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 Post subject: Plural ring definitionPosted: Thu Aug 11, 2005 5:32 pm
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

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 Post subject: Re: Plural ring definitionPosted: Thu Aug 11, 2005 8:46 pm

Joined: Thu Aug 11, 2005 8:03 pm
Posts: 37
Location: RWTH Aachen, Germany
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 +....

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.
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 do not 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 ncalgebra(C,D);
> the only way I found, was to do it as ab= ba + (ab - ba), and then taking a quotient by my relation.

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.

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???

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,

_________________
Viktor Levandovskyy

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