From 48a7ad09084a859da72e39e60312bfffb6b806e9 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Mon, 11 Jan 2016 09:16:37 -0500 Subject: [PATCH] Add some more Z_transformation_gens examples. --- mjo/cone/cone.py | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 68fd193..a327720 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -513,6 +513,33 @@ def Z_transformation_gens(K): sage: Z_transformation_gens(K) [] + Every operator is a Z-transformation on the ambient vector space:: + + sage: K = Cone([(1,),(-1,)]) + sage: K.is_full_space() + True + sage: Z_transformation_gens(K) + [[-1], [1]] + + sage: K = Cone([(1,0),(-1,0),(0,1),(0,-1)]) + sage: K.is_full_space() + True + sage: Z_transformation_gens(K) + [ + [-1 0] [1 0] [ 0 -1] [0 1] [ 0 0] [0 0] [ 0 0] [0 0] + [ 0 0], [0 0], [ 0 0], [0 0], [-1 0], [1 0], [ 0 -1], [0 1] + ] + + A non-obvious application is to find the Z-transformations on the + right half-plane:: + + sage: K = Cone([(1,0),(0,1),(0,-1)]) + sage: Z_transformation_gens(K) + [ + [-1 0] [1 0] [ 0 0] [0 0] [ 0 0] [0 0] + [ 0 0], [0 0], [-1 0], [1 0], [ 0 -1], [0 1] + ] + Z-transformations on a subspace are Lyapunov-like and vice-versa:: sage: K = Cone([(1,0),(-1,0),(0,1),(0,-1)]) -- 2.44.2