def check_some_core_hom_is_by_subspace(vs, G, H=None, require_isomorphic=True, limit=10000):
"""
Check if there is a retract from G to H that "contracts" a subspace of vs.
See hom.hom_is_by_subspace. If not given, H is a core of G.
Returns True/False.
"""
if not H:
H = hom.find_core(G)
return any((hom.hom_is_by_subspace(G, vs, h) for h in hom.extend_hom(G, H, limit=limit)))
def test():
"Run unit tests for the module."
log.getLogger().setLevel(log.DEBUG)
from sage.graphs.graph_generators import graphs
K2 = graphs.CompleteGraph(2)
K4 = graphs.CompleteGraph(4)
Z2_3 = VectorSpace(GF(2), 3)
Z2_2 = VectorSpace(GF(2), 2)
# nonisomorphic_cubes_Z2
assert len(list(nonisomorphic_cubes_Z2(1))) == 1
assert len(list(nonisomorphic_cubes_Z2(2))) == 2
assert len(list(nonisomorphic_cubes_Z2(3))) == 6
# CayleyGraph
K4b = CayleyGraph(Z2_2, [(1, 0), (0, 1), (1, 1)])
assert K4.is_isomorphic(K4b)
# squash_cube
Ge = CayleyGraph(Z2_2, [(1, 0), (0, 1)])
Smap = squash_cube(Ge, (1, 1))
K2e = Ge.subgraph(Smap.values())
assert K2.is_isomorphic(K2e)
assert is_hom(Ge, K2e, Smap)
# hom_is_by_subspace
Gg = CayleyGraph(Z2_3, [(1, 0, 0), (0, 1, 0)])
Hg = CayleyGraph(Z2_2, [(1, 0), (0, 1), (1, 1)])
homg = {
(0, 0, 0): (0, 0),
(1, 0, 0): (1, 0),
(0, 1, 0): (0, 1),
(1, 1, 0): (1, 1),
(0, 0, 1): (0, 0),
(1, 0, 1): (1, 0),
(0, 1, 1): (1, 1),
(1, 1, 1): (0, 1)
}
assert is_hom(Gg, Hg, homg)
assert hom_is_by_subspace(Gg, Z2_3, homg, require_isomorphic=False)
assert not hom_is_by_subspace(Gg, Z2_3, homg, require_isomorphic=True)
for h in extend_hom(Gg, K2, limit=10):
assert hom_is_by_subspace(Gg, Z2_3, h, require_isomorphic=True)
log.info("All tests passed.")
def test():
"Run unit tests for the module."
log.getLogger().setLevel(log.DEBUG)
from sage.graphs.graph_generators import graphs
K2 = graphs.CompleteGraph(2)
K4 = graphs.CompleteGraph(4)
Z2_3 = VectorSpace(GF(2), 3)
Z2_2 = VectorSpace(GF(2), 2)
# nonisomorphic_cubes_Z2
assert len(list(nonisomorphic_cubes_Z2(1))) == 1
assert len(list(nonisomorphic_cubes_Z2(2))) == 2
assert len(list(nonisomorphic_cubes_Z2(3))) == 6
# CayleyGraph
K4b = CayleyGraph(Z2_2, [(1,0), (0,1), (1,1)])
assert K4.is_isomorphic(K4b)
# squash_cube
Ge = CayleyGraph(Z2_2, [(1,0), (0,1)])
Smap = squash_cube(Ge, (1,1))
K2e = Ge.subgraph(Smap.values())
assert K2.is_isomorphic(K2e)
assert is_hom(Ge, K2e, Smap)
# hom_is_by_subspace
Gg = CayleyGraph(Z2_3, [(1,0,0), (0,1,0)])
Hg = CayleyGraph(Z2_2, [(1,0), (0,1), (1,1)])
homg = {(0,0,0):(0,0), (1,0,0):(1,0), (0,1,0):(0,1), (1,1,0):(1,1),
(0,0,1):(0,0), (1,0,1):(1,0), (0,1,1):(1,1), (1,1,1):(0,1)}
assert is_hom(Gg, Hg, homg)
assert hom_is_by_subspace(Gg, Z2_3, homg, require_isomorphic=False)
assert not hom_is_by_subspace(Gg, Z2_3, homg, require_isomorphic=True)
for h in extend_hom(Gg, K2, limit=10):
assert hom_is_by_subspace(Gg, Z2_3, h, require_isomorphic=True)
log.info("All tests passed.")
def parallel_extend_hom_partmaps(G, H, partmap, kwargs):
log.debug("Running extend_hom with %s" % (partmap))
res = hom.extend_hom(G, H, partmap=partmap, **kwargs)
log.debug("Done extend_hom with %s" % (partmap))
return res