{"id":"https://openalex.org/W2891033245","doi":"https://doi.org/10.1090/mcom/3695","title":"Degree bound for toric envelope of a linear algebraic group","display_name":"Degree bound for toric envelope of a linear algebraic group","publication_year":2021,"publication_date":"2021-10-27","ids":{"openalex":"https://openalex.org/W2891033245","doi":"https://doi.org/10.1090/mcom/3695","mag":"2891033245"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3695","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3695","pdf_url":"https://www.ams.org/mcom/2022-91-335/S0025-5718-2021-03695-9/S0025-5718-2021-03695-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2022-91-335/S0025-5718-2021-03695-9/S0025-5718-2021-03695-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070142343","display_name":"Eli Amzallag","orcid":null},"institutions":[{"id":"https://openalex.org/I121847817","display_name":"The Graduate Center, CUNY","ror":"https://ror.org/00awd9g61","country_code":"US","type":"education","lineage":["https://openalex.org/I121847817"]},{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eli Amzallag","raw_affiliation_strings":["Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York 10016","Department of Mathematics, The City College of New York, New York 10031"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York 10016","institution_ids":["https://openalex.org/I121847817"]},{"raw_affiliation_string":"Department of Mathematics, The City College of New York, New York 10031","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030824619","display_name":"Andrei Minchenko","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Andrei Minchenko","raw_affiliation_strings":["Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1019 Wein, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1019 Wein, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012130065","display_name":"Gleb Pogudin","orcid":"https://orcid.org/0000-0002-5731-8242"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Gleb Pogudin","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York 10012","LIX, CNRS, \u00c3\u0089cole Polytechnique, Institute Polytechnique de Paris, 91120 Palaiseau, France","LIX, CNRS, \u00c9cole Polytechnique, Institute Polytechnique de Paris, 91120 Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York 10012","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"LIX, CNRS, \u00c3\u0089cole Polytechnique, Institute Polytechnique de Paris, 91120 Palaiseau, France","institution_ids":["https://openalex.org/I4210139461","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIX, CNRS, \u00c9cole Polytechnique, Institute Polytechnique de Paris, 91120 Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070142343"],"corresponding_institution_ids":["https://openalex.org/I121847817","https://openalex.org/I125687163"],"apc_list":null,"apc_paid":null,"fwci":0.1522,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46296167,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"91","issue":"335","first_page":"1501","last_page":"1519"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998999834060669,"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":0.9998999834060669,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9991999864578247,"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":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.7689089775085449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6958826184272766},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.652407705783844},{"id":"https://openalex.org/keywords/linear-algebraic-group","display_name":"Linear algebraic group","score":0.6262500882148743},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5375141501426697},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5359746813774109},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5212141275405884},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5112645626068115},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5056965351104736},{"id":"https://openalex.org/keywords/algebraic-variety","display_name":"Algebraic variety","score":0.47990143299102783},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.46185386180877686},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4035799503326416},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38597795367240906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1325695514678955}],"concepts":[{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.7689089775085449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6958826184272766},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.652407705783844},{"id":"https://openalex.org/C2776756444","wikidata":"https://www.wikidata.org/wiki/Q6553407","display_name":"Linear algebraic group","level":3,"score":0.6262500882148743},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5375141501426697},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5359746813774109},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5212141275405884},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5112645626068115},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5056965351104736},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.47990143299102783},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.46185386180877686},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4035799503326416},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38597795367240906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1325695514678955},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/mcom/3695","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3695","pdf_url":"https://www.ams.org/mcom/2022-91-335/S0025-5718-2021-03695-9/S0025-5718-2021-03695-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1809.06489","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.06489","pdf_url":"https://arxiv.org/pdf/1809.06489","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":"doi:10.48550/arxiv.1809.06489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1809.06489","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"},{"id":"mag:2891033245","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1090/mcom/3695","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3695","pdf_url":"https://www.ams.org/mcom/2022-91-335/S0025-5718-2021-03695-9/S0025-5718-2021-03695-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1039923406","display_name":null,"funder_award_id":"DMS-1606334","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1188443709","display_name":null,"funder_award_id":"Y464-N18","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G1238590856","display_name":null,"funder_award_id":"DMS-1760448","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1427893484","display_name":"FRG: