Function intersections

Find the points at which two given functions intersect

Consider the example of finding the intersection of a polynomial and a line:

\(y_1=x_1^2\)

\(y_2=x_2+1\)

from scipy.optimize import fsolve

import numpy as np

def f(xy):
   x, y = xy
   z = np.array([y - x**2, y - x - 1.0])
   return z

fsolve(f, [1.0, 2.0])

 array([ 1.61803399,  2.61803399])

See also: http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fsolve.html#scipy.optimize.fsolve