{"id":"https://openalex.org/W1982227707","doi":"https://doi.org/10.1017/s0962492911000067","title":"Numerical algebraic geometry and algebraic kinematics","display_name":"Numerical algebraic geometry and algebraic kinematics","publication_year":2011,"publication_date":"2011-04-28","ids":{"openalex":"https://openalex.org/W1982227707","doi":"https://doi.org/10.1017/s0962492911000067","mag":"1982227707"},"language":"en","primary_location":{"id":"doi:10.1017/s0962492911000067","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492911000067","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-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/A5050683196","display_name":"Charles W. Wampler","orcid":"https://orcid.org/0000-0002-9790-1600"},"institutions":[{"id":"https://openalex.org/I118136607","display_name":"General Motors (United States)","ror":"https://ror.org/05addee68","country_code":"US","type":"company","lineage":["https://openalex.org/I118136607"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Charles W. Wampler","raw_affiliation_strings":["General Motors Research and Development, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055, USA E-mail:","General Motors Research and Development, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055, USA E-mail: Charles.W.Wampler@gm.com URL: www.nd.edu\u02dccwample1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"General Motors Research and Development, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055, USA E-mail:","institution_ids":["https://openalex.org/I118136607"]},{"raw_affiliation_string":"General Motors Research and Development, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055, USA E-mail: Charles.W.Wampler@gm.com URL: www.nd.edu\u02dccwample1","institution_ids":["https://openalex.org/I118136607"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103556278","display_name":"Andrew J. Sommese","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":"Andrew J. Sommese","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, USA E-mail:","Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, USA E-mail: sommese@nd.edu URL: www.nd.edu\u02dcsommese"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, USA E-mail:","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-4618, USA E-mail: sommese@nd.edu URL: www.nd.edu\u02dcsommese","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.8489,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.97301552,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"20","issue":null,"first_page":"469","last_page":"567"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.996999979019165,"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":0.996999979019165,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9735999703407288,"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/T11752","display_name":"Cancer Treatment and Pharmacology","score":0.9081000089645386,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.768028974533081},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.7342646718025208},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.6794003844261169},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.6620344519615173},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.658745527267456},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5404028296470642},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5211772322654724},{"id":"https://openalex.org/keywords/singular-point-of-an-algebraic-variety","display_name":"Singular point of an algebraic variety","score":0.48685020208358765},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"Algebraic geometry","score":0.4609326720237732},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.45246127247810364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43605512380599976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4314141273498535},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42244064807891846},{"id":"https://openalex.org/keywords/derived-algebraic-geometry","display_name":"Derived algebraic geometry","score":0.41923436522483826},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1867562234401703},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15696993470191956},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.09178423881530762},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.07368701696395874},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06889066100120544},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.06487920880317688}],"concepts":[{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.768028974533081},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.7342646718025208},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.6794003844261169},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.6620344519615173},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.658745527267456},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5404028296470642},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5211772322654724},{"id":"https://openalex.org/C201482947","wikidata":"https://www.wikidata.org/wiki/Q7524253","display_name":"Singular point of an algebraic variety","level":5,"score":0.48685020208358765},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.4609326720237732},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.45246127247810364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43605512380599976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4314141273498535},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42244064807891846},{"id":"https://openalex.org/C185382297","wikidata":"https://www.wikidata.org/wiki/Q16959942","display_name":"Derived algebraic geometry","level":5,"score":0.41923436522483826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1867562234401703},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15696993470191956},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.09178423881530762},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.07368701696395874},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06889066100120544},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.06487920880317688},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0962492911000067","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492911000067","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.221.5442","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.5442","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.nd.edu/%7Ecwample1/Preprints/NumAlgGeomAndAlgKinematics.