{"paper":{"title":"On the Parallelization of Triangular Decomposition of Polynomial Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.MS"],"primary_cat":"cs.SC","authors_text":"Alexander Brandt, Marc Moreno Maza, Mohammadali Asadi, Robert H. C. Moir, Yuzhen Xie","submitted_at":"2019-05-31T19:16:47Z","abstract_excerpt":"We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on polynomials and high-level procedures which produce the different components (points, curves, surfaces) of the solution set. The latter \"component-level\" parallelization of triangular decompositions, our focus here, belongs to the class of dynamic irregular parallel applications. Possible speedup factors depend on geometrical properties of the solution set (number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00039","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"}