Automatic Differentiation with Dual Numbers

main.py

### The Dual Number Class
# 
# A dual number is a number of the format "x + ε" where ε**2 = 0 but ε!= 0
# Given a function F it can be proven that
#    F(x + ε) = F(x) + F'(x)
# This allows us to quickly calculate the value of a function and it's first derivative in one go, without having to construct the derivative function first.
# https://en.wikipedia.org/wiki/Dual_number
##
# INCOMPLETE IMPLEMENTATION
#   - not possible to divide
#   - not possible to take a negative power
##

class Dual:
    def __init__(self, real, dual):
        self.real = real
        self.dual = dual
        
    def __add__(self, other):
        if isinstance(other, Dual):
            return Dual(self.real + other.real, self.dual + other.dual)
        else:
            return Dual(self.real + other, self.dual)
    def __radd__(self, other):
         return self + other
         
    def __sub__(self, other):
        if isinstance(other, Dual):
            return Dual(self.real - other.real, self.dual - other.dual)
        else:
            return Dual(self.real - other, self.dual)
    def __rsub__(self, other):
        return self + other
        
    def __mul__(self, other):
        if isinstance(other, Dual):
            return Dual(self.real * other.real, (self.real * other.dual) + (self.dual * other.real))
        else:
            return Dual(self.real * other, self.dual * other)
    def __rmul__(self, other): 
        return self * other
        
    def __pow__(self, other):
        if other == 0:
            return 1
        else:
            return self * (self**(other-1))

# Ask for a polynom
fun = input('Enter the polynomial: ')

# Ask for a value of x
x = input('Enter the value for x: ')

# Solve for "x + ε"
d = {}
d['x'] = Dual(real = float(x), dual = 1)
solution = eval(fun, d)

## Output
print("----------------------------------")
print("\nf(x)=" + fun)
print("f(" + str(x) + ")="+str(solution.real))
print("f'(" + str(x) + ")="+str(solution.dual))