A simple algorithm for GCD of polynomials

Main Article Content

Pasquale Nardone*
Giorgio Sonnino

Abstract

Based on the Bezout approach we propose a simple algorithm to determine the gcd of two polynomials that don't need division, like the Euclidean algorithm, or determinant calculations, like the Sylvester matrix algorithm. The algorithm needs only n steps for polynomials of degree n. Formal manipulations give the discriminant or the resultant for any degree without needing division or determinant calculation.

Downloads

Download data is not yet available.

Article Details

Nardone, P., & Sonnino, G. (2022). A simple algorithm for GCD of polynomials. Annals of Mathematics and Physics, 5(2), 193–195. https://doi.org/10.17352/amp.000065
Research Articles

Copyright (c) 2022 Nardone P, et al.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Licensing and protecting the author rights is the central aim and core of the publishing business. Peertechz dedicates itself in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. Peertechz licensing terms are formulated to facilitate reuse of the manuscripts published in journals to take maximum advantage of Open Access publication and for the purpose of disseminating knowledge.

We support 'libre' open access, which defines Open Access in true terms as free of charge online access along with usage rights. The usage rights are granted through the use of specific Creative Commons license.

Peertechz accomplice with- [CC BY 4.0]

Explanation

'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.

Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific license.

With this license, the authors are allowed that after publishing with Peertechz, they can share their research by posting a free draft copy of their article to any repository or website.
'CC BY' license observance:

License Name

Permission to read and download

Permission to display in a repository

Permission to translate

Commercial uses of manuscript

CC BY 4.0

Yes

Yes

Yes

Yes

The authors please note that Creative Commons license is focused on making creative works available for discovery and reuse. Creative Commons licenses provide an alternative to standard copyrights, allowing authors to specify ways that their works can be used without having to grant permission for each individual request. Others who want to reserve all of their rights under copyright law should not use CC licenses.

Knuth DE. The Art of Computer Programming. Addison-Wesley, Reading, Mass. 1969; 2.

Bini DA, Boito P. Structured matrix-based methods for polynomial -gcd: analysis and comparisons. In Proceedings of the 2007 international symposium on Symbolic and algebraic computation (ISSAC '07). Association for Computing Machinery, New York, NY. USA. 9-16. 2007. DOI:https://doi.org/10.1145/1277548.1277551

Fazzi A, Guglielmi N, Markovsky I. Generalized algorithms for the approximate matrix polynomial GCD of reducing data uncertainties with application to MIMO system and control. Journal of Computational and Applied Mathematics. 2021; 393: 113499. https://doi.org/10.1016/j.cam.2021.113499

Brown WS, Traub JF. On Euclid's Algorithm and the Theory of Subresultants. J ACM. 1971; 18: 505-514. DOI:https://doi.org/10.1145/321662.321665

http://www2.math.uu.se/ svante/papers/sjN5.pdf