| #### D.5.9.10 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[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)

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