{"id":"https://openalex.org/W2061165309","doi":"https://doi.org/10.1007/s11786-011-0086-1","title":"On Design and Implementation of a Generic Number Type for Real Algebraic Number Computations Based on Expression Dags","display_name":"On Design and Implementation of a Generic Number Type for Real Algebraic Number Computations Based on Expression Dags","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2061165309","doi":"https://doi.org/10.1007/s11786-011-0086-1","mag":"2061165309"},"language":"en","primary_location":{"id":"doi:10.1007/s11786-011-0086-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-011-0086-1","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","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/A5042788506","display_name":"Marc M\u00f6rig","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138551","display_name":"University Hospital Magdeburg","ror":"https://ror.org/03m04df46","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210138551"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marc M\u00f6rig","raw_affiliation_strings":["Department of Simulation and Graphics, Faculty of Computer Science, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","University of Magdeburg,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Simulation and Graphics, Faculty of Computer Science, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]},{"raw_affiliation_string":"University of Magdeburg,","institution_ids":["https://openalex.org/I4210138551"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025485120","display_name":"Ivo R\u00f6ssling","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138551","display_name":"University Hospital Magdeburg","ror":"https://ror.org/03m04df46","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210138551"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ivo R\u00f6ssling","raw_affiliation_strings":["Department of Simulation and Graphics, Faculty of Computer Science, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","University of Magdeburg,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Simulation and Graphics, Faculty of Computer Science, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]},{"raw_affiliation_string":"University of Magdeburg,","institution_ids":["https://openalex.org/I4210138551"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005637149","display_name":"Stefan Schirra","orcid":"https://orcid.org/0009-0006-5928-1494"},"institutions":[{"id":"https://openalex.org/I4210138551","display_name":"University Hospital Magdeburg","ror":"https://ror.org/03m04df46","country_code":"DE","type":"healthcare","lineage":["https://openalex.org/I4210138551"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Schirra","raw_affiliation_strings":["Department of Simulation and Graphics, Faculty of Computer Science, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","University of Magdeburg,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Simulation and Graphics, Faculty of Computer Science, University of Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I4210138551"]},{"raw_affiliation_string":"University of Magdeburg,","institution_ids":["https://openalex.org/I4210138551"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042788506"],"corresponding_institution_ids":["https://openalex.org/I4210138551"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.3438,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.62852497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"4","issue":"4","first_page":"539","last_page":"556"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9980999827384949,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/rounding","display_name":"Rounding","score":0.6670288443565369},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6188415884971619},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5814792513847351},{"id":"https://openalex.org/keywords/algebraic-expression","display_name":"Algebraic expression","score":0.558708667755127},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4792511463165283},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.47696956992149353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4739023745059967},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4649798572063446},{"id":"https://openalex.org/keywords/modularity","display_name":"Modularity (biology)","score":0.45615071058273315},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44602125883102417},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.43040239810943604},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.4144701659679413},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34201374650001526},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28426602482795715},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11855709552764893}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.6670288443565369},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6188415884971619},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5814792513847351},{"id":"https://openalex.org/C18912844","wikidata":"https://www.wikidata.org/wiki/Q4724001","display_name":"Algebraic expression","level":3,"score":0.558708667755127},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4792511463165283},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.47696956992149353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4739023745059967},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4649798572063446},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.45615071058273315},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44602125883102417},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43040239810943604},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4144701659679413},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34201374650001526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28426602482795715},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11855709552764893},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11786-011-0086-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11786-011-0086-1","pdf_url":null,"source":{"id":"https://openalex.org/S136038430","display_name":"Mathematics in Computer Science","issn_l":"1661-8270","issn":["1661-8270","1661-8289"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W85593233","https://openalex.org/W200176247","https://openalex.org/W605824955","https://openalex.org/W1486644300","https://openalex.org/W1501243125","https://openalex.org/W1567903304","https://openalex.org/W1649645444","https://openalex.org/W1941717577","https://openalex.org/W1968165559","https://openalex.org/W1978491945","https://openalex.org/W1981663184","https://openalex.org/W1986624837","https://openalex.org/W2012369998","https://openalex.org/W2012407419","https://openalex.org/W2020273787","https://openalex.org/W2041921428","https://openalex.org/W2043552663","https://openalex.org/W2104320999","https://openalex.org/W2110837821","https://openalex.org/W2119352997","https://openalex.org/W2134277629","https://openalex.org/W2139230981","https://openalex.org/W2161041230","https://openalex.org/W2609774945","https://openalex.org/W2752853835","https://openalex.org/W4285719527","https://openalex.org/W6669417358"],"related_works":["https://openalex.org/W2029407284","https://openalex.org/W1993884761","https://openalex.org/W2014542312","https://openalex.org/W2000405793","https://openalex.org/W2128184135","https://openalex.org/W1484338948","https://openalex.org/W3143745619","https://openalex.org/W2162177141","https://openalex.org/W2131297762","https://openalex.org/W3044739336"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
