{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T01:13:10Z","timestamp":1768093990056,"version":"3.49.0"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:p>\n            <jats:italic>Problem statement.<\/jats:italic>\n            Let K be a field and K be an algebraic closure of K. Consider the polynomial ring\n            <jats:italic>R<\/jats:italic>\n            = K[\n            <jats:italic>x<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            ,...,\n            <jats:italic>\n              x\n              <jats:sub>n<\/jats:sub>\n            <\/jats:italic>\n            ] over K and a finite sequence of polynomials\n            <jats:italic>f<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            ,...,\n            <jats:italic>\n              f\n              <jats:sub>c<\/jats:sub>\n            <\/jats:italic>\n            in\n            <jats:italic>R<\/jats:italic>\n            with\n            <jats:italic>c<\/jats:italic>\n            \u2264\n            <jats:italic>n.<\/jats:italic>\n            Let\n            <jats:italic>V<\/jats:italic>\n            \u2282 K\n            <jats:sup>\n              <jats:italic>n<\/jats:italic>\n            <\/jats:sup>\n            be the algebraic set defined by the simultaneous vanishing of the\n            <jats:italic>\n              f\n              <jats:sub>i<\/jats:sub>\n            <\/jats:italic>\n            's. Recall that\n            <jats:italic>V<\/jats:italic>\n            can be decomposed into finitely many irreducible components, whose codimension cannot be greater than\n            <jats:italic>c.<\/jats:italic>\n            The set\n            <jats:italic>\n              V\n              <jats:sub>c<\/jats:sub>\n            <\/jats:italic>\n            which is the union of all these irreducible components of codimension\n            <jats:italic>exactly c<\/jats:italic>\n            is named further the nondegenerate locus of\n            <jats:italic>f<\/jats:italic>\n            <jats:sub>1<\/jats:sub>\n            ,...,\n            <jats:italic>\n              f\n              <jats:sub>c<\/jats:sub>\n            <\/jats:italic>\n            .\n          <\/jats:p>","DOI":"10.1145\/3572867.3572872","type":"journal-article","created":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:37:32Z","timestamp":1669250252000},"page":"41-45","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Towards signature-based gr\u00f6bner basis algorithms for computing the nondegenerate locus of a polynomial system"],"prefix":"10.1145","volume":"56","author":[{"given":"Christian","family":"Eder","sequence":"first","affiliation":[{"name":"TU Kaiserslautern, Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre","family":"Lairez","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafael","family":"Mohr","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohab Safey El","family":"Din","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2022,11,23]]},"reference":[{"issue":"1","key":"e_1_2_1_1_1","first-page":"105","volume":"28","author":"Aubry Philippe","unstructured":"Philippe Aubry , Daniel Lazard , and Marc Moreno Maza . 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