sage.doctest.external.has_{cplex,gurobi}: Refactor through new Features

src/sage/databases/cremona.py

@@ -1699,13 +1699,13 @@ def CremonaDatabase(name=None,mini=None,set_global=None):
         sage: c = CremonaDatabase('should not exist',mini=True)
         Traceback (most recent call last):
         ...
-        FeatureNotPresentError: Cremona's database of elliptic curves is not available.
+        FeatureNotPresentError: database_should_not_exist_ellcurve is not available.
         '...db' not found in any of [...]
         ...Further installation instructions might be available at https://github.com/JohnCremona/ecdata.
         sage: c = CremonaDatabase('should not exist',mini=False)
         Traceback (most recent call last):
         ...
-        FeatureNotPresentError: Cremona's database of elliptic curves is not available.
+        FeatureNotPresentError: database_should_not_exist_ellcurve is not available.
         '...db' not found in any of [...]
         ...Further installation instructions might be available at https://github.com/JohnCremona/ecdata.
     """

src/sage/doctest/external.py

@@ -221,14 +221,10 @@ def has_cplex():
 
         sage: from sage.doctest.external import has_cplex
         sage: has_cplex() # random, optional - CPLEX
-        True
+        FeatureTestResult('cplex', True)
     """
-    from sage.numerical.mip import MixedIntegerLinearProgram
-    try:
-        MixedIntegerLinearProgram(solver='cplex')
-        return True
-    except Exception:
-        return False
+    from sage.features.mip_backends import CPLEX
+    return CPLEX().is_present()
 
 def has_gurobi():
     """
@@ -238,14 +234,10 @@ def has_gurobi():
 
         sage: from sage.doctest.external import has_gurobi
         sage: has_gurobi() # random, optional - Gurobi
-        True
+        FeatureTestResult('gurobi', True)
     """
-    from sage.numerical.mip import MixedIntegerLinearProgram
-    try:
-        MixedIntegerLinearProgram(solver='gurobi')
-        return True
-    except Exception:
-        return False
+    from sage.features.mip_backends import Gurobi
+    return Gurobi().is_present()
 
 def has_graphviz():
     """

src/sage/features/mip_backends.py

@@ -0,0 +1,38 @@
+from . import Feature
+from join_feature import JoinFeature
+
+
+class MIPBackend(Feature):
+    r"""
+    A feature describing whether a :class:`MixedIntegerLinearProgram` backend is available.
+    """
+
+    def _is_present(self):
+        try:
+            from sage.numerical.mip import MixedIntegerLinearProgram
+            MixedIntegerLinearProgram(solver=self.name)
+            return FeatureTestResult(self, True)
+        except Exception:
+            return FeatureTestResult(self, False)
+
+
+class CPLEX(MIPBackend):
+
+    def __init__(self):
+        MIPBackend.__init__('cplex',
+                            spkg='sage_numerical_backends_cplex')
+
+
+class Gurobi(MIPBackend):
+
+    def __init__(self):
+        MIPBackend.__init__('gurobi',
+                            spkg='sage_numerical_backends_gurobi')
+
+
+class COIN(JoinFeature):
+
+    def __init__(self):
+        JoinFeature.__init__('sage_numerical_backends_coin',
+                             [MIPBackend('coin')],
+                             spkg='sage_numerical_backends_coin')