From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 11 Jan 2016 15:04:50 +0000 (-0500)
Subject: Add tests for permutation/conjugation of cones/transformations.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=c9ab469a53dc691d2646e22bdbc0ea0b3f3961c1;p=sage.d.git

Add tests for permutation/conjugation of cones/transformations.
---

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 66d6ccf..21f9862 100644
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -441,6 +441,25 @@ def positive_operator_gens(K):
         ....:                check=False)
         sage: K.is_proper() == pi_cone.is_proper()
         True
+
+    The positive operators of a permuted cone can be obtained by
+    conjugation::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim=4)
+        sage: L = ToricLattice(K.lattice_dim()**2)
+        sage: p = SymmetricGroup(K.lattice_dim()).random_element().matrix()
+        sage: pK = Cone([ p*k for k in K ], K.lattice(), check=False)
+        sage: pi_of_pK = positive_operator_gens(pK)
+        sage: actual = Cone([t.list() for t in pi_of_pK],
+        ....:                lattice=L,
+        ....:                check=False)
+        sage: pi_of_K = positive_operator_gens(K)
+        sage: expected = Cone([(p*t*p.inverse()).list() for t in pi_of_K],
+        ....:                   lattice=L,
+        ....:                   check=False)
+        sage: actual.is_equivalent(expected)
+        True
     """
     # Matrices are not vectors in Sage, so we have to convert them
     # to vectors explicitly before we can find a basis. We need these
@@ -642,6 +661,25 @@ def Z_transformation_gens(K):
         sage: Z_cone = Cone([z.list() for z in Z_of_K], check=False)
         sage: Z_cone.dim() == 3
         True
+
+    The Z-transformations of a permuted cone can be obtained by
+    conjugation::
+
+        sage: set_random_seed()
+        sage: K = random_cone(max_ambient_dim=4)
+        sage: L = ToricLattice(K.lattice_dim()**2)
+        sage: p = SymmetricGroup(K.lattice_dim()).random_element().matrix()
+        sage: pK = Cone([ p*k for k in K ], K.lattice(), check=False)
+        sage: Z_of_pK = Z_transformation_gens(pK)
+        sage: actual = Cone([t.list() for t in Z_of_pK],
+        ....:                lattice=L,
+        ....:                check=False)
+        sage: Z_of_K = Z_transformation_gens(K)
+        sage: expected = Cone([(p*t*p.inverse()).list() for t in Z_of_K],
+        ....:                   lattice=L,
+        ....:                   check=False)
+        sage: actual.is_equivalent(expected)
+        True
     """
     # Matrices are not vectors in Sage, so we have to convert them
     # to vectors explicitly before we can find a basis. We need these