Monodromy Algorithms in Singular

单一单数算法

• 批准号: 171583866
• 负责人: Professor Dr. Duco van Straten
• 金额: --
• 依托单位: Arbeitsgruppe Algebraische Geometrie
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/171583866?language=en
• 关键词: Monodromy; Algorithms; Singular

The proposal fits into the DFG priority programme SPP 1489, which aims at combining Computer algebra methods from different areas of mathematics, and to apply the resulting algorithms to central problems of theoretical and practical interest. It is our aim to develop and implement algorithms to compute and analyse the mono-dromy representation for families of varieties depending on a parameter t. Rather than striving for complete generality, we propose to start with hypersurfaces and use special features like the appearance of special singularities in a fibre. The proposed algorithms combine Gröbner-basis calculations in polynomial rings and localisations, algorithms for primary decomposition, Gröbner-basis calculations in Weyl-algebras, normal-form algorithms, numerical techniques and algorithms from algorithmic group theory. It is our intention to develop these algorithms inside the Singular system.

该建议适合DFG优先计划SPP 1489，其目的是结合计算机代数方法从不同的数学领域，并将由此产生的算法的理论和实际利益的中心问题。我们的目标是开发和实现算法来计算和分析依赖于参数t的品种族的单值表示。而不是争取完整的一般性，我们建议从超曲面开始，并使用特殊的功能，如在纤维中的特殊奇点的外观。所提出的算法结合了联合收割机多项式环和局部化中的Gröbner基计算、初等分解算法、Weyl代数中的Gröbner基计算、规范型算法、数值技术和算法群论。我们打算在奇异系统中开发这些算法。