IPython Interactive Computing and Visualization Cookbook - Second Edition

Analyzing real-valued functions

SymPy contains a rich calculus toolbox to analyze real-valued functions: limits, power series, derivatives, integrals, Fourier transforms, and so on. In this recipe, we will show the very basics of these capabilities.

How to do it...

1. Let's define a few symbols and a function (which is just an expression depending on x):

   >>> from sympy import *
       init_printing()
   >>> var('x z')

   

   >>> f = 1 / (1 + x**2)

2. Let's evaluate this function at 1:

   >>> f.subs(x, 1)

   
3. We can compute the derivative of this function:

   >>> diff(f, x)

4. What is 's limit ...