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Root Separation for Reducible Monic Polynomials of Odd Degree
| Content Provider | Semantic Scholar |
|---|---|
| Author | Dujella, Andrej Pejkovic, Tomislav |
| Copyright Year | 2017 |
| Abstract | We study root separation of reducible monic integer polynomials of odd degree. Let H(P ) be the naïve height, sep(P ) the minimal distance between two distinct roots of an integer polynomial P (x) and sep(P ) = H(P )−e(P ). Let er(d) = lim supdeg(P )=d, H(P )→+∞ e(P ), where the lim sup is taken over the reducible monic integer polynomials P (x) of degree d. We prove that er(d) ≤ d − 2. We also obtain a lower bound for er(d) for d odd, which improves previously known lower bounds for er(d) when d ∈ {5, 7, 9}. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://bib.irb.hr/datoteka/864752.redmonsmall5.pdf |
| Alternate Webpage(s) | http://hrcak.srce.hr/file/274956 |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Emoticon Expanded memory Integer (number) Monic polynomial Naivety Plant Roots Polynomial ring Root-finding algorithm Separable polynomial |
| Content Type | Text |
| Resource Type | Article |
