ExponentialExpansion(R, FE, var, cen)

expexpan.spad line 347 [edit on github]

• R: Join(Comparable, RetractableTo Integer, LinearlyExplicitOver Integer, GcdDomain)

• FE: Join(AlgebraicallyClosedField, TranscendentalFunctionCategory, FunctionSpace R)

• var: Symbol

• cen: FE

UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums, where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, Integer) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> %

from RightModule UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), %) -> %

from LeftModule UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> %

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

<=: (%, %) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

from PartialOrder

<: (%, %) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

from PartialOrder

>: (%, %) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

from PartialOrder

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

from OrderedRing

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

ceiling: % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has IntegerNumberSystem

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

charthRoot: % -> Union(%, failed) if % has CharacteristicNonZero and UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit or UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has CharacteristicNonZero

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: Symbol -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Symbol

from CoercibleFrom Symbol

coerce: UnivariatePuiseuxSeries(FE, var, cen) -> %

coerce(f) converts a UnivariatePuiseuxSeries to an ExponentialExpansion.

coerce: UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) -> %

from Algebra UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

commutator: (%, %) -> %

from NonAssociativeRng

conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

convert: % -> DoubleFloat if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RealConstant

from ConvertibleTo DoubleFloat

convert: % -> Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RealConstant

from ConvertibleTo Float

convert: % -> InputForm if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has ConvertibleTo Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has ConvertibleTo Pattern Integer

from ConvertibleTo Pattern Integer

D: % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has DifferentialRing

from DifferentialRing

D: (%, List Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has DifferentialRing

from DifferentialRing

D: (%, Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> %

from DifferentialExtension UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

D: (%, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), NonNegativeInteger) -> %

from DifferentialExtension UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

denom: % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

denominator: % -> %

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

differentiate: % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has DifferentialRing

from DifferentialRing

differentiate: (%, List Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has DifferentialRing

from DifferentialRing

differentiate: (%, Symbol) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> %

from DifferentialExtension UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

differentiate: (%, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), NonNegativeInteger) -> %

from DifferentialExtension UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

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

from EuclideanDomain

elt: (%, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Eltable(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

from Eltable(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), %)

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

eval: (%, Equation UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

eval: (%, List Equation UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

eval: (%, List Symbol, List UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has InnerEvalable(Symbol, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

from InnerEvalable(Symbol, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

eval: (%, List UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), List UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from InnerEvalable(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

eval: (%, Symbol, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has InnerEvalable(Symbol, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

from InnerEvalable(Symbol, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

eval: (%, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from InnerEvalable(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

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

from PrincipalIdealDomain

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

from EntireRing

extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)

from EuclideanDomain

extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

floor: % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has IntegerNumberSystem

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

fractionPart: % -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has EuclideanDomain

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %

from PolynomialFactorizationExplicit

init: % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has StepThrough

from StepThrough

inv: % -> %

from DivisionRing

latex: % -> String

from SetCategory

lcm: (%, %) -> %

from GcdDomain

lcm: List % -> %

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)

from LeftOreRing

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

limitPlus: % -> Union(OrderedCompletion FE, failed)

limitPlus(f(var)) returns limit(var -> a+, f(var)).

map: (UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), %) -> %

from FullyEvalableOver UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

max: (%, %) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

from OrderedSet

min: (%, %) -> % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

from OrderedSet

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

from EuclideanDomain

negative?: % -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

from OrderedRing

nextItem: % -> Union(%, failed) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has StepThrough

from StepThrough

numer: % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

numerator: % -> %

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PatternMatchable Float

from PatternMatchable Float

patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PatternMatchable Integer

from PatternMatchable Integer

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

positive?: % -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

from OrderedRing

prime?: % -> Boolean

from UniqueFactorizationDomain

principalIdeal: List % -> Record(coef: List %, generator: %)

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

recip: % -> Union(%, failed)

from MagmaWithUnit

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), vec: Vector UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

from LinearlyExplicitOver UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

reducedSystem: Matrix % -> Matrix Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from LinearlyExplicitOver UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

from RetractableTo Fraction Integer

retract: % -> Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

from RetractableTo Integer

retract: % -> Symbol if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Symbol

from RetractableTo Symbol

retract: % -> UnivariatePuiseuxSeries(FE, var, cen)

from RetractableTo UnivariatePuiseuxSeries(FE, var, cen)

retract: % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

from RetractableTo UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

retractIfCan: % -> Union(Fraction Integer, failed) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

from RetractableTo Integer

retractIfCan: % -> Union(Symbol, failed) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Symbol

from RetractableTo Symbol

retractIfCan: % -> Union(UnivariatePuiseuxSeries(FE, var, cen), failed)

from RetractableTo UnivariatePuiseuxSeries(FE, var, cen)

retractIfCan: % -> Union(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), failed)

from RetractableTo UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sign: % -> Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

from OrderedRing

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Comparable

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

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

from CancellationAbelianMonoid

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

wholePart: % -> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has EuclideanDomain

from QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has CharacteristicNonZero

CharacteristicZero if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has CharacteristicZero

CoercibleFrom Fraction Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

CoercibleFrom Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

CoercibleFrom Symbol if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Symbol

CoercibleFrom UnivariatePuiseuxSeries(FE, var, cen)

CoercibleFrom UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Comparable

ConvertibleTo DoubleFloat if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RealConstant

ConvertibleTo Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RealConstant

ConvertibleTo InputForm if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has ConvertibleTo InputForm

ConvertibleTo Pattern Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has ConvertibleTo Pattern Integer

DifferentialExtension UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

DifferentialRing if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has DifferentialRing

DivisionRing

Eltable(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), %) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Eltable(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

EntireRing

EuclideanDomain

Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

Field

FullyEvalableOver UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

FullyLinearlyExplicitOver UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

FullyPatternMatchable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

GcdDomain

InnerEvalable(Symbol, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has InnerEvalable(Symbol, UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))

InnerEvalable(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)) if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has Evalable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

IntegralDomain

LeftModule %

LeftModule Fraction Integer

LeftModule UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

LeftOreRing

LinearlyExplicitOver Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has LinearlyExplicitOver Integer

LinearlyExplicitOver UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

OrderedAbelianMonoid if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

OrderedAbelianSemiGroup if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

OrderedCancellationAbelianMonoid if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

OrderedIntegralDomain if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

OrderedRing if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedIntegralDomain

OrderedSet if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

PartialDifferentialRing Symbol if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PartialDifferentialRing Symbol

PartialOrder if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has OrderedSet

Patternable UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

PatternMatchable Float if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PatternMatchable Float

PatternMatchable Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PatternMatchable Integer

PolynomialFactorizationExplicit if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit

PrincipalIdealDomain

QuotientFieldCategory UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

RealConstant if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RealConstant

RetractableTo Fraction Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

RetractableTo Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Integer

RetractableTo Symbol if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has RetractableTo Symbol

RetractableTo UnivariatePuiseuxSeries(FE, var, cen)

RetractableTo UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

RightModule %

RightModule Fraction Integer

RightModule Integer if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has LinearlyExplicitOver Integer

RightModule UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown