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D.15.5.8 PPolyS
Procedure from library goettsche.lib (see goettsche_lib).
- Usage:
- PPolyS(z, n, b); z polynomial, n integer, b list of non-negative integers
- Return:
- polynomial in z with integer coefficients
- Purpose:
- computes the Poincare polynomial of the n-th symmetric power
of a variety with Betti numbers b
- Note:
- zero is returned if n<0 or b is not a list of non-negative integers
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 third symmetric power of P_2
print( PPolyS(z, 3, b) );
==> 1+z2+2z4+2z6+2z8+z10+z12
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