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The aim is to connect classical algebraic theorems with variational equations through a categorical framework.

March 4, 2026Open Access

Generalizations of the Fundamental Theorem of Algebra and Vieta's Theorem in Variational Equations: A Unified Categorical Framework

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The aim is to connect classical algebraic theorems with variational equations through a categorical framework.
Established relationships between Jacobi equations and classical polynomial theory.
Proved Liouville-type formulas for Wronskians and coefficients of higher-order variational equations.
Developed a differential Galois interpretation of invariants related to variational equations.
Showed the generalization of Vieta's theorem to variational equations.
Established infinite conservation laws related to higher-order Liouville formulas.
Unified results under a categorical framework revealing deep connections among various mathematical concepts.

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Demonstrates a connection between algebraic theorems and variational equations, indicating profound implications for various mathematical fields.

shifa liu (2025) studied this question.

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Demonstrates a connection between algebraic theorems and variational equations, indicating profound implications for various mathematical fields.