{"id":"https://openalex.org/W2067240242","doi":"https://doi.org/10.1016/s0747-7171(85)80038-9","title":"Theory of Summation in Finite Terms","display_name":"Theory of Summation in Finite Terms","publication_year":1985,"publication_date":"1985-09-01","ids":{"openalex":"https://openalex.org/W2067240242","doi":"https://doi.org/10.1016/s0747-7171(85)80038-9","mag":"2067240242"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(85)80038-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(85)80038-9","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_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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-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/A5112183604","display_name":"Michael Karr","orcid":null},"institutions":[{"id":"https://openalex.org/I4210141060","display_name":"Community Options (United States)","ror":"https://ror.org/04nk31t13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210141060"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Karr","raw_affiliation_strings":["Software Options Inc., Cambridge, Massachusetts 02138, USA","Software Options Inc., Cambridge, Massachusetts 02138, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Software Options Inc., Cambridge, Massachusetts 02138, USA","institution_ids":[]},{"raw_affiliation_string":"Software Options Inc., Cambridge, Massachusetts 02138, USA#TAB#","institution_ids":["https://openalex.org/I4210141060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112183604"],"corresponding_institution_ids":["https://openalex.org/I4210141060"],"apc_list":{"value":2660,"currency":"USD","value_usd":2660},"apc_paid":null,"fwci":0.7382,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.8081011,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"1","issue":"3","first_page":"303","last_page":"315"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9937999844551086,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9937999844551086,"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/T11567","display_name":"semigroups and automata theory","score":0.9814000129699707,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9690999984741211,"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/mathematics","display_name":"Mathematics","score":0.9408254623413086},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6121240258216858},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.563156008720398},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"Summation by parts","score":0.53500896692276},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4821586012840271},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.46857237815856934},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37624213099479675},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33771252632141113}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9408254623413086},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6121240258216858},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.563156008720398},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.53500896692276},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4821586012840271},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.46857237815856934},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37624213099479675},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33771252632141113},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0747-7171(85)80038-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(85)80038-9","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_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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1975745059","https://openalex.org/W1983693613"],"related_works":["https://openalex.org/W2975923947","https://openalex.org/W2518630319","https://openalex.org/W2143822","https://openalex.org/W3013650182","https://openalex.org/W4249605382","https://openalex.org/W2181962679","https://openalex.org/W4313491656","https://openalex.org/W3279617","https://openalex.org/W2989283631","https://openalex.org/W2893614166"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
