def cyclic_flats_height3(config, groundset=None):
# Assume config is of a simple matroid with no isthmuses
# Replace default groundset with the given one
def change_groundset(cyclic_flats):
if groundset is None:
return cyclic_flats
permutation = dict(enumerate(groundset))
new_cfs = set()
for cf in cyclic_flats:
new_cfs.add(frozenset(permutation[elem] for elem in cf))
return new_cfs
matroid6_3_3 = BinaryMatroid2(
matrix(GF(2), [
[1, 0, 0, 1, 1, 1],
[0, 1, 0, 1, 0, 1],
[0, 0, 1, 0, 1, 1],
]))
if config == matroid6_3_3.cf_lattice_config():
return change_groundset(matroid6_3_3.cyclic_flats())
matroid7_3_4 = BinaryMatroid2(
matrix(GF(2), [
[1, 0, 0, 1, 1, 0, 1],
[0, 1, 0, 1, 0, 1, 1],
[0, 0, 1, 0, 1, 1, 1],
]))
if config == matroid7_3_4.cf_lattice_config():
return change_groundset(matroid7_3_4.cyclic_flats())
if config == matroid7_3_4.dual().cf_lattice_config():
return change_groundset(matroid7_3_4.dual().cyclic_flats())
matroid8_4_4 = BinaryMatroid2(
matrix(GF(2), [
[1, 0, 0, 0, 1, 0, 1, 1],
[0, 1, 0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 1, 1, 1, 0],
[0, 0, 0, 1, 0, 1, 1, 1],
]))
if config == matroid8_4_4.cf_lattice_config():
return change_groundset(matroid8_4_4.cyclic_flats())
# the matroid is none of the above, so it is one with nullity 2.
# assume those are also known
matroid5_3_2 = BinaryMatroid2(
matrix(GF(2), [
[1, 0, 0, 1, 0],
[0, 1, 0, 0, 1],
[0, 0, 1, 1, 1],
]))
if config == matroid5_3_2.cf_lattice_config():
return change_groundset(matroid5_3_2.cyclic_flats())
# uniform matroids
if len(config) == 2:
poset = config.poset()
assert poset.bottom().size == 0 and poset.bottom().rank == 0
matroid = Uniform(poset.top().rank, poset.top().size)
return change_groundset(matroid.cyclic_flats())
def iteration(matrix_):
global n
n += 1
if print_progress:
print('\r{}'.format(n), end='', file=sys.stderr)
matroid = BinaryMatroid2(matrix=matrix_)
# Only consider simple matroids with no isthmuses
if not matroid.is_simple() or matroid.coloops():
return
candidate_config = matroid.cf_lattice_config()
if candidate_config == search_config:
print("\nFound:")
print(matroid)
print(matrix_)
print('--------')
return matroid
def iteration(matrix_):
global n
n += 1
if print_progress:
print('\r{}'.format(n), end='', file=sys.stderr)
matroid = BinaryMatroid2(matrix=matrix_)
# Only consider simple matroids with no isthmuses
if not matroid.is_simple() or matroid.coloops():
return
config = matroid.cf_lattice_config()
if config in results:
if not matroid.is_isomorphic(results[config][0]):
print("\nFound:")
print(matrix_)
print('--------')
print(results[config][1])
config.show(index=True)
return config
else:
results[config] = (matroid, matrix_)
[0, 0, 1, 0, 1, 1, 1],
])
matrix8_4_4 = matrix(GF(2), [
[1, 0, 0, 0, 1, 0, 1, 1],
[0, 1, 0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 1, 1, 1, 0],
[0, 0, 0, 1, 0, 1, 1, 1],
])
matrix11_4_5 = matrix(GF(2), [
[1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1],
[0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1],
[0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0],
[0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1],
])
matroid6_3_3 = BinaryMatroid2(matrix6_3_3)
matroid6_4_2 = BinaryMatroid2(matrix6_4_2)
matroid7_3_4 = BinaryMatroid2(matrix7_3_4)
matroid8_4_4 = BinaryMatroid2(matrix8_4_4)
matroid11_4_5 = BinaryMatroid2(matrix11_4_5)
#print("Isomorphic:", matroid1.is_isomorphic(matroid2))
#print("Same config:",
# matroid1.cf_lattice_config() == matroid2.cf_lattice_config())
# Return atoms (in Z) of a poset, configuration or matroid
def atoms(data):
if isinstance(data, sage.matroids.matroid.Matroid):
poset = Poset((data.cyclic_flats(), operator.le))
elif isinstance(data, Configuration):
elements2 = [
Element(size=0, rank=0, index=6),
Element(3, 2, 5),
Element(3, 2, 4),
Element(5, 4, 3),
Element(5, 4, 2),
Element(5, 4, 1),
Element(8, 5, 0),
]
covers2 = make_covers(elements2,
[(6, 5), (6, 4), (6, 2), (6, 1), (5, 3), (4, 3), (3, 0), (2, 0), (1, 0)])
config2 = Configuration(elements2, covers2)
matroid = BinaryMatroid2(matrix=matrix(GF(2), [
[0, 0, 0, 0],
[0, 0, 0, 0],
[1, 0, 0, 1],
[0, 1, 1, 0],
]))
config3 = matroid.cf_lattice_config()
if SHOW:
config1.show(index=True, title='config1')
config2.show(index=True,
title="config2 ("
+ ("not " if config1 != config2 else "")
+ "equal to config1)")
config3.show(label=True, title=config3)
d = {config1: True}
for edge in config3.covers:
return None
# Finished
show_progress(cyclic_flats)
return cyclic_flats
# Tests
if __name__ == '__main__':
matrix11_4_5 = matrix(GF(2), [
[1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1],
[0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1],
[0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0],
[0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1],
])
matroid11_4_5 = BinaryMatroid2(matrix11_4_5)
h4 = matroid11_4_5.restrict({0, 2, 4, 5, 6, 7, 8, 9,
10}) # (9,4,3)-matroid
h4 = matroid11_4_5.restrict({0, 1, 3, 4, 5, 6, 7, 8, 9,
10}) # (10,4,4)-matroid
h4 = matroid11_4_5.restrict({0, 1, 3, 4, 5, 6, 7, 8, 9,
10}).restrict({0, 2, 3, 4, 5, 6,
7}) # (7,4,2)-matroid
print(h4)
config = h4.cf_lattice_config()
# Check correctness (up to isomorphism)
try:
cfs = sorted(
sorted(cf) for cf in cyclic_flats_height4(len(
h4), h4.cf_lattice_config()).values())