def test_Term():
a = Term(4 * x * y**2 / z / t**3)
b = Term(2 * x**3 * y**5 / t**3)
assert a == Term(4, Factors({x: 1, y: 2}), Factors({z: 1, t: 3}))
assert b == Term(2, Factors({x: 3, y: 5}), Factors({t: 3}))
assert a.as_expr() == 4 * x * y**2 / z / t**3
assert b.as_expr() == 2 * x**3 * y**5 / t**3
assert a.inv() == \
Term(Rational(1, 4), Factors({z: 1, t: 3}), Factors({x: 1, y: 2}))
assert b.inv() == Term(Rational(1, 2), Factors({t: 3}),
Factors({
x: 3,
y: 5
}))
assert a.mul(b) == a*b == \
Term(8, Factors({x: 4, y: 7}), Factors({z: 1, t: 6}))
assert a.quo(b) == a / b == Term(2, Factors({}), Factors({
x: 2,
y: 3,
z: 1
}))
assert a.pow(3) == a**3 == \
Term(64, Factors({x: 3, y: 6}), Factors({z: 3, t: 9}))
assert b.pow(3) == b**3 == Term(8, Factors({x: 9, y: 15}), Factors({t: 9}))
assert a.pow(-3) == a**(-3) == \
Term(Rational(1, 64), Factors({z: 3, t: 9}), Factors({x: 3, y: 6}))
assert b.pow(-3) == b**(-3) == \
Term(Rational(1, 8), Factors({t: 9}), Factors({x: 9, y: 15}))
assert a.gcd(b) == Term(2, Factors({x: 1, y: 2}), Factors({t: 3}))
assert a.lcm(b) == Term(4, Factors({x: 3, y: 5}), Factors({z: 1, t: 3}))
a = Term(4 * x * y**2 / z / t**3)
b = Term(2 * x**3 * y**5 * t**7)
assert a.mul(b) == Term(8, Factors({x: 4, y: 7, t: 4}), Factors({z: 1}))
assert Term((2 * x + 2)**3) == Term(8, Factors({x + 1: 3}), Factors({}))
assert Term((2*x + 2)*(3*x + 6)**2) == \
Term(18, Factors({x + 1: 1, x + 2: 2}), Factors({}))
A = Symbol('A', commutative=False)
pytest.raises(NonCommutativeExpression, lambda: Term(A))
f1, f2 = Factors({x: 2}), Factors()
assert Term(2, numer=f1) == Term(2, f1, f2)
assert Term(2, denom=f1) == Term(2, f2, f1)
pytest.raises(TypeError, lambda: a * 2)
pytest.raises(TypeError, lambda: a / 3)
pytest.raises(TypeError, lambda: a**3.1)
def test_Term():
a = Term(4*x*y**2/z/t**3)
b = Term(2*x**3*y**5/t**3)
assert a == Term(4, Factors({x: 1, y: 2}), Factors({z: 1, t: 3}))
assert b == Term(2, Factors({x: 3, y: 5}), Factors({t: 3}))
assert a.as_expr() == 4*x*y**2/z/t**3
assert b.as_expr() == 2*x**3*y**5/t**3
assert a.inv() == \
Term(Rational(1, 4), Factors({z: 1, t: 3}), Factors({x: 1, y: 2}))
assert b.inv() == Term(Rational(1, 2), Factors({t: 3}), Factors({x: 3, y: 5}))
assert a.mul(b) == a*b == \
Term(8, Factors({x: 4, y: 7}), Factors({z: 1, t: 6}))
assert a.quo(b) == a/b == Term(2, Factors({}), Factors({x: 2, y: 3, z: 1}))
assert a.pow(3) == a**3 == \
Term(64, Factors({x: 3, y: 6}), Factors({z: 3, t: 9}))
assert b.pow(3) == b**3 == Term(8, Factors({x: 9, y: 15}), Factors({t: 9}))
assert a.pow(-3) == a**(-3) == \
Term(Rational(1, 64), Factors({z: 3, t: 9}), Factors({x: 3, y: 6}))
assert b.pow(-3) == b**(-3) == \
Term(Rational(1, 8), Factors({t: 9}), Factors({x: 9, y: 15}))
assert a.gcd(b) == Term(2, Factors({x: 1, y: 2}), Factors({t: 3}))
assert a.lcm(b) == Term(4, Factors({x: 3, y: 5}), Factors({z: 1, t: 3}))
a = Term(4*x*y**2/z/t**3)
b = Term(2*x**3*y**5*t**7)
assert a.mul(b) == Term(8, Factors({x: 4, y: 7, t: 4}), Factors({z: 1}))
assert Term((2*x + 2)**3) == Term(8, Factors({x + 1: 3}), Factors({}))
assert Term((2*x + 2)*(3*x + 6)**2) == \
Term(18, Factors({x + 1: 1, x + 2: 2}), Factors({}))
A = Symbol('A', commutative=False)
pytest.raises(NonCommutativeExpression, lambda: Term(A))
f1, f2 = Factors({x: 2}), Factors()
assert Term(2, numer=f1) == Term(2, f1, f2)
assert Term(2, denom=f1) == Term(2, f2, f1)
pytest.raises(TypeError, lambda: a*2)
pytest.raises(TypeError, lambda: a/3)
pytest.raises(TypeError, lambda: a**3.1)
def test_Term():
a = Term(4 * x * y**2 / z / t**3)
b = Term(2 * x**3 * y**5 / t**3)
assert a == Term(4, Factors({x: 1, y: 2}), Factors({z: 1, t: 3}))
assert b == Term(2, Factors({x: 3, y: 5}), Factors({t: 3}))
assert a.as_expr() == 4 * x * y**2 / z / t**3
assert b.as_expr() == 2 * x**3 * y**5 / t**3
assert a.inv() == \
Term(Rational(1, 4), Factors({z: 1, t: 3}), Factors({x: 1, y: 2}))
assert b.inv() == Term(Rational(1, 2), Factors({t: 3}),
Factors({
x: 3,
y: 5
}))
assert a.mul(b) == a*b == \
Term(8, Factors({x: 4, y: 7}), Factors({z: 1, t: 6}))
assert a.quo(b) == a / b == Term(2, Factors({}), Factors({
x: 2,
y: 3,
z: 1
}))
assert a.pow(3) == a**3 == \
Term(64, Factors({x: 3, y: 6}), Factors({z: 3, t: 9}))
assert b.pow(3) == b**3 == Term(8, Factors({x: 9, y: 15}), Factors({t: 9}))
assert a.pow(-3) == a**(-3) == \
Term(Rational(1, 64), Factors({z: 3, t: 9}), Factors({x: 3, y: 6}))
assert b.pow(-3) == b**(-3) == \
Term(Rational(1, 8), Factors({t: 9}), Factors({x: 9, y: 15}))
assert a.gcd(b) == Term(2, Factors({x: 1, y: 2}), Factors({t: 3}))
assert a.lcm(b) == Term(4, Factors({x: 3, y: 5}), Factors({z: 1, t: 3}))
a = Term(4 * x * y**2 / z / t**3)
b = Term(2 * x**3 * y**5 * t**7)
assert a.mul(b) == Term(8, Factors({x: 4, y: 7, t: 4}), Factors({z: 1}))
assert Term((2 * x + 2)**3) == Term(8, Factors({x + 1: 3}), Factors({}))
assert Term((2*x + 2)*(3*x + 6)**2) == \
Term(18, Factors({x + 1: 1, x + 2: 2}), Factors({}))