tests

graph_tools/tests.py

@@ -3,10 +3,12 @@
 >>> from .all import *
 >>> from sage.all import *
 
->>> 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)
-
+>>> g2g = lambda gadget: gadget.eval(UnderlayingGraph)
+>>> assert graphs.CompleteGraph(4).is_isomorphic(g2g(Necklace.graph(1)))
+>>> assert graphs.PetersenGraph().is_isomorphic(g2g(Petersen))
+>>> assert all( \
+      g2g(CyclicLadder().graph(i)).is_isomorphic(g2g(GeneralizedPetersen(1).graph(i))) \
+    for i in range(3, 20) )
 >>> cdc_count = lambda gadget: gadget.eval(CircuitDoubleCover)
 >>> cdc_count(Petersen)
 52
@@ -18,13 +20,26 @@
 True
 >>> all( cdc_count(Flower.graph(k)) == (2**(k-1) + (-1)**k) // 3 + 1 for k in range(3, 20) )
 True
+
 >>> Necklace.stabilize(CircuitDoubleCover)
 Loop 1 done - 1 boundaries (0 new)
 {'variables': [((1, 2), (1, 2), None)], 'step_matrix': [4], 'initial_vector': [2], \
-'finalize': [1], 'simplified': ([1], [4], [2]), 'formula': 1/2*4^k}
+'finalize': [1], 'simplified': ([1], [4], [2]), 'formula': 1/2*4^k, 'formula_if': k - 1 >= 0}
 >>> Flower.stabilize(CircuitDoubleCover, 2)['formula']
 Loop 1 done - 3 boundaries (0 new)
 1/3*2^(k - 1) + 1/3*(-1)^k + 1
+>>> f = CyclicLadder().stabilize(CircuitDoubleCover, start_at=1)['formula']; f
+Loop 1 done - 6 boundaries (6 new)
+Loop 2 done - 13 boundaries (6 new)
+Loop 3 done - 15 boundaries (2 new)
+Loop 4 done - 15 boundaries (0 new)
+1/2*(-1)^k*(k - 1) + 1/6*4^(k - 1) + 3*2^(k - 1) + 1/3*(-2)^(k - 2) - 5/2*k - 3/2
+>>> assert all( f(k=k) == cdc_count(CyclicLadder().graph(k)) for k in range(3, 10) )
+>>> f = CyclicLadder(crossed=True).stabilize(CircuitDoubleCover, start_at=3)['formula']; f
+Loop 1 done - 12 boundaries (4 new)
+Loop 2 done - 14 boundaries (0 new)
+-1/2*(-1)^k*k + 1/6*4^(k - 1) + 3*2^(k - 1) + 1/3*(-2)^(k - 2) - 5/2*k
+>>> assert all( f(k=k) == cdc_count(CyclicLadder(True).graph(k)) for k in range(3, 10) )
 >>> sun_cdc = lambda n: sum( b.value for b in sun(n).eval_gadget(CircuitDoubleCover) )
 >>> all( sun_cdc(n) == 2**n - 2*n for n in range(3, 10) )
 True