def __init__(self, coxeter_diagram, init_dist):
if len(coxeter_diagram) != 6 or len(init_dist) != 4:
raise ValueError("Invalid input dimension")
# Coxeter matrix and its rank
self.cox_mat = helpers.make_symmetry_matrix(coxeter_diagram)
self.rank = len(self.cox_mat)
# generators of the symmetry group
self.gens = tuple(range(self.rank))
# symmetry group of this tiling
self.G = CoxeterGroup(self.cox_mat)
# a mirror is active iff the initial point is not on it
self.active = tuple(bool(x) for x in init_dist)
# reflection mirrors
self.mirrors = self.get_mirrors(coxeter_diagram)
# reflections (possibly affine) about the mirrors
self.reflections = self.get_reflections()
# coordinates of the initial point
self.init_v = self.get_init_point(init_dist)
self.edge_hash_set = set()
self.num_vertices = 0
self.num_edges = 0
def __init__(self, cox_mat, v0, active, reflections):
self.cox_mat = cox_mat
self.v0 = v0
self.active = active
self.reflections = reflections
self.G = CoxeterGroup(cox_mat)
self.vertices_coords = []
self.num_vertices = None
self.edge_coords = []
self.num_edges = None
def main():
parser = argparse.ArgumentParser()
parser.add_argument("filename", help="Coxeter matrix data file")
args = parser.parse_args()
cox_mat = np.loadtxt(args.filename, dtype=np.int, delimiter=" ")
print("Computing the shorlex DFA for Coxeter group:")
print(cox_mat)
G = CoxeterGroup(cox_mat).init()
print("The minimal DFA contains {} states".format(G.dfa.num_states))
imgname = os.path.splitext(os.path.basename(args.filename))[0] + ".png"
G.dfa.draw(imgname)
def __init__(self, coxeter_diagram, init_dist):
if len(coxeter_diagram) != 3 or len(init_dist) != 3:
raise ValueError("Invalid input dimension")
self.diagram = coxeter_diagram
# Coxeter matrix and its rank
self.cox_mat = helpers.get_coxeter_matrix(coxeter_diagram)
self.rank = len(self.cox_mat)
# generators of the symmetry group
self.gens = tuple(range(self.rank))
# symmetry group of this tiling
self.G = CoxeterGroup(self.cox_mat)
# a mirror is active iff the initial point is not on it
self.active = tuple(bool(x) for x in init_dist)
# reflection mirrors
self.mirrors = self.get_mirrors(coxeter_diagram)
# reflections (possibly affine) about the mirrors
self.reflections = self.get_reflections()
# coordinates of the initial point
self.init_v = self.get_init_point(init_dist)
# vertices of the fundamental triangle
self.triangle_verts = self.get_fundamental_triangle_verts()
# ----------------------
# to be calculated later
# ----------------------
# holds the words in the symmetry group up to a given depth
self.words = None
# holds the coset representatives of the standard parabolic
# subgroup of vertex-stabilizing subgroup
self.vwords = None
self.vertices_coords = []
self.num_vertices = None
self.num_edges = None
self.num_faces = None
self.edge_indices = {}
self.face_indices = {}
def __init__(self, coxeter_diagram, init_dist):
self.cox_mat = helpers.get_coxeter_matrix(coxeter_diagram)
self.G = CoxeterGroup(self.cox_mat)
self.active = tuple(bool(x) for x in init_dist)
self.words = None
self.mirrors = self.get_mirrors(coxeter_diagram)
self.init_v = helpers.get_point_from_distance(self.mirrors, init_dist)
self.reflections = self.get_reflections(init_dist)
# to be calculated later
self.vertices_coords = []
self.num_vertices = None
self.num_edges = None
self.num_faces = None
self.edge_indices = {}
self.face_indices = {}