Symbolic differentiation

demo.py

from symdiff import Term, Polynomial


expression = "4x**3 - x"

polynomial = Polynomial.from_string(expression)

print("Polynomial:", polynomial)
print("Differentiated:", polynomial.differentiate())

symdiff.py

class Term(object):
  def __init__(self, coefficient, degree):
    self.coefficient = float(coefficient)
    self.degree = float(degree)

  def __repr__(self):
    return f'Term(coefficient={self.coefficient}, degree={self.degree})'

  def __str__(self):
    if not self.degree or not self.coefficient:
      return f'{self.coefficient}'
    if self.coefficient == 1:
      coefficient_part = ''
    elif self.coefficient == -1:
      coefficient_part = '-'
    else:
      coefficient_part = self.coefficient
    degree_part = 'x' if self.degree == 1 else f'x**{self.degree}'
    return f'{coefficient_part}{degree_part}'

  @classmethod
  def from_string(cls, term_string):
    try:  # constant
      return cls(coefficient=term_string, degree=0)
    except ValueError:
      coefficient, degree_info = term_string.split("x")
      if coefficient == "": coefficient = 1
      if coefficient == "-": coefficient = -1
      # coefficient = 1 if coefficient == "" else -1 if coefficient == "-" else coefficient
      try:  # has an exponent
        degree = degree_info.split("**").pop()
        return cls(coefficient, degree=degree)
      except:  # degree 1
        return cls(coefficient, degree=1)

  def differentiate(self):
    if self.degree == 0:
      return Term(coefficient=0, degree=0)
    else:
      coefficient = self.coefficient * self.degree
      degree = self.degree - 1
      return Term(coefficient, degree)


class Polynomial(object):
  def __init__(self, terms):
    self.terms = terms
    # or, omit zeros:
    # self.terms = [t for t in terms if t is not None] or [Term(0, 0)]

  def __repr__(self):
    return f'Polynomial({repr(self.terms)})'

  def __str__(self):
    return " + ".join(str(t) for t in self.terms)

  @classmethod
  def from_string(cls, polynomial_string):
    without_spaces = polynomial_string.replace(" ", "")
    with_plus_signs = without_spaces.replace("-", "+-")
    term_strings = [t for t in with_plus_signs.split("+") if t != ""]
    terms = [Term.from_string(t) for t in term_strings]
    return cls(terms)

  def differentiate(self):
    return Polynomial([t.differentiate() for t in self.terms])