To Find the Derivative and the Roots

Fractpy has a class Function which can be used to perform basic calculus operations on a single-variable function. To initialise an object of this class we pass in the function as type str.

For example to initialise with function \(f(x) = x^4 - 3x^3 + 2x^2 - 9\):

>>> from fractpy import Function
>>> f = Function("x**4 - 4*x**3 + 4*x**2 - 4*x + 3")
>>> f
x**4 - 4*x**3 + 4*x**2 - 4*x + 3

Note

For complex values use I (upper case i) instead of commonly used convention of i. For example: function \(f(x) = (x - 1)(x + i)(x - i)\) would be passed as "(x - 1)(x + I)(x - I)".

To Calculate Roots

Use the method roots, which returns list of the roots:

>>> f.roots()
[1, 3, I, -I]

To Find the Derivative:

Use the method differentiate, which returns the derivative of the function in the form of a sympy expression:

>>> f.differentiate()
4*x**3 - 12*x**2 + 8*x - 4