Module finite_field_element

Elements of Finite Fields

EXAMPLES:
    sage: K = FiniteField(2)
    sage: V = VectorSpace(K,3)
    sage: w = V([0,1,2])
    sage: K(1)*w
    (0, 1, 0)

We do some arithmetic involving a bigger field and a Conway polynomial,
i.e., we verify compatibility condition.
    sage: f = conway_polynomial(2,63)
    sage: K.<a> = GF(2**63, name='a', modulus=f)
    sage: n = f.degree()
    sage: m = 3;
    sage: e = (2^n - 1) / (2^m - 1)
    sage: c = a^e
    sage: conway = conway_polynomial(2,m)
    sage: conway(c) == 0
    True

Returns if x is a finite field element.

EXAMPLE:
    sage: is_FiniteFieldElement(1)
        False
    sage: is_FiniteFieldElement(IntegerRing())
        False
    sage: is_FiniteFieldElement(GF(5)(2))
        True