NMUnivariatePowerSeries(R, x, prec, abs)

jnseries.spad line 1 [edit on github]

NMUnivariatePowerSeries is the Nemo univariate power series using Julia. prec determines the precision used which can be absolute or relative (:capped_absolute or :capped_relative). x := x::NUPS(NFRAC(NINT),'x,30,”capped_relative”) sin(x)

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) -> %

x n is the multiplication operation.

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

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NMInteger, %) -> JLObject

from JLObjectRing

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (R, %) -> %

from LeftModule R

+: (%, %) -> %

from AbelianSemiGroup

+: (%, Fraction Integer) -> % if R has Algebra NMFraction NMInteger

x + n is the addition operation.

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

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

x - n is the addition operation.

/: (%, Integer) -> % if R has Algebra NMFraction NMInteger

x / n is the division by an integer.

/: (%, NMInteger) -> % if R has Algebra NMFraction NMInteger

x / n is the division by an integer.

/: (%, R) -> % if R has Field or R has Algebra NMFraction NMInteger

x / n is the division operation.

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

acos: % -> % if R has Algebra NMFraction NMInteger

from ArcTrigonometricFunctionCategory

acosh: % -> % if R has Algebra NMFraction NMInteger

from ArcHyperbolicFunctionCategory

acot: % -> % if R has Algebra NMFraction NMInteger

from ArcTrigonometricFunctionCategory

acoth: % -> % if R has Algebra NMFraction NMInteger

from ArcHyperbolicFunctionCategory

acsc: % -> % if R has Algebra NMFraction NMInteger

from ArcTrigonometricFunctionCategory

acsch: % -> % if R has Algebra NMFraction NMInteger

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

asec: % -> % if R has Algebra NMFraction NMInteger

from ArcTrigonometricFunctionCategory

asech: % -> % if R has Algebra NMFraction NMInteger

from ArcHyperbolicFunctionCategory

asin: % -> % if R has Algebra NMFraction NMInteger

from ArcTrigonometricFunctionCategory

asinh: % -> % if R has Algebra NMFraction NMInteger

from ArcHyperbolicFunctionCategory

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

from EntireRing

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

from NonAssociativeRng

atan: % -> % if R has Algebra NMFraction NMInteger

from ArcTrigonometricFunctionCategory

atanh: % -> % if R has Algebra NMFraction NMInteger

from ArcHyperbolicFunctionCategory

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coefficient: (%, NonNegativeInteger) -> R

from AbelianMonoidRing(R, NonNegativeInteger)

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, NonNegativeInteger, SingletonAsOrderedSet)

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

from IndexedProductCategory(R, NonNegativeInteger)

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

from IndexedProductCategory(R, NonNegativeInteger)

convert: % -> String

from ConvertibleTo String

cos: % -> % if R has Algebra NMFraction NMInteger

from TrigonometricFunctionCategory

cosh: % -> % if R has Algebra NMFraction NMInteger

from HyperbolicFunctionCategory

cot: % -> % if R has Algebra NMFraction NMInteger

from TrigonometricFunctionCategory

coth: % -> % if R has Algebra NMFraction NMInteger

from HyperbolicFunctionCategory

csc: % -> % if R has Algebra NMFraction NMInteger

from TrigonometricFunctionCategory

csch: % -> % if R has Algebra NMFraction NMInteger

from HyperbolicFunctionCategory

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: % -> NonNegativeInteger

from PowerSeriesCategory(R, NonNegativeInteger, 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

equal?: (%, %) -> Boolean

from NMRing

exact?: % -> Boolean

from NMRing

exactDivide: (%, %) -> %

from NMRing

exp: % -> % if R has Algebra NMFraction NMInteger

exp(s) returns the exponential of the power 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 JLObjectType

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlType: % -> String

from JLObjectType

latex: % -> String

from SetCategory

leadingCoefficient: % -> R

from PowerSeriesCategory(R, NonNegativeInteger, SingletonAsOrderedSet)

leadingMonomial: % -> %

from PowerSeriesCategory(R, NonNegativeInteger, SingletonAsOrderedSet)

leadingSupport: % -> NonNegativeInteger

from IndexedProductCategory(R, NonNegativeInteger)

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

from IndexedProductCategory(R, NonNegativeInteger)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

log: % -> % if R has Algebra NMFraction NMInteger

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

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

from IndexedProductCategory(R, NonNegativeInteger)

monomial?: % -> Boolean

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

monomial: (R, NonNegativeInteger) -> %

from IndexedProductCategory(R, NonNegativeInteger)

mutable?: % -> Boolean

from JLObjectType

nothing?: % -> Boolean

from JLObjectType

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra R

pole?: % -> Boolean

from PowerSeriesCategory(R, NonNegativeInteger, SingletonAsOrderedSet)

recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

from IndexedProductCategory(R, NonNegativeInteger)

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if R has Algebra NMFraction NMInteger

from TrigonometricFunctionCategory

sech: % -> % if R has Algebra NMFraction NMInteger

from HyperbolicFunctionCategory

sin: % -> % if R has Algebra NMFraction NMInteger

from TrigonometricFunctionCategory

sinh: % -> % if R has Algebra NMFraction NMInteger

from HyperbolicFunctionCategory

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

tan: % -> % if R has Algebra NMFraction NMInteger

from TrigonometricFunctionCategory

tanh: % -> % if R has Algebra NMFraction NMInteger

from HyperbolicFunctionCategory

unit?: % -> Boolean

from EntireRing

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) power series variable of the power series f.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(R, NonNegativeInteger)

AbelianProductCategory R

AbelianSemiGroup

Algebra %

Algebra Fraction Integer if R has Algebra Fraction Integer

Algebra R if R has CommutativeRing

ArcHyperbolicFunctionCategory if R has Algebra NMFraction NMInteger

ArcTrigonometricFunctionCategory if R has Algebra NMFraction NMInteger

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

HyperbolicFunctionCategory if R has Algebra NMFraction NMInteger

IndexedProductCategory(R, NonNegativeInteger)

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, NonNegativeInteger, SingletonAsOrderedSet)

RightModule %

RightModule Fraction Integer if R has Algebra Fraction Integer

RightModule R

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TrigonometricFunctionCategory if R has Algebra NMFraction NMInteger

TwoSidedRecip

unitsKnown

VariablesCommuteWithCoefficients