//SINGULAR ExampleA.9.5

//==================we need================================
LIB "sing.lib";                 
ring r = 0,(x,y,z),ds;          //local ring
poly f = x7+y7+(x-y)^2*x2y2+z2;

ring R = 0,(x,y,z),dp;          //affine ring
poly f = x7+y7+(x-y)^2*x2y2+z2;
//=========================================================


setring R;
ideal j = jacob(f);           //ideal of critical locus
poly h = det(jacob(j));       //det of Hessian of f
ideal nn = j,h;               //ideal of non-nodes
vdim(std(nn));

setring r;                    //go back to local ring
ideal nn = jacob(f),det(jacob(jacob(f)));
vdim(std(nn));