|Bill Allombert on Tue, 08 Jan 2008 12:59:02 +0100|
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|Re: GAP4 group names|
On Mon, Jan 07, 2008 at 07:07:45PM -0500, Roger Lipsett wrote: > Can someone tell me where to find the "translation" of the GAP4 group names > given by PARI as well as GAP4? I've looked on line, and the only reference > appears to be a book that I don't care to purchase. Neither the GAP4 nor the > PARI docs seem to contain the algorithm. The group naming is explained in http://www.lms.ac.uk/jcm/1/lms1996-001/sub/lms1996-001.pdf > For example, "polgalois(x^8-3)" returns (among other things) [1/4.cD(4)^2]2, > and polgalois(x^8-2) returns 2D_8(8)=[D(4)]2. I am not quite sure you mean by algorithm here, but if GP returns e.g. ? polgalois(x^8-3) %1 = [32, -1, 15, "[1/4.cD(4)^2]2"] Then you can construct the transitive group under GAP with the command gap> G:=TransitiveGroup(8,15); [1/4.cD(4)^2]2 And then perform any computation on G. Cheers, Bill.