Project Details
Projekt
Fundamental Algorithms in Singular
Applicants
Professor Dr. Wolfram Decker; Professor Dr. Gerhard Pfister; Professor Dr. Mathias Schulze
Subject Area
Mathematics
Term
from 2010 to 2017
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 171584313
The overall goal of the DFG priority programme SPP 1489 is to push forward and combine computer algebra methods from different areas of mathematics, and to apply the resulting algorithms to central problems of theoretical and practical interest. To achieve this goal, the programme aims at creating a free and open source platform for linking computer algebra systems specializing in the areas covered by the programme. First and foremost, however, the individual systems have to be extended in view of the needs of the participating researchers. Our proposal aims at doing this for the system Singular which, as we believe, will be a key player in this context. Our goal is to improve the performance of the most fundamental algorithms for polynomial computations, but also to redesign some of the algorithms for applications in areas such as arithmetic geometry and non-commutative algebra. At the same time, we have a number of advanced computational tools in mind. These include the combination of computational methods in algebraic and convex geometry, with potential applications in toric and tropical geometry, and the computation of cohomology, with potential applications to Deligne–Lusztig varieties and monodromy. Another goal is to link symbolic and numerical algorithms, with particular emphasis on new algorithms for primary decomposition.
DFG Programme
Priority Programmes
