[GAP Forum] Factorizing polynomials over GF(2^m)?

[Jaco Versfeld]

Good day,

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.

What am I doing wrong?

Kind Regards,
Jaco


_______________________________
Jaco Versfeld (D.Ing)
Senior lecturer
Centre for Telecommunications Access and Services
School of Electrical and Information Engineering
University of the Witwatersrand
Johannesburg

Tel:         +27-11-717-7212
Email:     jaco.versfeld at wits.ac.za
web:       http://school.eie.wits.ac.za/~versfeld=
<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