#15311: Implement the classical Hall algebra and polynomials
--------------------------------------------+----------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: algebra | Resolution:
Keywords: Hall algebra polynomials | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15305 | Stopgaps:
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Changes (by tscrim):
* dependencies: => #15305
Comment:
Replying to [comment:3 darij]:
> Review patch uploaded. I've got only one issue I'd like you to fix
(unless it's intention), and that's the fact that the Hall algebra doesn't
coerce to the symmetric functions until you call the
`HallAlgebraMonomials` basis (because only the latter basis activates the
coercions).
I'll fix that in the next day or so.
> Comments on my changes:
>
> - Your patch contained some coercion fu in the coproduct method, where
you took an element of the tensor square of one basis and coerced it into
the tensor square of another. This doesn't work in the current version of
Sage, not even with #10963 applied (therefore the failing doctests). I
have replaced this by a manual implementation. Is this fixed on the
combinat queue?
Ah, sorry I forgot the #15305 dependency which does this.
> - I prevented the coercion to the symmetric functions from appearing
unless `q` is invertible. Is this unnecessarily restrictive? (The map does
involve division by `q`.)
I believe it makes the scalar product agree with the HL scalar product...
I saw something that this made the map "nice", but I don't think it was in
[http://arxiv.org/pdf/math/0611617v2.pdf Schiffmann].
> - Your scalar product functions had a `q` argument which seems pointless
to me (the `q` is already an attribute of the parent, and I don't think
you want to allow a different `q` in the scalar product -- if you do, you
are doing it wrong). I removed it.
Fair enough.
> Nice work!
Thanks, and thank you for reviewing this! I'll post a new version with
your changes folded in once I've fixed the coercion issue.
See you soon,[[BR]]
Travis
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Ticket URL: <http://trac.sagemath.org/ticket/15311#comment:5>
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