LaurentPolynomial(R, UP)ΒΆ
gpol.spad line 1 [edit on github]
Univariate polynomials with negative and positive exponents. Author: Manuel Bronstein Date Created: May 1988
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from Magma
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- charthRoot: % -> Union(%, failed) if R has CharacteristicNonZero
- coefficient: (%, Integer) -> R
coefficient(x, n)undocumented
- coerce: % -> %
from Algebra %
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer
from CoercibleFrom Fraction Integer
- coerce: Integer -> %
from NonAssociativeRing
- coerce: R -> %
from CoercibleFrom R
- coerce: UP -> %
from CoercibleFrom UP
- commutator: (%, %) -> %
from NonAssociativeRng
- convert: % -> Fraction UP
from ConvertibleTo Fraction UP
- D: % -> %
from DifferentialRing
- D: (%, List Symbol) -> %
- D: (%, List Symbol, List NonNegativeInteger) -> %
- D: (%, NonNegativeInteger) -> %
from DifferentialRing
- D: (%, Symbol) -> %
- D: (%, Symbol, NonNegativeInteger) -> %
- D: (%, UP -> UP) -> %
from DifferentialExtension UP
- D: (%, UP -> UP, NonNegativeInteger) -> %
from DifferentialExtension UP
- degree: % -> Integer
degree(x)undocumented
- differentiate: % -> %
from DifferentialRing
- differentiate: (%, List Symbol) -> %
- differentiate: (%, List Symbol, List NonNegativeInteger) -> %
- differentiate: (%, NonNegativeInteger) -> %
from DifferentialRing
- differentiate: (%, Symbol) -> %
- differentiate: (%, Symbol, NonNegativeInteger) -> %
- differentiate: (%, UP -> UP) -> %
from DifferentialExtension UP
- differentiate: (%, UP -> UP, NonNegativeInteger) -> %
from DifferentialExtension UP
- divide: (%, %) -> Record(quotient: %, remainder: %) if R has Field
from EuclideanDomain
- euclideanSize: % -> NonNegativeInteger if R has Field
from EuclideanDomain
- expressIdealMember: (List %, %) -> Union(List %, failed) if R has Field
from PrincipalIdealDomain
- exquo: (%, %) -> Union(%, failed)
from EntireRing
- extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %) if R has Field
from EuclideanDomain
- extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed) if R has Field
from EuclideanDomain
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if R has Field
from GcdDomain
- latex: % -> String
from SetCategory
- lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if R has Field
from LeftOreRing
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- monomial?: % -> Boolean
monomial?(x)undocumented
- monomial: (R, Integer) -> %
monomial(x, n)undocumented
- multiEuclidean: (List %, %) -> Union(List %, failed) if R has Field
from EuclideanDomain
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- order: % -> Integer
order(x)undocumented
- plenaryPower: (%, PositiveInteger) -> %
from NonAssociativeAlgebra %
- principalIdeal: List % -> Record(coef: List %, generator: %) if R has Field
from PrincipalIdealDomain
- quo: (%, %) -> % if R has Field
from EuclideanDomain
- recip: % -> Union(%, failed)
from MagmaWithUnit
- reductum: % -> %
reductum(x)undocumented
- rem: (%, %) -> % if R has Field
from EuclideanDomain
- 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: % -> UP
from RetractableTo UP
- 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(UP, failed)
from RetractableTo UP
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from AbelianMonoid
- separate: Fraction UP -> Record(polyPart: %, fracPart: Fraction UP) if R has Field
separate(x)undocumented
- sizeLess?: (%, %) -> Boolean if R has Field
from EuclideanDomain
- subtractIfCan: (%, %) -> Union(%, failed)
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
- zero?: % -> Boolean
from AbelianMonoid
Algebra %
BiModule(%, %)
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
EuclideanDomain if R has Field
LeftOreRing if R has Field
Module %
PartialDifferentialRing Symbol
PrincipalIdealDomain if R has Field
RetractableTo Fraction Integer if R has RetractableTo Fraction Integer
RetractableTo Integer if R has RetractableTo Integer