Adding an 3-ary example 'arity_three_order_inf'.

Tidying up __init__.py so that 'from thompson import *' will actually be useful.
Can now chain generators.expand()

Author: DMRobertson

scripts/test_quasinormal.py

@@ -1,8 +1,7 @@
 from test import setup_script
 setup_script(__file__)
 
-from thompson.word import Word
+from thompson import *
 from thompson.examples import *
 
-example_4_5.dump_mapping()
-orbit_types(example_4_5, example_4_5.domain)
+arity_three_order_inf.dump_mapping()

thompson/__init__.py

@@ -3,8 +3,8 @@
 .. moduleauthor:: David Robertson <david.m.robertson1@gmail.com>
 """
 
-from .drawing import Coord, new_drawing
-from .permutation import Permutation, random_permutation
-from .trees import DrawableTree, random_tree
-from .tree_pair import TreePair, random_pair
+from .word import Word
+from .generators import Generators
+from .automorphism import Automorphism, orbit_types
+from . import examples
 

thompson/automorphism.py

@@ -408,12 +408,14 @@ def _orbit_type(self, y, basis):
 		x1 a2: Orbit.incomplete
 		with respect to the basis [x1 a1, x1 a2]
 		>>> basis.expand(0)
+		Generators(2, 1, ['x1 a1 a1', 'x1 a1 a2', 'x1 a2'])
 		>>> orbit_types(example_4_12, basis)
 		x1 a1 a1: Orbit.complete_infinite
 		x1 a1 a2: Orbit.complete_infinite
 		x1 a2: Orbit.incomplete
 		with respect to the basis [x1 a1 a1, x1 a1 a2, x1 a2]
 		>>> basis.expand(2)
+		Generators(2, 1, ['x1 a1 a1', 'x1 a1 a2', 'x1 a2 a1', 'x1 a2 a2'])
 		>>> orbit_types(example_4_12, basis)
 		x1 a1 a1: Orbit.complete_finite
 		x1 a1 a2: Orbit.complete_finite
@@ -492,7 +494,16 @@ def _test_semi_infinite(self, y, basis, backward=False):
 #TODO the named elements A, B, C, X_n of Thompson's V.
 
 def orbit_types(aut, basis=None, words=None):
-	r"""Prints the classification of the orbits under *aut* of each word in *words* with respect to *basis*. If *basis* is omitted, it is taken to be the minimal expansion given by :meth:`~thompson.automorphism._minimal_expansion`. If *words* is omited, it is taken to be the same as *basis*. See the docstring for :meth:`~thompson.automorphism._orbit_type`"""
+	r"""Prints the classification of the orbits under *aut* of each word in *words* with respect to *basis*. If *basis* is omitted, it is taken to be the minimal expansion given by :meth:`~thompson.automorphism._minimal_expansion`. If *words* is omited, it is taken to be the same as *basis*. See the docstring for :meth:`~thompson.automorphism._orbit_type`.
+	
+		>>> orbit_types(arity_three_order_inf)
+		x1 a1: Orbit.left_semi_infinite
+		x1 a2: Orbit.complete_infinite
+		x1 a3 a1: Orbit.complete_infinite
+		x1 a3 a2: Orbit.complete_infinite
+		x1 a3 a3: Orbit.right_semi_infinite
+		with respect to the basis [x1 a1, x1 a2, x1 a3 a1, x1 a3 a2, x1 a3 a3]
+	"""
 	if basis is None:
 		basis = aut._minimal_expansion()
 	if words is None:

thompson/examples.py

@@ -3,7 +3,7 @@
 from .automorphism import Automorphism
 from .generators import Generators
 
-__all__ = ["cyclic_order_six",
+__all__ = ["cyclic_order_six", "arity_three_order_inf",
            "example_4_5", "example_4_11", "example_4_12", "example_4_25"]
 
 #Example 4.5
@@ -34,4 +34,10 @@
 leaves = ["x a1 a1", "x a1 a2 a1", "x a1 a2 a2 a1", "x a1 a2 a2 a2", "x a2 a1", "x a2 a2"]
 domain = Generators(2, 1, leaves)
 range = Generators(2, 1, [leaves[0], leaves[3], leaves[4], leaves[5], leaves[2], leaves[1]])
-cyclic_order_six = Automorphism(2, 1, domain, range)
+cyclic_order_six = Automorphism(2, 1, domain, range)
+
+#An example with arity n=3. 
+d = Generators.standard_basis(3, 1).expand(0).expand(2).expand(0)
+r = Generators.standard_basis(3, 1).expand(0).expand(2).expand(4)
+r[-3:] = reversed(r[-3:])
+arity_three_order_inf = Automorphism(3, 1, d, r)

thompson/generators.py

@@ -167,12 +167,13 @@ def expand(self, index):
 		
 			>>> g = Generators.standard_basis(3, 1); g
 			Generators(3, 1, ['x1'])
-			>>> g.expand(0); g
+			>>> g.expand(0)
 			Generators(3, 1, ['x1 a1', 'x1 a2', 'x1 a3'])
-			>>> g.expand(1); g
+			>>> g.expand(1)
 			Generators(3, 1, ['x1 a1', 'x1 a2 a1', 'x1 a2 a2', 'x1 a2 a3', 'x1 a3'])
 			
 			:raises IndexError: if there is no generator at index *index*.
 		"""
 		self[index: index+1] = [self[index].alpha(i) for i in range(1, self.arity+1)]
+		return self #allows chaining