Let us now deform a given 0-dimensional ideal j by introducing a parameter t and compute over the ground field Q(t). We compute the dimension at the generic point, i.e. dim_Q(t) Q(t)[x,y]/j.
For almost all a in Q this is the same as dim_Q Q[x,y]/j0, where j_0=j_t=a
ring Rt = (0,t),(x,y),lp; Rt; ==> // characteristic : 0 ==> // 1 parameter : t ==> // minpoly : 0 ==> // number of vars : 2 ==> // block 1 : ordering lp ==> // : names x y ==> // block 2 : ordering C poly f = x5+y11+xy9+x3y9; ideal i = jacob(f); ideal j = i,i[1]*i[2]+t*x5y8; // deformed ideal, parameter t vdim(std(j)); ==> 40 ring R=0,(x,y),lp; ideal i=imap(Rt,i); int a=random(1,30000); ideal j=i,i[1]*i[2]+a*x5y8; // deformed ideal, fixed integer a vdim(std(j)); ==> 40