Symbolic Differentiation in Python

symbolic-diff.py

  # I've left this here in case we want to implement diff for trig or other functions
class Function:
    def __init__(self):
        pass

    def diff(self):
        pass

class Polynomial(Function):
    def __init__(self, coeffs):
        # coeffs should be passed in highest order (e.g. x^7) to the lowest
        self._coeffs = coeffs

        # remove the leading zeroes
        while self._coeffs[0] == 0:
            self._coeffs.pop(0)

        self._degree = len(coeffs) - 1

    # evaluate the polynomial using Horner's method
    # (not the super optimized version)
    def eval(self, x):
        i = 1
        acc = self._coeffs[0]

        while i < self._degree+1:
            acc = self._coeffs[i] + x * acc
            i += 1

        return acc

    # one optional improvement could be not printing the leading 1
    # (e.g. 1x^2 + 3x + 4) --> (x^2 + 3x + 4)

    # another optional improvement could be not printing terms with a 0 coefficient
    # (e.g. 1x^2 + 0x + 4) --> (x^2 + 4)
    def __str__(self):
        pretty_str = ""
        i = 0

        while i < self._degree:
            if (self._degree - i) == 1:
                pretty_str += f"{self._coeffs[i]}x + "
            else:
                pretty_str += f"{self._coeffs[i]}x^{self._degree - i} + "
            i += 1

        pretty_str += f"{self._coeffs[self._degree]}"

        return pretty_str

    def diff(self):
        for i in range(self._degree):
            self._coeffs[i] *= (self._degree - i)

        self._degree -= 1

if __name__ == "__main__":
    f = Polynomial([0, 5, 3, 2])
    print(f)
    print(f.eval(5))
    print(f._degree)
    print()

    f.diff()
    print(f)
    print(f.eval(5))
    print(f._degree)