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*a^4 + 3/7*a^3 + 1/7*a + 1/7, a, a^2, a^3, a^4, a^5, a^6] The power basis is not 7-maximal. You're asking Sage and Magma for different things: sage: discriminant(x^7 - x^5 - 2*x^4 - 2*x^3 + 2*x^2 - x + 4).factor() 2^6 * 7^2 * 691^2 I'm fairly confident that if you ask Magma for the discriminant of W, you'll lose the factor of 7^2. David On Fri, Sep 28, 2018 at 4:54 AM Harry Smit <harryjustuss...@gmail.com> wrote: > 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*x^2 - x + 4 > > In Sage, I used as input: > > L.<a> = NumberField(x^7 - x^5 - 2*x^4 - 2*x^3 + 2*x^2 - x + 4) > L.absolute_discriminant().factor(); > > to obtain > > 2^6 * 691^2 > > In Magma, I used as input > > L := NumberField(x^7 - x^5 - 2*x^4 - 2*x^3 + 2*x^2 - x + 4); > g := DefiningPolynomial(L); > W := IntegerRing(); > Factorization(W ! Discriminant(g)) > > to obtain > > [ <2, 6>, <7, 2>, <691, 2> ] > > Checking this by hand, it seems that Magma is correct: the polynomial has > a double root (mod 7) at 5, hence 7 ramifies in the number field. > > The problem is not the factor function, this was only added for clarity. > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
