Bind Kieffer's `acb_theta` module from FLINT

[albinahlback]

Jean Kieffer has written an extensive and well-performing module in FLINT for theta functions, under the module acb_theta. He implements new algorithms, and it would be nice if it was wrapped in Nemo.

This should probably be done after flintlib/flint#2182 is merged, and we will shortly after release v3.3.0.

[thofma]

Here are some breadcrumbs (I wrote this for an Oscar user, who wanted to call these functions). It can be made free of Oscar, but I am too lazy right now:

using Oscar

function _theta_all(z::Vector{ComplexF64}, tau::Matrix{ComplexF64})
  CC = Oscar.ComplexField()
  zz = CC.(z)
  tauu = matrix(CC, tau)
  r = _theta_all(zz, tauu)
  return map(x -> Float64(real(x)) + Float64(imag(x))*im, r)
end

function _theta_all(z::Vector{ComplexFieldElem}, tau::ComplexMatrix)
  zz = Oscar.Hecke.acb_vec(z)
  g = nrows(tau)
  th = Oscar.Hecke.acb_vec(2^(2*g))
  @ccall Oscar.Nemo.libflint.acb_theta_all(th::Ptr{Oscar.Hecke.acb_struct}, zz::Ptr{Oscar.Hecke.acb_struct}, tau::Ref{ComplexMatrix}, 0::Cint, precision(Balls)::Int)::Nothing
  Oscar.Hecke.acb_vec_clear(zz, length(z))
  Oscar.Hecke.acb_vec_clear(th, 2^(2*g))
  res = Oscar.Hecke.array(base_ring(tau), th, 2^(2*g))
end

What is a bit tedious is how to expose the characteristics (a, b), which are tuples in {0,1}^g and the tuple (a,b) is in the acb_theta FLINT module encoded an ulong, where a corresponds to the most significant bits. Not too user friendly, if someone just has g = 3 and wants the value at, say, a = (0, 1, 0) and b = (1, 1, 0).