SymbolicModularSiftedEtaQuotient

qetafun.spad line 2879

SymbolicModularSiftedEtaQuotient holds data to compute an eta quotient expansions of $F_{r, s, m, t}(gamma tau)$ at all cusps of $Gamma_0(N)$. See eqref{eq:F_r-s-m-t(gamma*tau)}.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

cusps: % -> List Fraction Integer

cusps(x)=cuspsOfGamma0(level x)$QAuxiliaryModularEtaQuotientPackage.

elt: (%, Fraction Integer ) -> SymbolicModularSiftedEtaQuotientGamma

x.cusp returns the data corresponding to the respective cusp.

etaQuotient: (PositiveInteger , List Integer , PositiveInteger , List Integer , PositiveInteger , NonNegativeInteger ) -> %

etaQuotient(nn, r, mm, s, m, t) represents the expansion of $F_{r,s, m, t}(gamma tau)$ for all gamma corresponding to the cusps of $Gamma_0(nn)$.

etaQuotient: (PositiveInteger , List Integer , PositiveInteger , List Integer , PositiveInteger , NonNegativeInteger , List Fraction Integer ) -> %

etaQuotient(nn, r, mm, s, m, t, cusps) represents the expansion of $F_{r,s, m, t}(gamma tau)$ for all gamma corresponding to the given cusps.

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).

minimalRootOfUnity: % -> PositiveInteger

minimalRootOfUnity(x) returns lcm [minimalRootOfUnity(x.u) for u in cusps x].

BasicType

CoercibleTo OutputForm

SetCategory