def test_FiniteExtension_convert():
# Test from_MonogenicFiniteExtension
K1 = FiniteExtension(Poly(x**2 + 1))
K2 = QQ[x]
x1, x2 = K1(x), K2(x)
assert K1.convert(x2) == x1
assert K2.convert(x1) == x2
K = FiniteExtension(Poly(x**2 - 1, domain=QQ))
assert K.convert_from(QQ(1, 2), QQ) == K.one/2
def test_FiniteExtension_Poly():
K = FiniteExtension(Poly(x**2 - 2))
p = Poly(x, y, domain=K)
assert p.domain == K
assert p.as_expr() == x
assert (p**2).as_expr() == 2
K = FiniteExtension(Poly(x**2 - 2, x, domain=QQ))
K2 = FiniteExtension(Poly(t**2 - 2, t, domain=K))
assert str(K2) == 'QQ[x]/(x**2 - 2)[t]/(t**2 - 2)'
eK = K2.convert(x + t)
assert K2.to_sympy(eK) == x + t
assert K2.to_sympy(eK ** 2) == 4 + 2*x*t
p = Poly(x + t, y, domain=K2)
assert p**2 == Poly(4 + 2*x*t, y, domain=K2)