Mahshid Mirhashemi (Univ. Göttingen): Application of Machine Learning in Computation of Pommaret Bases


Abstract.  One of the important and noteworthy concepts for many calculations in algebraic geometry is the notion of Pommaret bases. Using these bases, some algebraic invariants such as the ideal dimension and depth, and Castelnuovo-Mumford regularity can be computed. However, finite Pommaret bases do not always exist. But due to the relationship between these bases and a property called quasi-stability, we are looking to transform ideals into quasi-stable positions. For this purpose, we may need to make several coordinate changes in the ideal. After each change, it is necessary to recalculate the modified Gröbner and Janet bases. Reducing the number of coordinate changes is crucial for us from a computational point of view (in terms of time and calculation). Therefore, in this work, while generating ideals and extracting input variables for each ideal and selecting the best variable change as the output variable,we try to predict the best coordinate change at each step with the help of machine learning methods.


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