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Solving polynomials with ordinary differential equations

Abstract : In this work we consider a given root of a family of n-degree polynomials as a one-variable function that depends only on the independent term. Then we prove that this function satisfies several ordinary differential equations (ODE). More concretely, it satisfies several simple separated variables ODE, a first order generalized Abel ODE of degree n-1 and an (n-1)-th order linear ODE. Although some of our results are not new, our approach is simple and self-contained. For n=2, 3 and 4 we recover, from these ODE, the classical formulas for solving these polynomials.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-02879497
Contributor : Hector Giacomini <>
Submitted on : Tuesday, June 23, 2020 - 9:14:05 PM
Last modification on : Wednesday, June 24, 2020 - 3:19:24 AM

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  • HAL Id : hal-02879497, version 1
  • ARXIV : 2006.09362

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Armengol Gasull, Hector Giacomini. Solving polynomials with ordinary differential equations. 2020. ⟨hal-02879497⟩

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