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Doing algebraic geometry with the RegularChains library

文献类型：会议论文

作者Alvandi, Parisa1; Chen, Changbo2; Marcus, Steffen3; Maza, Marc Moreno1; Schost, Éric1; Vrbik, Paul1
出版日期2014
会议日期August 5, 2014 - August 9, 2014
会议地点Seoul, Korea, Republic of
DOI10.1007/978-3-662-44199-2_71
页码472-479
英文摘要Traditionally, Groebner bases and cylindrical algebraic decomposition are the fundamental tools of computational algebraic geometry. Recent progress in the theory of regular chains has exhibited efficient algorithms for doing local analysis on algebraic varieties. In this note, we present the implementation of these new ideas within the module AlgebraicGeometryTools of the RegularChains library. The functionalities of this new module include the computation of the (non-trivial) limit points of the quasi-component of a regular chain. This type of calculation has several applications like computing the Zarisky closure of a constructible set as well as computing tangent cones of space curves, thus providing an alternative to the standard approaches based on Groebner bases and standard bases, respectively. From there, we have derived an algorithm which, under genericity assumptions, computes the intersection multiplicity of a zero-dimensional variety at any of its points. This algorithm relies only on the manipulations of regular chains. © 2014 Springer-Verlag.
会议录4th International Congress on Mathematical Software, ICMS 2014
语种英语
电子版国际标准刊号16113349
ISSN号03029743
源URL[http://119.78.100.138/handle/2HOD01W0/4739]  
专题自动推理与认知研究中心
作者单位1.University of Western Ontario, Canada;
2.Chongqing Institute of Green and Intelligent Technology, CAS, China;
3.College of New Jersey, Ewing, NJ, United States
推荐引用方式
GB/T 7714		 Alvandi, Parisa,Chen, Changbo,Marcus, Steffen,et al. Doing algebraic geometry with the RegularChains library[C]. 见:. Seoul, Korea, Republic of. August 5, 2014 - August 9, 2014.

入库方式： OAI收割

来源：重庆绿色智能技术研究院

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