def is_acyclic(self):
r"""
Return whether ``self`` is acyclic.
A vector configuration is acyclic if the origin is not in the relative
interior of the cone spanned by the vectors.
OUTPUT:
Boolean. Whether ``self`` is acyclic.
.. SEEALSO::
:meth:`is_totally_cyclic`.
EXAMPLES::
sage: from cn_hyperarr.vector_classes import *
sage: vc = VectorConfiguration([[1,0,0],[0,1,0],[0,0,1],[1,1,0],[0,1,1],[1,1,1]])
sage: vc.is_acyclic()
True
sage: v = [[1, -1, -1],
....: [1, 1, -1],
....: [1, 1, 1],
....: [1, -1, 1],
....: [-1, -1, 1],
....: [-1, -1, -1],
....: [-1, 1, -1],
....: [-1, 1, 1]]
sage: vc = VectorConfiguration(v)
sage: vc.is_acyclic()
False
TESTS::
sage: vc = VectorConfiguration([])
sage: vc.is_acyclic()
True
sage: vc2 = VectorConfiguration([[1,0,0],[-1,0,0]])
sage: vc2.is_acyclic()
False
sage: vc3 = VectorConfiguration([[0,0,0]])
sage: vc3.is_acyclic()
Traceback (most recent call last):
...
ValueError: PPL::ray(e):
e == 0, but the origin cannot be a ray.
sage: vc = VectorConfiguration([[1,0,0],[0,1,0],[0,0,1],[1,1,0],[0,1,1],[1,1,1],[-1,0,0]])
sage: vc.is_acyclic()
False
"""
acyc_vc = Polyhedron(rays=self, backend=self.backend())
if acyc_vc.relative_interior_contains(
vector([0] * acyc_vc.ambient_dim())):
return False
elif not acyc_vc.lines() == ():
return False
else:
return True
