ModularFunctionQSeriesCategory(C, L)ΒΆ
qetamodfunqseries.spad line 112 [edit on github]
ModularFunctionQSeriesCategory(C
, L
, gammas) represents the algebra of eta-quotients that are modular functions for a certain modular group and have only poles at the given cusps (given by explicit transformation matrices gammas).
- 0: %
from QEtaAlgebra C
- 1: %
from QEtaAlgebra C
- *: (%, %) -> %
from QEtaAlgebra C
- *: (C, %) -> %
from QEtaAlgebra C
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from QEtaAlgebra C
- -: % -> %
from QEtaAlgebra C
- -: (%, %) -> %
from QEtaAlgebra C
- /: (%, %) -> % if C has Field
from QEtaPowerGradedAlgebra C
- ^: (%, NonNegativeInteger) -> %
from QEtaAlgebra C
- ^: (%, PositiveInteger) -> %
from Magma
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- elt: (%, PositiveInteger) -> L
series(
x
,n
) or elt(x
,n
) orx
.n
returns the series corresponding to then
-th index. Indices can run from 1 to maxIndex().
- latex: % -> String
from SetCategory
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- maxIndex: () -> PositiveInteger
from QEtaPowerGradedAlgebra C
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- qetaGrade: (%, PositiveInteger) -> Integer
from QEtaPowerGradedAlgebra C
- qetaGrade: (%, PositiveInteger, Integer) -> Integer
from QEtaPowerGradedAlgebra C
- qetaGrades: % -> List Integer
from QEtaPowerGradedAlgebra C
- qetaIndex: % -> PositiveInteger
from QEtaPowerGradedAlgebra C
- qetaLeadingCoefficient: (%, PositiveInteger) -> C
from QEtaPowerGradedAlgebra C
- recip: % -> Union(%, failed)
from MagmaWithUnit
- removeZeroes: % -> %
removeZeroes(x)
removes initial zero coefficients from each entry ofx
. For each entryxi
, removal stops if degree(xi
)>0
.
- removeZeroes: (Integer, %) -> %
removeZeroes(n,x)
removes (at mostn
) initial zero coefficients from each entry ofx
. For each entryxi
, removal stops if degree(xi
)>0
.
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from MagmaWithUnit
- series: (%, PositiveInteger) -> L
series(x, n)
or elt(x
,n
) orx
.n
returns the series corresponding to then
-th index. Indices can run from 1 to maxIndex().
- subtractIfCan: (%, %) -> Union(%, failed)
- traceout: NonNegativeInteger -> % -> OutputForm
from QEtaAlgebra C
- zero?: % -> Boolean
from QEtaAlgebra C