#15150: Implement NCSym
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15143 | Stopgaps:
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Comment (by darij):
Some random comments on ncsym.py.
{{{
The ring of symmetric functions in non-commutative variables,
which is not to be confused with the :class:`non-commutative symmetric
functions<NonCommutativeSymmetricFunctions>`, are polynomials in `n`
non-commuting variables `{\bf k}[x_1, x_2, \ldots, x_n]` where the
dimension of the subspace of elements of degree `k` is equal to
the number of compositions of `k` (with less than `n` parts).
}}}
If the variables are non-commuting, use angular rather than square
brackets. Also, I assume you want infinitely many variables? And do you
really want compositions?
Typo:
{{{
Grothendeick
}}}
Old-style arXiv references like this:
{{{
:arxiv:`0208168`
}}}
should have a "math/" in front of them, I believe (also, I'd add a version
number, in this case math/0208168v2).
What is the \wedge operation on set partitions? It is used but not
defined. If it's the one from the Bergeron-Zabrocki paper, it is simply
the meet of set partitions (aka {{{__mul__}}}) and should be explained as
such.
On the right hand side of
{{{
S(\mathbf{p}_A) = \sum_{\gamma} (-1)^{\ell(\gamma)}
\gamma[A]
}}}
don't you mean to say {{{ p_{\gamma[A]} }}} rather than {{{ \gamma[A] }}}
? And on the next line, do you mean to say {{{of `[\ell(A)]`}}} instead of
{{{of length `\ell(A)`}}}?
Similarly here:
{{{
p(A) = \sum_{\gamma} (-1)^{\ell(\gamma)-1} \gamma[A]
}}}
I assume that "strictly coarser" in
{{{
where we sum over all strictly coarser set partitions `B`.
}}}
refers to the relation of strict coarsening as defined in
{{{set_partition.py}}}. If so, please say this explicitly, as the notation
is slightly counterintuitive (one normally thinks "strictly coarser" means
"coarser and not equal").
I'll eventually have a closer look at the patch if only to understand how
exactly internal-coproduct-by-coercion works (for use in NSym); I cannot
promise that I will ever give this an actual review. Nevertheless, great
work here, Travis.
--
Ticket URL: <http://trac.sagemath.org/ticket/15150#comment:19>
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