{"id":"https://openalex.org/W2958818648","doi":"https://doi.org/10.1145/3326229.3326279","title":"Linear Algebra for Zero-Dimensional Ideals","display_name":"Linear Algebra for Zero-Dimensional Ideals","publication_year":2019,"publication_date":"2019-07-08","ids":{"openalex":"https://openalex.org/W2958818648","doi":"https://doi.org/10.1145/3326229.3326279","mag":"2958818648"},"language":"en","primary_location":{"id":"doi:10.1145/3326229.3326279","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326279","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"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":["Universit\u00e0 degli Studi di Genova, Genova, Italy"],"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Genova, Genova, Italy","institution_ids":["https://openalex.org/I83816512"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024806913"],"corresponding_institution_ids":["https://openalex.org/I83816512"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10738055,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"21","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":1.0,"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":1.0,"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":0.9987999796867371,"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":0.9898999929428101,"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/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.8872330188751221},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.6744130849838257},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6669678688049316},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6488021612167358},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6046745777130127},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5991274118423462},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.544161319732666},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5275915265083313},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5116463303565979},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.506414532661438},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.44962790608406067},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43676093220710754},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.43511563539505005},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3521134853363037},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30695194005966187},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29630038142204285}],"concepts":[{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.8872330188751221},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.6744130849838257},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6669678688049316},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6488021612167358},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6046745777130127},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5991274118423462},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.544161319732666},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5275915265083313},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5116463303565979},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.506414532661438},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.44962790608406067},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43676093220710754},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.43511563539505005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3521134853363037},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30695194005966187},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29630038142204285},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3326229.3326279","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3326229.3326279","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:iris.unige.it:11567/965914","is_oa":false,"landing_page_url":"http://hdl.handle.net/11567/965914","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/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1550054248","https://openalex.org/W1712148379","https://openalex.org/W1968235836","https://openalex.org/W1968970774","https://openalex.org/W1974915343","https://openalex.org/W1982098398","https://openalex.org/W1982662469","https://openalex.org/W1989618424","https://openalex.org/W1991262648","https://openalex.org/W1991925681","https://openalex.org/W2017337676","https://openalex.org/W2050795120","https://openalex.org/W2056285518","https://openalex.org/W2059522106","https://openalex.org/W2077725083","https://openalex.org/W2079751279","https://openalex.org/W2092680457","https://openalex.org/W2094386737","https://openalex.org/W2099330996","https://openalex.org/W2157817077","https://openalex.org/W2314453479","https://openalex.org/W2511652683","https://openalex.org/W2592131065","https://openalex.org/W2778697438","https://openalex.org/W2808846210","https://openalex.org/W2963365858","https://openalex.org/W4238858352","https://openalex.org/W4298289021"],"related_works":["https://openalex.org/W2059826422","https://openalex.org/W2804213583","https://openalex.org/W3162124064","https://openalex.org/W2953857700","https://openalex.org/W2891690413","https://openalex.org/W2254275720","https://openalex.org/W1605709614","https://openalex.org/W2020888864","https://openalex.org/W2024795639","https://openalex.org/W2953113706"],"abstract_inverted_index":{"Given":[0],"a":[1,6,20,45,90,96,101,133],"zero-dimensional":[2,78],"ideal":[3,108],"I":[4],"in":[5,35,143],"polynomial":[7,31],"ring,":[8],"many":[9],"algorithms":[10,56,70],"start":[11,116],"by":[12,18],"finding":[13],"univariate":[14],"polynomials":[15,110],"in~I,":[16],"or":[17],"computing":[19,58,72],"lex-Groebner":[21],"basis":[22],"of~I.":[23],"These":[24],"are":[25],"related":[26],"to":[27],"considering":[28],"the":[29,107,118,137],"minimal":[30,59],"of":[32,62,77,92,104,109],"an":[33],"element":[34],"P/I,":[36],"which":[37,111],"may":[38],"be":[39,130],"computed":[40],"using":[41],"Linear":[42],"Algebra":[43],"from":[44,117],"Groebner":[46],"Basis":[47],"(for":[48],"any":[49],"term-ordering).":[50],"In":[51],"this":[52,128],"tutorial":[53],"we'll":[54],"see":[55],"for":[57,71,82],"polynomials,":[60],"applications":[61],"modular":[63],"methods,":[64],"and":[65,74,80,85,122,140],"then":[66],"some":[67,125],"applications,":[68],"namely":[69],"radicals":[73],"primary":[75],"decompositions":[76],"ideals,":[79],"also":[81,88],"testing":[83],"radicality":[84],"maximality.":[86],"We'll":[87],"address":[89],"kind":[91],"opposite":[93],"problem:":[94],"given":[95],"\"geometrical":[97],"description'',":[98],"such":[99],"as":[100],"finite":[102],"set":[103],"points,":[105],"find":[106],"vanish":[112],"at":[113],"it.":[114],"We":[115],"original":[119],"Buchberger-Moeller":[120],"algorithm,":[121],"we":[123],"show":[124],"developments.":[126],"All":[127],"will":[129],"done":[131],"with":[132,141],"special":[134],"eye":[135],"on":[136],"practical":[138],"implementations,":[139],"demostrations":[142],"CoCoA.":[144]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}