{"id":"https://openalex.org/W2495688539","doi":"https://doi.org/10.1007/978-3-319-42432-3_16","title":"Decomposing Solution Sets of Polynomial Systems Using Derivatives","display_name":"Decomposing Solution Sets of Polynomial Systems Using Derivatives","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2495688539","doi":"https://doi.org/10.1007/978-3-319-42432-3_16","mag":"2495688539"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-42432-3_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-42432-3_16","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","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/A5110283172","display_name":"Daniel A. Brake","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel A. Brake","raw_affiliation_strings":["Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007214938","display_name":"Jonathan D. Hauenstein","orcid":"https://orcid.org/0000-0002-9252-8210"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan D. Hauenstein","raw_affiliation_strings":["Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108274100","display_name":"Alan C. Liddell","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan C. Liddell","raw_affiliation_strings":["Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110283172"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.0023,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.85253165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"127","last_page":"135"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9624999761581421,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9537000060081482,"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/trace","display_name":"TRACE (psycholinguistics)","score":0.6938998699188232},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.612078070640564},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5734882950782776},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5722893476486206},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5465944409370422},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4957452714443207},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.48199644684791565},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4570898711681366},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.4265980124473572},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40014010667800903},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32318297028541565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28490716218948364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10730162262916565}],"concepts":[{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6938998699188232},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.612078070640564},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5734882950782776},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5722893476486206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5465944409370422},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4957452714443207},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.48199644684791565},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4570898711681366},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.4265980124473572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40014010667800903},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32318297028541565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28490716218948364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10730162262916565},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-42432-3_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-42432-3_16","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","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":13,"referenced_works":["https://openalex.org/W647818151","https://openalex.org/W1570420806","https://openalex.org/W1893214633","https://openalex.org/W1986180644","https://openalex.org/W1993702408","https://openalex.org/W2037402183","https://openalex.org/W2066723539","https://openalex.org/W2105303994","https://openalex.org/W2146292423","https://openalex.org/W2158639671","https://openalex.org/W2326362648","https://openalex.org/W4285719527","https://openalex.org/W4298231803"],"related_works":["https://openalex.org/W2131958170","https://openalex.org/W4247954915","https://openalex.org/W2273754158","https://openalex.org/W2336747664","https://openalex.org/W2357130048","https://openalex.org/W3036607390","https://openalex.org/W4206605161","https://openalex.org/W2092234295","https://openalex.org/W2528363695","https://openalex.org/W1509926844"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"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"}