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 -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
