#20302: Clean up MILP backend interface
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   Reporter:  mkoeppe    |            Owner:
       Type:  defect     |           Status:  new
   Priority:  major      |        Milestone:  sage-7.2
  Component:  numerical  |         Keywords:  lp
  Merged in:             |          Authors:
  Reviewers:             |  Report Upstream:  N/A
Work issues:             |           Branch:
     Commit:             |     Dependencies:
   Stopgaps:             |
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 While implementing `InteractiveLPBackend` for #20296, I noticed several
 deficiencies in the design of the MILP backend interface.

  - `add_col` and `add_variable` both add a variable to the problem; but
 `add_col` only allows to add a column with no name; whereas `add_variable`
 only allows to add a column with no coefficients. There should be one
 function (`add_variable`, probably) that can do both; should then
 deprecate `add_col`. (Also compare with `add_linear_constraint`, which
 takes as zipped index/coefficient list, whereas `add_col` takes two
 parallel lists.)

  - `variable_upper_bound`: This interface is bizarre.  Can't remove an
 upper bound from a variable because `None` means both 'no upper bound' and
 'get the upper bound'. Likewise `variable_lower_bound`. (Moreover, there's
 redundancy with `col_bounds`.)

  - `add_variables` and `add_linear_constraints` should have a default
 implementation in `GenericBackend`, like `add_linear_constraint_vector`.

 Also, I think the backends should be tested using a common `TestSuite`.
 Right now each backend uses its own doctests, which have slightly diverged
 from each other, so there is nothing (other than the fact that they were
 the result of copy-paste from each other) that ensures consistency.
 (#20296 fixes several wrong doctests in `GenericBackend`, from which I
 tried to copy-paste, for example.)

--
Ticket URL: <http://trac.sagemath.org/ticket/20302>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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