{"id":"https://openalex.org/W7104550210","doi":"https://doi.org/10.1145/3747199.3747563","title":"Solving bihomogeneous polynomial systems with a zero-dimensional projection","display_name":"Solving bihomogeneous polynomial systems with a zero-dimensional projection","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W7104550210","doi":"https://doi.org/10.1145/3747199.3747563"},"language":"en","primary_location":{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/0454c9da-b061-4d75-8c55-6f20de27dff2","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/0454c9da-b061-4d75-8c55-6f20de27dff2","pdf_url":"https://curis.ku.dk/ws/files/535652701/3747199.3747563.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bender , M , Bus\u00e9 , L , Checa , C & Tsigaridas , E 2025 , Solving bihomogeneous polynomial systems with a zero-dimensional projection . in C D'Andrea , S P Diaz & S Laplagne (eds) , ISSAC 2025 - Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation . Association for Computing Machinery, Inc. , pp. 206-214 , 50th International Symposium on Symbolic and Algebraic Computation, ISSAC 2025 , Guanajuato , Mexico , 28/07/2025 . https://doi.org/10.1145/3747199.3747563","raw_type":"contributionToPeriodical"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://curis.ku.dk/ws/files/535652701/3747199.3747563.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Bender, Mat\u00edas","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bender, Mat\u00edas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Bus\u00e9, Laurent","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bus\u00e9, Laurent","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Checa, Carles","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Checa, Carles","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Tsigaridas, Elias","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tsigaridas, Elias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58645026,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9842000007629395,"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":0.9842000007629395,"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":0.005400000140070915,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0031999999191612005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7276999950408936},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6410999894142151},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6351000070571899},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4943999946117401},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4799000024795532},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4661000072956085},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.45969998836517334},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40290001034736633}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7414000034332275},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7276999950408936},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6410999894142151},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6351000070571899},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4799000024795532},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.45969998836517334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4120999872684479},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.2874999940395355},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.2849999964237213},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.2847000062465668},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2833999991416931},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.26010000705718994},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/0454c9da-b061-4d75-8c55-6f20de27dff2","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/0454c9da-b061-4d75-8c55-6f20de27dff2","pdf_url":"https://curis.ku.dk/ws/files/535652701/3747199.3747563.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bender , M , Bus\u00e9 , L , Checa , C & Tsigaridas , E 2025 , Solving bihomogeneous polynomial systems with a zero-dimensional projection . in C D'Andrea , S P Diaz & S Laplagne (eds) , ISSAC 2025 - Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation . Association for Computing Machinery, Inc. , pp. 206-214 , 50th International Symposium on Symbolic and Algebraic Computation, ISSAC 2025 , Guanajuato , Mexico , 28/07/2025 . https://doi.org/10.1145/3747199.3747563","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/0454c9da-b061-4d75-8c55-6f20de27dff2","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/0454c9da-b061-4d75-8c55-6f20de27dff2","pdf_url":"https://curis.ku.dk/ws/files/535652701/3747199.3747563.pdf","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Bender , M , Bus\u00e9 , L , Checa , C & Tsigaridas , E 2025 , Solving bihomogeneous polynomial systems with a zero-dimensional projection . in C D'Andrea , S P Diaz & S Laplagne (eds) , ISSAC 2025 - Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation . Association for Computing Machinery, Inc. , pp. 206-214 , 50th International Symposium on Symbolic and Algebraic Computation, ISSAC 2025 , Guanajuato , Mexico , 28/07/2025 . https://doi.org/10.1145/3747199.3747563","raw_type":"contributionToPeriodical"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7104550210.pdf","grobid_xml":"https://content.openalex.org/works/W7104550210.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W363464033","https://openalex.org/W1483218536","https://openalex.org/W1486517759","https://openalex.org/W1519801683","https://openalex.org/W1635682819","https://openalex.org/W1979574955","https://openalex.org/W1992327202","https://openalex.org/W1993788865","https://openalex.org/W2003142294","https://openalex.org/W2007294075","https://openalex.org/W2010865943","https://openalex.org/W2012079420","https://openalex.org/W2031224077","https://openalex.org/W2031399497","https://openalex.org/W2031453829","https://openalex.org/W2034471690","https://openalex.org/W2059522106","https://openalex.org/W2071231019","https://openalex.org/W2077569399","https://openalex.org/W2238531909","https://openalex.org/W2485566865","https://openalex.org/W2950049430","https://openalex.org/W2963833429","https://openalex.org/W2963839416","https://openalex.org/W2965416181","https://openalex.org/W2984029018","https://openalex.org/W3035846117","https://openalex.org/W3106350071","https://openalex.org/W3154040421","https://openalex.org/W3180702431","https://openalex.org/W4241371538","https://openalex.org/W4249549360","https://openalex.org/W4285247876","https://openalex.org/W4294862396","https://openalex.org/W4308456931","https://openalex.org/W4368228234"],"related_works":[],"abstract_inverted_index":{"We":[0,66,113],"study":[1,115],"bihomogeneous":[2,173],"systems":[3],"defining,":[4],"non-zero":[5,110],"dimensional,":[6,111],"biprojective":[7],"varieties":[8],"for":[9,48,152],"which":[10],"the":[11,14,29,33,44,57,73,76,98,102,123,134,141,165,168,171],"projection":[12,31],"onto":[13],"first":[15],"group":[16],"of":[17,24,75,101,125,140,164,167,170],"variables":[18],"results":[19],"in":[20,162],"a":[21,79,147],"finite":[22],"set":[23],"points.":[25],"To":[26],"compute":[27,97,137],"(with)":[28],"0-dimensional":[30],"and":[32,122,128,156],"corresponding":[34,172],"quotient":[35],"ring,":[36],"we":[37,60,131,145,160],"introduce":[38],"linear":[39,70],"maps":[40,47,93,155],"that":[41,130,159],"greatly":[42],"extend":[43],"classical":[45],"multiplication":[46,64,92,154],"zero-dimensional":[49,142],"systems,":[50],"but":[51],"are":[52],"not":[53],"those":[54],"associated":[55],"to":[56,78,96,108,136],"elimination":[58,99],"ideal;":[59],"also":[61,114],"call":[62],"them":[63,68],"maps.":[65],"construct":[67],"using":[69],"algebra":[71],"on":[72],"restriction":[74],"ideal":[77,100],"carefully":[80],"chosen":[81],"bidegree":[82],"or,":[83],"if":[84],"available,":[85],"from":[86],"an":[87],"arbitrary":[88],"Gr\u00f6bner":[89,157],"basis.":[90],"The":[91],"allow":[94],"us":[95],"projection,":[103],"by":[104],"generalizing":[105],"FGLM":[106],"algorithm":[107],"bihomogenous,":[109],"varieties.":[112],"their":[116,119,126],"properties,":[117],"like":[118],"minimal":[120],"polynomials":[121],"multiplicities":[124],"eigenvalues,":[127],"show":[129],"can":[132],"use":[133],"eigenvalues":[135],"numerical":[138],"approximations":[139],"projection.":[143],"Finally,":[144],"establish":[146],"single":[148],"exponential":[149],"complexity":[150],"bound":[151],"computing":[153],"bases,":[158],"express":[161],"terms":[163],"bidegrees":[166],"generators":[169],"ideal.":[174]},"counts_by_year":[],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}