Thanks Dima and Peter Just to clarify here is sample output for a degree 6 and 8 polynomial: sage: NumberField(x^6-21*x^4+105*x^2-105, 'alpha').galois_group(type='pari') Galois group PARI group [48, -1, 11, "2S_4(6) = [2^3]S(3) = 2 wr S(3)"] of degree 6 of the Number Field in alpha with defining polynomial x^6 - 21*x^4 + 105*x^2 - 105
sage: NumberField(x^8-36*x^6+378*x^4-1260*x^2+945, 'alpha').galois_group(type='pari') Galois group PARI group [384, -1, 44, "[2^4]S(4)"] of degree 8 of the Number Field in alpha with defining polynomial x^8 - 36*x^6 + 378*x^4 - 1260*x^2 + 945 I think it is quite clear that the wreath product is intended in the degree 6 case, which appears as "S_4 x C_2 = [48,-1,11]" in the link that Peter gave. On Friday, August 15, 2014 7:27:04 PM UTC+10, Peter Bruin wrote: > > Hi Steve, > > The documentation of PARI's group labelling/naming conventions is here > (there are an "old" and a "new" convention, and Sage uses the new one): > > > http://pari.math.u-bordeaux.fr/dochtml/html.stable/Functions_related_to_general_number_fields.html#polgalois > > I don't see 2^n S_n mentioned here; I guess that is taken from the string > returned as the last component by polgalois(), and the documentation agrees > with Dima that this is the name of the group in GAP. > > Peter > > > Op vrijdag 15 augustus 2014 06:35:22 UTC+1 schreef s meagher: >> >> Apologies if this is answered elsewhere in this group or in the >> documentation, but I have not found the answer. >> >> When computing a galois group in sage using type='pari' Sage gives the >> group a name. I have not been able to find a guide for the nomenclature >> used. >> >> For example, names like S_3 and D(4) are fairly clear. But what is 2^3 >> S_3 and 2^4 S_4 - I presume they are the wreath products (\Z/2)^n . S_n. >> >> Is there a reference? And am I right about 2^n S_n >> >> Thanks >> >> Steve >> > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
