# Tracking the change in no: of real solutions from HomotopyContinuation.jl using Interval arithematic

**URL:** <https://discourse.julialang.org/t/tracking-the-change-in-no-of-real-solutions-from-homotopycontinuation-jl-using-interval-arithematic/119964>\
**Category:** General Usage\
**Created:** [September 27, 2024, 1:37pm UTC](https://discourse.julialang.org/t/tracking-the-change-in-no-of-real-solutions-from-homotopycontinuation-jl-using-interval-arithematic/119964 "2024-09-27T13:37:55Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![ij05](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ij05/32/209328_2.png) [@ij05](https://discourse.julialang.org/u/ij05)\
**Post date:** [September 27, 2024, 1:37pm UTC](https://discourse.julialang.org/t/tracking-the-change-in-no-of-real-solutions-from-homotopycontinuation-jl-using-interval-arithematic/119964/1 "2024-09-27T13:37:55Z")

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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.