On Thu, May 02, 2013 at 10:42:31AM +0000, Simon King wrote:
> - There is no mathematical difference between a quiver and a digraph.
> Hence, there will be no separate sub-class "Quiver" of "DiGraph".
(but we could imagine in the long run having such a subclass, in case
we would want to enforce further properties, like having a distinct
name for each edge, ...)
> - How shall we call the algebraic structure formed by the paths in a
> quiver? PathMonoid? PathMagma? QuiverMonoid? QuiverMagma?
I don't have a good suggestion, except for being consistent
PathAlgebra/PathMonoid or QuiverAlgebra/QuiverMonoid (where Monoid is
to be replaced by whatever is deemed appropriate).
> All the algebraic stuff (representations, path algebra, and also
> list of quiver paths in contrast to list of paths as a digraph)
> should be accessible from there. Methods like "is_sink" should be
> implemented on DiGraph.
> - In contrast to Jim's code, QuiverPath should be an element, namely an
> element of the afore-mentioned algebraic structure.
> - We should allow directed cycles and loops where possible. We can
> currently only have quiver representations for acyclic quivers. But
> there is no reason to restrict QuiverMonoid and QuiverAlgebra to the
> acyclic case.
> - "QuiverMonoid" should be a unique parent. I suggest using
> UniqueRepresentation.
> - A QuiverMonoid M is *not* a DiGraph. Of course, it can return the
> underlying quiver by M.quiver(), and M is uniquely determined by
> M.quiver().
+1
> The last point gives rise to a question: Is there a way to make a
> DiGraph immutable, so that it can be used as a cache key, and so that we
> can store the quiver as an attribute of QuiverMonoid?
> Jim constructs a class Quiver as a sub-class of DiGraph and makes its
> instances immutable, by overriding all self-changing methods on the
> level of the instance (not on the level of the class, because these
> methods are needed during initialisation). I think it would be much
> better to use sage.structure.mutability.Mutability on the level of
> DiGraph.
>
> Actually I'd be surprised if there'd be no patch for it yet.
> Nathann, what's the ticket number :) ?
We discussed this a couple times with Nathann indeed, and I guess
there is a ticket. For now, in similar situations, I have been using
the following hack:
sage: G = DiGraph([[1,2]])
sage: G = G.copy()
sage: G._immutable = True
sage: hash(G)
-6891319547016415084
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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