research-article

Algorithms for computing triangular decompositions of polynomial systems

Authors:

Marc Moreno MazaAuthors Info & Claims

ISSAC '11: Proceedings of the 36th international symposium on Symbolic and algebraic computation

Pages 83 - 90

https://doi.org/10.1145/1993886.1993904

Published: 08 June 2011 Publication History

Abstract

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a weakened notion of a polynomial GCD modulo a regular chain, which permits to greatly simplify and optimize the sub-algorithms. Extracting common work from similar expensive computations is also a key feature of our algorithms. In our experimental results the implementation of our new algorithms, realized with the RegularChains library in MAPLE, outperforms solvers with similar specifications by several orders of magnitude on sufficiently difficult problems.

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Cited By

Li XNiu W(2022)Analyzing the dual space of the saturated ideal of a regular set and the local multiplicities of its zerosMathematical Methods in the Applied Sciences10.1002/mma.815845:12(7243-7254)Online publication date: 19-May-2022
https://doi.org/10.1002/mma.8158
Chen C(2020)Chordality Preserving Incremental Triangular Decomposition and Its ImplementationMathematical Software – ICMS 202010.1007/978-3-030-52200-1_3(27-36)Online publication date: 8-Jul-2020
https://doi.org/10.1007/978-3-030-52200-1_3
Li WYuan C(2019)Elimination Theory in Differential and Difference AlgebraJournal of Systems Science and Complexity10.1007/s11424-019-8367-x32:1(287-316)Online publication date: 14-Feb-2019
https://doi.org/10.1007/s11424-019-8367-x
Show More Cited By

Index Terms

Algorithms for computing triangular decompositions of polynomial systems
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms

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cover image ACM Conferences

ISSAC '11: Proceedings of the 36th international symposium on Symbolic and algebraic computation

June 2011

372 pages

ISBN:9781450306751

DOI:10.1145/1993886

General Chair:
Éric Schost
The University of Western Ontario, Canada
,
Program Chair:
Ioannis Z. Emiris
University of Athens, Greece

Copyright © 2011 ACM.

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Published: 08 June 2011

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ISSAC '11: International Symposium on Symbolic and Algebraic Computation

June 8 - 11, 2011

California, San Jose, USA

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Li XNiu W(2022)Analyzing the dual space of the saturated ideal of a regular set and the local multiplicities of its zerosMathematical Methods in the Applied Sciences10.1002/mma.815845:12(7243-7254)Online publication date: 19-May-2022
https://doi.org/10.1002/mma.8158
Chen C(2020)Chordality Preserving Incremental Triangular Decomposition and Its ImplementationMathematical Software – ICMS 202010.1007/978-3-030-52200-1_3(27-36)Online publication date: 8-Jul-2020
https://doi.org/10.1007/978-3-030-52200-1_3
Li WYuan C(2019)Elimination Theory in Differential and Difference AlgebraJournal of Systems Science and Complexity10.1007/s11424-019-8367-x32:1(287-316)Online publication date: 14-Feb-2019
https://doi.org/10.1007/s11424-019-8367-x
Chen CMoreno Maza M(2014)An Incremental Algorithm for Computing Cylindrical Algebraic DecompositionsComputer Mathematics10.1007/978-3-662-43799-5_17(199-221)Online publication date: 1-Oct-2014
https://doi.org/10.1007/978-3-662-43799-5_17
Chen CDavenport JMoreno Maza MXia BXiao R(2013)Computing with semi-algebraic setsJournal of Symbolic Computation10.1016/j.jsc.2012.05.01352(72-96)Online publication date: 1-May-2013
https://dl.acm.org/doi/10.1016/j.jsc.2012.05.013
Strzeboński ATsigaridas Evan der Hoeven Jvan Hoeij M(2012)Univariate real root isolation in multiple extension fieldsProceedings of the 37th International Symposium on Symbolic and Algebraic Computation10.1145/2442829.2442878(343-350)Online publication date: 22-Jul-2012
https://dl.acm.org/doi/10.1145/2442829.2442878
Chen CMoreno Maza M(2012)Algorithms for computing triangular decomposition of polynomial systemsJournal of Symbolic Computation10.1016/j.jsc.2011.12.02347:6(610-642)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.1016/j.jsc.2011.12.023
Marcus SMaza MVrbik P(2012)On Fulton's algorithm for computing intersection multiplicitiesProceedings of the 14th international conference on Computer Algebra in Scientific Computing10.1007/978-3-642-32973-9_17(198-211)Online publication date: 3-Sep-2012
https://dl.acm.org/doi/10.1007/978-3-642-32973-9_17
Maza MVrbik P(2011)Inverting matrices modulo regular chainsACM Communications in Computer Algebra10.1145/2016567.201659045:1/2(129-130)Online publication date: 25-Jul-2011
https://dl.acm.org/doi/10.1145/2016567.2016590
Chen CDavenport JMoreno Maza MXia BXiao RSchost ÉEmiris I(2011)Computing with semi-algebraic sets represented by triangular decompositionProceedings of the 36th international symposium on Symbolic and algebraic computation10.1145/1993886.1993903(75-82)Online publication date: 8-Jun-2011
https://dl.acm.org/doi/10.1145/1993886.1993903
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