{"id":"https://openalex.org/W1902612769","doi":"https://doi.org/10.1007/s11424-015-4085-1","title":"On implementing the symbolic preprocessing function over Boolean polynomial rings in Gr\u00f6bner basis algorithms using linear algebra","display_name":"On implementing the symbolic preprocessing function over Boolean polynomial rings in Gr\u00f6bner basis algorithms using linear algebra","publication_year":2015,"publication_date":"2015-08-29","ids":{"openalex":"https://openalex.org/W1902612769","doi":"https://doi.org/10.1007/s11424-015-4085-1","mag":"1902612769"},"language":"en","primary_location":{"id":"doi:10.1007/s11424-015-4085-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-015-4085-1","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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/A5101536898","display_name":"Yao Sun","orcid":"https://orcid.org/0000-0002-1163-9630"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao Sun","raw_affiliation_strings":["SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China","SKLOIS Institute of Information Engineering, Chinese Academy of Sciences,Beijing,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"raw_affiliation_string":"SKLOIS Institute of Information Engineering, Chinese Academy of Sciences,Beijing,China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102921796","display_name":"Zhenyu Huang","orcid":"https://orcid.org/0000-0002-3499-538X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhenyu Huang","raw_affiliation_strings":["SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China","SKLOIS Institute of Information Engineering, Chinese Academy of Sciences,Beijing,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"raw_affiliation_string":"SKLOIS Institute of Information Engineering, Chinese Academy of Sciences,Beijing,China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008820992","display_name":"Dongdai Lin","orcid":"https://orcid.org/0000-0002-3951-7889"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongdai Lin","raw_affiliation_strings":["SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China","SKLOIS Institute of Information Engineering, Chinese Academy of Sciences,Beijing,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"raw_affiliation_string":"SKLOIS Institute of Information Engineering, Chinese Academy of Sciences,Beijing,China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101585436","display_name":"Dingkang Wang","orcid":"https://orcid.org/0000-0002-5844-1277"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dingkang Wang","raw_affiliation_strings":["KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100090, China","KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100090, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"raw_affiliation_string":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102921796"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.3347,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63686293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"29","issue":"3","first_page":"789","last_page":"804"},"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":0.9883999824523926,"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":0.9843999743461609,"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/monomial-basis","display_name":"Monomial basis","score":0.8386126756668091},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7782298922538757},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5540586113929749},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.5270897150039673},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5267438292503357},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.522942841053009},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5221255421638489},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4364013075828552},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4290291666984558},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.42767494916915894},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.4178527295589447},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3882215619087219},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.18465405702590942},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16320395469665527},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.13622459769248962}],"concepts":[{"id":"https://openalex.org/C46132437","wikidata":"https://www.wikidata.org/wiki/Q6901742","display_name":"Monomial basis","level":3,"score":0.8386126756668091},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7782298922538757},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5540586113929749},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5270897150039673},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5267438292503357},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.522942841053009},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5221255421638489},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4364013075828552},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4290291666984558},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.42767494916915894},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.4178527295589447},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3882215619087219},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.18465405702590942},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16320395469665527},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.13622459769248962},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11424-015-4085-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11424-015-4085-1","pdf_url":null,"source":{"id":"https://openalex.org/S45848134","display_name":"Journal of Systems Science and Complexity","issn_l":"1009-6124","issn":["1009-6124","1559-7067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Systems Science and Complexity","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":15,"referenced_works":["https://openalex.org/W1520511539","https://openalex.org/W1524190946","https://openalex.org/W1583871653","https://openalex.org/W1984635032","https://openalex.org/W2023845786","https://openalex.org/W2077870553","https://openalex.org/W2099172492","https://openalex.org/W2128687423","https://openalex.org/W2161420356","https://openalex.org/W2161736272","https://openalex.org/W2605036633","https://openalex.org/W2949351170","https://openalex.org/W4285719527","https://openalex.org/W4302771278","https://openalex.org/W6600547436"],"related_works":["https://openalex.org/W3027438086","https://openalex.org/W4287776222","https://openalex.org/W2068219544","https://openalex.org/W156666843","https://openalex.org/W4294223057","https://openalex.org/W3022055031","https://openalex.org/W2953113706","https://openalex.org/W2139281949","https://openalex.org/W2600791068","https://openalex.org/W2954609483"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}