def test_Domain_alg_field_from_poly():
f = Poly(x**2 - 2)
g = Poly(x**2 - 3)
h = Poly(x**4 - 10*x**2 + 1)
alg = ZZ.alg_field_from_poly(f)
assert alg.ext.minpoly == f
assert alg.dom == QQ
alg = QQ.alg_field_from_poly(f)
assert alg.ext.minpoly == f
assert alg.dom == QQ
alg = alg.alg_field_from_poly(g)
assert alg.ext.minpoly == h
assert alg.dom == QQ
