Dear Adrien, dear Jason,
Thanks so much for taking over the implementation of combinatorial
bases for multivariate polynomials and friends! This is a major step
for Sage-Combinat, and Alain will be happy to see things finally
happen! I very much hope that this will be useful to your own
research, for otherwise you should not feel pressured for spending
much time on it.
Some words of advice, if I may. Please follow as closely as possible
the design and conventions used for NCSF. It is far from perfect, but
the overall organization results from experience accumulated over many
years. Yes, the rationale for each design choice should eventually be
documented within Sage; for the moment, there are already quite a few
things in the MuPAD-Combinat handbook (available on MuPAD-Combinat's
web site. Strongly enforcing consistency among all our (Hopf) algebras
with several bases (Sym, QSym, NCSF, Pol, ...) will make it easier to
spot whatever can be factored out. It will also help newcomers see and
understand the overall logic and mimic it for their own examples.
If you notice parts which feel clumsy (you will!), or have suggestions
for improvements, please take good notes of them. But don't implement
them right away, or only in a separate experiment. Instead, we should
discuss them and update systematically all the algebras according to
the outcome of the discussion.
Sorry Adrien: between this and Alain's guidance for the algorithmic
part, there won't be much room for personal creativity in this
project, and I understand that this will kill a good part of the
fun. In exchange, thanks to the underlying foundations, the ratio
functionality/code should be pretty high, and I hope that this will
feel rewarding. And in the long run, there are many advanced open
design issues which will require everyone's creativity!
Cheers,
Nicolas
PS: to start the discussion: we currently loosely use the name "basis"
of an abstract algebra for what really is a concrete representation of
this algebra, with elements represented by their expansion on the
given basis. Any suggestions for a better name? Maybe:
Basis -> RepresentationOnBasis
Bases -> RepresentationsOnBasis
MultiplicativeBases -> RepresentationsOnMultiplicativeBasis
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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