What question did this study set out to answer?

To provide a rigorous machine-checked proof of Newton's inequalities for real-rooted polynomials using Lean 4.

June 17, 2026Open Access

The Inward Bow of a Real-Rooted Polynomial: Newton's Inequalities, Machine-Checked in Lean 4

View Full Paper

Ask AI

Bookmark

To provide a rigorous machine-checked proof of Newton's inequalities for real-rooted polynomials using Lean 4.
Used machine checking within Lean 4 over Mathlib to verify Newton's inequalities.
Applied classical reductions and systematic differentiation techniques.
Ensured proofs were complete for both symmetric-function and coefficient forms.
Established that for a real polynomial of degree n, e_k^2 C(n,k-1) C(n,k+1) ≥ e_{k-1} e_{k+1} C(n,k)^2 holds for 1 ≤ k ≤ n-1.
Demonstrated that normalized means p_k = e_k / C(n,k) exhibit log-concavity.
Confirmed that real-rootedness is preserved under differentiation and reversal processes.

No takes yet. Share an insight, caveat, or question.

This randomized trial demonstrates the log-concavity of symmetric functions in real-rooted polynomials, implying foundational mathematical insights.

CARLES MARÍN MUÑOZ (2026) studied this question.

View Full Paper

Ask AI

Bookmark

This randomized trial demonstrates the log-concavity of symmetric functions in real-rooted polynomials, implying foundational mathematical insights.