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 > > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
