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Contribution to Book
Randomized Detection of Extraneous Factors
ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (2014)
  • Manfred Minimair, Seton Hall University
Abstract

A projection operator of a system of parametric polynomials is a polynomial in the coefficients of the system that vanishes if the system has a common root. The projection operator is a multiple of the resultant of the system, and the factors of the projection operator that are not contained in the resultant are called extraneous factors. The main contribution of this work is to provide a randomized algorithm to check whether a factor is extraneous, which is an important task in applications. A lower bound for the success probability is determined which can be set arbitrarily close to one. This algorithm uses certain matrices rather than Gröbner bases and seems to be the first algorithm of this kind for this task.

Keywords
  • computer algebra,
  • resultant,
  • extranous factor,
  • randomized algorithm
Publication Date
July, 2014
Publisher
ACM
ISBN
978-1-4503-2501-1
Citation Information
Manfred Minimair. "Randomized Detection of Extraneous Factors" New York, NYISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (2014)
Available at: http://works.bepress.com/minimair/32/