Hi Simon! On Wed, Jan 26, 2011 at 09:17:09AM -0800, Simon King wrote: > Anyway. My aim is to implement finite-dimensional quotients of path > algebras as part of a project to compute modular cohomology rings of > basic algebras.
Cool! That's a feature we will have a use for :-) See also this thread: http://groups.google.com/group/sage-combinat-devel/browse_thread/thread/5dc980d086eb5a27/ > A path algebra should be a unique parent, associated with a base > ring and a labeled multi-digraph with loops. But since the graphs > themselves are not hashable, I guess one has to use some unique > description for them. I guess the ordered tuple of its edges (an > edge being a triple of start point, end point, and label) is an > appropriate key, usable in UniqueFactory. Using CombinatorialFreeModule (and thus UniqueRepresentation), this could look like (for the full PathAlgebra): class PathAlgebra(CombinatorialFreeModule): @staticmethod def __classcall__(cls, K, graph): graph = graph.copy() graph._immutable = True return super(PathAlgebra, cls).__classcall__(cls, K, graph) def __init__(self, K, graph): self._graph = graph CombinatorialFreeModule.__init__(self, K, GraphPaths(graph) , category = GradedAlgebrasWithBasis(K)) ... This way, there will be a single line to change when Sage will officially support for immutable graphs. And in the mean time it will be reasonably safe since the algebra encapsulates its own private copy of the graph, reducing the risk of someone inadvertently changing it. Notes: - GraphPaths does not exist yet. Maybe it should be graph.paths(). - Note: a variant would be to implement instead the path monoid (with zero when two paths do not concatenate) of the graph GraphPathsMonoid(graph), and just ask for the algebra of this monoid. A little caveat is the proper handling of the zero of the monoid, since we want it to be mapped to the 0 of the algebra. That's a general feature we want to have for monoids with a zero. Cheers, Nicolas -- Nicolas M. Thiéry "Isil" <nthi...@users.sf.net> http://Nicolas.Thiery.name/ -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
