Monodromy Algorithms in Singular

这项提议符合DFG优先方案SPP 1489，该方案旨在结合不同数学领域的计算机代数方法，并将产生的算法应用于理论和实践感兴趣的中心问题。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的变异族的单列表示。我们建议从超曲面开始，并使用特殊特征，如纤维中特殊奇点的出现，而不是争取完全的一般性。所提出的算法结合了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、范式算法、数值技术和算法群论中的算法。我们的目的是在奇异系统中开发这些算法。

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.