>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. The prime 83 splits as PQ, where P, Q have N(P)=83^5. 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 -~----------~----~----~----~------~----~------~--~---
