On Dec 17, 2007 5:26 PM, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> poly_reduced_grobner also seems very slow (I didn't wait 20 minutes this
> time...) in other trivial cases:
>
> poly_reduced_grobner([x=1,y=2],[x,y])
This is not supposed to work since the arguments are not polynomials,
poly_reduced_grobner([x-1, y-2], [x,y]);
works.
> And it seems not to understand constant expressions:
>
> eqs: [ sqrt(2)*y^2 + 2*x^2 - 1, 2*y^2 + sqrt(2)*x^2 - 1 ]
>
> fails though
>
> poly_reduced_grobner( eqs, [x,y,sqrt(2)])
>
> is fine (!!). Same if you substitute %e for sqrt(2).
>
> Is that the way it is supposed to work?
I think this should work without sqrt(2) in the variable list. This works:
(%i31) eqs: [ sqrt(2)*y^2 + x^2/2 - 1, 2*y^2 + a*x^2 - 1 ];
(%o31) [sqrt(2)*y^2+x^2/2-1,2*y^2+a*x^2-1]
(%i32) poly_grobner(eqs, [x,y]);
(%o32) [sqrt(2)*y^2+x^2/2-1,2*y^2+a*x^2-1,((4*sqrt(2)*a-4)*y^2)/2+(2-4*a)/2]
If poly_coefficient_ring is set to expression_ring (the default) the
coefficients can be any maxima expression. Too bad, I thought that
grobner didn't have that many bugs. I guess it's better not to use it
then.
--
Andrej