{"paper":{"title":"Set complexity of construction of a regular polygon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.NT","authors_text":"Eugene Kogan","submitted_at":"2017-11-15T21:06:09Z","abstract_excerpt":"Given a subset of $\\mathbb C$ containing $x,y$, one can add $x + y,\\,x - y,\\,xy$ or (when $y\\ne0$) $x/y$ or any $z$ such that $z^2=x$. Let $p$ be a prime Fermat number. We prove that it is possible to obtain from $\\{1\\}$ a set containing all the $p$-th roots of 1 by $12 p^2$ above operations. This result is different from the standard estimation of complexity of an algorithm computing the $p$-th roots of 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05807","kind":"arxiv","version":2},"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"}