Thomas Gueuning wrote :
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.
You also can type :
sage: RR.<x,y> = GF(2)[] # it means that variables are x and y. You may add ideal generators : y^2-y and x^2-x. In the polynomial space x^2 != x : degree aren't the same. But in the quotient you have x^2=x as you expect if x==0 or x==1. Then the Groebner basis is almost what you want : sage: ideal([x**2+y**2+1,x*y,x^2-x,y^2-y]).groebner_basis() [y^2 + y, x + y + 1] The second polynom is x+y+1 and you may forgot y^2+y. I don't know how you can proof that you get exactly the right result. Order over degree changes the Groebner basis... F. who maybe makes a mistake... -- 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
