Singular

Dear Mariana,
[quote]> I want to define a noncommutative ring in Plural.
> When the noncommutative relatition is ab= kba + f
> where k is a scalar and f is some polynomial I have no problems.
> But then I have relations like aba + ab^2 +....
[/quote]
PLURAL supports only relations of the kind Y*X = k X*Y + F(X,Y,...); where k is a nonzero constant and F is a polynomial whose leading monomial with respect to a given ordering is strictly smaller than XY.
Please consult
http://www.singular.uni-kl.de/Manual/3-0-0/sing_344.htm
and
http://www.singular.uni-kl.de/Manual/3-0-0/sing_404.htm

We [u]do not[/u] provide you with the possibility to build a quotient of a free noncommutative algebra subject to any ideal.

[quote]> and I cannot find a way to do it, because if I use [color=green]ncalgebra(C,D);[/color]
> the only way I found, was to do it as ab= ba + (ab - ba), and then taking a quotient by my relation.[/quote]

This is wrong - the leading monomial of the "rest" should be strictly smaller than ba.

[quote]> The problem basically is, is that I cannot find a way of using system"PLURAL" when I don't want to impose any conditions between ab and ba.[/quote]

PLURAL is not suitable for this situation. You can try either Felix (J.Apel) or Grobner (A.Cohen, D.Gijsbers) or OPAL (E.Green, B.Keller) or NCalgebra...
[quote]> Any ideas???[/quote]

If you have some relations which are close to that we use in PLURAL, please let us know - there are many tricks how to turn "bad" relations into possibly "good".

Best regards,

I want to define a noncommutative ring in Plural.
When the noncommutative relatition is ab= kba + f
where k is a scalar and f is some polynomial I have no problems.
But then I have relations like aba + ab^2 +....
and I cannot find a way to do it,because if I use system("PLURAL", C, D)
the only way I found, was to do it as ab= ba + (ab - ba), and then taking a quotient by my relation.
The problem basically is, is that I cannot find a way of using system"PLURAL" when I don't want to impose any conditions between ab and ba.
Any ideas???

email: pereira@math.umass.edu
Posted in old Singular Forum on: 2004-04-26 22:32:01+02