Before starting on writing your root-finding algorithm to solve nonlinear or even linear problems, take a look at the documentation of the
scipy.optimize methods. SciPy contains a collection of scientific computing functions as an extension of Python. Chances are that these open source algorithms might fit into your applications off-the-shelf.
Some root-finding functions that can be found in the scipy.optimize modules are bisect, newton, brentq, and ridder. Let's set up the examples that we have discussed using the implementations by SciPy:
"""
Documentation at
http://docs.scipy.org/doc/scipy/reference/optimize.html
"""
import scipy.optimize as optimize
y = lambda x: x**3 + 2.*x**2 - 5.
dy = lambda x: 3.*x**2 + 4.*x
# Call method: bisect(f, a, b[, args, xtol, rtol, maxiter, ...])
print "Bisection method: %s" \
% optimize.bisect(y, -5., 5., xtol=0.00001)
# Call method: newton(func, x0[, fprime, args, tol, ...])
print "Newton's method...