Singular Manual: PPolyH

| #### D.5.5.2 PPolyH Procedure from library `goettsche.lib` (see goettsche_lib). Usage: PPolyH(z, n, b); z polynomial, n integer, b list of non-negative integers Return: polynomial in z Purpose: computes the Poincare polynomial of the Hilbert scheme of n points on a surface with Betti numbers b Note: zero is returned if n<0 or b is not a list of non-negative integers or if there are not enough Betti numbers Example:
    LIB "goettsche.lib";
    ring r=0, (z), ls;
    // consider the projective plane P_2 with Betti numbers 1,0,1,0,1
    list b=1,0,1,0,1;
    // get the Poincare polynomial of the Hilbert scheme of 3 points on P_2
    print( PPolyH(z, 3, b) );
    ==> 1+2z2+5z4+6z6+5z8+2z10+z12

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