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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Güting, R.: Polynomials with Multiple Zeros. Mathematika 14, 181–196 (1967).
Mahler, K.: An Inequality for the Discriminant of a Polynomial. Michigan Math. J. 11, 257–262 (1964).
Marden, M.: The Geometry of the Zeros of a Polynomial in a Complex Variable. Publ. AMS 1949, Math. Surv. 3.
Mignotte, M.: Some Inequalities about Univariate Polynomials. SYMSAC 1981, 195–199.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag/Wien
About this chapter
Cite this chapter
Mignotte, M. (1983). Some Useful Bounds. In: Buchberger, B., Collins, G.E., Loos, R., Albrecht, R. (eds) Computer Algebra. Computing Supplementa, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7551-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-7091-7551-4_16
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81776-6
Online ISBN: 978-3-7091-7551-4
eBook Packages: Springer Book Archive