ModularEtaQuotient(C, mx, CX, xi, LX)ΒΆ
- C: Join(Algebra Fraction Integer , IntegralDomain )
- mx: PositiveInteger
- CX: Algebra C
- xi: CX
- LX: UnivariateLaurentSeriesCategory CX
ModularEtaQuotient(C
, mx
, CX
, xi
, LX
) represents the set of eta-quotients that are modular functions for Gamma_0
(N
). In fact, this domain is meant to do computation for a specific N
, but is actually implementing the union over all N
.
- =: (%, %) -> Boolean
- from BasicType
- ~=: (%, %) -> Boolean
- from BasicType
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- etaQuotient: (PositiveInteger , List Integer ) -> %
etaQuotient(m, r)
represents the expansion ofg_r
(tau) in terms ofx
= exp(2 pii
tau/w) where w=width(m
,c
) at all cusps ofGamma0
(m
). See eqref{eq:g_r(tau)}.
- etaQuotient: SymbolicEtaQuotient -> %
etaQuotient(y)
represents the expansion ofg_r
(tau) in terms ofx
= exp(2 pii
tau/w) where w=width(m
,c
) at all cusps ofGamma0
(levely
). See eqref{eq:g_r(tau)}.
- expansions: % -> XHashTable (Fraction Integer , LX)
expansions(x)
returns the Laurent series expansions of $g_r
(tau)$ at all cusps ofGamma_0
(levelx
) corresponding to cusps(symbolicEtaQuotientx
).- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState , %) -> HashState
- from SetCategory
- latex: % -> String
- from SetCategory
- level: % -> PositiveInteger
level(x)
returnsm
such thatx
corresponds to a modular function forGamma_0
(m
).
- symbolicEtaQuotient: % -> SymbolicEtaQuotient
symbolicEtaQuotient(x)
returns the meta data corresponding tox
. If x=etaQuotient(y
) then symbolicEtaQuotient(x
)=y.