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- W2095647738 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 infor- mation about singularities, for use in algebraic geometry. The ba- sic algorithms in Singular are several variants of a general stan- dard 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 polyno- mials and a factorizing Grobner basis algorithm. For a complete description of Singular see (Si)." @default.
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- W2095647738 date "1996-01-01" @default.
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- W2095647738 title "Algorithms in Singular" @default.
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