import numpy


class Polynomial:
    def __init__(self, coefficients):
        self.coeff = coefficients

    def __call__(self, x):
        """Evaluate the polynomial."""
        s = 0
        for i in range(len(self.coeff)):
            s += self.coeff[i] * x**i
        return s

    def __add__(self, other):
        # Start with the longest list and add in the other
        if len(self.coeff) > len(other.coeff):
            result_coeff = self.coeff[:]  # copy!
            for i in range(len(other.coeff)):
                result_coeff[i] += other.coeff[i]
        else:
            result_coeff = other.coeff[:]  # copy!
            for i in range(len(self.coeff)):
                result_coeff[i] += self.coeff[i]
        return Polynomial(result_coeff)

    def __mul__(self, other):
        c = self.coeff
        d = other.coeff
        M = len(c) - 1
        N = len(d) - 1
        result_coeff = numpy.zeros(M + N + 1)
        for i in range(0, M + 1):
            for j in range(0, N + 1):
                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, len(self.coeff)):
            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[:])  # make a copy
        dpdx.differentiate()
        return dpdx

    def __str__(self):
        s = ""
        for i in range(0, len(self.coeff)):
            if self.coeff[i] != 0:
                s += " + %g*x^%d" % (self.coeff[i], i)
        # Fix layout
        s = s.replace("+ -", "- ")
        s = s.replace("x^0", "1")
        s = s.replace(" 1*", " ")
        s = s.replace("x^1 ", "x ")
        s = s.replace("x^1", "x")
        if s[0:3] == " + ":  # remove initial +
            s = s[3:]
        if s[0:3] == " - ":  # fix spaces for initial -
            s = "-" + s[3:]
        return s

    def simplestr(self):
        s = ""
        for i in range(0, len(self.coeff)):
            s += " + %g*x^%d" % (self.coeff[i], i)
        return s


def _test():
    p1 = Polynomial([1, -1])
    p2 = Polynomial([0, 1, 0, 0, -6, -1])
    p3 = p1 + p2
    print(p1, "  +  ", p2, "  =  ", p3)
    p4 = p1 * p2
    print(p1, "  *  ", p2, "  =  ", p4)
    print("p2(3) =", p2(3))
    p5 = p2.derivative()
    print("d/dx", p2, "  =  ", p5)
    print(
        "d/dx",
        p2,
    )
    p2.differentiate()
    print("  =  ", p5)
    p4 = p2.derivative()
    print("d/dx", p2, "  =  ", p4)


if __name__ == "__main__":
    _test()