[GAP Forum] How to compute a simplified Groebner basis

[Dmitrii Pasechnik]

Dear Jason, 
there is  ReducedGroebnerBasis command, to compute the reduced GB.
(at least it is in the current version on GAP, 4.4.12.)
As expected, it computes the right thing:

gap> ReducedGroebnerBasis( I, ord );                                  
[ y^3-1/2, x ]

HTH,
Dmitrii

On Thu, Aug 13, 2009 at 03:00:23PM +0800, Jason wrote:
> Hello, 
> I am a first time user in GAP, if the following question is dummy,
> please execute me:
> 
> I tried to use Buchberger's Algorithm to compute a Groebner basis for an
> ideal of a polynomial ring in rational field, here is my GAP script:
> 
> F := Rationals;
> R := PolynomialRing( F, [ "x", "y", "z" ]);
> x := IndeterminatesOfPolynomialRing(R)[1];
> y := IndeterminatesOfPolynomialRing(R)[2];
> z := IndeterminatesOfPolynomialRing(R)[3];
> I := Ideal (R, [x^2+2*x*y^2, x*y + 2*y^3 - 1]);
> ord := MonomialLexOrdering(x,y,z);
> 
> GroebnerBasis( I, ord );
> 
> but the result is always this:
> 
> [ 2*x*y^2+x^2, 2*y^3+x*y-1, -x, -4*y^4+2*y, 2*y^3-1 ]
> 
> Obviously, the fourth can be completely divided by the last basis, the
> first and second can be completely divided by the third basis. The
> expected result should be like this:
> 
>  [ -x, 2*y^3-1 ]
> 
> So my question is how to get the simplified Groebner basis in GAP ?
> 
> Here is my GAP info: 
> GAP4, Version: 4.4.10 of 02-Oct-2007,
> i486-pc-linux-gnu-i486-linux-gnu-gcc
> 
> 
> regards,
> jason
> 
> 
> 
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