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]


  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 ?


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/