class Polynomial:
    def __init__(self, coefficients):
        self.coeffs = []
        for item in coefficients:
            item = float(item)
            self.coeffs.insert(0, item)
    # list of coefficients is in ascending power
        self.length = len(self.coeffs)
    def __str__(self):
        string = ''
        coeffs = self.coeffs
        coeffs.reverse()
        i = self.length - 1
        for coeff in coeffs:
            if i != (self.length - 1 or coeff > 0):
                string += ' + '
            if i == 0:
                string += (str(coeff))
            elif i == 1:
                string += (str(coeff) + ' x ')
            elif coeff == 0:
                pass
            else:
                string += (str(coeff) + ' x**' + str(i))
            i -= 1
        return string

    def coeff(self, i):
        return self.coeffs[i]
    def add(self, other):
        if self.length > other.length:
            shorter = other.coeffs
            longer = self.coeffs
        else:
            shorter = self.coeffs
            longer = other.coeffs
        i = 0
        sumPoly = []
        while i < len(shorter):
            sumPoly.append(shorter[i] + longer[i])
            i += 1
        while i < len(longer):
            sumPoly.append(longer[i])
            i += 1
        sumPoly.reverse()
        poly = Polynomial(sumPoly)
        return poly
    def mul(self, other):
        i = 0
        product = Polynomial([])
        for item1 in self.coeffs:

            new_list = []
            n = i
        # if item is coef. to x^power, move values up list
            while i > 0:
                new_list.append(0)
                i -= 1
            for item2 in other.coeffs:
                new_list.append(item1*item2)
            i = n + 1
            new_list.reverse()
            # for each iteration, add produced polynomial to product
            newPoly = Polynomial(new_list)
            product = product.add(newPoly)
        return product
    def val(self, v):
        value = 0
        for exp in range(0, self.length):
            value += self.coeffs[exp]*(v**exp)
        return value
    def roots(self):
        def root(x, y):
                if det < 0:
                    roots = [(complex(x, y)), (complex(x, -y))]
                elif det == 0:
                    roots = [x]
                else:
                    roots = [(x + y), (x - y)]
                return roots
        if self.length == 2:
            c = self.coeffs[0]
            b = self.coeffs[1]
            roots = [-c/b]
            return roots
        elif self.length == 3:
            a = self.coeffs[2]
            b = self.coeffs[1]
            c = self.coeffs[0]
            det = b**2 - 4*a*c
            y = (abs(det)**0.5)/(2*a)
            x = -b/(2*a)
            return root(x, y)
        else:
            return 'Error! First or second order polynomials only.'
    def __add__(self, other):
        return self.add(other)
    def __mul__(self, other):
        return self.mul(other)
    def __call__(self, x):
        return self.val(x)
    def __repr__(self):
        return str(self)