{"id":"https://openalex.org/W2028552691","doi":"https://doi.org/10.1016/s0747-7171(85)80035-3","title":"Ideal Bases and Primary Decomposition: Case of Two Variables","display_name":"Ideal Bases and Primary Decomposition: Case of Two Variables","publication_year":1985,"publication_date":"1985-09-01","ids":{"openalex":"https://openalex.org/W2028552691","doi":"https://doi.org/10.1016/s0747-7171(85)80035-3","mag":"2028552691"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(85)80035-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0747-7171(85)80035-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0747717185800353/pdf","source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/S0747717185800353/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046142695","display_name":"Daniel Lazard","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"D. Lazard","raw_affiliation_strings":["Institut de Programmation, Universit\u00e9 Paris VI, F-75230 Paris Cedex 05","Institut de Programmation, Universit\u00e9 Paris VI, F-75230 Paris Cedex 05#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Programmation, Universit\u00e9 Paris VI, F-75230 Paris Cedex 05","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081"]},{"raw_affiliation_string":"Institut de Programmation, Universit\u00e9 Paris VI, F-75230 Paris Cedex 05#TAB#","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046142695"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I39804081"],"apc_list":{"value":2660,"currency":"USD","value_usd":2660},"apc_paid":null,"fwci":2.0885,"has_fulltext":true,"cited_by_count":88,"citation_normalized_percentile":{"value":0.86604485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"1","issue":"3","first_page":"261","last_page":"270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9330862164497375},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6993825435638428},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.6538974046707153},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6037783026695251},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.5821022987365723},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5667020082473755},{"id":"https://openalex.org/keywords/factorization-of-polynomials","display_name":"Factorization of polynomials","score":0.519548237323761},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4930233657360077},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4848371744155884},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4752490222454071},{"id":"https://openalex.org/keywords/irreducible-polynomial","display_name":"Irreducible polynomial","score":0.4685669243335724},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44512978196144104},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.43951547145843506},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.43077442049980164},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.42402809858322144},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.4168274998664856},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.19646793603897095},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10509681701660156},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.09377250075340271},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.086416095495224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08077263832092285}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9330862164497375},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6993825435638428},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.6538974046707153},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6037783026695251},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.5821022987365723},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5667020082473755},{"id":"https://openalex.org/C108741685","wikidata":"https://www.wikidata.org/wiki/Q392477","display_name":"Factorization of polynomials","level":4,"score":0.519548237323761},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4930233657360077},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4848371744155884},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4752490222454071},{"id":"https://openalex.org/C165030954","wikidata":"https://www.wikidata.org/wiki/Q1476663","display_name":"Irreducible polynomial","level":4,"score":0.4685669243335724},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44512978196144104},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.43951547145843506},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.43077442049980164},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.42402809858322144},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.4168274998664856},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.19646793603897095},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10509681701660156},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.09377250075340271},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.086416095495224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08077263832092285},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0747-7171(85)80035-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0747-7171(85)80035-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0747717185800353/pdf","source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0747-7171(85)80035-3","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0747-7171(85)80035-3","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0747717185800353/pdf","source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7699999809265137,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2028552691.pdf","grobid_xml":"https://content.openalex.org/works/W2028552691.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W163492745","https://openalex.org/W1481997196","https://openalex.org/W1524190946","https://openalex.org/W1662032257","https://openalex.org/W1885685550","https://openalex.org/W1968936725","https://openalex.org/W1989763544","https://openalex.org/W2015681973","https://openalex.org/W2055909024","https://openalex.org/W2077725083","https://openalex.org/W4237045330","https://openalex.org/W4285719527","https://openalex.org/W6606725030","https://openalex.org/W6807887954"],"related_works":["https://openalex.org/W3174430488","https://openalex.org/W2288130547","https://openalex.org/W1576380577","https://openalex.org/W4249593543","https://openalex.org/W2068749660","https://openalex.org/W4214607495","https://openalex.org/W2012320470","https://openalex.org/W1997080184","https://openalex.org/W2024250625","https://openalex.org/W1544197109"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}