{"id":"https://openalex.org/W2108314778","doi":"https://doi.org/10.1016/s0747-7171(85)80013-4","title":"Decreasing the nesting depth of expressions involving square roots","display_name":"Decreasing the nesting depth of expressions involving square roots","publication_year":1985,"publication_date":"1985-06-01","ids":{"openalex":"https://openalex.org/W2108314778","doi":"https://doi.org/10.1016/s0747-7171(85)80013-4","mag":"2108314778"},"language":"en","primary_location":{"id":"doi:10.1016/s0747-7171(85)80013-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(85)80013-4","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/A5109583026","display_name":"Allan Borodin","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Allan Borodin","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 1A4","Department of Computer Science, University of Toronto, Toronto, Ontario CANADA M5S 1A4#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 1A4","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario CANADA M5S 1A4#TAB#","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027117465","display_name":"Ronald Fagin","orcid":"https://orcid.org/0000-0002-7374-0347"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald Fagin","raw_affiliation_strings":["IBM Research Laboratory, 5600 Cottle Road, San Jose, California 95193, U.S.A","IBM Research Laboratory, 5600 Cottle Road, San Jose, California 95193, U.S.A.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research Laboratory, 5600 Cottle Road, San Jose, California 95193, U.S.A","institution_ids":["https://openalex.org/I1341412227"]},{"raw_affiliation_string":"IBM Research Laboratory, 5600 Cottle Road, San Jose, California 95193, U.S.A.#TAB#","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043211393","display_name":"John E. Hopcroft","orcid":"https://orcid.org/0000-0001-8681-6075"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John E. Hopcroft","raw_affiliation_strings":["Department of Computer Science, Cornell University, Ithaca, New York 14853, U.S.A","Department of Computer Science Cornell University Ithaca, New York 14853 U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Cornell University, Ithaca, New York 14853, U.S.A","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Department of Computer Science Cornell University Ithaca, New York 14853 U.S.A","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008676408","display_name":"Martin Tompa","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Martin Tompa","raw_affiliation_strings":["Department of Computer Science, University of Washington, Seattle, Washington 98195, U .S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Washington, Seattle, Washington 98195, U .S.A","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2660,"currency":"USD","value_usd":2660},"apc_paid":null,"fwci":0.7721,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.68985507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"1","issue":"2","first_page":"169","last_page":"188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9861999750137329,"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":0.9641000032424927,"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":0.8954457640647888},{"id":"https://openalex.org/keywords/nesting","display_name":"Nesting (process)","score":0.8567444086074829},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.8329391479492188},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.7965618371963501},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.47754916548728943},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36206716299057007},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34395134449005127},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2126569151878357},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0669822096824646}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8954457640647888},{"id":"https://openalex.org/C2776937656","wikidata":"https://www.wikidata.org/wiki/Q2229669","display_name":"Nesting (process)","level":2,"score":0.8567444086074829},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.8329391479492188},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.7965618371963501},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.47754916548728943},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36206716299057007},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34395134449005127},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2126569151878357},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0669822096824646},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0747-7171(85)80013-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0747-7171(85)80013-4","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.70.8748","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.8748","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.almaden.ibm.com/cs/people/fagin/symb85.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":7,"referenced_works":["https://openalex.org/W1558611215","https://openalex.org/W2050306584","https://openalex.org/W2059683211","https://openalex.org/W2063402394","https://openalex.org/W2087588073","https://openalex.org/W2090988053","https://openalex.org/W2577333307"],"related_works":["https://openalex.org/W2914004531","https://openalex.org/W4281484538","https://openalex.org/W2006768240","https://openalex.org/W2389214938","https://openalex.org/W2014747044","https://openalex.org/W2388992405","https://openalex.org/W1978756817","https://openalex.org/W2376728977","https://openalex.org/W38974703","https://openalex.org/W2315441795"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
