research-article

On efficient algorithms for computing parametric local cohomology classes associated with semi-quasihomogeneous singularities and standard bases

Authors:

Katsusuke Nabeshima,

Shinichi TajimaAuthors Info & Claims

ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation

Pages 351 - 358

https://doi.org/10.1145/2608628.2608639

Published: 23 July 2014 Publication History

Abstract

A new algorithm is given for computing parametric local cohomology classes associated with semi-quasihomogeneous singularities. The essential point of the proposed algorithm involves Poincaré polynomials and weighted degrees. The proposed algorithm gives a suitable decomposition of the parameter space depending on the structure of the parametric local cohomology classes. As an application, an algorithm for computing parametric standard bases of zero-dimensional ideals, is given. These algorithms work for non-parametric cases, too.

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Digital Library

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K. Nabeshima, Y. Nakamura and S. Tajima, An algorithm to compute parametric standard bases using algebraic local cohomology for zero-dimensional ideals (Extended abstract), Proc. the Joint Conference of ASCM 2009 and MACIS 2009, COE Lecture Notes 22, pp. 123--126, Kyushu Univ. (2009).

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Cited By

Nabeshima KTajima S(2022)CSSg method for several genericities of parametric systemsJapan Journal of Industrial and Applied Mathematics10.1007/s13160-022-00520-340:1(315-337)Online publication date: 14-Jul-2022
https://doi.org/10.1007/s13160-022-00520-3
Nabeshima KTajima S(2021)A new algorithm for computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor idealsJournal of Symbolic Computation10.1016/j.jsc.2021.03.003Online publication date: Mar-2021
https://doi.org/10.1016/j.jsc.2021.03.003
Nabeshima K(2020)Computing Parametric Standard Bases for Semi-weighted Homogeneous Isolated Hypersurface SingularitiesComputer Algebra in Scientific Computing10.1007/978-3-030-60026-6_26(447-460)Online publication date: 2-Oct-2020
https://doi.org/10.1007/978-3-030-60026-6_26
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Index Terms

On efficient algorithms for computing parametric local cohomology classes associated with semi-quasihomogeneous singularities and standard bases
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms

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cover image ACM Other conferences

ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation

July 2014

444 pages

ISBN:9781450325011

DOI:10.1145/2608628

Editor:
Katsusuke Nabeshima
The University of Tokushima, Japan
,
General Chairs:
Kosaku Nagasaka
Kobe University, Japan
,
Franz Winkler
RISC, University Linz, Austria
,
Program Chair:
Agnes Szanto
North Carolina State University

Copyright © 2014 ACM.

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Publication History

Published: 23 July 2014

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Japan Society for the Promotion of Science

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ISSAC '14

ISSAC '14: International Symposium on Symbolic and Algebraic Computation

July 23 - 25, 2014

Kobe, Japan

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ISSAC '14 Paper Acceptance Rate 51 of 96 submissions, 53%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Nabeshima KTajima S(2022)CSSg method for several genericities of parametric systemsJapan Journal of Industrial and Applied Mathematics10.1007/s13160-022-00520-340:1(315-337)Online publication date: 14-Jul-2022
https://doi.org/10.1007/s13160-022-00520-3
Nabeshima KTajima S(2021)A new algorithm for computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor idealsJournal of Symbolic Computation10.1016/j.jsc.2021.03.003Online publication date: Mar-2021
https://doi.org/10.1016/j.jsc.2021.03.003
Nabeshima K(2020)Computing Parametric Standard Bases for Semi-weighted Homogeneous Isolated Hypersurface SingularitiesComputer Algebra in Scientific Computing10.1007/978-3-030-60026-6_26(447-460)Online publication date: 2-Oct-2020
https://doi.org/10.1007/978-3-030-60026-6_26
Nabeshima KTajima S(2020)Generalized Integral Dependence RelationsMathematical Aspects of Computer and Information Sciences10.1007/978-3-030-43120-4_6(48-63)Online publication date: 18-Mar-2020
https://doi.org/10.1007/978-3-030-43120-4_6
Nabeshima KTajima S(2016)Computing μ ∗-Sequences of Hypersurface Isolated Singularities via Parametric Local Cohomology SystemsActa Mathematica Vietnamica10.1007/s40306-016-0198-442:2(279-288)Online publication date: 19-Dec-2016
https://doi.org/10.1007/s40306-016-0198-4
Nabeshima KTajima S(2016)Computing Tjurina stratifications of $$\mu $$μ-constant deformations via parametric local cohomology systemsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-016-0289-427:6(451-467)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s00200-016-0289-4
Nabeshima KTajima SRobertz DLinton SYokoyama K(2015)Computing Logarithmic Vector Fields Associated with Parametric Semi-Quasihomogeneous Hypersurface Isolated SingularitiesProceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2755996.2756641(291-298)Online publication date: 24-Jun-2015
https://dl.acm.org/doi/10.1145/2755996.2756641
Nabeshima KTajima S(2015)Solving Extended Ideal Membership Problems in Rings of Convergent Power Series via Gröbner BasesRevised Selected Papers of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences - Volume 958210.1007/978-3-319-32859-1_22(252-267)Online publication date: 11-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-32859-1_22
Nabeshima KTajima S(2015)Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard BasesProceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 930110.1007/978-3-319-24021-3_25(334-348)Online publication date: 14-Sep-2015
https://dl.acm.org/doi/10.1007/978-3-319-24021-3_25
Nabeshima KTajima S(2014)An Algorithm for Computing Tjurina Stratifications of μ-Constant Deformations by Using Local Cohomology Classes with ParametersMathematical Software – ICMS 201410.1007/978-3-662-44199-2_79(523-530)Online publication date: 2014
https://doi.org/10.1007/978-3-662-44199-2_79
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