#18050: Implement dual equivalence graphs
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: combinatorics | Resolution:
Keywords: dual equivalence | Merged in:
graphs | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 618141c49451360ea24abc512fb4fe86f74ca469
public/crystals/dual_equivalence-18050| Stopgaps:
Dependencies: |
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Comment (by tscrim):
Replying to [comment:19 darij]:
> Replying to [comment:18 tscrim]:
> > > My question is still standing: Where are the `= 0 or 1` conditions
in Assaf's (4.1) reflected in your code and doc? Or are they redundant, or
wrong, or your notion of dual equivalence graphs different?
> >
> > It's in the code, see this line:
> > {{{
> > if x.epsilon(i) == 1 and x.epsilon(im) == 0:
> > }}}
>
> But what about the doc? Without this condition it sounds like your graph
has a lot more (isolated) vertices than it should have.
I forgot to say that this is in the doc as well.
> > It looks okay. I think instead of writing `a - b` we should do `a \to
b` in both files for directed edges (especially since it's in latex).
>
> I think it's fine the way it is. The edge is undirected a priori; we
direct it by assigning it a head. You'd have to reword my definition if
you want to put an arrow there.
I made a change which I think is more clear. Comments welcomed.
> > I also feel this statement is too verbose:
> > {{{
> > - In the one-line notation of the permutation `p`, the letter
> > `i` appears either to the left of both `i-1` and `i+1`, or
> > to the right of both `i-1` and `i+1` (but not between the
> > two).
> > }}}
> > and we should just say `i` does not appear between `i-1` and `i+1`.
Does this sound okay?
>
> That's fine; feel free to change it (I won't return to this until
tomorrow).
I've made this change.
> > > In regular_crystals.py, what is required of X ? Should it be closed
under e_i and f_i?
> >
> > No, I wanted it to be as general as possible (at least this is what I
needed for my research; I didn't necessarily know if my set of elements
was the full dual equivalence class).
>
> OK, but it seems (from a brief glance) that if you don't have a union of
equivalence classes, then your code can leak some non-X vertices into the
graph by constructing edges one of whose endpoints is not in X. Is that OK
to you?
Eeek, you're right. I made changes so that non-X vertices are not added to
the DEG.
--
Ticket URL: <http://trac.sagemath.org/ticket/18050#comment:21>
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