> Instead of using vectors, you should just use the indexing on the
> polynomials to extract the coefficients you want:
>
> sage: matrix([[p[i] for i in range(3)] for p in [x^10%p1, x^11%p1, x^12%p1]])
> [1 0 1]
> [1 1 1]
> [1 1 0]
>

There's also the "padded_list" method, used exactly for getting
vectors of a specific length:

sage: R.<x> = GF(2)[]
sage: f = x^2-3
sage: f.list()
[1, 0, 1]

sage: f.padded_list(5)
[1, 0, 1, 0, 0]

sage: p2 = x^5-4*x^2-1

sage: [ ((x^i)%p2).list() for i in range(8,12) ]
[[0, 0, 0, 1], [0, 0, 0, 0, 1], [1], [0, 1]]

sage: [ ((x^i)%p2).padded_list(p2.degree()) for i in range(8,12) ]
[[0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0]]

-cc

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