Author(s): Udo-Akpan Itoro Ubom

Abstract: The determination of Galois groups plays a fundamental role in computational algebraic number theory, aiding in solving various problems related to algebraic equations and fields. This paper introduces an enhanced resolvent-based method for efficiently computing Galois groups, building upon the existing framework outlined by Bosma, Cannon, and Playoust in the Magma algebra system. Our approach aims to improve the performance and accuracy of Galois group determination, addressing limitations and enhancing computational efficiency. Through rigorous theoretical analysis and experimental validation, we demonstrate the effectiveness of our proposed method in handling diverse classes of algebraic equations and fields, showcasing its potential for practical applications in computational mathematics.

Pages: 23-26 | Views: 78 | Downloads: 6

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