{"id":"https://openalex.org/W3010509178","doi":"https://doi.org/10.1145/3373207.3404052","title":"Computation of free non-commutative gr\u00f6bner bases over Z with Singular:Letterplace","display_name":"Computation of free non-commutative gr\u00f6bner bases over Z with Singular:Letterplace","publication_year":2020,"publication_date":"2020-07-20","ids":{"openalex":"https://openalex.org/W3010509178","doi":"https://doi.org/10.1145/3373207.3404052","mag":"3010509178"},"language":"en","primary_location":{"id":"doi:10.1145/3373207.3404052","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404052","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02496535/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059697607","display_name":"Viktor Levandovskyy","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Viktor Levandovskyy","raw_affiliation_strings":["Aachen University, Aachen, Germany","Institute for Industrial Management [RWTH Aachen University]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aachen University, Aachen, Germany","institution_ids":[]},{"raw_affiliation_string":"Institute for Industrial Management [RWTH Aachen University]","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068976904","display_name":"Tobias Metzlaff","orcid":"https://orcid.org/0000-0002-0688-7074"},"institutions":[{"id":"https://openalex.org/I4210150884","display_name":"Fondation Sophia Antipolis","ror":"https://ror.org/05nkcfv27","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210150884"]},{"id":"https://openalex.org/I4210146074","display_name":"Analyse, G\u00e9om\u00e9trie et Mod\u00e9lisation","ror":"https://ror.org/03qgt2624","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210142324","https://openalex.org/I4210146074"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tobias Metzlaff","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d'Azur, Sophia Antipolis, France","AlgebRe, geOmetrie, Modelisation et AlgoriTHmes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d'Azur, Sophia Antipolis, France","institution_ids":["https://openalex.org/I4210150884","https://openalex.org/I201841394"]},{"raw_affiliation_string":"AlgebRe, geOmetrie, Modelisation et AlgoriTHmes","institution_ids":["https://openalex.org/I4210146074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044241033","display_name":"Karim Abou Zeid","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Karim Abou Zeid","raw_affiliation_strings":["Aachen University, Aachen, Germany","Institute for Industrial Management [RWTH Aachen University]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aachen University, Aachen, Germany","institution_ids":[]},{"raw_affiliation_string":"Institute for Industrial Management [RWTH Aachen University]","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059697607"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":0.4374,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67731182,"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":"312","last_page":"319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9970999956130981,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/polynomial-ring","display_name":"Polynomial ring","score":0.7892500162124634},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.7830296754837036},{"id":"https://openalex.org/keywords/principal-ideal","display_name":"Principal ideal","score":0.6128311157226562},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5937553644180298},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5601844787597656},{"id":"https://openalex.org/keywords/commutative-algebra","display_name":"Commutative algebra","score":0.5578492879867554},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5559899806976318},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5358065366744995},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5335928201675415},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.48241791129112244},{"id":"https://openalex.org/keywords/associative-algebra","display_name":"Associative algebra","score":0.4730590581893921},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46270751953125},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.4445565342903137},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4133774936199188},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.4112274646759033},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.23839569091796875},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20749154686927795},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11053696274757385},{"id":"https://openalex.org/keywords/division-algebra","display_name":"Division algebra","score":0.06399476528167725}],"concepts":[{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.7892500162124634},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.7830296754837036},{"id":"https://openalex.org/C78766492","wikidata":"https://www.wikidata.org/wiki/Q44382","display_name":"Principal ideal","level":3,"score":0.6128311157226562},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5937553644180298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5601844787597656},{"id":"https://openalex.org/C78313660","wikidata":"https://www.wikidata.org/wiki/Q727659","display_name":"Commutative algebra","level":2,"score":0.5578492879867554},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5559899806976318},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5358065366744995},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5335928201675415},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.48241791129112244},{"id":"https://openalex.org/C51292594","wikidata":"https://www.wikidata.org/wiki/Q744960","display_name":"Associative