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21 years of SINGULAR experiments in mathematics. (English) Zbl 1101.14070
Lossen, Christoph (ed.) et al., Singularities and computer algebra. Selected papers of the conference, Kaiserslautern, Germany, October 18–20, 2004 on the occasion of Gert-Martin Greuel’s 60th birthday. Cambridge: Cambridge University Press (ISBN 0-521-68309-2/pbk). London Mathematical Society Lecture Note Series 324, 247-272 (2006).
Summary: This article gives some overview on SINGULAR, a computer algebra system for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry and singularity theory, which has been developed under the guidance of G.-M. Greuel, G. Pfister and the second author [http://www.singular.uni-kl.de]. We draw the bow from SINGULAR’s early years to its latest features. Moreover, we present some explicit calculations, focusing on applications in singularity theory.
For the entire collection see [Zbl 1086.14001].
14Q99 Computational aspects in algebraic geometry
14B05 Singularities in algebraic geometry
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
32S10 Invariants of analytic local rings