{"id":"https://openalex.org/W53033798","doi":"https://doi.org/10.1007/978-3-540-33275-6_1","title":"Algebraic geometry and geometric modeling: insight and computation","display_name":"Algebraic geometry and geometric modeling: insight and computation","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W53033798","doi":"https://doi.org/10.1007/978-3-540-33275-6_1","mag":"53033798"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-33275-6_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-33275-6_1","pdf_url":null,"source":{"id":"https://openalex.org/S4210191043","display_name":"Mathematics and visualization","issn_l":"1612-3786","issn":["1612-3786","2197-666X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Visualization","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/A5086134113","display_name":"Ron Goldman","orcid":"https://orcid.org/0000-0001-8720-3860"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ron Goldman","raw_affiliation_strings":["Department of Computer Science, Rice University, 6100 Main Street, TX 77005, Houston"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rice University, 6100 Main Street, TX 77005, Houston","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086134113"],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.0174692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9970999956130981,"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":0.9970999956130981,"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/T12504","display_name":"Mathematics and Applications","score":0.9951000213623047,"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.7974764108657837},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.7557446956634521},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.7227798700332642},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.6140873432159424},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.6005475521087646},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.595413088798523},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5068178772926331},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.4973137676715851},{"id":"https://openalex.org/keywords/algebraic-surface","display_name":"Algebraic surface","score":0.49631553888320923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4757549464702606},{"id":"https://openalex.org/keywords/transformation-geometry","display_name":"Transformation geometry","score":0.4539276957511902},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44981247186660767},{"id":"https://openalex.org/keywords/conformal-geometric-algebra","display_name":"Conformal geometric algebra","score":0.4416259825229645},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.4381096661090851},{"id":"https://openalex.org/keywords/singular-point-of-an-algebraic-variety","display_name":"Singular point of an algebraic variety","score":0.4339093267917633},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3402882218360901},{"id":"https://openalex.org/keywords/geometric-algebra","display_name":"Geometric algebra","score":0.235234797000885},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19553375244140625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11360421776771545},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.09395340085029602}],"concepts":[{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.7974764108657837},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.7557446956634521},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.7227798700332642},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6140873432159424},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.6005475521087646},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.595413088798523},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5068178772926331},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.4973137676715851},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.49631553888320923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4757549464702606},{"id":"https://openalex.org/C32990609","wikidata":"https://www.wikidata.org/wiki/Q306542","display_name":"Transformation geometry","level":2,"score":0.4539276957511902},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44981247186660767},{"id":"https://openalex.org/C147898140","wikidata":"https://www.wikidata.org/wiki/Q5160252","display_name":"Conformal geometric algebra","level":5,"score":0.4416259825229645},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.4381096661090851},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.4339093267917633},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3402882218360901},{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.235234797000885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19553375244140625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11360421776771545},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.09395340085029602},{"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/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-33275-6_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-33275-6_1","pdf_url":null,"source":{"id":"https://openalex.org/S4210191043","display_name":"Mathematics and visualization","issn_l":"1612-3786","issn":["1612-3786","2197-666X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Visualization","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W61015070","https://openalex.org/W393262623","https://openalex.org/W1483218536","https://openalex.org/W1540740892","https://openalex.org/W1546935257","https://openalex.org/W1564889833","https://openalex.org/W1587069887","https://openalex.org/W1587445444","https://openalex.org/W1823333623","https://openalex.org/W1968297701","https://openalex.org/W1971343670","https://openalex.org/W1971419216","https://openalex.org/W1973180078","https://openalex.org/W1977415556","https://openalex.org/W1977574397","https://openalex.org/W1977792410","https://openalex.org/W1980829704","https://openalex.org/W1981613180","https://openalex.org/W1983693193","https://openalex.org/W2013899348","https://openalex.org/W2018887783","https://openalex.org/W2024672868","https://openalex.org/W2033123084","https://openalex.org/W2034966370","https://openalex.org/W2042691439","https://openalex.org/W2048329955","https://openalex.org/W2048966962","https://openalex.org/W2049645908","https://openalex.org/W2055898191","https://openalex.org/W2059541972","https://openalex.org/W2059906458","https://openalex.org/W2060390851","https://openalex.org/W2062429253","https://openalex.org/W2062605698","https://openalex.org/W2064044318","https://openalex.org/W2070769763","https://openalex.org/W2072899396","https://openalex.org/W2074879283","https://openalex.org/W2084783913","https://openalex.org/W2084860168","https://openalex.org/W2087794615","https://openalex.org/W2088129367","https://openalex.org/W2117140824","https://openalex.org/W2121296219","https://openalex.org/W2121752747","https://openalex.org/W2131141154","https://openalex.org/W2144049808","https://openalex.org/W2149153582","https://openalex.org/W2158631937","https://openalex.org/W2162828800","https://openalex.org/W2170734305","https://openalex.org/W2232657515","https://openalex.org/W2316141172","https://openalex.org/W2488410224","https://openalex.org/W2912685169","https://openalex.org/W3123664756","https://openalex.org/W4229792880","https://openalex.org/W4234761564","https://openalex.org/W4234941087","https://openalex.org/W4240520596","https://openalex.org/W4242117121","https://openalex.org/W4255151293","https://openalex.org/W4285719527","https://openalex.org/W4292096448","https://openalex.org/W4388321161","https://openalex.org/W6600168703"],"related_works":["https://openalex.org/W2032847817","https://openalex.org/W2061587972","https://openalex.org/W4297800099","https://openalex.org/W3197833978","https://openalex.org/W2170846659","https://openalex.org/W2154318968","https://openalex.org/W415152954","https://openalex.org/W2076085433","https://openalex.org/W2018745696","https://openalex.org/W53033798"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}