[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-29 Thread Rob Beezer
There is now a patch available for the original suggestion that graph eigenvalues could be improved. In the course of doing this, I discovered that any eigenvalue of a graph was having its complex part stripped off. Presumably, this was to clean up annoying nearly-zero complex parts for graphs (

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-13 Thread John Cremona
2009/6/13 Rob Beezer : > > On Jun 12, 1:17 am, John Cremona wrote: >> I think there's a case for having a more basic class for holding >> "things with multiplicities";  the the spectrum could be one of these >> (or a class derived from it) and Factorization would also be a derived >> class. > > H

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-12 Thread Rob Beezer
On Jun 12, 1:17 am, John Cremona wrote: > I think there's a case for having a more basic class for holding > "things with multiplicities";  the the spectrum could be one of these > (or a class derived from it) and Factorization would also be a derived > class. Hi John, Yes, I agree. There's a

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-12 Thread Nicolas M. Thiery
On Fri, Jun 12, 2009 at 09:17:29AM +0100, John Cremona wrote: > > 2009/6/12 Rob Beezer : > > > > Hi John, > > > > Thanks for the reply, the suggestions and the examples. I've seen the > > Factorization object and briefly thought of building a Spectrum > > object, but thought it sounded like over

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-12 Thread John Cremona
2009/6/12 Rob Beezer : > > Hi John, > > Thanks for the reply, the suggestions and the examples. I've seen the > Factorization object and briefly thought of building a Spectrum > object, but thought it sounded like overkill. But maybe I can just > subclass Factorization and override the _repr_ me

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-11 Thread Rob Beezer
Hi John, Thanks for the reply, the suggestions and the examples. I've seen the Factorization object and briefly thought of building a Spectrum object, but thought it sounded like overkill. But maybe I can just subclass Factorization and override the _repr_ method (or similar) to print the spect

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-11 Thread John Cremona
2009/6/11 Rob Beezer : > > On Jun 8, 7:47 pm, Jason Grout wrote: >> I've never had to use the left eigenvectors of a graph. > > And I've never needed a directed graph so my matrices are always > symmetric. (Just kidding.) ;-) > > The above is now: http://trac.sagemath.org/sage_trac/ticket/6258

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-10 Thread Rob Beezer
On Jun 8, 7:47 pm, Jason Grout wrote: > I've never had to use the left eigenvectors of a graph. And I've never needed a directed graph so my matrices are always symmetric. (Just kidding.) ;-) The above is now: http://trac.sagemath.org/sage_trac/ticket/6258 A related question: matrices and

[sage-devel] Re: Eigenvalues, eigenspaces for graphs

2009-06-08 Thread Jason Grout
Rob Beezer wrote: > Currently, eigenspaces of graphs are computed by constructing the > adjacency matrix, then converting to a matrix over RDF, and finally > computing the eigenspaces of this matrix. When the graph has integer > eigenvalues of high multiplicity, numerical inaccuracy is leading to