Solving system of nonlinear equations with python

Question

Can I solve a system of nonlinear equations in terms of parameters in python? Is there a example or tutorial? I can do this easily in maple, but the expressions for my parti

Answer 1

Warning I'm a Sage developper, so I might not be neutral.

I don't know how to do that in pure Python, but I would recommend the Sage system whose interface is in Python (actually the command line is a specifically configured IPython) and which allows to do such thing:

+--------------------------------------------------------------------+
| Sage Version 5.10, Release Date: 2013-06-17                        |
| Type "notebook()" for the browser-based notebook interface.        |
| Type "help()" for help.                                            |
+--------------------------------------------------------------------+
sage: var("sigma y x rho beta z")
(sigma, y, x, rho, beta, z)
sage: sys = [sigma*(y-x), x*(rho-z)-y, x*y-beta*z]
sage: solve(sys, x, y, z)
[[x == sqrt(beta*rho - beta), y == (beta*rho - beta)/(sqrt(rho - 1)*sqrt(beta)), z == rho - 1], [x == -sqrt(beta*rho - beta), y == -(beta*rho - beta)/(sqrt(rho - 1)*sqrt(beta)), z == rho - 1], [x == 0, y == 0, z == 0]]

It is usually easier to use like this:

sage: solve(sys, x, y, z, solution_dict=True)
[{z: rho - 1,
  x: sqrt(beta*rho - beta),
  y: (beta*rho - beta)/(sqrt(rho - 1)*sqrt(beta))},
 {z: rho - 1,
  x: -sqrt(beta*rho - beta),
  y: -(beta*rho - beta)/(sqrt(rho - 1)*sqrt(beta))},
 {z: 0, x: 0, y: 0}]

The main drawback is that Sage is a full distribution of math Software which ships its own Python interpreter (together with a huge bunch of other things written in many language including C/C++, Cython, lisp, fortran) and is notoriously hard to install if you want to use your own interpreter.

A good news for your problem is that Scipy is already shipped with sage.