Hi again, in the meantime I made some progress on my problem:
I use FreeMonoid to generate the set of finite words, I use FormalSums over the integers to get the linear combinations and I wrote a simple method to multiply two such formal sums (should this go into the class of FormalSums?). The problem I am left with is that I can not just define matrices with entries such formal sums, as SAGE can not find a ring containing them (this should be the ring of formal sums I guess). Is there any way to generate this ring or to tell SAGE how to handle/ generate those matrices? (I would prefer this in order to avoid writing my own methods to define and handle those matrices.) Any ideas? Best M. On Sep 28, 7:35 pm, mhs <[email protected]> wrote: > Hi sage-support readers, > > I would like to know if there is any way to construct special matrices > as follows: > > Start with a FreeMonoid on n generators a,b,c,.... > Now (like in the case of a group ring) form linear combinations with > NON-NEGATIVE integer coeffs of elements of this FreeMonoid, an example > of such an element would be > 5*aa+2*ababba+ba > (Is there a name for this algebraic structure?) > > What I would like to define in SAGE is the space of matrices with > entries in those symbolic linear combinations, where the usual > arithmetic operations for matrices like sum, product etc. are working. > Is there any SAGE class which is close to doing this? > If not (i.e. if I have to implement this algebraic construct), what > base objects/classes should I use? > > Is it possible to define a class of matrices over algebraic structures > which are not a ring (as in the case above)? > > Looking forward to any clues. Thanks. > M. -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
