def test_Monomial():
m = Monomial((3, 4, 1), (x, y, z))
n = Monomial((1, 2, 0), (x, y, z))
assert m.as_expr() == x**3 * y**4 * z
assert n.as_expr() == x**1 * y**2
assert m.as_expr(a, b, c) == a**3 * b**4 * c
assert n.as_expr(a, b, c) == a**1 * b**2
assert m.exponents == (3, 4, 1)
assert m.gens == (x, y, z)
assert n.exponents == (1, 2, 0)
assert n.gens == (x, y, z)
assert m == (3, 4, 1)
assert n != (3, 4, 1)
assert m != (1, 2, 0)
assert n == (1, 2, 0)
assert m[0] == m[-3] == 3
assert m[1] == m[-2] == 4
assert m[2] == m[-1] == 1
assert n[0] == n[-3] == 1
assert n[1] == n[-2] == 2
assert n[2] == n[-1] == 0
assert m[:2] == (3, 4)
assert n[:2] == (1, 2)
assert m * n == Monomial((4, 6, 1))
assert m / n == Monomial((2, 2, 1))
assert m * (1, 2, 0) == Monomial((4, 6, 1))
assert m / (1, 2, 0) == Monomial((2, 2, 1))
assert m.gcd(n) == Monomial((1, 2, 0))
assert m.lcm(n) == Monomial((3, 4, 1))
assert m.gcd((1, 2, 0)) == Monomial((1, 2, 0))
assert m.lcm((1, 2, 0)) == Monomial((3, 4, 1))
assert m**0 == Monomial((0, 0, 0))
assert m**1 == m
assert m**2 == Monomial((6, 8, 2))
assert m**3 == Monomial((9, 12, 3))
pytest.raises(ExactQuotientFailed, lambda: m / Monomial((5, 2, 0)))
def test_Monomial():
m = Monomial((3, 4, 1), (x, y, z))
l = Monomial((3, 4, 1))
n = Monomial((1, 2, 0), (x, y, z))
assert m.as_expr() == x**3*y**4*z
assert n.as_expr() == x**1*y**2
assert m.as_expr(a, b, c) == a**3*b**4*c
assert n.as_expr(a, b, c) == a**1*b**2
pytest.raises(ValueError, lambda: l.as_expr())
assert m.exponents == (3, 4, 1)
assert m.gens == (x, y, z)
assert n.exponents == (1, 2, 0)
assert n.gens == (x, y, z)
assert m == (3, 4, 1)
assert n != (3, 4, 1)
assert m != (1, 2, 0)
assert n == (1, 2, 0)
assert n != object()
assert m != n
assert hash(m) != hash(n)
assert m[0] == m[-3] == 3
assert m[1] == m[-2] == 4
assert m[2] == m[-1] == 1
assert n[0] == n[-3] == 1
assert n[1] == n[-2] == 2
assert n[2] == n[-1] == 0
assert m[:2] == (3, 4)
assert n[:2] == (1, 2)
assert m*n == Monomial((4, 6, 1))
assert m/n == Monomial((2, 2, 1))
assert m*(1, 2, 0) == Monomial((4, 6, 1))
assert m/(1, 2, 0) == Monomial((2, 2, 1))
pytest.raises(TypeError, lambda: m*object())
pytest.raises(TypeError, lambda: m/object())
assert m.gcd(n) == Monomial((1, 2, 0))
assert m.lcm(n) == Monomial((3, 4, 1))
assert m.gcd((1, 2, 0)) == Monomial((1, 2, 0))
assert m.lcm((1, 2, 0)) == Monomial((3, 4, 1))
pytest.raises(TypeError, lambda: m.gcd(object()))
pytest.raises(TypeError, lambda: m.lcm(object()))
assert m**0 == Monomial((0, 0, 0))
assert m**1 == m
assert m**2 == Monomial((6, 8, 2))
assert m**3 == Monomial((9, 12, 3))
pytest.raises(ValueError, lambda: m**-3)
pytest.raises(ExactQuotientFailed, lambda: m/Monomial((5, 2, 0)))
assert str(m) == "x**3*y**4*z**1"
assert str(l) == "Monomial((3, 4, 1))"