ModularFunctionExpansions(C, m)ΒΆ
qetamodfunexp.spad line 214 [edit on github]
ModularFunctionExpansions(C, m) represents the algebra of eta-quotients that are modular functions for Gamma_0(m).
- 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 XEtaGradedAlgebra C
- ^: (%, NonNegativeInteger) -> %
from QEtaAlgebra C
- ^: (%, PositiveInteger) -> %
from Magma
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: XHashTable(Cusp, QEtaLaurentSeries C) -> %
If
tis a hashtable containing (for each cusp ofGamma_0(m) the series expansions at the cusps, then etaQuotient(t) creates a data structure that can be used for computations.
- hash: % -> SingleInteger
from SetCategory
- hashUpdate!: (HashState, %) -> HashState
from SetCategory
- latex: % -> String
from SetCategory
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- maxIndex: () -> PositiveInteger
from XEtaGradedAlgebra C
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- qetaGrade: (%, PositiveInteger) -> Integer
from XEtaGradedAlgebra C
- qetaGrade: (%, PositiveInteger, Integer) -> Integer
from XEtaGradedAlgebra C
- qetaGrades: % -> List Integer
from XEtaGradedAlgebra C
- qetaIndex: % -> PositiveInteger
from XEtaGradedAlgebra C
- qetaLeadingCoefficient: (%, PositiveInteger) -> C
from XEtaGradedAlgebra C
- recip: % -> Union(%, failed)
from MagmaWithUnit
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from MagmaWithUnit
- series: (%, PositiveInteger) -> QEtaLaurentSeries C
series(x, 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