#14775: Symmetric functions: extending Kronecker product, implementing Kronecker
product, extending forgotten basis, implementing Witt basis
---------------------------------------------------------------------------+
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:
---------------------------------------------------------------------------+
Changes (by darij):
* cc: nthiery (added)
Old description:
> Will supply description in half an hour.
>
> "extend" == The current version only works when the ground ring is an
> algebra over the rationals, whereas mathematically this is not necessary.
>
> I'd love someone to check the hacks used in the current file (even if
> it's far from complete -- it only attempts to implement the Kronecker
> product over any base ring) and tell me which of them are bad before I
> spread them into other functions.
New description:
Goals for this ticket:
- The current version of itensor (the Kronecker product on the ring of
symmetric function) only works when the ground ring is an algebra over the
rationals. This is not a mathematically reasonable restriction. Fix this.
- The Kronecker coproduct on the ring of symmetric function has to be
implemented. Implement it.
- The forgotten basis of Symm is defined by duality rather than by
explicit formulas. As a consequence, it cannot be computed when the ground
ring is not a field. This might be easily fixable or not depending on how
smart our dual basis methods are; either way, fix it.
- The Witt symmetric functions form another basis of Symm. Implement them.
The current file has the first goal achieved, but it uses some sly hacks.
Can anyone tell me which of them are bad before I spread them into other
functions (particularly for the second goal)?
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14775#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
