SymbolicSiftedEtaQuotientGamma

qetafun.spad line 2593

SymbolicSiftedEtaQuotientGamma is a generalization of SymbolicEtaQuotientGamma. It holds data to compute an eta quotient expansion of $g_{s,m,t}(gamma tau)$ or $g_{s,m}(gamma tau)$. See eqref{eq:g_s-m-t(gamma*tau)} and eqref{eq:g_s-m(gamma*tau)}.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

divisors: % -> List PositiveInteger

divisors(x) returns the divisors of level(x) that were given at creation time of x.

elt: (%, NonNegativeInteger ) -> SymbolicSiftedEtaQuotientLambdaGamma

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

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

etaQuotient(mm, divs, s, m, t, gamma) represents the expansion of $g_{s,m,t}(gamma tau)$.

exponents: % -> List Integer

exponents(x) returns the list of exponents corresponding to all divisors.

gamma: % -> Matrix Integer

gamma(x) returns the transformation corresponding to x.

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState , %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

level: % -> PositiveInteger

level(x) returns the level of the eta quotient.

minimalRootOfUnity: % -> PositiveInteger

minimalRootOfUnity(x) returns lcm [minimalRootOfUnity(x.lambda) for lambda in 0..m-1].

multiplier: % -> PositiveInteger

multiplier(x) returns the subsequence multiplier. Returns m.

offset: % -> Integer

offset(x) returns the subsequence offset. Returns t.

BasicType

CoercibleTo OutputForm

SetCategory