First of all, congratulations for this free and wonderfull software. I have a question about GF(2).This is maybe a bit stupid but I cannot find the answer anywere.
When I use this code, I don't understand why y^3 is still there because I think this is equal to y for both 0 and 1. So why the Groebner basis is [y^3 + y, x^2 + y^2 + 1, x*y] and not [x+y+1,x*y], which should be reduced to [x+y+1]. I tried to add a modulus but it does'nt seem to work. I am quite disappointed because all the interest of Groebner basis in cryptanalysis is that the degree of polynomes don't grow a lot due to the fact that x^2 + x =0. sage: Q.<x,y> = PolynomialRing(GF(2)) sage: R2 = GF(2,name='x,y') sage: R2 Finite Field of size 2 sage: e=[x**2+y**2+1,x*y] sage: e [x^2 + y^2 + 1, x*y] sage: I=ideal(e) sage: I Ideal (x^2 + y^2 + 1, x*y) of Multivariate Polynomial Ring in x, y over Finite Field of size 2 sage: B=I.groebner_basis(); B [y^3 + y, x^2 + y^2 + 1, x*y] So my question is : why SAGE doesn't take into account the fact that x^2 = x in GF(2) and how do force him to do it. Thanks for your help PS : I tried with integer(2) but there is exactly the same matter -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
