def test_Format(self):
self.assertEqual("1+2", s(c(1), c(2)).fmt())
self.assertEqual("8*x**5", p(c(-8), x(5)).abs_fmt())
self.assertEqual("8*x**5", p(c(8), x(5)).abs_fmt())
term1 = p(c(8), x(5))
term2 = p(c(-2), x(2))
self.assertEqual("8*x**5-2*x**2", s(term1, term2).fmt())
self.assertEqual(term1, term1)
def test_Format(self):
self.assertEqual("1+2", s(c(1), c(2)).fmt())
self.assertEqual("8*x**5", p(c(-8), x(5)).abs_fmt())
self.assertEqual("8*x**5", p(c(8), x(5)).abs_fmt())
term1 = p(c(8), x(5))
term2 = p(c(-2), x(2))
self.assertEqual("8*x**5-2*x**2", s(term1, term2).fmt())
self.assertEqual(term1, term1)
def test_Distributivity_of_Multiplication(self):
def eq(expect, original):
self.assertEqual(expect, original.apply_distributivity())
# x * 2 + x * 3 <-- x * (2 + 3)
eq(s(p(x(1), c(2)), p(x(1), c(3))), p(x(1), s(c(2), c(3))))
# 5 * (8x^5 - 2x^2) = 5*(8*x^5) + 5*(-2*x^2)
term1 = p(c(8), x(5))
term2 = p(c(-2), x(2))
eq(s(p(c(5), p(c(8), x(5))), p(c(5), p(c(-2), x(2)))),
p(c(5), s(term1, term2)))
def test_Distributivity_of_Multiplication(self):
def eq(expect, original):
self.assertEqual(expect, original.apply_distributivity())
# x * 2 + x * 3 <-- x * (2 + 3)
eq(s(
p(x(1), c(2)),
p(x(1), c(3))),
p(x(1), s(c(2), c(3))))
# 5 * (8x^5 - 2x^2) = 5*(8*x^5) + 5*(-2*x^2)
term1 = p(c(8), x(5))
term2 = p(c(-2), x(2))
eq(s(p(c(5), p(c(8), x(5))),
p(c(5), p(c(-2), x(2)))),
p(c(5), s(term1, term2)))
def test_Product_Associativity(self):
def eq(factors, expr):
self.assertEqual(set(factors), set(expr.apply_associativity().factors))
# 1 * (2 * 3) --> 1 * 2 * 3
eq({1, 2, 3}, p(1, p(2, 3)))
# (1 * 2 ) * 3 --> 1 * 2 * 3
eq({1, 2, 3}, p(p(1, 2), 3))
# (1 * (2 * (3 * 4))) --> 1 * 2 * 3 * 4
self.assertEqual(p(1, 2, 3, 4), p(1, p(2, p(3, 4))).apply_associativity())
def test_GivenExpressions(self):
#"(x-1)*(x+1)"
self.assertEqual("x**2-1", p(s(x(1), c(-1)), s(x(1), c(1))).simplify().fmt())
self.assertEqual("x**2+2*x+1", simplify("(x+1)*(x+1)"))
self.assertEqual("x**2+6*x", simplify("(x+3)*x*2-x*x"))
self.assertEqual("x**3+x**2+x", simplify("x+x*x+x*x*x"))
self.assertEqual("x**4+3*x+6", simplify("(2*x+3)*2-x+x*x*x*x"))
self.assertEqual("0", simplify("x*x-(x-1)*(x+1)-1"))
self.assertEqual( "-x", simplify("5-5-x"))
self.assertEqual("-1", simplify("x*x*x-x*x*x-1"))
def test_GivenExpressions(self):
#"(x-1)*(x+1)"
self.assertEqual("x**2-1",
p(s(x(1), c(-1)), s(x(1), c(1))).simplify().fmt())
self.assertEqual("x**2+2*x+1", simplify("(x+1)*(x+1)"))
self.assertEqual("x**2+6*x", simplify("(x+3)*x*2-x*x"))
self.assertEqual("x**3+x**2+x", simplify("x+x*x+x*x*x"))
self.assertEqual("x**4+3*x+6", simplify("(2*x+3)*2-x+x*x*x*x"))
self.assertEqual("0", simplify("x*x-(x-1)*(x+1)-1"))
