So when k = 19, sage.interfaces.latte.count
<http://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/latte.html>
and P.integral_points_count() give different answers. This seems to be the
cause of the difference. Here is some more code showing the difference.
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from sage.all import Polyhedron
from sage.interfaces.latte import count
eqns = [
[0, -1, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 0, 0, 1, 1, -1, 0, 0],
[0, 0, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0],
[0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 1, -1],
[0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0],
[0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1],
[-100, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[-19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
]
ieqs = [
[-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
]
P = Polyhedron(eqns=eqns, ieqs=ieqs)
print(P.integral_points_count())
print(count(P.cdd_Hrepresentation(), cdd=True))
