It's difficult to see ``orthogonal=True`` working because Sage
(via PPL) minimizes the generating sets of its cones by
- default. In many cases, this minimization process will do the same
- thing that our orthogonalization does, subtracting out the lineal
- portions of the generators that do not live in the lineality
- space. Here is one example of the ell-one cone living above a
- line::
-
- sage: N = ToricLattice(3)
- sage: G = [ (1,0,0), (-1,0,0),
- ....: (1,0,1), (-1,0,1), (0,1,1), (0,-1,1) ]
- sage: K = Cone(list(map(N,G)), check=False, normalize=False)
- sage: P = nonlineal_part(K, orthogonal=True)
- sage: P.rays()
- N(0, -1, 1),
- N(0, 1, 1)
- in 3-d lattice N
- sage: K.lines()
- N(1, 0, 0)
- in 3-d lattice N
-
- These are the same rays that we get if we allow the ``Cone``
- constructor to reduce the generating set::
-
- sage: Cone(G).rays()
- N( 0, 1, 1),
- N( 0, -1, 1),
- N( 1, 0, 0),
- N(-1, 0, 0)
- in 3-d lattice N
-
- Here is an example where PPL does not do this implicitly::
+ default. Here is an example where PPL does not do this
+ implicitly::
sage: K = Cone([(-13, 3, 0, -1),
....: (11, -1, -1, 0),