CachedQFunctions(C, L)ΒΆ
cachedqfunct.spad line 90 [edit on github]
C: Ring
CachedQFunctions implements a cache for powers of functions from QFunctions.
- eulerFunctionPower: (PositiveInteger, Integer) -> L
eulerFunctionPower(n, e)
computes (prod_{k=1
}^infty(1-q^
{kn
}))^e.
- jacobiFunctionPower: (PositiveInteger, PositiveInteger, Integer) -> L
jacobiFunctionPower(d,g,e)
computes and caches jacobiFunction(d
,g
)^e from QFunctions(C
,L
).
- kleinJInvariantPower: (PositiveInteger, Integer) -> L
kleinJInvariantPower(d,e)
computes and caches multiplyExponents((kleinJInvariant()$QFunctions(C
,L
))^e,d
).
- modularLambdaPower: (PositiveInteger, Integer) -> L
modularLambdaPower(n, e)
computes theq
-series (q=exp(pi*i*tau)) of $lambda(n
tau)^e$. The modular lambda function is defined by $lambda(tau)=theta_2(0,q
)^4/
theta_3(0,q
)^4
$. See https://en.wikipedia.org/wiki/Modular_lambda_function https://fungrim.org/topic/Modular_lambda_function/
- thetaPower4: PositiveInteger -> L
The function
thetaPower4
(j
) returns $theta_j(0,q
)^4
$ forj=2
,3,4, i.e. the 4th power of the theta constants.