{"id":"https://openalex.org/W4284702580","doi":"https://doi.org/10.1145/3476446.3536189","title":"Bounding the Number of Roots of Multi-Homogeneous Systems","display_name":"Bounding the Number of Roots of Multi-Homogeneous Systems","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4284702580","doi":"https://doi.org/10.1145/3476446.3536189"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3536189","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536189","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","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/A5091017449","display_name":"Evangelos Bartzos","orcid":"https://orcid.org/0000-0002-3117-9694"},"institutions":[{"id":"https://openalex.org/I4210156054","display_name":"Athena Research and Innovation Center In Information Communication & Knowledge Technologies","ror":"https://ror.org/0576by029","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210156054"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Evangelos Bartzos","raw_affiliation_strings":["Department of Informatics and Telecommunications NKUA & ATHENA Research Center, Athens, Greece","AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes (2004 route des Lucioles BP 93 06902 Sophia Antipolis cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications NKUA & ATHENA Research Center, Athens, Greece","institution_ids":["https://openalex.org/I4210156054"]},{"raw_affiliation_string":"AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes (2004 route des Lucioles BP 93 06902 Sophia Antipolis cedex - France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087662998","display_name":"Ioannis Z. Emiris","orcid":"https://orcid.org/0000-0002-2339-5303"},"institutions":[{"id":"https://openalex.org/I4210156054","display_name":"Athena Research and Innovation Center In Information Communication & Knowledge Technologies","ror":"https://ror.org/0576by029","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210156054"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Ioannis Z. Emiris","raw_affiliation_strings":["ATHENA Research Center & Department of Informatics and Telecommunications NKUA, Athens, Greece","AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes (2004 route des Lucioles BP 93 06902 Sophia Antipolis cedex - France)","ARC - Athena Research and Innovation Centre (Greece)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ATHENA Research Center & Department of Informatics and Telecommunications NKUA, Athens, Greece","institution_ids":["https://openalex.org/I4210156054"]},{"raw_affiliation_string":"AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes (2004 route des Lucioles BP 93 06902 Sophia Antipolis cedex - France)","institution_ids":[]},{"raw_affiliation_string":"ARC - Athena Research and Innovation Centre (Greece)","institution_ids":["https://openalex.org/I4210156054"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069151859","display_name":"Ilias Kotsireas","orcid":"https://orcid.org/0000-0003-2126-8383"},"institutions":[{"id":"https://openalex.org/I4210156054","display_name":"Athena Research and Innovation Center In Information Communication & Knowledge Technologies","ror":"https://ror.org/0576by029","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210156054"]},{"id":"https://openalex.org/I75381157","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05","country_code":"CA","type":"education","lineage":["https://openalex.org/I75381157"]}],"countries":["CA","GR"],"is_corresponding":false,"raw_author_name":"Ilias S. Kotsireas","raw_affiliation_strings":["ATHENA Research Center, Athens, Greece","WLU - Wilfrid Laurier University (75 University Avenue West, Waterloo, Ontario - Canada)","ARC - Athena Research and Innovation Centre (Greece)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ATHENA Research Center, Athens, Greece","institution_ids":["https://openalex.org/I4210156054"]},{"raw_affiliation_string":"WLU - Wilfrid Laurier University (75 University Avenue West, Waterloo, Ontario - Canada)","institution_ids":["https://openalex.org/I75381157"]},{"raw_affiliation_string":"ARC - Athena Research and Innovation Centre (Greece)","institution_ids":["https://openalex.org/I4210156054"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051757549","display_name":"Charalambos Tzamos","orcid":"https://orcid.org/0000-0001-7029-6431"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]},{"id":"https://openalex.org/I4210156054","display_name":"Athena Research and Innovation Center In Information Communication & Knowledge Technologies","ror":"https://ror.org/0576by029","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210156054"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Charalambos Tzamos","raw_affiliation_strings":["Department of Informatics and Telecommunications NKUA, Athens, Greece","DI NKUA - Department of Informatics and Telecomunications [Kapodistrian Univ] (National and Kapodistrian University of Athens, Panepistimiopolis, Ilissia Athens 15784 - Greece)","ARC - Athena Research and Innovation Centre (Greece)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications NKUA, Athens, Greece","institution_ids":[]},{"raw_affiliation_string":"DI NKUA - Department of Informatics and Telecomunications [Kapodistrian Univ] (National and Kapodistrian University of Athens, Panepistimiopolis, Ilissia Athens 15784 - Greece)","institution_ids":["https://openalex.org/I200777214"]},{"raw_affiliation_string":"ARC - Athena Research and Innovation Centre (Greece)","institution_ids":["https://openalex.org/I4210156054"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1017079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"255","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9983000159263611,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9854000210762024,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.8774476647377014},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.693220317363739},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.6674845218658447},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6086145043373108},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5883080959320068},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5687477588653564},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4406055808067322},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34526199102401733},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32663631439208984},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27970337867736816},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2174161970615387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21065258979797363},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.14772510528564453}],"concepts":[{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.8774476647377014},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.693220317363739},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.6674845218658447},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6086145043373108},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5883080959320068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5687477588653564},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4406055808067322},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34526199102401733},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32663631439208984},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27970337867736816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2174161970615387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21065258979797363},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.14772510528564453},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3476446.3536189","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536189","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-03905697v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03905697","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://dl.acm.org/doi/proceedings/10.1145/3476446","raw_type":"Conference papers"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W90640287","https://openalex.org/W1570420806","https://openalex.org/W1644572710","https://openalex.org/W1991844548","https://openalex.org/W2055287661","https://openalex.org/W2098571099","https://openalex.org/W2105664651","https://openalex.org/W2112660220","https://openalex.org/W2115305364","https://openalex.org/W2120901716","https://openalex.org/W2134771095","https://openalex.org/W2143023483","https://openalex.org/W2148417962","https://openalex.org/W2240347590","https://openalex.org/W2245714385","https://openalex.org/W2295465424","https://openalex.org/W2623293810","https://openalex.org/W2963232267","https://openalex.org/W2980517378","https://openalex.org/W3102759601","https://openalex.org/W3179653669","https://openalex.org/W3195408583","https://openalex.org/W3216465419","https://openalex.org/W4231402266","https://openalex.org/W4233121052"],"related_works":["https://openalex.org/W3166204570","https://openalex.org/W3121246613","https://openalex.org/W2049845757","https://openalex.org/W4284702580","https://openalex.org/W2137227686","https://openalex.org/W2116921991","https://openalex.org/W2068109952","https://openalex.org/W3156147585","https://openalex.org/W4307350259","https://openalex.org/W2240347535"],"abstract_inverted_index":{"Determining":[0],"the":[1,25],"number":[2,21,26],"of":[3,5,27,30],"solutions":[4,29],"a":[6,11,31,38],"multi-homogeneous":[7,18,32],"polynomial":[8],"system":[9],"is":[10,37],"fundamental":[12],"problem":[13],"in":[14],"algebraic":[15],"geometry.":[16],"The":[17],"B\u00e9zout":[19],"(m-B\u00e9zout)":[20],"bounds":[22],"from":[23],"above":[24],"non-singular":[28],"system,":[33],"but":[34],"its":[35],"computation":[36],"#P>-hard":[39],"problem.":[40]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2022-07-08T00:00:00"}