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The study aims to extend the Fundamental Theorem of Algebra and Vieta's Theorem to exterior differential equations through rigorous proofs and applications.

March 3, 2026Open Access

Generalizations of the Fundamental Theorem of Algebra and Vieta's Theorem in Exterior Differential Equations: Complete Theory with Rigorous Proofs

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SLshifa liuPeking University

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Explores the extensions of key algebraic theorems to exterior differential equations, highlighting their implications.

Key Points

The study aims to extend the Fundamental Theorem of Algebra and Vieta's Theorem to exterior differential equations through rigorous proofs and applications.
Introduced characteristic forms and the characteristic polynomial for linear exterior differential equations.
Defined the Wronskian determinant for variable coefficients and established Liouville formulas.
Used Grassmann algebra to establish relations between coefficients and wedge product determinants.
Proved the dimension of the solution space equals the order of the operator for constant coefficients.
Demonstrated that the logs of the Wronskian determinant satisfy a Liouville formula correlating to Vieta's relations.
Established rigorous formulations relating differential invariance to Pl"ucker relations in various emerging fields.

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shifa liu (2025) studied this question.

synapsesocial.com/papers/69a67f12f353c071a6f0ae75 https://doi.org/10.5281/zenodo.18827849

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Generalizations of the Fundamental Theorem of Algebra and Vieta's Theorem in Exterior Differential Equations: Complete Theory with Rigorous Proofs

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Implication

Key Points

Cite This Study

Generalizations of the Fundamental Theorem of Algebra and Vieta's Theorem in Exterior Differential Equations: Complete Theory with Rigorous Proofs

Discussion

Member takes

Implication

Key Points

Cite This Study

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