Sometimes Singular creates unknown coefficient fields, which make Oscar unhappy

[thofma]

Best illustrated with an example:

julia> Qx, x = QQ["x"]; K, = number_field([x - 1, x^2 + 2], cached = false); # or any complicated field that translates into a generic `N_Field`

julia> R, = polynomial_ring(K, 2);

julia> I = ideal(R, [gen(R, 1)]);

julia> S, = quo(R, I);

julia> Oscar.singular_poly_ring(R) |> coefficient_ring |> typeof
Singular.N_Field{NfAbsNSElem}

julia> Oscar.singular_poly_ring(S) |> coefficient_ring |> typeof
Singular.N_UnknownSingularCoefficientRing

This happens, because for the construction of the Singular quotient ring we go via:

Oscar.jl/src/Rings/MPolyQuo.jl

Line 31 in 32b7e89

r.SQR = Singular.create_ring_from_singular_ring(Singular.libSingular.rQuotientRing(SG.ptr, base_ring(SG).ptr))

(this is the Singular quotient ring, of which the coefficient_ring is of the N_Unknown[...] type.

As a consequence, on the Singular side we don't have the identical coefficient ring, which yields problems like #3080.

This is ultimately a Singular.jl issue, but I guess here the issue gets more attention. I think the discussion in oscar-system/Singular.jl#187 (comment) and oscar-system/Singular.jl#336 is relevant.

One option is ditch the generic N_Field interface and just refuse to do anything with coefficient rings that cannot be handled by native Singular coefficient fields. In most cases we can transform the input to the appropriate type. For the rest we will throw a "sorry, can't do this" error. This is a rather drastic solution, but maybe the only realistic one given our manpower?

Any thoughts @fieker @fingolfin @hannes14?

[thofma]

Here is another simple example. Lots of things are broken for prime fields of large characteristic:

julia> F = GF(next_prime(ZZ(2)^100))
Finite field of characteristic 1267650600228229401496703205653

julia> Fx, (x, y) = F["x", "y"];

julia> I = ideal(Fx, [x, y]);

julia> Q, = quo(Fx, I);

julia> J = ideal(Q, [Q(x)]);

julia> Q(x) in J
ERROR: MethodError: no method matching (::Singular.N_UnknownSingularCoefficientRing)(::FpFieldElem)

[HechtiDerLachs]

Is there any progress on this issue. The workarounds in #3173 only cause other troubles and it seems that I will never get the tests to run there.

[fieker]

it should be, as of last Wedesday(??) be fixed. We confirm and close.
Thanks @hannes14

[fieker]

update: still open(ish), but making progress

[hannes14]

Status: fixed with master branch of Oscar, not fixed with released version of Oscar

[lgoettgens]

I can confirm the fix on e86fe09.