SymbolicSiftedEtaQuotientOrbitProductGammaΒΆ
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 elementu
.
- 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 tox
.- 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)
returnslcm
[minimalRootOfUnity(x
.u
) foru
in orbit(shat,m
,t
)] where $shat = sum_delta deltas_
delta$
- multiplier: % -> PositiveInteger
multiplier(x)
returns the subsequence multiplier. Returnsm
.
- offset: % -> NonNegativeInteger
offset(x)
returns the subsequence offset. Returnst
.
- 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