I am not sure if what I am asking is a bug. In any case, I did not find an appropriate thread where I can post my question. I hope you do not mind me posting here.
Consider the following code (giac, I ran both in giac and giacpy and got the same results):
Code : Tout sélectionner
h1:=x0-x1; h2:=x2-x3; h3:=d2*x2-y0-y1; h4:=-d2*x0-y2-y3; greduce(x0*y0+x1*y1+x2*y2+x3*y3,[h1,h2,h3,h4],[x0,x1,x2,x3,y0,y1,y2,y3]);
But the polynomial x0*y0+x1*y1+x2*y2+x3*y3 is clearly in the ideal generated by h1,h2,h3,h4:
By inspecting their corresponding vanishing sets: substitute x1 with x0, substitute x3 with x2, substitute y1 for d2*x2-y0, substitute y3 for -d2*x0-y2 in the equation x0*y0+x1*y1+x2*y2+x3*y3 will yield 0 (so the vanishing set of <h1,h2,h3,h4> is in the vanishing set of the irreducible polynomial x0*y0+x1*y1+x2*y2+x3*y3).
I was expecting that Giac returns 0 because of Groebner reduction (this is what I get with other computer algebra system).
Could someone explain whether I am doing something wrong or whether this is indeed a bug?