#6258: [with patch, needs review] Improve accuracy of graph eigenvalues
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Reporter: rbeezer | Owner: rbeezer
Type: defect | Status: new
Priority: critical | Milestone: sage-4.1
Component: graph theory | Keywords:
Reviewer: | Author:
Merged: |
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Changes (by rbeezer):
* priority: minor => critical
Comment:
The patch generally improves graph eigenvalues by not altering the
adjacency matrix and therefore allowing new routines to take advantage of
the adjacency matrix being a matrix of integers. It also corrects a
serious bug for eigenvalues of digraphs. More specifically
1. The adjacency matrix is no longer converted to a matrix of reals or
complexes.
2. Eigenspaces are now more abstract (but are exact). More numerical
results come from the new {{{eigenvectors()}}} method.
3. Any complex part of an eigenvalue was previously being stripped, as if
a graph could never be a digraph. This has been corrected and a simple
doctest added.
4. While in the neighborhood, the {{{characteristic_polynomial()}}} got
some cosmetic changes in its docstring.
5. Long-term, the {{{spectrum()}}} command should return some sort of
object, like a {{{Factorization}}} object, as discussed on sage-devel.
Then the current {{{spectrum()}}} could be renamed as {{{eigenvalues()}}}.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6258#comment:2>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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