Computational results accompanying the article: "Algorithmic aspects of Newman polynomials and their divisors"

This dataset contains the computational results and verification scripts accompanying the article:A detailed description of all files and their roles is provided in the README.txt file included in the dataset."Algorithmic aspects of Newman polynomials and their divisors"by M. Idris and J.-M. Sac-Epée.These data support the results presented in Sections 2–4 of the article, including:- the analysis of polynomials with Mahler measure < 1.3,- the construction of Newman multiples via mixed-integer linear programming,- the identification of unresolved cases,- the certification of polynomials that do not divide any Newman polynomial, following the Hare–Mossinghoff approach,- and the construction of Newman polynomials divisible by powers of Lehmer's polynomial.Contents of the dataset: - Known180.txt: list of polynomials with Mahler measure < 1.3 used in the computations,- newman.txt: polynomials already belonging to the class of Newman polynomials,- positive.txt: polynomials excluded because of a positive real root,- outputP.txt, outputQ.txt, outputD.txt: corresponding polynomials p, q and products p*q,- nonsol.txt: unresolved cases up to degree 1000,- resulthexa.txt: hexadecimal representations of Newman polynomials divisible by powers of Lehmer's polynomial,- resultcoeffs.txt: coefficient representations of the same polynomials,- verifNewman.gp: verification script in GP/PARI.All computations were performed using Julia, JuMP and Gurobi, and independently verified using GP/PARI.