Factorize a polynomial with coefficients in a Galois field : factor

factor can also factorize a univariate polynomial with coefficients in a Galois field.
Input for example to have G= $\mathbb {F}$₄:

G:=GF(2,2,['w','G'])

Output :

GF(2,w^2+w+1,[w,G],undef)

Input for example :

a:=G(w)

factor(a^2*x^2+1))

Output :

(G(w+1))*(x+G(w+1))^2