{"id":"https://openalex.org/W4386215605","doi":"https://doi.org/10.1007/s10208-023-09619-6","title":"Implicitisation and Parameterisation in Polynomial Functors","display_name":"Implicitisation and Parameterisation in Polynomial Functors","publication_year":2023,"publication_date":"2023-08-28","ids":{"openalex":"https://openalex.org/W4386215605","doi":"https://doi.org/10.1007/s10208-023-09619-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-023-09619-6","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10208-023-09619-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09619-6.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09619-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022290429","display_name":"A. Blatter","orcid":"https://orcid.org/0000-0001-5201-4672"},"institutions":[{"id":"https://openalex.org/I118564535","display_name":"University of Bern","ror":"https://ror.org/02k7v4d05","country_code":"CH","type":"education","lineage":["https://openalex.org/I118564535"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Andreas Blatter","raw_affiliation_strings":["Mathematical Institute, University of Bern, Alpeneggstrasse 22, 3012, Bern, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Bern, Alpeneggstrasse 22, 3012, Bern, Switzerland","institution_ids":["https://openalex.org/I118564535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084270459","display_name":"Jan Draisma","orcid":"https://orcid.org/0000-0001-7248-8250"},"institutions":[{"id":"https://openalex.org/I118564535","display_name":"University of Bern","ror":"https://ror.org/02k7v4d05","country_code":"CH","type":"education","lineage":["https://openalex.org/I118564535"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["CH","NL"],"is_corresponding":true,"raw_author_name":"Jan Draisma","raw_affiliation_strings":["Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O.\u00a0Box 513, 5600MB, Eindhoven, The Netherlands","Mathematical Institute, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O.\u00a0Box 513, 5600MB, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Mathematical Institute, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland","institution_ids":["https://openalex.org/I118564535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034067558","display_name":"Emanuele Ventura","orcid":"https://orcid.org/0000-0002-6035-309X"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Emanuele Ventura","raw_affiliation_strings":["Dipartimento di Scienze Matematiche \u201cG.L. Lagrange\u201d, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy","Dipartimento di Scienze Matematiche \"G.L. Lagrange\", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze Matematiche \u201cG.L. Lagrange\u201d, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Dipartimento di Scienze Matematiche \"G.L. Lagrange\", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084270459"],"corresponding_institution_ids":["https://openalex.org/I118564535","https://openalex.org/I83019370"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18852697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"5","first_page":"1567","last_page":"1593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9972000122070312,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9965999722480774,"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/functor","display_name":"Functor","score":0.8654379844665527},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.7538954615592957},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7010371685028076},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6594151854515076},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47023481130599976},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36109432578086853},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33367031812667847},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2752227485179901},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1297312080860138}],"concepts":[{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.8654379844665527},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.7538954615592957},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7010371685028076},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6594151854515076},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47023481130599976},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36109432578086853},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33367031812667847},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2752227485179901},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1297312080860138}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-023-09619-6","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10208-023-09619-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09619-6.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10208-023-09619-6","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10208-023-09619-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09619-6.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2826706790","display_name":null,"funder_award_id":"639.033.514","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4048152890","display_name":null,"funder_award_id":"200021_191981","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4156143258","display_name":null,"funder_award_id":"200021_191981","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6721511665","display_name":null,"funder_award_id":"639.033.514","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310992","display_name":"University of Bern","ror":"https://ror.org/02k7v4d05"},{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386215605.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W641594974","https://openalex.org/W1579709540","https://openalex.org/W1592163810","https://openalex.org/W1986127216","https://openalex.org/W2042574347","https://openalex.org/W2058392834","https://openalex.org/W2066181227","https://openalex.org/W2094779019","https://openalex.org/W2164693112","https://openalex.org/W2576373567","https://openalex.org/W2786737120","https://openalex.org/W2963495298","https://openalex.org/W2963515582","https://openalex.org/W3101297335","https://openalex.org/W3164665432","https://openalex.org/W4236326203","https://openalex.org/W4240837394"],"related_works":["https://openalex.org/W2952244080","https://openalex.org/W4287907471","https://openalex.org/W2997323880","https://openalex.org/W4387294058","https://openalex.org/W3020978243","https://openalex.org/W2957364268","https://openalex.org/W2801796713","https://openalex.org/W1493617524","https://openalex.org/W4287668766","https://openalex.org/W4253982276"],"abstract_inverted_index":{"Abstract":[0],"In":[1,25,73],"earlier":[2],"work,":[3],"the":[4,54,62,110,113],"second":[5],"author":[6],"showed":[7],"that":[8,45,78,94,123,147],"a":[9,13,57,65,70,98,101,127,133,137,142],"closed":[10,51,134,148],"subset":[11,52,135],"of":[12,56,64,112,130,136],"polynomial":[14,23,71,102,138],"functor":[15,103,139],"can":[16,81],"always":[17],"be":[18,82],"defined":[19],"by":[20],"finitely":[21,106],"many":[22,107],"equations.":[24],"follow-up":[26],"work":[27],"on":[28],"$${\\text":[29],"{GL}}_\\infty":[30],"$$":[31],"<mml:math":[32,90,119],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[33,91,120],"<mml:msub>":[34],"<mml:mtext>GL</mml:mtext>":[35],"<mml:mi>\u221e</mml:mi>":[36],"</mml:msub>":[37],"</mml:math>":[38,93,122],"-varieties,":[39],"Bik\u2013Draisma\u2013Eggermont\u2013Snowden":[40],"showed,":[41],"among":[42],"other":[43],"things,":[44],"in":[46],"characteristic":[47],"zero":[48],"every":[49],"such":[50],"is":[53,61,146],"image":[55,145],"morphism":[58,99,143],"whose":[59,144],"domain":[60],"product":[63],"finite-dimensional":[66],"affine":[67],"variety":[68],"and":[69,104,115,140],"functor.":[72],"this":[74],"paper,":[75],"we":[76],"show":[77],"both":[79],"results":[80],"made":[83],"algorithmic:":[84],"there":[85],"exists":[86],"an":[87,116],"algorithm":[88,117],"$$\\textbf{implicitise}$$":[89],"<mml:mi>implicitise</mml:mi>":[92],"takes":[95,124],"as":[96,125],"input":[97,126],"into":[100],"outputs":[105,141],"equations":[108,131],"defining":[109,132],"closure":[111],"image;":[114],"$$\\textbf{parameterise}$$":[118],"<mml:mi>parameterise</mml:mi>":[121],"finite":[128],"set":[129],"subset.":[149]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
