Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

Teresa Cortadellas; Carlos D'Andrea; M. Eulalia Montoro

doi:10.1145/3373207.3404039

Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

Teresa Cortadellas
, Carlos D'Andrea
, M. Eulalia Montoro

Research output: Book chapter › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

By adapting the effective version of Quillen-Suslin Theorem given in [8], we show that if the ideal defining a rational parametrization of degree d of an algebraic surface in 3-dimensional space is radical and has D points, then a mu-basis of this parametrization can be found of degree bounded by 5 max(1, D - 1)(4)(2d + 1)(4). This bound improves those obtained recently in [4] in our setup, and it is also sensitive to the number of base points.

Original language	English
Title of host publication	Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020
Editors	A Mantzaflaris
Place of Publication	New York
Publisher	Association for Computing Machinery
Pages	107-113
Number of pages	7
ISBN (Electronic)	978-1-4503-7100-1
DOIs	https://doi.org/10.1145/3373207.3404039
Publication status	Published - 2020
Externally published	Yes
Event	45th International Symposium on Symbolic and Algebraic Computation - Duration: 20 Jul 2020 → 23 Jul 2020

Conference

Conference	45th International Symposium on Symbolic and Algebraic Computation
Period	20/07/20 → 23/07/20

Keywords

Quillen-Suslin Theorem
Effective bounds
Mu-bases
Parametrization
Syzygies

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10.1145/3373207.3404039

Cite this

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title = "Bounds for Degrees of Minimal μ-bases of Parametric Surfaces",

abstract = "By adapting the effective version of Quillen-Suslin Theorem given in [8], we show that if the ideal defining a rational parametrization of degree d of an algebraic surface in 3-dimensional space is radical and has D points, then a mu-basis of this parametrization can be found of degree bounded by 5 max(1, D - 1)(4)(2d + 1)(4). This bound improves those obtained recently in [4] in our setup, and it is also sensitive to the number of base points.",

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note = "45th International Symposium on Symbolic and Algebraic Computation ; Conference date: 20-07-2020 Through 23-07-2020",

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Cortadellas, T, D'Andrea, C & Eulalia Montoro, M 2020, Bounds for Degrees of Minimal μ-bases of Parametric Surfaces. in A Mantzaflaris (ed.), Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020. Association for Computing Machinery, New York, pp. 107-113, 45th International Symposium on Symbolic and Algebraic Computation, 20/07/20. https://doi.org/10.1145/3373207.3404039

Bounds for Degrees of Minimal μ-bases of Parametric Surfaces. / Cortadellas, Teresa; D'Andrea, Carlos; Eulalia Montoro, M.
Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020. ed. / A Mantzaflaris. New York: Association for Computing Machinery, 2020. p. 107-113.

Research output: Book chapter › Conference contribution › peer-review

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AB - By adapting the effective version of Quillen-Suslin Theorem given in [8], we show that if the ideal defining a rational parametrization of degree d of an algebraic surface in 3-dimensional space is radical and has D points, then a mu-basis of this parametrization can be found of degree bounded by 5 max(1, D - 1)(4)(2d + 1)(4). This bound improves those obtained recently in [4] in our setup, and it is also sensitive to the number of base points.

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KW - Syzygies

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ER -

Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

Abstract

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Keywords

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