We generalize the notion of characteristic polynomial for a system of linear equations to systems of multivariate polynomial equations. The generalization is natural in the sense that it reduces to the usual definition when all the polynomials are linear. Whereas the constant coefficient of the general characteristic polynomial is the resultant of the system. This construction is applied to solve a traditional problem with efficient methods for solving systems of polynomial equations: the presence of infinitely many solutions "at infinity". We give a single-exponential time method for finding all the isolated solution points of a system of polynomials, even in the presence of infinitely many solutions at infinity or elsewhere.
Title
Generalized Characteristic Polynomials
Published
1988-08-01
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
CSD-88-440
Type
Text
Extent
11 p
Archive
The Engineering Library
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