PariError when creating a relative number field

[culler]

Please close as duplicate of #252

sage: t = QQ['t'].gen() 
sage: K.<a> = QQ.extension(t^6 - 1/4*t^3 - 1/64)
sage: s = K['s'].gen() 
sage: g = s^4 + 2*a^2*s^2 + a^4 + a
sage: L.<b> = K.extension(g)

fails with PariError?: inconsistent data (12)

The failure occurs in: rings.number_field.number_field_rel.pari_relative_polynomial().polisirreducible()

If, instead, one tries:

sage: L.<b> = K.extension(g, check=False)

it fails with PariError?: (5)

This time it fails in: pari_absolute_base_polynomial().rnfequation(self.pari_relative_polynomial(), 1)

[culler]

I see now that this is just another example of NumberField? not working with polynomials that are not monic or not integral, which goes back 5 years to #252. So feel free to close the ticket. Unfortunately I don't see any way to work around it in my project. Too bad.

[fwclarke]

Replying to culler:

Unfortunately I don't see any way to work around it in my project.

I think the following works:

sage: PQ.<t> = QQ[]
sage: f = t^6 - 1/4*t^3 - 1/64
sage: f = PQ(pari(f).polredabs())
sage: K.<a> = QQ.extension(f)
sage: s = K['s'].gen()
sage: g = s^4 + 2*a^2*s^2 + a^4 + a
sage: L.<b> = K.extension(g)
sage: L
Number Field in b with defining polynomial s^4 + 2*a^2*s^2 + a^4 + a over its base field
sage: K
Number Field in a with defining polynomial t^6 - 2*t^3 - 1

I think this technique could be used to sort out #252. But there are many details to be got right.

[culler]

Replying to fwclarke:

Thanks! That is very helpful. It is not the whole story, I'm afraid, since I am working in a tower of extensions and the call pari(f) seems to fail if f does not have rational coefficients. Still, it gets things off the ground and gives me a hint about where to look for the rest of the answer.