#15311: Implement the classical Hall algebra and polynomials
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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: | Stopgaps:
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Comment (by 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).
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?
- 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`.)
- 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.
Nice work!
--
Ticket URL: <http://trac.sagemath.org/ticket/15311#comment:3>
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