Vincent's theorem, named after Alexandre Joseph Hidulphe Vincent, isolates the real roots of polynomials with rational coefficients and underlies the fastest known method for real-root isolation. Despite this practical importance, the theorem was largely forgotten during the twentieth century, overshadowed by Sturm's theorem and omitted from nearly every classical text on the theory of equations except one by Uspensky. Two variants of Vincent's theorem exist, each giving rise to its own family of root-isolation methods based on continued fractions or bisection.
Facts
Classification
Statement FormCharacterization Theorem 1 StatementA theorem that isolates the real roots of polynomials with rational coefficients. 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Vincent's theorem - Wikipedia
Introduction, sentence 1Quote, Introduction, sentence 1
is a theorem that isolates the real roots of polynomials with rational coefficients.
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