{"id":"https://openalex.org/W40451353","doi":"https://doi.org/10.1007/978-1-4613-9647-5_6","title":"Practical Determination of the Dimension of an Algebraic Variety","display_name":"Practical Determination of the Dimension of an Algebraic Variety","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W40451353","doi":"https://doi.org/10.1007/978-1-4613-9647-5_6","mag":"40451353"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4613-9647-5_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_6","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"},"type":"book-chapter","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/A5111902088","display_name":"Andr\u00e9 Galligo","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Andr\u00e9 Galligo","raw_affiliation_strings":["Universit\u00e9 de Nice et INRIA, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Nice et INRIA, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5098538757","display_name":"Carlo Traverso","orcid":null},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo Traverso","raw_affiliation_strings":["Universit\u00e9 di Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 di Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111902088"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":3.2431,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"46","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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":0.9994999766349792,"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":0.998199999332428,"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":0.9969000220298767,"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/hyperplane","display_name":"Hyperplane","score":0.7848877906799316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.768444299697876},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.709070086479187},{"id":"https://openalex.org/keywords/affine-variety","display_name":"Affine variety","score":0.702983021736145},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.647254467010498},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5892499685287476},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.5552583932876587},{"id":"https://openalex.org/keywords/affine-hull","display_name":"Affine hull","score":0.5418984889984131},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4623490571975708},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4534305930137634},{"id":"https://openalex.org/keywords/singular-point-of-an-algebraic-variety","display_name":"Singular point of an algebraic variety","score":0.4437296688556671},{"id":"https://openalex.org/keywords/toric-variety","display_name":"Toric variety","score":0.44366610050201416},{"id":"https://openalex.org/keywords/irreducible-component","display_name":"Irreducible component","score":0.4395981431007385},{"id":"https://openalex.org/keywords/algebraic-variety","display_name":"Algebraic variety","score":0.43924108147621155},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.43826791644096375},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43688082695007324},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.4176335036754608},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40362241864204407},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.3748418688774109},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3013235032558441},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14891120791435242},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12730470299720764},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07986319065093994}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7848877906799316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.768444299697876},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.709070086479187},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.702983021736145},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.647254467010498},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5892499685287476},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.5552583932876587},{"id":"https://openalex.org/C112128483","wikidata":"https://www.wikidata.org/wiki/Q382504","display_name":"Affine hull","level":4,"score":0.5418984889984131},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4623490571975708},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4534305930137634},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.4437296688556671},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.44366610050201416},{"id":"https://openalex.org/C54654531","wikidata":"https://www.wikidata.org/wiki/Q6073574","display_name":"Irreducible component","level":5,"score":0.4395981431007385},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.43924108147621155},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.43826791644096375},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43688082695007324},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.4176335036754608},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40362241864204407},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3748418688774109},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3013235032558441},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14891120791435242},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12730470299720764},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07986319065093994},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"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/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4613-9647-5_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4613-9647-5_6","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers and Mathematics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1552234546","https://openalex.org/W1594278443","https://openalex.org/W1604184456","https://openalex.org/W1996344378","https://openalex.org/W2003701640","https://openalex.org/W2026617627","https://openalex.org/W2031399497","https://openalex.org/W2073407186","https://openalex.org/W6814994134"],"related_works":["https://openalex.org/W2018745696","https://openalex.org/W877371868","https://openalex.org/W2154318968","https://openalex.org/W818858998","https://openalex.org/W2579878394","https://openalex.org/W4239067620","https://openalex.org/W2094986222","https://openalex.org/W2053749944","https://openalex.org/W40451353","https://openalex.org/W2615395014"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}