def get_sn_up_to_conjugation_data(q, is_unitary):
representation_class = get_representation_class(is_unitary)
action = SNGroupAction(q + 1)
elements_generator = action.get_elements_generator()
conjugation_classes = get_sn_conjugation_classes(q + 1)
labelling = UpToConjugationGraphLabelling(conjugation_classes,
elements_generator)
representation = representation_class(action, q)
return representation, labelling
def get_pgl2_up_to_conjugation_data(q, is_unitary):
representation_class = get_representation_class(is_unitary)
pgl2 = PGL2(q)
action = PGLGroupAction(pgl2)
elements_generator = pgl2
conjugation_classes = pgl2.get_conjugation_classes()
labelling = UpToConjugationGraphLabelling(conjugation_classes,
elements_generator)
representation = representation_class(action, pgl2.get_pf().infinity())
return representation, labelling
def get_cn_up_to_conjugation_data(q, is_unitary):
representation_class = get_representation_class(is_unitary)
action = CNGroupAction(q + 1)
elements_generator = action.get_elements_generator()
conjugation_classes = {0: 1}
for i in range(1, q + 1):
d = math.gcd(i, q + 1)
if d not in conjugation_classes:
conjugation_classes[d] = 0
conjugation_classes[d] += 1
labelling = UpToConjugationGraphLabelling(conjugation_classes,
elements_generator)
representation = representation_class(action, q)
return representation, labelling
def get_pgl2_up_to_conjugation_filtered_data(
q, is_unitary, pgl_filter: Callable[[PGL2Element], bool]):
representation_class = get_representation_class(is_unitary)
pgl2 = PGL2(q)
action = PGLGroupAction(pgl2)
elements_generator = ConditionalElementsGenerator(pgl2, pgl_filter)
conjugation_classes = pgl2.get_conjugation_classes()
conjugation_classes = {
element: conjugation_classes[element]
for element in conjugation_classes if pgl_filter(element)
}
labelling = UpToConjugationGraphLabelling(conjugation_classes,
elements_generator)
representation = representation_class(action, pgl2.get_pf().infinity())
return representation, labelling
number_of_elements = sum(conjugation_classes.values())
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] *
from representations import PermutationRepresentation
from projective_sets.pxl2_subsets import *
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)