{"paper":{"title":"A Modular Algorithm for Computing Polynomial GCDs over Number Fields presented with Multiple Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Mark van Hoeij, Michael Monagan","submitted_at":"2016-01-06T01:03:52Z","abstract_excerpt":"We consider the problem of computing the monic gcd of two polynomials over a number field L = Q(alpha_1,...,alpha_n). Langemyr and McCallum have already shown how Brown's modular GCD algorithm for polynomials over Q can be modified to work for Q(alpha) and subsequently, Langemyr extended the algorithm to L[x]. Encarnacion also showed how to use rational number to make the algorithm for Q(alpha) output sensitive, that is, the number of primes used depends on the size of the integers in the gcd and not on bounds based on the input polynomials.\n  Our first contribution is an extension of Encarnac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01038","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"}