I am just thinking out loud here and would deeply appreciate any pointers regarding the following problem.
I use the “HomotopyContinuation.jl” package to solve a system of polynomial equations. Now there are two parameters (let’s call them a and b) in the polynomial equations, such that the changing these parameters would yield different solutions. I am particularly interested in the real solutions. In general, the number of real solutions were found to be 4, but on certain occasions of a and b, the real solutions were found to be 6. There could be possibilities that it could be neither 4 or 6, for other values of (a,b).
Is it possible to discretise the workspace (a,b) into intervals, such that within a given interval, the number of real solutions is constant (either 4, or 5 or 6 etc)? How shall I go about it?
Thanks in advance.