The Fundamental Theorem of Algebra Made Effective: An Elementary Real-algebraic Proof via Sturm Chains

DOI10.4169/amer.math.monthly.119.09.715zbMath1267.26016arXiv0808.0097OpenAlexW2951378515MaRDI QIDQ4923948

Michael Eisermann

Publication date: 28 May 2013

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.0097

zbMATH Keywords

Sturm's theoremintermediate value theoremSturm chainsGauss' geometric notion of winding number

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: location of zeros (26C10) Algorithms with automatic result verification (65G20) Numerical computation of roots of polynomial equations (65H04) Mappings and functions (educational aspects) (97I20)

Related Items (8)

A new general formula for the Cauchy index on an interval with subresultants ⋮ Formally-verified decision procedures for univariate polynomial computation based on Sturm's and Tarski's theorems ⋮ Local Bézout theorem for Henselian rings ⋮ How to count the number of zeros that a polynomial has on the unit circle? ⋮ Quantitative fundamental theorem of algebra ⋮ A NOTE ON THE FUNDAMENTAL THEOREM OF ALGEBRA ⋮ Evaluating winding numbers and counting complex roots through Cauchy indices in Isabelle/HOL ⋮ A NOTE ON p-ADIC SIMPLICIAL VOLUMES

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