algebra","level":5,"score":0.4730590581893921},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46270751953125},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.4445565342903137},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4133774936199188},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.4112274646759033},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.23839569091796875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20749154686927795},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11053696274757385},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.06399476528167725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.0},{"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":3,"locations":[{"id":"doi:10.1145/3373207.3404052","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3373207.3404052","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:HAL:hal-02496535v2","is_oa":true,"landing_page_url":"https://hal.science/hal-02496535","pdf_url":"https://hal.science/hal-02496535/document","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 2020 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. ⟨10.1145/3373207.3404052⟩","raw_type":"Conference papers"},{"id":"pmh:oai:HAL:hal-02496535v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02496535","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":"https://hal.archives-ouvertes.fr/hal-02496535","raw_type":"info:eu-repo/semantics/other"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02496535v2","is_oa":true,"landing_page_url":"https://hal.science/hal-02496535","pdf_url":"https://hal.science/hal-02496535/document","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 2020 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. ⟨10.1145/3373207.3404052⟩","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1326879771","display_name":null,"funder_award_id":"TRR 195","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3432697646","display_name":null,"funder_award_id":"CRC/Transregio 195","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7001502250","display_name":"Polynomial Optimization, Efficiency through Moments and Algebra","funder_award_id":"813211","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7534893990","display_name":"Polynomial Optimization, Efficiency through Moments and Algebra","funder_award_id":"813211","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G7955706205","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G8548417885","display_name":null,"funder_award_id":"SFB-TRR 195","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324232","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3010509178.pdf","grobid_xml":"https://content.openalex.org/works/W3010509178.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1649405732","https://openalex.org/W1939578276","https://openalex.org/W1974915343","https://openalex.org/W1976529759","https://openalex.org/W1982125594","https://openalex.org/W2024479048","https://openalex.org/W2028679097","https://openalex.org/W2039225816","https://openalex.org/W2109805516","https://openalex.org/W2138402185","https://openalex.org/W2175098281","https://openalex.org/W2229264317","https://openalex.org/W2269221822","https://openalex.org/W2286490152","https://openalex.org/W2767133026","https://openalex.org/W2901383090","https://openalex.org/W2988075093","https://openalex.org/W3045732501","https://openalex.org/W3169608708","https://openalex.org/W4254045038","https://openalex.org/W6637815231"],"related_works":["https://openalex.org/W4312973762","https://openalex.org/W4242834385","https://openalex.org/W616357245","https://openalex.org/W2591661506","https://openalex.org/W2351503126","https://openalex.org/W2964870960","https://openalex.org/W2384848686","https://openalex.org/W175716389","https://openalex.org/W2202270624","https://openalex.org/W3010509178"],"abstract_inverted_index":{"The":[0],"extension":[1],"of":[2,22,25,47,65,92,119,133,152],"Gr\u00f6bner":[3,28,120,167],"bases":[4,31,121],"concept":[5],"from":[6],"polynomial":[7,12],"algebras":[8,54,124],"over":[9,14,55,77],"fields":[10,91],"to":[11,17,81,128,137,170],"rings":[13,15,49,68],"allows":[16,79],"tackle":[18],"numerous":[19],"applications,":[20],"both":[21],"theoretical":[23],"and":[24,29,38,50,104,125,173],"practical":[26],"importance.":[27],"Gr\u00f6bner-Shirshov":[30],"can":[32,85],"be":[33,86,138],"defined":[34],"for":[35,90,144],"various":[36],"non-commutative":[37],"even":[39],"non-associative":[40],"algebraic":[41],"structures.":[42],"We":[43,59,112,148],"study":[44],"the":[45,63,97,102,106,109,117,131,142,155],"case":[46,64],"associative":[48],"aim":[51],"at":[52],"free":[53,123],"principal":[56],"ideal":[57],"rings.":[58],"concentrate":[60],"ourselves":[61],"on":[62],"commutative":[66],"coefficient":[67],"without":[69],"zero":[70],"divisors":[71],"(i.e.":[72],"a":[73],"domain).":[74],"Even":[75,130],"working":[76],"Z":[78],"one":[80],"do":[82],"computations,":[83],"which":[84,160],"treated":[87],"as":[88],"universal":[89],"arbitrary":[93],"characteristic.":[94],"By":[95],"using":[96],"systematic":[98],"approach,":[99],"we":[100],"revisit":[101],"theory":[103],"present":[105,149],"algorithms":[107,153],"in":[108,116,154],"implementable":[110],"form.":[111],"show":[113],"drastic":[114],"differences":[115],"behavior":[118],"between":[122],"algebras,":[126],"close":[127],"commutative.":[129],"formation":[132],"critical":[134],"pairs":[135],"has":[136],"reengineered,":[139],"together":[140],"with":[141],"criteria":[143],"their":[145],"quick":[146],"discarding.":[147],"an":[150],"implementation":[151],"Singular":[156],"subsystem":[157],"called":[158],"Letterplace,":[159],"internally":[161],"uses":[162],"Letterplace":[163,166],"techniques":[164],"(and":[165],"bases),":[168],"due":[169],"La":[171],"Scala":[172],"Levandovskyy.":[174],"Interesting":[175],"examples":[176],"accompany":[177],"our":[178],"presentation.":[179]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-17T08:19:37.847499","created_date":"2025-10-10T00:00:00"}