Solve Simultaneous Algebraic Equations (x eqns and x unknowns)

[rwalters31]

I have been looking for a Julia package to solve simultaneous algebraic equations. A simple example for two equations and two unknowns might look like:
x^{2}+y^{2}=5
y=\frac{1}{2}x^{3}+3x^{2}-2x-3

Here is a plot of the two equations:

The packages that I have run across seem to be aimed at linear systems or ODEs. I apologize if there is a simple solution that I have missed.

[Paulo_Jabardo]

There are a few packages that can do this.

• NLsolve.jl
• NonlinearSolve.jl This one uses the interface used by SciML
• If you are limited to polynomial equations, you can try HomotopyContinuation.jl
• https://github.com/ctkelley/SIAMFANLEquations.jl Code for a classic book (with a new edition coming out, using Julia).
• Try IntervalRootFinding.jl if you need to find all the roots in an interval.

I hope this helps

Paulo

[stevengj]

@Paulo_Jabardo

If you are limited to polynomial equations, you can try HomotopyContinuation.jl

This seems to be definitely the most robust option for systems of polynomial equations.