doctests

graph_tools/parameters.py

@@ -54,6 +54,19 @@ def _init_():
 
   @OneOfKind
   class EdgeColoring(SimpleParameterBase):
+    """Edge coloring of gadget.
+
+    Colors have identity.
+
+    >>> from .sequences import Necklace
+    >>> Necklace.graph(1).eval(EdgeColoring(2))
+    0
+    >>> Necklace.graph(1).eval(EdgeColoring(3))
+    6
+    >>> Necklace.graph(2).eval(EdgeColoring(3))
+    12
+    """
+
     def __init__(self, k):
       self.k = k
       self.FREE_EDGE = [ Boundary((i, i), 1) for i in range(k) ]
@@ -211,6 +224,18 @@ def _init_():
       yield Boundary(ret_b, prod( b.value for b in x ))
 
     def join_edges(self, b, e1, e2):
+      """
+      >>> from .definitions import Boundary as B
+      >>> def test(*args): return list(CircuitDoubleCover.join_edges(*args))
+      >>> test(B(((1,2), (2,3), (1,3), None), 1), 1, 2)
+      []
+      >>> test(B(((1,2), (2,3), (1,4), (3,4), None), 1), 1, 2)
+      [Boundary(boundary=((3, 2), (2, 3), (3, 2), (3, 2), None), value=1)]
+      >>> test(B(((1,2), (2,3), (1,4), (3,4), None, (1,3)), 1), 1, 2)
+      []
+      >>> len(test(B(((1,2), (2,3), (4,5), (1,3), (4,5), None), 1), 1, 2))
+      2
+      """
       assert len(b.boundary[e1]) == len(b.boundary[e2])
 
       def do_join(uf):
@@ -272,6 +297,17 @@ def _init_():
       return b[0].value
 
     def enumerate_boundaries(self, n):
+      """Enumerate all possible boundaries on cut of size `n`.
+
+      >>> list(CircuitDoubleCover.enumerate_boundaries(2))
+      [((1, 2), (1, 2), None)]
+      >>> list(CircuitDoubleCover.enumerate_boundaries(3))
+      [((1, 2), (1, 3), (2, 3), None)]
+      >>> sum( 1 for _ in CircuitDoubleCover.enumerate_boundaries(4) )
+      60
+      >>> sum( 1 for _ in CircuitDoubleCover.enumerate_boundaries(5) )
+      1024
+      """
       if n == 0: yield (None,)
       if n <= 1: return
 

graph_tools/tests.py

@@ -7,14 +7,35 @@ so we put them here instead.
 >>> from .all import *
 >>> from sage.all import *
 
->>> graphs.CompleteGraph(4).is_isomorphic(Necklace.graph(1).eval(UnderlayingGraph))
-
->>> all( Necklace.graph(i).eval(CircuitDoubleCover) == 2 * 4**(i-1) for i in range(1, 10) )
+>>> is_isomorphic = lambda g, gadget: g.is_isomorphic(gadget.eval(UnderlayingGraph))
+>>> assert is_isomorphic(graphs.CompleteGraph(4), Necklace.graph(1))
+>>> assert is_isomorphic(graphs.PetersenGraph(), Petersen)
+
+>>> cdc_count = lambda gadget: gadget.eval(CircuitDoubleCover)
+>>> cdc_count(Petersen)
+52
+>>> cdc_count(GeneralizedPetersen(2).graph(5))
+52
+>>> cdc_count(FlowerSnark.graph(3))
+104
+>>> all( cdc_count(Necklace.graph(i)) == 2 * 4**(i-1) for i in range(1, 100) )
 True
->>> GeneralizedPetersen(2).graph(5).eval(CircuitDoubleCover) == 52
+>>> all( cdc_count(Flower.graph(k)) == (2**(k-1) + (-1)**k) // 3 + 1 for k in range(3, 20) )
 True
->>> FlowerSnark.graph(3).eval(CircuitDoubleCover)
-104
+>>> Necklace.stabilize(CircuitDoubleCover)
+Loop 1 done - 1 boundaries (0 new)
+{'variables': [((1, 2), (1, 2), None)], 'step_matrix': [4], 'initial_vector': [2], 'finalize': [1]}
+>>> sun_cdc = lambda n: sum( v for _, v in sun(n).eval_gadget(CircuitDoubleCover) )
+>>> all( sun_cdc(n) == 2**n - 2*n for n in range(3, 10) )
+True
+
+>>> d = [ list(range(5)), list(range(5, 10)) ]
+>>> graph_to_gadget(graphs.PetersenGraph(), d).eval(GroupFlow(Integers(3), False))
+729
+>>> graph_to_gadget(graphs.PetersenGraph(), d).eval(GroupFlow(Integers(4), True))
+0
+>>> graph_to_gadget(graphs.PetersenGraph(), d).eval(GroupFlow(Integers(5), True))
+240
 
 
 """