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Some Useful Bounds

  • M. Mignotte
Part of the Computing Supplementum book series (COMPUTING, volume 4)

Abstract

Some fundamental inequalities for the following values are listed: the determinant of a matrix, the absolute value of the roots of a polynomial, the coefficients of divisors of polynomials, and the minimal distance between the roots of a polynomial. These inequalities are useful for the analysis of algorithms in various areas of computer algebra.

Keywords

Computer Algebra Irreducible Polynomial Integer Coefficient Arbitrary Complex Number Side Member 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Güting, R.: Polynomials with Multiple Zeros. Mathematika 14, 181–196 (1967).MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Mahler, K.: An Inequality for the Discriminant of a Polynomial. Michigan Math. J. 11, 257–262 (1964).MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Marden, M.: The Geometry of the Zeros of a Polynomial in a Complex Variable. Publ. AMS 1949, Math. Surv. 3.MATHGoogle Scholar
  4. [4]
    Mignotte, M.: Some Inequalities about Univariate Polynomials. SYMSAC 1981, 195–199.Google Scholar

Copyright information

© Springer-Verlag Wien 1982

Authors and Affiliations

  • M. Mignotte
    • 1
  1. 1.Centre de CalculUniversité Louis PasteurStrasbourgFrance

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