Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

被引：0

作者：

Cortadellas, Teresa ^{[1
]}

D'Andrea, Carlos ^{[2
]}

Eulalia Montoro, M. ^{[2
]}

机构：

[1] Univ Barcelona, Fac Educ, Barcelona, Spain

[2] Univ Barcelona, Dept Matemat & Informat, Barcelona, Spain

来源：

PROCEEDINGS OF THE 45TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2020 | 2020年

基金：

欧盟地平线“2020”;

关键词：

mu-bases; syzygies; parametrization; Quillen-Suslin Theorem; effective bounds;

D O I：

10.1145/3373207.3404039

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：107 / 113

页数：7

共 12 条

[1]

Becker E., 1994, ISSAC'94. Proceedings of the International Symposium on Symbolic and Algebraic Computation, P129, DOI 10.1145/190347.190382

[2] The μ-basis and implicitization of a rational parametric surface [J].