Avoid using symbolic expressions together with real algebra.  This works fine:

sage: Fq.<a> = GF(3^10)
sage: (2*a^9 + 2*a^8 + a^4 +1)/(a^5+2*a+2)
a^9 + a^8 + a^7 + a^5 + 2*a^4 + a^3 + 2*a^2 + 2*a

The a here was defined in the first line to be the generator of your field:

sage: type(a)
<type 'sage.rings.finite_rings.element_givaro.FiniteField_givaroElement'>

sage: a.parent()
Finite Field in a of size 3^10

On 14 June 2014 06:49, Lian Liu <csliul...@gmail.com> wrote:
> I created a finite field
>
> Fq.<a> = GF(3^10)
>
> there is a symbolic expression, for example,
> ex = (2*a^9 + 2*a^8 + a^4 +1)/(a^5+2*a+2)
> and we have
> type(ex) = <type 'sage.symbolic.expression.Expression'>
>
> how can we convert the symbolic expression ex so that it is evaluated as an
> element in Fq,
> That is,
> eval = a^9 + a^8 + a^7 + a^5 + 2*a^4 + a^3 + 2*a^2 + 2*a
> such that
> type(eval) = <type
> 'sage.rings.finite_rings.element_givaro.FiniteField_givaroElement'>?
>
> I tried to use AA(ex) and algebraic(ex, Fq), but they both gave errors.
> Please help.
> Thank you.
>
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