SymbolicEtaGamma

qetasymb.spad line 200 [edit on github]

SymbolicEtaGamma collects data for the expansion of eta_{delta,m,lambda}(gammatau)$ and $eta_{delta,g,m,lambda}^{[R]}(gammatau)$. See eqref{eq:eta_delta-m-lambda(gamma*tau)} and eqref{eq:eta_delta-g-m-lambda^[R](gamma*tau)}.

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

cdExponent: % -> Fraction Integer

If pure?(x) cdExponent(x)=1/2, otherwise cdExponent(x)=0.

coerce: % -> OutputForm

from CoercibleTo OutputForm

delta: % -> PositiveInteger

If x=eta(delta,g,m,lambda,gamma) then delta(x) returns delta.

eta: (PositiveInteger, Integer, PositiveInteger, NonNegativeInteger, Matrix Integer) -> %

eta(delta,g,m,lambda,gamma) represents the meta-data for the expansion of $eta_{delta,g,m,lambda}^{[R]}(gamma tau)$ in terms of $q=exp(2ipitau)$. We require that c>0 in gamma=matrix[[a,b],[c,d]].

gamma1: % -> Matrix Integer

If x=eta(delta,g,m,lambda,gamma) then gamma1(x) returns the SL2Z part of splitMatrix(gamma,delta,m,lambda).

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

lambda: % -> NonNegativeInteger

If x=eta(delta,g,m,lambda,gamma) then lambda(x) returns lambda.

latex: % -> String

from SetCategory

multiplier: % -> PositiveInteger

If x=eta(delta,g,m,lambda,gamma) then multiplier(x) returns m.

pure?: % -> Boolean

pure?(x) returns true if x corresponds to a pure eta function.

qExponent: % -> Fraction Integer

qExponent(x) returns the (fractional) exponent for the order of the expansion of x in the original variable q, see eqref{eq:eta_delta-m-lambda(gamma*tau)} and eqref{eq:eta_delta-g-m-lambda^[R](gamma*tau)}.

rationalPrefactor: % -> Fraction Integer

rationalPrefactor(x) returns the square of the second product in eqref{eq:eta_delta-m-lambda(gamma*tau)} if pure?(x). See ref{thm:c*tau+d}. If not pure?(x) then rationalPrefactor(x)=1.

subindex: % -> Integer

If x=eta(delta,g,m,lambda,gamma) then subindex(x) returns g.

transformationMatrix: % -> Matrix Integer

If x=eta(delta,g,m,lambda,gamma) then transformationMatrix(x) returns gamma.

udelta: % -> Fraction Integer

Returns $u_{delta,m,lambda}$. See eqref{eq:eta_delta-m-lambda(gamma*tau)}. See eqref{eq:uv_delta}

unityExponent: % -> Fraction Integer

unityExponent(x) returns the (fractional) exponent for the unity factor of the expansion of x, see eqref{eq:eta_delta-m-lambda(gamma*tau)} and eqref{eq:eta_delta-g-m-lambda^[R](gamma*tau)}.

vdelta: % -> Fraction Integer

Returns $v_{delta,m,lambda}$. See eqref{eq:eta_delta-m-lambda(gamma*tau)}. See eqref{eq:uv_delta}.

BasicType

CoercibleTo OutputForm

SetCategory