{"id":"https://openalex.org/W2914306439","doi":"https://doi.org/10.1145/3326229.3326248","title":"Gr\u00f6bner Basis over Semigroup Algebras","display_name":"Gr\u00f6bner Basis over Semigroup Algebras","publication_year":2019,"publication_date":"2019-07-08","ids":{"openalex":"https://openalex.org/W2914306439","doi":"https://doi.org/10.1145/3326229.3326248","mag":"2914306439"},"language":"en","primary_location":{"id":"doi:10.1145/3326229.3326248","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326248","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1902.00208","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005945415","display_name":"Mat\u00edas R. Bender","orcid":"https://orcid.org/0000-0001-9341-287X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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":"Mat\u00edas R. Bender","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, INRIA, Paris, France"],"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, INRIA, Paris, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107405594","display_name":"Jean\u2010Charles Faug\u00e8re","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"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":"Jean-Charles Faug\u00e8re","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, INRIA, Paris, France"],"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, INRIA, Paris, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002548887","display_name":"Elias Tsigaridas","orcid":"https://orcid.org/0009-0003-5015-3988"},"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"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Elias Tsigaridas","raw_affiliation_strings":["Sorbonne Universit\u00e9, CNRS, INRIA, Paris, France"],"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, CNRS, INRIA, Paris, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005945415"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I39804081"],"apc_list":null,"apc_paid":null,"fwci":1.07097258,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77011097,"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":"42","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9980999827384949,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9927999973297119,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6368644833564758},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6133564114570618},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5475630760192871},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5274631977081299},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5049434304237366},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.49885106086730957},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.44003283977508545},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4326028823852539},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.42229244112968445},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35509541630744934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3541490137577057},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21020099520683289}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6368644833564758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6133564114570618},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5475630760192871},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5274631977081299},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5049434304237366},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.49885106086730957},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.44003283977508545},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4326028823852539},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.42229244112968445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35509541630744934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3541490137577057},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21020099520683289},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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":4,"locations":[{"id":"doi:10.1145/3326229.3326248","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326248","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1902.00208","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.00208","pdf_url":"https://arxiv.org/pdf/1902.00208","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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02002689v2","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-02002689","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC 2019 - 44th International Symposium on Symbolic and Algebraic Computation, Jul 2019, Beijing, China. pp.42-49, &#x27E8;10.1145/3326229.3326248&#x27E9;","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.1902.00208","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1902.00208","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1902.00208","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.00208","pdf_url":"https://arxiv.org/pdf/1902.00208","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5386038833","display_name":null,"funder_award_id":"ANR JCJC GALOP (ANR-17- CE40-0009)","funder_id":"https://openalex.org/F4320325505","funder_display_name":"Agence Nationale pour le D\u00e9veloppement de la Recherche Universitaire"}],"funders":[{"id":"https://openalex.org/F4320325505","display_name":"Agence Nationale pour le D\u00e9veloppement de la Recherche Universitaire","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W17081737","https://openalex.org/W217710249","https://openalex.org/W382720801","https://openalex.org/W1495410784","https://openalex.org/W1512237513","https://openalex.org/W1537258143","https://openalex.org/W1586660875","https://openalex.org/W1930933668","https://openalex.org/W1976673195","https://openalex.org/W1977415556","https://openalex.org/W1988821632","https://openalex.org/W1989690103","https://openalex.org/W1989923040","https://openalex.org/W1995786326","https://openalex.org/W2017643152","https://openalex.org/W2034471690","https://openalex.org/W2034955763","https://openalex.org/W2038345254","https://openalex.org/W2059522106","https://openalex.org/W2064751579","https://openalex.org/W2081659888","https://openalex.org/W2085482277","https://openalex.org/W2140863255","https://openalex.org/W2295465424","https://openalex.org/W2475486651","https://openalex.org/W2769857238","https://openalex.org/W2799913292","https://openalex.org/W2893452648","https://openalex.org/W2962892663","https://openalex.org/W2962928298","https://openalex.org/W2963059192","https://openalex.org/W2963833429","https://openalex.org/W3098862099","https://openalex.org/W3102759601","https://openalex.org/W3105833047","https://openalex.org/W3106350071","https://openalex.org/W4205502224","https://openalex.org/W4206077821"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W1605162252","https://openalex.org/W2138135391","https://openalex.org/W2055878129","https://openalex.org/W2138496493","https://openalex.org/W2686471609","https://openalex.org/W2015689303","https://openalex.org/W2230441834","https://openalex.org/W3026223998","https://openalex.org/W109420984"],"abstract_inverted_index":{"Gr{\u00f6}bner":[0,93,154],"bases":[1,94],"is":[2,14,81,125],"one":[3],"the":[4,27,35,37,68,84,101,109,113,117,120,126,132,157,166,172,176],"most":[5,33],"powerful":[6],"tools":[7],"in":[8,26,32,53,86,112,156],"algorithmic":[9],"non-linear":[10],"algebra.":[11,97],"Their":[12],"computation":[13],"an":[15],"intrinsically":[16],"hard":[17],"problem":[18],"with":[19],"a":[20,72,87],"complexity":[21,170],"at":[22],"least":[23],"single":[24],"exponential":[25],"number":[28],"of":[29,34,46,171],"variables.":[30],"However,":[31],"cases,":[36],"polynomial":[38],"systems":[39,66,85,164],"coming":[40],"from":[41,108],"applications":[42],"have":[43,71,119],"some":[44],"kind":[45],"structure.":[47],"For":[48],"example":[49],",":[50,59],"several":[51],"problems":[52],"computer-aided":[54],"design,":[55],"robotics,":[56],"vision,":[57],"biology":[58],"kinematics,":[60],"cryptography,":[61],"and":[62,90,160],"optimization":[63],"involve":[64],"sparse":[65,162],"where":[67,115],"input":[69],"polynomials":[70,118,163],"few":[73],"non-zero":[74],"terms.":[75],"Our":[76],"approach":[77,106],"to":[78,82,91,99,152],"exploit":[79],"sparsity":[80,110,122],"embed":[83],"semigroup":[88],"algebra":[89,159],"compute":[92,153],"over":[95,165],"this":[96,105,137,150],"Up":[98],"now,":[100],"algorithms":[102],"that":[103,124,135],"follow":[104],"benefit":[107],"only":[111],"case":[114],"all":[116],"same":[121,127],"structure,":[123],"Newton":[128,177],"polytope.":[129],"We":[130],"introduce":[131],"first":[133],"algorithm":[134,151,173],"overcomes":[136],"restriction.":[138],"Under":[139],"regularity":[140],"assumptions,":[141],"it":[142],"performs":[143],"no":[144],"redundant":[145],"computations.":[146],"Further,":[147],"we":[148],"extend":[149],"basis":[155],"standard":[158],"solve":[161],"torus":[167],"$(C*)^n$.":[168],"The":[169],"depends":[174],"on":[175],"polytopes.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2019-02-21T00:00:00"}
