1 | | 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`. |

| 1 | 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`. |

| 2 | |

| 3 | Example: |

| 4 | {{{ |

| 5 | sage: poly = polytopes.dodecahedron(base_ring=AA) |

| 6 | sage: lp = poly.to_linear_program(solver='InteractiveLP') |

| 7 | sage: b = lp.get_backend() |

| 8 | sage: b.set_objective([1, 1, 1]) |

| 9 | sage: lp.solve() |

| 10 | 2.291796067500631? |

| 11 | }}} |

| 12 | (This example uses backend functions because of #20301 .) |