{"id":"https://openalex.org/W3097262658","doi":"https://doi.org/10.1007/978-3-030-61864-3_42","title":"Optimal Parenthesizing of Geometric Algebra Products","display_name":"Optimal Parenthesizing of Geometric Algebra Products","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3097262658","doi":"https://doi.org/10.1007/978-3-030-61864-3_42","mag":"3097262658"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-61864-3_42","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-61864-3_42","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-03168974","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047133071","display_name":"St\u00e9phane Breuils","orcid":"https://orcid.org/0000-0002-8636-4977"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"St\u00e9phane Breuils","raw_affiliation_strings":["National Institute of Informatics, Tokyo, Japan","NII - National Institute of Informatics (2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 - Japan)"],"raw_orcid":"https://orcid.org/0000-0002-8636-4977","affiliations":[{"raw_affiliation_string":"National Institute of Informatics, Tokyo, Japan","institution_ids":["https://openalex.org/I184597095"]},{"raw_affiliation_string":"NII - National Institute of Informatics (2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 - Japan)","institution_ids":["https://openalex.org/I184597095"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083779733","display_name":"Vincent Nozick","orcid":"https://orcid.org/0000-0001-8792-7164"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Nozick","raw_affiliation_strings":["Universit\u00e9 Gustave Eiffel, LIGM, CNRS - ENPC - ESIEE Paris -UPEM, Paris, France","LIGM - Laboratoire d'Informatique Gaspard-Monge (Universit\u00e9 Gustave Eiffel, Cit\u00e9 Descartes, B\u00e2timent Copernic, 5 bd Descartes, 77454 Marne-la-Vall\u00e9e Cedex 2 - France)"],"raw_orcid":"https://orcid.org/0000-0001-8792-7164","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Gustave Eiffel, LIGM, CNRS - ENPC - ESIEE Paris -UPEM, Paris, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I1294671590","https://openalex.org/I4210154111"]},{"raw_affiliation_string":"LIGM - Laboratoire d'Informatique Gaspard-Monge (Universit\u00e9 Gustave Eiffel, Cit\u00e9 Descartes, B\u00e2timent Copernic, 5 bd Descartes, 77454 Marne-la-Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I4210154111"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101463320","display_name":"Akihiro Sugimoto","orcid":"https://orcid.org/0000-0001-9148-9822"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akihiro Sugimoto","raw_affiliation_strings":["National Institute of Informatics, Tokyo, Japan","NII - National Institute of Informatics (2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 - Japan)"],"raw_orcid":"https://orcid.org/0000-0001-9148-9822","affiliations":[{"raw_affiliation_string":"National Institute of Informatics, Tokyo, Japan","institution_ids":["https://openalex.org/I184597095"]},{"raw_affiliation_string":"NII - National Institute of Informatics (2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430 - Japan)","institution_ids":["https://openalex.org/I184597095"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047133071"],"corresponding_institution_ids":["https://openalex.org/I184597095"],"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":0.27858293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"492","last_page":"500"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.975600004196167,"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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.975600004196167,"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"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.972599983215332,"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":0.9704999923706055,"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/conformal-geometric-algebra","display_name":"Conformal geometric algebra","score":0.7930147051811218},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6438050866127014},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.6105929017066956},{"id":"https://openalex.org/keywords/geometric-algebra","display_name":"Geometric algebra","score":0.5786181688308716},{"id":"https://openalex.org/keywords/quadric","display_name":"Quadric","score":0.547797679901123},{"id":"https://openalex.org/keywords/universal-geometric-algebra","display_name":"Universal geometric algebra","score":0.5244072675704956},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5181980729103088},{"id":"https://openalex.org/keywords/geometric-programming","display_name":"Geometric programming","score":0.5091246962547302},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5027046203613281},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.495206743478775},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4630994498729706},{"id":"https://openalex.org/keywords/binary-expression-tree","display_name":"Binary expression tree","score":0.4525916874408722},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4454602897167206},{"id":"https://openalex.org/keywords/algebraic-expression","display_name":"Algebraic expression","score":0.4442741870880127},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.42915552854537964},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.42369601130485535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34502512216567993},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.33359673619270325},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.3175269067287445},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2002408802509308},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1717020571231842},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.12675213813781738},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.12614241242408752},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10995319485664368},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09088632464408875}],"concepts":[{"id":"https://openalex.org/C147898140","wikidata":"https://www.wikidata.org/wiki/Q5160252","display_name":"Conformal geometric algebra","level":5,"score":0.7930147051811218},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6438050866127014},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.6105929017066956},{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.5786181688308716},{"id":"https://openalex.org/C2779219049","wikidata":"https://www.wikidata.org/wiki/Q852117","display_name":"Quadric","level":2,"score":0.547797679901123},{"id":"https://openalex.org/C64228544","wikidata":"https://www.wikidata.org/wiki/Q17152794","display_name":"Universal geometric algebra","level":5,"score":0.5244072675704956},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5181980729103088},{"id":"https://openalex.org/C20729856","wikidata":"https://www.wikidata.org/wiki/Q2078279","display_name":"Geometric programming","level":2,"score":0.5091246962547302},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5027046203613281},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.495206743478775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4630994498729706},{"id":"https://openalex.org/C166055160","wikidata":"https://www.wikidata.org/wiki/Q4913895","display_name":"Binary expression tree","level":3,"score":0.4525916874408722},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4454602897167206},{"id":"https://openalex.org/C18912844","wikidata":"https://www.wikidata.org/wiki/Q4724001","display_name":"Algebraic expression","level":3,"score":0.4442741870880127},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.42915552854537964},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.42369601130485535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34502512216567993},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.33359673619270325},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3175269067287445},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2002408802509308},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1717020571231842},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.12675213813781738},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.12614241242408752},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10995319485664368},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09088632464408875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-030-61864-3_42","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-61864-3_42","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"},{"id":"pmh:oai:HAL:hal-03168974v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03168974","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CGI 2020, Oct 2020, Geneva, Switzerland. pp.492-500, &#x27E8;10.1007/978-3-030-61864-3_42&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03168974v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03168974","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CGI 2020, Oct 2020, Geneva, Switzerland. pp.492-500, &#x27E8;10.1007/978-3-030-61864-3_42&#x27E9;","raw_type":"Conference papers"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1600874933","https://openalex.org/W1655990431","https://openalex.org/W2116021467","https://openalex.org/W2167406894","https://openalex.org/W2481578392","https://openalex.org/W2795258309","https://openalex.org/W2950755372","https://openalex.org/W2981426306","https://openalex.org/W3009025664","https://openalex.org/W4238323774"],"related_works":["https://openalex.org/W2579897398","https://openalex.org/W4229936397","https://openalex.org/W4236366864","https://openalex.org/W4302390815","https://openalex.org/W2132811011","https://openalex.org/W2982251507","https://openalex.org/W4312628385","https://openalex.org/W2767525306","https://openalex.org/W2188862809","https://openalex.org/W2383614270"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
