{"id":"https://openalex.org/W4288080171","doi":"https://doi.org/10.1145/3373207.3404061","title":"Fast in-place algorithms for polynomial operations","display_name":"Fast in-place algorithms for polynomial operations","publication_year":2020,"publication_date":"2020-07-20","ids":{"openalex":"https://openalex.org/W4288080171","doi":"https://doi.org/10.1145/3373207.3404061"},"language":"en","primary_location":{"id":"doi:10.1145/3373207.3404061","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404061","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.10304","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064771365","display_name":"Pascal Giorgi","orcid":"https://orcid.org/0000-0002-0489-5134"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pascal Giorgi","raw_affiliation_strings":["Univ. Montpellier, Montpellier, France"],"affiliations":[{"raw_affiliation_string":"Univ. Montpellier, Montpellier, France","institution_ids":["https://openalex.org/I19894307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003590565","display_name":"Bruno Grenet","orcid":"https://orcid.org/0000-0003-2057-5429"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bruno Grenet","raw_affiliation_strings":["Univ. Montpellier, Montpellier, France"],"affiliations":[{"raw_affiliation_string":"Univ. Montpellier, Montpellier, France","institution_ids":["https://openalex.org/I19894307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029873080","display_name":"Daniel S. Roche","orcid":"https://orcid.org/0000-0003-1408-6872"},"institutions":[{"id":"https://openalex.org/I189158971","display_name":"United States Naval Academy","ror":"https://ror.org/00znex860","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I189158971","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel S. Roche","raw_affiliation_strings":["United States Naval Academy"],"affiliations":[{"raw_affiliation_string":"United States Naval Academy","institution_ids":["https://openalex.org/I189158971"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064771365"],"corresponding_institution_ids":["https://openalex.org/I19894307"],"apc_list":null,"apc_paid":null,"fwci":0.5776,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75295453,"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":"210","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9983999729156494,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9977999925613403,"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/multiplication","display_name":"Multiplication (music)","score":0.6594406962394714},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6200335621833801},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5554097890853882},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.5345268845558167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5246115922927856},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5040730237960815},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.4805788993835449},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.477520614862442},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4752102792263031},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4410395622253418},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40437883138656616},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.22479981184005737},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12575453519821167}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6594406962394714},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6200335621833801},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5554097890853882},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.5345268845558167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5246115922927856},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5040730237960815},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.4805788993835449},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.477520614862442},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4752102792263031},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4410395622253418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40437883138656616},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.22479981184005737},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12575453519821167},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3373207.3404061","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404061","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2002.10304","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.10304","pdf_url":"https://arxiv.org/pdf/2002.10304","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:lirmm-02493066v3","is_oa":true,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-02493066","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://issac-conference.org/2020/","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.10304","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.10304","pdf_url":"https://arxiv.org/pdf/2002.10304","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1596421275","https://openalex.org/W1649758727","https://openalex.org/W1983892874","https://openalex.org/W1998322533","https://openalex.org/W2002980260","https://openalex.org/W2017320189","https://openalex.org/W2055957023","https://openalex.org/W2083368929","https://openalex.org/W2084801848","https://openalex.org/W2088823599","https://openalex.org/W2095875205","https://openalex.org/W2096280747","https://openalex.org/W2121228963","https://openalex.org/W2540879644","https://openalex.org/W2918410320","https://openalex.org/W4205630623"],"related_works":["https://openalex.org/W4315487898","https://openalex.org/W2088904828","https://openalex.org/W617989196","https://openalex.org/W2032199336","https://openalex.org/W2051058708","https://openalex.org/W2904183727","https://openalex.org/W2347282152","https://openalex.org/W2140321063","https://openalex.org/W2039575089","https://openalex.org/W4385351587"],"abstract_inverted_index":{"We":[0,72,99],"consider":[1],"space-saving":[2],"versions":[3],"of":[4,53,66,118],"several":[5],"important":[6],"operations":[7],"on":[8],"univariate":[9],"polynomials,":[10],"namely":[11],"power":[12],"series":[13],"inversion":[14],"and":[15,22,88],"division,":[16],"division":[17],"with":[18],"remainder,":[19],"multi-point":[20],"evaluation,":[21],"interpolation.":[23],"Now-classical":[24],"results":[25],"show":[26],"that":[27,107],"such":[28],"problems":[29],"can":[30],"be":[31],"solved":[32],"in":[33],"(nearly)":[34],"the":[35,78,90,115,119],"same":[36,91],"asymptotic":[37,92],"time":[38,94],"as":[39,95],"fast":[40,54],"polynomial":[41,55,80],"multiplication.":[42],"However,":[43],"these":[44],"reductions,":[45],"even":[46],"when":[47],"applied":[48],"to":[49],"an":[50],"in-place":[51,75],"variant":[52],"multiplication,":[56],"yield":[57],"algorithms":[58,76],"which":[59,82],"require":[60,83],"at":[61],"least":[62],"a":[63,102],"linear":[64],"amount":[65],"extra":[67,86],"space":[68,87,116],"for":[69,77],"intermediate":[70],"results.":[71],"demonstrate":[73],"new":[74],"aforementioned":[79],"computations":[81],"only":[84],"constant":[85],"achieve":[89],"running":[93],"their":[96],"out-of-place":[97],"counterparts.":[98],"also":[100],"provide":[101],"precise":[103],"complexity":[104],"analysis":[105],"so":[106],"all":[108],"constants":[109],"are":[110],"made":[111],"explicit,":[112],"parameterized":[113],"by":[114],"usage":[117],"underlying":[120],"multiplication":[121],"algorithms.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2022-07-28T00:00:00"}