{"id":"https://openalex.org/W2149997044","doi":"https://doi.org/10.1145/1837934.1837963","title":"Decomposition of generic multivariate polynomials","display_name":"Decomposition of generic multivariate polynomials","publication_year":2010,"publication_date":"2010-07-25","ids":{"openalex":"https://openalex.org/W2149997044","doi":"https://doi.org/10.1145/1837934.1837963","mag":"2149997044"},"language":"en","primary_location":{"id":"doi:10.1145/1837934.1837963","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837963","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","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/A5107405594","display_name":"Jean\u2010Charles Faug\u00e8re","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Charles Faug\u00e8re","raw_affiliation_strings":["SALSA Project INRIA Paris-Rocquencourt, UPMC, Univ Paris, Paris, Cedex"],"affiliations":[{"raw_affiliation_string":"SALSA Project INRIA Paris-Rocquencourt, UPMC, Univ Paris, Paris, Cedex","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111464444","display_name":"Joachim von zur Gathen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joachim von zur Gathen","raw_affiliation_strings":["B-IT, Universit\u00e4t Bonn, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"B-IT, Universit\u00e4t Bonn, Bonn, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109009110","display_name":"Ludovic Perret","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ludovic Perret","raw_affiliation_strings":["SALSA Project INRIA Paris-Rocquencourt, UPMC, Univ Paris, Paris, Cedex"],"affiliations":[{"raw_affiliation_string":"SALSA Project INRIA Paris-Rocquencourt, UPMC, Univ Paris, Paris, Cedex","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5107405594"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":1.7085,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85097096,"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":"131","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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/T11435","display_name":"Polynomial and algebraic computation","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/T11130","display_name":"Coding theory and cryptography","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9929999709129333,"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/uniqueness","display_name":"Uniqueness","score":0.7968937158584595},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7708683013916016},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.7173613905906677},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6761936545372009},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6649507284164429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6537497639656067},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5308818817138672},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4770725965499878},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44171416759490967},{"id":"https://openalex.org/keywords/composition","display_name":"Composition (language)","score":0.4114935100078583},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2775397002696991},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1574864387512207},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11580681800842285},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08095064759254456},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06519296765327454}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7968937158584595},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7708683013916016},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7173613905906677},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6761936545372009},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6649507284164429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6537497639656067},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5308818817138672},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4770725965499878},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44171416759490967},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.4114935100078583},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2775397002696991},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1574864387512207},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11580681800842285},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08095064759254456},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06519296765327454},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1837934.1837963","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1837934.1837963","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.182.7000","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.7000","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-calfor.lip6.fr/%7Ejcf/Papers/ISSAC_FGP_2010.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.8618","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.8618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-salsa.lip6.fr/%7Ejcf/Papers/ISSAC_FGP_2010.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01292620v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01292620","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC 2010 - 35th International Symposium on Symbolic and Algebraic Computation, Jul 2010, Munich, Germany. pp.131-137, &#x27E8;10.1145/1837934.1837963&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W135409917","https://openalex.org/W1481263923","https://openalex.org/W1518341038","https://openalex.org/W1564055510","https://openalex.org/W1573673207","https://openalex.org/W1911562251","https://openalex.org/W1986983950","https://openalex.org/W1987872599","https://openalex.org/W1988660762","https://openalex.org/W2002352305","https://openalex.org/W2016652508","https://openalex.org/W2022942044","https://openalex.org/W2029317328","https://openalex.org/W2034193857","https://openalex.org/W2038345254","https://openalex.org/W2063911803","https://openalex.org/W2063927631","https://openalex.org/W2077725083","https://openalex.org/W2087154100","https://openalex.org/W2087404473","https://openalex.org/W2097120215","https://openalex.org/W2112271215","https://openalex.org/W2113186437","https://openalex.org/W2116765137","https://openalex.org/W2131218687","https://openalex.org/W2140702311","https://openalex.org/W2163155542","https://openalex.org/W2165225265","https://openalex.org/W2809815422","https://openalex.org/W2955705967","https://openalex.org/W4238858352","https://openalex.org/W6659228947","https://openalex.org/W6683831528"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2372627074"],"abstract_inverted_index":{"We":[0,79],"consider":[1],"the":[2,68,71,82,92,108,122],"composition":[3],"f":[4],"=":[5,11,15,43,50],"g\u25e6h":[6],"of":[7,17,62,70,110,112,126,139],"two":[8],"systems":[9],"g":[10,27],"(g0,...,gt)":[12],"and":[13,41,101,106],"h":[14],"(h0,...,hs)":[16],"homogeneous":[18],"multivariate":[19,128],"polynomials":[20],"over":[21],"a":[22,113,127,130],"field":[23],"K,":[24],"where":[25,95],"each":[26,34],"j":[28],"\u2208":[29,36,45],"K[y0,...,ys]":[30],"has":[31,38,47],"degree":[32,39,48],"\u2113,":[33],"hk":[35],"K[x0,...,xr]":[37,46],"m,":[40,53],"fi":[42],"gi(h0,...,hs)":[44],"n":[49],"\u2113":[51,96],"\u2219":[52],"for":[54,86],"0":[55],"\u2264":[56,58],"i":[57],"t.":[59],"The":[60,117],"motivation":[61],"this":[63,135],"paper":[64],"is":[65,97,103,119,138],"to":[66],"investigate":[67,107],"behavior":[69],"decomposition":[72],"algorithm":[73,83],"Multi-ComPoly":[74],"proposed":[75],"at":[76],"ISSAC\u201909":[77],"[18].":[78],"prove":[80],"that":[81],"works":[84],"correctly":[85],"generic":[87,114],"decomposable":[88,115],"instances":[89],"\u2013":[90,105],"in":[91,134],"special":[93],"cases":[94],"2":[98,104],"or":[99],"3,":[100],"m":[102],"issue":[109],"uniqueness":[111,118],"instance.":[116],"defined":[120],"w.r.t.":[121],"\u201cnormal":[123],"form":[124],"&amp;quot;":[125],"decomposition,":[129],"new":[131],"notion":[132],"introduced":[133],"paper,":[136],"which":[137],"independent":[140],"interest.":[141]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
