Discrete Geometry for Algebraic Elimination

Ioannis Z. Emiris ()
Additional contact information
Ioannis Z. Emiris: INRIA Sophia-Antipolis

A chapter in Algebra, Geometry and Software Systems, 2003, pp 77-91 from Springer

Abstract: Abstract Multivariate resultants provide efficient methods for eliminating variables in algebraic systems. The theory of toric (or sparse) elimination generalizes the results of the classical theory to polynomials described by their supports, thus exploiting their sparseness. This is based on a discrete geometric model of the polynomials and requires a wide range of geometric notions as well as algorithms. This survey introduces toric resultants and their matrices, and shows how they reduce system solving and variable elimination to a problem in linear algebra. We also report on some practical experience.

Keywords: Matrix Polynomial; Polynomial System; Integer Point; Mixed Volume; Common Root (search for similar items in EconPapers)
Date: 2003
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:978-3-662-05148-1_4

Ordering information: This item can be ordered from
http://www.springer.com/9783662051481

DOI: 10.1007/978-3-662-05148-1_4

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 ().