{"id":"https://openalex.org/W2018701055","doi":"https://doi.org/10.1007/s00454-004-1107-5","title":"Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set","display_name":"Properness Defects of Projections and Computation of at Least One Point in Each Connected Component of a Real Algebraic Set","publication_year":2004,"publication_date":"2004-07-14","ids":{"openalex":"https://openalex.org/W2018701055","doi":"https://doi.org/10.1007/s00454-004-1107-5","mag":"2018701055"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-004-1107-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1107-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1107-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1107-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048254079","display_name":"Mohab Safey El Din","orcid":"https://orcid.org/0000-0001-9463-1257"},"institutions":[{"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"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mohab Safey El Din","raw_affiliation_strings":["LIP6, Universit\u00e9 Paris 6, 75015 Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIP6, Universit\u00e9 Paris 6, 75015 Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210159731"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5096751326","display_name":"\ufffdric Schost","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"\ufffdric Schost","raw_affiliation_strings":["STIX, \u00c9cole Polytechnique, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"STIX, \u00c9cole Polytechnique, Palaiseau, France","institution_ids":["https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048254079"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210159731"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.4046,"has_fulltext":true,"cited_by_count":51,"citation_normalized_percentile":{"value":0.88081161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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":0.9997000098228455,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7472182512283325},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6528640985488892},{"id":"https://openalex.org/keywords/singular-point-of-an-algebraic-variety","display_name":"Singular point of an algebraic variety","score":0.6346744298934937},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.6186699867248535},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6050684452056885},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.5861178040504456},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.5539631843566895},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.540481448173523},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.508309543132782},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4934338629245758},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.49045464396476746},{"id":"https://openalex.org/keywords/algebraic-cycle","display_name":"Algebraic cycle","score":0.48085910081863403},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.44673582911491394},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44046974182128906},{"id":"https://openalex.org/keywords/algebraic-surface","display_name":"Algebraic surface","score":0.4136742353439331},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39146888256073},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3247448205947876},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21477213501930237},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19506990909576416},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.076422780752182}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7472182512283325},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6528640985488892},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.6346744298934937},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.6186699867248535},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6050684452056885},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.5861178040504456},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5539631843566895},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.540481448173523},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.508309543132782},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4934338629245758},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.49045464396476746},{"id":"https://openalex.org/C199793520","wikidata":"https://www.wikidata.org/wiki/Q4723996","display_name":"Algebraic cycle","level":3,"score":0.48085910081863403},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.44673582911491394},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44046974182128906},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.4136742353439331},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39146888256073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3247448205947876},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21477213501930237},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19506990909576416},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.076422780752182},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00454-004-1107-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1107-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1107-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:HAL:inria-00099962v1","is_oa":false,"landing_page_url":"https://inria.hal.science/inria-00099962","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, 2004, 32 (3), pp.417-430. &#x27E8;10.1007/s00454-004-1107-5&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00454-004-1107-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-004-1107-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-004-1107-5.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018701055.pdf","grobid_xml":"https://content.openalex.org/works/W2018701055.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W20998216","https://openalex.org/W29697380","https://openalex.org/W32754932","https://openalex.org/W60917887","https://openalex.org/W111612204","https://openalex.org/W269145335","https://openalex.org/W395006078","https://openalex.org/W1494515121","https://openalex.org/W1504054803","https://openalex.org/W1520462245","https://openalex.org/W1558198085","https://openalex.org/W1560124954","https://openalex.org/W1564507111","https://openalex.org/W1603189944","https://openalex.org/W1606655282","https://openalex.org/W1813686459","https://openalex.org/W1968297701","https://openalex.org/W1973494154","https://openalex.org/W1973993014","https://openalex.org/W1976541507","https://openalex.org/W1981557748","https://openalex.org/W1990451653","https://openalex.org/W2006394656","https://openalex.org/W2007391649","https://openalex.org/W2007438578","https://openalex.org/W2011693299","https://openalex.org/W2016390696","https://openalex.org/W2022078407","https://openalex.org/W2023715740","https://openalex.org/W2028576930","https://openalex.org/W2037381995","https://openalex.org/W2038345254","https://openalex.org/W2039228526","https://openalex.org/W2059522106","https://openalex.org/W2077725083","https://openalex.org/W2077961479","https://openalex.org/W2080589685","https://openalex.org/W2082387287","https://openalex.org/W2089339786","https://openalex.org/W2103745248","https://openalex.org/W2104223485","https://openalex.org/W2120467997","https://openalex.org/W2126534535","https://openalex.org/W2128687423","https://openalex.org/W2130918732","https://openalex.org/W2134386365","https://openalex.org/W2137174847","https://openalex.org/W2151549243","https://openalex.org/W2201727811","https://openalex.org/W2738437438","https://openalex.org/W2952171880","https://openalex.org/W3217399827","https://openalex.org/W4212780959","https://openalex.org/W4285719527","https://openalex.org/W4299482635","https://openalex.org/W6602514562","https://openalex.org/W6610008052","https://openalex.org/W6643956174","https://openalex.org/W6651983078","https://openalex.org/W6677926129","https://openalex.org/W6765007222"],"related_works":["https://openalex.org/W2032847817","https://openalex.org/W2170846659","https://openalex.org/W3197833978","https://openalex.org/W2061587972","https://openalex.org/W4297800099","https://openalex.org/W2076085433","https://openalex.org/W2154318968","https://openalex.org/W635989923","https://openalex.org/W1502419693","https://openalex.org/W619496859"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
