Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Algorithms in Singular
Authors: Hans Schonemann
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Abstract
Some algorithms for singularity theory and algebraic geometry The use of Grobner basis computations for treating systems of polynomial equations has become an important tool in many areas. This paper introduces of the concept of standard bases (a generalization of Grobner bases) and the application to some problems from algebraic geometry. The examples are presented as SINGULAR commands. A general introduction to Grobner bases can be found in the textbook [CLO], an introduction to syzygies in [E] and [St1]. SINGULAR is a computer algebra system for computing information about singularities, for use in algebraic geometry. The basic algorithms in SINGULAR are several variants of a general standard basis algorithm for general monomial orderings (see [GG]). This includes wellorderings (Buchberger algorithm ([B1], [B2])) and tangent cone orderings (Mora algorithm ([M1], [MPT])) as special cases: It is able to work with non-homogeneous and homogeneous input and also to compute in the localization of the polynomial ring in 0. Recent versions include algorithms to factorize polynomials and a factorizing Grobner basis algorithm. For a complete description of SINGULAR see [Si].Hannes Schonemann,
Department of Mathematics,
University of Kaiserslautern
Germany
e-mail:
Department of Mathematics,
University of Kaiserslautern
Germany
e-mail:
Fulltext
– 0.23 Mb
Contents
- Some Features of CoCoA 3
- Algorithms in Singular
- Replicable functions: a computational approach
- Rewrite Rules and Simplification of Matrix Expressions
- An Implementation in C of an Algorithm for Construction of Finitely Presented Lie Superalgebrasz
- Constructing the Grobner basis using Anick's resolution in the noncommutative algebras
