> | ### D.15.11 goettsche_lib Library: goettsche.lib Purpose: Goettsche's formula for the Betti numbers of the Hilbert scheme of points on a surface, Macdonald's formula for the symmetric product Author: Oleksandr Iena, o.g.yena@gmail.com, yena@mathematik.uni-kl.de References: [1] Goettsche, Lothar, The Betti numbers of the Hilbert scheme of ponts on a smooth projective surface. Mathematische Annalen: 286, 193-208, (1990). [2] Macdonald, I. G., The Poincare polynomial of a symmetric product, Mathematical proceedings of the Cambridge Philosophical Society: 58, 563 - 568, (1962). Procedures:
> D.15.11.1 GoettscheF |  | The Goettsche's formula up to n-th degree
> D.15.11.2 PPolyH |  | Poincare Polynomial of the Hilbert scheme of n points on a surface
> D.15.11.3 BettiNumsH |  | Betti numbers of the Hilbert scheme of n points on a surface
> D.15.11.4 MacdonaldF |  | The Macdonald's formula up to n-th degree
> D.15.11.5 PPolyS |  | Poincare Polynomial of the n-th symmetric power of a variety
> D.15.11.6 BettiNumsS |  | Betti numbers of the n-th symmetric power of a variety

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