{"id":"https://openalex.org/W2043552663","doi":"https://doi.org/10.1016/0925-7721(95)00040-2","title":"Towards exact geometric computation","display_name":"Towards exact geometric computation","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2043552663","doi":"https://doi.org/10.1016/0925-7721(95)00040-2","mag":"2043552663"},"language":"en","primary_location":{"id":"doi:10.1016/0925-7721(95)00040-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00040-2","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/0925-7721(95)00040-2","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111579019","display_name":"Chee-Keng Yap","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chee-Keng Yap","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA","\u2021 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA ("],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"\u2021 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA (","institution_ids":["https://openalex.org/I36672615"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111579019"],"corresponding_institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"],"apc_list":{"value":2180,"currency":"USD","value_usd":2180},"apc_paid":{"value":2180,"currency":"USD","value_usd":2180},"fwci":18.0635,"has_fulltext":false,"cited_by_count":179,"citation_normalized_percentile":{"value":0.99646323,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"1-2","first_page":"3","last_page":"23"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","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"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.8262702226638794},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7736178040504456},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.666469395160675},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.5496901869773865},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5221091508865356},{"id":"https://openalex.org/keywords/model-of-computation","display_name":"Model of computation","score":0.4555964469909668},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4256581664085388},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3731737732887268},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24809274077415466},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11099657416343689}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.8262702226638794},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7736178040504456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.666469395160675},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.5496901869773865},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5221091508865356},{"id":"https://openalex.org/C184596265","wikidata":"https://www.wikidata.org/wiki/Q2651576","display_name":"Model of computation","level":3,"score":0.4555964469909668},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4256581664085388},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3731737732887268},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24809274077415466},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11099657416343689},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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:10.1016/0925-7721(95)00040-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00040-2","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.30.7586","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.7586","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://cs.nyu.edu/pub/local/yap/exact/towards.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1016/0925-7721(95)00040-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00040-2","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W35767324","https://openalex.org/W338467186","https://openalex.org/W435007089","https://openalex.org/W1480515154","https://openalex.org/W1500138203","https://openalex.org/W1539809939","https://openalex.org/W1555915743","https://openalex.org/W1556844982","https://openalex.org/W1567646530","https://openalex.org/W1964108206","https://openalex.org/W1983836447","https://openalex.org/W2008581147","https://openalex.org/W2021348401","https://openalex.org/W2022266599","https://openalex.org/W2024693023","https://openalex.org/W2024763304","https://openalex.org/W2028785191","https://openalex.org/W2032860274","https://openalex.org/W2033013465","https://openalex.org/W2049773063","https://openalex.org/W2055142438","https://openalex.org/W2056501879","https://openalex.org/W2060698770","https://openalex.org/W2067754486","https://openalex.org/W2073034253","https://openalex.org/W2074843875","https://openalex.org/W2081768503","https://openalex.org/W2081777693","https://openalex.org/W2082135154","https://openalex.org/W2116349848","https://openalex.org/W2121752747","https://openalex.org/W2125512233","https://openalex.org/W2161477758","https://openalex.org/W2162294210","https://openalex.org/W2170220350","https://openalex.org/W2337946189","https://openalex.org/W2409282645","https://openalex.org/W2737074378","https://openalex.org/W2943291370","https://openalex.org/W3217399827","https://openalex.org/W4210521711","https://openalex.org/W4248226364","https://openalex.org/W4300559773","https://openalex.org/W4300640952","https://openalex.org/W6601424620","https://openalex.org/W6628830742","https://openalex.org/W6630021386","https://openalex.org/W6632433482","https://openalex.org/W6633400801","https://openalex.org/W6638588722","https://openalex.org/W6641085452","https://openalex.org/W6650816904","https://openalex.org/W6652620132","https://openalex.org/W6657867553","https://openalex.org/W6666018379","https://openalex.org/W6669535157","https://openalex.org/W6683424660","https://openalex.org/W6684846674"],"related_works":["https://openalex.org/W124095581","https://openalex.org/W2014394412","https://openalex.org/W1496964288","https://openalex.org/W4243513839","https://openalex.org/W154258522","https://openalex.org/W814988660","https://openalex.org/W4240937967","https://openalex.org/W4221140179","https://openalex.org/W1967093019","https://openalex.org/W2009114240"],"abstract_inverted_index":{"Exact":[0],"computation":[1,14,75,88,107,133,157],"is":[2,145],"assumed":[3],"in":[4,7,15,59,168],"most":[5],"algorithms":[6,45],"computational":[8,140],"geometry.":[9],"In":[10],"practice,":[11,39],"implementors":[12,62],"perform":[13],"some":[16],"fixed-precision":[17,54],"model,":[18],"usually":[19],"the":[20,83,96,102,115,121,131,147,153,184],"machine":[21],"floating-point":[22],"arithmetic.":[23,55],"Such":[24],"implementations":[25],"have":[26,41],"many":[27,60,78,165],"well-known":[28],"problems,":[29],"here":[30],"informally":[31],"called":[32],"\u201crobustness":[33],"issues\u201d.":[34],"To":[35],"reconcile":[36],"theory":[37],"and":[38,92],"authors":[40],"suggested":[42],"that":[43,58,130,146,151],"theoretical":[44,103],"ought":[46],"to":[47,50,79,119,161,178],"be":[48,159,179],"redesigned":[49],"become":[51],"robust":[52],"under":[53],"We":[56,112],"suggest":[57],"cases,":[61],"should":[63],"make":[64,120],"robustness":[65,97],"a":[66,124,136],"non-issue":[67],"by":[68],"computing":[69],"exactly.":[70],"The":[71],"advantages":[72],"of":[73,82,86,139,164,183],"exact":[74,87,106,122,132,156],"are":[76,89],"too":[77],"ignore.":[80],"Many":[81],"presumed":[84],"difficulties":[85],"partly":[90,93],"surmountable":[91],"inherent":[94],"with":[95],"goal.":[98],"This":[99],"paper":[100],"formulates":[101],"framework":[104],"for":[105,155],"based":[108],"on":[109,181],"algebraic":[110],"numbers.":[111],"then":[113],"examine":[114],"practical":[116],"support":[117],"needed":[118],"approach":[123],"viable":[125],"alternative.":[126],"It":[127],"turns":[128],"out":[129],"paradigm":[134],"encompasses":[135],"rich":[137],"set":[138],"tactics.":[141],"Our":[142],"fundamental":[143],"premise":[144],"traditional":[148],"\u201cBigNumber\u201d":[149],"package":[150],"forms":[152],"work-horse":[154],"must":[158],"reinvented":[160],"take":[162],"advantage":[163],"features":[166],"found":[167],"geometric":[169],"algorithms.":[170],"Beyond":[171],"this,":[172],"we":[173],"postulate":[174],"several":[175],"other":[176],"packages":[177],"built":[180],"top":[182],"BigNumber":[185],"package.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}