Monodromy Algorithms in Singular

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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.