{"id":"https://openalex.org/W2092703038","doi":"https://doi.org/10.1145/1838599.1838618","title":"Abstract only","display_name":"Abstract only","publication_year":2010,"publication_date":"2010-07-29","ids":{"openalex":"https://openalex.org/W2092703038","doi":"https://doi.org/10.1145/1838599.1838618","mag":"2092703038"},"language":"en","primary_location":{"id":"doi:10.1145/1838599.1838618","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1838599.1838618","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"},"type":"conference-abstract","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/A5101477853","display_name":"Tingting Fang","orcid":"https://orcid.org/0000-0003-0728-562X"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tingting Fang","raw_affiliation_strings":["Florida State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida State University","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045195686","display_name":"Mark van Hoeij","orcid":"https://orcid.org/0000-0003-0789-1523"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark van Hoeij","raw_affiliation_strings":["Florida State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida State University","institution_ids":["https://openalex.org/I103163165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I103163165"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"44","issue":"1/2","first_page":"26","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9962999820709229,"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":0.9962999820709229,"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":0.9714999794960022,"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":0.9373000264167786,"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/gravitational-singularity","display_name":"Gravitational singularity","score":0.8502881526947021},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.8245604634284973},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7707626819610596},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5598924160003662},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5478004813194275},{"id":"https://openalex.org/keywords/hypergeometric-distribution","display_name":"Hypergeometric distribution","score":0.5409994125366211},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.48883408308029175},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.47543764114379883},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46349287033081055},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4547724723815918},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4376601576805115},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40960749983787537},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3975297212600708},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.3915693163871765},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09917423129081726},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07169356942176819},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06440117955207825}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.8502881526947021},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.8245604634284973},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7707626819610596},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5598924160003662},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5478004813194275},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.5409994125366211},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.48883408308029175},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.47543764114379883},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46349287033081055},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4547724723815918},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4376601576805115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40960749983787537},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3975297212600708},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.3915693163871765},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09917423129081726},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07169356942176819},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06440117955207825},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1838599.1838618","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1838599.1838618","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2092703038","https://openalex.org/W3083427607","https://openalex.org/W4242603392","https://openalex.org/W4319879599","https://openalex.org/W3114583818","https://openalex.org/W4309210394","https://openalex.org/W4286971377","https://openalex.org/W2920806997","https://openalex.org/W4309643004","https://openalex.org/W2056550768"],"abstract_inverted_index":{"For":[0],"second":[1],"order":[2],"linear":[3],"ordinary":[4],"differential":[5],"equations":[6],"with":[7],"coefficients":[8],"in":[9],"C(x),":[10],"we":[11,33,52,95],"present":[12],"an":[13,22],"algorithm":[14],"to":[15,21,45,75,89,108,117],"reduce,":[16],"whenever":[17],"possible,":[18],"the":[19,31,59,70,85],"equation":[20,23,106],"defined":[24],"over":[25],"a":[26,43,46],"subfield":[27,47],"of":[28,48,61,72,84,100,126],"C(x).":[29],"At":[30],"moment,":[32],"have":[34],"implemented":[35],"2-descent,":[36,65],"which":[37,111],"means":[38,112],"that":[39,97,113],"if":[40,66],"there":[41],"exists":[42],"reduction":[44],"index":[49],"2,":[50],"then":[51,64],"can":[53],"find":[54,118],"it.":[55],"If":[56],"n":[57],"is":[58],"number":[60,71],"true":[62,73],"singularities,":[63,110],"it":[67],"exists,":[68],"reduces":[69],"singularities":[74],"at":[76],"most":[77],"n/2":[78],"+":[79],"2.":[80],"In":[81],"12":[82],"out":[83],"17":[86],"examples":[87],"sent":[88],"us":[90,116],"by":[91],"Bostan":[92],"and":[93],"Kauers,":[94],"found":[96],"repeated":[98],"use":[99],"2-descent":[101,114],"reduced":[102],"their":[103,127],"regular":[104],"singular":[105],"down":[107],"3":[109],"allows":[115],"2F1-hypergeometric":[119],"type":[120],"solutions":[121],"for":[122],"about":[123],"two":[124],"third's":[125],"equations.":[128]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2016-06-24T00:00:00"}