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)
- ^: (%, NonNegativeInteger) -> %
from QEtaAlgebra C
- ^: (%, PositiveInteger) -> %
from Magma
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associates?: (%, %) -> Boolean if C has EntireRing
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- binomThmExpt: (%, %, NonNegativeInteger) -> %
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- charthRoot: % -> Union(%, failed) if C has CharacteristicNonZero or % has CharacteristicNonZero and C has 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 elementx
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 -> %
- 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
- 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
- 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) -> %
- D: (%, List SingletonAsOrderedSet, List NonNegativeInteger) -> %
- D: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol
- D: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol
- D: (%, NonNegativeInteger) -> %
from DifferentialRing
- D: (%, SingletonAsOrderedSet) -> %
- D: (%, SingletonAsOrderedSet, NonNegativeInteger) -> %
- D: (%, Symbol) -> % if C has PartialDifferentialRing Symbol
- D: (%, Symbol, NonNegativeInteger) -> % if C has 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) -> %
- differentiate: (%, List SingletonAsOrderedSet, List NonNegativeInteger) -> %
- differentiate: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol
- differentiate: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol
- differentiate: (%, NonNegativeInteger) -> %
from DifferentialRing
- differentiate: (%, SingletonAsOrderedSet) -> %
- differentiate: (%, SingletonAsOrderedSet, NonNegativeInteger) -> %
- differentiate: (%, Symbol) -> % if C has PartialDifferentialRing Symbol
- differentiate: (%, Symbol, NonNegativeInteger) -> % if C has 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
- 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
- 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
- factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if C has PolynomialFactorizationExplicit
- factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if C has PolynomialFactorizationExplicit
- fmecg: (%, NonNegativeInteger, C, %) -> %
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if C has GcdDomain
from GcdDomain
- ground: % -> C
- 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
- lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if C has GcdDomain
from LeftOreRing
- leadingCoefficient: % -> C
from IndexedProductCategory(C, NonNegativeInteger)
- leadingMonomial: % -> %
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)
- 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, %) -> %
- minimumDegree: % -> 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
- 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, %) -> %
- prime?: % -> Boolean if C has PolynomialFactorizationExplicit
- 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
- reducedSystem: Matrix % -> Matrix C
from LinearlyExplicitOver C
- reducedSystem: Matrix % -> Matrix Integer if C has 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
- 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)
- 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
- 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
- subResultantGcd: (%, %) -> % if C has IntegralDomain
from UnivariatePolynomialCategory C
- subtractIfCan: (%, %) -> Union(%, failed)
- 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
AbelianMonoidRing(C, NonNegativeInteger)
additiveValuation if C has Field
Algebra %
Algebra C
Algebra Fraction Integer if C has Algebra Fraction Integer
BiModule(%, %)
BiModule(C, C)
BiModule(Fraction Integer, Fraction Integer) if C has Algebra Fraction Integer
canonicalUnitNormal if C has canonicalUnitNormal
CharacteristicNonZero if C has CharacteristicNonZero
CharacteristicZero if C has CharacteristicZero
CoercibleFrom Fraction Integer if C has RetractableTo Fraction Integer
CoercibleFrom Integer if C has RetractableTo Integer
CoercibleFrom SingletonAsOrderedSet
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
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)
IndexedDirectProductCategory(C, NonNegativeInteger)
IndexedProductCategory(C, NonNegativeInteger)
InnerEvalable(%, %)
InnerEvalable(SingletonAsOrderedSet, %)
InnerEvalable(SingletonAsOrderedSet, C)
IntegralDomain if C has IntegralDomain
LeftModule Fraction Integer if C has Algebra Fraction Integer
LeftOreRing if C has GcdDomain
LinearlyExplicitOver Integer if C has LinearlyExplicitOver Integer
MaybeSkewPolynomialCategory(C, NonNegativeInteger, SingletonAsOrderedSet)
Module %
Module C
Module Fraction Integer if C has Algebra Fraction Integer
NonAssociativeAlgebra Fraction Integer if C has Algebra Fraction Integer
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
RetractableTo Fraction Integer if C has RetractableTo Fraction Integer
RetractableTo Integer if C has RetractableTo Integer
RetractableTo SingletonAsOrderedSet
RightModule Fraction Integer if C has Algebra Fraction Integer
RightModule Integer if C has LinearlyExplicitOver Integer
StepThrough if C has StepThrough
UniqueFactorizationDomain if C has PolynomialFactorizationExplicit