{"id":"https://openalex.org/W2054292870","doi":"https://doi.org/10.1145/1576702.1576757","title":"Exact numerical computation in algebra and geometry","display_name":"Exact numerical computation in algebra and geometry","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W2054292870","doi":"https://doi.org/10.1145/1576702.1576757","mag":"2054292870"},"language":"en","primary_location":{"id":"doi:10.1145/1576702.1576757","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576757","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 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/A5078989577","display_name":"Chee Yap","orcid":"https://orcid.org/0000-0003-2952-3545"},"institutions":[{"id":"https://openalex.org/I125608817","display_name":"Korea Institute for Advanced Study","ror":"https://ror.org/041hz9568","country_code":"KR","type":"facility","lineage":["https://openalex.org/I125608817"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Chee K. Yap","raw_affiliation_strings":["New York University, New York, NY, USA and Korea Institute of Advanced Study, Seoul, Korea"],"affiliations":[{"raw_affiliation_string":"New York University, New York, NY, USA and Korea Institute of Advanced Study, Seoul, Korea","institution_ids":["https://openalex.org/I125608817"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078989577"],"corresponding_institution_ids":["https://openalex.org/I125608817"],"apc_list":null,"apc_paid":null,"fwci":0.6856,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.70380653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"387","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9990000128746033,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/computation","display_name":"Computation","score":0.6853848099708557},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.6030094027519226},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5605237483978271},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5265158414840698},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.5164266228675842},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.49218979477882385},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4730781018733978},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4676705598831177},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4602929353713989},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4601403474807739},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.44999396800994873},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.41436949372291565},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3951212167739868},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3734731674194336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34493374824523926},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1429988443851471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10365289449691772}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6853848099708557},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.6030094027519226},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5605237483978271},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5265158414840698},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.5164266228675842},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.49218979477882385},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4730781018733978},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4676705598831177},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4602929353713989},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4601403474807739},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.44999396800994873},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.41436949372291565},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3951212167739868},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3734731674194336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34493374824523926},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1429988443851471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10365289449691772},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1576702.1576757","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576757","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W170497285","https://openalex.org/W274444295","https://openalex.org/W1496801598","https://openalex.org/W1555471913","https://openalex.org/W1573473130","https://openalex.org/W1576347883","https://openalex.org/W1986748775","https://openalex.org/W2025941018","https://openalex.org/W2120694921","https://openalex.org/W2132710642","https://openalex.org/W2496687662","https://openalex.org/W4248594911","https://openalex.org/W4320800818","https://openalex.org/W6679840910","https://openalex.org/W6996447555"],"related_works":["https://openalex.org/W2118921095","https://openalex.org/W15572050","https://openalex.org/W4298305189","https://openalex.org/W2738220517","https://openalex.org/W153360611","https://openalex.org/W2686471609","https://openalex.org/W2034475779","https://openalex.org/W57037965","https://openalex.org/W402921825","https://openalex.org/W2549857394"],"abstract_inverted_index":{"Many":[0],"problems":[1,17],"in":[2,35],"Computational":[3],"Science":[4],"&":[5],"Engineering":[6],"(CSE)":[7],"are":[8,18,32,84],"defined":[9],"on":[10,91],"the":[11,71],"continuum.":[12],"Standard":[13],"algorithms":[14,75,83],"for":[15,76],"these":[16],"numerical":[19,51,58],"and":[20,28,68,79,87,104],"approximate.":[21],"Their":[22],"computational":[23,80],"techniques":[24,31],"include":[25],"iteration,":[26,66],"subdivision,":[27],"approximation.":[29,59],"Such":[30,82],"rarely":[33],"seen":[34],"exact":[36,50,74],"or":[37],"algebraic":[38],"algorithms.":[39],"In":[40],"this":[41],"tutorial,":[42],"we":[43,62],"discuss":[44],"a":[45],"mode":[46],"of":[47,73,107],"computation":[48,52],"called":[49],"(ENC)":[53],"that":[54],"achieves":[55],"exactness":[56],"through":[57],"Through":[60],"ENC,":[61],"can":[63],"naturally":[64],"incorporate":[65],"subdivision":[67],"approximation":[69],"into":[70,95],"design":[72],"computer":[77],"algebra":[78],"geometry.":[81],"both":[85],"novel":[86],"practical.":[88],"This":[89],"tutorial":[90],"ENC":[92],"is":[93],"divided":[94],"three":[96],"equal":[97],"parts:(a)":[98],"Zero":[99],"Problems(b)":[100],"Explicitation":[101],"Problems(c)":[102],"Techniques":[103],"Complexity":[105],"Analysis":[106],"Adaptivity":[108]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
