improve experiments' docs

experiments/cdc_4_boundaries.py

 #!/usr/bin/python
 
 """
-Calculate a lower bound on the number of 4-boundaries
-of a linear representation of the number of circuit double
-covers.
+  Calculate a the number of 4-boundaries of a linear
+  representation of the number of circuit double covers.
 
   It uses cyclic ladder gadgets with sizes 2 up to 7 with
   permutations of all half-edges except the first one.
-This gives matrix of size 36 with rank 21.
+  This gives matrix of size 36 with rank 21 which matches
+  the upper bound which is the rank of the join matrix.
 """
 
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
 from itertools import permutations
 from graph_tools.all import *
 
-
 LadderGadget = lambda k: CyclicLadder().gadget(k)
 ladders = list(map(LadderGadget, range(2, 8)))
 gadgets = [ l.permute((1,) + p) 

experiments/cdc_5_boundaries.py

 #!/usr/bin/python
 
 """
-Calculate a lower bound on the number of 4-boundaries
+  Calculate a lower bound on the number of 5-boundaries
   of a linear representation of the number of circuit double
   covers.
 
   It uses cyclic ladder gadgets with sizes 2 up to 7 with
   permutations of all half-edges except the first one.
-This gives matrix of size 36 with rank 21.
-"""
+  This gives matrix of size 576 with rank 161. The upper
+  bound is 202 -- the rank of the join matrix.
 
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
+  WARNING: This experiment takes a long time to complete.
+"""
 
+import _experiment
 from itertools import permutations
 from graph_tools.all import *
 

experiments/flower-snarks.py

 #!/usr/bin/python
 
-DOC = """
+"""
   Calculate that the number of CDCs of Flower snark $J_k$ is $c16^k \pm O(15^k)$.
 
   We calculate the step matrix $M$, show that 16 is its eigenvalue by finding
@@ -9,9 +9,7 @@ of $M^10 x$ and $M^9 x$ where $x$ is the initial vector. This eigenvector
   shares one non-zero coordinate with the final vector.
 """
 
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
 from graph_tools.all import *
 from sage.all import identity_matrix, QQ, DiGraph, matrix
 
@@ -77,7 +75,6 @@ def matrix_to_rev_graph(M):
 
 
 if __name__ == "__main__":
-  print(DOC)
   print("Stabilizing...")
   S = FlowerSnark.stabilize(CircuitDoubleCover, jordan=False)
   print("Done")

experiments/ladders.py

@@ -5,16 +5,13 @@ Derive a formula for the number of circuit double covers
   of cyclic ladders and crossed cyclic ladders.
 """
 
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
 from graph_tools.all import *
 
 L = CyclicLadder().stabilize(CircuitDoubleCover, jordan=True)
 CL = CyclicLadder(True).stabilize(CircuitDoubleCover, jordan=True)
 
 if __name__ == "__main__":
-  print(__doc__)
   print("Cyclic ladders:\n  Formula: %s\n  Under the condition %s\n" %
     (L["formula"], L["formula_if"]))
   print("Crossed cyclic ladders:\n  Formula: %s\n  Under the condition %s" %

experiments/reduce-cycle.py

@@ -2,14 +2,12 @@
 
 """
 Application of Theorem 6.12 to triangles, 4-cycles (Theorem 6.13)
-and 5.cycles (Theorem 6.14). Note that the results are numeric
+and 5-cycles (Theorem 6.14). Note that the results are numeric
 calculation so it is necessary to review the system of equations
 by hand. (It is printed by the command-line parameter -v.)
 """
 
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
 from graph_tools.base import *
 from graph_tools.parameters import CircuitDoubleCover, VertexCount
 from graph_tools.misc import sun

experiments/small-snarks.py

@@ -2,12 +2,10 @@
 
 """
   Calculate the number of circuit double covers for the Petersen
-graph a Blanusa snarks.
+  graph and Blanusa snarks.
 """
 
-import sys, os
-sys.path.append(os.path.dirname(__file__) + "/..")
-
+import _experiment
 from graph_tools.all import *
 from sage.all import graphs
 
@@ -18,7 +16,6 @@ L = {
 }
 
 if __name__ == "__main__":
-  print(__doc__)
   for n, g in L.items():
     print("%s: %i" % (n, graph_to_gadget(g).eval(CircuitDoubleCover)))