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) or- x.- nreturns the series corresponding to the- n-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 of- x. For each entry- xi, removal stops if degree(- xi)- >0.
- removeZeroes: (Integer, %) -> %
- removeZeroes(n,x)removes (at most- n) initial zero coefficients from each entry of- x. For each entry- xi, 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) or- x.- nreturns the series corresponding to the- n-th index. Indices can run from 1 to maxIndex().
- subtractIfCan: (%, %) -> Union(%, failed)
- traceout: NonNegativeInteger -> % -> OutputForm
- from QEtaAlgebra C 
- zero?: % -> Boolean
- from QEtaAlgebra C