test_polynomial.py

from algorithms.maths.polynomial import (
	Polynomial,
	Monomial
)
from fractions import Fraction
import math


import unittest

class TestSuite(unittest.TestCase):

	def setUp(self):
		self.p0 = Polynomial([
			Monomial({})
		])
		self.p1 = Polynomial([
			Monomial({}), Monomial({})
		])
		self.p2 = Polynomial([
			Monomial({1: 1}, 2)
		])
		self.p3 = Polynomial([
			Monomial({1: 1}, 2),
			Monomial({1: 2, 2: -1}, 1.5)
		])
		self.p4 = Polynomial([
			Monomial({2: 1, 3: 0}, Fraction(2, 3)),
			Monomial({1: -1, 3: 2}, math.pi),
			Monomial({1: -1, 3: 2}, 1)
		])
		self.p5 = Polynomial([
			Monomial({150: 5, 170: 2, 10000:3}, 0),
			Monomial({1: -1, 3: 2}, 1),	
		])
		self.p6 = Polynomial([
			2,
			-3,
			Fraction(1, 7),
			2**math.pi,
			Monomial({2: 3, 3: 1}, 1.25)
		])
		self.p7 = Polynomial([
			Monomial({1: 1}, -2),
			Monomial({1: 2, 2: -1}, -1.5)
		])

		self.m1 = Monomial({1: 2, 2: 3}, -1)

		return

	def test_polynomial_addition(self):
		
		# The zero polynomials should add up to
		# itselves only.
		self.assertEqual(self.p0 + self.p1, self.p0)
		self.assertEqual(self.p0 + self.p1, self.p1)
		
		# Additive inverses should add up to the
		# zero polynomial.
		self.assertEqual(self.p3 + self.p7, self.p0)
		self.assertEqual(self.p3 + self.p7, self.p1)

		# Like terms should combine.
		# The order of monomials should not matter.
		self.assertEqual(self.p2 + self.p3, Polynomial([
			Monomial({1: 1}, 4),
			Monomial({1: 2, 2: -1}, 1.5)
		]))
		self.assertEqual(self.p2 + self.p3, Polynomial([
			Monomial({1: 2, 2: -1}, 1.5),
			Monomial({1: 1}, 4),
		]))

		# Another typical computation.
		self.assertEqual(self.p5 + self.p6, Polynomial([
			Monomial({}, 7.96783496993343),
			Monomial({2: 3, 3: 1}, 1.25),
			Monomial({1: -1, 3: 2})
		]))

		return

	def test_polynomial_subtraction(self):

		self.assertEqual(self.p3 - self.p2, Polynomial([
			Monomial({1: 2, 2: -1}, 1.5)
		]))

		self.assertEqual(self.p3 - self.p3, Polynomial([]))

		self.assertEqual(self.p2 - self.p3, Polynomial([
			Monomial({1: 2, 2: -1}, -1.5)
		]))

		pass

	def test_polynomial_multiplication(self):
		self.assertEqual(self.p0 * self.p2, Polynomial([]))
		self.assertEqual(self.p1 * self.p2, Polynomial([]))

		self.assertEqual(self.p2 * self.p3, Polynomial([
			Monomial({1: 2}, 4),
			Monomial({1: 3, 2: -1}, Fraction(3, 1))
		]))
		return

	def test_polynomial_division(self):

		# Should raise a ValueError if the divisor is not a monomial
		# or a polynomial with only one term.
		self.assertRaises(ValueError, lambda x, y: x / y, self.p5, self.p3)
		self.assertRaises(ValueError, lambda x, y: x / y, self.p6, self.p4)

		self.assertEqual(self.p3 / self.p2, Polynomial([
			Monomial({}, 1),
			Monomial({1: 1, 2: -1}, 0.75)
		]))
		self.assertEqual(self.p7 / self.m1, Polynomial([
			Monomial({1: -1, 2: -3}, 2),
			Monomial({1: 0, 2: -4}, 1.5)
		]))
		self.assertEqual(self.p7 / self.m1, Polynomial([
			Monomial({1: -1, 2: -3}, 2),
			Monomial({2: -4}, 1.5)
		]))
		return

	def test_polynomial_variables(self):
		# The zero polynomial has no variables.

		self.assertEqual(self.p0.variables(), set())
		self.assertEqual(self.p1.variables(), set())

		# The total variables are the union of the variables
		# from the monomials.
		self.assertEqual(self.p4.variables(), {1, 2, 3})

		# The monomials with coefficient 0 should be dropped.
		self.assertEqual(self.p5.variables(), {1, 3})
		return

	def test_polynomial_subs(self):
		# Anything substitued in the zero polynomial
		# should evaluate to 0.
		self.assertEqual(self.p1.subs(2), 0)
		self.assertEqual(self.p0.subs(-101231), 0)

		# Should raise a ValueError if not enough variables are supplied.
		self.assertRaises(ValueError, lambda x, y: x.subs(y), self.p4, {1: 3, 2: 2})
		self.assertRaises(ValueError, lambda x, y: x.subs(y), self.p4, {})

		# Should work fine if a complete subsitution map is provided.
		self.assertAlmostEqual(self.p4.subs({1: 1, 2: 1, 3: 1}), (1 + math.pi + Fraction(2, 3)), delta=1e-9)
		# Should work fine if more than enough substitutions are provided.
		self.assertAlmostEqual(self.p4.subs({1: 1, 2: 1, 3: 1, 4: 1}), (1 + math.pi + Fraction(2, 3)), delta=1e-9)
		return

	def test_polynomial_clone(self):

		# The zero polynomial always clones to itself.
		self.assertEqual(self.p0.clone(), self.p0)
		self.assertEqual(self.p1.clone(), self.p0)
		self.assertEqual(self.p0.clone(), self.p1)
		self.assertEqual(self.p1.clone(), self.p1)

		# The polynomial should clone nicely.
		self.assertEqual(self.p4.clone(), self.p4)

		# The monomial with a zero coefficient should be dropped
		# in the clone.
		self.assertEqual(self.p5.clone(), Polynomial([
			Monomial({1: -1, 3: 2}, 1)
		]))
		return