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The pair $(V,F)$ determines a vector bundle $E$ of rank $s-p$ over $W:=\\{x\\in V:\\mathrm{rk} F(x)=p\\}$. We associate with $(V,F)$ a descending chain of degeneracy loci of E (the generic polar varieties of $V$ represent a typical example of this situation).\n  The maximal degree of these degeneracy loci constitutes the essential ingredient for the uniform, bounded error probabilistic pseudo-polynomial time alg"},"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":"1306.3390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-14T13:23:48Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"a0d33d67d1c4d43e7bdb732a81f7cccae07fc302d62a7cfaeb95ced62859f5f9","abstract_canon_sha256":"18225c9f7886956bce66b39728b9d6eef5d4b108caed680bec977c1726c9b74f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:37.704380Z","signature_b64":"OscdBbTucxQSVO9lP8tdLOaHCFBhgXiRUMYbHXhG7wPqBbaLcRC0T0LMZUyeaCE20da60L2E03ZVT+8Iz1VQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b543f0522dccf26b9e50d456c2bd35c2499c362af7183d379a92d43df9b256d2","last_reissued_at":"2026-05-18T03:04:37.703612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:37.703612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degeneracy loci and polynomial equation solving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"Bernd Bank, Gr\\'egoire Lecerf, Guillermo Matera, Joos Heintz, Marc Giusti, Pablo Solern\\'o","submitted_at":"2013-06-14T13:23:48Z","abstract_excerpt":"Let V be a smooth equidimensional quasi-affine variety of dimension r over the complex numbers $C$ and let $F$ be a $(p\\times s)$-matrix of coordinate functions of $C[V]$, where $s\\ge p+r$. 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