self.assertEqual("-x", simplify("5-5-x"))
self.assertEqual("-1", simplify("x*x*x-x*x*x-1"))
def test_Product_Associativity(self):
def eq(factors, expr):
self.assertEqual(set(factors),
set(expr.apply_associativity().factors))
# 1 * (2 * 3) --> 1 * 2 * 3
eq({1, 2, 3}, p(1, p(2, 3)))
# (1 * 2 ) * 3 --> 1 * 2 * 3
eq({1, 2, 3}, p(p(1, 2), 3))
# (1 * (2 * (3 * 4))) --> 1 * 2 * 3 * 4
self.assertEqual(p(1, 2, 3, 4),
p(1, p(2, p(3, 4))).apply_associativity())
def test_sum_factors(self):
c1, c2, c3 = c(1), c(2), c(3)
u, v = s(c1, c2), s(c2, c3)
self.assertSequenceEqual((u, v), tuple(p(u, v).sum_factors()))
self.assertSequenceEqual((u, v), tuple(p(u, v, c(1)).sum_factors()))
def test_Format(self):
self.assertEqual("8*x**5", p(c(-8), x(5)).abs_fmt())
self.assertEqual("8*x**5", p(c(8), x(5)).abs_fmt())
def test_simplify_adds_equal_powers(self):
self.assertEqual(s(p(c(2), x(1))), s(x(1), x(1)).simplify())
def test_PowerTerm(self):
self.assertEqual(x(2), p(x(2)).power_factors())
self.assertEqual(x(5), p(x(2), x(3)).power_factors())
self.assertEqual(None, p(x(2), x(-2)).power_factors())
def test_ConstantTerm(self):
self.assertEqual(c(5), p(c(5)).constant_factor())
self.assertEqual(c(15), p(c(5), c(3)).constant_factor())
def test_Format(self):
self.assertEqual("8*x**5", p(c(-8), x(5)).abs_fmt())
self.assertEqual("8*x**5", p(c(8), x(5)).abs_fmt())
def test___factors(self):
self.assertEqual(1, len(p([x(1)]).factors))
self.assertSequenceEqual((x(1),), p(x(1)).factors)
def test_Negative(self):
self.assertEqual(True, p(c(-1), c(1)).negative())
def test_ProductOfProducts(self):
self.assertEqual(c(10), p(c(2), p(c(5))).simplify())
self.assertEqual(c(10), p(p(c(5)), c(2)).simplify())
def test___factors(self):
self.assertEqual(1, len(p([x(1)]).factors))
self.assertSequenceEqual((x(1), ), p(x(1)).factors)
def test_ProductOfProducts(self):
self.assertEqual(c(10), p(c(2), p(c(5))).simplify())
self.assertEqual(c(10), p(p(c(5)), c(2)).simplify())
def test_PowerTerm(self):
self.assertEqual(x(2), p(x(2)).power_factors())
self.assertEqual(x(5), p(x(2), x(3)).power_factors())
self.assertEqual(None, p(x(2), x(-2)).power_factors())
def test_sum_factors(self):
c1, c2, c3 = c(1), c(2), c(3)
u, v = s(c1, c2), s(c2, c3)
self.assertSequenceEqual((u, v), tuple(p(u, v).sum_factors()))
self.assertSequenceEqual((u, v), tuple(p(u, v, c(1)).sum_factors()))
def test_simplify_adds_equal_powers(self):
self.assertEqual(s(p(c(2), x(1))), s(x(1), x(1)).simplify())
def test_Negative(self):
self.assertEqual(True, p(c(-1), c(1)).negative())
def test_ConstantTerm(self):
self.assertEqual(c(5), p(c(5)).constant_factor())
self.assertEqual(c(15), p(c(5), c(3)).constant_factor())