diff --git a/algorithms/maths/polynomial.py b/algorithms/maths/polynomial.py index 07a0c3b8a..81faf2b7e 100644 --- a/algorithms/maths/polynomial.py +++ b/algorithms/maths/polynomial.py @@ -438,10 +438,7 @@ def __floordiv__(self, other: Union[int, float, Fraction, Monomial]): # def __truediv__(self, other: Union[int, float, Fraction, Monomial, Polynomial]) -> Polynomial: def __truediv__(self, other: Union[int, float, Fraction, Monomial]): """ - For Polynomials, only division by a monomial - is defined. - - TODO: Implement polynomial / polynomial. + For Polynomial division, no remainder is provided. Must use poly_long_division() to capture remainder """ if isinstance(other, int) or isinstance(other, float) or isinstance(other, Fraction): return self.__truediv__( Monomial({}, other) ) @@ -449,17 +446,11 @@ def __truediv__(self, other: Union[int, float, Fraction, Monomial]): poly_temp = reduce(lambda acc, val: acc + val, map(lambda x: x / other, [z for z in self.all_monomials()]), Polynomial([Monomial({}, 0)])) return poly_temp elif isinstance(other, Polynomial): - if Monomial({}, 0) in other.all_monomials(): - if len(other.all_monomials()) == 2: - temp_set = {x for x in other.all_monomials() if x != Monomial({}, 0)} - only = temp_set.pop() - return self.__truediv__(only) - elif len(other.all_monomials()) == 1: - temp_set = {x for x in other.all_monomials()} - only = temp_set.pop() - return self.__truediv__(only) - - raise ValueError('Can only divide a polynomial by an int, float, Fraction, or a Monomial.') + # Call long division + quotient, remainder = self.poly_long_division(other) + return quotient # Return just the quotient, remainder is ignored here + + raise ValueError('Can only divide a polynomial by an int, float, Fraction, Monomial, or Polynomial.') return @@ -526,7 +517,59 @@ def subs(self, substitutions: Union[int, float, Fraction, Dict[int, Union[int, f def __str__(self) -> str: """ - Get a string representation of - the polynomial. + Get a properly formatted string representation of the polynomial. + """ + sorted_monos = sorted(self.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True), + reverse=True) + return ' + '.join(str(m) for m in sorted_monos if m.coeff != Fraction(0, 1)) + + def poly_long_division(self, other: 'Polynomial') -> tuple['Polynomial', 'Polynomial']: """ - return ' + '.join(str(m) for m in self.all_monomials() if m.coeff != Fraction(0, 1)) + Perform polynomial long division + Returns (quotient, remainder) + """ + if not isinstance(other, Polynomial): + raise ValueError("Can only divide by another Polynomial.") + + if len(other.all_monomials()) == 0: + raise ValueError("Cannot divide by zero polynomial.") + + quotient = Polynomial([]) + remainder = self.clone() + + divisor_monos = sorted(other.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True), + reverse=True) + divisor_lead = divisor_monos[0] + + while remainder.all_monomials() and max(remainder.variables(), default=-1) >= max(other.variables(), + default=-1): + remainder_monos = sorted(remainder.all_monomials(), key=lambda m: sorted(m.variables.items(), reverse=True), + reverse=True) + remainder_lead = remainder_monos[0] + + if not all(remainder_lead.variables.get(var, 0) >= divisor_lead.variables.get(var, 0) for var in + divisor_lead.variables): + break + + lead_quotient = remainder_lead / divisor_lead + quotient = quotient + Polynomial([lead_quotient]) # Convert Monomial to Polynomial + + remainder = remainder - ( + Polynomial([lead_quotient]) * other) # Convert Monomial to Polynomial before multiplication + + return quotient, remainder + +dividend = Polynomial([ + Monomial({1: 3}, 4), # 4(a_1)^3 + Monomial({1: 2}, 3), # 3(a_1)^2 + Monomial({1: 1}, -2), # -2(a_1) + Monomial({}, 5) # +5 +]) + +divisor = Polynomial([ + Monomial({1: 1}, 2), # 2(a_1) + Monomial({}, -1) # -1 +]) + +quotient = dividend / divisor +print("Quotient:", quotient) diff --git a/tests/test_polynomial.py b/tests/test_polynomial.py index 4ba2ba6b7..ab5674017 100644 --- a/tests/test_polynomial.py +++ b/tests/test_polynomial.py @@ -105,27 +105,6 @@ def test_polynomial_multiplication(self): ])) 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. @@ -172,4 +151,51 @@ def test_polynomial_clone(self): self.assertEqual(self.p5.clone(), Polynomial([ Monomial({1: -1, 3: 2}, 1) ])) - return \ No newline at end of file + return + + def test_polynomial_long_division(self): + """ + Test polynomial long division + """ + + # Dividend: 4a_1^3 + 3a_1^2 - 2a_1 + 5 + dividend = Polynomial([ + Monomial({1: 3}, 4), # 4(a_1)^3 + Monomial({1: 2}, 3), # 3(a_1)^2 + Monomial({1: 1}, -2), # -2(a_1) + Monomial({}, 5) # +5 + ]) + + # Divisor: 2a_1 - 1 + divisor = Polynomial([ + Monomial({1: 1}, 2), # 2(a_1) + Monomial({}, -1) # -1 + ]) + + # Expected Quotient: 2a_1^2 + (5/2)a_1 + 1/4 + expected_quotient = Polynomial([ + Monomial({1: 2}, 2), # 2(a_1)^2 + Monomial({1: 1}, Fraction(5, 2)), # (5/2)(a_1) + Monomial({}, Fraction(1, 4)) # +1/4 + ]) + + # Expected Remainder: 21/4 + expected_remainder = Polynomial([ + Monomial({}, Fraction(21, 4)) # 21/4 + ]) + + quotient_long_div, remainder_long_div = dividend.poly_long_division(divisor) + + quotient_truediv = dividend / divisor # Calls __truediv__, which returns only the quotient + + # Check if quotient from poly_long_division matches expected + self.assertEqual(quotient_long_div, expected_quotient) + + # Check if remainder from poly_long_division matches expected + self.assertEqual(remainder_long_div, expected_remainder) + + # Check if quotient from __truediv__ matches quotient from poly_long_division + self.assertEqual(quotient_truediv, quotient_long_div) + + return +