# Solve a pair of coupled nonlinear equations within certain limits

This answer to this question works only for situations in which the desired solution to the coupled functions is not restricted to a certain range.

But what if, for example, we wanted a solution such that 0 < x < 10 and 0 < y < 10?

There are functions within scipy.optimize that find roots to a function within a given interval (e.g., brentq), but these work only for functions of one variable.

Why does scipy fall short of providing a root solver that works for multi-variable functions within specific ranges? How might such a solver be implemented?

• Transform your variables so they remain restricted. Sep 14 '15 at 16:08
• Numerical Recipes has a good discussion on multivariate root finding, and all the evilness that an extra dimension adds that you can trip on. Sep 15 '15 at 19:16