A.1.5 Parameters

Let us deform the ideal in Long coefficients by introducing a parameter t and compute over the ground field Q(t). We compute the dimension at the generic point, i.e., .(This gives the same result as for the deformed ideal above. Hence, the above small deformation was "generic".)

For almost all this is the same as ,where .

ring Rt = (0,t),(x,y),lp; Rt; ==> // coefficients: QQ(t) ==> // 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