Roadmap for combinatorial species and decomposable classes

[nthiery]

This is a meta ticket for tracking improvements on `combinatorial species <http://en.wikipedia.org/wiki/Combinatorial_species>`_ and
decomposable classes.

Projects
--------

(TODO: create a ticket for each of them)

- Port over the beautiful documentation on species of Aldor-Combinat

- Support for my_species().structures() returning the decomposable
  class of all labelled structures for this species. Same thing for
  unlabelled classes

- Support for weighted enumeration, as in MuPAD-Combinat

- Support for the "Alias" feature of MuPAD-Combinat

- Support for pluging in unlabelled and labelled enumerated sets
  into a species

- Make labelled enumerated sets (i.e. enumerated sets which take a
  bunch of distinct labels as input) into species.

- Add a module sage.combinat.species.labeled (and unlabelled)
  containing objects like Atom, Prod, Union, ... to almost emulate
  the syntax of combstruct/CS/decomposableObjects, while using
  species under the scene

- Improve the user interface and error messages

- Standalone Python library containing just what is needed for simple
  species

- Generation of C code? This feature is probably not needed anymore.

- Random generation (based on counting, or Boltzman)

- Ranking/unranking

- Refactor using one class per species as in #20622?

See also the roadmap for generating series (TODO: add a link)

Related Tickets
---------------

#3665, #5512, #6630, #10227, #12648, #12649, #10931, #20622

Related Software
----------------

 - Maple: combstruct
 - MuPAD: CS and then MuPAD-Combinat's `combinat::decomposableObjects <http://mupad-combinat.sourceforge.net/doc/en/combinat/decomposableObjects.html>`_
 - Aldor/Axiom: Species in `Aldor-Combinat <http://www.risc.jku.at/people/hemmecke/AldorCombinat/>`_

See http://arxiv.org/abs/0912.2619 p. 64 for some historical and
design notes.

CC: @sagetrac-joudinet

Component: combinatorics

Keywords: species

Issue created by migration from https://trac.sagemath.org/ticket/10662

[sagetrac-joudinet]

comment:4

Hi,
This ticket is almost 2 years old. Is there any progress on using combinatorial species for random generation (based on counting or Boltzmann)?

Thanks.

Best regards,

[fchapoton]

Changed keywords from none to species