{"id":"https://openalex.org/W2736522906","doi":"https://doi.org/10.1145/3087604.3087614","title":"On Signature-Based Gr\u00f6bner Bases Over Euclidean Rings","display_name":"On Signature-Based Gr\u00f6bner Bases Over Euclidean Rings","publication_year":2017,"publication_date":"2017-07-19","ids":{"openalex":"https://openalex.org/W2736522906","doi":"https://doi.org/10.1145/3087604.3087614","mag":"2736522906"},"language":"en","primary_location":{"id":"doi:10.1145/3087604.3087614","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087604.3087614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-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/A5027815561","display_name":"Christian Eder","orcid":"https://orcid.org/0000-0002-8814-8493"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian Eder","raw_affiliation_strings":["University of Kaiserslautern, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035101218","display_name":"Gerhard Pfister","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard Pfister","raw_affiliation_strings":["University of Kaiserslautern, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103350701","display_name":"Adrian Popescu","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Adrian Popescu","raw_affiliation_strings":["University of Kaiserslautern, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027815561"],"corresponding_institution_ids":["https://openalex.org/I153267046"],"apc_list":null,"apc_paid":null,"fwci":1.3627,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82827496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"141","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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":0.9998000264167786,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/signature","display_name":"Signature (topology)","score":0.7844508290290833},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6449729204177856},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6340234279632568},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5847718715667725},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5650779604911804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5445066690444946},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4817662239074707},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41826874017715454},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3794477880001068},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36402127146720886},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17633017897605896},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1418682038784027},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05459973216056824}],"concepts":[{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.7844508290290833},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6449729204177856},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6340234279632568},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5847718715667725},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5650779604911804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5445066690444946},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4817662239074707},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41826874017715454},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3794477880001068},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36402127146720886},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17633017897605896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1418682038784027},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05459973216056824}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3087604.3087614","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087604.3087614","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1481997196","https://openalex.org/W1563257127","https://openalex.org/W1993974377","https://openalex.org/W1993995116","https://openalex.org/W1999875564","https://openalex.org/W2004746351","https://openalex.org/W2038345254","https://openalex.org/W2077725083","https://openalex.org/W2175098281","https://openalex.org/W2229264317","https://openalex.org/W2475486651","https://openalex.org/W2599077812"],"related_works":["https://openalex.org/W4287600976","https://openalex.org/W2090152127","https://openalex.org/W1965169884","https://openalex.org/W3125580510","https://openalex.org/W2008939113","https://openalex.org/W14679004","https://openalex.org/W1566651525","https://openalex.org/W2977652649","https://openalex.org/W2318206461","https://openalex.org/W37157938"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"present":[4,24],"first":[5],"steps":[6],"in":[7],"using":[8],"signature-based":[9,52],"Gr\u00f6bner":[10,55],"basis":[11,56],"algorithms":[12],"like":[13],"Faug\u00e8re's":[14],"F5":[15],"or":[16],"GVW":[17],"for":[18],"computation":[19],"over":[20],"Euclidean":[21],"rings.":[22],"We":[23],"problems":[25],"appearing":[26],"when":[27],"having":[28],"to":[29,47,65],"deal":[30],"with":[31,70],"coefficients":[32],"and":[33,36,53],"zero":[34],"divisors":[35],"give":[37],"practical":[38],"solution":[39],"techniques.":[40],"A":[41],"hybrid":[42,72],"algorithm":[43],"is":[44],"presented":[45],"trying":[46],"combine":[48],"the":[49,71],"advantages":[50],"of":[51],"non-signature-based":[54],"computation.":[57],"For":[58],"some":[59],"examples":[60],"speedups":[61],"are":[62],"achieved":[63],"due":[64],"faster":[66],"finding":[67],"good":[68],"reducers":[69],"technique.":[73]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}