Bug in mapping to residue fields

[cremona]

See #9417:

sage: K.<a> = NumberField(x^2+18*x+1)
sage: P = K.ideal(2)
sage: F = K.residue_field(P)
sage: R = PolynomialRing(F, 'x')
sage: R([0, a, a, 1])
x^3 + abar*x^2 + abar*x
sage: F(a)
1
sage: a.minpoly()
x^2 + 18*x + 1
sage: F.gen()
abar
sage: F.gen().minpoly()
x^2 + x + 1

The polynomial x^3+a*x^2+a*x reduced modulo P=(2) wrongly to x^3+abar*x^2+abar*x. Although the generator of the residue field F is suggestively called abar, it it *not* the reduction of a mod P (which is 1 mod P).

[cremona]

Note that this is correct:

R([F(co) for co in [0,a,a,1]])

I think the problem lies in lines 94-108 of sage/rings/polynomial/polynomial_zz_pex.pyx, hence I am CC-int Yann L-C! Meanwhile I am using that work-around for #9417.

[ylchapuy]

see my comments on #9389

polynomial_zz_pex.pyx is not intended to be used for this base ring (maybe it could but it wasn't thought like this). The constructor of the univariate polynomials ring should be more careful.

And I'm sorry, but I won't have time to do this myself.

[cremona]

Thanks for reporting back. I'll try to fix this myself, but in any case I was able to use a simple workaround.

[jakobkroeker]

fixed?

[cremona]

With 6.9.beta3 I see this:

K.<a> = NumberField(x^2+18*x+1)
sage: P = K.ideal(2)
sage: F = K.residue_field(P)
sage: R = PolynomialRing(F, 'x')
sage: R([0, a, a, 1])
x^3 + x^2 + x

which shows that the original issue has been fixed, though I do not know where or when.

I cannot see the "won't fix" option but that is what this should now get.

[pbruin]

Replying to cremona:

With 6.9.beta3 I see this:

K.<a> = NumberField(x^2+18*x+1)
sage: P = K.ideal(2)
sage: F = K.residue_field(P)
sage: R = PolynomialRing(F, 'x')
sage: R([0, a, a, 1])
x^3 + x^2 + x

which shows that the original issue has been fixed, though I do not know where or when.

It might be #11239.

[pbruin]

Replying to cremona:

I cannot see the "won't fix" option but that is what this should now get.

I agree.