{"id":"https://openalex.org/W2505454963","doi":"https://doi.org/10.1145/2930889.2930943","title":"Compact Formulae in Sparse Elimination","display_name":"Compact Formulae in Sparse Elimination","publication_year":2016,"publication_date":"2016-07-19","ids":{"openalex":"https://openalex.org/W2505454963","doi":"https://doi.org/10.1145/2930889.2930943","mag":"2505454963"},"language":"en","primary_location":{"id":"doi:10.1145/2930889.2930943","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2930889.2930943","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.04856","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ioannis Z. Emiris","orcid":null},"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"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Ioannis Z. Emiris","raw_affiliation_strings":["University of Athens, Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Athens, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I200777214"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08557579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"4"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9883999824523926,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.7269999980926514},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7060999870300293},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5034000277519226},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5029000043869019},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.5009999871253967},{"id":"https://openalex.org/keywords/multilinear-algebra","display_name":"Multilinear algebra","score":0.4837000072002411},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.4593999981880188},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4239000082015991},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4018999934196472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7339000105857849},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.7269999980926514},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7060999870300293},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5034000277519226},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5029000043869019},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.5009999871253967},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.4837000072002411},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.4593999981880188},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4239000082015991},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4018999934196472},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38999998569488525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38769999146461487},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3797000050544739},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37720000743865967},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3393000066280365},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.3310999870300293},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.2953999936580658},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28619998693466187},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.26330000162124634},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.25529998540878296},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2930889.2930943","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2930889.2930943","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1710.04856","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.04856","pdf_url":"https://arxiv.org/pdf/1710.04856","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01401132v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01401132","pdf_url":"https://inria.hal.science/hal-01401132v1/file/emiris2016.pdf","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":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSAC 2016 - International Symposium on Symbolic and Algebraic Computation, Jul 2016, Waterloo, Canada. pp.1 - 8, &#x27E8;10.1145/2930889.2930943&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.04856","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.04856","pdf_url":"https://arxiv.org/pdf/1710.04856","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1043840428","https://openalex.org/W1588948421","https://openalex.org/W1857034947","https://openalex.org/W1964665841","https://openalex.org/W1977574397","https://openalex.org/W2021741586","https://openalex.org/W2027815348","https://openalex.org/W2048329955","https://openalex.org/W2050711638","https://openalex.org/W2052078521","https://openalex.org/W2066663656","https://openalex.org/W2066758283","https://openalex.org/W2067754443","https://openalex.org/W2070769763","https://openalex.org/W2075751193","https://openalex.org/W2079531639","https://openalex.org/W2087794615","https://openalex.org/W2088129367","https://openalex.org/W2151329291","https://openalex.org/W2154376488","https://openalex.org/W2232657515","https://openalex.org/W2601407116","https://openalex.org/W2962759704","https://openalex.org/W3037529266","https://openalex.org/W4237539763","https://openalex.org/W6635788517","https://openalex.org/W6717013976","https://openalex.org/W6721201552","https://openalex.org/W6989982117"],"related_works":[],"abstract_inverted_index":{"It":[0,156],"has":[1],"by":[2,74],"now":[3],"become":[4],"a":[5,23,59,67,77,84,95,123,131,174],"standard":[6],"approach":[7],"to":[8,27,108,159,180],"use":[9],"the":[10,19,31,63,71,81,109,128,149,153,170],"theory":[11],"of":[12,22,33,62,76,86,98,130,145,152,173,185],"sparse":[13,47,82,132,164],"(or":[14],"toric)":[15],"elimination,":[16],"based":[17],"on":[18],"Newton":[20,150],"polytope":[21,151],"polynomial,":[24],"in":[25,46,136],"order":[26],"reveal":[28],"and":[29,43,54,66],"exploit":[30],"structure":[32],"algebraic":[34],"systems.":[35],"This":[36,177],"talk":[37],"surveys":[38],"compact":[39,114,146],"formulae,":[40],"including":[41],"older":[42],"recent":[44,57],"results,":[45],"elimination.":[48],"We":[49,121,140],"start":[50],"with":[51,101],"root":[52],"bounds":[53],"juxtapose":[55],"two":[56],"formulae:":[58],"generating":[60],"function":[61],"m-Bezout":[64],"bound":[65],"closed-form":[68],"expression":[69],"for":[70,94,117,127,163],"mixed":[72],"volume":[73],"means":[75],"matrix":[78,183],"permanent.":[79],"For":[80],"resultant,":[83],"bevy":[85],"results":[87],"have":[88],"established":[89],"determinantal":[90,125],"or":[91],"rational":[92],"formulae":[93],"large":[96],"class":[97],"systems,":[99],"starting":[100],"Macaulay.":[102],"The":[103],"discriminant":[104,129],"is":[105,157],"closely":[106],"related":[107],"resultant":[110],"but":[111],"admits":[112],"no":[113],"formula":[115,126],"except":[116],"very":[118],"simple":[119],"cases.":[120],"offer":[122],"new":[124],"multilinear":[133],"system":[134],"arising":[135],"computing":[137],"Nash":[138],"equilibria.":[139],"introduce":[141],"an":[142],"alternative":[143],"notion":[144],"formula,":[147],"namely":[148],"unknown":[154],"polynomial.":[155],"possible":[158],"compute":[160],"it":[161],"efficiently":[162],"resultants,":[165],"discriminants,":[166],"as":[167,169],"well":[168],"implicit":[171,182],"equation":[172],"parameterized":[175],"variety.":[176],"leads":[178],"us":[179],"consider":[181],"representations":[184],"geometric":[186],"objects.":[187]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2016-08-23T00:00:00"}
