Title  The geometry of multivariate polynomial division and elimination. 
Author(s)  Kim Batselier, Philippe Dreesen, Brian Moore 
Type  Article in Journal 
Abstract  Multivariate polynomials are usually discussed in the framework of algebraic geometry. Solving problems in algebraic geometry usually involves the use of a Gröbner basis. This article shows that linear algebra without any Gröbner basis computation suffices to solve basic problems from algebraic geometry by describing three operations: multiplication, division, and elimination. This linear algebra framework will also allow us to give a geometric interpretation. Multivariate division will involve oblique projections, and a link between elimination and principal angles between subspaces (CS decomposition) is revealed. The main computational tool in this approach is the QR decomposition.

ISSN  08954798; 10957162/e 
URL 
http://epubs.siam.org/doi/abs/10.1137/120863782 
Language  English 
Journal  SIAM J. Matrix Anal. Appl. 
Volume  34 
Number  1 
Pages  102125 
Publisher  Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA 
Year  2013 
Edition  0 
Translation 
No 
Refereed 
No 