On Fri, Jul 11, 2014 at 09:42:11AM -0700, Travis Scrimshaw wrote:
> I would say this is like matrices: do you want the iterator for
> matrices to iterate by default over all elements or rows? Currently the
> iterator goes over all rows and you can call M.list() to get a flat
> list of entries.
> Actually, this is a question for graded objects in general: should
> the default iterator go over each graded component or all elements? I
> would say there should be methods for both. My thought is the default
> iterator being over graded components since each component might be
> infinite, but I don't have a good/strong opinion/reason for this.
Right, though the difference is that containment for a matrix does not
have a strong mathematical meaning. On the other hand, when we speak
of a parent - that models some mathematical set like an algebra, the
notion of containment is unambiguous; it's about the set w.r.t its
elements. Furthermore, whenever we model a set in Python by some
collection, it's expected that containment and iteration are about the
same notion. In particular:
sage: all( x in S for x in S )
True
So I would find quite unnatural to have:
sage: Partitions(4) in Partitions()
True
On the other hand,
sage: Partitions(4) in Partitions().graded_components()
or
sage: for Pk in Partitions().graded_components()
would look natural.
So, what shall we do with this "feature" of quiver algebras?
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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