MixedIntegerLinearProgram backend using polymake (for LP over quadratic extensions)

[mkoeppe]

polymake has a simple implementation of the dual simplex method, which works with polymake's quadratic extensions.

It appears to be much faster than our InteractiveLPbackend. It is unknown (because no benchmarking has been done) how much of the speed differential is due to InteractiveLP latexing all intermediate tableaux.

We should make it available as a MixedIntegerLinearProgram backend. (Of course, there are no integer variables.)

This could be based directly on

• Create a Polymake pexpect interface #22452: Create a polymake pexpect interface
  or use
• backend_polymake for Polyhedron #22683: backend_polymake for Polyhedron

See also: #22710: Meta-ticket: polymake

Depends on #22452

Component: numerical

Keywords: polymake

Issue created by migration from https://trac.sagemath.org/ticket/22724

[mkoeppe]

Dependencies: #22452

[mkoeppe]

comment:3

Moving some tickets to 9.2. This is not a promise that I will be working on them.

[mkoeppe]

comment:5

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.