//SINGULAR ExampleA.8.12



LIB"random.lib";
int r = 5;
ring R = 0,x(0..r),dp;

ring S = 0,(s,t),dp;
ideal I = maxideal(r); //s^r, s^(r-1)*t,..., s*t^(r-1), t^r
ideal zero;
map phi = R,I;         //R --> S, x(i) --> s^(r-i)*t^i

setring R;
ideal I = preimage(S,phi,zero); //kernel of map phi R --> S
I = std(I);            //ideal of rational normal curve C
dim(I);                //dimension of affine cone over C

degree(I); 

ideal L = sparsepoly(1,1,0,10); //a general linear form
                       //?sparsepoly; explains the syntax
ideal CL = std(I+L+(x(0)-1)); //ideal of intersection of C 
                       //with L=0
                       //in affine chart x(0)=1         
vdim(CL);              //number of intersection points is 5

LIB"primdec.lib";
vdim(std(radical(CL)));