SymbolicSiftedEtaQuotientOrbitProductGammaΒΆ

qetafun.spad line 2681

SymbolicSiftedEtaQuotientOrbitProductGamma holds data to compute an eta quotient expansions of $P_{s, m, t}(gamma tau)$. See eqref{eq:P_s-m-t(gamma*tau)}.}

=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
elt: (%, NonNegativeInteger ) -> SymbolicSiftedEtaQuotientGamma
x.u returns the data corresponding to the respective orbit element u.
etaQuotient: (PositiveInteger , List PositiveInteger , List Integer , PositiveInteger , NonNegativeInteger , Matrix Integer ) -> %
etaQuotient(mm, s, m, t, gamma) represents the expansion of $P_{s, m, t}(gamma tau)$.
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.u) for u in orbit(shat,m,t)] where $shat = sum_delta delta s_delta$
multiplier: % -> PositiveInteger
multiplier(x) returns the subsequence multiplier. Returns m.
offset: % -> NonNegativeInteger
offset(x) returns the subsequence offset. Returns t.
orbit: % -> List NonNegativeInteger
orbit(x) returns $modularOrbit{s, m, t}$ where s=exponents(x), m=multiplier(x), t=offset(x). See definition of orbit in qetakolberg.spad

BasicType

CoercibleTo OutputForm

SetCategory