Collaborative Research: Model Theory of Differential and Difference Equations with Applications","funder_award_id":"1760448","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1514782840","display_name":null,"funder_award_id":"DMS-1760448","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G1839766299","display_name":null,"funder_award_id":"DMS-160633","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G1883248099","display_name":null,"funder_award_id":"PSC-CUNY #60098-00 48","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G2061284171","display_name":null,"funder_award_id":"DMS-160633","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2213365449","display_name":null,"funder_award_id":"60098-00 48","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G2324219109","display_name":null,"funder_award_id":"CCF-1564132","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G2394437122","display_name":null,"funder_award_id":"PSC-CUNY 69827-00 47","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2530187076","display_name":null,"funder_award_id":"P 28079-N35","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G2899508766","display_name":null,"funder_award_id":"P 28079-N35","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G2930217972","display_name":null,"funder_award_id":"P28079-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2987393479","display_name":null,"funder_award_id":"#H98230-15-1-0245","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3162083851","display_name":null,"funder_award_id":"PSC-CUNY 69827-00 47","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3248499258","display_name":null,"funder_award_id":"CCF-1564132","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3395555127","display_name":null,"funder_award_id":"Y464-N18","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3422136410","display_name":null,"funder_award_id":"CCF-095259","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G3484574211","display_name":null,"funder_award_id":"CIRG #2248","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3578873310","display_name":null,"funder_award_id":"#H98230-15-1-0245","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G3625141657","display_name":null,"funder_award_id":"DMS-176044","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3682770940","display_name":null,"funder_award_id":"PSC-CUNY #60098-00 48","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3916089190","display_name":null,"funder_award_id":"CCF-095259","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4531350919","display_name":null,"funder_award_id":"CIRG #2248","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G4531453472","display_name":null,"funder_award_id":"CCF-1563942","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G4536607585","display_name":"Nil-affine crystallographic groups and algebraic structures","funder_award_id":"P28079","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4676549872","display_name":null,"funder_award_id":"CCF-095259","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G4797646019","display_name":null,"funder_award_id":"CCF-1563942","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4817279656","display_name":null,"funder_award_id":"1563942","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4926460422","display_name":null,"funder_award_id":"PSC-CUNY #60098-00 48","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5078897786","display_name":null,"funder_award_id":"DMS-176044","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G5194165747","display_name":null,"funder_award_id":"1564132","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5216150843","display_name":"Algebraic Theory of Differential and Functional Equations: from Foundations to Computation","funder_award_id":"1606334","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5583035079","display_name":null,"funder_award_id":"PSC-CUNY 69827-00 47","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G5657575916","display_name":null,"funder_award_id":"P28079-N35","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5729838775","display_name":null,"funder_award_id":"P 28079-N35","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5793983945","display_name":null,"funder_award_id":"Y464-N18","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G594036044","display_name":null,"funder_award_id":"P 28079-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6121083166","display_name":null,"funder_award_id":"CCF-1563942","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G61283242","display_name":null,"funder_award_id":"CCF-1563942","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6299524015","display_name":null,"funder_award_id":"CIRG #2248","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6313996474","display_name":null,"funder_award_id":"DMS-176044","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G6320400872","display_name":null,"funder_award_id":"#H98230-15-1-0245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6378149398","display_name":null,"funder_award_id":"CCF-1564132","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G6506187044","display_name":null,"funder_award_id":"DMS-160633","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G6583763962","display_name":null,"funder_award_id":"CIRG #2248","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G665297864","display_name":null,"funder_award_id":"P28079-N35","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G6865702419","display_name":null,"funder_award_id":"DMS-160633","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7006507563","display_name":null,"funder_award_id":"P28079-N35","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G7162032960","display_name":null,"funder_award_id":"PSC-CUNY #60098-00 48","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G7269483701","display_name":null,"funder_award_id":"-1564132","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7351920479","display_name":null,"funder_award_id":"CCF-1564132","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7757149258","display_name":null,"funder_award_id":"PSC-CUNY 