def test_27(self):
"""
Nodes and partitions
"""
d0 = POSetOps.instance().sym2basis('ABCD')
x0 = POSetOps.instance().adjacency(d0)
logger.info("dict: {}".format(x0['m']))
nodes = tuple(x0['n'])
logger.info("nodes: {} {}".format(len(nodes), nodes))
edges = tuple(x0['e'])
logger.info("edges: {} {}".format(len(edges), edges))
def test_09(self):
"""
Partitions
"""
l0 = POSetOps.instance().partitions(set('ABC'))
l0 = list(l0)
logger.info("unordered: " + str(l0))
def test_13(self):
"""
weak orderings
"""
l0 = POSetOps.instance().partitions(list('ABC'))
l0 = [ list(l) for l in list(l0) ]
l1 = [ len(l) for l in list(l0) ]
logger.info("ordered: {} {} {}".format(len(l0), l1, l0))
def test_15(self):
"""
Partial order
Partial order: A000670
"""
p0 = POSetOps.instance()
for s in self.ss:
x0 = p0.partial_order(s)
logger.info("partial: {} {:.80}".format(len(x0), str(x0)))
def test_21(self):
"""
Nodes and partitions
"""
p0 = POSetOps.instance()
x0 = p0.adjacency('ABC')
self.assertIsNotNone(x0)
logger.info("counts: {}".format(p0._counts(x0)))
s0 = [ string.ascii_letters[0:n] for n in range(1,6) ]
for s in s0:
logger.info(p0._counts(p0.adjacency(s)))
def test_29(self):
"""
Nodes and partitions
"""
x0 = POSetOps.instance().adjacency('ABC')
self.assertIsNotNone(x0)
logger.info("dict: {}".format(x0['m']))
nodes = tuple(x0['n'])
logger.info("nodes: {} {}".format(len(nodes), nodes))
edges = tuple(x0['e'])
logger.info("edges: {} {}".format(len(edges), edges))
x1 = POSetOps.instance().remap(adjacency0=x0)
self.assertIsNotNone(x1)
logger.info("keys: {}".format(x1.keys()))
nodes = tuple(x1['nodes'].values())
logger.info("nodes: {} {}".format(len(nodes), nodes))
edges = tuple(x1['edges'])
logger.info("edges: {} {}".format(len(edges), edges))
def test_10(self):
"""
Unordered Bell
Total ordering: A000142
"""
p0 = POSetOps.instance()
for s in self.ss:
n0 = int(scis.perm(len(s), len(s)))
n1 = len(tuple(p0.total_order(s)))
self.assertEqual(n0, n1)
logger.info("total ordering: {}: {} == {}".format(len(s), n0, n1))
def test_11(self):
"""
Unordered Bell
Equivalence relation: A000110
"""
p0 = POSetOps.instance()
logger.info("unordered Bell: {}".format(p0.unordered_Bell(3)))
for s in self.ss:
n0 = p0.unordered_Bell(len(s))
n1 = len(tuple(p0.partitions(set(s))))
self.assertEqual(n0, n1)
logger.info("eqivalence: {}: {} == {}".format(len(s), n0, n1))
def test_13(self):
"""
Ordered Bell
Total preorder: A000670
"""
p0 = POSetOps.instance()
logger.info("ordered Bell: {}".format(p0.ordered_Bell(3)))
for s in self.ss:
n0 = p0.ordered_Bell(len(s))
n1 = len(tuple(p0.weak_orderings(syms=s)))
self.assertEqual(n0, n1)
logger.info("ordered Bell: {}: {} == {}".format(len(s), n0, n1))
def test_23(self):
"""
Nodes and partitions
"""
p0 = POSetOps.instance()
n = 4
s0 = string.ascii_letters[0:n]
a0 = p0.sym2basis(s0)
logger.info(a0)
nodes = p0._nodes(a0)
logger.info(nodes)
faces = p0._faces(nodes, ndiff=2, nX=1)
logger.info(faces)
logger.info("n: {}; nodes: {}; faces: {}".format(n, len(nodes), len(faces)))
logger.info("n: {}; #faces: {}".format(n, 2 - (len(nodes) - len(faces))))
def test_03(self):
s0 = POSetOps.instance().strong("ABCD")
logger.info("strong: " + str(s0))
def test_23(self):
"""
Nodes and partitions
"""
d0 = POSetOps.instance().sym2basis('ABC')
logger.info("dict: {}".format(d0))