def cayley_digraph(self, gens, color=False):
""" Returns dict of edges of Cayley digraph. If color=True,
returns separate dicts for each color arcs, where one color
corresponds to one generator.
"""
M, elems = self.array, self.elems
ind = self.index
dgraphs = []
xgens, elem = [gens], []
for i in gens:
for j in gens:
xgens.append([M[i - ind, j - ind]])
xgens = allelems(xgens)
for i in xgens:
elem.append(self.cycle(i))
elem = allelems(elem)
for i in gens:
dgraph = {j: [] for j in elems}
for j in elem:
cyc = self.cycle(i, [j])
if len(cyc) > 1:
dgraph[j].append(cyc[1])
dgraphs.append(dgraph)
if color:
return tuple(dgraphs)
return mergedicts(dgraphs)
def __init__(self, matrix):
if issquare(matrix):
self.array = np.array(matrix)
self.order = len(matrix[0])
self.index = np.amin(self.array)
self.elems = allelems(self.array.tolist())
self.finite_set = self.elems
else:
raise TypeError('Input %s not a square matrix.' % (matrix))
def __init__(self, n):
self.perm_order = n
self.order = factorial(n)
self.op = None
self.perms = list(permutations(range(n)))
self.array = self._matrix()
self.finite_set = allelems(self.array)
self.index = 0
self.identity = self._identity()
def __init__(self, n):
self.perm_order = n
self.order = 2 * n
self.op = None
self.perms = self._gens()
self.array = self._matrix()
self.finite_set = allelems(self.array)
self.index = 0
self.identity = self._identity()
def __init__(self, finite_set, op=None):
if op is None:
super().__init__(finite_set)
self.finite_set = allelems(finite_set)
self.identity = self._identity()
self.op = op
elif callable(op):
self.finite_set, self.op = list(finite_set), op
self.order = len(self.finite_set)
self.index = min(self.finite_set)
super().__init__(self._matrix())
self.identity = self._identity()
else:
raise TypeError('Input %s not a function.' % (op))