Year of publication
- Algorithms in Singular (1999)
- MRC - A System for Computing Gröbner Bases in Monoid and Group Rings (1998)
- Gröbner bases and Buchberger's algorithm have been generalized to monoid and group rings. In this paper we summarize procedures from this field and present a description of their implementation in the system Mrc V 1.0.
- Description of SINGULAR: A Computer Algebra System for Singularity Theory, Algebraic Geometry and Commutative Algebra (1999)
- Introducing Reduction to Polycyclic Group Rings - A Comparison of Methods (1996)
- t is well-known that for the integral group ring of a polycyclic group several decision problems are decidable. In this paper a technique to solve themembership problem for right ideals originating from Baumslag, Cannonito and Miller and studied by Sims is outlined. We want to analyze, how thesedecision methods are related to Gröbner bases. Therefore, we define effective reduction for group rings over Abelian groups, nilpotent groups and moregeneral polycyclic groups. Using these reductions we present generalizations of Buchberger's Gröbner basis method by giving an appropriate definition of"Gröbner bases" in the respective setting and by characterizing them using concepts of saturation and s-polynomials.
- Reinitialization for Level Set Methods (1998)
- In the following an introduction to the level set method will be givenso that one becomes aware of the arising problems, which lead to the needof reinitialization. The problems concerning reinitialization itself will be analysed more detailed and a solution for area loss will be proposed. This solution consists in a combination of the commonly used PDE for reinitialization and extrapolation around the zero level set. Numericalexperiments show rather satisfactory results as far as area loss and computation of curvature are concerned.