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 the- q-series (q=exp(pi*i*tau)) of $lambda(- ntau)^e$. 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 $theta_j(0,- q)- ^4$ for- j=2,3,4, i.e. the 4th power of the theta constants.