> C, NonNegativeInteger) -> %

from DifferentialExtension C

differentiate: (%, List SingletonAsOrderedSet) -> %

from PartialDifferentialRing SingletonAsOrderedSet

differentiate: (%, List SingletonAsOrderedSet, List NonNegativeInteger) -> %

from PartialDifferentialRing SingletonAsOrderedSet

differentiate: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, SingletonAsOrderedSet) -> %

from PartialDifferentialRing SingletonAsOrderedSet

differentiate: (%, SingletonAsOrderedSet, NonNegativeInteger) -> %

from PartialDifferentialRing SingletonAsOrderedSet

differentiate: (%, Symbol) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

discriminant: % -> C

from UnivariatePolynomialCategory C

discriminant: (%, SingletonAsOrderedSet) -> %

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

divide: (%, %) -> Record(quotient: %, remainder: %) if C has Field

from EuclideanDomain

divideExponents: (%, NonNegativeInteger) -> Union(%, failed)

from UnivariatePolynomialCategory C

elt: (%, %) -> %

from Eltable(%, %)

elt: (%, C) -> C

from Eltable(C, C)

elt: (%, Fraction %) -> Fraction % if C has IntegralDomain

from Eltable(Fraction %, Fraction %)

elt: (Fraction %, C) -> C if C has Field

from UnivariatePolynomialCategory C

elt: (Fraction %, Fraction %) -> Fraction % if C has IntegralDomain

from UnivariatePolynomialCategory C

euclideanSize: % -> NonNegativeInteger if C has Field

from EuclideanDomain

eval: (%, %, %) -> %

from InnerEvalable(%, %)

eval: (%, Equation %) -> %

from Evalable %

eval: (%, List %, List %) -> %

from InnerEvalable(%, %)

eval: (%, List Equation %) -> %

from Evalable %

eval: (%, List SingletonAsOrderedSet, List %) -> %

from InnerEvalable(SingletonAsOrderedSet, %)

eval: (%, List SingletonAsOrderedSet, List C) -> %

from InnerEvalable(SingletonAsOrderedSet, C)

eval: (%, SingletonAsOrderedSet, %) -> %

from InnerEvalable(SingletonAsOrderedSet, %)

eval: (%, SingletonAsOrderedSet, C) -> %

from InnerEvalable(SingletonAsOrderedSet, C)

expressIdealMember: (List %, %) -> Union(List %, failed) if C has Field

from PrincipalIdealDomain

exquo: (%, %) -> Union(%, failed) if C has EntireRing

from EntireRing

exquo: (%, C) -> Union(%, failed) if C has EntireRing

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %) if C has Field

from EuclideanDomain

extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed) if C has Field

from EuclideanDomain

factor: % -> Factored % if C has PolynomialFactorizationExplicit

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if C has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if C has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

fmecg: (%, NonNegativeInteger, C, %) -> %

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

gcd: (%, %) -> % if C has GcdDomain

from GcdDomain

gcd: List % -> % if C has GcdDomain

from GcdDomain

gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if C has GcdDomain

from GcdDomain

ground?: % -> Boolean

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

ground: % -> C

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

hash: % -> SingleInteger if C has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if C has Hashable

from Hashable

init: % if C has StepThrough

from StepThrough

integrate: % -> % if C has Algebra Fraction Integer

from UnivariatePolynomialCategory C

isExpt: % -> Union(Record(var: SingletonAsOrderedSet, exponent: NonNegativeInteger), failed)

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

isPlus: % -> Union(List %, failed)

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

isTimes: % -> Union(List %, failed)

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

karatsubaDivide: (%, NonNegativeInteger) -> Record(quotient: %, remainder: %)

from UnivariatePolynomialCategory C

latex: % -> String

from SetCategory

lcm: (%, %) -> % if C has GcdDomain

from GcdDomain

lcm: List % -> % if C has GcdDomain

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if C has GcdDomain

from LeftOreRing

leadingCoefficient: % -> C

from IndexedProductCategory(C, NonNegativeInteger)

leadingMonomial: % -> %

from IndexedProductCategory(C, NonNegativeInteger)

leadingSupport: % -> NonNegativeInteger

from IndexedProductCategory(C, NonNegativeInteger)

leadingTerm: % -> Record(k: NonNegativeInteger, c: C)

from IndexedProductCategory(C, NonNegativeInteger)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

linearExtend: (NonNegativeInteger -> C, %) -> C

from FreeModuleCategory(C, NonNegativeInteger)

listOfTerms: % -> List Record(k: NonNegativeInteger, c: C)

from IndexedDirectProductCategory(C, NonNegativeInteger)

mainVariable: % -> Union(SingletonAsOrderedSet, failed)

