Testing Positiveness of Polynomials

Authors:
Hoon Hong;Dalibor Jakuš
Affiliations:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205. e-mail: hong@math.ncsu.edu www: http://www.math.ncsu.edu/~hong;Research Institute for Symbolic Computation, Johannes Kepler University, A-4040 Linz, Austria. e-mail: djakus@risc.uni-linz.ac.at www: http://www.risc.uni-linz/people/djakus
Venue:
Journal of Automated Reasoning
Year:
1998

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Abstract

Many problems in mathematics, logic, computer science, and engineeringcan be reduced to the problem of testing positiveness of polynomials (overreal numbers). Although the problem is decidable (shown by Tarski in 1930),the general decision methods are not always practically applicable becauseof their high computational time requirements. Thus several partial methodswere proposed in the field of term rewriting systems. In this paper, weexactly determine how partial these methods are, and we propose simplerand/or more efficient methods with the same power.