{"id":"https://openalex.org/W7124934559","doi":"https://doi.org/10.1145/3787957.3787958","title":"Integer Hulls, Z-Polyhedra and Presburger Arithmetic in Action","display_name":"Integer Hulls, Z-Polyhedra and Presburger Arithmetic in Action","publication_year":2025,"publication_date":"2025-09-01","ids":{"openalex":"https://openalex.org/W7124934559","doi":"https://doi.org/10.1145/3787957.3787958"},"language":"en","primary_location":{"id":"doi:10.1145/3787957.3787958","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3787957.3787958","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-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/A5091101857","display_name":"Rui-Juan Jing","orcid":"https://orcid.org/0000-0001-6932-8862"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Rui-Juan Jing","raw_affiliation_strings":["School of Mathematical Science, Jiangsu University, Zhenjiang, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Jiangsu University, Zhenjiang, China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113373878","display_name":"Y. Skylar Lei","orcid":null},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yuzhuo Lei","raw_affiliation_strings":["Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048698162","display_name":"Christopher F. S. Maligec","orcid":null},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Christopher F. S. Maligec","raw_affiliation_strings":["Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123407633","display_name":"Marc Moreno Maza","orcid":null},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Marc Moreno Maza","raw_affiliation_strings":["Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123435815","display_name":"Chirantan Mukherjee","orcid":null},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Chirantan Mukherjee","raw_affiliation_strings":["Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Ontario Research Center for Computer Algebra, University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5091101857"],"corresponding_institution_ids":["https://openalex.org/I115592961"],"apc_list":null,"apc_paid":null,"fwci":1.6516,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89818317,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"59","issue":"3","first_page":"41","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.7868000268936157,"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":0.7868000268936157,"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":0.08169999718666077,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.044599998742341995,"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/presburger-arithmetic","display_name":"Presburger arithmetic","score":0.814300000667572},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.6585999727249146},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6238999962806702},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.4878000020980835},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4828000068664551},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.47189998626708984},{"id":"https://openalex.org/keywords/integer-points-in-convex-polyhedra","display_name":"Integer points in convex polyhedra","score":0.4253999888896942},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.3928999900817871}],"concepts":[{"id":"https://openalex.org/C5852641","wikidata":"https://www.wikidata.org/wiki/Q956059","display_name":"Presburger arithmetic","level":3,"score":0.814300000667572},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.6585999727249146},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6238999962806702},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5091000199317932},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.47189998626708984},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46560001373291016},{"id":"https://openalex.org/C147700949","wikidata":"https://www.wikidata.org/wiki/Q6042594","display_name":"Integer points in convex polyhedra","level":4,"score":0.4253999888896942},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.3928999900817871},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34439998865127563},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3787957.3787958","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3787957.3787958","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2015738361","https://openalex.org/W2068602618","https://openalex.org/W2129740858","https://openalex.org/W2888796762"],"related_works":[],"abstract_inverted_index":{"When":[0],"solving":[1],"systems":[2,61],"of":[3,10,24,31,41,59,62,67,73,97,106,127,149],"polynomial":[4],"equations":[5,63],"and":[6,64,87,95,130,139],"inequalities,":[7],"the":[8,39,56,92,112,125,147],"task":[9,45],"computing":[11,25,32],"their":[12,26,34],"solutions":[13,28,58],"with":[14,114,133],"integer":[15,57,84,115],"coordinates":[16,116],"is":[17,66,123],"a":[18,104,118],"much":[19],"harder":[20],"problem":[21,51],"than":[22],"that":[23,30],"real":[27],"or":[29],"all":[33],"solutions.":[35],"In":[36],"fact,":[37],"in":[38,70,100,117],"presence":[40],"non-linear":[42],"constraints,":[43],"this":[44],"may":[46],"simply":[47],"become":[48],"an":[49],"undecidable":[50],"[12,":[52],"15].":[53],"However,":[54],"studying":[55],"linear":[60,85],"inequalities":[65],"practical":[68],"importance":[69],"various":[71],"areas":[72,78],"scientific":[74],"computing.":[75],"Two":[76],"such":[77,135],"are":[79],"combinatorial":[80],"optimization":[81,89],"(in":[82,90],"particular,":[83,91],"programming)":[86],"compiler":[88],"analysis,":[93],"transformation,":[94],"scheduling":[96],"nested":[98],"loops":[99],"computer":[101,128],"programs),":[102],"where":[103],"variety":[105],"algorithms":[107],"solve":[108],"questions":[109],"related":[110],"to":[111],"points":[113],"given":[119],"polyhedron.":[120],"Another":[121],"area":[122],"at":[124],"crossroads":[126],"algebra":[129],"polyhedral":[131],"geometry,":[132],"topics":[134],"as":[136,144,146],"toric":[137],"ideals":[138],"Hilbert":[140],"bases,":[141],"see":[142,152],"[16],":[143],"well":[145],"manipulation":[148],"Laurent":[150],"series,":[151],"[1].":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2026-01-21T00:00:00"}
