If G is a graph and A = G.am() is its adjacency matrix and B =
G.complement().am() is
the adjacency matrix of its complement, then A+B should be a 01-
matrix. The code below
shows that sage does not always share this viewpoint.
Cheers
Chris
#####
##
----------------------------------------------------------------------
## | Sage Version 4.4.4, Release Date:
2010-06-23 |
## | Type notebook() for the GUI, and license() for
information. |
##
----------------------------------------------------------------------
## sage: load whine.sage
## sage: mcl = McL()
## sage: A = mcl.am()
## sage: B = mcl.complement().am()
## sage: A.fcp()
##
## These are what they should be
##
## (x - 112) * (x + 28)^22 * (x - 2)^252
## sage: B.fcp()
## (x - 162) * (x - 27)^22 * (x + 3)^252
##
## Here's the problem: C should be a 01-matrix (in fact it should be J-
I)
##
## sage: C = A+B
## sage: max(C[0].list())
## 2
##
## If use mcl.relabel() before computing A and B, there are no
problems. So its the
## complicated vertices that are causing the problem, I expect.
##
## Here's the content of whine.sage:
##
def switch(G,sub):
H = G.copy()
rest = Set(H.vertices()).difference(Set(sub))
for u in sub:
for v in rest:
if H.has_edge(u,v): H.delete_edge(u,v)
else: H.add_edge(u,v)
return H
def McL():
C = ExtendedBinaryGolayCode()
D = C.punctured([0])
words = [ Set(it.support()) for it in D if hamming_weight(it)==7]
MG = Graph( [words, lambda a,b: len(a.intersection(b))==1])
MM = MG.copy()
MM.add_vertices([0..22])
edges = [ (i,a) for i in [0..22] for a in words if i not in a]
MM.add_edges( edges)
McL = switch( MM, MM[0])
McL.delete_vertex(0)
return McL
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