MixedIntegerLinearProgram: Remove _variables dictionary

[mkoeppe]

The '_variables' attribute dictionary maps a "variable" (an "element" of a MIPVariable "dictionary") to an index in the backend. This is redundant because these "variables" are elements of type LinearFunction, and as such know their index in the backend already.

sage: p = MixedIntegerLinearProgram(solver='GLPK')
sage: pv = p.new_variable(nonnegative=True)
sage: pv[0]
x_0
sage: pv[77]
x_1
sage: pv[0].dict().keys()
[0]
sage: pv[77].dict().keys()
[1]

See also: #20461, #20602

Depends on #20461
Depends on #20462

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

Component: numerical

Author: Matthias Koeppe

Branch/Commit: u/mkoeppe/mixedintegerlinearprogram__remove__variables_dictionary @ be0e0f0

Issue created by migration from https://trac.sagemath.org/ticket/20656

[mkoeppe]

Branch: u/mkoeppe/mixedintegerlinearprogram__remove__variables_dictionary

[mkoeppe]

New commits:

ca1298b	MixedIntegerLinearProgram._linear_variable_index: New
b7906ff	MixedIntegerLinearProgram: Remove _variables

[mkoeppe]

Commit: b7906ff

[mkoeppe]

Author: Matthias Koeppe

[tscrim]

comment:3

Needs a rebase. However, I'm worried this could cause a speed regression as a dict lookup is a system python call whereas you are now doing a number of python function calls. Also storing a (relatively?) small dict doesn't cost much memory I would think.

[mkoeppe]

comment:4

I haven't done any timings regarding this patch.

[sagetrac-git]

Changed commit from b7906ff to be0e0f0

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

fe2a85f	MixedIntegerLinearProgram._linear_variable_index: New
be0e0f0	MixedIntegerLinearProgram: Remove _variables

[mkoeppe]

comment:7

Setting a new milestone for this ticket based on a cursory review.