More minor cleanup of motzkin_decomposition().

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 84c3adb57d8396735460f5aefe5d669416e18ff1..eb5316330f6afefdc3b452482bfbd6d59deabbd2 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -83,7 +83,7 @@ def motzkin_decomposition(K):
     REFERENCES:
 
     .. [Stoer-Witzgall] J. Stoer and C. Witzgall. Convexity and
-       Optimization in Finite Dimensions I.  Springer-Verlag, New
+       Optimization in Finite Dimensions I. Springer-Verlag, New
        York, 1970.
 
     EXAMPLES:
@@ -152,18 +152,17 @@ def motzkin_decomposition(K):
         sage: S.is_equivalent(expected_S)
         True
     """
-    linspace_gens  = [ copy(b) for b in K.linear_subspace().basis() ]
-    linspace_gens += [ -b for b in linspace_gens ]
+    # The lines() method only gives us one generator for each line,
+    # so we negate the result and combine everything for the full set.
+    S = Cone([p*l for p in [1,-1] for l in K.lines()], K.lattice())
 
-    S = Cone(linspace_gens, K.lattice())
-
-    # Since ``S`` is a subspace, its dual is its orthogonal complement
-    # (albeit in the wrong lattice).
-    S_perp = Cone(S.dual(), K.lattice())
-    P = K.intersection(S_perp)
+    # Since ``S`` is a subspace, the rays of its dual generate its
+    # orthogonal complement.
+    P = K.intersection( Cone(S.dual(), K.lattice()) )
 
     return (P,S)
 
+
 def positive_operator_gens(K):
     r"""
     Compute generators of the cone of positive operators on this cone.