On real factors of real interval polynomials

  • Authors:

  • Hiroshi Sekigawa

  • Affiliations:

  • Nippon Telegraph and Telephone Corporation, Kanagawa, Japan

  • Venue:
  • Proceedings of the 2007 international symposium on Symbolic and algebraic computation
  • Year:
  • 2007

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Abstract

For a real multivariate interval polynomial P and a real multivariate polynomial f, we provide a rigorous method for deciding whether there exists a polynomial p in P such that p is divisible by f. When P is univariate, there is a well-known criterion for whether there exists a polynomial p(χ)in P such that p(α)=0 for a given real number α. Since p(α)=0 if and only if p(χ) is divisible by χ--α, our result is a generalization of the criterion to multivariate polynomials and higher degree factors.