A `replacement sequence' method for finding the largest real root of an integer monic polynomial

1999/12/30 by A. K. Gupta, Ashok Kumar Gupta, Gupta, A. K. +3 · 1 citation
Computer Science · Mathematics · #Algorithms and Data Compression #FOS: Mathematics #General Mathematics (math.GM) #Numerical Methods and Algorithms #math.GM

paper · pdf · doi:10.48550/arxiv.math/9912230

4 pages, no figures

arxiv created 1999/12/30 · openalex publication_date 1999/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To every integer monic polynomial of degree m can be associated a `replacement rule' that generates a word W* from another word W consisting of symbols belonging to a finite `alphabet' of size 2m. This rule applied iteratively on almost any initial word Wo, yields a sequence of words Wi. From acount of different symbols in the word Wi, one can obtain a rational approximate to the largest real root of the polynomial.

Citations

• A counting method for finding rational approximates to arbitrary order roots of integers

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• Symbolic computation of the roots of any polynomial with integer coefficients

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