{"id":"https://openalex.org/W1963919699","doi":"https://doi.org/10.1145/1277548.1277571","title":"Systems of three polynomials with two separated variables","display_name":"Systems of three polynomials with two separated variables","publication_year":2007,"publication_date":"2007-07-29","ids":{"openalex":"https://openalex.org/W1963919699","doi":"https://doi.org/10.1145/1277548.1277571","mag":"1963919699"},"language":"en","primary_location":{"id":"doi:10.1145/1277548.1277571","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019923233","display_name":"Mohamed Elkadi","orcid":null},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mohamed Elkadi","raw_affiliation_strings":["Universit\u00e9 de Nice"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Nice","institution_ids":["https://openalex.org/I201841394"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111902088","display_name":"Andr\u00e9 Galligo","orcid":null},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andr\u00e9 Galligo","raw_affiliation_strings":["Universit\u00e9 de Nice"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Nice","institution_ids":["https://openalex.org/I201841394"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019923233"],"corresponding_institution_ids":["https://openalex.org/I201841394"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.08375231,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"5","issue":null,"first_page":"159","last_page":"166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9979000091552734,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9283000230789185,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.8028064370155334},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.688450813293457},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6211868524551392},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6143343448638916},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6094703674316406},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.6058958172798157},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5639165043830872},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5236454010009766},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49928903579711914},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.4964638352394104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4926305413246155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3478606939315796},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3218199610710144},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29482707381248474},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.22100374102592468},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1205534040927887}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.8028064370155334},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.688450813293457},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6211868524551392},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6143343448638916},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6094703674316406},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.6058958172798157},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5639165043830872},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5236454010009766},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49928903579711914},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.4964638352394104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4926305413246155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3478606939315796},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3218199610710144},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29482707381248474},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.22100374102592468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1205534040927887},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1277548.1277571","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277571","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W154930435","https://openalex.org/W656055053","https://openalex.org/W1490867194","https://openalex.org/W1828839365","https://openalex.org/W1963627383","https://openalex.org/W1970997649","https://openalex.org/W2002691828","https://openalex.org/W2011114755","https://openalex.org/W2016691347","https://openalex.org/W2041532189","https://openalex.org/W2056205358","https://openalex.org/W2059541972","https://openalex.org/W2068958514","https://openalex.org/W2301183701","https://openalex.org/W2465837685","https://openalex.org/W2782941102","https://openalex.org/W4210772217","https://openalex.org/W4214936342","https://openalex.org/W4285719527","https://openalex.org/W4300076833"],"related_works":["https://openalex.org/W4394590985","https://openalex.org/W2348840575","https://openalex.org/W2030498341","https://openalex.org/W3122841410","https://openalex.org/W2046205453","https://openalex.org/W2770017172","https://openalex.org/W89977309","https://openalex.org/W2183901182","https://openalex.org/W2030930882","https://openalex.org/W4300013323"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,17,70,75,91],"computation":[3],"of":[4,22,42,65,80,90],"intersection":[5],"loci":[6],"in":[7],"Computer":[8],"Aided":[9],"Geometric":[10],"Design":[11],"(CAGD),":[12],"we":[13],"introduce":[14],"and":[15,47,54,72,84],"study":[16],"elimination":[18],"problem":[19],"for":[20,51],"systems":[21,31,41],"three":[23],"bivariate":[24,35],"polynomial":[25,92],"equations":[26,44],"with":[27],"separated":[28],"variables.":[29],"Such":[30],"are":[32],"simple":[33],"sparse":[34],"ones":[36],"but":[37],"resemble":[38],"to":[39,68,86],"univariate":[40],"two":[43],"both":[45],"geometrically":[46],"algebraically.":[48],"Interesting":[49],"structures":[50,67],"generalized":[52],"Sylvester":[53],"bezoutian":[55],"matrices":[56],"can":[57,62],"be":[58],"explicited.":[59],"Then":[60],"one":[61],"take":[63],"advantage":[64],"these":[66],"represent":[69],"objects":[71],"speed":[73],"up":[74],"computations.":[76],"A":[77],"corresponding":[78],"notion":[79],"subresultant":[81],"is":[82],"presented":[83],"related":[85],"a":[87],"Gr\u00f6bner":[88],"basis":[89],"system.":[93]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
