If one has to solve a small LP with irrational (say, AA) data (and needs access to the exact solution), the only available tool is the didactical implementation of the simplex method in InteractiveLPProblem (but see #18735). This ticket implements a MixedIntegerLinearProgram backend using InteractiveLPProblem.

Example:

            sage: poly = polytopes.dodecahedron(base_ring=AA)
            sage: lp = poly.to_linear_program(solver='InteractiveLP')
            sage: b = lp.get_backend()
            sage: b.set_objective([1, 1, 1])
            sage: lp.solve()
            2.291796067500631?

(This example uses backend functions because of #20301; and the base_ring=AA is there because of #13041.)

CC: @dimpase @novoselt @nathanncohen @videlec @fchapoton

Component: numerical

Author: Matthias Koeppe

Branch/Commit: 8c1fd4a

Reviewer: Andrey Novoseltsev, Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/20296