Combinatorics in SAGE

[Nicolas M. Thiery]

Dear Mike,

while making it a bit more Pythonic where it can be. For example, I
sage: Permutation([3,4,1,5,2]).cycle_type().hook_lengths()
[[4, 3, 1], [2, 1]]

That's good. We are also moving in this direction; MuPAD has always
been object oriented, but lacked so far a short syntax for method
calls. You had to write object::dom::method(object), which is at best
clumsy. Thanksfully, MuPAD is rather flexible and I could tweak the

t := tableaux([[4,5],[1,2,3]])

+---+---+
| 4 | 5 |
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+

t::shape()

[3, 2]

There is an issue left. We decided not to type some basic objects like
partitions or permutations; so you can't use object oriented syntax on
them, like in t::shape()::hook_lengths(). This has some advantages
(see our design article in SLC 2004) but whether this was a good or
bad design decision is still an open question. I'll be interested to
see how things feel if one goes the over way.

As a first goal, I just wanted to be able to do all the examples in
http://mupad-combinat.sourceforge.net/doc/en/combinat/index.html from
within SAGE. I'd say I'm not too far from being there. The biggest
things I have left is the code for trees, integer vectors/matrices,
and the stuff with the Littlewood-Richardson coefficients.

Do you have something for species / decomposable classes? This really
is the underlying engine that you want to have, in order to later get
for free the zillion combinatorial classes that can be defined
recursively, including of course all sorts of trees. You probably want
to check out the species implementation that Martin Rubey and Ralf
Hemecke are currently working on in aldor.

I'd like to go, but I don't think that that will be possible due to
costs. It's too bad that it isn't a month later since I'm planning
to be in Austria around then. But, I'd be happy to listen /
contribute to the discussion once classes finish for the semester,
and I have a bit more time.

Out of curiosity, where are you physically?

P.S. Thanks for all the great work in mupad-combinat!

You are very welcome!

Best regards,
Nicolas

PS: please forward this e-mail to sage-devel, as I guess it will again
be rejected since I am not (yet?) a subscriber.

[Ralf Hemmecke]

Thank you, Nicolas, for including Aldor-Combinat in your mail and
notifying us.

Hello Mike,

I'd like to go, but I don't think that that will be possible due to
costs.

It seems that you mean the Axiom Workshop, right?

It's too bad that it isn't a month later since I'm planning

to be in Austria around then.

Where exactly will you go? What about a private meeting?

Ralf

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