def test_conversion():
L = QQ.old_poly_ring(x, y, order="ilex")
G = QQ.old_poly_ring(x, y)
assert L.convert(x) == L.convert(G.convert(x), G)
assert G.convert(x) == G.convert(L.convert(x), L)
pytest.raises(CoercionFailed, lambda: G.convert(L.convert(1 / (1 + x)), L))
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))
def test_build_order():
R = QQ.old_poly_ring(x, y, order=(("lex", x), ("ilex", y)))
assert R.order((1, 5)) == ((1, ), (-5, ))
def test_old_poly_frac():
pytest.raises(GeneratorsNeeded, lambda: QQ.old_poly_ring())
pytest.raises(GeneratorsNeeded, lambda: QQ.old_frac_field())
