#16606: Bernstein creation operators and other fixes on symmetric functions
-------------------------------------+-------------------------------------
Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.3
Component: combinatorics | Resolution:
Keywords: symmetric | Merged in:
functions, sage-combinat | Reviewers:
Authors: Darij Grinberg | Work issues:
Report Upstream: N/A | Commit:
Branch: public/combinat | 494cc5ce34c44c60d1691486fb1663a247ce44f2
/witt-sf-fix | Stopgaps:
Dependencies: |
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Description changed by darij:
Old description:
> {{{
> Sym = SymmetricFunctions(ZZ)
> w = Sym.w()
> w[4].coproduct()
> }}}
> This would fail because {{{w[4]}}} would be transformed into the h-basis,
> which would make some of its coefficients into rationals even though they
> should be integers.
>
> The cause is the fact that inverting an integer matrix can turn its
> entries into rationals even if the matrix is invertible over ZZ. I have
> fixed this in a way I believe to be suboptimal, but this is all I have
> time for...
New description:
This patch introduces the Bernstein creation operators on the symmetric
and the noncommutative symmetric functions. I don't know whether the
implementation on the latter is anywhere near optimal, but the former
should be fairly fast.
It also fixes a mistake I made long ago when implementing the Witt basis
of Sym and the Hazewinkel basis of QSym, which caused the following to
break:
{{{
Sym = SymmetricFunctions(ZZ)
w = Sym.w()
w[4].coproduct()
}}}
This failed because {{{w[4]}}} would be transformed into the h-basis,
which would make some of its coefficients into rationals even though they
should be integers. The cause was the fact that inverting an integer
matrix can turn its entries into rationals even if the matrix is
invertible over ZZ. I have fixed this in a way I believe to be suboptimal,
but this is all I have time for...
A few more cases of broken documentation are fixed.
--
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Ticket URL: <http://trac.sagemath.org/ticket/16606#comment:6>
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