Solving rational number Linear Programming problem in Python

Question

I have an LP with integer constraints that I want to solve in exact arithmetic, using Python. In fact, I only need a feasible point.

Edit: "Exact arithmetic" here means rational numbers, of unbounded enumerator and denominator.

Previous attempts:

• Find exact solutions to Linear Program mentions qsoptex, but when I try to import it, I get ImportError: libqsopt_ex.so.2: cannot open shared object file: No such file or directory , although to my knowledge, I gave to path to that library.
• SoPlex works on the console, but I could not find a Python interface.
• PySCIPOpt ( https://github.com/SCIP-Interfaces/PySCIPOpt ) is the Python interface for SCIP, including SoPlex, but I don't see how to call a specific solver (with specific options).
• cdd ( https://pycddlib.readthedocs.io/en/latest/linprog.html ) does something , calling it LP, but I have no idea which problem they actually solve.

Speed is only a moderate issue. My larger instances have about 500 variables with box-constraints and 40 equalities, but the numbers involved might be large.

Answer 1

Maybe I am missing the point but any Linear Programming task where you want rational number solution is in fact an Integer Programming problem where you find LCD (Least Common Denominator) for all of the fractional variables and agree the numerators which you later use as integers. So, it seems like the problem only needs reformulation and you can get the exact solution.