EtaQuotientGamma(C, mx, CX, xi, LX)ΒΆ

qetafun.spad line 2996

EtaQuotientGamma(C, mx, CX, xi, LX) represents the semigroup of eta-quotient expansions at gamma. The eta quotient need not be a modular function, but the (c*tau+d) factor is always ignored.

=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
etaQuotient: SymbolicEtaQuotientGamma -> %
etaQuotient(s) represents the expansion of g_r(gamma tau) in terms of x = exp(2 pi i tau/w) where w=width(m, c), r = exponents(s), and g_r is defined by $g_r(tau) = prod_{delta in divisors(s)} eta(delta gamma tau)^{r_{delta}}$.
eulerExpansion: % -> LX
eulerExpansion(e) returns the series expansion of e without any prefactor. The true series expansion (in terms of fractional x powers of e is given by lc * x^p * s where lc = leadingCoefficient e, x = exp(2 pi i tau/w) where w=width(m, c), s = symbolicEtaQuotient e, c = gamma(s)(2,1), p = (xExponent s) / 24, s = eulerExpansion e.
eulerFunctionPower: (PositiveInteger , NonNegativeInteger , Integer ) -> LX
eulerFunctionPower(u, v, p) computes eulerFunction(1)^p and replaces q=monomial(1,1)$LC by monomial(xi^v, u)$LX
expansion: % -> LX
expansion(e) should only be called if modular?(e) holds, otherwise it might return an error. expansion(e) returns the series expansion of e in terms of x = exp(2 pi i tau/w) where w=width(m, c), c = gamma(symbolicEtaQuotient e)(2,1).
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState , %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leadingCoefficient: % -> CX
leadingCoefficient(x) returns the coefficient corresponding to the smallest q-power with non-zero coefficient.
modular?: % -> Boolean
modular?(x) returns true if the eta quotient is a modular function for Gamma0(nn) where nn=level(symbolicEtaQuotient x).
substituteVariable: (PositiveInteger , NonNegativeInteger ) -> Record(k: Integer , c: C) -> Record(k: Integer , c: CX)
Is the function [k, c] +-> [u*k, xi^v*c]
symbolicEtaQuotient: % -> SymbolicEtaQuotientGamma
symbolicEtaQuotient(x) returns meta-data corresponding to x.

BasicType

CoercibleTo OutputForm

SetCategory