add example and code to generate dot file

coxeter_automaton.py

@@ -1,10 +1,4 @@
-#!/usr/bin/python
-
-# 0 is infinity
-coxeter_matrix = [[1, 5, 5],
-                  [5, 1, 5],
-                  [5, 5, 1]]
-
+import numpy as np
 import math
 from copy import copy
 from collections import deque
@@ -48,7 +42,7 @@ def apply_gen_to_root(form, k, root):
 	root[k] -= 2*form_gen_root(form, k, root)
 
 # find a sequence of generators to apply to obtain a negative root, from left to right
-# "startwidth" argument can be used to force the first entry
+# "startwith" argument can be used to force the first entry
 def find_word_to_negative(form, root_, startwith = None):
 	rank = len(form)
 	root = root_.copy()
@@ -169,29 +163,24 @@ def generate_automaton(small_roots, lex_reduced = False):
 		graph[fr][gen] = to
 	return graph
 
-# main program
 
-form = [[-math.cos(math.pi/m) if m > 0 else -1 for m in row] for row in coxeter_matrix]
-rank = len(coxeter_matrix)
-small_roots = find_small_roots(form)
-graph = generate_automaton(small_roots, lex_reduced = False)
-graph_lex = generate_automaton(small_roots, lex_reduced = True)
+def enumerate_group(graph, graph_lex, max_len):
+	rank = len(graph[0])
+	group = [Groupelement(0, rank, tuple())]
+	group[0].inverse = group[0]
+	group[0].node = group[0].lex_node = 0
 
-group = [Groupelement(0, rank, tuple())]
-group[0].inverse = group[0]
-group[0].node = group[0].lex_node = 0
-
-i = 0
-size = 1
-while True:
+	i = 0
+	size = 1
+	while True:
 		current = group[i]
 		i+=1
 
-	if current.length >= 10:
+		# break if current has the max length we have, as that's when we would start adding elements 1 longer
+		if current.length >= max_len:
 			break
 
-	for gen, new_lex_node in enumerate(graph_lex[current.lex_node]):
-		if new_lex_node:
+		for gen, new_lex_node in filter(lambda x: x[1], enumerate(graph_lex[current.lex_node])):
 			new_element = Groupelement(size, rank, current.word + (gen,))
 			new_element.lex_node = new_lex_node
 			new_element.node = graph[current.node][gen]
@@ -199,10 +188,8 @@ while True:
 			size += 1
 
 			# w = w_1 t, w s = w_1
-			# right multiplication (and left in case it does the same as a right mult)
+			# right multiplication, if it decreases length
 			for k in range(rank):
-
-				# if right multiplication by k decreases length
 				if not graph[new_element.node][k]:
 					word = list(new_element.word)
 					longer_suffix = group[0]
@@ -213,7 +200,6 @@ while True:
 
 						# w = w_1 t w_2, w_2 s_k = t w_2
 						# in the case word = [] longer_suffix could be None
-						# found it
 						if len(word) == 0 or shorter_suffix.right[k] == longer_suffix:
 							# finish word
 							while len(word) > 0:
@@ -240,8 +226,25 @@ while True:
 						other = new_element.right[k].inverse
 						inverse.left[k] = other
 						other.left[k] = inverse
+	return group
 
-length = 0
-for i in range(1,len(group)+1):
-	if i == len(group) or group[i].length > group[i-1].length:
-		print("{number:d} elements up to length {length:d}".format(number = i, length = group[i-1].length))
+def word(w):
+	return ''.join([chr(ord('a')+x) for x in w])
+
+def generate_automaton_coxeter_matrix(coxeter_matrix, lex_reduced = False):
+        form = [[-math.cos(math.pi/m) if m > 0 else -1 for m in row] for row in coxeter_matrix]
+        rank = len(coxeter_matrix)
+        small_roots = find_small_roots(form)
+        return generate_automaton(small_roots, lex_reduced)
+
+def even_graph(graph):
+	rank = len(graph[0])
+	result = []
+	for node in graph:
+		newnode = {}
+		for i in range(rank):
+			for j in range(rank):
+				if node[i] and graph[node[i]][j]:
+					newnode[(i,j)] = graph[node[i]][j]
+		result.append(newnode)
+	return result

dot_graph.py

@@ -0,0 +1,48 @@
+#!/usr/bin/python
+
+# outputs the automaton as a graphviz dot file, arranging the vertices
+# in levels according to their distance from the starting vertex
+# to convert to a PDF, run:
+# ./dot_graph.py | dot -Tpdf > output.pdf
+
+import coxeter_automaton
+from collections import deque
+
+coxeter_matrix = [[1, 2, 0, 0, 0, 2],
+                  [2, 1, 2, 0, 0, 0],
+                  [0, 2, 1, 2, 0, 0],
+                  [0, 0, 2, 1, 2, 0],
+                  [0, 0, 0, 2, 1, 2],
+                  [2, 0, 0, 0, 2, 1]]
+
+graph = coxeter_automaton.generate_automaton_coxeter_matrix(coxeter_matrix, lex_reduced = False)
+
+colors = {0: "red", 1: "darkgreen", 2: "blue", 3: "orange", 4: "black", 5: "gray"}
+
+todo = deque([0])
+distances = [None]*len(graph)
+distances[0] = 0
+
+while todo:
+    node = todo.pop()
+    for newnode in graph[node]:
+        if newnode:
+            if not distances[newnode] or distances[newnode] > distances[node] + 1:
+                distances[newnode] = distances[node] + 1
+                todo.appendleft(newnode)
+
+max_distance = max(filter(None, distances))
+nodes_by_distance = [[] for _ in range(max_distance+1)]
+for n,d in enumerate(distances):
+    if d != None:
+        nodes_by_distance[d].append(n)
+
+print('digraph test123 {')
+for dn in nodes_by_distance:
+    print('{rank = same; %s}' % "; ".join([str(x) for x in dn]))
+
+for i,node in enumerate(graph):
+    for edge,j in enumerate(node):
+        if j:
+            print('{i:d} -> {j:d} [color={color}];'.format(i = i, j = j, color = colors[edge]))
+print('}')

example.py

@@ -0,0 +1,18 @@
+#!/usr/bin/python
+
+import coxeter_automaton
+
+# (2, 3, infinity) triangle group; 0 stands for infinity
+coxeter_matrix = [[1, 0, 3],
+                  [0, 1, 2],
+                  [3, 2, 1]]
+
+graph = coxeter_automaton.generate_automaton_coxeter_matrix(coxeter_matrix, lex_reduced = False)
+graph_shortlex = coxeter_automaton.generate_automaton_coxeter_matrix(coxeter_matrix, lex_reduced = True)
+
+print(graph)
+
+group = coxeter_automaton.enumerate_group(graph, graph_shortlex, 10)
+
+# for each group element g and generator a, print index of a*g
+print([[l.id if l else None for l in g.left] for g in group])