From 75d8908c2da5a64ab289dcdfbc03e72d7878f58d Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 7 Jan 2016 13:57:06 -0500 Subject: [PATCH] Add tests for Corollary 2 in the paper (lineality of pi-star). --- mjo/cone/cone.py | 26 +++++++++++++++++++++----- 1 file changed, 21 insertions(+), 5 deletions(-) diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 8b07f86..332d4b2 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -118,7 +118,7 @@ def motzkin_decomposition(K): sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8) sage: (P,S) = motzkin_decomposition(K) - sage: x = K.random_element() + sage: x = K.random_element(ring=QQ) sage: P.contains(x) or S.contains(x) True sage: x.is_zero() or (P.contains(x) != S.contains(x)) @@ -257,7 +257,7 @@ def positive_operator_gens(K): sage: set_random_seed() sage: K = random_cone(max_ambient_dim=5) sage: pi_of_K = positive_operator_gens(K) - sage: all([ K.contains(P*K.random_element()) for P in pi_of_K ]) + sage: all([ K.contains(P*K.random_element(QQ)) for P in pi_of_K ]) True A random element of the positive operator cone should send the @@ -268,7 +268,7 @@ def positive_operator_gens(K): sage: pi_of_K = positive_operator_gens(K) sage: L = ToricLattice(K.lattice_dim()**2) sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L) - sage: P = matrix(K.lattice_dim(), pi_cone.random_element().list()) + sage: P = matrix(K.lattice_dim(), pi_cone.random_element(QQ).list()) sage: all([ K.contains(P*x) for x in K ]) True @@ -280,8 +280,8 @@ def positive_operator_gens(K): sage: pi_of_K = positive_operator_gens(K) sage: L = ToricLattice(K.lattice_dim()**2) sage: pi_cone = Cone([ g.list() for g in pi_of_K ], lattice=L) - sage: P = matrix(K.lattice_dim(), pi_cone.random_element().list()) - sage: K.contains(P*K.random_element()) + sage: P = matrix(K.lattice_dim(), pi_cone.random_element(QQ).list()) + sage: K.contains(P*K.random_element(ring=QQ)) True The lineality space of the dual of the cone of positive operators @@ -303,6 +303,22 @@ def positive_operator_gens(K): sage: actual == expected True + The lineality of the dual of the cone of positive operators + is known from its lineality space:: + + sage: set_random_seed() + sage: K = random_cone(max_ambient_dim=5) + sage: n = K.lattice_dim() + sage: m = K.dim() + sage: l = K.lineality() + sage: pi_of_K = positive_operator_gens(K) + sage: L = ToricLattice(n**2) + sage: pi_cone = Cone([p.list() for p in pi_of_K], lattice=L) + sage: actual = pi_cone.dual().lineality() + sage: expected = l*(m - l) + m*(n - m) + sage: actual == expected + True + The dimension of the cone of positive operators is given by the corollary in my paper:: -- 2.43.2