Trac #34878: MixedIntegerLinearProgram.add_constraint: Option to return row indices, fix handling of empty constraints

(from https://trac.sagemath.org/ticket/21003#comment:136)

... for use with methods that take row indices as input, such as `row`,
`row_bounds`, `remove_constraint`.

If a backend does not map a constraint to a unique new row (or
`check_redundant=True` and the constraint is discarded by the frontend),
the method may return `None`.

We also fix a longstanding bug in how empty constraints are handled in
`add_constraint`.

The changed interface (an optional return value) is backward-compatible
with user code.

We also add a Feature CVXOPT so that the backend gets tested again.

URL: https://trac.sagemath.org/34878
Reported by: mkoeppe
Ticket author(s): Matthias Koeppe, Martin Rubey
Reviewer(s): Martin Rubey, Matthias Koeppe

Author: Release Manager

src/sage/features/mip_backends.py

@@ -2,7 +2,7 @@
 Features for testing the presence of :class:`MixedIntegerLinearProgram` backends
 """
 
-from . import Feature, FeatureTestResult
+from . import Feature, PythonModule, FeatureTestResult
 from .join_feature import JoinFeature
 
 
@@ -77,7 +77,26 @@ def __init__(self):
                              spkg='sage_numerical_backends_coin')
 
 
+class CVXOPT(JoinFeature):
+    r"""
+    A :class:`~sage.features.Feature` describing whether the :class:`MixedIntegerLinearProgram` backend ``CVXOPT`` is available.
+    """
+    def __init__(self):
+        r"""
+        TESTS::
+
+            sage: from sage.features.mip_backends import CVXOPT
+            sage: CVXOPT()._is_present()  # optional - cvxopt
+            FeatureTestResult('cvxopt', True)
+        """
+        JoinFeature.__init__(self, 'cvxopt',
+                             [MIPBackend('CVXOPT'),
+                              PythonModule('cvxopt')],
+                             spkg='cvxopt')
+
+
 def all_features():
     return [CPLEX(),
             Gurobi(),
-            COIN()]
+            COIN(),
+            CVXOPT()]