{"paper":{"title":"Computing the $p$-adic Canonical Quadratic Form in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RA"],"primary_cat":"cs.DS","authors_text":"Chandan Dubey, Thomas Holenstein","submitted_at":"2014-09-22T15:27:52Z","abstract_excerpt":"An $n$-ary integral quadratic form is a formal expression $Q(x_1,..,x_n)=\\sum_{1\\leq i,j\\leq n}a_{ij}x_ix_j$ in $n$-variables $x_1,...,x_n$, where $a_{ij}=a_{ji} \\in \\mathbb{Z}$. We present a randomized polynomial time algorithm that given a quadratic form $Q(x_1,...,x_n)$, a prime $p$, and a positive integer $k$ outputs a $\\mathtt{U} \\in \\text{GL}_n(\\mathbb{Z}/p^k\\mathbb{Z})$ such that $\\mathtt{U}$ transforms $Q$ to its $p$-adic canonical form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6199","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"}