def test_Domain__algebraic_field():
alg = ZZ.algebraic_field(sqrt(2))
assert alg.ext.minpoly == Poly(x**2 - 2)
assert alg.dom == QQ
alg = QQ.algebraic_field(sqrt(2))
assert alg.ext.minpoly == Poly(x**2 - 2)
assert alg.dom == QQ
alg = alg.algebraic_field(sqrt(3))
assert alg.ext.minpoly == Poly(x**4 - 10*x**2 + 1)
assert alg.dom == QQ
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