Dear Simon, Thanks a lot. With regards, Santanu
On 25 August 2011 23:02, Simon King <simon.k...@uni-jena.de> wrote: > Hi Santanu! > > On 25 Aug., 18:03, Santanu Sarkar <sarkar.santanu....@gmail.com> > wrote: > > How to calculate inverse of a polynomial f(x) modulo g(x) in the finite > > field GF(2^10)? > > The usual way to compute modular inverses in a polynomial ring over a > field is the extended Euclidean algorithm, xgcd. > > We start with a polynomial ring over GF(2^10): > sage: P.<x> = GF(2^10,'z')[] > > Next, we get two random polynomials. They happen to be relatively > prime, hence, there *is* an inverse of the first polynomial modulo the > second polynomial: > sage: p = P.random_element() > sage: q = P.random_element() > sage: gcd(p,q) > 1 > > Now, xgcd is a method of q, and I suggest that you read its > documentation. > > sage: d, _, pinv = q.xgcd(p) > sage: d # test again that the gcd is one > 1 > > Now, we verify that pinv really is the inverse of p modulo q: > > sage: q.divides(1-p*pinv) > True > > Best regards, > Simon > > -- > 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 > -- 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
