Dear GAP Forum, > On Jun 5, 2015, at 7:19 AM, Jaco Versfeld <[email protected]> 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 _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
