X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Frearrangement.py;h=fd792c4b481351a37ab3a0d73227120109de1dc1;hb=8bed8a3c21a0d19d01a7625b3849ac07c9a9f9e6;hp=6ea993c3b1b441980e648ee2e1a6d4ebaf964c57;hpb=edbce26685b7e62d04da8f037e51621551292225;p=sage.d.git

diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py
index 6ea993c..fd792c4 100644
--- a/mjo/cone/rearrangement.py
+++ b/mjo/cone/rearrangement.py
@@ -1,10 +1,3 @@
-# Sage doesn't load ~/.sage/init.sage during testing (sage -t), so we
-# have to explicitly mangle our sitedir here so that "mjo.cone"
-# resolves.
-from os.path import abspath
-from site import addsitedir
-addsitedir(abspath('../../'))
-
 from sage.all import *
 
 def rearrangement_cone(p,n):
@@ -35,6 +28,25 @@ def rearrangement_cone(p,n):
     A polyhedral closed convex cone object representing a rearrangement
     cone of order ``p`` in ``n`` dimensions.
 
+    REFERENCES:
+
+    .. [HenrionSeeger] Rene Henrion and Alberto Seeger.
+       Inradius and Circumradius of Various Convex Cones Arising in
+       Applications. Set-Valued and Variational Analysis, 18(3-4),
+       483-511, 2010. doi:10.1007/s11228-010-0150-z
+
+    .. [GowdaJeong] Muddappa Seetharama Gowda and Juyoung Jeong.
+       Spectral cones in Euclidean Jordan algebras.
+       Linear Algebra and its Applications, 509, 286-305.
+       doi:10.1016/j.laa.2016.08.004
+
+    .. [Jeong] Juyoung Jeong.
+       Spectral sets and functions on Euclidean Jordan algebras.
+
+    SETUP::
+
+        sage: from mjo.cone.rearrangement import rearrangement_cone
+
     EXAMPLES:
 
     The rearrangement cones of order one are nonnegative orthants::
@@ -53,20 +65,84 @@ def rearrangement_cone(p,n):
         sage: rearrangement_cone(5,5).lineality()
         4
 
+    All rearrangement cones are proper::
+
+        sage: all( rearrangement_cone(p,n).is_proper()
+        ....:              for n in xrange(10)
+        ....:              for p in xrange(1, n) )
+        True
+
+    The Lyapunov rank of the rearrangement cone of order ``p`` in ``n``
+    dimensions is ``n`` for ``p == 1`` or ``p == n`` and one otherwise::
+
+        sage: all( rearrangement_cone(p,n).lyapunov_rank() == n
+        ....:              for n in xrange(2, 10)
+        ....:              for p in [1, n-1] )
+        True
+        sage: all( rearrangement_cone(p,n).lyapunov_rank() == 1
+        ....:              for n in xrange(3, 10)
+        ....:              for p in xrange(2, n-1) )
+        True
+
     TESTS:
 
-    todo.
-    should be permutation invariant.
-    should have the expected lyapunov rank.
-    just loop through them all for n <= 10 and p < n?
+    The rearrangement cone is permutation-invariant::
+
+        sage: n = ZZ.random_element(2,10).abs()
+        sage: p = ZZ.random_element(1,n)
+        sage: K = rearrangement_cone(p,n)
+        sage: P = SymmetricGroup(n).random_element().matrix()
+        sage: all( K.contains(P*r) for r in K )
+        True
+
+    The smallest ``p`` components of every element of the rearrangement
+    cone should sum to a nonnegative number (this tests that the
+    generators really are what we think they are)::
+
+        sage: set_random_seed()
+        sage: def _has_rearrangement_property(v,p):
+        ....:     return sum( sorted(v)[0:p] ) >= 0
+        sage: all( _has_rearrangement_property(
+        ....:      rearrangement_cone(p,n).random_element(),
+        ....:      p
+        ....:    )
+        ....:    for n in xrange(2, 10)
+        ....:    for p in xrange(1, n-1)
+        ....: )
+        True
+
+    The rearrangenent cone of order ``p`` is contained in the
+    rearrangement cone of order ``p + 1``::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(2,10)
+        sage: p = ZZ.random_element(1,n)
+        sage: K1 = rearrangement_cone(p,n)
+        sage: K2 = rearrangement_cone(p+1,n)
+        sage: all( x in K2 for x in K1 )
+        True
+
+    The order ``p`` should be between ``1`` and ``n``, inclusive::
+
+        sage: rearrangement_cone(0,3)
+        Traceback (most recent call last):
+        ...
+        ValueError: order p=0 should be between 1 and n=3, inclusive
+        sage: rearrangement_cone(5,3)
+        Traceback (most recent call last):
+        ...
+        ValueError: order p=5 should be between 1 and n=3, inclusive
 
     """
+    if p < 1 or p > n:
+        raise ValueError('order p=%d should be between 1 and n=%d, inclusive'
+                         %
+                         (p,n))
 
     def d(j):
         v = [1]*n    # Create the list of all ones...
         v[j] = 1 - p # Now "fix" the ``j``th entry.
         return v
 
-    V = VectorSpace(QQ, n)
-    G = V.basis() + [ d(j) for j in range(n) ]
+    G = identity_matrix(ZZ,n).rows() + [ d(j) for j in xrange(n) ]
     return Cone(G)