The Vanishing Ideal of a Finite Set of Points with Multiplicity Structures

Na Lei (), Xiaopeng Zheng () and Yuxue Ren ()
Additional contact information
Na Lei: Jilin University, School of Mathematics
Xiaopeng Zheng: Jilin University, School of Mathematics
Yuxue Ren: Jilin University, School of Mathematics

A chapter in Computer Mathematics, 2014, pp 275-296 from Springer

Abstract: Abstract Given a finite set of arbitrarily distributed points in affine space with multiplicity structures, we present an algorithm to compute the reduced Gr $${\ddot{\mathrm{o}}}$$ o ¨ bner basis of the vanishing ideal under the lexicographic order. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the leading monomials of the reduced Gr $${\ddot{\mathrm{o}}}$$ o ¨ bner basis of the vanishing ideal.

Keywords: Vanishing ideal; Points with multiplicity structures; Reduced Gr $${\ddot{\mathrm{o}}}$$ o ¨ bner basis; Intersection of ideals (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-43799-5_21

Ordering information: This item can be ordered from
http://www.springer.com/9783662437995

DOI: 10.1007/978-3-662-43799-5_21

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().