With:
sage: m=f.list()[0]
sage: m
2*a + 4
you get an element of the field of size 25:
sage: m.parent()
Finite Field in a of size 5^2
To separate 2*a
and 4
, you need to see it as a polynomial on the field on 5 elements (with indeterminate a
):
sage: m.polynomial()
2*a + 4
sage: m.polynomial().parent()
Univariate Polynomial Ring in a over Finite Field of size 5
So, you can get the coefficients as follows:
sage: p = m.polynomial()
sage: p.dict()
{0: 4, 1: 2}
sage: p.dict().items()
[(0, 4), (1, 2)]
So you can get the list you want as follows:
sage: [a^i*j for i,j in p.dict().items()]
[4, 2*a]
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