the coefficients of the leading terms of the generators of a reduced Groebner basis should be equal to one (1) as far as I know. Now consider the following code:
> ring r=0,(x,y),lp;
> ideal i=x4+x2+xy3+2,x2+y2-1;
> ideal g=std(i);
Here the leading terms have the coefficients 2 and 16. How comes? What am I missing?