{"id":"https://openalex.org/W2038814674","doi":"https://doi.org/10.1145/1277548.1277583","title":"Gr\u00f6bner bases with respect to several term orderings and multivariate dimension polynomials","display_name":"Gr\u00f6bner bases with respect to several term orderings and multivariate dimension polynomials","publication_year":2007,"publication_date":"2007-07-29","ids":{"openalex":"https://openalex.org/W2038814674","doi":"https://doi.org/10.1145/1277548.1277583","mag":"2038814674"},"language":"en","primary_location":{"id":"doi:10.1145/1277548.1277583","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277583","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 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/A5084284634","display_name":"Alexander Levin","orcid":"https://orcid.org/0000-0001-7066-4396"},"institutions":[{"id":"https://openalex.org/I168959743","display_name":"University of America","ror":"https://ror.org/03s0c9350","country_code":"US","type":"education","lineage":["https://openalex.org/I168959743"]},{"id":"https://openalex.org/I84470341","display_name":"Catholic University of America","ror":"https://ror.org/047yk3s18","country_code":"US","type":"education","lineage":["https://openalex.org/I84470341"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexander B. Levin","raw_affiliation_strings":["The Catholic University of America, Washington, D.C"],"affiliations":[{"raw_affiliation_string":"The Catholic University of America, Washington, D.C","institution_ids":["https://openalex.org/I168959743","https://openalex.org/I84470341"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084284634"],"corresponding_institution_ids":["https://openalex.org/I168959743","https://openalex.org/I84470341"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.13325116,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"251","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9980000257492065,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.930899977684021,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/dimension","display_name":"Dimension (graph theory)","score":0.7497072219848633},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7295383810997009},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6118214130401611},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.557456910610199},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38245832920074463},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3635665774345398},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34089523553848267},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2856375277042389},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2831653952598572},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20953980088233948},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06434237957000732}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7497072219848633},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7295383810997009},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6118214130401611},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.557456910610199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38245832920074463},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3635665774345398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34089523553848267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2856375277042389},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2831653952598572},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20953980088233948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06434237957000732},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1277548.1277583","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1277548.1277583","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2007 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/W646873552","https://openalex.org/W1561016548","https://openalex.org/W1967805950","https://openalex.org/W1968784109","https://openalex.org/W1980662086","https://openalex.org/W2003785740","https://openalex.org/W2022561942","https://openalex.org/W2024284700","https://openalex.org/W2040535738","https://openalex.org/W2056636645","https://openalex.org/W2168031759","https://openalex.org/W2312807092","https://openalex.org/W2316260859","https://openalex.org/W2489598138","https://openalex.org/W3004336097","https://openalex.org/W4246493034"],"related_works":["https://openalex.org/W2406638334","https://openalex.org/W4390961098","https://openalex.org/W42295635","https://openalex.org/W1991765889","https://openalex.org/W1973996291","https://openalex.org/W1990068454","https://openalex.org/W2472172556","https://openalex.org/W2280920478","https://openalex.org/W1570805059","https://openalex.org/W2357266745"],"abstract_inverted_index":{"Let":[0],"D":[1,37],"be":[2,33,39],"a":[3,16,21,42,55,61,84,92,99,105,121],"ring":[4,44],"of":[5,23,58,83,101,103,112,120],"Ore":[6],"polynomials":[7],"in":[8,60,87],"m":[9,14],"variables":[10,89],"x":[11],"1":[12,27],",...,x":[13,28],"over":[15],"field":[17,123],"K":[18],"and":[19,66,80,107],"let":[20],"partition":[22],"the":[24,46,52,68,78,113,117],"set":[25],"{x":[26],"m}into":[29],"p":[30,88],"disjoint":[31],"subsets":[32],"fixed,":[34],"so":[35],"that":[36,73],"can":[38],"treated":[40],"as":[41],"filtered":[43],"with":[45,51,91],"natural":[47],"p-dimensional":[48],"ltration":[49],"associated":[50,90],"partition.We":[53],"introduce":[54],"special":[56],"type":[57],"reduction":[59],"finitely":[62,93],"generated":[63,94],"free":[64],"D-module":[65],"develop":[67],"corresponding":[69],"Gr\u00f6bner":[70],"basis":[71],"technique":[72],"allows":[74],"one":[75],"to":[76],"prove":[77],"existence":[79],"find":[81],"invariants":[82],"dimension":[85,118],"polynomial":[86,106,119],"D-module.":[95],"We":[96],"also":[97],"outline":[98],"method":[100],"computation":[102],"such":[104],"obtain":[108],"an":[109],"essential":[110],"generalization":[111],"Kolchin":[114],"theorem":[115],"on":[116],"differential":[122],"extension.":[124]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}