class Polynomial:
    """Class for dealing with polynomials"""

    def __init__(self, coefficients):
        self.coeff = coefficients.copy()
        while len(self.coeff)>0 and self.coeff[-1] == 0:
            self.coeff.pop()
        self.n = len(self.coeff)

    def __call__(self, x):
        """Evaluate the polynomial.""" 
        s=0
        for i,c in enumerate(self.coeff):
            s += c * x**i
        return s

    def __str__(self):
        s = []
        for i,c in enumerate(self.coeff):
            if c != 0:
                s.append(f'{c}*x^{i}')
        result = " + ".join(s)
        if result == '':
            result = '0'
        return result
    
    def __add__(self, other):
        # Start with the longest list and add in the other
        if self.n > other.n:
            result_coeff = self.coeff.copy()
            for i in range(other.n):
                result_coeff[i] += other.coeff[i]
        else:
            result_coeff = other.coeff.copy()
            for i in range(self.n):
                result_coeff[i] += self.coeff[i]
        return Polynomial(result_coeff)

    def __sub__(self, other):
        if self.n > other.n:
            result_coeff = self.coeff.copy()
            for i in range(other.n):
                result_coeff[i] -= other.coeff[i]
        else:
            result_coeff = []
            for i in other.coeff:
                result_coeff.append(-i)
            for i in range(self.n):
                result_coeff[i] += self.coeff[i]
        return Polynomial(result_coeff)
    
    def __mul__(self, other):
        c = self.coeff
        d = other.coeff
        result_coeff = [0 for i in range(self.n + other.n - 1)]
        for i in range(self.n):
            for j in range(other.n):
                result_coeff[i+j] += c[i]*d[j]
        return Polynomial(result_coeff)  

    def differentiate(self):
        """Differentiate this polynomial in-place."""
        for i in range(1, self.n):
            self.coeff[i-1] = i * self.coeff[i]
        del self.coeff[-1]

    def derivative(self):
        """Copy this polynomial and return its derivative."""
        dpdx = Polynomial(self.coeff)
        dpdx.differentiate()
        return dpdx


if __name__ == "__main__":
    p1 = Polynomial([1, -1])
    print("p1:", p1)
    p2 = Polynomial([0, 1, 0, 0, -6, -1])
    print("p2:", p2)
    p3 = p1 + p2
    print("p1 + p2:", p3)
    p4 = p1*p2
    print("p1 * p2:", p4)
    p5 = p2.derivative()
    print("dp2/dx:", p5)