On Mon, May 4, 2009 at 1:07 PM, gtg <yih0siang0l...@gmail.com> wrote: > > Hi I'm new to sage. Can you tell me how to construct finite fields > using quotient of poly ring? For instance suppose I want to construct > GF(5^2) using a GF(5) poly ring mod out by x^2 + x + 1 how do I do > that? I can construct the quotient like this: > > p = 5 > F = GF(p) > R.<x> = F['x'] > f = x * x + x + 1 > S = R.quotient(f, 'a') > > How do I force S to a field so that I can use it with elliptic curves? > I know that I can simply do GF(5^2) but I want to be able to specify > the modulus explicitly.
Use the modulus option to GF: sage: p = 5 sage: F = GF(p) sage: R.<x> = F['x'] sage: S.<a> = GF(p^2,modulus=x^2+x+1) sage: S Finite Field in a of size 5^2 sage: a^2 + a + 1 0 sage: GF? # get more help! --~--~---------~--~----~------------~-------~--~----~ 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 URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
