{"id":"https://openalex.org/W2164300104","doi":"https://doi.org/10.1145/2465506.2465518","title":"Separating linear forms for bivariate systems","display_name":"Separating linear forms for bivariate systems","publication_year":2013,"publication_date":"2013-06-25","ids":{"openalex":"https://openalex.org/W2164300104","doi":"https://doi.org/10.1145/2465506.2465518","mag":"2164300104"},"language":"en","primary_location":{"id":"doi:10.1145/2465506.2465518","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465506.2465518","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1303.5041","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028843700","display_name":"Yacine Bouzidi","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Yacine Bouzidi","raw_affiliation_strings":["INRIA, Nancy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041225170","display_name":"Sylvain Lazard","orcid":"https://orcid.org/0000-0002-6032-0802"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sylvain Lazard","raw_affiliation_strings":["INRIA, Nancy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024458284","display_name":"Marc Pouget","orcid":"https://orcid.org/0000-0001-8085-4134"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210127166","display_name":"Centre Inria de l'Universit\u00e9 de Lorraine","ror":"https://ror.org/03fcjvn64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210127166"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc Pouget","raw_affiliation_strings":["INRIA, Nancy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Nancy, France","institution_ids":["https://openalex.org/I4210127166","https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016765679","display_name":"Fabrice Rouillier","orcid":"https://orcid.org/0009-0004-2972-822X"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fabrice Rouillier","raw_affiliation_strings":["INRIA, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Paris, France","institution_ids":["https://openalex.org/I1326498283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9797,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.91474808,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"117","last_page":"124"},"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/T10142","display_name":"Formal Methods in Verification","score":0.9882000088691711,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9783999919891357,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.6667563915252686},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6513097882270813},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6380544304847717},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.570466160774231},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.5548424124717712},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.48229506611824036},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43744632601737976},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.4265438914299011},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40909746289253235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4027494788169861},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3814893364906311},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36850911378860474},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3201143741607666},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11630663275718689}],"concepts":[{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.6667563915252686},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6513097882270813},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6380544304847717},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.570466160774231},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.5548424124717712},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48229506611824036},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43744632601737976},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4265438914299011},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40909746289253235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4027494788169861},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3814893364906311},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36850911378860474},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3201143741607666},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11630663275718689},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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:10.1145/2465506.2465518","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465506.2465518","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1303.5041","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.5041","pdf_url":"https://arxiv.org/pdf/1303.5041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1303.5041","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.5041","pdf_url":"https://arxiv.org/pdf/1303.5041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1506764403","https://openalex.org/W1562183207","https://openalex.org/W1574151794","https://openalex.org/W1966047467","https://openalex.org/W1968561983","https://openalex.org/W1990451653","https://openalex.org/W1994094598","https://openalex.org/W1997509004","https://openalex.org/W2010393691","https://openalex.org/W2011693299","https://openalex.org/W2018946319","https://openalex.org/W2059173068","https://openalex.org/W2074967544","https://openalex.org/W2075500668","https://openalex.org/W2091909596","https://openalex.org/W2108371780","https://openalex.org/W2113672208","https://openalex.org/W2130918732","https://openalex.org/W2130952444","https://openalex.org/W2397762352","https://openalex.org/W2951849341","https://openalex.org/W4244862983","https://openalex.org/W4255213956","https://openalex.org/W6630178116"],"related_works":["https://openalex.org/W2595172197","https://openalex.org/W2084856301","https://openalex.org/W2127970246","https://openalex.org/W4382618745","https://openalex.org/W2885125400","https://openalex.org/W1001352512","https://openalex.org/W1989889224","https://openalex.org/W2748922771","https://openalex.org/W1987128138","https://openalex.org/W2541180809"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"algorithm":[3],"for":[4],"computing":[5,91],"a":[6,11,21,43,48,102],"separating":[7,44,103],"linear":[8,22,45,77,104],"form":[9,46,105],"of":[10,13,24,37,50,75,83,94,101,109,114],"system":[12,53,58],"bivariate":[14],"polynomials":[15],"with":[16],"integer":[17],"coefficients,":[18],"that":[19,27,54,65,86],"is":[20,79,106],"combination":[23],"the":[25,38,51,56,63,81,95,99,107],"variables":[26],"takes":[28],"different":[29],"values":[30],"when":[31],"evaluated":[32],"at":[33,80],"distinct":[34,68],"(complex)":[35],"solutions":[36,69,96],"system.":[39],"In":[40],"other":[41],"words,":[42],"defines":[47],"shear":[49],"coordinate":[52],"sends":[55],"algebraic":[57,88],"in":[59,62,112],"generic":[60],"position,":[61],"sense":[64],"no":[66],"two":[67],"are":[70],"vertically":[71],"aligned.":[72],"The":[73],"computation":[74,100],"such":[76],"forms":[78],"core":[82],"most":[84],"algorithms":[85],"solve":[87],"systems":[89],"by":[90],"rational":[92],"parameterizations":[93],"and,":[97],"moreover,":[98],"bottleneck":[108],"these":[110],"algorithms,":[111],"terms":[113],"worst-case":[115],"bit":[116],"complexity.":[117]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
