Thank you very much. ________________________________________ From: Alexander Hulpke [hul...@fastmail.fm] Sent: 05 June 2015 03:28 PM To: Jaco Versfeld Cc: fo...@gap-system.org Subject: Re: [GAP Forum] Factorizing polynomials over GF(2^m)?
Dear GAP Forum, > On Jun 5, 2015, at 7:19 AM, Jaco Versfeld <jaco.versf...@wits.ac.za> wrote: > > I want to factor polynomials over GF(2^m). As a quick test, I did the > following: > > R:=PolynomialRing(GF(8),["x"]); > x:=Indeterminate(GF(8),"x"); > p := x^7 + 1; > Factors(p); > > The result that I obtain is: > [ x+Z(2)^0, x^3+x+Z(2)^0, x^3+x^2+Z(2)^0 ] > > This doesn't make sense, since I expected (x-\alpha^0), (x-\alpha^1) ... > (x-\alpha^6) to have been the roots. Polynomials do not carry the actual ring, but only the characteristic and get factored over their coefficient rings. To factor over GF(8), specify the polynomial ring, i.e. gap> Factors(R,p); [ x+Z(2)^0, x+Z(2^3), x+Z(2^3)^2, x+Z(2^3)^3, x+Z(2^3)^4, x+Z(2^3)^5, x+Z(2^3)^6 ] Regards, Alexander Hulpke <table width="100%" border="0" cellspacing="0" cellpadding="0" style="width:100%;"> <tr> <td align="left" style="text-align:justify;"><font face="arial,sans-serif" size="1" color="#999999"><span style="font-size:11px;">This communication is intended for the addressee only. It is confidential. If you have received this communication in error, please notify us immediately and destroy the original message. You may not copy or disseminate this communication without the permission of the University. Only authorised signatories are competent to enter into agreements on behalf of the University and recipients are thus advised that the content of this message may not be legally binding on the University and may contain the personal views and opinions of the author, which are not necessarily the views and opinions of The University of the Witwatersrand, Johannesburg. All agreements between the University and outsiders are subject to South African Law unless the University agrees in writing to the contrary. </span></font></td> </tr> </table _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
