Hi Alasdair!

What about this:

sage: F.<x>=GF(2^8,name='x')
sage: R.<y>=PolynomialRing(GF(2))
sage: p = F.random_element()
sage: p
x^7 + x^5 + x^4 + x
sage: pp = p.polynomial()
sage: pp(x=y)
y^7 + y^5 + y^4 + y

The only difference to your approach is that R is defined over the
field GF(2) rather than the ring Zmod(2).

sage: GF(2)==Zmod(2)
False

Cheers,
Simon

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