David is right. In Magma, when you ask for the discriminant of a number
field you get the discriminant of its defining poynomial which is a
multiple of the field discriminant. You have to ask for the discriminant
of its ring of integers:
> R := PolynomialRing(Rationals());
> L := NumberField(x^7
This looks like a discrepancy between the discriminant of the polynomial
and the discriminant of the number field (which should be the discriminant
of the maximal order). Sure enough:
sage: O = L.maximal_order()
sage: O.discriminant().factor()
2^6 * 691^2
sage: O.basis()
[4/7*a^6 + 6/7*a^5 + 5/7*
The following computations were done on cocalc.com, version'SageMath
version 8.3, Release Date: 2018-08-03'
There seems to be a disagreement with Sage and Magma over the discriminant
of the number field defined by adjoining a root of the following polynomial
to Q:
x^7 - x^5 - 2*x^4 - 2*x^3 + 2
