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Abstract: The Bernstein-Sato polynomial or global b-function is an importantinvariant in singularity theory, which can be computed using symbolic methodsin the theory of D-modules. After surveying algorithms for computing the globalb-function, we develop a new method to compute the local b-function for asingle polynomial. We then develop algorithms that compute generalizedBernstein-Sato polynomials of Budur-Mustata-Saito and Shibuta for an arbitrarypolynomial ideal. These lead to computations of log canonical thresholds,jumping coefficients, and multiplier ideals. Our algorithm for multiplierideals simplifies that of Shibuta and shares a common subroutine with our localb-function algorithm. The algorithms we present have been implemented in theD-modules package of the computer algebra system Macaulay2.



Author: Christine Berkesch, Anton Leykin

Source: https://arxiv.org/







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