ModularSiftedEtaQuotient(C, mx, CX, xi, LX)

qetafun.spad line 3373

• C: Join(Algebra Fraction Integer , IntegralDomain )
• mx: PositiveInteger
• CX: Algebra C
• xi: CX
• LX: UnivariateLaurentSeriesCategory CX

ModularSiftedEtaQuotient is a generalization of ModularEtaQuotient. It holds the expansions of F_{r, s, m, t}(tau) at all cusps of $Gamma_0(N)$. See eqref{eq:F_r-s-m-t(gamma*tau)}. The domain serves as the representation of the underlying q-series.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

expandAtAllCusps: SymbolicModularSiftedEtaQuotient -> %

expandAtAllCusps(y) represents the q-expansion of $F_{r,s,m,t}(gamma tau)$ at all cusps of $Gamma_0(N)$ where N=level(y).

expansions: % -> XHashTable (Fraction Integer , LX)

expansions(x) returns the Laurent series expansions of $F_{r, s, m, t}(tau)$ at all cusps of Gamma_0(N).

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState , %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

level: % -> PositiveInteger

level(x) returns nn such that x corresponds to a modular function for Gamma_0(nn).

metadata: % -> SymbolicModularSiftedEtaQuotient

metadata(x) returns y such that expandAtAllCusps(y)=x

BasicType

CoercibleTo OutputForm

SetCategory