{"id":"https://openalex.org/W7104531817","doi":"https://doi.org/10.1145/3747199.3747576","title":"Optimal Bounds for the Number of Pieces of Real Near-Circuit Hypersurfaces","display_name":"Optimal Bounds for the Number of Pieces of Real Near-Circuit Hypersurfaces","publication_year":2025,"publication_date":"2025-07-28","ids":{"openalex":"https://openalex.org/W7104531817","doi":"https://doi.org/10.1145/3747199.3747576"},"language":null,"primary_location":{"id":"doi:10.1145/3747199.3747576","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747576","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747576","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747576","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Weixun Deng","orcid":"https://orcid.org/0009-0009-9071-6291"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Weixun Deng","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX, USA"],"raw_orcid":"https://orcid.org/0009-0009-9071-6291","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":null,"display_name":"J. Maurice Rojas","orcid":"https://orcid.org/0000-0002-1657-2674"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Maurice Rojas","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, Texas, USA"],"raw_orcid":"https://orcid.org/0000-0002-1657-2674","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, Texas, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":null,"display_name":"Cordelia Russell","orcid":"https://orcid.org/0009-0008-1554-4226"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cordelia Russell","raw_affiliation_strings":["Department of Mathematics, University of New Mexico, Albuquerque, New Mexico, USA"],"raw_orcid":"https://orcid.org/0009-0008-1554-4226","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of New Mexico, Albuquerque, New Mexico, USA","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58743149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"319","last_page":"327"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.8324999809265137,"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":0.8324999809265137,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.04960000142455101,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.02500000037252903,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.8019999861717224},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7677000164985657},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5464000105857849},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.49540001153945923},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.47369998693466187},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4661000072956085},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.4650999903678894},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.46470001339912415},{"id":"https://openalex.org/keywords/zero-set","display_name":"Zero set","score":0.37439998984336853},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3693999946117401}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8431000113487244},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.8019999861717224},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7677000164985657},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5464000105857849},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4909999966621399},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.47369998693466187},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4674000144004822},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46470001339912415},{"id":"https://openalex.org/C17183583","wikidata":"https://www.wikidata.org/wiki/Q214604","display_name":"Zero set","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.32440000772476196},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.30399999022483826},{"id":"https://openalex.org/C2778408900","wikidata":"https://www.wikidata.org/wiki/Q1329258","display_name":"Cardinal number (linguistics)","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.2711000144481659},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26080000400543213},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25699999928474426},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3747199.3747576","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747576","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747576","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3747199.3747576","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3747199.3747576","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3747199.3747576","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.7767652273178101,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3270324873","display_name":null,"funder_award_id":"DMS-2150094","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7104531817.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1971367839","https://openalex.org/W1977415556","https://openalex.org/W2007456941","https://openalex.org/W2035378589","https://openalex.org/W2054267869","https://openalex.org/W2080881761","https://openalex.org/W2098888552","https://openalex.org/W2123100908","https://openalex.org/W2239908585","https://openalex.org/W2963758142","https://openalex.org/W4213199372","https://openalex.org/W4237431628","https://openalex.org/W4250375092","https://openalex.org/W4410740734"],"related_works":[],"abstract_inverted_index":{"Suppose":[0],"f":[1,29],"is":[2,34,66,94],"a":[3,35,95],"polynomial":[4],"in":[5,30,38,47],"n":[6,13],"variables":[7],"with":[8,88],"real":[9,39,89],"coefficients":[10,57],"and":[11,42,50,58],"exactly":[12],"+":[14],"k":[15,71],"monomial":[16],"terms.":[17],"Estimating":[18],"the":[19,25,31,61,99],"number":[20,62],"of":[21,24,28,63,98],"connected":[22,64],"components":[23,65],"zero":[26],"set":[27],"positive":[32],"orthant":[33],"fundamental":[36],"problem":[37],"algebraic":[40],"geometry,":[41],"tight":[43],"estimates":[44],"have":[45],"applications":[46],"computational":[48],"complexity":[49],"topology.":[51],"We":[52],"prove":[53],"that,":[54],"for":[55,108],"generic":[56],"exponent":[59],"vectors,":[60],"at":[67],"most":[68],"3":[69],"when":[70],"=":[72],"3,":[73],"settling":[74],"an":[75],"open":[76],"question":[77],"from":[78],"Fewnomial":[79],"Theory.":[80],"Our":[81],"results":[82],"also":[83],"extend":[84],"to":[85],"exponential":[86],"sums":[87],"exponents.":[90],"A":[91],"key":[92],"contribution":[93],"deeper":[96],"analysis":[97],"underlying":[100],"\\(\\mathcal":[101],"{A}\\)-discriminant":[102],"contours,":[103],"which":[104],"should":[105],"be":[106],"useful":[107],"other":[109],"quantitative":[110],"geometric":[111],"problems.":[112]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-11-10T00:00:00"}