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

makeSUP: % -> SparseUnivariatePolynomial C

from UnivariatePolynomialCategory C

map: (C -> C, %) -> %

from IndexedProductCategory(C, NonNegativeInteger)

mapExponents: (NonNegativeInteger -> NonNegativeInteger, %) -> %

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

minimumDegree: % -> NonNegativeInteger

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

minimumDegree: (%, List SingletonAsOrderedSet) -> List NonNegativeInteger

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

minimumDegree: (%, SingletonAsOrderedSet) -> NonNegativeInteger

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

monicDivide: (%, %) -> Record(quotient: %, remainder: %)

from UnivariatePolynomialCategory C

monicDivide: (%, %, SingletonAsOrderedSet) -> Record(quotient: %, remainder: %)

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

monomial?: % -> Boolean

from IndexedProductCategory(C, NonNegativeInteger)

monomial: (%, List SingletonAsOrderedSet, List NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

monomial: (%, SingletonAsOrderedSet, NonNegativeInteger) -> %

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

monomial: (C, NonNegativeInteger) -> %

from IndexedProductCategory(C, NonNegativeInteger)

monomials: % -> List %

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

multiEuclidean: (List %, %) -> Union(List %, failed) if C has Field

from EuclideanDomain

multiplyExponents: (%, NonNegativeInteger) -> %

from UnivariatePolynomialCategory C

multivariate: (SparseUnivariatePolynomial %, SingletonAsOrderedSet) -> %

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

multivariate: (SparseUnivariatePolynomial C, SingletonAsOrderedSet) -> %

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

nextItem: % -> Union(%, failed) if C has StepThrough

from StepThrough

numberOfMonomials: % -> NonNegativeInteger

from IndexedDirectProductCategory(C, NonNegativeInteger)

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: (%, %) -> NonNegativeInteger if C has IntegralDomain

from UnivariatePolynomialCategory C

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if C has PatternMatchable Float and SingletonAsOrderedSet has PatternMatchable Float

from PatternMatchable Float

patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if C has PatternMatchable Integer and SingletonAsOrderedSet has PatternMatchable Integer

from PatternMatchable Integer

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

pomopo!: (%, C, NonNegativeInteger, %) -> %

from FiniteAbelianMonoidRing(C, NonNegativeInteger)

prime?: % -> Boolean if C has PolynomialFactorizationExplicit

from UniqueFactorizationDomain

primitiveMonomials: % -> List %

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

primitivePart: % -> % if C has GcdDomain

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

primitivePart: (%, SingletonAsOrderedSet) -> % if C has GcdDomain

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

principalIdeal: List % -> Record(coef: List %, generator: %) if C has Field

from PrincipalIdealDomain

pseudoDivide: (%, %) -> Record(coef: C, quotient: %, remainder: %) if C has IntegralDomain

from UnivariatePolynomialCategory C

pseudoQuotient: (%, %) -> % if C has IntegralDomain

from UnivariatePolynomialCategory C

pseudoRemainder: (%, %) -> %

from UnivariatePolynomialCategory C

qetaCoefficient: (%, Integer) -> C

from QEtaGradedAlgebra C

qetaGrade: % -> Integer

from QEtaGradedAlgebra C

qetaLeadingCoefficient: % -> C

from QEtaGradedAlgebra C

quo: (%, %) -> % if C has Field

from EuclideanDomain

recip: % -> Union(%, failed)

from MagmaWithUnit

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix C, vec: Vector C)

from LinearlyExplicitOver C

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if C has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix C

from LinearlyExplicitOver C

reducedSystem: Matrix % -> Matrix Integer if C has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reductum: % -> %

from IndexedProductCategory(C, NonNegativeInteger)

rem: (%, %) -> % if C has Field

from EuclideanDomain

resultant: (%, %) -> C

from UnivariatePolynomialCategory C

resultant: (%, %, SingletonAsOrderedSet) -> %

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

retract: % -> C

from RetractableTo C

retract: % -> Fraction Integer if C has RetractableTo Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer if C has RetractableTo Integer

from RetractableTo Integer

retract: % -> SingletonAsOrderedSet

from RetractableTo SingletonAsOrderedSet

retractIfCan: % -> Union(C, failed)

from RetractableTo C

retractIfCan: % -> Union(Fraction Integer, failed) if C has RetractableTo Fraction Integer

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed) if C has RetractableTo Integer

from RetractableTo Integer

retractIfCan: % -> Union(SingletonAsOrderedSet, failed)

from RetractableTo SingletonAsOrderedSet

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

separate: (%, %) -> Record(primePart: %, commonPart: %) if C has GcdDomain

from UnivariatePolynomialCategory C

shiftLeft: (%, NonNegativeInteger) -> %

from UnivariatePolynomialCategory C

shiftRight: (%, NonNegativeInteger) -> %

from UnivariatePolynomialCategory C

sizeLess?: (%, %) -> Boolean if C has Field

from EuclideanDomain

smaller?: (%, %) -> Boolean if C has Comparable

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if C has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

squareFree: % -> Factored % if C has GcdDomain

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

squareFreePart: % -> % if C has GcdDomain

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if C has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

