Allow (::Singular.N_FField)(::fmpq_poly) ?

[YueRen]

Not sure whether this should be allowed, but when casting a Oscar polynomial to a Singular polynomial over the rationals, Singular does not care whether the Oscar polynomial was defined over QQ or ZZ:

Kx,(x0,x1,x2,x3,x4,x5) = PolynomialRing(QQ,6);
g = 2*x1+(2^2+1)*x2+(2^3+2)*x3+(2^4+2^2+1)*x4+(2^5+2^3+2)*x5;
S,_ = Singular.PolynomialRing(singular_ring(K),map(string,symbols(Kx)))
S(g) # works perfectly

Rx,(x0,x1,x2,x3,x4,x5) = PolynomialRing(ZZ,6);
g = 2*x1+(2^2+1)*x2+(2^3+2)*x3+(2^4+2^2+1)*x4+(2^5+2^3+2)*x5;
S(g) # works perfectly as well

In contrast, when casting a Oscar polynomial to a Singular polynomial over the rational function field, Singular complains if the Oscar polynomial was defined over a univariate polynomial ring:

K,s = RationalFunctionField(QQ,"s");
Kx,(x0,x1,x2,x3,x4,x5) = PolynomialRing(K,6);
g = s*x1+(s^2+1)*x2+(s^3+s)*x3+(s^4+s^2+1)*x4+(s^5+s^3+s)*x5;
S,_ = Singular.PolynomialRing(singular_ring(K),map(string,symbols(Kx)))
S(g) # works perfectly

R,s = PolynomialRing(QQ,"s")
Rx,(x0,x1,x2,x3,x4,x5) = PolynomialRing(R,6);
g = s*x1+(s^2+1)*x2+(s^3+s)*x3+(s^4+s^2+1)*x4+(s^5+s^3+s)*x5;
S(g) # ERROR
S(change_base_ring(K,g)) # workaround

For the sake of consistency, I think that (::Singular.N_FField)(::fmpq_poly) should be allowed. Are there any reasons why function fields should behave differently to rationals (honest question)?

[fingolfin]

Most likely this is simply an oversight. PR welcome:-)

[thofma]

We will take care of it when overhauling thesingular_ring, see also oscar-system/Oscar.jl#975 and oscar-system/Oscar.jl#976. It is a broken design, so I would not spend too much time on it.