For teaching, presentation, and debugging purposes, it could be powerful
to have a function that sets up a sage.numerical.interactive_simplex_method.LPDictionary
corresponding to the current basis of a MixedIntegerLinearProgram (with all variables real).

The plan is as follows:

• MixedIntegerLinearProgram.construct_interactive_lp() return an interactive LP (by querying the backend for problem data) and a list of basic variables (by querying the backend for col_stat, row_stat)
• from that information, can make an LPDictionary or LPRevisedDictionary by invoking the dictionary or revised_dictionary methods.

#18685 added the prerequisite basis status information for the case of the GLPK backend. #18763 did the same for the COIN backend.

See also: #18688, #18733

Follow-up: #18804 (LPBackendDictionary)

Depends on #18685
Depends on #18732

CC: @nathanncohen @yuan-zhou @uduse @novoselt @dimpase @videlec

Component: numerical

Author: Aedi Wang, Matthias Koeppe

Branch/Commit: e8ffa20

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/18734