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.306.9346","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.306.9346","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www3.nd.edu/~cwample1/Preprints/NumAlgGeomAndAlgKinematics.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":130,"referenced_works":["https://openalex.org/W59564462","https://openalex.org/W59605967","https://openalex.org/W61948969","https://openalex.org/W79836551","https://openalex.org/W183725081","https://openalex.org/W208460288","https://openalex.org/W289820477","https://openalex.org/W430587328","https://openalex.org/W577615873","https://openalex.org/W596131791","https://openalex.org/W647604146","https://openalex.org/W654253895","https://openalex.org/W1498729261","https://openalex.org/W1509205003","https://openalex.org/W1515192744","https://openalex.org/W1518341038","https://openalex.org/W1526117436","https://openalex.org/W1529743226","https://openalex.org/W1540352123","https://openalex.org/W1544017368","https://openalex.org/W1547967568","https://openalex.org/W1560823561","https://openalex.org/W1570420806","https://openalex.org/W1597009130","https://openalex.org/W1607862333","https://openalex.org/W1645810705","https://openalex.org/W1676198905","https://openalex.org/W1680574791","https://openalex.org/W1835627343","https://openalex.org/W1938785554","https://openalex.org/W1965520434","https://openalex.org/W1970845222","https://openalex.org/W1972592935","https://openalex.org/W1974280961","https://openalex.org/W1974730120","https://openalex.org/W1975041748","https://openalex.org/W1975306541","https://openalex.org/W1975927407","https://openalex.org/W1976464801","https://openalex.org/W1977145560","https://openalex.org/W1983443215","https://openalex.org/W1983858112","https://openalex.org/W1984396462","https://openalex.org/W1985456081","https://openalex.org/W1985548249","https://openalex.org/W1986859143","https://openalex.org/W1989369020","https://openalex.org/W1991844548","https://openalex.org/W1992601993","https://openalex.org/W1993702408","https://openalex.org/W2001490025","https://openalex.org/W2007860444","https://openalex.org/W2009126887","https://openalex.org/W2013905571","https://openalex.org/W2014374061","https://openalex.org/W2015535530","https://openalex.org/W2028099324","https://openalex.org/W2028576930","https://openalex.org/W2028622243","https://openalex.org/W2033244327","https://openalex.org/W2033936708","https://openalex.org/W2035352599","https://openalex.org/W2041176477","https://openalex.org/W2041945504","https://openalex.org/W2042398689","https://openalex.org/W2050292516","https://openalex.org/W2052195169","https://openalex.org/W2061631683","https://openalex.org/W2062754393","https://openalex.org/W2065014532","https://openalex.org/W2066058234","https://openalex.org/W2066409969","https://openalex.org/W2067437385","https://openalex.org/W2071860648","https://openalex.org/W2075692480","https://openalex.org/W2076067331","https://openalex.org/W2083261573","https://openalex.org/W2085851553","https://openalex.org/W2086808289","https://openalex.org/W2091186243","https://openalex.org/W2093101196","https://openalex.org/W2093314258","https://openalex.org/W2096323543","https://openalex.org/W2100699731","https://openalex.org/W2101855097","https://openalex.org/W2105303994","https://openalex.org/W2106885928","https://openalex.org/W2109596995","https://openalex.org/W2112741905","https://openalex.org/W2115628062","https://openalex.org/W2131474035","https://openalex.org/W2132476962","https://openalex.org/W2136938510","https://openalex.org/W2137837586","https://openalex.org/W2143628714","https://openalex.org/W2146632936","https://openalex.org/W2158358539","https://openalex.org/W2158639671","https://openalex.org/W2167360454","https://openalex.org/W2168776222","https://openalex.org/W2170316960","https://openalex.org/W2170485468","https://openalex.org/W2197526461","https://openalex.org/W2319466955","https://openalex.org/W2326858015","https://openalex.org/W2326878727","https://openalex.org/W2336126276","https://openalex.org/W2467611443","https://openalex.org/W2486993449","https://openalex.org/W2489016459","https://openalex.org/W2492039749","https://openalex.org/W2493230279","https://openalex.org/W2494797023","https://openalex.org/W2801061932","https://openalex.org/W2923052200","https://openalex.org/W3190282975","https://openalex.org/W4210556961","https://openalex.org/W4230656725","https://openalex.org/W4237766344","https://openalex.org/W4241062739","https://openalex.org/W4243775434","https://openalex.org/W4245114601","https://openalex.org/W4250154342","https://openalex.org/W4253566036","https://openalex.org/W4255213956","https://openalex.org/W4285719527","https://openalex.org/W4292096448","https://openalex.org/W4300790088","https://openalex.org/W6657491335","https://openalex.org/W6750091278"],"related_works":["https://openalex.org/W2061587972","https://openalex.org/W2170846659","https://openalex.org/W415152954","https://openalex.org/W2032847817","https://openalex.org/W4245935002","https://openalex.org/W1533474758","https://openalex.org/W2023276140","https://openalex.org/W2090221370","https://openalex.org/W14751844","https://openalex.org/W649831100"],"abstract_inverted_index":{"In":[0,51],"this":[1,39],"article,":[2],"the":[3,34,55,73,83],"basic":[4],"constructs":[5],"of":[6,24,28,57,72,76,82,99,107,118],"algebraic":[7,40,49,59,92,102],"kinematics":[8,103],"(links,":[9],"joints,":[10],"and":[11,79,113],"mechanism":[12],"spaces)":[13],"are":[14,27,36,62],"introduced.":[15],"This":[16],"provides":[17,104],"a":[18,70,105],"common":[19],"schema":[20],"for":[21,110,114],"many":[22],"kinds":[23],"problems":[25,35],"that":[26],"interest":[29],"in":[30,38],"kinematic":[31],"studies.":[32],"Once":[33],"cast":[37],"framework,":[41],"they":[42],"can":[43],"be":[44],"attacked":[45],"by":[46],"tools":[47],"from":[48],"geometry.":[50],"particular,":[52],"we":[53],"review":[54,71],"techniques":[56],"numerical":[58,91],"geometry,":[60],"which":[61],"primarily":[63],"based":[64],"on":[65],"homotopy":[66],"methods.":[67],"We":[68],"include":[69],"main":[74],"developments":[75],"recent":[77],"years":[78],"outline":[80],"some":[81],"frontiers":[84],"where":[85],"further":[86],"research":[87],"is":[88],"occurring.":[89],"While":[90],"geometry":[93],"applies":[94],"broadly":[95],"to":[96],"any":[97],"system":[98],"polynomial":[100],"equations,":[101],"body":[106],"interesting":[108],"examples":[109],"testing":[111],"algorithms":[112],"inspiring":[115],"new":[116],"avenues":[117],"work.":[119]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}