{"id":"https://openalex.org/W3104637733","doi":"https://doi.org/10.1016/j.jsc.2023.03.002","title":"Representation of hypergeometric products of higher nesting depths in difference rings","display_name":"Representation of hypergeometric products of higher nesting depths in difference rings","publication_year":2023,"publication_date":"2023-03-22","ids":{"openalex":"https://openalex.org/W3104637733","doi":"https://doi.org/10.1016/j.jsc.2023.03.002","mag":"3104637733"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jsc.2023.03.002","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.jsc.2023.03.002","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007310005","display_name":"Evans Doe Ocansey","orcid":"https://orcid.org/0009-0007-4281-2567"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]},{"id":"https://openalex.org/I4210140024","display_name":"RISC Software (Austria)","ror":"https://ror.org/0533vxh11","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210140024"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Evans Doe Ocansey","raw_affiliation_strings":["Johannes Kepler University Linz, Institute for Algebra, Linz, Austria","Johannes Kepler University Linz, Research Institute for Symbolic Computation (RISC), Linz, Austria","RISC Software GmbH, Softwarepark 32a, 4232 Hagenberg, Austria"],"affiliations":[{"raw_affiliation_string":"Johannes Kepler University Linz, Research Institute for Symbolic Computation (RISC), Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"RISC Software GmbH, Softwarepark 32a, 4232 Hagenberg, Austria","institution_ids":["https://openalex.org/I4210140024"]},{"raw_affiliation_string":"Johannes Kepler University Linz, Institute for Algebra, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012740956","display_name":"Carsten Schneider","orcid":"https://orcid.org/0000-0002-5703-4530"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Carsten Schneider","raw_affiliation_strings":["Johannes Kepler University Linz, Research Institute for Symbolic Computation (RISC), Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johannes Kepler University Linz, Research Institute for Symbolic Computation (RISC), Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007310005","https://openalex.org/A5012740956"],"corresponding_institution_ids":["https://openalex.org/I121883995","https://openalex.org/I4210140024","https://openalex.org/I121883995"],"apc_list":{"value":2770,"currency":"USD","value_usd":2770},"apc_paid":{"value":2770,"currency":"USD","value_usd":2770},"fwci":0.618,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.481538,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":82,"max":85},"biblio":{"volume":"120","issue":null,"first_page":"102220","last_page":"102220"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994,"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":0.9994,"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/T11130","display_name":"Coding theory and cryptography","score":0.9848,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9728,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.6361896},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.603358},{"id":"https://openalex.org/keywords/representation","display_name":"Representation","score":0.5615292},{"id":"https://openalex.org/keywords/hypergeometric-distribution","display_name":"Hypergeometric distribution","score":0.5431271},{"id":"https://openalex.org/keywords/nesting","display_name":"Nesting (process)","score":0.53423524}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.86911094},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.6361896},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.603358},{"id":"https://openalex.org/C158241908","wikidata":"https://www.wikidata.org/wiki/Q109744257","display_name":"Generalized hypergeometric function","level":3,"score":0.59506243},{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.57567},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5615292},{"id":"https://openalex.org/C176671685","wikidata":"https://www.wikidata.org/wiki/Q730600","display_name":"Hypergeometric distribution","level":2,"score":0.5431271},{"id":"https://openalex.org/C2776937656","wikidata":"https://www.wikidata.org/wiki/Q2229669","display_name":"Nesting (process)","level":2,"score":0.53423524},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5306916},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5100742},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47589076},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.465676},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0999873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08515814},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.05053389},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jsc.2023.03.002","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2011.08775","pdf_url":"https://arxiv.org/pdf/2011.08775","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jsc.2023.03.002","pdf_url":null,"source":{"id":"https://openalex.org/S18904315","display_name":"Journal of Symbolic Computation","issn_l":"0747-7171","issn":["0747-7171","1095-855X"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund","award_id":"P32301"},{"funder":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund","award_id":"F5009-N15"},{"funder":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund","award_id":"P33530"}],"datasets":[],"versions":[],"referenced_works_count":51,"referenced_works":["https://openalex.org/W1672862537","https://openalex.org/W1909201467","https://openalex.org/W1970359497","https://openalex.org/W1978059199","https://openalex.org/W1981746549","https://openalex.org/W1983693613","https://openalex.org/W1991191994","https://openalex.org/W1995044098","https://openalex.org/W2004834120","https://openalex.org/W2010225963","https://openalex.org/W2010345794","https://openalex.org/W2018339436","https://openalex.org/W2023697602","https://openalex.org/W2026897841","https://openalex.org/W2027384932","https://openalex.org/W2046078423","https://openalex.org/W2048214141","https://openalex.org/W2055087228","https://openalex.org/W2064305618","https://openalex.org/W2067240242","https://openalex.org/W2085350446","https://openalex.org/W2087893470","https://openalex.org/W2094144431","https://openalex.org/W2094965692","https://openalex.org/W2102215343","https://openalex.org/W2102658840","https://openalex.org/W2102981110","https://openalex.org/W2117392239","https://openalex.org/W2119371075","https://openalex.org/W2127861036","https://openalex.org/W2129208333","https://openalex.org/W2139308731","https://openalex.org/W2140443967","https://openalex.org/W2141040012","https://openalex.org/W2141505290","https://openalex.org/W2149584320","https://openalex.org/W2153531485","https://openalex.org/W2153757816","https://openalex.org/W2483492749","https://openalex.org/W2484577753","https://openalex.org/W2502395597","https://openalex.org/W2610427301","https://openalex.org/W2627037788","https://openalex.org/W3016600692","https://openalex.org/W3022384651","https://openalex.org/W3101169656","https://openalex.org/W3126493290","https://openalex.org/W4239103125","https://openalex.org/W4241695442","https://openalex.org/W4245291382","https://openalex.org/W602391989"],"related_works":["https://openalex.org/W4327524493","https://openalex.org/W4306707509","https://openalex.org/W4255357714","https://openalex.org/W4246122464","https://openalex.org/W2997127250","https://openalex.org/W2090151112","https://openalex.org/W2047062626","https://openalex.org/W2028620627","https://openalex.org/W2010866598","https://openalex.org/W1977217926"],"abstract_inverted_index":{"A":[0],"non-trivial":[1],"symbolic":[2,85],"machinery":[3,98],"is":[4,78],"presented":[5],"that":[6,99],"can":[7,56,100],"rephrase":[8],"algorithmically":[9],"a":[10,23,38,96],"finite":[11],"set":[12],"of":[13,32,40,64,91],"nested":[14,43,65,104,108],"hypergeometric":[15,44,66],"products":[16,45,67],"in":[17,30,88],"appropriately":[18],"designed":[19],"difference":[20,92],"rings.":[21],"As":[22],"consequence,":[24],"one":[25,33,55,94],"obtains":[26,95],"an":[27],"alternative":[28],"representation":[29],"terms":[31],"single":[34],"product":[35],"defined":[36,106],"over":[37,107],"root":[39],"unity":[41],"and":[42,72],"which":[46],"are":[47],"algebraically":[48],"independent":[49],"among":[50],"each":[51],"other.":[52],"In":[53],"particular,":[54],"solve":[57],"the":[58,61,75,79,89],"zero-recognition":[59],"problem:":[60],"input":[62],"expression":[63,77],"evaluates":[68],"to":[69],"zero":[70,80],"if":[71,74],"only":[73],"output":[76],"expression.":[81],"Combined":[82],"with":[83],"available":[84],"summation":[86],"algorithms":[87],"setting":[90],"rings,":[93],"general":[97],"represent":[101],"(and":[102],"simplify)":[103],"sums":[105],"products.":[109]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3104637733","counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-04-25T00:34:04.668710","created_date":"2020-11-23"}