Adding doctest for example 4.25

Author: DMRobertson

thompson/automorphism.py

@@ -420,6 +420,13 @@ def _orbit_type(self, y, basis):
 		x1 a2 a1: Orbit.complete_finite
 		x1 a2 a2: Orbit.complete_finite
 		with respect to the basis [x1 a1 a1, x1 a1 a2, x1 a2 a1, x1 a2 a2]
+		
+		>>> #Example 4.25
+		>>> orbit_types(example_4_25)
+		x1 a1: Orbit.right_semi_infinite
+		x1 a2 a1: Orbit.complete_infinite
+		x1 a2 a2: Orbit.left_semi_infinite
+		with respect to the basis [x1 a1, x1 a2 a1, x1 a2 a2]
 		"""
 		# print('Forward Orbit for', y)
 		# input()

thompson/examples.py

@@ -20,13 +20,12 @@
 example_4_11 = Automorphism(2, 1, domain, range)
 
 #Example 4.12
-#TODO minimal expansion and orbit types, semi-normal form (in progress)
 domain = Generators(2, 1, ["x a1 a1", "x a1 a2", "x a2"])
 range  = Generators(2, 1, ["x a2 a2", "x a2 a1", "x a1"])
 example_4_12 = Automorphism(2, 1, domain, range)
 
 #Example 4.25
-#Gives: reduced form, minimal expansion for QNF basis start, orbits and characteristics
+#Todo. Characteristics?
 domain = Generators(2, 1, ["x a1",       "x a2 a1",    "x a2 a2 a1 a1", "x a2 a2 a1 a2", "x a2 a2 a2"])
 range  = Generators(2, 1, ["x a1 a1 a1", "x a1 a1 a2", "x a2 a2",       "x a1 a2",       "x a2 a1"   ])
 example_4_25 = Automorphism(2, 1, domain, range)