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Sparse differential resultant for laurent differential polynomials

Authors:

Wei Li,

Chun-Ming Yuan,

Xiao-Shan GaoAuthors Info & Claims

ACM Communications in Computer Algebra, Volume 46, Issue 3/4

Pages 110 - 111

https://doi.org/10.1145/2429135.2429158

Published: 15 January 2013 Publication History

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Abstract

In this poster, we first introduce the concept of Laurent differentially essential systems and give a criterion for them in terms of their supports. Then the sparse differential resultant for a Laurent differentially essential system is defined and its basic properties are given. In particular, order and degree bounds for the sparse differential resultant, as well as a BKK-type degree bound for the differential resultant, are given. Based on these bounds, an algorithm to compute the sparse differential resultant is proposed, which is single exponential.

Reference

[1]

Wei Li, Chun-Ming Yuan, Xiao-Shan Gao. Sparse Differential Resultant for Laurent Differential Polynomials. ArXiv:1111.1084v2, p. 1--62, Dec. 2011

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Zhang ZYuan CGao X(2014)Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential PolynomialsComputer Mathematics10.1007/978-3-662-43799-5_32(479-503)Online publication date: 1-Oct-2014
https://doi.org/10.1007/978-3-662-43799-5_32
Rueda S(2013)Linear sparse differential resultant formulasLinear Algebra and its Applications10.1016/j.laa.2013.01.016438:11(4296-4321)Online publication date: Jun-2013
https://doi.org/10.1016/j.laa.2013.01.016
Li WGao X(2012)Chow form for projective differential varietyJournal of Algebra10.1016/j.jalgebra.2012.07.047370(344-360)Online publication date: Nov-2012
https://doi.org/10.1016/j.jalgebra.2012.07.047

Index Terms

Sparse differential resultant for laurent differential polynomials
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on polynomials

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Published In

cover image ACM Communications in Computer Algebra

ACM Communications in Computer Algebra Volume 46, Issue 3/4

September/December 2012

111 pages

ISSN:1932-2232

EISSN:1932-2240

DOI:10.1145/2429135

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Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 15 January 2013

Published in SIGSAM-CCA Volume 46, Issue 3/4

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Cited By

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Zhang ZYuan CGao X(2014)Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential PolynomialsComputer Mathematics10.1007/978-3-662-43799-5_32(479-503)Online publication date: 1-Oct-2014
https://doi.org/10.1007/978-3-662-43799-5_32
Rueda S(2013)Linear sparse differential resultant formulasLinear Algebra and its Applications10.1016/j.laa.2013.01.016438:11(4296-4321)Online publication date: Jun-2013
https://doi.org/10.1016/j.laa.2013.01.016
Li WGao X(2012)Chow form for projective differential varietyJournal of Algebra10.1016/j.jalgebra.2012.07.047370(344-360)Online publication date: Nov-2012
https://doi.org/10.1016/j.jalgebra.2012.07.047

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