{"paper":{"title":"The Resultant of Developed Systems of Laurent Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Askold Khovanskii, Leonid Monin","submitted_at":"2017-02-01T21:58:30Z","abstract_excerpt":"Let $R_\\Delta (f_1,\\ldots,f_{n+1})$ be the {\\it $\\Delta$-resultant} (see below) of $(n+1)$-tuple of Laurent polynomials. We provide an algorithm for computing $R_\\Delta$ assuming that an $n$-tuple $(f_2,\\dots,f_{n+1})$ is {\\it developed} (see sec.6). We provide a relation between the product of $f_1$ over roots of $f_2=\\dots=f_{n+1}=0$ in $(\\mathbb C^*)^n$ and the product of $f_2$ over roots of $f_1=f_3=\\dots=f_{n+1}=0$ in $(\\mathbb C^*)^n$ assuming that the $n$-tuple $(f_1f_2,f_3,\\ldots,f_{n+1})$ is developed. If all $n$-tuples contained in $(f_1,\\dots,f_{n+1})$ are developed we provide a sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00470","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"}