#14981: Descent algebra
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Reporter: tscrim | Owner: sage-
Type: enhancement | combinat
Priority: major | Status: needs_review
Component: combinatorics | Milestone: sage-5.12
Keywords: Solomon's descent algebra | Resolution:
Authors: Travis Scrimshaw | Merged in:
Report Upstream: N/A | Reviewers:
Branch: | Work issues:
Stopgaps: | Dependencies:
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Comment (by darij):
I've attached a partial review patch
[attachment:trac_14981-descent_review_part_1-dg.patch]. Please look it
over. I've removed {{{one_basis}}} from the universal methods and added it
to the D and B basis, since the version you had would give wrong answers
in the D case. I believe that in the I basis, the 1 is not a basis element
(but I might be wrong here).
I'll eventually return and finish the review, but first I'd prefer to see
the following issue resolved:
It's way too tricky to call an element of the D basis. The usual trick
people are doing works for subsets of size >= 2:
{{{
sage: D = DescentAlgebra(QQ, 4).D()
sage: D[1,3]
D{1, 3}
}}}
but this is widely agreed to be syntactic sugar. One-element sets work
only if a comma is added at the end ({{{D[4,]}}} works, but {{{D[4]}}}
does not), and the empty set doesn't work at all. Moreover, this syntax is
unchecked ({{{D[666,444]}}} works just as well) and falsely suggests that
it takes compositions where it really takes subsets.
Neither of {{{D({1,3})}}}, {{{D(set([1,3]))}}}, {{{D(Set([1,3]))}}} works.
The only thing that reliably works for all subsets is this:
{{{
sage: D.basis()[(1,3)]
D{1, 3}
sage: D.basis()[(1,)]
D{1}
sage: D.basis()[()]
D{}
}}}
But I don't think such a detour should be necessary.
Eventually there should be conversions into the symmetric group algebra
and into and from NSym. The latter should be easy to do; the former is
probably best done after dealing with the #14885 mess.
--
Ticket URL: <http://trac.sagemath.org/ticket/14981#comment:3>
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