# Finite0Series CΒΆ

Finite0Series represents Laurent series such that if x is such a series and order(x)>0 then x=0. Quotients of Dedekind eta-functions that are modular functions that only have a pole (if any) at infinity, can be represented as such series.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, C) -> %

from RightModule C

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

from LeftModule C

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

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

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

from Field

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

from AbelianMonoidRing(C, Integer)

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> % if C has Algebra Fraction Integer
^: (%, Fraction Integer) -> % if C has Algebra Fraction Integer

^: (%, Integer) -> % if C has Field

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

acos: % -> % if C has Algebra Fraction Integer
acosh: % -> % if C has Algebra Fraction Integer
acot: % -> % if C has Algebra Fraction Integer
acoth: % -> % if C has Algebra Fraction Integer
acsc: % -> % if C has Algebra Fraction Integer
acsch: % -> % if C has Algebra Fraction Integer
annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
approximate: (%, Integer) -> C if C has coerce: Symbol -> C and C has ^: (C, Integer) -> C
asec: % -> % if C has Algebra Fraction Integer
asech: % -> % if C has Algebra Fraction Integer
asin: % -> % if C has Algebra Fraction Integer
asinh: % -> % if C has Algebra Fraction Integer
associates?: (%, %) -> Boolean if C has IntegralDomain

from EntireRing

associator: (%, %, %) -> %
atan: % -> % if C has Algebra Fraction Integer
atanh: % -> % if C has Algebra Fraction Integer
center: % -> C
characteristic: () -> NonNegativeInteger
charthRoot: % -> Union(%, failed) if C has CharacteristicNonZero
choose: (PositiveInteger, NonNegativeInteger, %) -> %
coefficient: (%, Integer) -> C

from AbelianMonoidRing(C, Integer)

coerce: % -> %

from Algebra %

coerce: % -> OutputForm
coerce: % -> QEtaLaurentSeries C

coerce(x) returns the element x as a QEta Laurent series.

coerce: % -> UnivariateLaurentSeries(C, QUOTE q, Sel(C, Zero))
coerce: C -> %

from Algebra C

coerce: Fraction Integer -> % if C has Algebra Fraction Integer
coerce: Integer -> %
coerce: QEtaLaurentSeries C -> %

coerce(x) assumes that the QEta Laurent series x belongs to the subalgebra of series with the properties of this damain. No check is made.

coerce: QEtaTaylorSeries C -> %
coerce: UnivariateLaurentSeries(C, QUOTE q, Sel(C, Zero)) -> %
commutator: (%, %) -> %
complete: % -> %
construct: List Record(k: Integer, c: C) -> %

from IndexedProductCategory(C, Integer)

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

from IndexedProductCategory(C, Integer)

cos: % -> % if C has Algebra Fraction Integer
cosh: % -> % if C has Algebra Fraction Integer
cot: % -> % if C has Algebra Fraction Integer
coth: % -> % if C has Algebra Fraction Integer
csc: % -> % if C has Algebra Fraction Integer
csch: % -> % if C has Algebra Fraction Integer
D: % -> % if C has *: (Integer, C) -> C

from DifferentialRing

D: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
D: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
D: (%, NonNegativeInteger) -> % if C has *: (Integer, C) -> C

from DifferentialRing

D: (%, Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
D: (%, Symbol, NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
degree: % -> Integer
differentiate: % -> % if C has *: (Integer, C) -> C

from DifferentialRing

differentiate: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
differentiate: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
differentiate: (%, NonNegativeInteger) -> % if C has *: (Integer, C) -> C

from DifferentialRing

differentiate: (%, Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
differentiate: (%, Symbol, NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C
divide: (%, %) -> Record(quotient: %, remainder: %) if C has Field

from EuclideanDomain

elt: (%, %) -> %

from Eltable(%, %)

elt: (%, Integer) -> C
euclideanSize: % -> NonNegativeInteger if C has Field

from EuclideanDomain

eval: (%, C) -> Stream C if C has ^: (C, Integer) -> C
exp: % -> % if C has Algebra Fraction Integer
expressIdealMember: (List %, %) -> Union(List %, failed) if C has Field
exquo: (%, %) -> Union(%, failed) if C has IntegralDomain

from EntireRing

extend: (%, Integer) -> %
extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %) if C has Field

