# Example of how to do some basic numerical calculations using Python and SciPy
# by Dan Schroeder, January 2013

# To run this program you need a Python installation that includes SciPy.
# I recommend the EPD free distribution from Enthought, www.enthought.com.

# Import libraries for general math and the SciPy stuff we'll use:
import math, scipy.integrate, scipy.optimize

# Define a function to integrate:
def integrand(x):
	return (x**2) * math.exp(-x**2)

# Use the quad function to do the integral; limits are from 0 to 0.5:
(result, error) = scipy.integrate.quad(lambda x: integrand(x), 0, 0.5)
print 'The integral is', result, '+/-', error

# Now define a function with a nontrivial zero:
def functionwithroot(x):
	return math.tanh(x) - x/2

# Use the brentq function to find where the function is zero between x=1 and 2:
result = scipy.optimize.brentq(lambda x: functionwithroot(x), 1, 2)
print 'The root is at x =', result