Examples of hand-checked non-conjugate elements

docs/examples_table.txt

@@ -78,6 +78,10 @@ non_revealing
 	A purely infinite automorphism for which
 	- The minimal representation does NOT correspond to a revealing pair; and
 	- The quasinormal basis does NOT correspond to a revealing pair.
+not_conjugate_f
+	At first glance this automorphism looks like it could be conjugate to ``not_conjugate_g``; indeed this satisfies the criteria of theorem 2 in [SD10]_. However the :meth:`infinite conjugacy test <thompson.infinite.InfiniteAut.test_conjugate_to>` only yields one potential conjugator :math:`\rho` which turns out not to be an automorphism (in fact, just an endomorphism) of :math:`V_{2,1}`.
+not_conjugate_g
+	At first glance this automorphism looks like it could be conjugate to ``not_conjugate_f``; indeed this satisfies the criteria of theorem 2 in [SD10]_. However the :meth:`infinite conjugacy test <thompson.infinite.InfiniteAut.test_conjugate_to>` only yields one potential conjugator :math:`\rho` which turns out not to be an automorphism (in fact, just an endomorphism) of :math:`V_{2,1}`.
 olga_f
 	An automorphism described in example 5 of [SD10]_. Nathan had this to say: "*olga_f is conjugate to olga_g, via a rho that can be found using your program or olga_h. Note that characteristics are not the same for two of the semi-infinite orbits.*"
 olga_g

thompson/examples/not_conjugate_f.aut

@@ -0,0 +1,8 @@
+5
+(2, 1) -> (2, 1)
+x a1             -> x a1 a2 a2   
+x a2 a1          -> x a1 a2 a1 a1
+x a2 a2 a1       -> x a2         
+x a2 a2 a2 a1    -> x a1 a2 a1 a2
+x a2 a2 a2 a2    -> x a1 a1      
+At first glance this automorphism looks like it could be conjugate to ``not_conjugate_g``; indeed this satisfies the criteria of theorem 2 in [SD10]_. However the :meth:`infinite conjugacy test <thompson.infinite.InfiniteAut.test_conjugate_to>` only yields one potential conjugator :math:`\rho` which turns out not to be an automorphism (in fact, just an endomorphism) of :math:`V_{2,1}`.

thompson/examples/not_conjugate_g.aut

@@ -0,0 +1,8 @@
+5
+(2, 1) -> (2, 1)
+x a1 a1 a1 -> x a2 a1 a1
+x a1 a1 a2 -> x a1      
+x a1 a2 a1 -> x a2 a1 a2
+x a1 a2 a2 -> x a2 a2 a1
+x a2       -> x a2 a2 a2
+At first glance this automorphism looks like it could be conjugate to ``not_conjugate_f``; indeed this satisfies the criteria of theorem 2 in [SD10]_. However the :meth:`infinite conjugacy test <thompson.infinite.InfiniteAut.test_conjugate_to>` only yields one potential conjugator :math:`\rho` which turns out not to be an automorphism (in fact, just an endomorphism) of :math:`V_{2,1}`.

thompson/infinite.py

@@ -62,6 +62,10 @@ def test_conjugate_to(self, other):
 			Conjugate: True  Conjugator works: True
 			Conjugate: True  Conjugator works: True
 			Conjugate: True  Conjugator works: True
+			
+			>>> f, g = (load_example('not_conjugate_' + c) for c in 'fg')
+			>>> f.is_conjugate_to(g)
+			False
 		
 		.. doctest::
 			:hide: