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Question: Strange result using Groebner[Basis], why?

Question:Strange result using Groebner[Basis], why?

domo 52 Maple
groebner basis
September 23 2007
0
Hi! I'm using Maple 10 on my Laptop. OS is Fedora 7. I want to compute a Groebnerbasis for the following ideal. the_ideal:=[x3, x2, x1, x0, -1274687*x0^2-890931*x1^2-1178748*x2^2-986870*x3^2+1740*y2*x0-1740*y0*x2-4104*y1*x3+4104*y3*x1-580*sqrt(3)*y3*x0+580*sqrt(3)*y0*x3+1368*sqrt(3)*y2*x1-1368*sqrt(3)*y1*x2+191878*x3*x2*sqrt(3)+12*y2^2+12*y3^2+12*y0^2+12*y1^2, -1740*y2*x0+1740*y0*x2+4104*y1*x3-4104*y3*x1-580*sqrt(3)*y3*x0+580*sqrt(3)*y0*x3+1368*sqrt(3)*y2*x1-1368*sqrt(3)*y1*x2-191878*x3*x2*sqrt(3)-6656903*x0^2-6273147*x1^2-6560964*x2^2-6369086*x3^2+12*y2^2+12*y3^2+12*y0^2+12*y1^2, 1160*sqrt(3)*y3*x0-1160*sqrt(3)*y0*x3-2736*sqrt(3)*y2*x1+2736*sqrt(3)*y1*x2-7282367*x0^2-6898611*x1^2-6898611*x2^2-7282367*x3^2+12*y0^2+12*y1^2+12*y2^2+12*y3^2, k*(x0^2+x1^2+x2^2+x3^2)-1]; The unknowns are x0,x1,x2,x3,y0,y1,y2,y3,k. No parameters. As one can see, the first four equations and the last one lead to the result that 1 is contained in the ideal. So Groebner[Basis]( the_ideal, tdeg(x0,x1,x2,x3,y0,y1,y2,y3)); should return [1]. But it returns [], and that's nonsense. [] normally stands for the result, that all values are solutions. Am I right? gbasis from Maple V returns the correct result: [1]. Does anybody know that problem? Is this a bug? Is there a mistake in my argumentation? Lg domo
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