{"id":"https://openalex.org/W2112635342","doi":"https://doi.org/10.1145/2442829.2442837","title":"Computing Puiseux series for algebraic surfaces","display_name":"Computing Puiseux series for algebraic surfaces","publication_year":2012,"publication_date":"2012-07-22","ids":{"openalex":"https://openalex.org/W2112635342","doi":"https://doi.org/10.1145/2442829.2442837","mag":"2112635342"},"language":"en","primary_location":{"id":"doi:10.1145/2442829.2442837","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442837","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th 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/A5063265682","display_name":"Danko Adrovic","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Danko Adrovic","raw_affiliation_strings":["University of Illinois at Chicago, South Morgan, Chicago, IL","University of Illinois at Chicago, South Morgan, Chicago, IL#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago, South Morgan, Chicago, IL","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"University of Illinois at Chicago, South Morgan, Chicago, IL#TAB#","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112224754","display_name":"Jan Verschelde","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jan Verschelde","raw_affiliation_strings":["University of Illinois at Chicago, South Morgan, Chicago, IL","University of Illinois at Chicago, South Morgan, Chicago, IL#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago, South Morgan, Chicago, IL","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"University of Illinois at Chicago, South Morgan, Chicago, IL#TAB#","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063265682"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":3.7066,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.93486507,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"20","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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":0.9997000098228455,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9896000027656555,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9835000038146973,"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/algebraic-number","display_name":"Algebraic number","score":0.6635431051254272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.656186580657959},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6402906179428101},{"id":"https://openalex.org/keywords/dimension-of-an-algebraic-variety","display_name":"Dimension of an algebraic variety","score":0.6231094598770142},{"id":"https://openalex.org/keywords/algebraic-surface","display_name":"Algebraic surface","score":0.614898145198822},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6105575561523438},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5840283632278442},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5489453077316284},{"id":"https://openalex.org/keywords/real-algebraic-geometry","display_name":"Real algebraic geometry","score":0.5036293864250183},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47463974356651306},{"id":"https://openalex.org/keywords/algebraic-solution","display_name":"Algebraic solution","score":0.4604339003562927},{"id":"https://openalex.org/keywords/function-field-of-an-algebraic-variety","display_name":"Function field of an algebraic variety","score":0.451822966337204},{"id":"https://openalex.org/keywords/algebraic-variety","display_name":"Algebraic variety","score":0.4170827567577362},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.4102190434932709},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.380519300699234},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3758963942527771},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3163756728172302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1549924910068512},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14685025811195374},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1285039782524109}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6635431051254272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.656186580657959},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6402906179428101},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.6231094598770142},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.614898145198822},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6105575561523438},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5840283632278442},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5489453077316284},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.5036293864250183},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47463974356651306},{"id":"https://openalex.org/C87563608","wikidata":"https://www.wikidata.org/wiki/Q2900186","display_name":"Algebraic solution","level":5,"score":0.4604339003562927},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.451822966337204},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.4170827567577362},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.4102190434932709},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.380519300699234},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3758963942527771},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3163756728172302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1549924910068512},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14685025811195374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1285039782524109},{"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},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2442829.2442837","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442837","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3660961569","display_name":null,"funder_award_id":"1115777","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W133422652","https://openalex.org/W642365271","https://openalex.org/W1526262508","https://openalex.org/W1585026243","https://openalex.org/W1862515573","https://openalex.org/W1990875092","https://openalex.org/W2001929832","https://openalex.org/W2028153996","https://openalex.org/W2028576930","https://openalex.org/W2033340455","https://openalex.org/W2035352599","https://openalex.org/W2048862576","https://openalex.org/W2053967969","https://openalex.org/W2054337147","https://openalex.org/W2070510548","https://openalex.org/W2074064659","https://openalex.org/W2081659888","https://openalex.org/W2088216433","https://openalex.org/W2124415308","https://openalex.org/W2130509998","https://openalex.org/W2130918732","https://openalex.org/W2141708381","https://openalex.org/W2143023483","https://openalex.org/W2146632936","https://openalex.org/W2155163206","https://openalex.org/W2158639671","https://openalex.org/W2172194430","https://openalex.org/W2324501057","https://openalex.org/W2602645338","https://openalex.org/W4206077821","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W415152954","https://openalex.org/W2032847817","https://openalex.org/W2170846659","https://openalex.org/W2061587972","https://openalex.org/W2042795994","https://openalex.org/W2039329794","https://openalex.org/W4387637555","https://openalex.org/W1502419693","https://openalex.org/W1996217084","https://openalex.org/W2408624816"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"outline":[4],"an":[5,81],"algorithmic":[6],"approach":[7,40],"to":[8,46,52,123],"compute":[9,47],"Puiseux":[10,101],"series":[11,17,102],"expansions":[12,18],"for":[13,95,110,118],"algebraic":[14,25,37,64,78],"sets.":[15],"The":[16],"originate":[19],"at":[20],"the":[21,24,33,36,53,57,63,71,74,77,96,100,114],"intersection":[22],"of":[23,35,49,56,76,99,113,126],"set":[26,79],"with":[27,42],"as":[28,32,67,73],"many":[29,68],"coordinate":[30],"planes":[31],"dimension":[34,75],"set.":[38,65],"Our":[39,104],"starts":[41],"a":[43,124],"polyhedral":[44],"method":[45],"cones":[48],"normal":[50],"vectors":[51,69,91],"Newton":[54],"polytopes":[55],"given":[58],"polynomial":[59],"system":[60,84],"that":[61,85],"defines":[62],"If":[66],"in":[70],"cone":[72],"define":[80],"initial":[82,97],"form":[83],"has":[86],"isolated":[87],"solutions,":[88],"then":[89],"those":[90],"are":[92],"potential":[93],"tropisms":[94],"term":[98],"expansion.":[103],"preliminary":[105],"methods":[106],"produce":[107],"exact":[108],"representations":[109],"solution":[111],"sets":[112],"cyclic":[115],"n-roots":[116],"problem,":[117],"n":[119],"=":[120],"m2,":[121],"corresponding":[122],"result":[125],"Backelin.":[127]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
