Dear Prof. Stein,
Gregory forwarded the mail below to me. (Many thanks!) I would like to draw
your attention to the fact, that, together with Ralf Hemmecke I am developing a
package which is related to MuPAD-Combinat. (written in Aldor, compatible with
Axiom) More precisely, it implements "truly", i.e., extremely close to the
mathematical theory, Joyal's "combinatorial species".
This week Ralf has finished the algorithms for the computation of
cycleindexseries of compositions. For example, to generate and enumerate all
binary forests, you can say
B(L: LabelType): CS L == Plus(SingletonSpecies;, Times(B,B))(L) add;
F(L: LabelType): CS L == Compose(SetSpecies, B)(L) add;
(I'm not cheating, that's all)
After this definition
generatingSeries$F gives the (exponential) generating series for
labelled binary forests
isomorphismTypeSeries$F gives the (ordinary) generating series for
unlabelled binary forests
cycleIndexSeries$F gives the cycle index series for binary forests
structures([a,b,c,d)$F produces all binary forests with vertices
labelled a,b,c,d
isomorphismTypes([1,1,2)$F produces all binary forests with vertices
labelled 1,1,2, *not* repeating isomorphic forests
Personally, I have also written a small package that deals with shapes, i.e.,
polyominoes, tableaux, etc., but it is in a *very* early stage of
development. In fact, it is rather experimental, but I think that the ideas are
quite OK. (Well, at least Robinson Schensted Knuth and Jeu de Taquin are
already there...)
Support for combinatorics in Axiom is not so bad. For example, Polya theory is
there. However, it will very likely improve a lot towards the end of this year,
since there will be a Workshop on symmetric functions in June...
I think it would be a shame to redevelop the same things again. If you are
interested in joining us, you are very welcome. Maybe one of you could even
attend the Workshop (June 14 - June 16 ?
Martin
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