[GAP Forum] Iterated algebraic extensions.

[Borges-Trenard]

Dear GAP forum,

I am trying to compute the finite field F_{3^6} by means of extending first F_3 through x^2+2*x+2 and then the second extension with
y^3+a1*y^2+a1*y+a1^3, where a1 is a root of x^2+2*x+2.

Then I have used the following instructions (GAP 4.7.2):
gap> x := Indeterminate( GF( 3 ) );; SetName( x, "x" );;
gap> e1 := AlgebraicExtension( GF( 3 ), x^2 + 2 * x + 2 );;
gap> a1 := RootOfDefiningPolynomial( e1 );;
gap> y := Indeterminate( e1 );; SetName( y, "y" );;
gap> e2 := AlgebraicExtension( e1, y^3 + a1 * y^2 + a1 * y + a1^3 );;
gap> a2 := RootOfDefiningPolynomial( e2 );;

Now I face at least two troubles:

1) I can perform operations with a1 and a2 but the result is not clear, for example:
gap> a1 * a2;
a*a
The point is that RootOfDefiningPolynomial always prints like "a", I have not found a way to change it.

2) A simple operation like the following one is not already possible:
gap> a2^2;

I will be very grateful for any help.

Many thanks,   Miguel.

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