Are there any options to reduce the tracking paths in the function "regeneration"?

[Xinli-zjut]

Dear developers, for the function "regeneration", there are so many tracking paths when the number of polynomial equations increased.
This makes the polynomial system hard to solve. For example, the polynomial system in the picture below is hard to solve, it only has 20 equations.

Are there any ways to control the number of tracking paths? Thank you.

[Xinli-zjut]

When the number of equation is 11, the number of tracking paths are 13668. The tracking paths will become huge when the number of equations increased.

[PBrdng]

Hi, I'm moving this to the discussion section.

Without knowing anything about your system, there is not much one can do. In fact, 20 equations is a lot of equations. For instance, a random system of 20 polynomials each of degree 3 has $3^{20} = 3486784401$ solutions.

So, the number of paths (usually) increases exponentially with the number of equations and that's was causing you trouble. In this case, I always take a step back and wonder if one can model the problem differently. Could you give me an idea of what you are trying to compute?

[Xinli-zjut]

Thanks for the comments. The polynomial system is my testing example which comes from tensor decomposition.