ModularFunctionQSeriesConstructor(C, L, gammas)ΒΆ
qetamodfunqseries.spad line 162 [edit on github]
ModularFunctionQSeriesConstructor(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). The domain is meant to handle modular functions (weight 0), but can hold (and do arithmetic with) modular forms. However, the function zero? assumes that the object is a modular function, i.e. will return 0 for modular cusp forms.
- 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
- coerce: XHashTable(Matrix Integer, L) -> %
If
tis a hashtable containing (for each gamma of gammas) the respective series expansions at that gamma, then coerce(t) creates a data structure that can be used for computations as aC-algebra.
- elt: (%, PositiveInteger) -> L
from ModularFunctionQSeriesCategory(C, L)
- 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: % -> %
from ModularFunctionQSeriesCategory(C, L)
- removeZeroes: (Integer, %) -> %
from ModularFunctionQSeriesCategory(C, L)
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from MagmaWithUnit
- series: (%, PositiveInteger) -> L
from ModularFunctionQSeriesCategory(C, L)
- subtractIfCan: (%, %) -> Union(%, failed)
- traceout: NonNegativeInteger -> % -> OutputForm
from QEtaAlgebra C
- zero?: % -> Boolean
from QEtaAlgebra C