{"paper":{"title":"Putting F\\\"urer Algorithm into Practice with the BPAS Library","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Davood Mohajerani, Lin-Xiao Wang, Marc Moreno-Maza, Sviatoslav Covanov","submitted_at":"2018-11-05T02:29:36Z","abstract_excerpt":"Fast algorithms for integer and polynomial multiplication play an important role in scientific computing as well as in other disciplines. In 1971, Sch{\\\"o}nhage and Strassen designed an algorithm that improved the multiplication time for two integers of at most $n$ bits to $\\mathcal{O}(\\log n \\log \\log n)$. In 2007, Martin F\\\"urer presented a new algorithm that runs in $O \\left(n \\log n\\ \\cdot 2^{O(\\log^* n)} \\right)$, where $\\log^* n$ is the iterated logarithm of $n$.\n  We explain how we can put F\\\"urer's ideas into practice for multiplying polynomials over a prime field $\\mathbb{Z} / p \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01490","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}