On 01/10/2012 11:37 AM, Raymond N. Greenwell wrote:
Hello everyone!
I tried using the HasseDiagram and rank features of Sage as described
on
http://www.sagemath.org/doc/reference/sage/combinat/posets/hasse_diagram.html
Things worked ok, but when I then tried: m=
Matrix([[0,1,1],[0,0,1],[0,0,0]]) g = DiGraph(m) h2 =
HasseDiagram(g) h2.rank(2)
I got the message:
...
Please tell me what this means and how I can get rank working
properly.
This is a bad error message. The code is doing this:
self.rank_function()(element)
But the "rank_function" method can return None:
def rank_function(self):
r"""
Returns a rank function of the poset, if it exists.
...
So, sage can't come up with a rank function, and the error you got is
the result of trying to evaluate None(2).
Also, I have a complaint about HasseDiagram, in that for the matrix
above, it draws a link from 0 to 1, from 1 to 2, and from 0 to 2. In
the usual definition of a Hasse diagram, the link from 0 to 2
shouldn't show, since 0> 1> 2. (I'm referring to the nodes;
obviously the previous inequalities are nonsense numerically.) (For
example, see http://mathworld.wolfram.com/HasseDiagram.html
and http://mathworld.wolfram.com/CoverRelation.html.)
Sage is drawing the diagram correctly (this is why it can't find a rank
function), you just don't have the DiGraph that you think you should have.
We could do a lot better here -- I had to read the source for
DiGraph.__init__ -- but it looks like when you called DiGraph(m), it
considered 'm' to be an adjacency matrix.
[0,1,1]
m = [0,0,1]
[0,0,0]
That means that there's an arrow from,
row -> column
-------------
0 -> 1
0 -> 2
1 -> 2
So that explains why you have the Hasse diagram that you have. Getting
the one that you actually want probably just requires a different matrix.
--
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