LaurentPolynomial(R, UP)ΒΆ

gpol.spad line 1

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
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
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) undocumented
coerce: % -> %
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
coerce: Integer -> %
from NonAssociativeRing
coerce: R -> %
from RetractableTo R
coerce: UP -> %
from RetractableTo UP
commutator: (%, %) -> %
from NonAssociativeRng
convert: % -> Fraction UP
from ConvertibleTo Fraction UP
D: % -> %
from DifferentialRing
D: (%, List Symbol) -> %
from PartialDifferentialRing Symbol
D: (%, List Symbol, List NonNegativeInteger) -> %
from PartialDifferentialRing Symbol
D: (%, NonNegativeInteger) -> %
from DifferentialRing
D: (%, Symbol) -> %
from PartialDifferentialRing Symbol
D: (%, Symbol, NonNegativeInteger) -> %
from PartialDifferentialRing Symbol
D: (%, UP -> UP) -> %
from DifferentialExtension UP
D: (%, UP -> UP, NonNegativeInteger) -> %
from DifferentialExtension UP
degree: % -> Integer
degree(x) undocumented
differentiate: % -> %
from DifferentialRing
differentiate: (%, List Symbol) -> %
from PartialDifferentialRing Symbol
differentiate: (%, List Symbol, List NonNegativeInteger) -> %
from PartialDifferentialRing Symbol
differentiate: (%, NonNegativeInteger) -> %
from DifferentialRing
differentiate: (%, Symbol) -> %
from PartialDifferentialRing Symbol
differentiate: (%, Symbol, NonNegativeInteger) -> %
from PartialDifferentialRing Symbol
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
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
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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 ``undocumented
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
monomial: (R, Integer) -> %
monomial(x, n) undocumented
monomial?: % -> Boolean
monomial?(x) 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
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)
from CancellationAbelianMonoid
trailingCoefficient: % -> R
``trailingCoefficient ``undocumented
unit?: % -> Boolean
from EntireRing
unitCanonical: % -> %
from EntireRing
unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CharacteristicNonZero if R has CharacteristicNonZero

CharacteristicZero if R has CharacteristicZero

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

ConvertibleTo Fraction UP

DifferentialExtension UP

DifferentialRing

EntireRing

EuclideanDomain if R has Field

FullyRetractableTo R

GcdDomain if R has Field

IntegralDomain

LeftModule %

LeftOreRing if R has Field

Magma

MagmaWithUnit

Module %

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol

PrincipalIdealDomain if R has Field

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer

RetractableTo Integer if R has RetractableTo Integer

RetractableTo R

RetractableTo UP

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown