{"id":"https://openalex.org/W2073711740","doi":"https://doi.org/10.1145/2110170.2110177","title":"Defect polytopes and counter-examples with polymake","display_name":"Defect polytopes and counter-examples with polymake","publication_year":2012,"publication_date":"2012-01-23","ids":{"openalex":"https://openalex.org/W2073711740","doi":"https://doi.org/10.1145/2110170.2110177","mag":"2073711740"},"language":"en","primary_location":{"id":"doi:10.1145/2110170.2110177","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2110170.2110177","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/A5035639170","display_name":"Michael Joswig","orcid":"https://orcid.org/0000-0002-4974-9659"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Joswig","raw_affiliation_strings":["TU Darmstadt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Darmstadt","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075556519","display_name":"Andreas Paffenholz","orcid":"https://orcid.org/0000-0001-9718-523X"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Paffenholz","raw_affiliation_strings":["TU Darmstadt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Darmstadt","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13948947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"3/4","first_page":"177","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9995999932289124,"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":0.9995999932289124,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9975000023841858,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9970999956130981,"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/polytope","display_name":"Polytope","score":0.9716662168502808},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7479043006896973},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.48734793066978455},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4369734823703766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43202081322669983},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3670433759689331},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3277422785758972},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27016645669937134},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06817862391471863}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9716662168502808},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7479043006896973},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.48734793066978455},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4369734823703766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43202081322669983},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3670433759689331},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3277422785758972},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27016645669937134},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06817862391471863}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2110170.2110177","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2110170.2110177","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1536409494","https://openalex.org/W2082759220","https://openalex.org/W2963038114","https://openalex.org/W2963505083","https://openalex.org/W3039948875"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4289703404","https://openalex.org/W4387265813","https://openalex.org/W3103454236","https://openalex.org/W4320410061","https://openalex.org/W2999175164"],"abstract_inverted_index":{"It":[0],"is":[1],"demonstrated":[2],"how":[3],"the":[4],"software":[5],"system":[6],"polymake":[7],"can":[8],"be":[9],"used":[10],"for":[11],"computations":[12],"in":[13],"toric":[14],"geometry.":[15],"More":[16],"precisely,":[17],"counter-examples":[18],"to":[19,22],"conjectures":[20],"related":[21],"A-determinants":[23],"and":[24],"defect":[25],"polytopes":[26],"are":[27],"constructed.":[28]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
