Inefficient conversion from OSCAR to Singular

[fingolfin]

It seems there is quite some inefficient conversion code from OSCAR to Singular (perhaps also the other way around) in e.g. src/Rings/mpoly.jl. One example:

function (SF::Singular.N_AlgExtField)(a::fqPolyRepFieldElem)
  F = parent(a)
  SFa = gen(SF)
  res = SF(coeff(a, 0))
  for i in 1:degree(F)-1
    res += SF(coeff(a, i))*SFa^i # <- very inefficient
  end
  return res
end

At the very least don't compute SFa^i in each iteration, reuse the previous one. But really, we should use the coefficient vector and directly construct the output from that.

Multiple other functions in that file have the exact same problem.

I assume the algebraic geometry / commutative algebra team will want to resolve this.

[ederc]

Dumb question: Shouldn't these conversion functions not be part of Singular.jl?

[fingolfin]

@ederc agreed

[fingolfin]

Searching for ^i in this file reveals more instances.

[fingolfin]

We also just noticed that there may be a correctness issue here if the field on the OSCAR and Singular sides use different defining polynomials?

It also doesn't even check if the size of the fields coincides

[thofma]

Should be addressed together with #976