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from algorithms.maths.polynomial import Monomial

from fractions import Fraction

import math

import unittest

class TestSuite(unittest.TestCase):

def setUp(self):

self.m1 = Monomial({})

self.m2 = Monomial({1: 1}, 2)

self.m3 = Monomial({1: 2, 2: -1}, 1.5)

self.m4 = Monomial({1: 1, 2: 2, 3: -2}, 3)

self.m5 = Monomial({2: 1, 3: 0}, Fraction(2, 3))

self.m6 = Monomial({1: 0, 2: 0, 3: 0}, -2.27)

self.m7 = Monomial({1: 2, 7: 2}, -math.pi)

self.m8 = Monomial({150: 5, 170: 2, 10000:3}, 0)

self.m9 = 2

self.m10 = math.pi

self.m11 = Fraction(3, 8)

self.m12 = 0

self.m13 = Monomial({1: 1}, -2)

self.m14 = Monomial({1: 2}, 3)

self.m15 = Monomial({1: 1}, 3)

self.m16 = Monomial({1: 2, 7: 2}, math.pi)

self.m17 = Monomial({1: -1})

def test_monomial_addition(self):

# Monomials with different underlying variables or

# even different power of those variables must not be added!

self.assertRaises(ValueError, lambda x, y: x + y, self.m1, self.m2)

self.assertRaises(ValueError, lambda x, y: x + y, self.m2, self.m3)

self.assertRaises(ValueError, lambda x, y: x + y, self.m2, self.m14)

# Additive inverses of each other should produce the zero monomial.

self.assertEqual(self.m13 + self.m2, self.m1)

# Zero monomial + Zero monomial = Zero monomial

self.assertEqual(self.m1 + self.m1, self.m1)

# Coefficient float.

self.assertEqual(self.m7 + self.m7, Monomial({1: 2, 7: 2}, -2*math.pi))

# Coefficient 0 so should equal the zero monomial.

self.assertEqual(self.m8, self.m1)

# The constant term cannot be added to any monomial

# that has any variables.

self.assertRaises(ValueError, lambda x, y: x + y, self.m2, self.m9)

# Any literal cannot be added to a Monomial. However, a monomial

# can be added to any int, float, Fraction, or Monomial.

# So 2 + Monomial is raises TypeError but Monomial + 2 may work fine!

self.assertRaises(TypeError, lambda x, y: x + y, self.m9, self.m2)

# Any constant added to a zero monomial produces

# a monomial.

self.assertEqual(self.m1 + self.m9, Monomial({}, 2))

self.assertEqual(self.m1 + self.m12, Monomial({}, 0))

return

def test_monomial_subtraction(self):

# Monomials with different underlying variables or

# even different power of those variables must not be subtracted!

self.assertRaises(ValueError, lambda x, y: x - y, self.m1, self.m2)

self.assertRaises(ValueError, lambda x, y: x - y, self.m2, self.m3)

self.assertRaises(ValueError, lambda x, y: x - y, self.m2, self.m14)

# Additive inverses of each other should produce the zero monomial.

self.assertEqual(self.m2 - self.m2, self.m1)

self.assertEqual(self.m2 - self.m2, Monomial({}, 0))

# Zero monomial - Zero monomial = Zero monomial

self.assertEqual(self.m1 - self.m1, self.m1)

# Coefficient int.

self.assertEqual(self.m2 - self.m15, Monomial({1: 1}, -1))

# Coefficient float.

self.assertEqual(self.m16 - self.m7, Monomial({1: 2, 7: 2}, 2*math.pi))

# The constant term cannot be added to any monomial

# that has any variables.

self.assertRaises(ValueError, lambda x, y: x - y, self.m2, self.m9)

# Any literal cannot be added to a Monomial. However, a monomial

# can be added to any int, float, Fraction, or Monomial.

# So 2 + Monomial is raises TypeError but Monomial + 2 may work fine!

self.assertRaises(TypeError, lambda x, y: x - y, self.m9, self.m2)

# Any constant added to a zero monomial produces

# a monomial.

self.assertEqual(self.m1 - self.m9, Monomial({}, -2))

self.assertEqual(self.m1 - self.m12, Monomial({}, 0))

return

def test_monomial_multiplication(self):

