Is there a way to output the start_system used in the calculation

[jasonrong001]

I am trying to solve a set polynomial equations, the system is quite big. When running on a small workstation, the program takes up all the memories and is killed by the system. I am wondering if it is possible to output the start_system (I am using the total degree system) so that I can break the calculation into small parts which are less memory-demanding.

[saschatimme]

There are multiple options here:

1. You can use the total_degree https://www.juliahomotopycontinuation.org/HomotopyContinuation.jl/stable/start_systems/#HomotopyContinuation.total_degree function to get a tracker and an iterator of the start solutions:

 f = [(x - 10)^2]
tracker, starts = total_degree(System(f))
res = track.(tracker, starts)

2. Additionally you can set the compile option in solve to :none, i.e.

solve(f; compile=:none)

This reduces the amount of code generation which is most likely the reason that your are running out of memory

[jasonrong001]

Thank you for the nice answer! Yet I have some further questions.

I tried to solve the most simple system,

@var x
result=solve([x^4])

The result shows that there are no solutions, only four excess solutions. Do you know the reason behind this?

The reason that I am asking this is that I was trying to solve a large system, and many of the paths terminate because "terminated_step_size_too_small". However, when I extract the solutions I got (which is at t=10^(-7) for example), they are very close the the actual solutions of the system. I suspect that maybe the homotopy path becomes tangential to the t=0 plane in the end. Do you have any suggestions about how to improve the result?

[PBrdng]

In your example, you have 1 zero of multiplicity 4. "No solutions" means no non-singular solutions.

The software falsely labels the singular solution as excess solution (this means solutions at infinity). This only happens when you have one variable and is a bug that we are already aware of.