{"id":"https://openalex.org/W2014894062","doi":"https://doi.org/10.1145/2110170.2110175","title":"Software for exact integration of polynomials over polyhedra","display_name":"Software for exact integration of polynomials over polyhedra","publication_year":2012,"publication_date":"2012-01-23","ids":{"openalex":"https://openalex.org/W2014894062","doi":"https://doi.org/10.1145/2110170.2110175","mag":"2014894062"},"language":"en","primary_location":{"id":"doi:10.1145/2110170.2110175","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2110170.2110175","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/A5055755657","display_name":"Jes\u00fas A. De Loera","orcid":"https://orcid.org/0000-0002-9556-1112"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. A. De Loera","raw_affiliation_strings":["University of California, Davis, CA","University of California, Davis, CA,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Davis, CA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"University of California, Davis, CA,#TAB#","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067293909","display_name":"Brandon Dutra","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Dutra","raw_affiliation_strings":["University of California, Davis, CA","University of California, Davis, CA,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Davis, CA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"University of California, Davis, CA,#TAB#","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091730054","display_name":"Matthias K\u00f6ppe","orcid":"https://orcid.org/0000-0003-2492-4139"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. K\u00f6ppe","raw_affiliation_strings":["University of California, Davis, CA","University of California, Davis, CA,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Davis, CA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"University of California, Davis, CA,#TAB#","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088938647","display_name":"S. Moreinis","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Moreinis","raw_affiliation_strings":["University of California, Davis, CA","University of California, Davis, CA,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Davis, CA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"University of California, Davis, CA,#TAB#","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089631410","display_name":"Gregory Pinto","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. Pinto","raw_affiliation_strings":["","Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA#TAB#","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108563019","display_name":"Juwen Wu","orcid":"https://orcid.org/0009-0008-0828-4139"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Wu","raw_affiliation_strings":["","Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, UC Davis, One Shields Avenue, Davis, CA 95616, USA#TAB#","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":null,"apc_paid":null,"fwci":2.7199,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.90197749,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"45","issue":"3/4","first_page":"169","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9994999766349792,"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":0.9994999766349792,"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/T12504","display_name":"Mathematics and Applications","score":0.9941999912261963,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9940999746322632,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.9342944622039795},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.6807745695114136},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6681278944015503},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.6086187958717346},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6048744916915894},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5540197491645813},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5295876860618591},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4578368663787842},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.45029330253601074},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4189434349536896},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37422460317611694},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36454954743385315},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3350520730018616},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3218022882938385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30789855122566223},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22915679216384888},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14024677872657776},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0694456696510315},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06519696116447449}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.9342944622039795},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.6807745695114136},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6681278944015503},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.6086187958717346},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6048744916915894},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5540197491645813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5295876860618591},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4578368663787842},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.45029330253601074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4189434349536896},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37422460317611694},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36454954743385315},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3350520730018616},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3218022882938385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30789855122566223},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22915679216384888},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14024677872657776},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0694456696510315},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06519696116447449},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/2110170.2110175","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2110170.2110175","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"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt13r6m7sb","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/13r6m7sb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Geometry: Theory and Applications, vol 46, iss 3","raw_type":"article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt5142f2wk","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/5142f2wk","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:qt13r6m7sb","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/13r6m7sb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"De Loera, JA; Dutra, B; K\u00c3\u00b6ppe, M; Moreinis, S; Pinto, G; & Wu, J. (2013). Software for exact integration of polynomials over polyhedra. Computational Geometry: Theory and Applications, 46(3), 232 - 252. doi: 10.1016/j.comgeo.2012.09.001. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/13r6m7sb","raw_type":"article"},{"id":"pmh:qt5142f2wk","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/5142f2wk","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"De Loera, Jesus; Dutra, Brandon; Koeppe, Matthias; Moreinis, Stanislav; Pinto, Gregory; & Wu, Jianqiu. (2011). Software for Exact Integration of Polynomials over Polyhedra. Comput. Geom., 46, 232-252. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/5142f2wk","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332564","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W116212968","https://openalex.org/W1489298643","https://openalex.org/W1526262508","https://openalex.org/W1531327550","https://openalex.org/W1534719102","https://openalex.org/W1566753159","https://openalex.org/W1570707370","https://openalex.org/W1571893839","https://openalex.org/W1583652109","https://openalex.org/W1707866322","https://openalex.org/W1971216370","https://openalex.org/W1974745849","https://openalex.org/W1978089913","https://openalex.org/W1986690046","https://openalex.org/W1986698569","https://openalex.org/W1987679122","https://openalex.org/W1988942087","https://openalex.org/W2005900349","https://openalex.org/W2026226892","https://openalex.org/W2032298981","https://openalex.org/W2033084216","https://openalex.org/W2033398663","https://openalex.org/W2039934364","https://openalex.org/W2071667967","https://openalex.org/W2072727857","https://openalex.org/W2076216229","https://openalex.org/W2081659888","https://openalex.org/W2083181070","https://openalex.org/W2096735200","https://openalex.org/W2160273855","https://openalex.org/W2233474732","https://openalex.org/W2264065105","https://openalex.org/W2288450576","https://openalex.org/W2477102943","https://openalex.org/W3104134886"],"related_works":["https://openalex.org/W4239526988","https://openalex.org/W4235007892","https://openalex.org/W2396049332","https://openalex.org/W2922863847","https://openalex.org/W1802456315","https://openalex.org/W2186513065","https://openalex.org/W2518606980","https://openalex.org/W2582711371","https://openalex.org/W139605340","https://openalex.org/W2971340537"],"abstract_inverted_index":{"We":[0,31],"are":[1,17],"interested":[2],"in":[3],"quickly":[4],"computing":[5],"the":[6,38],"exact":[7],"value":[8],"of":[9,11,29,37],"integrals":[10],"polynomial":[12],"functions":[13],"over":[14],"domains":[15],"that":[16],"decomposable":[18],"into":[19],"convex":[20],"polyhedra":[21],"(e.g.,":[22],"a":[23,33],"tetrahedral":[24],"or":[25],"cubical":[26],"mesh":[27],"decomposition":[28],"space).":[30],"describe":[32],"software":[34,39],"implementation,":[35],"part":[36],"LattE,":[40],"and":[41],"provide":[42],"benchmark":[43],"computations.":[44]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}