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All Journal Jurnal Yudistira Bilangan: Jurnal Ilmiah Matematika, Kebumian dan Angkasa
Rasha Thnoon Taieb Alrawi
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Astronomy Education Languange, Linguistic, Communication & Media Library & Information Science Mathematics

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Factorization of Polynomials Over Finite Fields Rasha Thnoon Taieb Alrawi
Jurnal Yudistira : Publikasi Riset Ilmu Pendidikan dan Bahasa Vol. 3 No. 4 (2025): Jurnal Yudistira : Publikasi Riset Ilmu Pendidikan dan Bahasa
Publisher : Asosiasi Riset Ilmu Pendidikan Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.61132/yudistira.v3i4.2392

Abstract

This paper discusses basic concepts in finite fields and emphasizes the meaning of irreducible polynomials and their relevance in algebraic analysis. The main focus is directed at the algorithms used to factor polynomials in finite fields through three important stages: distinct degree factorization, square-free factorization, and equal degree factorization. These stages are considered core procedures in determining the structure of polynomials and their relationship to more complex algebraic properties. Furthermore, this paper reviews the role of other algorithms that support this process, such as the Berlekamp algorithm, the Cantor–Zassenhaus algorithm, and several normalization techniques that enhance the effectiveness of the analysis. The combination of these various approaches allows the breakdown of polynomials into simpler factors, while also highlighting how the algorithms work synergistically to achieve accurate analysis results. Thus, this paper emphasizes the importance of a thorough understanding of polynomial factorization algorithms in finite fields, both in theory and application, and their contribution to the development of applied mathematics, particularly in the field of computational algebra.
Kronecker Method With Generalized And Application Rasha Thnoon Taieb Alrawi
Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa Vol. 2 No. 4 (2024): Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/bilangan.v2i4.138

Abstract

The aim of this paper is to study the Kronecker method then we explain the relationship between proposed method and the matrix. Also we can be generalize this method on the matrix and we give some examples for clear this method and importance in solving a lot of problems.
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