#14775: Symmetric functions: extending Kronecker product, implementing Kronecker
product, extending antipode, extending forgotten basis, implementing Witt
basis
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Reporter: darij |
Owner: sage-combinat
Type: enhancement |
Status: new
Priority: major |
Milestone: sage-5.11
Component: combinatorics |
Resolution:
Keywords: symmetric function, combinat, kronecker product, days49 |
Work issues:
Report Upstream: N/A |
Reviewers:
Authors: Darij Grinberg |
Merged in:
Dependencies: |
Stopgaps:
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Comment (by darij):
While there are good formulas for the h, e, p bases in terms of the w
bases, as well as not-too-slow algorithms for the w basis in terms of the
h, e, p bases (basically by inverting the formulas just mentioned), I am
not sure which of them I should implement. Right now I have implemented
h-to-w and w-to-h, declaring them as coercions, and p-to-w. The h-to-w and
w-to-h coercions use a cache like the ones in {{{dual.py}}}. Now I need
guidance on the following:
1) Is it a good idea to also use cache for e-to-w and w-to-e? (The
downside is that there will be more caches in memory.) Same for p-to-w (my
current implementation is cacheless, thus not as fast as it could be) and
w-to-p.
2) If I implement these maps, should I register them as coersions? (This
would normally make sense, but I fear they could significantly slow down
coercions between standard classical bases because of the asinine way the
current system generates coercion paths.)
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14775#comment:9>
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