CoCoA » CoCoALib

I'm halfway through the process, but this is tricky.
[I think this is interesting, because it's the first try in changing the design for ideals]

myElim is a member function of the class IdealBase, so returning an ideal (smart pointer) doesn't feel quite right.

I would like to swap the computed generators (vector of RingElem) into the new ideal, but to do that I'd need to call ourGetPtr (dynamic_cast), and also that does not seem right.

New question: elim(I, X) (currently in CoCoALib) or elim(X, I) (traditionally in CoCoA)?

They have to be same!!
Investigate what other systems do, and decide.

Anna Maria Bigatti wrote:

New question: elim(I, X) (currently in CoCoALib) or elim(X, I) (traditionally in CoCoA)?

They have to be same!!
Investigate what other systems do, and decide.

Singular: elim(i,3..4);
Oscar: eliminate(I::PBWAlgIdeal, V::Vector{<:PBWAlgElem}; ordering = nothing)
M2: eliminate(x,ideal(f,g))
Magma: EliminationIdeal(I, k: parameters)

elim of (I,X) or (X,I)?

1. respects the rule "more structured argument first"
2. like Singular/Oscar and Magma

1. respects the rule "as you would say in words": "eliminate X from I"
2. respects backward compatibility in CoCoA
3. like Macaulay/2

In fact, there would be no ambiguity in providing both ways (a bit tedious, but possible), but I don't think it is a good idea.

Anna Maria Bigatti wrote:

elim of (I,X) or (X,I)?

comparison with other functions in CoCoA/CoCoALib: (I,X) seems winning (but breaks CoCoA backward compatibility)

deg(x*y^2+y, x)  
homog(x^3-y, w)
CoeffListWRT(F, y)