from EuclideanDomain

extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed) if C has Field

from EuclideanDomain

factor: % -> Factored % if C has Field
gcd: (%, %) -> % if C has Field

from GcdDomain

gcd: List % -> % if C has Field

from GcdDomain

gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if C has Field

from GcdDomain

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

integrate: % -> % if C has Algebra Fraction Integer
integrate: (%, Symbol) -> % if C has TranscendentalFunctionCategory and C has PrimitiveFunctionCategory and C has AlgebraicallyClosedFunctionSpace Integer and C has Algebra Fraction Integer or C has integrate: (C, Symbol) -> C and C has Algebra Fraction Integer and C has variables: C -> List Symbol
inv: % -> % if C has Field

from DivisionRing

latex: % -> String

from SetCategory

laurent: (Integer, QEtaTaylorSeries C) -> %
laurent: (Integer, Stream C) -> %
lcm: (%, %) -> % if C has Field

from GcdDomain

lcm: List % -> % if C has Field

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if C has Field

from LeftOreRing

from IndexedProductCategory(C, Integer)

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

from IndexedProductCategory(C, Integer)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

log: % -> % if C has Algebra Fraction Integer
map: (C -> C, %) -> %

from IndexedProductCategory(C, Integer)

monomial?: % -> Boolean

from IndexedProductCategory(C, Integer)

monomial: (C, Integer) -> %

from IndexedProductCategory(C, Integer)

multiEuclidean: (List %, %) -> Union(List %, failed) if C has Field

from EuclideanDomain

multiplyCoefficients: (Integer -> C, %) -> %
multiplyExponents: (%, PositiveInteger) -> %
nthRoot: (%, Integer) -> % if C has Algebra Fraction Integer

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> Integer
order: (%, Integer) -> Integer
pi: () -> % if C has Algebra Fraction Integer
pole?: % -> Boolean
prime?: % -> Boolean if C has Field
principalIdeal: List % -> Record(coef: List %, generator: %) if C has Field
qetaCoefficient: (%, Integer) -> C

qetaTaylorRep: % -> QEtaTaylorSeries C
quo: (%, %) -> % if C has Field

from EuclideanDomain

rationalFunction: (%, Integer) -> Fraction Polynomial C if C has IntegralDomain
rationalFunction: (%, Integer, Integer) -> Fraction Polynomial C if C has IntegralDomain
recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

from IndexedProductCategory(C, Integer)

rem: (%, %) -> % if C has Field

from EuclideanDomain

removeZeroes: % -> %
removeZeroes: (Integer, %) -> %
retract: % -> QEtaTaylorSeries C
retractIfCan: % -> Union(QEtaTaylorSeries C, failed)
rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if C has Algebra Fraction Integer
sech: % -> % if C has Algebra Fraction Integer
series: Stream Record(k: Integer, c: C) -> %
sin: % -> % if C has Algebra Fraction Integer
sinh: % -> % if C has Algebra Fraction Integer
sizeLess?: (%, %) -> Boolean if C has Field

from EuclideanDomain

sqrt: % -> % if C has Algebra Fraction Integer

squareFree: % -> Factored % if C has Field
squareFreePart: % -> % if C has Field
subtractIfCan: (%, %) -> Union(%, failed)
tan: % -> % if C has Algebra Fraction Integer
tanh: % -> % if C has Algebra Fraction Integer
terms: % -> Stream Record(k: Integer, c: C)
traceout: NonNegativeInteger -> % -> OutputForm

from QEtaAlgebra C

truncate: (%, Integer) -> %
truncate: (%, Integer, Integer) -> %
unit?: % -> Boolean if C has IntegralDomain

from EntireRing

unitCanonical: % -> % if C has IntegralDomain

from EntireRing

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

from EntireRing

variable: % -> Symbol
zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

BiModule(C, C)

CancellationAbelianMonoid

canonicalsClosed if C has Field

canonicalUnitNormal if C has Field

CommutativeRing

CommutativeStar

DifferentialRing if C has *: (Integer, C) -> C

DivisionRing if C has Field

Eltable(%, %)

EntireRing if C has IntegralDomain

EuclideanDomain if C has Field

Field if C has Field

GcdDomain if C has Field

IntegralDomain if C has IntegralDomain

LeftOreRing if C has Field

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if C has IntegralDomain

PartialDifferentialRing Symbol if C has PartialDifferentialRing Symbol and C has *: (Integer, C) -> C

PrincipalIdealDomain if C has Field

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

UniqueFactorizationDomain if C has Field

unitsKnown

VariablesCommuteWithCoefficients