{"id":"https://openalex.org/W4409037680","doi":"https://doi.org/10.1007/s00200-025-00684-8","title":"A new iterative algorithm for comprehensive Gr\u00f6bner systems","display_name":"A new iterative algorithm for comprehensive Gr\u00f6bner systems","publication_year":2025,"publication_date":"2025-03-31","ids":{"openalex":"https://openalex.org/W4409037680","doi":"https://doi.org/10.1007/s00200-025-00684-8"},"language":"en","primary_location":{"id":"doi:10.1007/s00200-025-00684-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-025-00684-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-025-00684-8.pdf","source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"Applicable Algebra in Engineering, Communication and Computing","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/s00200-025-00684-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024806913","display_name":"Anna Maria Bigatti","orcid":"https://orcid.org/0000-0002-2987-9333"},"institutions":[{"id":"https://openalex.org/I83816512","display_name":"University of Genoa","ror":"https://ror.org/0107c5v14","country_code":"IT","type":"education","lineage":["https://openalex.org/I83816512"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Anna Maria Bigatti","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 degli Studi di Genova, Via Dodecaneso 35, 16146, Genova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Genova, Via Dodecaneso 35, 16146, Genova, Italy","institution_ids":["https://openalex.org/I83816512"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084024396","display_name":"Elisa Palezzato","orcid":null},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Elisa Palezzato","raw_affiliation_strings":["Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085209235","display_name":"Michele Torielli","orcid":"https://orcid.org/0000-0001-6828-4458"},"institutions":[{"id":"https://openalex.org/I203172682","display_name":"Northern Arizona University","ror":"https://ror.org/0272j5188","country_code":"US","type":"education","lineage":["https://openalex.org/I203172682"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michele Torielli","raw_affiliation_strings":["Department of Mathematics and Statistics, Northern Arizona University, 801 S. Osborne Dr., Flagstaff, AZ, 86001, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Northern Arizona University, 801 S. Osborne Dr., Flagstaff, AZ, 86001, USA","institution_ids":["https://openalex.org/I203172682"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024806913","https://openalex.org/A5084024396","https://openalex.org/A5085209235"],"corresponding_institution_ids":["https://openalex.org/I203172682","https://openalex.org/I205349734","https://openalex.org/I83816512"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04843094,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"3","first_page":"681","last_page":"694"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9976999759674072,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9950000047683716,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/mathematics","display_name":"Mathematics","score":0.7110701203346252},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6632730960845947},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5632582902908325},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4783610701560974},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38871005177497864},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.354587584733963},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1472240388393402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7110701203346252},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6632730960845947},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5632582902908325},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4783610701560974},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38871005177497864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.354587584733963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1472240388393402}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00200-025-00684-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-025-00684-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-025-00684-8.pdf","source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},{"id":"pmh:oai:iris.unige.it:11567/1245397","is_oa":false,"landing_page_url":"https://hdl.handle.net/11567/1245397","pdf_url":null,"source":{"id":"https://openalex.org/S4377196291","display_name":"CINECA IRIS Institutial Research Information System (University of Genoa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83816512","host_organization_name":"University of Genoa","host_organization_lineage":["https://openalex.org/I83816512"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00200-025-00684-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00200-025-00684-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00200-025-00684-8.pdf","source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"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":"Applicable Algebra in Engineering, Communication and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322794","display_name":"Universit\u00e0 degli Studi di Genova","ror":"https://ror.org/0107c5v14"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4409037680.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W22319829","https://openalex.org/W105797038","https://openalex.org/W2057105460","https://openalex.org/W2095764258","https://openalex.org/W2113205422","https://openalex.org/W2116273190","https://openalex.org/W2501430986","https://openalex.org/W3007626758","https://openalex.org/W3086943959"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2057289358","https://openalex.org/W2040941802","https://openalex.org/W2412311587","https://openalex.org/W4238207569","https://openalex.org/W2339251345"],"abstract_inverted_index":{"Abstract":[0],"A":[1,13,41,60,79,106],"comprehensive":[2,127],"Gr\u00f6bner":[3,22,70,84,128],"system":[4],"for":[5,49],"a":[6,83,121],"parametric":[7],"ideal":[8,55],"I":[9,27],"in":[10,29,43,57,103],"K":[11,30,44,58,104],"(":[12],")[":[14],"X":[15,32,62],"]":[16,33],"represents":[17],"the":[18,25,36,39,53,77,89,95,98,114,137],"collection":[19],"of":[20,24,38,69,72,76,86,97,100,136,155],"all":[21],"bases":[23,71],"ideals":[26,73],"\u2032":[28],"[":[31,59,105],"obtained":[34],"as":[35],"values":[37],"parameters":[40,78],"vary":[42],".":[45,80],"The":[46],"recent":[47],"algorithms":[48],"computing":[50],"them":[51],"consider":[52],"corresponding":[54],"J":[56,87],",":[61,88],"],":[63],"and":[64,142],"are":[65],"based":[66],"on":[67,94],"stability":[68],"under":[74],"specializations":[75],"Starting":[81],"from":[82,113],"basis":[85],"computation":[90,148],"splits":[91],"recursively":[92],"depending":[93],"vanishing":[96],"evaluation":[99],"some":[101,146],"\u201ccoefficients\u201d":[102],"].":[107],"In":[108],"this":[109],"paper,":[110],"taking":[111],"inspiration":[112],"algorithm":[115,124],"described":[116],"by":[117],"Nabeshima,":[118],"we":[119,133,144],"create":[120],"new":[122],"iterative":[123],"to":[125,139],"compute":[126],"systems.":[129],"We":[130],"show":[131],"how":[132,143],"keep":[134],"track":[135],"sub-cases":[138],"be":[140],"considered,":[141],"avoid":[145],"redundant":[147],"branches":[149],"using":[150],"\u201ccomparatively-cheap\u201d":[151],"ideal-membership":[152],"tests,":[153],"instead":[154],"radical-membership":[156],"tests.":[157]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
