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2019-11-18 07:44:36 -0500 received badge  Student (source)
2019-11-18 07:43:03 -0500 asked a question simple script gives "ValueError: element is not in the prime field"

I have a very simple script that does not work. It is the following.

for a in range(1,r):
    for b in range(1,r):
        g=a+b*x^2+x^4
        if g.is_irreducible():
            K.<a>=FiniteField(r^4, name='a', modulus = g)
            if a^l != 1:
                print("hooray")

Here l is defined somewhere else, but that is not what gives the error I think. I think the error occurs when sage goes over the line "K.=FiniteField(r^4, name='a', modulus = g)", because maybe the line "g=a+b*x^2+x^4" does not work? If I do this script manually without the for loops, by just assigning some values to a and b, then it works fine.