Hi Sam and everyone,
thanks @Sam for bringing this up. src/sage/graphs/tutte_polynomial.py has
been scaring me for some time and I hope this will lead to its becoming
better.
One thing that goes wrong in your example (but I am unsure if it is the
main issue!) is this:
sage: G = Graph();
sage: G.allow_multiple_edges(True);
sage: #edges are (u,v,l), where (u,v) is the edge and l is the label, which
determines edge order
sage:
G.add_edges([(0,1,1),(1,5,2),(5,3,3),(5,2,4),(2,4,5),(0,2,6),(0,3,7),(0,4,8),(0,5,9)]);
sage: g = G.tutte_polynomial();
sage: G.edges()
[(0, 1, 1),
(0, 2, 6),
(0, 3, 7),
(0, 4, 8),
(0, 5, 9),
(1, 5, 2),
(2, 4, 5),
(2, 5, 4),
(3, 5, 3)]
sage: with removed_edge(G, (1,5)):
show(G)
....:
sage: G.edges()
[(0, 1, 1),
(0, 2, 6),
(0, 3, 7),
(0, 4, 8),
(0, 5, 9),
(1, 5, None),
(2, 4, 5),
(2, 5, 4),
(3, 5, 3)]
The "removed_edge" context manager was supposed to either re-insert the
removed edge upon finishing, or not removing it in the original G to begin
with. From what we see, it has *tried* to re-insert it, but it forgot the
label. This is doubly strange because the "contract_edge" context manager
in the same file is well aware of labels.
I am not sure if this explains the bug, however.
Best regards,
Darij
On Sat, Feb 21, 2015 at 5:09 PM, Sam Hopkins <samuelfhopk...@gmail.com>
wrote:
> I believe there must be some error in the code that implements the Tutte
> polynomial of a graph in Sage. For example, the code
>
> G = Graph();
> G.allow_multiple_edges(True);
> #edges are (u,v,l), where (u,v) is the edge and l is the label, which
> determines edge order
>
> G.add_edges([(0,1,1),(1,5,2),(5,3,3),(5,2,4),(2,4,5),(0,2,6),(0,3,7),(0,4,8),(0,5,9)]);
> g = G.tutte_polynomial();
> print g(1,1);
> print G.spanning_trees_count();
>
> produces
>
> T(1,1): 60 Number of spanning trees: 52
>
> But of course T_G(1,1) should be equal to the number of spanning trees.
> And I am tending to believe that the error is with the Tutte polynomial
> computation and not the second "spanning_trees_count()" method.
>
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