some tests

.gitignore

@@ -0,0 +1,116 @@
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+*.py[cod]
+*$py.class
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+*.so
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+# Distribution / packaging
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+# Installer logs
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+
+# Unit test / coverage reports
+htmlcov/
+.tox/
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+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+.hypothesis/
+.pytest_cache/
+
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+
+# pyenv
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+# SageMath parsed files
+*.sage.py
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+# Environments
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+# Pyre type checker
+.pyre/

orbitgen.py

@@ -1,8 +1,21 @@
 from sage.all import *
 import cProfile, pstats, StringIO
+import itertools
+from sage.groups.perm_gps.partn_ref.refinement_graphs import isomorphic
 
-### foldrep
+def findsubsets(S,m):
+    return set(itertools.combinations(S, m))
+
+### foldrep: applies f to each canonical representative, maintains an
+### accumulator
+### graph: a sage graph
+### colors: a list of lists which partitions the vertices in G into colors
+###   colors[0]: True vertices
+###   colors[1]: False vertices
+###   colors[3] is reserved for the algorithm
+### fold: apply a fold method to each orbit
 def foldrep(graph, colors, acc, f):
+    # TODO: reduce number of isomorphism calls if possible
     acc = f(acc, graph, colors)
     if len(colors[0]) >= (len(graph.vertices()) / 2):
         return acc
@@ -36,15 +49,74 @@ def foldrep(graph, colors, acc, f):
     return acc
 
 ### genrep: generates a representative of each orbit class of a graph
-### graph: a sage graph
-### colors: a list of lists which partitions the vertices in G into colors
-###   colors[0]: True vertices
-###   colors[1]: False vertices
-###   colors[3] is reserved for the algorithm
-### fold: apply a fold method to each orbit
 def genrep(G):
     colors = [[], [i for i in G.vertices()]]
-    return foldrep(G, colors, [], lambda acc, g, color: acc + [(g, color)])
+    # folding function
+    def add_vertex(acc, g, color):
+        # check if inversion is isomorphic to the current graph
+        if len(color[0]) < len(g.vertices()) / 2.0:
+            return acc + [color] + [color[::-1]]
+
+        # we know it's a 50/50 color split, check if this is an isomorphic
+        # inversion or not
+        g2 = Graph(g)
+        g.canonical_label(partition=color)
+        g2.canonical_label(partition=color[::-1])
+        if g == g2:
+            # inversions are isomorphic, return one
+            return acc + [color]
+        else:
+            # inversion are non-isomorphic, return both
+           print("non isomorphic inversion: %s, %s" % (color, color[::-1]))
+           return acc + [color] + [color[::-1]]
+    return foldrep(G, colors, [], add_vertex)
+
+### generates a friends and smokers graph with n people
+def gen_friends_smokers(n):
+    g = Graph(sparse=True)
+    # make n smoker vertices
+    smokers = [x for x in range(0,n)]
+    # connect all the smokers
+    smokeredges = findsubsets(smokers, 2)
+    # make friends
+    friends = []
+    friendedges = []
+    count = n
+    for (s1,s2) in findsubsets(smokers, 2):
+        friends += [count]
+        friendedges += [(s1, count), (s2, count)]
+        count += 1
+
+    g.add_vertices(smokers)
+    g.add_vertices(friends)
+    g.add_edges(friendedges)
+    g.add_edges(smokeredges)
+    return g
+
+# generates a graph which is fully-connected in m and connected across n
+def gen_pigeonhole(n,m):
+    g = Graph()
+    v = []
+    e = []
+    # generate vertices
+    for x in range(0,n):
+        for y in range(0,m):
+            v += [x*m + y]
+
+    # generate edges
+    # generate fully connected graph in n
+    for x in range(0,n):
+        for y in findsubsets(range(0, m), 2):
+            e += [(x*m + y[0], x*m + y[1])]
+
+    # connect between n and m
+    for x in range(0,n):
+        for y in range (0,m):
+            e += [(x*m + y, ((x + 1) % n)*m + y)]
+
+    g.add_vertices(v)
+    g.add_edges(e)
+    return g
 
 # given a graph g, count the number of distinct 2-colorings using Polya's
 # theorem.
@@ -58,19 +130,14 @@ def main():
     # pr = cProfile.Profile()
     # pr.enable()
 
-    G = graphs.CycleGraph(4)
+    # G = gen_friends_smokers(3)
+    G = graphs.CycleGraph(8)
     num_vert = len(G.vertices())
     r = genrep(G)
-    tot = 0
-    for k in r:
-        if len(k[1][0]) == num_vert/2.0:
-            tot += 1
-        else:
-            tot+= 2
-        print(k)
-    print("Found configurations: %d" % tot)
+    for x in r:
+        print(x)
+    print("Found configurations: %d" % len(r))
     print("Expected configurations: %d" % count_num_distinct(G))
-    # print("size: %d" % len(r))
 
     # pr.disable()
     # s = StringIO.StringIO()

test.py

@@ -6,13 +6,7 @@ def count_num_generated(G):
     colors = [[], [i for i in G.vertices()]]
     num_vert = len(G.vertices())
     l = orbitgen.genrep(G)
-    tot = 0
-    for k in l:
-        if len(k[1][0]) == num_vert/2.0:
-            tot += 1
-        else:
-            tot+= 2
-    return tot
+    return len(l)
 
 class TestGen(unittest.TestCase):
     def test_complete(self):