def test_localring(): Qxy = QQ.old_frac_field(x, y) R = QQ.old_poly_ring(x, y, order="ilex") X = R.convert(x) Y = R.convert(y) assert x in R assert 1 / x not in R assert 1 / (1 + x) in R assert Y in R assert X.ring == R assert X * (Y**2 + 1) / (1 + X) == R.convert(x * (y**2 + 1) / (1 + x)) assert X * y == X * Y pytest.raises(ExactQuotientFailed, lambda: X / Y) pytest.raises(ExactQuotientFailed, lambda: x / Y) pytest.raises(ExactQuotientFailed, lambda: X / y) assert X + y == X + Y == R.convert(x + y) == x + Y assert X - y == X - Y == R.convert(x - y) == x - Y assert X + 1 == R.convert(x + 1) assert X**2 / X == X assert R.from_GlobalPolynomialRing( ZZ.old_poly_ring(x, y).convert(x), ZZ.old_poly_ring(x, y)) == X assert R.from_FractionField(Qxy.convert(x), Qxy) == X pytest.raises(CoercionFailed, lambda: R.from_FractionField(Qxy.convert(x) / y, Qxy)) pytest.raises(ExactQuotientFailed, lambda: X / Y) pytest.raises(NotReversible, lambda: X.invert()) assert R._sdm_to_vector( R._vector_to_sdm([X/(X + 1), Y/(1 + X*Y)], R.order), 2) == \ [X*(1 + X*Y), Y*(1 + X)]
def test_globalring(): Qxy = QQ.old_frac_field(x, y) R = QQ.old_poly_ring(x, y) X = R.convert(x) Y = R.convert(y) assert x in R assert 1 / x not in R assert 1 / (1 + x) not in R assert Y in R assert X.ring == R assert X * (Y**2 + 1) == R.convert(x * (y**2 + 1)) assert X * y == X * Y == R.convert(x * y) == x * Y assert X + y == X + Y == R.convert(x + y) == x + Y assert X - y == X - Y == R.convert(x - y) == x - Y assert X + 1 == R.convert(x + 1) pytest.raises(ExactQuotientFailed, lambda: X / Y) pytest.raises(ExactQuotientFailed, lambda: x / Y) pytest.raises(ExactQuotientFailed, lambda: X / y) assert X**2 / X == X assert R.from_GlobalPolynomialRing( ZZ.old_poly_ring(x, y).convert(x), ZZ.old_poly_ring(x, y)) == X assert R.from_FractionField(Qxy.convert(x), Qxy) == X assert R.from_FractionField(Qxy.convert(x) / y, Qxy) is None assert R._sdm_to_vector(R._vector_to_sdm([X, Y], R.order), 2) == [X, Y]
def test_units(): R = QQ.old_poly_ring(x) assert R.is_unit(R.convert(1)) assert R.is_unit(R.convert(2)) assert not R.is_unit(R.convert(x)) assert not R.is_unit(R.convert(1 + x)) R = QQ.old_poly_ring(x, order='ilex') assert R.is_unit(R.convert(1)) assert R.is_unit(R.convert(2)) assert not R.is_unit(R.convert(x)) assert R.is_unit(R.convert(1 + x)) R = ZZ.old_poly_ring(x) assert R.is_unit(R.convert(1)) assert not R.is_unit(R.convert(2)) assert not R.is_unit(R.convert(x)) assert not R.is_unit(R.convert(1 + x))