This is a follow-up on #18734.

This ticket creates:

• a new class, LPBackendDictionary (inheriting from LPAbstractDictionary), would avoid going through InteractiveLP and rather be tied directly to the MILP backend, using tableau data query functions such as getBInvArow etc.
  (It would be in a separate file perhaps interactive_backend_dictionary.py, so as not to add clutter to the didactical implementation in interactive_simplex_method.py.)

#18732 added most of the missing functions for retrieving the data of the dictionary (for the GLPK backend) such as getBInvARow etc. The remaining functions are provided by #19472.
#18763 and #19471 do the same for the COIN backend.

See also: #18733

Doctests could then test that:

• A backend has implemented all the necessary methods to get tableau information.
• The information is consistent, by checking that the LPBackendDictionary (in this ticket) and the LPDictionary (created in Construct an interactive_simplex_method.LPDictionary from a MixedIntegerLinearProgram #18734) are the same.

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

Component: numerical

Work Issues: Add methods add_row, eq so that TestSuite passes

Author: Aedi Wang

Branch/Commit: u/mkoeppe/zeyi-wang--lpbackenddictionary-trac18804--lpcleandictionary-trac20203--rebased-to-9.1.beeta1 @ 06ec022

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/18804