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Re: [Axiom-math] Simplification rules


From: Bertfried Fauser
Subject: Re: [Axiom-math] Simplification rules
Date: Thu, 10 Aug 2006 20:01:58 +0200 (CEST)

On 10 Aug 2006, Martin Rubey wrote:

Hi Martin,

> PS: if you are going to do more serious stuff with symmetric functions, please
> contact me once more. I'd expect that it would be wise to have an appropriate
> domain. Maybe something like that does already exist...

I am currently working on my SchurFkt package (for maple). I would be
_very_ interested to transfere this package into AXIOM. However, I seem to
need some help, since I do not find all teh domains etc needed. A good
point would be to look first at MupadCombinat, since they have good data
structures.
I need compositions, partitions, multiset form of partitons, rimhook
representation of partitions, and Yound tableaux. I know that AXIOM has
some symmetric functiion abilities, but what is written in teh book and
what I found in several spad algebra files is rather poor, eg no Murnaghan
Nakayama rule implemented, no Littlewood Richardson implemented.

I am on the way to implement an alternative way to compute the Littewood
Richardsons using a Hopf algebra algorithm which might be faster than the
recursive addition of boxed (hope so, no prove yet). For that reason I
would need a domain s-poly which can distinguish teh main basies for
symmetric functions (p,s,h,m,e,f) since algorithms need to know the
representation.

With rafal Ablamowicz, we were working on some Groebern issues, which also
might habe implications for symmetric function and invariant theory.

I am not sure how much time I hve next two month, but I am continually
testing what AXIOM can do for me and what I can do for AXIOM. Would you be
interested in a symmetric function category in AXIOM?

ciao
BF.

% PD Dr Bertfried Fauser
%     Institution: Max Planck Institute for Math, Leipzig 
<http://www.mis.mpg.de>
%   Privat Docent: University of Konstanz, Phys Dept 
<http://www.uni-konstanz.de>
%  contact|->URL : http://clifford.physik.uni-konstanz.de/~fauser/
%          Phone : Leipzig +49 341 9959 735  Konstanz +49 7531 693491





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