Singular

LIB "numerDecom.lib";
ring r=0,(x,y,z),dp;
poly f1=(x2+y2+z2-6)*(x-y)*(x-1);
poly f2=(x2+y2+z2-6)*(x-z)*(y-2);
poly f3=(x2+y2+z2-6)*(x-y)*(x-z)*(z-3);
ideal I=f1,f2,f3;
list W=NumIrrDecom(I);
==>
Dimension
0
Number of Components
1
Dimension
1
Number of Components
3
Dimension
2
Number of Components
1
def A(0)=W[1];
// corresponding 0-dimensional components
setring A(0);
w(1);
// corresponding 0-dimensional irreducible component
==> 0-Witness point set (one point)
def A(1)=W[2];
// corresponding 1-dimensional components
setring A(1);
w(1);
// corresponding 1-dimensional irreducible component
==> 1-Witness point set (one point)
w(2);
// corresponding 1-dimensional irreducible component
==> 1-Witness point set (one point)
w(3);
// corresponding 1-dimensional irreducible component
==> 1-Witness point set (one point)
def A(2)=W[3];
// corresponding 2-dimensional components
setring A(2);
w(1);
// corresponding 2-dimensional irreducible component
==> 1-Witness point set (two points)