On Sep 29, 2008, at 8:50 AM, David Møller Hansen wrote:

>
> Let F2=GF(2^7,'a'), E=EllipticCurve(F1,[0,0,1,1,1]),
> P=E.random_point(), F2=GF((2^7)^4,'a')
>
> Purpose: I want to look at the point P in the curve over F2 instead of
> F1. So I some way I want to extend F1.
>
> My question is how do I, when I already have an extension field F1,
> extend it to F2 in a way s.t. I can reuse element from F1 in F2?

Does this do what you want?

sage: F1.<a> = GF(2^7)
sage: f=x^2+x+F1(1)
sage: F2=F1.extension(f,'u')
sage: F2
Univariate Quotient Polynomial Ring in u over Finite Field in a of  
size 2^7 with modulus u^2 + u + 1
sage: a in F2
True

HTH

Justin

--
Justin C. Walker, Curmudgeon-At-Large, Director
Institute for the Enhancement of the Director's Income
--------
The path of least resistance:
it's not just for electricity any more.
--------




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