A Primer on Polynomial Resultants
Abstract
Nonlinearity is one of the most stubborn difficulties of contemporary engineering and science. In this paper we are concerned with a broadly useful tool, the resultant, for manipulating polynomial nonlinearities, and we review several techniques for solving systems of nonlinear polynomial equations. The resultant, a classical algebraic tool, has become much more practical recently with the advent of symbolic software (such as Mathematics and Maple) which can evaluate 10x10 symbolic determinants in a matter of minutes on a desktop computer. While much of this paper is concerned with applying resultants to systems of univariate equations, the last section considers the generalization to the multivariate situation. Nonlinear multivariate applications appear in various areas of engineering such as chaos, signal processing, circuit theory, robotics and control theory. Two illustrations of the power of the resultant formalism are provided. First, the problem of finding the coordinates on the Earth's surface viewed by each pixel of a reconnaissance aircraft camera is discussed. Second, the Lorenz model of chaos theory if considered.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 05, 1991
- Accession Number
- ADA246883
Entities
People
- Robert M. Williams
- Ronald F. Gleeson
Organizations
- Naval Air Warfare Center Warminster