ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 10 Dec 2013 05:31:45 +0100Splitting field and mu invarianthttps://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/Please inform me how to compute the following two problems
1) Splitting field of a polynomial over Z, its degree of extension over Q and it's roots.
2) The mu invariant of other elliptic curves in an isogeny class from the mu invariant of the minimal curve in that isogeny class.
Sun, 22 Sep 2013 04:13:23 +0200https://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/Answer by John Cremona for <p>Please inform me how to compute the following two problems</p>
<p>1) Splitting field of a polynomial over Z, its degree of extension over Q and it's roots.</p>
<p>2) The mu invariant of other elliptic curves in an isogeny class from the mu invariant of the minimal curve in that isogeny class.</p>
https://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/?answer=15779#post-id-15779For question 1:
sage: R.<x> = ZZ[]
sage: f = x^3-2
sage: K.<a> = NumberField(f)
sage: L.<b> = K.galois_closure()
sage: L
Number Field in b with defining polynomial x^6 + 40*x^3 + 1372
Tue, 10 Dec 2013 05:31:45 +0100https://ask.sagemath.org/question/10556/splitting-field-and-mu-invariant/?answer=15779#post-id-15779