{"id":"https://openalex.org/W2017107367","doi":"https://doi.org/10.1145/2331684.2331705","title":"Implicitization of curves and surfaces using predicted support","display_name":"Implicitization of curves and surfaces using predicted support","publication_year":2012,"publication_date":"2012-06-07","ids":{"openalex":"https://openalex.org/W2017107367","doi":"https://doi.org/10.1145/2331684.2331705","mag":"2017107367"},"language":"en","primary_location":{"id":"doi:10.1145/2331684.2331705","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331684.2331705","pdf_url":null,"source":null,"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 International Workshop on Symbolic-Numeric 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/A5087662998","display_name":"Ioannis Z. Emiris","orcid":"https://orcid.org/0000-0002-2339-5303"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Ioannis Z. Emiris","raw_affiliation_strings":["University of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091076075","display_name":"Tatjana Kalinka","orcid":null},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Tatjana Kalinka","raw_affiliation_strings":["University of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065246440","display_name":"Christos Konaxis","orcid":"https://orcid.org/0000-0002-0420-2465"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Christos Konaxis","raw_affiliation_strings":["University of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1677,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.94131633,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"137","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9995999932289124,"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":0.9995999932289124,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9993000030517578,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9887999892234802,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7029372453689575},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6282824277877808},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6005425453186035},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5750157237052917},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5095798969268799},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.49205416440963745},{"id":"https://openalex.org/keywords/parametric-surface","display_name":"Parametric surface","score":0.4817788302898407},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45576250553131104},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.42863017320632935},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40414178371429443},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3964329957962036},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3253750801086426},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21436184644699097},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.15975213050842285},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15648052096366882},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15507721900939941}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7029372453689575},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6282824277877808},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6005425453186035},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5750157237052917},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5095798969268799},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.49205416440963745},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.4817788302898407},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45576250553131104},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.42863017320632935},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40414178371429443},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3964329957962036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3253750801086426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21436184644699097},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15975213050842285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15648052096366882},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15507721900939941},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2331684.2331705","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331684.2331705","pdf_url":null,"source":null,"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8876806070","display_name":null,"funder_award_id":"PITN-GA-2008-214584","funder_id":"https://openalex.org/F4320334960","funder_display_name":"Seventh Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320334960","display_name":"Seventh Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W14739149","https://openalex.org/W35099400","https://openalex.org/W1483218536","https://openalex.org/W1508888334","https://openalex.org/W1512237513","https://openalex.org/W1534719102","https://openalex.org/W1539076476","https://openalex.org/W1584197217","https://openalex.org/W1600752240","https://openalex.org/W1619680849","https://openalex.org/W1743245773","https://openalex.org/W1791330396","https://openalex.org/W1801306671","https://openalex.org/W1943663571","https://openalex.org/W1967265325","https://openalex.org/W1967787874","https://openalex.org/W1977415556","https://openalex.org/W1986116224","https://openalex.org/W1990568802","https://openalex.org/W1995786326","https://openalex.org/W1999896001","https://openalex.org/W2005536816","https://openalex.org/W2008278996","https://openalex.org/W2010692503","https://openalex.org/W2023831525","https://openalex.org/W2026317840","https://openalex.org/W2028444458","https://openalex.org/W2032315313","https://openalex.org/W2039791875","https://openalex.org/W2043606168","https://openalex.org/W2044164387","https://openalex.org/W2048078410","https://openalex.org/W2054267869","https://openalex.org/W2058393311","https://openalex.org/W2059860265","https://openalex.org/W2066663656","https://openalex.org/W2070279173","https://openalex.org/W2071483197","https://openalex.org/W2073139439","https://openalex.org/W2083244827","https://openalex.org/W2083567817","https://openalex.org/W2096543568","https://openalex.org/W2103370353","https://openalex.org/W2108888104","https://openalex.org/W2122005371","https://openalex.org/W2299450869","https://openalex.org/W2320437408","https://openalex.org/W2327732228","https://openalex.org/W2335197782","https://openalex.org/W2596326330","https://openalex.org/W2952887459","https://openalex.org/W2967153401","https://openalex.org/W3038127566","https://openalex.org/W4255982026","https://openalex.org/W4292096448","https://openalex.org/W6601435401","https://openalex.org/W6676290813","https://openalex.org/W6780181731","https://openalex.org/W6830684888"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W1493684871","https://openalex.org/W2886567582","https://openalex.org/W4390962314","https://openalex.org/W4289703404","https://openalex.org/W2999175164","https://openalex.org/W2095627444","https://openalex.org/W2354039148","https://openalex.org/W2379877967","https://openalex.org/W2058351347"],"abstract_inverted_index":{"We":[0,32,59],"reduce":[1],"implicitization":[2,91],"of":[3,16,43,55,64,77,95],"rational":[4],"parametric":[5],"curves":[6,79],"and":[7,67,72,80,82],"(hyper)surfaces":[8],"to":[9],"linear":[10],"algebra,":[11],"by":[12,50],"interpolating":[13],"the":[14,17,29,41,52,56,93],"coefficients":[15],"implicit":[18,30,57],"equation.":[19],"For":[20],"this,":[21],"we":[22],"may":[23],"use":[24],"any":[25],"method":[26],"for":[27,89],"predicting":[28],"support.":[31],"focus":[33],"on":[34,74],"methods":[35],"that":[36],"exploit":[37],"input":[38],"structure":[39],"in":[40,92],"sense":[42],"sparse":[44,96],"(or":[45],"toric)":[46],"elimination":[47],"theory,":[48],"namely":[49],"computing":[51],"Newton":[53],"polytope":[54],"polynomial.":[58],"offer":[60],"a":[61],"public-domain":[62],"implementation":[63],"our":[65],"methods,":[66],"study":[68],"their":[69],"numerical":[70],"stability":[71],"efficiency":[73],"several":[75],"classes":[76],"plane":[78],"surfaces,":[81],"discuss":[83],"how":[84],"it":[85],"can":[86],"be":[87],"used":[88],"approximate":[90],"setting":[94],"elimination.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}