mjo/cone/decomposition.py: add a NOTE

I'm becoming more and more convinced that PPL will do the
lineality-space decomposition on its own.

diff --git a/mjo/cone/decomposition.py b/mjo/cone/decomposition.py
index fe022e28b8660c3ba9e98022df29a74f07cc6f8e..d581d83dc65db6f02b464d6f5ab85159d48e26e7 100644 (file)
--- a/mjo/cone/decomposition.py
+++ b/mjo/cone/decomposition.py
@@ -89,6 +89,15 @@ def pointed_linspace_decomposition(K):
     to the lineality space and its orthogonal complement. This is a
     direct sum decomposition of the original cone.
 
+    .. NOTE::
+
+    I strongly believe that PPL does this anyway, since it claims to
+    implement the double-description method from Fukuda and Prodon,
+    and they mention this. If we're implementing an algorithm in Sage,
+    it probably suffices to verify that the lineal subset (the
+    generators that live in the cone's ``linear_subspace()`` is
+    orthogonal to the remaining generators.
+
     SETUP::
 
         sage: from mjo.cone.decomposition import (
@@ -141,7 +150,6 @@ def pointed_linspace_decomposition(K):
         sage: J = Cone(P.rays() + L.rays(), lattice=lat)
         sage: J.is_equivalent(K)
         True
-
     """
     from sage.geometry.cone import Cone