LaurentPolynomial(R, UP)

gpol.spad line 1 [edit on github]

• R : IntegralDomain
• UP : UnivariatePolynomialCategory(R)

Univariate polynomials with negative and positive exponents.

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

D : % -> %

from DifferentialRing

D : (%, List(Symbol)) -> %

from PartialDifferentialRing(Symbol)

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

from PartialDifferentialRing(Symbol)

D : (%, Mapping(UP, UP)) -> %

from DifferentialExtension(UP)

D : (%, Mapping(UP, UP), NonNegativeInteger) -> %

from DifferentialExtension(UP)

D : (%, NonNegativeInteger) -> %

from DifferentialRing

D : (%, Symbol) -> %

from PartialDifferentialRing(Symbol)

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

from PartialDifferentialRing(Symbol)

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

associates? : (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

charthRoot : % -> Union(%, "failed") if R has CharacteristicNonZero

from CharacteristicNonZero

coefficient : (%, Integer) -> R

coefficient(x, n) is undocumented

coerce : % -> %

from Algebra(%)

coerce : R -> %

from CoercibleFrom(R)

coerce : UP -> %

from CoercibleFrom(UP)

coerce : Fraction(Integer) -> % if R has RetractableTo(Fraction(Integer))

from CoercibleFrom(Fraction(Integer))

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

convert : % -> Fraction(UP)

from ConvertibleTo(Fraction(UP))

degree : % -> Integer

degree(x) is undocumented

differentiate : % -> %

from DifferentialRing

differentiate : (%, List(Symbol)) -> %

from PartialDifferentialRing(Symbol)

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

from PartialDifferentialRing(Symbol)

differentiate : (%, Mapping(UP, UP)) -> %

from DifferentialExtension(UP)

differentiate : (%, Mapping(UP, UP), NonNegativeInteger) -> %

from DifferentialExtension(UP)

differentiate : (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate : (%, Symbol) -> %

from PartialDifferentialRing(Symbol)

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

from PartialDifferentialRing(Symbol)

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

gcd : (%, %) -> % if R has Field

from GcdDomain

gcd : List(%) -> % if R has Field

from GcdDomain

gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has Field

from GcdDomain

latex : % -> String

from SetCategory

lcm : (%, %) -> % if R has Field

from GcdDomain

lcm : List(%) -> % if R has Field

from GcdDomain

lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %) if R has Field

from LeftOreRing

leadingCoefficient : % -> R

leadingCoefficient is undocumented

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

leftRecip : % -> Union(%, "failed")

from MagmaWithUnit

monomial : (R, Integer) -> %

monomial(x, n) is undocumented

monomial? : % -> Boolean

monomial?(x) is undocumented

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

from EuclideanDomain

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

order : % -> Integer

order(x) is 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) is undocumented

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

from EuclideanDomain

retract : % -> R

from RetractableTo(R)

retract : % -> UP

from RetractableTo(UP)

retract : % -> Fraction(Integer) if R has RetractableTo(Fraction(Integer))

from RetractableTo(Fraction(Integer))

retract : % -> Integer if R has RetractableTo(Integer)

from RetractableTo(Integer)

retractIfCan : % -> Union(R, "failed")

from RetractableTo(R)

retractIfCan : % -> Union(UP, "failed")

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)

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) is undocumented

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

from EuclideanDomain

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

from CancellationAbelianMonoid

trailingCoefficient : % -> R

trailingCoefficient is undocumented

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

unitNormal : % -> Record(unit : %, canonical : %, associate : %)

from EntireRing

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CharacteristicNonZero

CoercibleFrom(R)

SetCategory

PrincipalIdealDomain

noZeroDivisors

RightModule(%)

DifferentialExtension(UP)

Monoid

AbelianMonoid

Algebra(%)

EuclideanDomain

CoercibleFrom(Fraction(Integer))

CancellationAbelianMonoid

GcdDomain

MagmaWithUnit

NonAssociativeRing

RetractableTo(Fraction(Integer))

RetractableTo(Integer)

CommutativeStar

RetractableTo(R)

LeftModule(%)

ConvertibleTo(Fraction(UP))

RetractableTo(UP)

Module(%)

LeftOreRing

BiModule(%, %)

CoercibleTo(OutputForm)

Rng

CommutativeRing

IntegralDomain

TwoSidedRecip

Magma

NonAssociativeRng

PartialDifferentialRing(Symbol)

CoercibleFrom(Integer)

unitsKnown

AbelianGroup

AbelianSemiGroup

SemiGroup

NonAssociativeSemiRing

CoercibleFrom(UP)

NonAssociativeAlgebra(%)

DifferentialRing

Ring

SemiRng

EntireRing

NonAssociativeSemiRng

CharacteristicZero

BasicType

SemiRing

FullyRetractableTo(R)