{"paper":{"title":"On the complexity of computing Gr\\\"obner bases for weighted homogeneous systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Jean-Charles Faug\\`ere (PolSys), Mohab Safey El Din (PolSys), PolSys), Thibaut Verron (LIP6","submitted_at":"2014-12-23T21:15:05Z","abstract_excerpt":"Solving polynomial systems arising from applications is frequently    made easier by the structure of the systems. Weighted homogeneity    (or quasi-homogeneity) is one example of such a structure: given a    system of weights $W=(w\\_{1},\\dots,w\\_{n})$, $W$-homogeneous    polynomials are polynomials which are homogeneous w.r.t the weighted    degree    $\\deg\\_{W}(X\\_{1}^{\\alpha\\_{1}},\\dots,X\\_{n}^{\\alpha\\_{n}}) = \\sum    w\\_{i}\\alpha\\_{i}$.        Gr\\\"obner bases for weighted homogeneous systems can be computed by    adapting existing algorithms for homogeneous systems to the weighted    homog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7547","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"}