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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.00470","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-02-01T21:58:30Z","cross_cats_sorted":[],"title_canon_sha256":"f73e11e9d5d3d3b6ebddddeeada033b370f4d309ea0dbc8a62a8165b2b913623","abstract_canon_sha256":"f50fcba811986c8dcc1c1b3581e6e6b749de93ea5654bbb2597891d5216a550e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:26.193828Z","signature_b64":"uy/dHgi5xlorinesXBY9ITAI5zEU/M5ylEMu0rEYIdgkTlpwehx9LSHnU1l9NZC7TGVJtpMlYRfjfJjOrwEcAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b7aac2ae2468cb415b22e81836601e63554fa85fa5dcfad8c9072d950a4280d","last_reissued_at":"2026-05-18T00:47:26.193173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:26.193173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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