Root separation for trinomials
نویسندگان
چکیده
منابع مشابه
Root Separation for Trinomials
We give a separation bound for the complex roots of a trinomial f ∈ Z[X ]. The logarithm of the inverse of our separation bound is polynomial in the size of the sparse encoding of f ; in particular, it is polynomial in log(deg f). It is known that no such bound is possible for 4-nomials (polynomials with 4 monomials). For trinomials, the classical results (which are based on the degree of f rat...
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The minimum root separation of an arbitrary polynomial P is defined as the minimum of the distances between distinct (real or complex) roots of P. Some asymptotically good lower bounds for the root separation of P are given, where P may have multiple zeros. There are applications in the analysis of complexity of algorithms and in the theory of algebraic and transcendental numbers.
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where the latter limsup is taken over the irreducible integer polynomials P (x) of degree d. A classical result of Mahler [10] asserts that e(d) ≤ d− 1 for all d, and it is easy to check that eirr(2) = e(2) = 1. There is only one other value of d for which e(d) or eirr(d) is known, namely d = 3, and we have eirr(3) = e(3) = 2, as proved, independently, by Evertse [9] and Schönhage [11]. For lar...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2019
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2019.02.004