This is an ID10T error. The following assertion from the bug report is false:
> The prime 83 splits as PQ, where > P, Q have N(P)=83^5. sage: [P.residue_class_degree() for P in M.primes_above(83)] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] So the output is correct. David On Aug 17, 10:41 am, Harald Schilly <[email protected]> wrote: > From the notebook's report a problem bugtracker: > > Problem Computing Artin Symbol > > ------------ problem description > > The command artin_symbol(P) doesn't compute the Artin Symbol in a > specific case. Below is the code. There is an Artin symbol, but the > command > returns an empty result. For other primes like 3, 7, there is no > problem. > > sage: M.<g>=NumberField(x^10 + 2*x^9 + 11*x^8 - 14*x^7 + 13*x^6 - > 160*x^5 + 575*x^4 + 1288*x^3 + 4890*x^2 + 4764*x + > 4483,'h').galois_closure() > sage: print(M); > sage: G=M.galois_group() > sage: print(M.discriminant().factor()) > sage: [G.artin_symbol(P) for P in M.primes_above(83)] > > Number Field in g with defining polynomial x^10 + 2*x^9 + 11*x^8 - > 14*x^7 + 13*x^6 - 160*x^5 + 575*x^4 + 1288*x^3 + 4890*x^2 + 4764*x + > 4483 > > -1 * 47^5 > > [(), (), (), (), (), (), (), (), (), ()] > > --------- expected output > > Should get an output like > > [(1,3,9,5,8)(2,6,4,7,10), (1,8,5,9,3)(2,10,7,4,6)] > > which is the Artin symbol for 3 > > ------------ note > > I can confirm this in 4.1.1 > > H --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
