Hi,

if you don't find the solution, could you post your 3104 points and the code you use to find the facets?

By the way: you have 32 factes (not 31) as you for some reason start counting at 0.

Best regards,
Thomas

Good news: My algorithm terminated. Result: Normally Finished. Solution status: optimal Optimal value: 178 3104 solutions . So with the file containing the above mentioned substitutions, I obtain the same optimal value and the same amount of lattice points. While I did not check that these are the s...

Hi, I solved your IP file in exact arithmetic and obtained 217 as optimal value. The polytope has 704 lattice points. Maybe the CPLEX solution is slightly infeasible in respect to your data. Your file contains some fractional values like 4.61538461538461. This might be ill-posed. While floating poin...

I re-ran my code with your second example and it terminated after 3-4 hours. It found 287301 lattice points. Is this the same number that you get? Yes. Good. That indicates that my algorithm works correctly :) You might try the other algorithms that are implemented in polymake, but I would not expe...

I generated a random tree of 30 nodes, and got \( b=(148,58,30)^T \) with \( i_{min}=1 \), \( i_{max}=6 \). This gave me 14 solutions.

For this example, I also get 14 solutions (instantaneously).

Best regards,
Thomas

Hi, I re-ran my code with your second example and it terminated after 3-4 hours. It found 287301 lattice points. Is this the same number that you get? My approach is slow, because it does a lot of operations on rational coordinates. I am not very surprised that a specialized algorithm is much faster...

Thank you for the information. I ran my code on both examples. For the first example, I think you provided the wrong solution. The example is three-dimensional and your solution is 15-dimensional. I think the correct solution is (0,13,2)^T . This is found instantaneously (for obvious reasons). I als...

I wish to enumerate all lattice points contained in the intersection of three hyperplanes in the non-negative half-space. That is to say, I have three linear equations of d variables and I would like to find all non-negative integer solutions. I would be happy if you could share your equations with...

Hi! I am not sure, but I think this is due to bad numerics. I do not get these errors when using your coordinates in a rational polytope. I would never ever rely on numbers like 5.09802551220429 e-18 in floating point arithmetic. I have not checked the whole dataset, but the numbers differ at least ...