From d3561bfcfea6f26e5942e6e49992bf34efc24b5c Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 1 Nov 2018 23:42:28 -0400 Subject: [PATCH] cone/faces.py: test the relationship between dual_face and face_generated_by. --- mjo/cone/faces.py | 15 ++++++++++++++- 1 file changed, 14 insertions(+), 1 deletion(-) diff --git a/mjo/cone/faces.py b/mjo/cone/faces.py index a682016..ee16890 100644 --- a/mjo/cone/faces.py +++ b/mjo/cone/faces.py @@ -149,7 +149,7 @@ def dual_face(K,F): SETUP:: - sage: from mjo.cone.faces import dual_face + sage: from mjo.cone.faces import (dual_face, face_generated_by) EXAMPLES: @@ -189,6 +189,19 @@ def dual_face(K,F): sage: dual_face(K,trivial_face).is_equivalent(K.dual()) True + The dual of the cone of ``K`` at ``y`` is the dual face of the face + of ``K`` generated by ``y`` ([Tam]_ Corollary 3.2):: + + sage: set_random_seed() + sage: K = random_cone(max_ambient_dim=8, max_rays=10) + sage: y = K.random_element() + sage: S = [y] + sage: phi_y = face_generated_by(K,S) + sage: points_cone_gens = list(K.rays()) + [-z for z in phi_y.rays()] + sage: points_cone = Cone(points_cone_gens, K.lattice()) + sage: points_cone.dual().is_equivalent(dual_face(K, phi_y)) + True + """ # Ensure that F is actually a face of K before continuing. if not F.is_face_of(K): -- 2.44.2