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TitlePolynomial root separation examples
Author(s) Arnold Schönhage
TypeArticle in Journal
AbstractIn vol. 32 of this Journal, G.E. Collins reported on extensive calculations supporting his conjecture that the exponent 1 − n in the well-known Mahler–Mignotte bound for the root separation of squarefree integral polynomials of degree n might be replaceable with − n / 2 . This paper exhibits infinite sequences of cubic polynomials with ‘true’ exponent − 2 , thus disproving that conjecture for degree n = 3 , and extends this to analogous bounds for close root triplets of quartic polynomials.
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717106000472
LanguageEnglish
JournalJournal of Symbolic Computation
Volume41
Number10
Pages1080 - 1090
Year2006
Edition0
Translation No
Refereed No
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