### Abstract

The Bernstein-Sato polynomial (or global b-function) is an important invariant in singularity theory, which can be computed using symbolic methods in the theory of D-modules. After providing a survey of known algorithms for computing the global b-function, we develop a new method to compute the local b-function for a single polynomial. We then develop algorithms that compute generalized Bernstein-Sato polynomials of Budur-MustaÇâ-Saito and Shibuta for an arbitrary polynomial ideal. These lead to computations of log canonical thresholds, jumping coefficients, and multiplier ideals. Our algorithm for multiplier ideals simplifies that of Shibuta and shares a common subroutine with our local b-function algorithm. The algorithms we present have been implemented in the D-modules package of the computer algebra system Macaulay2.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 |

Publisher | Association for Computing Machinery (ACM) |

Pages | 99-106 |

Number of pages | 8 |

ISBN (Print) | 9781450301503 |

DOIs | |

State | Published - 2010 |

Event | 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 - Munich, Germany Duration: Jul 25 2010 → Jul 28 2010 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
---|

### Other

Other | 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 |
---|---|

Country | Germany |

City | Munich |

Period | 7/25/10 → 7/28/10 |

### Keywords

- Bernstein-Sato polynomial
- D-modules
- Jumping coefficients
- Log-canonical threshold
- Multiplier ideals
- V-filtration

## Fingerprint Dive into the research topics of 'Algorithms for Bernstein-Sato polynomials and multiplier ideals'. Together they form a unique fingerprint.

## Cite this

*Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010*(pp. 99-106). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). Association for Computing Machinery (ACM). https://doi.org/10.1145/1837934.1837958