Add the has_rearrangement_property() function for vectors.

diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py
index 5da9b284ab66d7ca816167e2729a31eabbc22700..2cde6386ddefe8c2384030d7f1ab25bdd4491c58 100644 (file)
--- a/mjo/cone/rearrangement.py
+++ b/mjo/cone/rearrangement.py
@@ -6,7 +6,7 @@ from site import addsitedir
 addsitedir(abspath('../../'))
 
 from sage.all import *
-from mjo.cone.cone import lyapunov_rank
+from mjo.cone.cone import lyapunov_rank, random_element
 
 def rearrangement_cone(p,n):
     r"""
@@ -94,3 +94,49 @@ def rearrangement_cone(p,n):
     V = VectorSpace(QQ, n)
     G = V.basis() + [ d(j) for j in range(n) ]
     return Cone(G)
+
+
+def has_rearrangement_property(v, p):
+    r"""
+    Test if the vector ``v`` has the "rearrangement property."
+
+    The rearrangement cone of order ``p`` in `n` dimensions has its
+    members vectors of length `n`. The "rearrangement property,"
+    satisfied by its elements, is to have its smallest ``p`` components
+    sum to a nonnegative number.
+
+    We believe that we have a description of the extreme vectors of the
+    rearrangement cone: see ``rearrangement_cone()``. This function is
+    used to test that conic combinations of those extreme vectors are in
+    fact elements of the rearrangement cone. We can't test all conic
+    combinations, obviously, but we can test a random one.
+
+    To become more sure of the result, generate a bunch of vectors with
+    ``random_element()`` and test them with this function.
+
+    INPUT:
+
+    - ``v`` -- An element of a cone suspected of being the rearrangement
+               cone of order ``p``.
+
+    - ``p`` -- The suspected order of the rearrangement cone.
+
+    OUTPUT:
+
+    If ``v`` has the rearrangement property (that is, if its smallest ``p``
+    components sum to a nonnegative number), ``True`` is returned. Otherwise
+    ``False`` is returned.
+
+    EXAMPLES:
+
+    Every element of a rearrangement cone should have the property::
+
+        sage: for n in range(2,10):
+        ....:     for p in range(1, n-1):
+        ....:         K = rearrangement_cone(p,n)
+        ....:         v = random_element(K)
+        ....:         if not has_rearrangement_property(v,p): print v
+
+    """
+    components = sorted(v)[0:p]
+    return sum(components) >= 0