Trying GAPs on a nine variable problem; generated solver is inaccurate about gaps HOT 2 OPEN

Hi @snsinha

I just reply your Email in this thread.

1. Rank deficiency. I had similar experiences with certain problems. However, I did not find specific reasons yet. This seems related with the problem structure (easily ill-posed or not) and complexity. From your output, the problem has Quotient ring basis (degree = 512), meaning it "equivalent" to a univariate polynomial with 512 roots. This is an extremely large problem. The template size template size = [13163,13679] is also the largest I have ever met. So I am not surprise if we meet numerical issues with it. I think the usual problem size should be degree < 100 and template size < 500. See the tables in [1] or [2] for the summary of sizes of some common problems.

2. Solver speed. I am not surprised that such a large problem will be slow to solve. However, There is still a small hint: Setting opt.optimize_coefficients = true reduces output solver complexity by avoiding duplicated coefficients but may take time long. Setting the opposite saves time but outputs inefficient solvers.

[1] http://openaccess.thecvf.com/content_cvpr_2017/papers/Larsson_Efficient_Solvers_for_CVPR_2017_paper.pdf
[2] https://arxiv.org/pdf/2007.07686.pdf

from gaps.

Another config to try.

-- Found 1 symmetries.
c = [ 1 1 1 1 1 0 0 0 0 ], p = 2

This means there is some symmetric structure in the unknowns. Although not optimistic for such large size, try flipping opt.use_sym and see if there is any different results.

from gaps.