We are working on a didactical implementation of the cutting plane method using tableau cutting planes,
such as Gomory's fractional cut and Gomory's mixed integer cut.

This would work with InteractiveLP, LPAbstractDictionary, etc.
(Via #18804, one could run the cutting plane method also on a backend tableau.)

To work correctly with mixed integer problems, one would need to remember which variables are real and which are integer.

Would it be acceptable to add a slot such as ._integer_variables (a set), and a corresponding accessor .integer_variables() to the various classes of interactive_simplex_method?

Depends on #18742
Depends on #19097
Depends on #20500

CC: @novoselt @yuan-zhou @uduse @pgxiao

Component: numerical

Work Issues: doc format

Author: Peijun Xiao

Branch/Commit: u/pjxiao/add_didactical_implementation_of_tableau_cutting_planes_to_interactive_simplex_method @ e7765c2

Reviewer: Andrey Novoseltsev

Issue created by migration from https://trac.sagemath.org/ticket/18805