- sage: K = Cone([(1,0),(0,1)])
- sage: discrete_complementarity_set(K)
- [((1, 0), (0, 1)), ((0, 1), (1, 0))]
-
- If the cone consists of a single ray, the second components of the
- discrete complementarity set should generate the orthogonal
- complement of that ray::
-
- sage: K = Cone([(1,0)])
- sage: discrete_complementarity_set(K)
- [((1, 0), (0, 1)), ((1, 0), (0, -1))]
- sage: K = Cone([(1,0,0)])
- sage: discrete_complementarity_set(K)
- [((1, 0, 0), (0, 1, 0)),
- ((1, 0, 0), (0, -1, 0)),
- ((1, 0, 0), (0, 0, 1)),
- ((1, 0, 0), (0, 0, -1))]
-
- When the cone is the entire space, its dual is the trivial cone, so
- the discrete complementarity set is empty::
+ sage: K = Cone([(1,0,0),(0,1,0),(0,0,1)])
+ sage: (P,S) = motzkin_decomposition(K)
+ sage: K.is_equivalent(P)
+ True
+ sage: S.is_trivial()
+ True
+
+ Likewise, full spaces are their own subspace components::