""""
Ex 7.25 from "A primer on...
Implement a __sub__ special method to support 
subtraction of polynomials. The method can be based 
on the structure of the __add__ method, but some
modifications are needed since the order of the
arguments is not arbitrary in substraction. 
"""



class Polynomial:
    """
    class implementation of a polynomial, using a list to
    represent the polynomial coefficients.
    """

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

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

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


    def __sub__(self, other):
        # return self - other
        if len(self.coeff) > len(other.coeff): #copy self, subtract other
            coeffdiff = self.coeff[:]  # copy!
            for i in range(len(other.coeff)):
                coeffdiff[i] -= other.coeff[i]
        else:    #other is longest, needs some care to avoid index error                               
            coeffdiff = [0] * len(other.coeff) #list of zeros, same length as other
            for i in range(len(self.coeff)):  #fill first entries with values from self, rest remain zero
                coeffdiff[i] = self.coeff[i]  
            for i in range(len(other.coeff)):  #subtract coefficients from other
                coeffdiff[i] -= other.coeff[i]
            
        return Polynomial(coeffdiff)
            

    def __str__(self):
        s = ''
        for i in range(0, len(self.coeff)):
            if self.coeff[i] != 0:
                s += f' + {self.coeff[i]:g}*x^{i:g}'
        # fix layout (many special cases):
        s = s.replace('+ -', '- ')
        s = s.replace(' 1*', ' ')
        s = s.replace('x^0', '1')
        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


if __name__ == '__main__':

    p1 = Polynomial([1, -1])
    print(p1)

    p2 = Polynomial([0, 1, 0, 0, -6, -1])
    p3 = p1 + p2

    p4 = p2 - p1
    print(p4.coeff) #[-1, 2, 0, , -6, -1]
    print(p4)

    print(p3.coeff)
    print(p3)
    print(p3(2.0))
    
"""
Terminal> python Polynomial_sub.py 
1 - x^1
[-1, 2, 0, 0, -6, -1]
-1 + 2*x - 6*x^4 - x^5
[1, 0, 0, 0, -6, -1]
1 - 6*x^4 - x^5
-127.0
"""