Thank you very much.

From: Alexander Hulpke []
Sent: 05 June 2015 03:28 PM
To: Jaco Versfeld
Subject: Re: [GAP Forum] Factorizing polynomials over GF(2^m)?

Dear GAP Forum,

> On Jun 5, 2015, at 7:19 AM, Jaco Versfeld <> 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 ]


   Alexander Hulpke

<table width="100%" border="0" cellspacing="0" cellpadding="0" 
<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>

Forum mailing list

Reply via email to