GenericBackend: Add default implementation of add_variables and add_linear_constraints

[mkoeppe]

The backend methods add_variables and add_linear_constraints should have a default implementation in GenericBackend, like add_linear_constraint_vector.

add_variables can be taken from Gurobi and also removed from CVXOPT and InteractiveLP.
add_linear_constraints can be taken from COIN and also removed from CVXOPT and InteractiveLP.
(The other backends have specific implementations of these methods; one supposes that they are faster, though this probably has not been tested.)

Since the removal of the copy-pasted functions from the backends would remove doctests, I mark this ticket as dependent on #20323.

---

The new tests revealed a bug in the PPL backend, which has been fixed.
Also, the CPLEX backend used to add variables in reverse order for no good reason; changed that.

Depends on #20323

CC: @dimpase @videlec @jdemeyer @fchapoton @nbruin

Component: numerical

Author: Matthias Koeppe

Branch/Commit: 40876ee

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/20325

[mkoeppe]

Dependencies: #20323

[mkoeppe]

Branch: u/mkoeppe/genericbackend__add_default_implementation_of__add_variables__and__add_linear_constraints_

[mkoeppe]

Last 10 new commits:

f2d52f5	CPLEXBackend._test_add_variables: Make test suitable for InteractiveLPBackend
6604442	GenericBackend._test_add_linear_constraint_vector: Make test suitable for InteractiveLPBackend
e6ba997	GenericBackend._test_solve: Remove again for now; too many failures
c3d2959	CVXOPTBackend, InteractiveLPBackend: Remove add_variables implementations, inherit them from GenericBackend
d061abf	GenericBackend.add_linear_constraints: New
8b73e2d	CoinBackend.add_linear_constraints: Remove, inherit from GenericBackend
16ed7e9	CVXOPTBackend.add_linear_constraints: Remove, inherit from GenericBackend
afad991	InteractiveLPBackend.add_linear_constraints: Remove, inherit from GenericBackend
941d30b	GurobiBackend.add_variables: Remove, inherit from GenericBackend
987f609	GenericBackend._test_add_linear_constraints: Add tests from COINBackend, CVXOPTBackend

[mkoeppe]

Commit: 987f609

[mkoeppe]

Author: Matthias Koeppe

[vbraun]

comment:5

Falilures in the patch bot

[sagetrac-git]

Changed commit from 987f609 to 40876ee

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

40876ee

PPLBackend.add_linear_constraints: Fix handling of 'names' argument

[mkoeppe]

comment:9

Needs review.

[mkoeppe]

comment:10

ping?

[dimpase]

comment:11

So you moved these implementations into the generic backend, basically?

[mkoeppe]

comment:12

Yes, and added a _test method and fixed a bug in the PPL method (which was tested by a wrong test).

[dimpase]

comment:13

ok, good.

[dimpase]

Reviewer: Dima Pasechnik

[mkoeppe]

comment:14

Thanks for reviewing, Dima.
When you have a moment, could you look at #20600?

[vbraun]

Changed branch from u/mkoeppe/genericbackend__add_default_implementation_of__add_variables__and__add_linear_constraints_ to 40876ee