//SINGULAR Example 1.4.9


ring S = 0,(x,y,z),dp;          
ideal I = y*(x-1), z*(x-1);
ideal J = std(I);   //compute a standard basis J of I in S 
J;                  //J = <z(x-1),y(x-1)>

dim(J);             //the (global) dimension of V(I) is 2

reduce(y,J);        //y is not in I 
                    //(result is 0 iff y is in I)

ring R = 0,(x,y,z),ds;          
ideal I = fetch(S,I);//fetch I from S to basering
ideal J = std(I);  //compute a standard basis J of I in R
J;

dim(J);

reduce(y,J);

map trans = S, x+1,y,z;  //replace x by x+1 and leave 
                         //y,z fixed, i.e. translate (0,0,0)
                         //to (1,0,0)
ideal I1 = trans(I);
I1;

dim(std(I1));            //dimension of V(I) at (1,0,0) is 2

setring S;               //go back to global ring S
map trans = S, x+1,y,z; 
ideal I1 = trans(I);     //translate I, as in (3)
I1;

dim(std(I1));            //(global) dimension of translated 

kill S,R;