Distances from differences of roots of polynomials to the nearest integers

V. I. Galiev; A. F. Polupanov; I. E. Shparlinski

doi:10.1016/0020-0190(92)90006-H

Distances from differences of roots of polynomials to the nearest integers

V. I. Galiev, A. F. Polupanov^*, I. E. Shparlinski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We present tight bounds for distances from differences of roots of the polynomial f(x)∈R[x] over a discrete normed commutative ring R without zero divisors to the nearest element of R. In the case most interesting for applications, R=Z, an algorithm for the determination of the existence of nonzero integers among these differences in time (n⁴log(H(f)+1))^1+ε is given. This problem arises when constructing algorithms for solving some systems of ODE.

Original language	English
Pages (from-to)	143-146
Number of pages	4
Journal	Information Processing Letters
Volume	43
Issue number	3
DOIs	https://doi.org/10.1016/0020-0190(92)90006-H
Publication status	Published - 14 Sept 1992
Externally published	Yes

Keywords

Algorithms
computational complexity
polynomials with integer coefficients
systems of differential equations

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10.1016/0020-0190(92)90006-H

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abstract = "We present tight bounds for distances from differences of roots of the polynomial f(x)∈R[x] over a discrete normed commutative ring R without zero divisors to the nearest element of R. In the case most interesting for applications, R=Z, an algorithm for the determination of the existence of nonzero integers among these differences in time (n4log(H(f)+1))1+ε is given. This problem arises when constructing algorithms for solving some systems of ODE.",

keywords = "Algorithms, computational complexity, polynomials with integer coefficients, systems of differential equations",

author = "Galiev, {V. I.} and Polupanov, {A. F.} and Shparlinski, {I. E.}",

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AU - Galiev, V. I.

AU - Polupanov, A. F.

AU - Shparlinski, I. E.

PY - 1992/9/14

Y1 - 1992/9/14

N2 - We present tight bounds for distances from differences of roots of the polynomial f(x)∈R[x] over a discrete normed commutative ring R without zero divisors to the nearest element of R. In the case most interesting for applications, R=Z, an algorithm for the determination of the existence of nonzero integers among these differences in time (n4log(H(f)+1))1+ε is given. This problem arises when constructing algorithms for solving some systems of ODE.

AB - We present tight bounds for distances from differences of roots of the polynomial f(x)∈R[x] over a discrete normed commutative ring R without zero divisors to the nearest element of R. In the case most interesting for applications, R=Z, an algorithm for the determination of the existence of nonzero integers among these differences in time (n4log(H(f)+1))1+ε is given. This problem arises when constructing algorithms for solving some systems of ODE.

KW - Algorithms

KW - computational complexity

KW - polynomials with integer coefficients

KW - systems of differential equations

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U2 - 10.1016/0020-0190(92)90006-H

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VL - 43

SP - 143

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JO - Information Processing Letters

JF - Information Processing Letters

IS - 3

ER -

Distances from differences of roots of polynomials to the nearest integers

Abstract

Keywords

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