{"id":"https://openalex.org/W2047896452","doi":"https://doi.org/10.1090/s0025-5718-07-02010-8","title":"Square form factorization","display_name":"Square form factorization","publication_year":2007,"publication_date":"2007-10-29","ids":{"openalex":"https://openalex.org/W2047896452","doi":"https://doi.org/10.1090/s0025-5718-07-02010-8","mag":"2047896452"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-07-02010-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-02010-8","pdf_url":"https://www.ams.org/mcom/2008-77-261/S0025-5718-07-02010-8/S0025-5718-07-02010-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2008-77-261/S0025-5718-07-02010-8/S0025-5718-07-02010-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062414717","display_name":"Jason E. Gower","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jason E. Gower","raw_affiliation_strings":["Institute for Mathematics and its Applications, University of Minnesota, 424 Lind Hall, 207 Church St. S.E., Minneapolis, Minnesota 55455-0436"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics and its Applications, University of Minnesota, 424 Lind Hall, 207 Church St. S.E., Minneapolis, Minnesota 55455-0436","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065022787","display_name":"Samuel S. Wagstaff","orcid":"https://orcid.org/0000-0001-6855-784X"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel S. Wagstaff","raw_affiliation_strings":["Center for Education and Research in Information Assurance and Security, and Department of Computer Science, Purdue University, West Lafayette, Indiana 47907"],"affiliations":[{"raw_affiliation_string":"Center for Education and Research in Information Assurance and Security, and Department of Computer Science, Purdue University, West Lafayette, Indiana 47907","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062414717"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":null,"apc_paid":null,"fwci":2.9886,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.90722394,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"77","issue":"261","first_page":"551","last_page":"588"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9934999942779541,"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":0.9934999942779541,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.991100013256073,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.989799976348877,"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/mathematics","display_name":"Mathematics","score":0.8920799493789673},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.6112861037254333},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5327962040901184},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18948227167129517},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14129483699798584}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8920799493789673},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6112861037254333},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5327962040901184},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18948227167129517},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14129483699798584}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-07-02010-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-02010-8","pdf_url":"https://www.ams.org/mcom/2008-77-261/S0025-5718-07-02010-8/S0025-5718-07-02010-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:docs.lib.purdue.edu:dissertations-5414","is_oa":false,"landing_page_url":"https://docs.lib.purdue.edu/dissertations/AAI3166624","pdf_url":null,"source":{"id":"https://openalex.org/S4377196310","display_name":"Purdue e-Pubs (Purdue University System)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801333002","host_organization_name":"Purdue University System","host_organization_lineage":["https://openalex.org/I2801333002"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theses and Dissertations Available from ProQuest","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.5907","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.5907","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2008-77-261/S0025-5718-07-02010-8/S0025-5718-07-02010-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.159.383","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.383","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cerias.purdue.edu/ssl/techreports-ssl/S0025-5718-07-02010-8.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-07-02010-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-02010-8","pdf_url":"https://www.ams.org/mcom/2008-77-261/S0025-5718-07-02010-8/S0025-5718-07-02010-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320307758","display_name":"Eli Lilly and Company","ror":"https://ror.org/01qat3289"},{"id":"https://openalex.org/F4320309036","display_name":"Purdue University","ror":"https://ror.org/02dqehb95"},{"id":"https://openalex.org/F4320309409","display_name":"Lilly Endowment","ror":"https://ror.org/00cpsd622"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2047896452.pdf","grobid_xml":"https://content.openalex.org/works/W2047896452.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1501162952","https://openalex.org/W1536498428","https://openalex.org/W1596400416","https://openalex.org/W1606822455","https://openalex.org/W1988524997","https://openalex.org/W2015669348","https://openalex.org/W2044150726","https://openalex.org/W2047896452","https://openalex.org/W2049742719","https://openalex.org/W2057182494","https://openalex.org/W2184036715","https://openalex.org/W2487302930","https://openalex.org/W3038928148","https://openalex.org/W3157578321","https://openalex.org/W4245046265","https://openalex.org/W4296300736"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0,13,23],"present":[1],"a":[2,32],"detailed":[3],"analysis":[4],"of":[5,27],"SQUFOF,":[6],"Daniel":[7],"Shanks\u00e2\u0080\u0099":[8],"Square":[9],"Form":[10],"Factorization":[11],"algorithm.":[12],"give":[14],"the":[15,25,38],"average":[16],"time":[17],"and":[18],"space":[19],"requirements":[20],"for":[21,31],"SQUFOF.":[22],"analyze":[24],"effect":[26],"multipliers,":[28],"either":[29],"used":[30],"single":[33],"factorization":[34],"or":[35],"when":[36],"racing":[37],"algorithm":[39],"in":[40],"parallel.":[41]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}