{"id":"https://openalex.org/W2130275347","doi":"https://doi.org/10.1145/1576702.1576745","title":"Computation of inverses in residue class rings of parametric polynomial ideals","display_name":"Computation of inverses in residue class rings of parametric polynomial ideals","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W2130275347","doi":"https://doi.org/10.1145/1576702.1576745","mag":"2130275347"},"language":"en","primary_location":{"id":"doi:10.1145/1576702.1576745","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576745","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5050208307","display_name":"Yosuke Sato","orcid":"https://orcid.org/0000-0002-2772-2332"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yosuke Sato","raw_affiliation_strings":["Tokyo University of Science, Tokyo, Japan","Tokyo Univ. of Science, Tokyo, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Tokyo University of Science, Tokyo, Japan","institution_ids":["https://openalex.org/I161296585"]},{"raw_affiliation_string":"Tokyo Univ. of Science, Tokyo, Japan#TAB#","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006300612","display_name":"Akira Suzuki","orcid":"https://orcid.org/0000-0002-5950-8808"},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akira Suzuki","raw_affiliation_strings":["Kobe University, Kobe, Japan","[Kobe University, Kobe, JAPAN]"],"affiliations":[{"raw_affiliation_string":"Kobe University, Kobe, Japan","institution_ids":["https://openalex.org/I65837984"]},{"raw_affiliation_string":"[Kobe University, Kobe, JAPAN]","institution_ids":["https://openalex.org/I65837984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050208307"],"corresponding_institution_ids":["https://openalex.org/I161296585"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.20610481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"311","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9994999766349792,"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"}},{"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/T11130","display_name":"Coding theory and cryptography","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.784550130367279},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7276912927627563},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6249942779541016},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5155134201049805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4799354672431946},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.47278404235839844},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46817344427108765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43193280696868896},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.43075573444366455},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.386372447013855},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15663278102874756},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08028793334960938}],"concepts":[{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.784550130367279},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7276912927627563},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6249942779541016},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5155134201049805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4799354672431946},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.47278404235839844},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46817344427108765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43193280696868896},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.43075573444366455},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.386372447013855},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15663278102874756},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08028793334960938},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1576702.1576745","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576745","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2009 international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W3002826","https://openalex.org/W22319829","https://openalex.org/W64656188","https://openalex.org/W1481776881","https://openalex.org/W1518341038","https://openalex.org/W1576325106","https://openalex.org/W1969466615","https://openalex.org/W1990119084","https://openalex.org/W1994234357","https://openalex.org/W2036883244","https://openalex.org/W2045154989","https://openalex.org/W2078863580","https://openalex.org/W2095764258","https://openalex.org/W2168553897","https://openalex.org/W3007626758","https://openalex.org/W3102191769"],"related_works":["https://openalex.org/W2375822445","https://openalex.org/W1485944311","https://openalex.org/W2056024401","https://openalex.org/W2630947625","https://openalex.org/W4288684336","https://openalex.org/W2059565606","https://openalex.org/W3216258873","https://openalex.org/W2360979461","https://openalex.org/W2149734642","https://openalex.org/W4311251537"],"abstract_inverted_index":{"For":[0],"a":[1,10,15,20,29,72,83],"given":[2],"polynomial":[3,11,97],"f":[4,36],"and":[5,22,67],"an":[6],"ideal":[7,31,56],"I":[8,26,87],"of":[9,63,86],"ring":[12,43],"K[X]":[13],"over":[14],"field":[16],"K,":[17],"we":[18],"give":[19],"necessary":[21],"sufficient":[23],"condition":[24,47],"for":[25,96],"to":[27,52],"have":[28],"smallest":[30],"extension":[32],"J":[33,49],"such":[34,75],"that":[35,76],"is":[37,50,71],"invertible":[38],"in":[39],"the":[40,46,54,64],"residue":[41],"class":[42],"K[X]/J.":[44],"If":[45],"holds,":[48],"shown":[51],"be":[53],"saturation":[55],"I:\u221e.":[57],"We":[58],"also":[59],"show":[60],"primary":[61,84],"decompositions":[62],"ideals":[65],"I:\u221e":[66,77],"I+9fm;:,":[68],"where":[69],"m":[70],"natural":[73],"number":[74],"=":[78],"I:fm,":[79],"all":[80],"together":[81],"forms":[82],"decomposition":[85],"with":[88,99],"no":[89],"modification.":[90],"These":[91],"observations":[92],"are":[93],"especially":[94],"useful":[95],"rings":[98],"parameters.":[100]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}