On 16 September 2012 05:29, Jori Mantysalo <[email protected]> wrote: > For example x^3-3*x-1 has Galois group C_3, and galois_group(type="pari") > can tell it. But how to get roots as function of others? In this example, if > r1 is one of the roots, others are r^2-r-2 and -r^2+2.
sage: K.<a> = NumberField(x^3-3*x-1) sage: [s(a) for s in K.galois_group()] [a, a^2 - a - 2, -a^2 + 2] (The interface for Galois groups is rather confusing because there are actually two independent implementations: one which calculates the Galois group as an abstract group, and one which actually calculates it as an explicit group of automorphisms of an explicitly given splitting field, which is much slower. It would be a good coding project to get the two to play a bit more nicely together, and improve the docs, but nobody's done this so far.) Hope this helps, David -- You received this message because you are subscribed to the Google Groups "sage-support" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en.
