On Mon, Mar 30, 2015 at 10:47 AM, kcrisman <[email protected]> wrote:
> http://stackoverflow.com/questions/29347686/sage-roots-on-the-root-field
>
> sage: R.<x>=PolynomialRing(GF(9,'a'))
> sage: f=x^3+2*x+1
> sage: K.<alpha>=f.root_field()
> sage: f.roots(ring=K)
>
> apparently returns an error but Magma can compute it... reply at the SO.com
> question, please.

Thanks -- I just posted this...  That said, what happens when you try
the original persons code is basically best described as a litany of
bugs...

Sage doesn't support relative extensions of finite fields really.
(It would be nice if it did, but it doesn't.)  One can find the roots
at least in an absolute field, as follows:


F.<alpha> = GF(3^6)
R.<x> = PolynomialRing(F)
f = x^3+2*x+1
f.roots()

output:  [(2*alpha^5 + 2*alpha^4, 1), (2*alpha^5 + 2*alpha^4 + 2, 1),
(2*alpha^5 + 2*alpha^4 + 1, 1)]

https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2015-03-30-112034-root-stack-overflow.sagews

-- 
William (http://wstein.org)

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