NMUnivariateLaurentSeries(R, x, prec)ΒΆ

jnseries.spad line 157 [edit on github]

NMUnivariateLaurentSeries is the Nemo univariate Laurent series using Julia. x := x::NULS(NFRAC(NINT),'x,30) x^(-1)

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> % if R has Algebra Fraction Integer

from RightModule Fraction Integer

*: (%, Integer) -> %

s * n is the product of s with an integer.

*: (%, NonNegativeInteger) -> %

s * n is the product of s with a non negative integer.

*: (%, PositiveInteger) -> %

s * n is the product of s with a positive integer.

*: (%, R) -> %

from RightModule R

*: (Fraction Integer, %) -> % if R has Algebra Fraction Integer

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NMInteger, %) -> %

from JLObjectRing

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

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

from AbelianMonoidRing(R, Integer)

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

s ^ z computes the z-th power of s.

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean if R has IntegralDomain

from EntireRing

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

from NonAssociativeRng

characteristic: % -> NonNegativeInteger

from NMRing

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from CharacteristicNonZero

coefficient: (%, Integer) -> R

from AbelianMonoidRing(R, Integer)

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> % if R has Algebra Fraction Integer

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: R -> % if R has CommutativeRing

from Algebra R

coerce: Variable x -> %

coerce(x) converts the variable x to a Nemo univariate power serie.

commutator: (%, %) -> %

from NonAssociativeRng

complete: % -> %

from PowerSeriesCategory(R, Integer, SingletonAsOrderedSet)

construct: List Record(k: Integer, c: R) -> %

from IndexedProductCategory(R, Integer)

constructOrdered: List Record(k: Integer, c: R) -> %

from IndexedProductCategory(R, Integer)

convert: % -> String

from ConvertibleTo String

D: % -> %

from DifferentialRing

D: (%, List Symbol) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, Symbol) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

degree: % -> Integer

from PowerSeriesCategory(R, Integer, SingletonAsOrderedSet)

differentiate: % -> %

from DifferentialRing

differentiate: (%, List Symbol) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, Symbol) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

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

from NMRing

equal?: (%, %) -> Boolean

from NMRing

exact?: % -> Boolean

from NMRing

exactDivide: (%, %) -> %

from NMRing

exp: % -> %

exp(s) returns the exponential of the Laurent serie s.

exquo: (%, %) -> Union(%, failed) if R has IntegralDomain

from EntireRing

integrate: % -> %

integrate(f(x)) returns an anti-derivative of the power series f(x) with constant coefficient 0.

inverse: % -> %

inverse(s) returns the inverse of s. Throw a Julia error if no such inverse exists.

jlAbout: % -> Void

from JLObjectType

jlApply: (String, %) -> %

from JLObjectType

jlApply: (String, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %, %) -> %

from JLObjectType

jlDisplay: % -> Void

from JLObjectType

jlDump: JLObject -> Void

from JLObjectType

jlId: % -> JLInt64

from JLObjectType

jlNMRing: () -> String

from NMRing

jlObject: () -> String

from NMRing

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlType: % -> String

from JLObjectType

latex: % -> String

from SetCategory

leadingCoefficient: % -> R

from PowerSeriesCategory(R, Integer, SingletonAsOrderedSet)

leadingMonomial: % -> %

from PowerSeriesCategory(R, Integer, SingletonAsOrderedSet)

leadingSupport: % -> Integer

from IndexedProductCategory(R, Integer)

leadingTerm: % -> Record(k: Integer, c: R)

from IndexedProductCategory(R, Integer)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

log: % -> %

exp(s) returns the logarithm of the Laurent serie s.

map: (R -> R, %) -> %

from IndexedProductCategory(R, Integer)

monomial?: % -> Boolean

monomial?(f) tests if f is a single monomial.

monomial: (R, Integer) -> %

from IndexedProductCategory(R, Integer)

mutable?: % -> Boolean

from JLObjectType

nothing?: % -> Boolean

from JLObjectType

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

pole?: % -> Boolean

from PowerSeriesCategory(R, Integer, SingletonAsOrderedSet)

recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

from IndexedProductCategory(R, Integer)

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sqrt: % -> %

sqrt(f) return square root of f if it exists, a Julia error is thrown if f has no square root.

string: % -> String

from JLType

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

from CancellationAbelianMonoid

unit?: % -> Boolean

from NMRing

unitCanonical: % -> % if R has IntegralDomain

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %) if R has IntegralDomain

from EntireRing

valuation: % -> NonNegativeInteger

valuation(s) returns the valuation of the given power series, the degree of the first nonzero term

variable: % -> Symbol

variable(f) returns the (unique) Laurent series variable of the power series f.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(R, Integer)

AbelianProductCategory R

AbelianSemiGroup

Algebra %

Algebra Fraction Integer if R has Algebra Fraction Integer

Algebra R if R has CommutativeRing

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer) if R has Algebra Fraction Integer

BiModule(R, R)

CancellationAbelianMonoid

CharacteristicNonZero if R has CharacteristicNonZero

CharacteristicZero if R has CharacteristicZero

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

ConvertibleTo String

DifferentialRing

EntireRing if R has IntegralDomain

IndexedProductCategory(R, Integer)

IntegralDomain if R has IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

LeftModule Fraction Integer if R has Algebra Fraction Integer

LeftModule R

Magma

MagmaWithUnit

Module %

Module Fraction Integer if R has Algebra Fraction Integer

Module R if R has CommutativeRing

Monoid

NMCommutativeRing

NMRing

NMType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer if R has Algebra Fraction Integer

NonAssociativeAlgebra R if R has CommutativeRing

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if R has IntegralDomain

PartialDifferentialRing Symbol if R has PartialDifferentialRing Symbol

PowerSeriesCategory(R, Integer, SingletonAsOrderedSet)

RightModule %

RightModule Fraction Integer if R has Algebra Fraction Integer

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

unitsKnown

VariablesCommuteWithCoefficients