{"id":"https://openalex.org/W4392972736","doi":"https://doi.org/10.1145/3666000.3669690","title":"Gr\u00f6bner Bases Over Polytopal Affinoid Algebras","display_name":"Gr\u00f6bner Bases Over Polytopal Affinoid Algebras","publication_year":2024,"publication_date":"2024-07-15","ids":{"openalex":"https://openalex.org/W4392972736","doi":"https://doi.org/10.1145/3666000.3669690"},"language":"en","primary_location":{"id":"doi:10.1145/3666000.3669690","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669690","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2403.13382","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105411881","display_name":"Moulay A. Barkatou","orcid":"https://orcid.org/0000-0001-9892-9448"},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Moulay Barkatou","raw_affiliation_strings":["Universit\u00e9 de Limoges, France","XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (123 avenue Albert Thomas 87060 Limoges Cedex - France)","XLIM - XLIM (123 Avenue Albert Thomas 87060 Limoges Cedex - France)"],"raw_orcid":"https://orcid.org/0000-0001-9892-9448","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Limoges, France","institution_ids":["https://openalex.org/I65806277"]},{"raw_affiliation_string":"XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (123 avenue Albert Thomas 87060 Limoges Cedex - France)","institution_ids":[]},{"raw_affiliation_string":"XLIM - XLIM (123 Avenue Albert Thomas 87060 Limoges Cedex - France)","institution_ids":["https://openalex.org/I4210093397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5094196587","display_name":"Lucas Legrand","orcid":null},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lucas Legrand","raw_affiliation_strings":["Universit\u00e9 de Limoges, France","XLIM - XLIM (123 Avenue Albert Thomas 87060 Limoges Cedex - France)","XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (123 avenue Albert Thomas 87060 Limoges Cedex - France)"],"raw_orcid":"https://orcid.org/0009-0007-5797-8228","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Limoges, France","institution_ids":["https://openalex.org/I65806277"]},{"raw_affiliation_string":"XLIM - XLIM (123 Avenue Albert Thomas 87060 Limoges Cedex - France)","institution_ids":["https://openalex.org/I4210093397"]},{"raw_affiliation_string":"XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (123 avenue Albert Thomas 87060 Limoges Cedex - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061019239","display_name":"Tristan Vaccon","orcid":"https://orcid.org/0000-0003-4208-8349"},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]},{"id":"https://openalex.org/I65806277","display_name":"Universit\u00e9 de Limoges","ror":"https://ror.org/02cp04407","country_code":"FR","type":"education","lineage":["https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tristan Vaccon","raw_affiliation_strings":["Computer Science, Universit\u00e9 de Limoges, France","XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (123 avenue Albert Thomas 87060 Limoges Cedex - France)","XLIM - XLIM (123 Avenue Albert THOMAS 87060 LIMOGES CEDEX - France)"],"raw_orcid":"https://orcid.org/0000-0003-4208-8349","affiliations":[{"raw_affiliation_string":"Computer Science, Universit\u00e9 de Limoges, France","institution_ids":["https://openalex.org/I65806277"]},{"raw_affiliation_string":"XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (123 avenue Albert Thomas 87060 Limoges Cedex - France)","institution_ids":[]},{"raw_affiliation_string":"XLIM - XLIM (123 Avenue Albert THOMAS 87060 LIMOGES CEDEX - France)","institution_ids":["https://openalex.org/I4210093397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5105411881"],"corresponding_institution_ids":["https://openalex.org/I4210093397","https://openalex.org/I65806277"],"apc_list":null,"apc_paid":null,"fwci":0.3359,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56714643,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"188","last_page":"197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9944999814033508,"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":0.9944999814033508,"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":0.9915000200271606,"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":0.980400025844574,"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/mathematics","display_name":"Mathematics","score":0.6846048831939697},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5681493282318115},{"id":"https://openalex.org/keywords/laurent-polynomial","display_name":"Laurent polynomial","score":0.553353488445282},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5095608234405518}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6846048831939697},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5681493282318115},{"id":"https://openalex.org/C106639798","wikidata":"https://www.wikidata.org/wiki/Q1701125","display_name":"Laurent polynomial","level":2,"score":0.553353488445282},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5095608234405518}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3666000.3669690","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3666000.3669690","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2403.13382","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.13382","pdf_url":"https://arxiv.org/pdf/2403.13382","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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-04510822v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04510822","pdf_url":"https://hal.science/hal-04510822v1/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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"Preprints, Working Papers, ..."}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2403.13382","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2403.13382","pdf_url":"https://arxiv.org/pdf/2403.13382","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4392972736.pdf"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1975356036","https://openalex.org/W2913325462","https://openalex.org/W2963147012","https://openalex.org/W2964048859","https://openalex.org/W3177984113","https://openalex.org/W4221157043","https://openalex.org/W4401534979"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Polyhedral":[0],"affinoid":[1,38],"algebras":[2,39,52],"have":[3],"been":[4],"introduced":[5],"by":[6],"Einsiedler,":[7],"Kapranov":[8],"and":[9,23,55],"Lind":[10],"in":[11],"[5]":[12],"to":[13],"connect":[14],"rigid":[15],"analytic":[16],"geometry":[17,19],"(analytic":[18],"over":[20],"non-archimedean":[21],"fields)":[22],"tropical":[24],"geometry.":[25],"In":[26],"this":[27],"article,":[28],"we":[29],"present":[30],"a":[31],"theory":[32,46,59],"of":[33,47,53,60,66],"Gr\u00f6bner":[34,48,61],"bases":[35,49,62],"for":[36],"polytopal":[37],"that":[40],"extends":[41],"both":[42],"Caruso":[43],"et":[44,57],"al.\u2019s":[45,58],"on":[50,63],"Tate":[51],"[1]":[54],"Pauer":[56],"Laurent":[64],"polynomials":[65],"[9].":[67]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-10-10T00:00:00"}
