ExponentialExpansion(R, FE, var, cen)

expexpan.spad line 347 [edit on github]

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.

* : (%, %) -> %
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))
0 : () -> %
from AbelianMonoid
1 : () -> %
from MagmaWithUnit
< : (%, %) -> 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
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 : (%, Mapping(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))) -> %
from DifferentialExtension(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))
D : (%, Mapping(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)), NonNegativeInteger) -> %
from DifferentialExtension(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))
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)
^ : (%, Integer) -> %
from DivisionRing
^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
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 UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has CharacteristicNonZero or % has CharacteristicNonZero and UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen) has PolynomialFactorizationExplicit
from CharacteristicNonZero
coerce : % -> %
from Algebra(%)
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))
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
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))
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 : (%, Mapping(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))) -> %
from DifferentialExtension(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))
differentiate : (%, Mapping(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen), UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen)), NonNegativeInteger) -> %
from DifferentialExtension(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))
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)
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 : (Mapping(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(UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, var, cen))
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(%) -> 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))
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))
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
~= : (%, %) -> Boolean
from BasicType

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

Module(Fraction(Integer))

ConvertibleTo(Float)

PrincipalIdealDomain

NonAssociativeSemiRing

BiModule(%, %)

ConvertibleTo(InputForm)

Field

canonicalUnitNormal

Rng

CoercibleFrom(Integer)

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

TwoSidedRecip

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

OrderedAbelianGroup

SemiRing

EntireRing

PatternMatchable(Float)

RetractableTo(UnivariatePuiseuxSeries(FE, var, cen))

NonAssociativeAlgebra(Fraction(Integer))

CharacteristicNonZero

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

unitsKnown

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

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

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

noZeroDivisors

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

RetractableTo(Fraction(Integer))

UniqueFactorizationDomain

SemiGroup

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

RightModule(Fraction(Integer))

Magma

RetractableTo(Symbol)

IntegralDomain

LeftModule(%)

NonAssociativeRing

GcdDomain

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

PartialDifferentialRing(Symbol)

CharacteristicZero

OrderedIntegralDomain

Algebra(%)

CoercibleFrom(Fraction(Integer))

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

DifferentialRing

OrderedAbelianMonoid

DivisionRing

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

CommutativeRing

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

PartialOrder

NonAssociativeSemiRng

CancellationAbelianMonoid

EuclideanDomain

canonicalsClosed

RetractableTo(Integer)

OrderedCancellationAbelianMonoid

OrderedRing

SetCategory

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

CommutativeStar

AbelianMonoid

MagmaWithUnit

Comparable

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

RightModule(%)

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

NonAssociativeAlgebra(%)

RealConstant

ConvertibleTo(DoubleFloat)

OrderedAbelianSemiGroup

Module(%)

CoercibleTo(OutputForm)

LinearlyExplicitOver(Integer)

ConvertibleTo(Pattern(Float))

SemiRng

CoercibleFrom(Symbol)

Monoid

PolynomialFactorizationExplicit

LeftOreRing

OrderedSet

StepThrough

Algebra(Fraction(Integer))

BasicType

Ring

CoercibleFrom(UnivariatePuiseuxSeries(FE, var, cen))

RightModule(Integer)

LeftModule(Fraction(Integer))

AbelianSemiGroup

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

ConvertibleTo(Pattern(Integer))

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

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

NonAssociativeRng

PatternMatchable(Integer)

BiModule(Fraction(Integer), Fraction(Integer))

AbelianGroup