Karim BELABAS on Sun, 9 Jun 2002 23:23:57 +0200 (MEST) |
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22- polgalois() |
[ Cc-ed to pari-users since this might be of general interest, although it discusses features of the alpha version 2.2.3 ] On Sun, 9 Jun 2002, Karim BELABAS wrote: > 22- INCOMPATIBILITY: polgalois(); changed 3rd component of result so that > it gives the numbering among all transitive subgroups of S_n [ was ad > hoc up to 7, then as described above for n >= 8 ] The output of polgalois was specifically documented for degree n <= 7, with reference to Butler & McKay's paper for the remaining n up to 11. The output was a vector [N, s, k] with N the degree of the Galois closure s the signature of the group (1 if G \subset A_n, -1 otherwise) k For n <= 7, was an ad hoc integer equal to 1 or 2 (almost always 1), to resolve ambiguities For n > 7, it gave the standard ordering among all transitive subgroups of S_n, in particular (n,k) already determine the group, and N, s only give nice additional information about it. In the unstable branch (pari-2.2.3), I've changed the output so that the latter scheme is used for n <= 7 also, to improve consistency. Unfortunately, it will break existing scripts checking for a specific 3-component output, and also those that check explicitly the old k to distinguish between two groups, which occured only twice, in degree 6, for C_6 = [6,-1,1] vs. S_3 = [6,-1,2] and S_4^- = [24,-1,1] vs. A_4 x C_2 = [24,-1,2] Currently, the change is in effect whatever the value of the 'compatible' default. It can be considered as a bug. Any opinion ? Karim. P.S: Also polgalois(x) returned [1, -1, 1] which was inconsistent with the documentation since {1} \subset A_1. So I've changed s for that specific group, but I consider it a bugfix since it ran contrary to the docs. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dép. de Mathematiques, Bat. 425 Fax: (+33) (0)1 69 15 60 19 Université Paris-Sud Email: Karim.Belabas@math.u-psud.fr F-91405 Orsay (France) http://www.math.u-psud.fr/~belabas -- PARI/GP Home Page: http://www.parigp-home.de/