#20302: Clean up MILP backend interface
-----------------------------+------------------------
       Reporter:  mkoeppe    |        Owner:
           Type:  defect     |       Status:  new
       Priority:  major      |    Milestone:  sage-7.2
      Component:  numerical  |   Resolution:
       Keywords:  lp         |    Merged in:
        Authors:             |    Reviewers:
Report Upstream:  N/A        |  Work issues:
         Branch:             |       Commit:
   Dependencies:  #20296     |     Stopgaps:
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Description changed by mkoeppe:

Old description:

> 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 - see #20296 for a
> possible interface) that can do both; should then deprecate `add_col`.
> (Also compare with `add_linear_constraint`, which takes a zipped
> index/coefficient list, whereas `add_col` takes two parallel lists.)
>
>  - `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.)

New description:

 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 - see #20296 for a possible interface)
 that can do both; should then deprecate `add_col`. Note that `add_col` is
 not used by `MixedIntegerLinearProgram`; it is only used in doctests of
 the backends.  (Also compare with `add_linear_constraint`, which takes a
 zipped index/coefficient list, whereas `add_col` takes two parallel
 lists.)

  - `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#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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