Meta-ticket: MixedIntegerLinearProgram/MIPVariable API cleanup

[mkoeppe]

Follow-up on #20462:

• MIPVariable: Better names for backend variables #31791 MIPVariable: Better names for backend variables

• MIPVariable: Change to a subclass of FiniteFamily #31750 MIPVariable: Change to a subclass of FiniteFamily

• MixedIntegerLinearProgram: New generator method 'variables' #31749 MixedIntegerLinearProgram: New generator method variables

• A MIPVariable's repr should include some useful information #20331 A MIPVariable's repr should include some useful information

• MixedIntegerLinearProgram: Remove _variables dictionary #20656 MixedIntegerLinearProgram: Remove _variables dictionary

• MixedIntegerLinearProgram should provide a way to get the variables in the order they are provided to the polyhedron method #26302 MixedIntegerLinearProgram should provide a way to get the variables in the order they are provided to the polyhedron method

• Setting a default max/min bound when calling MixedIntegerLinearProgram.new_variable #7790 Setting a default max/min bound when calling MixedIntegerLinearProgram.new_variable

• More fixes for copying a MIP and the MIPVariables created by new_variable #20657: More fixes for copying a MIP and the MIPVariables created by new_variable

• Why does a MIPVariable only have set_max, but no get_max?

• Why does MixedIntegerLinearProgram.set_max delegate to a MIPVariable method of the same name, when other MixedIntegerLinearProgram methods such as set_integer etc. just do everything directly, and no corresponding MIPVariable methods exist?

• Actually these things should properly be referred to as lower_bound and upper_bound rather than min and max. Some deprecation fun to be had.

• Why is there no way to query the values of the components of the _default_mipvariable?

Depends on #20462

CC: @dimpase @videlec @jdemeyer @yuan-zhou

Component: numerical

Issue created by migration from https://trac.sagemath.org/ticket/20664

[mkoeppe]

comment:6

We may want to use weakref for solving the mutual ownership problem of a MixedIntegerLinearProgram and MIPVariable

• weakref — Weak references — Python 3.9.4 documentation - https://docs.python.org/3/library/weakref.html

• cython/weakref.pxd at master · cython/cython - https://github.com/cython/cython/blob/master/Cython/Includes/cpython/weakref.pxd

• Python's weak references, __slots__, and Cython - https://dev.nextthought.com/blog/2018/05/python-weakref-cython-slots.html