Titlebook: Algorithmic Algebra and Number Theory; Selected Papers From B. Heinrich Matzat,Gert-Martin Greuel,Gerhard Hiss Conference proceedings 1999

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Hilbert Series and Degree Bounds in Invariant TheoryThe algorithm for computing a miniversal deformation of an isolated singularity using Massey products and its implementation in SINGULAR is explained. For completeness the cotangent cohomology and the obstruction calculus is described in concrete terms as well.

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Algorithms for the Computation of Free ResolutionsR. Brauer posed in his famous lectures on modern mathematics 1963 more than 40 problems, questions and conjectures about the representation theory of finite groups, cf. [.]. These questions have had a big influence on the development of the theory since then. Most of the problems may be summarized under the following central question.

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Sieving Methods for Class Group Computationfastest method known has conjectured sub-exponential running time and was proposed in [.]. . this paper we show how sieving methods developed for factoring algorithms can be used to speed up this algorithm in practice. We present numerical experiments which demonstrate the efficiency of our new stra

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Fortschritte in der inversen Galoistheorie tiber seither erreichte neue Resultate. Da inzwischen mehrere einftihrende Texte in Buchform von Matzat (1987), Serre (1992), V6lklein (1996) sowie Ishkhanov, Lure und Faddeev (1997) vorhanden sind, kann ich mich bei der Zusammenstellung der Grundlagen sehr kurz fassen. Eine ausftihrliche Darstellu