What question did this study set out to answer?

To formally generate the concept of virtual roots for real polynomials and their counting method in Lean 4.

June 19, 2026Open Access

Roots That Are Always There: the Virtual Roots of a Real Polynomial, Machine-Checked in Lean 4

View Full Paper

Ask AI

Bookmark

To formally generate the concept of virtual roots for real polynomials and their counting method in Lean 4.
Machine-checked formalization in Lean 4 over Mathlib
Utilized recursive R_d construction with properties of real polynomials
Implemented exact Budan-Fourier counting through virtual roots
Demonstrated that real polynomials have exactly d virtual roots
Established an exact count of virtual roots equating to the sign-variation drop of the derivative tower
Formalization is unprecedented in interactive theorem provers, ensuring accuracy and reliability

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

Randomized trial formalizes the virtual roots of real polynomials using Lean 4, indicating a new method of counting.

CARLES MARÍN MUÑOZ (2026) studied this question.

View Full Paper

Ask AI

Bookmark