{"id":"https://openalex.org/W1986347052","doi":"https://doi.org/10.1080/10586458.1994.10504290","title":"A Practical Version of the Generalized Lagrange Algorithm","display_name":"A Practical Version of the Generalized Lagrange Algorithm","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W1986347052","doi":"https://doi.org/10.1080/10586458.1994.10504290","mag":"1986347052"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.1994.10504290","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1994.10504290","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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/A5058021952","display_name":"Johannes Buchmann","orcid":"https://orcid.org/0000-0001-8995-3446"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Johannes Buchmann","raw_affiliation_strings":["Universit\u00e4t des Saarlandes, FB-14 Informatik , 66041 , Saarbr\u00fccken , Germany E-mail: buchmann@cs.uni-sb.de"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t des Saarlandes, FB-14 Informatik , 66041 , Saarbr\u00fccken , Germany E-mail: buchmann@cs.uni-sb.de","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5098284935","display_name":"Max l\u00fcntgen","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Max l\u00fcntgen","raw_affiliation_strings":["Fachbereich 3 Mathematik MA 8-1, Technische Universit\u00e4t Berlin , Stra\u00dfe des 17. Juni 136, 10623 , Berlin , Germany E-mail: juentgen@math.tu-berlin.de"],"affiliations":[{"raw_affiliation_string":"Fachbereich 3 Mathematik MA 8-1, Technische Universit\u00e4t Berlin , Stra\u00dfe des 17. Juni 136, 10623 , Berlin , Germany E-mail: juentgen@math.tu-berlin.de","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040566925","display_name":"Michael Pohst","orcid":"https://orcid.org/0000-0002-1691-2675"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Pohst","raw_affiliation_strings":["Fachbereich 3 Mathematik MA 8-1, Technische Universit\u00e4t Berlin , Stra\u00dfe des 17. Juni 136, 10623 , Berlin , Germany E-mail: pohst@math.tu-berlin.de"],"affiliations":[{"raw_affiliation_string":"Fachbereich 3 Mathematik MA 8-1, Technische Universit\u00e4t Berlin , Stra\u00dfe des 17. Juni 136, 10623 , Berlin , Germany E-mail: pohst@math.tu-berlin.de","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058021952"],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.09466303,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":"3","first_page":"199","last_page":"207"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9988999962806702,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7372187376022339},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.6983720064163208},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.6879389882087708},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6047452092170715},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5559263825416565},{"id":"https://openalex.org/keywords/constraint-algorithm","display_name":"Constraint algorithm","score":0.5288661122322083},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.46064049005508423},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4269344210624695},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.2751502990722656},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1815912425518036},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1481766402721405},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.14495420455932617},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12499591708183289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10669910907745361}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7372187376022339},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.6983720064163208},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.6879389882087708},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6047452092170715},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5559263825416565},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.5288661122322083},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.46064049005508423},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4269344210624695},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.2751502990722656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1815912425518036},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1481766402721405},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.14495420455932617},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12499591708183289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10669910907745361}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.1994.10504290","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1994.10504290","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1048515871","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1048515871","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.56.4700","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.4700","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.expmath.com/restricted/3/3.3/buchmann.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1527643685","https://openalex.org/W1587781051","https://openalex.org/W1966914095","https://openalex.org/W1984127541","https://openalex.org/W2009132957","https://openalex.org/W2025038814","https://openalex.org/W2054849631","https://openalex.org/W4247463614","https://openalex.org/W6810039783"],"related_works":["https://openalex.org/W3213823732","https://openalex.org/W4212963951","https://openalex.org/W4286859198","https://openalex.org/W2724248644","https://openalex.org/W2041669931","https://openalex.org/W2122542404","https://openalex.org/W2980799738","https://openalex.org/W2023206789","https://openalex.org/W2570358410","https://openalex.org/W4288092579"],"abstract_inverted_index":{"We":[0,37],"describe":[1],"an":[2,40],"implementation":[3],"of":[4,23,33],"the":[5,24],"generalized":[6],"Lagrange":[7],"algorithm":[8],"for":[9],"computing":[10],"units":[11],"in":[12],"algebraic":[13],"number":[14],"fields":[15,32],"[Buchmann":[16],"1987a],":[17],"together":[18],"with":[19,43],"extensive":[20],"experimental":[21,45],"data":[22],"algorithm's":[25],"application":[26],"(to":[27],"all":[28],"totally":[29],"real":[30],"quartic":[31],"discriminant":[34],"below":[35],"60000).":[36],"also":[38],"present":[39],"improved":[41],"algorithm,":[42],"related":[44],"data.":[46]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}