triangular_subset = pgl2_upper_triangular(q)
number_of_triangular_elements = len(triangular_subset)
elements_generator = IterableElementsGenerator(triangular_subset)
projective_zero = pgl2.get_pf().zero()
action = StabilizedPGLGroupAction(pgl2, [projective_zero], elements_generator)
representation = PermutationRepresentation(action)
up_to_conjugation_elements = {}
for element in triangular_subset:
conjugation_class = pgl2.get_conjugation_class(element)
if conjugation_class not in up_to_conjugation_elements:
up_to_conjugation_elements[conjugation_class] = 0
up_to_conjugation_elements[conjugation_class] += 1
graph_labelling = UpToConjugationGraphLabelling(up_to_conjugation_elements, elements_generator)
graph_covering = GraphCovering(graph, representation)
action2 = PGLGroupAction(pgl2)
representation2 = TransitiveActionUnitaryStandardRepresentation(action2, pgl2.get_pf().infinity())
graph_labelling2 = UpToConjugationGraphLabelling(conjugation_classes, pgl2)
graph_covering2 = GraphCovering(graph, representation2)
matching_polynomials = {}
characteristic_polynomials = {}
for labelling, weight in graph_labelling.weighted_labellings(graph):
adjacency = graph_covering.adjacency(labelling).astype(int)
lifted_graph = from_numpy_matrix(adjacency, create_using=nx.MultiGraph, parallel_edges=True)
polynomial = get_matching_polynomial(lifted_graph)
matching_polynomials[list(labelling.values())[0]] = (polynomial, weight)
return minimizing_function
graph = nx.configuration_model((2, ))
q = 5
pgl2 = PGL2(q)
conjugation_classes = pgl2.get_conjugation_classes()
number_of_elements = sum(conjugation_classes.values())
action2 = PGLGroupAction(pgl2)
representation = TransitiveActionUnitaryStandardRepresentation(
action2,
pgl2.get_pf().infinity())
graph_labelling = UpToConjugationGraphLabelling(conjugation_classes, pgl2)
graph_covering = GraphCovering(graph, representation)
characteristic_polynomials = {}
for labelling, weight in graph_labelling.weighted_labellings(graph):
polynomial = graph_covering.get_polynomial(labelling)
characteristic_polynomials[list(labelling.values())[0]] = (polynomial,
weight)
m = []
elements = list(characteristic_polynomials.keys())
for g in characteristic_polynomials:
m.append(characteristic_polynomials[g][1] *
characteristic_polynomials[g][0])
next(qs)
n = 5
d = 4
graph = nx.random_regular_graph(d, n)
rho = get_rho(d)
for q in qs:
pgl2 = PGL2(q)
action = PGLGroupAction(pgl2)
representation = TransitiveActionUnitaryStandardRepresentation(
action,
pgl2.get_pf().infinity())
covering = GraphCovering(graph, representation)
graph_labelling = GraphLabelling(pgl2)
labellings = list(graph_labelling.random_labellings(graph, 100))
adjacencies = [covering.adjacency(labelling) for labelling in labellings]
roots = [
sorted(GraphCoveringSpectrumAnalyzer.get_eigenvalues(matrix))
for matrix in adjacencies
]
roots = np.round(roots, 2)
good_roots = []
bad_roots = []
good_roots_found = False
for x in roots:
graph = nx.configuration_model((2, ))
graph2 = nx.configuration_model((4, ))
pgl2 = PGL2(q)
action = PGLGroupAction(pgl2)
representation = TransitiveActionUnitaryStandardRepresentation(
action,
pgl2.get_pf().infinity())
characters = [
WedgeCharacter.create_wedge_character(representation, i)
for i in range(q + 1)
]
conjugation_classes = list(pgl2.get_conjugation_classes().keys())
graph_covering = GraphCovering(graph, representation)
graph_covering2 = GraphCovering(graph2, representation)
graph_labelling = UpToConjugationGraphLabelling(pgl2.get_conjugation_classes(),
pgl2)
def trace_measure(x):
return q - characters[1].apply(x)
def cycle_length_measure_1(x):
fixed_points = characters[1].apply(x)
fixed_points = round(fixed_points) + 1
if fixed_points == q + 1:
return 1 / (q * (q + 1))
elif fixed_points == 2:
from group_actions.pgl2_group_action import PGLGroupAction
graph = nx.random_regular_graph(2, 3)
# graph = nx.configuration_model((2,))
q = 7
pgl2 = PGL2(q)
conjugation_classes = pgl2.get_conjugation_classes()
elements_generator = pgl2
action = PGLGroupAction(pgl2)
representation = PermutationRepresentation(action)
up_to_conjugation_elements = pgl2.get_conjugation_classes()
graph_labelling = UpToConjugationGraphLabelling(up_to_conjugation_elements,
elements_generator)
graph_covering = GraphCovering(graph, representation)
matching_polynomials = []
matching_polynomials2 = {}
weights = []
for labelling, weight in graph_labelling.weighted_labellings(graph):
adjacency = graph_covering.adjacency(labelling).astype(int)
lifted_graph = from_numpy_matrix(adjacency,
create_using=nx.MultiGraph,
parallel_edges=True)
polynomial = get_matching_polynomial(lifted_graph)
matching_polynomials.append(polynomial)
matching_polynomials2[list(labelling.values())[0]] = polynomial
weights.append(weight)