# Singular          #### D.5.2.10 NumIrrDecom

Procedure from library `numerDecom.lib` (see numerDecom_lib).

Return:
w(1),..., w(t) lists of irreducible witness point sets of irreducible components of V(J)

Example:
 ```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; // corresponding 0-dimensional components setring A(0); w(1); // corresponding 0-dimensional irreducible component ==> 0-Witness point set (one point) def A(1)=W; // 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; // corresponding 2-dimensional components setring A(2); w(1); // corresponding 2-dimensional irreducible component ==> 1-Witness point set (two points) ```

### Misc 