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Hi,
Finite field elements are almost stored as vectors. It is actually a bit more complicated since there are several implementation and most of the time it uses external libraries (givaro, pari or ntl). You can nevertheless convert your element into a vector with
sage: K = GF(16, 'a')
sage: V = K.vector_space()
sage: K.inject_variables()
sage: V(a^2 + 3*a + 1)
sage: v =V(a^2 + a + 1)
sage: v
(1, 1, 1, 0)
sage: v.parent()
Vector space of dimension 4 over Finite Field of size 2
Vincent
