SymbolicSiftedEtaQuotientOrbitProductGamma

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