{"id":"https://openalex.org/W1982472147","doi":"https://doi.org/10.1145/1277548.1277579","title":"Symbolic summation with radical expressions","display_name":"Symbolic summation with radical expressions","publication_year":2007,"publication_date":"2007-07-29","ids":{"openalex":"https://openalex.org/W1982472147","doi":"https://doi.org/10.1145/1277548.1277579","mag":"1982472147"},"language":"en","primary_location":{"id":"doi:10.1145/1277548.1277579","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 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/A5007541022","display_name":"Manuel Kauers","orcid":"https://orcid.org/0000-0001-8641-6661"},"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":"Manuel Kauers","raw_affiliation_strings":["Johannes Kepler Universit\u00e4t, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johannes Kepler Universit\u00e4t, 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":false,"raw_author_name":"Carsten Schneider","raw_affiliation_strings":["Johannes Kepler Universit\u00e4t, Linz, Austria"],"affiliations":[{"raw_affiliation_string":"Johannes Kepler Universit\u00e4t, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007541022"],"corresponding_institution_ids":["https://openalex.org/I121883995"],"apc_list":null,"apc_paid":null,"fwci":0.7471,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.71216558,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"219","last_page":"226"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9952999949455261,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/summation-by-parts","display_name":"Summation by parts","score":0.7494944334030151},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6849727630615234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.504970133304596},{"id":"https://openalex.org/keywords/the-symbolic","display_name":"The Symbolic","score":0.49944329261779785},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47484853863716125},{"id":"https://openalex.org/keywords/symbolic-data-analysis","display_name":"Symbolic data analysis","score":0.42742589116096497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3513684570789337},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.29152536392211914},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21216431260108948},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07404518127441406},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.057262271642684937}],"concepts":[{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.7494944334030151},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6849727630615234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.504970133304596},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.49944329261779785},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47484853863716125},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.42742589116096497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3513684570789337},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29152536392211914},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21216431260108948},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07404518127441406},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.057262271642684937},{"id":"https://openalex.org/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1277548.1277579","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.3164","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.3164","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.risc.uni-linz.ac.at/publications/download/risc_3028/Radical.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.63.8579","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.8579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.risc.uni-linz.ac.at/publications/download/risc_3090/Radical.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1966394702","https://openalex.org/W1983693613","https://openalex.org/W1987081771","https://openalex.org/W1992876100","https://openalex.org/W1993441116","https://openalex.org/W2019932310","https://openalex.org/W2041696113","https://openalex.org/W2079232464","https://openalex.org/W2089722995","https://openalex.org/W2102658840","https://openalex.org/W2129208333","https://openalex.org/W2171377114","https://openalex.org/W2389495257","https://openalex.org/W6678898040"],"related_works":["https://openalex.org/W2042560047","https://openalex.org/W2186150309","https://openalex.org/W2096406490","https://openalex.org/W1552151841","https://openalex.org/W2079564097","https://openalex.org/W2736010003","https://openalex.org/W1489085734","https://openalex.org/W2132514413","https://openalex.org/W2141396837","https://openalex.org/W1951895578"],"abstract_inverted_index":{"An":[0],"extension":[1],"of":[2,22,44,50],"Karr\u2019s":[3],"summation":[4],"algorithm":[5],"is":[6,39],"presented":[7],"by":[8,41],"which":[9],"symbolic":[10],"sums":[11],"involving":[12],"radical":[13],"expressions":[14],"can":[15],"be":[16],"simplified.":[17],"We":[18],"discuss":[19],"the":[20],"construction":[21],"appropriate":[23],"difference":[24,32],"fields":[25],"as":[26,28],"well":[27],"algorithms":[29],"for":[30],"solving":[31],"equations":[33],"in":[34],"these":[35],"fields.":[36],"The":[37],"paper":[38],"concluded":[40],"a":[42],"list":[43],"identities":[45],"found":[46],"with":[47],"an":[48],"implementation":[49],"our":[51],"techniques.":[52]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