69827-00 47","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G7930246752","display_name":null,"funder_award_id":"Y464-N18","funder_id":"https://openalex.org/F4320309102","funder_display_name":"City University of New York"},{"id":"https://openalex.org/G8316760742","display_name":null,"funder_award_id":"DMS-176044","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8835295443","display_name":null,"funder_award_id":"CCF-095259","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8975245072","display_name":null,"funder_award_id":"#H98230-15-1-0245","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309102","display_name":"City University of New York","ror":"https://ror.org/00453a208"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2891033245.pdf","grobid_xml":"https://content.openalex.org/works/W2891033245.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W29710420","https://openalex.org/W1503569487","https://openalex.org/W1516882977","https://openalex.org/W1541350594","https://openalex.org/W1560726565","https://openalex.org/W1582015855","https://openalex.org/W1666394328","https://openalex.org/W1973360680","https://openalex.org/W1975599459","https://openalex.org/W1985818610","https://openalex.org/W1993485537","https://openalex.org/W1998630682","https://openalex.org/W2035153735","https://openalex.org/W2039361498","https://openalex.org/W2039660064","https://openalex.org/W2042569408","https://openalex.org/W2052179590","https://openalex.org/W2054530509","https://openalex.org/W2058369414","https://openalex.org/W2067358142","https://openalex.org/W2067417767","https://openalex.org/W2079399401","https://openalex.org/W2084690469","https://openalex.org/W2115432992","https://openalex.org/W2154798936","https://openalex.org/W2316858811","https://openalex.org/W2478362166","https://openalex.org/W2542140666","https://openalex.org/W2752112864","https://openalex.org/W2792293721","https://openalex.org/W3103601006","https://openalex.org/W4210405807","https://openalex.org/W4248269519","https://openalex.org/W4252501836","https://openalex.org/W6677176977"],"related_works":["https://openalex.org/W2244034814","https://openalex.org/W2062435542","https://openalex.org/W2098958718","https://openalex.org/W2126875210","https://openalex.org/W3203987932","https://openalex.org/W1489238023","https://openalex.org/W2803711344","https://openalex.org/W2963548828","https://openalex.org/W2126534535","https://openalex.org/W2902302528","https://openalex.org/W1969466615","https://openalex.org/W2027966173","https://openalex.org/W2901785898","https://openalex.org/W2088922099","https://openalex.org/W2738437438","https://openalex.org/W1491431298","https://openalex.org/W3096344391","https://openalex.org/W2476472602","https://openalex.org/W2952171880","https://openalex.org/W3023736450"],"abstract_inverted_index":{"Algorithms":[0],"working":[1],"with":[2],"linear":[3,43,133],"algebraic":[4,21,36,44,142],"groups":[5],"often":[6,297],"represent":[7],"them":[8],"via":[9],"defining":[10,17],"polynomial":[11],"equations.":[12],"One":[13,118],"can":[14,91],"always":[15],"choose":[16],"equations":[18],"for":[19,96,126,217,231,258],"an":[20,35,137,233,247],"group":[22,33,45,130,184],"to":[23,139,256,265],"be":[24,92],"of":[25,31,41,119,123,131,144,189,262],"degree":[26,30,40,188,229],"at":[27],"most":[28],"the":[29,32,39,120,128,187,190,219,251,259,270],"as":[34],"variety.":[37],"However,":[38],"a":[42,132,182,227,238,266],"<inline-formula":[46,97,145,196,272],"content-type=\"math/mathml\">":[47,98,146,197,273],"<mml:math":[48,99,147,198,274],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[49,100,148,199,275],"alttext=\"upper":[50,149],"G":[51,54,150],"subset-of":[52],"upper":[53,55,61,151,157],"L":[56,152],"Subscript":[57,153],"n":[58,154],"Baseline":[59,155],"left-parenthesis":[60,156],"C":[62,158],"right-parenthesis\">":[63,159],"<mml:semantics>":[64,104,160,201,281],"<mml:mrow>":[65,105,161,282],"<mml:mi>G</mml:mi>":[66],"<mml:mo>":[67,74,166],"\u2282":[68],"</mml:mo>":[69,76,168],"<mml:msub>":[70,162],"<mml:mi>GL</mml:mi>":[71,163],"<mml:mi>n</mml:mi>":[72,106,164,202,283],"</mml:msub>":[73,165],"\u2061":[75,167],"<mml:mo":[77,80,169,172],"stretchy=\"false\">(</mml:mo>":[78,170],"<mml:mi>C</mml:mi>":[79,171],"stretchy=\"false\">)</mml:mo>":[81,173],"</mml:mrow>":[82,109,174,288],"<mml:annotation":[83,110,175,203,289],"encoding=\"application/x-tex\">G":[84],"\\subset":[85],"\\operatorname":[86],"{GL}_n(C)</mml:annotation>":[87,177],"</mml:semantics>":[88,114,178,205,294],"</mml:math>":[89,115,179,206,295],"</inline-formula>":[90,116,180,207,296],"arbitrarily":[93],"large":[94],"even":[95],"alttext=\"n":[101,276],"equals":[102,277],"1\">":[103],"<mml:mo>=</mml:mo>":[107,284],"<mml:mn>1</mml:mn>":[108],"encoding=\"application/x-tex\">n":[111,290],"=":[112,291],"1</mml:annotation>":[113],".":[117,208],"key":[121],"ingredients":[122],"Hrushovski\u2019s":[124,263],"algorithm":[125,220,264],"computing":[127],"Galois":[129],"differential":[134],"equation":[135],"was":[136],"idea":[138],"\u201capproximate\u201d":[140],"every":[141],"subgroup":[143],"encoding=\"application/x-tex\">\\operatorname":[176],"by":[181],"\u201csimilar\u201d":[183],"so":[185],"that":[186],"latter":[191],"is":[192,215,243],"bounded":[193],"uniformly":[194],"in":[195,299],"alttext=\"n\">":[200],"encoding=\"application/x-tex\">n</mml:annotation>":[204],"Making":[209],"this":[210,223],"uniform":[211],"bound":[212,230,254],"computationally":[213],"feasible":[214],"crucial":[216],"making":[218],"practical.":[221],"In":[222],"paper,":[224],"we":[225,249,301],"derive":[226],"single-exponential":[228,267],"such":[232],"approximation":[234],"(we":[235],"call":[236],"it":[237],"<italic>toric":[239],"envelope</italic>":[240],"),":[241],"which":[242],"qualitatively":[244],"optimal.":[245],"As":[246],"application,":[248],"improve":[250],"quintuply":[252],"exponential":[253],"due":[255],"Feng":[257],"first":[260],"step":[261],"bound.":[268,306],"For":[269],"cases":[271],"2":[278],"comma":[279],"3\">":[280],"<mml:mn>2</mml:mn>":[285],"<mml:mo>,</mml:mo>":[286],"<mml:mn>3</mml:mn>":[287],"2,":[292],"3</mml:annotation>":[293],"arising":[298],"practice,":[300],"further":[302],"refine":[303],"our":[304],"general":[305]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