# Usual multiplication.

# The positive and negative powers of the same variable

# should cancel out.

self.assertEqual(self.m2 * self.m13, Monomial({1: 2}, -4))

self.assertEqual(self.m2 * self.m17, Monomial({}, 2))

# A coefficient of zero should make the product zero.

# Zero monomial * any int, float, Fraction, or Monomial = Zero monomial

self.assertEqual(self.m8 * self.m5, self.m1)

self.assertEqual(self.m1 * self.m2, self.m1)

# Test usual float multiplication.

self.assertEqual(self.m7 * self.m3, Monomial({1: 4, 2: -1, 7: 2}, -1.5*math.pi))

return

def test_monomial_inverse(self):

# The Zero monomial is not invertible.

self.assertRaises(ValueError, lambda x: x.inverse(), self.m1)

self.assertRaises(ValueError, lambda x: x.inverse(), self.m8)

self.assertRaises(ValueError, lambda x: x.inverse(), Monomial({},self.m12))

# Check some inverses.

self.assertEqual(self.m7.inverse(), Monomial({1: -2, 7: -2}, -1/math.pi))

# Doesn't matter if the coefficient is Fraction or float.

# Both should be treated as same.

self.assertEqual(self.m5.inverse(), Monomial({2: -1}, Fraction(3, 2)))

self.assertEqual(self.m5.inverse(), Monomial({2: -1}, 1.5))

# Should work fine without variables too!

self.assertTrue(self.m6.inverse(), Monomial({}, Fraction(-100, 227)))

self.assertEqual(self.m6.inverse(), Monomial({}, -1/2.27))

return

def test_monomial_division(self):

# Any monomial divided by the Zero Monomial should raise a ValueError.

self.assertRaises(ValueError, lambda x, y: x.__truediv__(y), self.m2, self.m1)

self.assertRaises(ValueError, lambda x, y: x.__truediv__(y), self.m2, self.m8)

self.assertRaises(ValueError, lambda x, y: x.__truediv__(y), self.m2, self.m12)

# Test some usual cases.

self.assertEqual(self.m7 / self.m3, Monomial({2: 1, 7: 2}, -2*math.pi/3))

self.assertEqual(self.m14 / self.m13, Monomial({1: 1}) * Fraction(-3, 2))

return

def test_monomial_substitution(self):

# Test with int.

self.assertAlmostEqual(self.m7.substitute(2), -16*math.pi, delta=1e-9)

# Test with float.

self.assertAlmostEqual(self.m7.substitute(1.5), (1.5 ** 4)* -math.pi, delta=1e-9)

# Test with Fraction.

self.assertAlmostEqual(self.m7.substitute(Fraction(-1, 2)), (Fraction(-1, 2) ** 4)*-math.pi, delta=1e-9)

# Test with a complete substitution map.

self.assertAlmostEqual(self.m7.substitute({1: 3, 7: 0}), (3 ** 2) * (0 ** 2) * -math.pi, delta=1e-9)

# Test with a more than complete substitution map.

self.assertAlmostEqual(self.m7.substitute({1: 3, 7: 0, 2: 2}), (3 ** 2) * (0 ** 2) * -math.pi, delta=1e-9)

# Should raise a ValueError if not enough variables are supplied!

self.assertRaises(ValueError, lambda x, y: x.substitute(y), self.m7, {1: 3, 2: 2})

self.assertRaises(ValueError, lambda x, y: x.substitute(y), self.m7, {2: 2})

# The zero monomial always gives zero upon substitution.

self.assertEqual(self.m8.substitute(2), 0)

self.assertEqual(self.m8.substitute({1231: 2, 1: 2}), 0)

return

def test_monomial_all_variables(self):

# Any variable with zero power should not exist in the set

# of variables.

self.assertEqual(self.m5.all_variables(), {2})

self.assertEqual(self.m6.all_variables(), set())

# The zero monomial should output empty set.

self.assertEqual(self.m8.all_variables(), set())

return

def test_monomial_clone(self):

# A monomial should produce its copy

# with same underlying variable dictionary

# and same coefficient.

self.assertEqual(self.m3, self.m3.clone())

# The zero monomial is identified and

# always clones to itself.

self.assertEqual(self.m1, self.m8.clone())

self.assertEqual(self.m1, self.m1.clone())

self.assertEqual(self.m8, self.m1.clone())

self.assertEqual(self.m8, self.m8.clone())

return

if __name__ == '__main__':

unittest.main()