{"id":"https://openalex.org/W7161181947","doi":"https://doi.org/10.1145/3815436.3815473","title":"A Data Structure for Monomial Ideals with Applications to Signature Gr\u00f6bner Bases","display_name":"A Data Structure for Monomial Ideals with Applications to Signature Gr\u00f6bner Bases","publication_year":2026,"publication_date":"2026-07-09","ids":{"openalex":"https://openalex.org/W7161181947","doi":"https://doi.org/10.1145/3815436.3815473"},"language":"en","primary_location":{"id":"doi:10.1145/3815436.3815473","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3815436.3815473","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2026 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3815436.3815473","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043305689","display_name":"Pierre Lairez","orcid":"https://orcid.org/0000-0003-3756-0151"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Lairez","raw_affiliation_strings":["INRIA, Saclay, France"],"raw_orcid":"https://orcid.org/0000-0003-3756-0151","affiliations":[{"raw_affiliation_string":"INRIA, Saclay, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052034154","display_name":"Rafael Mohr","orcid":"https://orcid.org/0009-0000-9869-7122"},"institutions":[{"id":"https://openalex.org/I4210115377","display_name":"VIB-KU Leuven Center for Microbiology","ror":"https://ror.org/02bpp8r91","country_code":"BE","type":"facility","lineage":["https://openalex.org/I2802017950","https://openalex.org/I4210115377","https://openalex.org/I99464096"]},{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Rafael Mohr","raw_affiliation_strings":["Dep. of Computer Science, KU Leuven, Leuven, Belgium"],"raw_orcid":"https://orcid.org/0009-0000-9869-7122","affiliations":[{"raw_affiliation_string":"Dep. of Computer Science, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I4210115377","https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092733639","display_name":"Theo Ternier","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Th\u00e9o Ternier","raw_affiliation_strings":["INRIA, Saclay, France"],"raw_orcid":"https://orcid.org/0009-0007-7508-2863","affiliations":[{"raw_affiliation_string":"INRIA, Saclay, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.52850313,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"246","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9667999744415283,"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":0.9667999744415283,"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":0.021299999207258224,"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/T10142","display_name":"Formal Methods in Verification","score":0.003100000089034438,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.8810999989509583},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6977999806404114},{"id":"https://openalex.org/keywords/signature","display_name":"Signature (topology)","score":0.6607000231742859},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.4876999855041504},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.47040000557899475},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.4602999985218048},{"id":"https://openalex.org/keywords/canonical-form","display_name":"Canonical form","score":0.43630000948905945}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8810999989509583},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6977999806404114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6643999814987183},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.6607000231742859},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.4876999855041504},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.47040000557899475},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.4602999985218048},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.43630000948905945},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4059999883174896},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40230000019073486},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3799000084400177},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3246999979019165},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30320000648498535},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2874999940395355},{"id":"https://openalex.org/C2779954242","wikidata":"https://www.wikidata.org/wiki/Q6031227","display_name":"Information structure","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C57900377","wikidata":"https://www.wikidata.org/wiki/Q7979855","display_name":"Weight-balanced tree","level":4,"score":0.2596000134944916},{"id":"https://openalex.org/C46132437","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Monomial basis","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3815436.3815473","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3815436.3815473","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2026 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2601.05026","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2601.05026","pdf_url":"https://arxiv.org/pdf/2601.05026","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05619456v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05619456","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC 2026 -51st International Symposium on Symbolic and Algebraic Computation, Christoph Koutschan; Alin Bostan; Cl\u00e9ment Pernet; Anne Fr\u00fchbis-Kr\u00fcger; Florian Hess; Thi Xuan Vu; Ali Kemal Uncu; Arne Storjohann; Hao Du; Katsusuke Nabeshima, Jul 2026, Oldenburg, Germany. ⟨10.1145/3815436.3815473⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1145/3815436.3815473","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3815436.3815473","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2026 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,39],"introduce":[1],"monomial":[2,10,75],"divisibility":[3],"diagrams":[4],"(MDDs),":[5],"a":[6,25,35],"data":[7],"structure":[8],"for":[9,44],"ideals":[11,76],"that":[12],"supports":[13],"insertion":[14],"of":[15,53,67,88,101],"new":[16],"generators":[17,102],"and":[18,46,48,85],"fast":[19],"membership":[20,45],"tests.":[21],"MDDs":[22,60,89],"stem":[23],"from":[24],"canonical":[26],"tree":[27],"representation":[28,98],"by":[29,99],"maximally":[30],"sharing":[31],"equal":[32],"subtrees,":[33],"yielding":[34],"directed":[36],"acyclic":[37],"graph.":[38],"establish":[40],"basic":[41],"complexity":[42],"bounds":[43],"insertion,":[47],"study":[49],"empirically":[50],"the":[51,62,68,86,96],"size":[52],"MDDs.":[54],"As":[55],"an":[56],"application,":[57],"we":[58],"integrate":[59],"into":[61],"signature":[63],"Gr\u00f6bner":[64],"basis":[65],"implementation":[66],"Julia":[69],"package":[70],"AlgebraicSolving.jl.":[71],"Membership":[72],"tests":[73],"in":[74],"are":[77],"used":[78],"to":[79,83,91,95],"detect":[80],"some":[81],"reductions":[82],"zero,":[84],"use":[87],"leads":[90],"substantial":[92],"speed-ups":[93],"compared":[94],"existing":[97],"lists":[100],"with":[103],"divmasks.":[104]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2026-05-15T00:00:00"}