Resumen

SANCHEZ SMITH, Edgar Cesar. Performance Evaluation of the Chain Resolution Method (MRLBS): A Structurally Aware Algorithm for Symbolic Polynomial Resolution. Tribunal [online]. 2025, vol.5, n.13, pp.598-611.  Epub 02-Oct-2025. ISSN 2959-6513.  https://doi.org/10.59659/revistatribunal.v5i13.290.

Efficiency in the symbolic resolution of higher-degree polynomials remains a persistent challenge in computational algebra, where general-purpose methods often fail to exploit the problem's internal structure. This paper introduces and empirically evaluates the Lagrange-Bring-Sánchez Chained Resolvent Method (MRLBS), a novel algorithm based on the Algebraic Theory of Chained Resolvents (TGRAE) that leverages structural factorization guided by Galois theory. A comparative performance study was conducted against two benchmark solvers using a stratified corpus of 150 polynomials. Statistical analysis, through a two-way ANOVA, revealed a significant interaction effect (F(4, 441) = 8.92, p < .001, ηp² = 0.075), demonstrating that MRLBS's performance advantage is not only significant but also magnifies as the polynomial degree increases. These findings, robust after controlling for term density, quantitatively validate the effectiveness of a structurally-aware approach. This work not only presents a superior and scalable algorithm but also advocates for a deeper integration of abstract algebraic theory into the design of high-performance computational tools.

Palabras clave : Computational Algebra; Symbolic Polynomial Solving; Galois Theory; Algorithm Performance; Chained Resolvents; Computational Efficiency.

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