The geometry of multivariate polynomial division and elimination

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. © 2013 Society for Industrial and Applied Mathematics.

Publication year:2013

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Authors from:Higher Education

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