Fix quadratic_defect

[nbruin]

Steps To Reproduce

No response

Expected Behavior

From https://groups.google.com/g/sage-devel/c/KfvLDTqf4rk/m/_4SAoCDtAgAJ :

Qx.<x> = QQ[]
K.<t> = NumberField(x^10 - x^8 - 2*x^7 - x^6 + 2*x^5 + 2*x^4 - x^2 + 1)
p = K.prime_factors(2)[0]
pi = K.uniformizer(p)
a = 1 + pi^3
K.quadratic_defect(a,p)

should work

Actual Behavior

It actually produces a

TypeError: cannot convert non-integral float to integer

Additional Information

Reason is clear:
the line that produces the error is:

sage/src/sage/rings/number_field/number_field.py

Line 2605 in ccc11b6

s = self(q((a - 1) / pi**w)**(1/2))

That code can never have worked properly, but in python 3, 1/2 will be a float and the finite field element constructed here cannot be raised to a float power. A line that could work is:

s = self(q((a - 1) / pi**w).sqrt())

although it would probably worth checking if there are no other bugs in the code. Doctests need to be improved for this code too, since this error must have been lurking since the implementation was merged.

The post has another suggestion to change the computation of a uniformizing element, presently:

sage/src/sage/rings/number_field/number_field.py

Lines 2583 to 2587 in ccc11b6

	# compute uniformizer pi
	for g in p.gens():
	if g.valuation(p) == 1:
	pi = g
	break

and use pi = K.uniformizer(p) instead. It looks like that is indeed a more robust way (and internally does actually much the same thing but with more knowledge of the internal representation)

Environment

- **Sage Version**: 10.3

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide