compute Groebner Basis over Galois Field (2^m)

Hi, all,
I want to know how to compute Groebner Basis over Galois Field (2^m)?
For example, let m=4, given the irreducible polynomial x^4+x+1, how to generate the finite field?
and when I use command "groebner", whether it will work over GF(2^4)?

thanks.

You can specify an extension with a specific minimal polynomial like this:

In fact in your case you can go with the default declaration

since in this case Singular uses a^4+a+1=0 as a default minimal polynomial.
GB-functionality works in such rings, no problem.
More on declarations of rings you can find at http://www.singular.uni-kl.de/Manual/latest/sing_28.htm#SEC38

Thank you a lot.

In the second situation, how can i know the default irreducible polynomial?

Thanks

> ring r=(2^4,a),x,dp;
> minpoly;
1*a^4+1*a^1+1*a^0