Reproduce “Finding Integer Roots of Polynomials in Nearly Optimal Time” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Yansong Feng, Itamar Nir
The authors present a deterministic algorithm to find all distinct integer roots of a dense integer-coefficient polynomial. It uses approximate complex roots to generate candidates, then checks them exactly; a Mahler-measure bound controls their total bit length. With Pan’s approximate-factorization theorem, it takes \(\widetilde O(nb)\) bit operations without a square-free assumption. A self-contained alternative is near-linear when \(b\le n^{1/4}\).
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.