def test_conversion(): L = QQ.poly_ring(x, y, order="ilex") G = QQ.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_units(): R = QQ.poly_ring(x) assert R.is_unit(R.convert(1)) assert not R.is_unit(R.convert(x)) assert not R.is_unit(R.convert(1 + x)) R = QQ.poly_ring(x, order='ilex') assert R.is_unit(R.convert(1)) assert not R.is_unit(R.convert(x)) R = ZZ.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_localring(): Qxy = QQ.frac_field(x, y) R = QQ.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 Y in R assert X.ring == R.ring assert X + Y == R.convert(x + y) assert X - Y == R.convert(x - y) assert X + 1 == R.convert(x + 1) assert X**2 / X == X assert R.from_PolynomialRing(ZZ.poly_ring(x, y).convert(x), ZZ.poly_ring(x, y)) == X assert R.from_FractionField(Qxy.convert(x), Qxy) == X
def test_globalring(): Qxy = QQ.frac_field(x, y) R = QQ.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.ring assert X * (Y**2 + 1) == R.convert(x * (y**2 + 1)) assert X * Y == R.convert(x * y) assert X + Y == R.convert(x + y) assert X - Y == R.convert(x - y) assert X + 1 == R.convert(x + 1) assert X**2 / X == X assert R.from_PolynomialRing(ZZ.poly_ring(x, y).convert(x), ZZ.poly_ring(x, y)) == X assert R.from_FractionField(Qxy.convert(x), Qxy) == X
def test_Domain_unify_composite(): assert unify(ZZ.poly_ring(x), ZZ) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), QQ) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), ZZ) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), QQ) == QQ.poly_ring(x) assert unify(ZZ, ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(QQ, ZZ.poly_ring(x)) == QQ.poly_ring(x) assert unify(ZZ, QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ, QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(ZZ.poly_ring(x, y), ZZ) == ZZ.poly_ring(x, y) assert unify(ZZ.poly_ring(x, y), QQ) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), ZZ) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), QQ) == QQ.poly_ring(x, y) assert unify(ZZ, ZZ.poly_ring(x, y)) == ZZ.poly_ring(x, y) assert unify(QQ, ZZ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(ZZ, QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(QQ, QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(ZZ.frac_field(x), ZZ) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ) == QQ.frac_field(x) assert unify(QQ.frac_field(x), ZZ) == QQ.frac_field(x) assert unify(QQ.frac_field(x), QQ) == QQ.frac_field(x) assert unify(ZZ, ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(QQ, ZZ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ, QQ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ, QQ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ.frac_field(x, y), ZZ) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), QQ) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), ZZ) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), QQ) == QQ.frac_field(x, y) assert unify(ZZ, ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(QQ, ZZ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ, QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(QQ, QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x)) == ZZ.poly_ring(x) assert unify(ZZ.poly_ring(x), QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), ZZ.poly_ring(x)) == QQ.poly_ring(x) assert unify(QQ.poly_ring(x), QQ.poly_ring(x)) == QQ.poly_ring(x) assert unify(ZZ.poly_ring(x, y), ZZ.poly_ring(x)) == ZZ.poly_ring(x, y) assert unify(ZZ.poly_ring(x, y), QQ.poly_ring(x)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), ZZ.poly_ring(x)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x, y), QQ.poly_ring(x)) == QQ.poly_ring(x, y) assert unify(ZZ.poly_ring(x), ZZ.poly_ring(x, y)) == ZZ.poly_ring(x, y) assert unify(ZZ.poly_ring(x), QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x), ZZ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(QQ.poly_ring(x), QQ.poly_ring(x, y)) == QQ.poly_ring(x, y) assert unify(ZZ.poly_ring(x, y), ZZ.poly_ring(x, z)) == ZZ.poly_ring(x, y, z) assert unify(ZZ.poly_ring(x, y), QQ.poly_ring(x, z)) == QQ.poly_ring(x, y, z) assert unify(QQ.poly_ring(x, y), ZZ.poly_ring(x, z)) == QQ.poly_ring(x, y, z) assert unify(QQ.poly_ring(x, y), QQ.poly_ring(x, z)) == QQ.poly_ring(x, y, z) assert unify(ZZ.frac_field(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ.frac_field(x), ZZ.frac_field(x)) == QQ.frac_field(x) assert unify(QQ.frac_field(x), QQ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ.frac_field(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), ZZ.frac_field(x)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x), ZZ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(QQ.frac_field(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(ZZ.frac_field(x, y), QQ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), ZZ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), QQ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(ZZ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(ZZ.poly_ring(x), QQ.frac_field(x)) == ZZ.frac_field(x) assert unify(QQ.poly_ring(x), ZZ.frac_field(x)) == ZZ.frac_field(x) assert unify(QQ.poly_ring(x), QQ.frac_field(x)) == QQ.frac_field(x) assert unify(ZZ.poly_ring(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(ZZ.poly_ring(x, y), QQ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x, y), ZZ.frac_field(x)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x, y), QQ.frac_field(x)) == QQ.frac_field(x, y) assert unify(ZZ.poly_ring(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(ZZ.poly_ring(x), QQ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x), ZZ.frac_field(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.poly_ring(x), QQ.frac_field(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.poly_ring(x, y), ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(ZZ.poly_ring(x, y), QQ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.poly_ring(x, y), ZZ.frac_field(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.poly_ring(x, y), QQ.frac_field(x, z)) == QQ.frac_field(x, y, z) assert unify(ZZ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x) assert unify(ZZ.frac_field(x), QQ.poly_ring(x)) == ZZ.frac_field(x) assert unify(QQ.frac_field(x), ZZ.poly_ring(x)) == ZZ.frac_field(x) assert unify(QQ.frac_field(x), QQ.poly_ring(x)) == QQ.frac_field(x) assert unify(ZZ.frac_field(x, y), ZZ.poly_ring(x)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), QQ.poly_ring(x)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x, y), ZZ.poly_ring(x)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x, y), QQ.poly_ring(x)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x), ZZ.poly_ring(x, y)) == ZZ.frac_field(x, y) assert unify(ZZ.frac_field(x), QQ.poly_ring(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x), ZZ.poly_ring(x, y)) == ZZ.frac_field(x, y) assert unify(QQ.frac_field(x), QQ.poly_ring(x, y)) == QQ.frac_field(x, y) assert unify(ZZ.frac_field(x, y), ZZ.poly_ring(x, z)) == ZZ.frac_field(x, y, z) assert unify(ZZ.frac_field(x, y), QQ.poly_ring(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), ZZ.poly_ring(x, z)) == ZZ.frac_field(x, y, z) assert unify(QQ.frac_field(x, y), QQ.poly_ring(x, z)) == QQ.frac_field(x, y, z)
def test_poly_frac(): pytest.raises(GeneratorsNeeded, lambda: QQ.poly_ring()) pytest.raises(GeneratorsNeeded, lambda: QQ.frac_field())
def test_build_order(): R = QQ.poly_ring(x, y, order=build_product_order((("lex", x), ("ilex", y)), (x, y))) assert R.order((1, 5)) == ((1,), (-5,))