Polynomials - operations

https://docs.python.org/3/tutorial/classes.html

COMPARISONS

class Poly:

    def __eq__(self, other):   # poly1 == poly2
        return (self - other).is_zero()   # it works when the substraction is defined

    def __ne__(self, other):   # poly1 != poly2
        return not self == other

# There is a problem with <, <=, >, >=.

ADDITION, SUBSTRACTION, MULTIPLICATION

class Poly:

    def __add__(self, other):   # poly1 + poly2
        new_poly = Poly(0, max(len(self.data), len(other.data)) -1)
        for (i, c) in enumerate(self.data):
            new_poly.data[i] += c
        for (i, c) in enumerate(other.data):
            new_poly.data[i] += c
        return new_poly

    def __sub__(self, other):   # poly1 - poly2
        new_poly = Poly(0, max(len(self.data), len(other.data)) -1)
        for (i, c) in enumerate(self.data):
            new_poly.data[i] += c
        for (i, c) in enumerate(other.data):
            new_poly.data[i] -= c
        return new_poly

    def __mul__(self, other):   # poly1 * poly2
        new_poly = Poly(0, len(self.data) + len(other.data) -2)
        for (i, c) in enumerate(self.data):
            for (j, d) in enumerate(other.data):
                new_poly.data[i+j] += c * d
        return new_poly

    def __pos__(self):      # +poly1 = (+1)*poly1
        return self

    def __neg__(self):      # -poly1 = (-1)*poly1
        new_poly = Poly()
        new_poly.data = [-c for c in self.data]
        return new_poly

poly1 = Poly(3, 5)
poly2 = Poly(1, 2)
assert poly1 == poly1   # testing comparisons
assert poly1 != poly2   # testing comparisons
assert poly1 * poly2 == Poly(3, 7)
assert poly1.__mul__(poly2) == Poly(3, 7)
assert Poly.__mul__(poly1, poly2) == Poly(3, 7)

COMPOSITION

class Poly:

    def __call__(self, x):   # Horner, polynomials are callable now
        result = 0
        for c in reversed(self.data):
            result = result * x + c
        return result

    def combine(self, other):   # Horner
        new_poly = Poly()
        for c in reversed(self.data):
            new_poly = new_poly * other + Poly(c)
        return new_poly

poly1 = Poly(3, 5)
poly2 = Poly(1, 2)
assert poly1(2) == 96
assert poly2(9) == 81
assert poly1.combine(poly2) == Poly(3, 10)   # 3*(x^2)^5 = 3*x^10

EXERCISES

Add new methods to the Poly class.

class Poly:

    def copy(self): pass   # shallow copy

    def __pow__(self, n): pass   # poly1 ** n, pow(poly1, n)

    def __len__(self): pass   # len(poly1), the number of monomials

    def diff(self): pass   # derivative

    def integrate(self): pass   # indefinite integral