subResultantGcd: (%, %) -> % if C has IntegralDomain

from UnivariatePolynomialCategory C

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

support: % -> List NonNegativeInteger

from FreeModuleCategory(C, NonNegativeInteger)

totalDegree: % -> NonNegativeInteger

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

totalDegree: (%, List SingletonAsOrderedSet) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

totalDegreeSorted: (%, List SingletonAsOrderedSet) -> NonNegativeInteger

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

traceout: NonNegativeInteger -> % -> OutputForm

from QEtaAlgebra C

unit?: % -> Boolean if C has EntireRing

from EntireRing

unitCanonical: % -> % if C has EntireRing

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %) if C has EntireRing

from EntireRing

univariate: % -> SparseUnivariatePolynomial C

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

univariate: (%, SingletonAsOrderedSet) -> SparseUnivariatePolynomial %

from PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

unmakeSUP: SparseUnivariatePolynomial C -> %

from UnivariatePolynomialCategory C

unvectorise: Vector C -> %

from UnivariatePolynomialCategory C

variables: % -> List SingletonAsOrderedSet

from MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

vectorise: (%, NonNegativeInteger) -> Vector C

from UnivariatePolynomialCategory C

zero?: % -> Boolean

from QEtaAlgebra C

AbelianGroup

AbelianMonoid

AbelianMonoidRing(C, NonNegativeInteger)

AbelianProductCategory C

AbelianSemiGroup

additiveValuation if C has Field

Algebra %

Algebra C

Algebra Fraction Integer if C has Algebra Fraction Integer

BasicType

BiModule(%, %)

BiModule(C, C)

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

CancellationAbelianMonoid

canonicalUnitNormal if C has canonicalUnitNormal

CharacteristicNonZero if C has CharacteristicNonZero

CharacteristicZero if C has CharacteristicZero

CoercibleFrom C

CoercibleFrom Fraction Integer if C has RetractableTo Fraction Integer

CoercibleFrom Integer if C has RetractableTo Integer

CoercibleFrom SingletonAsOrderedSet

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable if C has Comparable

ConvertibleTo InputForm if C has ConvertibleTo InputForm and SingletonAsOrderedSet has ConvertibleTo InputForm

ConvertibleTo Pattern Float if C has ConvertibleTo Pattern Float and SingletonAsOrderedSet has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if C has ConvertibleTo Pattern Integer and SingletonAsOrderedSet has ConvertibleTo Pattern Integer

DifferentialExtension C

DifferentialRing

Eltable(%, %)

Eltable(C, C)

Eltable(Fraction %, Fraction %) if C has IntegralDomain

EntireRing if C has EntireRing

EuclideanDomain if C has Field

Evalable %

FiniteAbelianMonoidRing(C, NonNegativeInteger)

FreeModuleCategory(C, NonNegativeInteger)

FullyLinearlyExplicitOver C

FullyRetractableTo C

GcdDomain if C has GcdDomain

Hashable if C has Hashable

IndexedDirectProductCategory(C, NonNegativeInteger)

IndexedProductCategory(C, NonNegativeInteger)

InnerEvalable(%, %)

InnerEvalable(SingletonAsOrderedSet, %)

InnerEvalable(SingletonAsOrderedSet, C)

IntegralDomain if C has IntegralDomain

LeftModule %

LeftModule C

LeftModule Fraction Integer if C has Algebra Fraction Integer

LeftOreRing if C has GcdDomain

LinearlyExplicitOver C

LinearlyExplicitOver Integer if C has LinearlyExplicitOver Integer

Magma

MagmaWithUnit

MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

Module %

Module C

Module Fraction Integer if C has Algebra Fraction Integer

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra C

NonAssociativeAlgebra Fraction Integer if C has Algebra Fraction Integer

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if C has EntireRing

PartialDifferentialRing SingletonAsOrderedSet

PartialDifferentialRing Symbol if C has PartialDifferentialRing Symbol

PatternMatchable Float if C has PatternMatchable Float and SingletonAsOrderedSet has PatternMatchable Float

PatternMatchable Integer if C has PatternMatchable Integer and SingletonAsOrderedSet has PatternMatchable Integer

PolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

PolynomialFactorizationExplicit if C has PolynomialFactorizationExplicit

PrincipalIdealDomain if C has Field

QEtaAlgebra C

QEtaGradedAlgebra C

RetractableTo C

RetractableTo Fraction Integer if C has RetractableTo Fraction Integer

RetractableTo Integer if C has RetractableTo Integer

RetractableTo SingletonAsOrderedSet

RightModule %

RightModule C

RightModule Fraction Integer if C has Algebra Fraction Integer

RightModule Integer if C has LinearlyExplicitOver Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if C has StepThrough

TwoSidedRecip

UniqueFactorizationDomain if C has PolynomialFactorizationExplicit

unitsKnown

UnivariatePolynomialCategory C

VariablesCommuteWithCoefficients