{"id":"https://openalex.org/W7160826178","doi":"https://doi.org/10.1007/978-3-032-22539-9_12","title":"Normal Forms of\u00a0Coordinate-Free Quaternionic Polynomials","display_name":"Normal Forms of\u00a0Coordinate-Free Quaternionic Polynomials","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7160826178","doi":"https://doi.org/10.1007/978-3-032-22539-9_12"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-22539-9_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-22539-9_12","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5065859286","display_name":"Hui Li","orcid":"https://orcid.org/0000-0001-9198-3951"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongbo Li","raw_affiliation_strings":["SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135902861","display_name":"Zhengyang Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengyang Wang","raw_affiliation_strings":["SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100644814","display_name":"Ying Liu","orcid":"https://orcid.org/0000-0002-8951-2648"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Liu","raw_affiliation_strings":["SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135898316","display_name":"Lei Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Huang","raw_affiliation_strings":["SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044887714","display_name":"Changpeng Shao","orcid":"https://orcid.org/0000-0002-3008-7296"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changpeng Shao","raw_affiliation_strings":["SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SKLMS, AMSS, UCAS, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5065859286"],"corresponding_institution_ids":["https://openalex.org/I4210165038"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.94035088,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"165","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.5443999767303467,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.5443999767303467,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.052799999713897705,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.045499999076128006,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.9142000079154968},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.6912000179290771},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6272000074386597},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5570999979972839},{"id":"https://openalex.org/keywords/quaternion-algebra","display_name":"Quaternion algebra","score":0.5526000261306763},{"id":"https://openalex.org/keywords/quaternionic-representation","display_name":"Quaternionic representation","score":0.43959999084472656},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.3718999922275543}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9142000079154968},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.6912000179290771},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6272000074386597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6144000291824341},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5570999979972839},{"id":"https://openalex.org/C151640129","wikidata":"https://www.wikidata.org/wiki/Q2835967","display_name":"Quaternion algebra","level":5,"score":0.5526000261306763},{"id":"https://openalex.org/C25398135","wikidata":"https://www.wikidata.org/wiki/Q7269569","display_name":"Quaternionic representation","level":4,"score":0.43959999084472656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4147999882698059},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.34709998965263367},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.32820001244544983},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.31949999928474426},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.3003999888896942},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.2667999863624573},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.2563999891281128},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.25589999556541443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-032-22539-9_12","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-032-22539-9_12","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W165259598","https://openalex.org/W1993304545","https://openalex.org/W2039864462","https://openalex.org/W2047019369","https://openalex.org/W2078064020","https://openalex.org/W2884392345","https://openalex.org/W3086412101","https://openalex.org/W3126996113","https://openalex.org/W4230663566","https://openalex.org/W4367293029"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-05-13T06:04:23.736269","created_date":"2026-05-12T00:00:00"}
