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The Gröbner Cover pp 15–40Cite as

Constructible Sets

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Part of the book series: Algorithms and Computation in Mathematics ((AACIM,volume 27))

Abstract

Constructible sets and particularly locally closed sets are central in describing subsets of the parameter space for which a parametric polynomial system has the same type of solution. Moreover, canonical forms of these subsets are needed to obtain nice algorithms for dealing with parametric ideals.

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References

  1. J. Allouche, Note on the constructible sets of a topological space, in: Papers on general topology and applications (Gorham, ME, 1995), 1–10, vol. 806, Annals of New York Academy of Sciences, 1996, pp. 1–10.

    Google Scholar 

  2. J. M. Brunat, A. Montes, Computing the canonical representation of constructible sets, International Journal of Mathematics in Computer Science 10 (2016) 165–178.

    MathSciNet  MATH  Google Scholar 

  3. C. Chen, F. Lemaire, L. Li, M. M. Maza, W. Pan, Y. Xie, The ConstructibleSetTools and ParametricSystemTools modules of the RegularChains library in Maple, in: Proceedings of ICCSA’2008, IEEE Computer Society, 2008, pp. 342–352.

    Google Scholar 

  4. C. Chen, L. Li, M. Moreno-Maza, W. Pan, Y. Xie, On the representation of constructible sets, in: Proceedings of Milestones in Computer Algebra 2008, Trinidad and Tobago, 2008, pp. 103–108.

    Google Scholar 

  5. P. Gianni, B. Trager, G. Zacharias, Gröbner bases and primary decomposition of polynomial ideals, Journal of Symbolic Computation 6 (1988) 149–167.

    Article  MathSciNet  Google Scholar 

  6. D. Kapur, Y. Sun, D. Wang, A new algorithm for computing comprehensive Gröbner systems, in: Proceedings of ISSAC’2010, ACM Press, New York, 2010, pp. 29–36.

    MATH  Google Scholar 

  7. G. Kemper, Preprint: Morphisms and constructible sets: Making two theorems of Chevalley constructive (2007).

    Google Scholar 

  8. A. Leykin, Constructibility of the set of polynomials with a fixed Bernstein-Sato polynomial: an algorithmic approach, Journal of Symbolic Computation 32(6) (2001) 663–675.

    Article  MathSciNet  Google Scholar 

  9. A. Montes, H. Schönemann, Singular “grobcov.lib” library D.2.4, http://www.singular.uni-kl.de, Computer Algebra System for polynomial computations. Center for Computer Algebra, University of Kaiserslautern, free software under the GNU General Public Licence (2017).

  10. A. Montes, M. Wibmer, Gröbner bases for polynomial systems with parameters, Journal of Symbolic Computation 45 (2010) 1391–1425.

    Article  MathSciNet  Google Scholar 

  11. J. O’Halloran, M. Schilmoeller, Gröbner bases for constructible sets, Communications in Algebra 30:11 (2002) 5479–5483.

    Article  MathSciNet  Google Scholar 

  12. M. Wibmer, Gröbner bases for families of affine or projective schemes, Journal of Symbolic Computation 42 (2007) 803–834.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Antonio Montes

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  1. Antonio Montes
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Montes, A. (2018). Constructible Sets. In: The Gröbner Cover . Algorithms and Computation in Mathematics, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-030-03904-2_2

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