From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 28 Sep 2015 03:27:24 +0000 (-0400)
Subject: Add the cone.permutation_invariant module.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=f14bcc7d014547bca733363b2a32ce9b0722f251;p=sage.d.git

Add the cone.permutation_invariant module.
---

diff --git a/mjo/all.py b/mjo/all.py
index 246f1a0..580cca5 100644
--- a/mjo/all.py
+++ b/mjo/all.py
@@ -6,6 +6,7 @@ in his script. Instead, he can just `from mjo.all import *`.
 from cone.cone import *
 from cone.completely_positive import *
 from cone.doubly_nonnegative import *
+from cone.permutation_invariant import *
 from cone.rearrangement import *
 from cone.symmetric_psd import *
 from interpolation import *
diff --git a/mjo/cone/permutation_invariant.py b/mjo/cone/permutation_invariant.py
new file mode 100644
index 0000000..65e22f5
--- /dev/null
+++ b/mjo/cone/permutation_invariant.py
@@ -0,0 +1,85 @@
+# 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 random_permutation_invariant_cone(lattice=None,
+                                      min_ambient_dim=0,
+                                      max_ambient_dim=None,
+                                      min_rays=0,
+                                      max_rays=None,
+                                      strictly_convex=None,
+                                      solid=None):
+    r"""
+    Return a random permutation-invariant cone.
+
+    A cone ``K`` is said to be permutation-invariant if ``P(K) == K``
+    for all permutation matrices ``P``. To generate one, we can begin
+    with any cone, and construct the set of all permutations of its
+    generators. The resulting set will generate a permutation-invariant
+    cone by construction.
+
+    All of this function's parameters are passed to ``random_cone()``
+    function used to generate the initial cone whose generators we will
+    permute.
+    """
+    K = random_cone(lattice=lattice,
+                    min_ambient_dim=min_ambient_dim,
+                    max_ambient_dim=max_ambient_dim,
+                    min_rays=min_rays,
+                    max_rays=max_rays,
+                    strictly_convex=strictly_convex,
+                    solid=solid)
+
+    # We'll need this to turn rays into vectors so that we can permute
+    # them with permutation matrices.
+    V = K.lattice().vector_space()
+
+    # The set of all permutatin matrices on ``V``.
+    Sn = [ p.matrix() for p in SymmetricGroup(V.dimension()) ]
+
+    # Set of permuted generators
+    pgens = []
+
+    for g in K.rays():
+        for permutation in Sn:
+            pgens.append(permutation * V(g))
+
+    L = ToricLattice(V.dimension())
+    return Cone(pgens, lattice=L)
+
+
+def is_permutation_invariant(K):
+    r"""
+    Determine if ``K`` is permutation-invariant.
+
+    A cone is said to be permutation-invariant if ``P(K)`` is a subset
+    of ``K`` for every permutation matrix ``P``.
+
+    EXAMPLES:
+
+        sage: all([ is_permutation_invariant(rearrangement_cone(p,n))
+        ....:               for n in range(3, 6)
+        ....:               for p in range(1, n) ])
+        True
+
+    """
+    # We'll need this to turn rays into vectors so that we can permute
+    # them with permutation matrices.
+    V = K.lattice().vector_space()
+
+    # The set of all permutation matrices on ``V``.
+    Sn = [ p.matrix() for p in SymmetricGroup(V.dimension()) ]
+
+    for permutation in Sn:
+        L = ToricLattice(V.dimension())
+        permuted_gens = [ permutation * V(g) for g in K.rays() ]
+        for g in permuted_gens:
+            if not K.contains(g):
+                return False
+
+    return True