Hi Florent,
Maybe you could give Victor some pointers to what Éric Laugerotte had
implemented in MuPAD-Combinat.
Cheers,
Nicolas
On Thu, Oct 28, 2010 at 11:41:34PM +0200, Florent hivert wrote:
> On Thu, Oct 28, 2010 at 09:05:39AM -0700, VictorMiller wrote:
> > Florent, Thanks for pointing that out. There are a few semirings
> > which I'd like to see in there:
> >
> > 1) Boolean semiring: where '+' is 'or' and '*' is and
>
> +1 at least to this one: if you look at
>
> http://combinat.sagemath.org/hgwebdir.cgi/patches/file/3b4696e639e0/finite_semigroup-nt.patch#l1
>
> You can see that I fakely implemented some kinds of matrices monoid on it:
>
> class BooleanSubMatrices(UniqueRepresentation, Parent):
>
> > 2) Tropical semiring: if R is an ordered abelian group then there is a
> > semiring whose elements are R union {Infinity}, and '+' is min, '*' is
> > plus
> > 3) Noncommutative polynomials and power series: if X is a finite set,
> > and M is the free monoid on X (which is already in sage):
> >
> > If R is a semiring, then noncommutative polynomials (usually written
> > as R<X>) is the semiring of maps from M --> R with finite support,
> > and noncommutative power series are maps from M-->R with the obvious
> > + and multiplication. There is also a subcategory of semirings called
> > "starred" semirings (J. H. Conway has a monograph on these), in which
> > there is an ideal of R with an additional operation called '*' only
> > defined on elements of that ideal (I won't bother to give to the
> > axioms). This also extends in standard ways to power series.
>
> +1 again ! I know that all of these is closely related to automaton theory and
> I'm trying to push forward to get several people from
> Rouen/Marne-la-Vallée/Paris 7 in touch to have some implementation of it. I'm
> not very successful right now.
>
> By the way I'm ccing sage-combinat-devel since there may be some interrested
> people there.
>
> Cheers,
>
> Florent
>
> --
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Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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