X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Fcone%2Ffaces.py;h=6c5843e860ef9da5151150103223a1d507914fe1;hp=acd9802c0ee953d28723da484c148ccd7b4a0b6d;hb=928b7d49fda98ff105c92293b5797bb7a2b9873a;hpb=a9a40bcc98ebf4e4821a068c7b6273430a2b459a diff --git a/mjo/cone/faces.py b/mjo/cone/faces.py index acd9802..6c5843e 100644 --- a/mjo/cone/faces.py +++ b/mjo/cone/faces.py @@ -51,7 +51,6 @@ def face_generated_by(K,S): The face generated by should be a face:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, max_rays=10) sage: S = ( K.random_element() for idx in range(5) ) sage: F = face_generated_by(K, S) @@ -60,7 +59,6 @@ def face_generated_by(K,S): The face generated by a set should always contain that set:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, max_rays=10) sage: S = ( K.random_element() for idx in range(5) ) sage: F = face_generated_by(K, S) @@ -70,7 +68,6 @@ def face_generated_by(K,S): The generators of a proper cone are all extreme vectors of the cone, and therefore generate their own faces:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, ....: max_rays=10, ....: strictly_convex=True, @@ -82,7 +79,6 @@ def face_generated_by(K,S): that ``x`` is in the relative interior of ``F`` if and only if ``F`` is the face generated by ``x`` [Tam]_:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, max_rays=10) sage: x = K.random_element() sage: S = [x] @@ -96,7 +92,6 @@ def face_generated_by(K,S): and ``G`` in the face lattice is equal to the face generated by ``F + G`` (in the Minkowski sense) [Tam]_:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, max_rays=10) sage: L = K.face_lattice() sage: F = L.random_element() @@ -109,7 +104,6 @@ def face_generated_by(K,S): Combining Proposition 3.1 and Corollary 3.9 in [Tam]_ gives the following equality for any ``y`` in ``K``:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, max_rays=10) sage: y = K.random_element() sage: S = [y] @@ -172,7 +166,6 @@ def dual_face(K,F): The dual face of ``K`` with respect to itself should be the lineality space of its dual [Tam]_:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, max_rays=10) sage: K_dual = K.dual() sage: lKd_gens = ( dir*l for dir in [1,-1] for l in K_dual.lines() ) @@ -183,7 +176,6 @@ def dual_face(K,F): If ``K`` is proper, then the dual face of its trivial face is the dual of ``K`` [Tam]_:: - sage: set_random_seed() sage: K = random_cone(max_ambient_dim=8, ....: max_rays=10, ....: strictly_convex=True, @@ -196,7 +188,6 @@ def dual_face(K,F): 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] @@ -209,7 +200,6 @@ def dual_face(K,F): Since all faces of a polyhedral cone are exposed, the dual face of a dual face should be the original face [HilgertHofmannLawson]_:: - sage: set_random_seed() sage: def check_prop(K,F): ....: return dual_face(K.dual(), dual_face(K,F)).is_equivalent(F) sage: K = random_cone(max_ambient_dim=8, max_rays=10)