{"paper":{"title":"On Certain Computations of Pisot Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jincheng Zhuang, Qi Cheng","submitted_at":"2012-02-26T18:04:23Z","abstract_excerpt":"This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number $\\alpha$ such that $\\Q[\\alpha] = \\F$ given a real Galois extension $\\F$ of $\\Q$ by its integral basis. This algorithm is based on the lattice reduction, and it runs in time polynomial in the size of the integral basis. Next, we show that for a fixed Pisot number $\\alpha$, one can compute $ [\\alpha^n] \\pmod{m}$ in time polynomial in $(\\log (m n))^{O(1)}$, where $m$ and $n$ are positive integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5785","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"}