X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fschur.py;h=53607a948ef26a3cb9f5fae2d86c8d895a4fab71;hb=7fe29009a2fa2e6a2ceaf623e860e23a0fa22b1a;hp=dca7292807096997a18bf5a57ae7dc400f3be187;hpb=f79e891ca154b0fa935a14001b0b6ed194425741;p=sage.d.git

diff --git a/mjo/cone/schur.py b/mjo/cone/schur.py
index dca7292..53607a9 100644
--- a/mjo/cone/schur.py
+++ b/mjo/cone/schur.py
@@ -19,6 +19,11 @@ def schur_cone(n):
 
     REFERENCES:
 
+    .. [GourionSeeger] Daniel Gourion and Alberto Seeger.
+       Critical angles in polyhedral convex cones: numerical and
+       statistical considerations. Mathematical Programming, 123:173-198,
+       2010, doi:10.1007/s10107-009-0317-2.
+
     .. [IusemSeegerOnPairs] Alfredo Iusem and Alberto Seeger.
        On pairs of vectors achieving the maximal angle of a convex cone.
        Mathematical Programming, 104(2-3):501-523, 2005,
@@ -47,6 +52,17 @@ def schur_cone(n):
         sage: abs(actual - expected).n() < 1e-12
         True
 
+    The dual of the Schur cone is the "downward monotonic cone"
+    [GourionSeeger]_, whose elements' entries are in non-increasing
+    order::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(10)
+        sage: K = schur_cone(n).dual()
+        sage: x = K.random_element()
+        sage: all( x[i] >= x[i+1] for i in xrange(n-1) )
+        True
+
     TESTS:
 
     We get the trivial cone when ``n`` is zero::