ModularEtaQuotient(C, mx, CX, xi, LX)ΒΆ

qetafun.spad line 3129

ModularEtaQuotient(C, mx, CX, xi, LX) represents the set of eta-quotients that are modular functions for Gamma_0(N). In fact, this domain is meant to do computation for a specific N, but is actually implementing the union over all N.

=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
etaQuotient: (PositiveInteger , List Integer ) -> %
etaQuotient(m, r) represents the expansion of g_r(tau) in terms of x = exp(2 pi i tau/w) where w=width(m, c) at all cusps of Gamma0(m). See eqref{eq:g_r(tau)}.
etaQuotient: SymbolicEtaQuotient -> %
etaQuotient(y) represents the expansion of g_r(tau) in terms of x = exp(2 pi i tau/w) where w=width(m, c) at all cusps of Gamma0(level y). See eqref{eq:g_r(tau)}.
expansions: % -> XHashTable (Fraction Integer , LX)
expansions(x) returns the Laurent series expansions of $g_r(tau)$ at all cusps of Gamma_0(level x) corresponding to cusps(symbolicEtaQuotient x).
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState , %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
level: % -> PositiveInteger
level(x) returns m such that x corresponds to a modular function for Gamma_0(m).
symbolicEtaQuotient: % -> SymbolicEtaQuotient
symbolicEtaQuotient(x) returns the meta data corresponding to x. If x=etaQuotient(y) then symbolicEtaQuotient(x)=y.

BasicType

CoercibleTo OutputForm

SetCategory