Problem computing weak splitting field/weak p-adic Galois extension over 2-adics

[Asconik]

In the following, I attempt to calculate the weak splitting field of a polynomial over the $$2$$-adics:

from mclf import *
v0 = QQ.valuation(2)
QQ2 = FakepAdicCompletion(QQ,v0)
K. = QQ[]

f = -28x^6 - 1064x^4 - 9296*x^2 - 224

L = QQ2.weak_splitting_field(f)

This raises a

ValueError: defining polynomial (x^6 + 38x^4 + 76x^2 + 8) must be irreducible

The same error appears when attempting to calculate

L = WeakPadicGaloisExtension(QQ2,f)

In total, I found seven polynomials f raising a Value Error like this. They are:

$$f_1 = 36 x^6 - 240x^5 + 280x^4 + 832x^3 - 976x^2 - 1984x - 736$$ $$f_2 = -28x^6 - 1064x^4 - 9296x^2 - 224$$ $$f_3 = 28x^6 + 4648x^4 + 2128x^2 + 224$$ $$f_4 = -32x^6 - 304x^4 - 664x^2 - 4$$ $$f_5 = 4x^6 + 152x^4 + 1328x^2 + 32$$ $$f_6 = -32x^6 - 448x^5 - 176x^4 + 64x^3 - 88x^2 + 16x - 4$$ $$f_7 = 32x^6 + 448x^5 + 176x^4 - 64x^3 + 88x^2 - 16x + 4$$

For each of these polynomials, the splitting field over the $$2$$-adics is of degree $$6$$ with Galois group 6T1. Their ramification degrees are all equal to $$2$$, hence their weak splitting fields should be of degree $$2$$.

[swewers]

The problem arises with the method extensionof the class FakepAdicCompletion:

sage: from mclf import *
sage: v_2 = QQ.valuation(2)
sage: QQ2 = FakepAdicCompletion(QQ, v_2)
sage: R.<x> = QQ[]
sage: f = x^6 + 38*x^4 + 332*x^2 + 8
sage: QQ2.extension(f)
2-adic completion of Number Field in pi6 with defining polynomial x^6 + 38*x^4 + 332*x^2 + 8

Before the change, this produced an error.

There a certainly other cases where the error still occurs. I'll try to fix this soon.