On Thu, Mar 24, 2011 at 01:39:52AM -0700, Anne Schilling wrote:
> >Zitat von Burcin Erocal<bur...@erocal.org>:
> >>Letterplace should be able to handle quotients of free algebras:
> >>
> >>http://www.singular.uni-kl.de/Manual/latest/sing_441.htm#SEC493
> >
> >Letterplace, on the one hand, is fairly general: It provides an
> >implementation of free algebras.
>
> Looking at the link, it seems this is working with monomials in
> commutative variables. But this would still apply for monoids/
> algebras where the generators do not necessarily all commute?
As mentionned by Simon, the trick is not to consider the subalgebra
generated by those monomials (for indeed it would be commutative).
Instead, the non commutative product is emulated by a combination of
commutative product and shift. Namely, the words `aab` and `cab` are
encoded as the commutative monomials a_1a_2b_3 and c_1a_2b_3. And then
the multiplication is done by shifting the indices of the latter:
aab . cab = a_1a_2b_3 * shift(c_1a_2_b_3, 3)
= a_1a_2b_3 * c_4a_5b_6
= aabcab
And now the miracle would be that this encoding would allow to somehow
reduce non commutative Gröbner basis calculations to commutative ones.
Fun. I need to learn more about that at some point.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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