{"id":"https://openalex.org/W1859958926","doi":"https://doi.org/10.1007/978-3-7091-6282-8_1","title":"Proving Conjectures by Use of Interval Arithmetic","display_name":"Proving Conjectures by Use of Interval Arithmetic","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1859958926","doi":"https://doi.org/10.1007/978-3-7091-6282-8_1","mag":"1859958926"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-7091-6282-8_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6282-8_1","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Perspectives on Enclosure Methods","raw_type":"book-chapter"},"type":"book-chapter","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/A5072635213","display_name":"Andreas Frommer","orcid":"https://orcid.org/0000-0002-6901-0114"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Andreas Frommer","raw_affiliation_strings":["Universit\u00e4t Wuppertal, Fachbereich Mathematik, D-42097, Wuppertal, Germany","Universit\u00e4t Wuppertal, Fachbereich Mathematik, Wuppertal, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Wuppertal, Fachbereich Mathematik, D-42097, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"Universit\u00e4t Wuppertal, Fachbereich Mathematik, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072635213"],"corresponding_institution_ids":["https://openalex.org/I167360494"],"apc_list":null,"apc_paid":null,"fwci":1.2612,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.79940209,"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":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9998999834060669,"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":0.9941999912261963,"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/T12170","display_name":"History and Theory of Mathematics","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/interval-arithmetic","display_name":"Interval arithmetic","score":0.8922370672225952},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.8177250623703003},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7055585980415344},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6919302940368652},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5870745778083801},{"id":"https://openalex.org/keywords/saturation-arithmetic","display_name":"Saturation arithmetic","score":0.5438429117202759},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5054705142974854},{"id":"https://openalex.org/keywords/affine-arithmetic","display_name":"Affine arithmetic","score":0.48855480551719666},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4860897362232208},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.4683719575405121},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44417059421539307},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33053913712501526},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30950862169265747},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.292354553937912},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.2874751091003418},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11933645606040955},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10287854075431824}],"concepts":[{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.8922370672225952},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8177250623703003},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7055585980415344},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6919302940368652},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5870745778083801},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.5438429117202759},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5054705142974854},{"id":"https://openalex.org/C167315692","wikidata":"https://www.wikidata.org/wiki/Q3622729","display_name":"Affine arithmetic","level":3,"score":0.48855480551719666},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4860897362232208},{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.4683719575405121},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44417059421539307},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33053913712501526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30950862169265747},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.292354553937912},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.2874751091003418},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11933645606040955},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10287854075431824},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-7091-6282-8_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-7091-6282-8_1","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Perspectives on Enclosure Methods","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1511900881","https://openalex.org/W1566410171","https://openalex.org/W1588000771","https://openalex.org/W1601874263","https://openalex.org/W1607529908","https://openalex.org/W1656795039","https://openalex.org/W1915198610","https://openalex.org/W1966287322","https://openalex.org/W1980066758","https://openalex.org/W1994397922","https://openalex.org/W1998126423","https://openalex.org/W2013737143","https://openalex.org/W2020804487","https://openalex.org/W2044399102","https://openalex.org/W2057612756","https://openalex.org/W2060924166","https://openalex.org/W2069902401","https://openalex.org/W2129480103","https://openalex.org/W2166761858","https://openalex.org/W2248977116","https://openalex.org/W2531770935","https://openalex.org/W3022136271","https://openalex.org/W3022909171","https://openalex.org/W4246630630","https://openalex.org/W6635132063","https://openalex.org/W6653932534","https://openalex.org/W6655892977","https://openalex.org/W6661588082","https://openalex.org/W7038630121"],"related_works":["https://openalex.org/W2568181300","https://openalex.org/W2118036253","https://openalex.org/W1965905913","https://openalex.org/W2181927644","https://openalex.org/W2349168892","https://openalex.org/W1885677000","https://openalex.org/W2134029906","https://openalex.org/W2078477494","https://openalex.org/W1531645310","https://openalex.org/W1859958926"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}