mjo/cone/trivial_cone.py

   1 from sage.all import *
   2
   3 def trivial_cone(n, lattice=None):
   4     r"""
   5     The trivial cone with no generators in ``n`` dimensions.
   6
   7     INPUT:
   8
   9       - ``n`` -- the dimension of the ambient space.
  10
  11       - ``lattice`` -- (default: ``None``) an ambient lattice of rank ``n``
  12                        to be passed to the :func:`Cone` constructor.
  13
  14     OUTPUT:
  15
  16     The trivial cone with no generators.
  17
  18     If a ``lattice`` was specified, then the resulting cone will live in
  19     that lattice unless its rank is incompatible with the dimension
  20     ``n`` (in which case a ``ValueError`` is raised).
  21
  22     SETUP::
  23
  24         sage: from mjo.cone.trivial_cone import trivial_cone
  25
  26     EXAMPLES::
  27
  28     We can construct the trivial cone as the nonnegative orthant in a
  29     trivial ambient space::
  30
  31         sage: trivial_cone(0)
  32         0-d cone in 0-d lattice N
  33
  34     Or in a nontrivial ambient space::
  35
  36         sage: trivial_cone(3)
  37         0-d cone in 3-d lattice N
  38
  39     If a ``lattice`` is given, the trivial cone will live in that lattice::
  40
  41         sage: L = ToricLattice(3, 'M')
  42         sage: trivial_cone(3, lattice=L)
  43         0-d cone in 3-d lattice M
  44
  45     TESTS:
  46
  47     An error is raised if the rank of the lattice disagrees with ``n``::
  48
  49         sage: L = ToricLattice(1, 'M')
  50         sage: trivial_cone(3, lattice=L)
  51         Traceback (most recent call last):
  52         ...
  53         ValueError: lattice rank=1 and dimension n=3 are incompatible
  54
  55     """
  56     if lattice is None:
  57         lattice = ToricLattice(n)
  58
  59     if lattice.rank() != n:
  60         raise ValueError('lattice rank=%d and dimension n=%d are incompatible'
  61                          %
  62                          (lattice.rank(), n))
  63
  64     return Cone([], lattice)