mjo/cone/schur.py

   1 """
   2 The Schur cone, as described in the "Critical angles..." papers by
   3 Seeger and Sossa.
   4 """
   5
   6 from sage.all import *
   7
   8 def is_pointed(P,Q):
   9     newP = Cone([ list(p) for p in P ])
  10     newQ = Cone([ list(q) for q in Q ])
  11     return newP.intersection(-newQ).is_trivial()
  12
  13 def ext_angles(P,Q):
  14     angles = []
  15     for p in P:
  16         for q in Q:
  17             p = vector(SR, p)
  18             q = vector(SR, q)
  19             p = p/p.norm()
  20             q = q/q.norm()
  21             angles.append(arccos(p.inner_product(q)))
  22
  23     return angles
  24
  25 def schur(n):
  26     r"""
  27     Return the Schur cone in ``n`` dimensions.
  28
  29     INPUT:
  30
  31     - ``n`` -- the ambient dimension of the Schur cone and its ambient space.
  32
  33     OUTPUT:
  34
  35     A rational closed convex Schur cone of dimension ``n``.
  36     """
  37
  38     hs = []
  39     for i in range(1,n):
  40         h_i = [0]*n
  41         h_i[i-1] = QQ(1)
  42         h_i[i] = -QQ(1)
  43         hs.append(vector(QQ,n,h_i))
  44
  45     return Cone(hs)