{"id":"https://openalex.org/W4360985570","doi":"https://doi.org/10.1134/s0361768823010048","title":"Implementation of Geometric Algebra in Computer Algebra Systems","display_name":"Implementation of Geometric Algebra in Computer Algebra Systems","publication_year":2023,"publication_date":"2023-02-01","ids":{"openalex":"https://openalex.org/W4360985570","doi":"https://doi.org/10.1134/s0361768823010048"},"language":"en","primary_location":{"id":"doi:10.1134/s0361768823010048","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s0361768823010048","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","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/A5003038545","display_name":"Migran N. Gevorkyan","orcid":"https://orcid.org/0000-0002-4834-4895"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"M. N. Gevorkyan","raw_affiliation_strings":["Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]},{"raw_affiliation_string":"Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011482984","display_name":"Anna V. Korolkova","orcid":"https://orcid.org/0000-0001-7141-7610"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. V. Korol\u2019kova","raw_affiliation_strings":["Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009706296","display_name":"Dmitry S. Kulyabov","orcid":"https://orcid.org/0000-0002-0877-7063"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]},{"id":"https://openalex.org/I32699454","display_name":"Joint Institute for Nuclear Research","ror":"https://ror.org/044yd9t77","country_code":"RU","type":"facility","lineage":["https://openalex.org/I32699454"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"D. S. Kulyabov","raw_affiliation_strings":["Joint Institute for Nuclear Research, 141980, Dubna, Moscow oblast, Russia","Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Joint Institute for Nuclear Research, 141980, Dubna, Moscow oblast, Russia","institution_ids":["https://openalex.org/I32699454"]},{"raw_affiliation_string":"Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]},{"raw_affiliation_string":"Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088133446","display_name":"Anastasia V. Demidova","orcid":"https://orcid.org/0000-0003-1000-9650"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. V. Demidova","raw_affiliation_strings":["Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]},{"raw_affiliation_string":"Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007177069","display_name":"Tatyana R. Velieva","orcid":"https://orcid.org/0000-0003-4466-8531"},"institutions":[{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"T. R. Velieva","raw_affiliation_strings":["Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Peoples\u2019 Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]},{"raw_affiliation_string":"Peoples' Friendship University of Russia (RUDN University), 117198, Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5003038545"],"corresponding_institution_ids":["https://openalex.org/I126527374"],"apc_list":null,"apc_paid":null,"fwci":1.5624,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7898793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"49","issue":"1","first_page":"42","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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/T12504","display_name":"Mathematics and Applications","score":0.9794999957084656,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9509000182151794,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/geometric-algebra","display_name":"Geometric algebra","score":0.9215333461761475},{"id":"https://openalex.org/keywords/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.9037419557571411},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.7246608138084412},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.6685289144515991},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.6374481320381165},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.6116443276405334},{"id":"https://openalex.org/keywords/spinor","display_name":"Spinor","score":0.5922392010688782},{"id":"https://openalex.org/keywords/tensor-algebra","display_name":"Tensor algebra","score":0.561869204044342},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.5594661235809326},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45872777700424194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44886553287506104},{"id":"https://openalex.org/keywords/multivector","display_name":"Multivector","score":0.42469531297683716},{"id":"https://openalex.org/keywords/covariant-transformation","display_name":"Covariant transformation","score":0.42295822501182556},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.4136753976345062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3868536949157715},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.34807705879211426},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2847006916999817},{"id":"https://openalex.org/keywords/cellular-algebra","display_name":"Cellular algebra","score":0.22549191117286682},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17972150444984436},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12968039512634277}],"concepts":[{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.9215333461761475},{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.9037419557571411},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.7246608138084412},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.6685289144515991},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.6374481320381165},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.6116443276405334},{"id":"https://openalex.org/C43506125","wikidata":"https://www.wikidata.org/wiki/Q604907","display_name":"Spinor","level":2,"score":0.5922392010688782},{"id":"https://openalex.org/C1680195","wikidata":"https://www.wikidata.org/wiki/Q2296021","display_name":"Tensor algebra","level":5,"score":0.561869204044342},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5594661235809326},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45872777700424194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44886553287506104},{"id":"https://openalex.org/C26238338","wikidata":"https://www.wikidata.org/wiki/Q2377336","display_name":"Multivector","level":5,"score":0.42469531297683716},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.42295822501182556},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4136753976345062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3868536949157715},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.34807705879211426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2847006916999817},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.22549191117286682},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17972150444984436},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12968039512634277},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","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},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0361768823010048","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1134/s0361768823010048","pdf_url":null,"source":{"id":"https://openalex.org/S150218641","display_name":"Programming and Computer Software","issn_l":"0361-7688","issn":["0361-7688","1608-3261"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Programming and Computer Software","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":15,"referenced_works":["https://openalex.org/W1527786550","https://openalex.org/W1585680900","https://openalex.org/W1595823061","https://openalex.org/W1971615759","https://openalex.org/W2008326757","https://openalex.org/W2323433001","https://openalex.org/W2481578392","https://openalex.org/W2964265862","https://openalex.org/W3037464210","https://openalex.org/W3104808187","https://openalex.org/W3105287098","https://openalex.org/W3155738275","https://openalex.org/W3196528307","https://openalex.org/W4200541301","https://openalex.org/W4210353177"],"related_works":["https://openalex.org/W2099345067","https://openalex.org/W2014430590","https://openalex.org/W2294799822","https://openalex.org/W1538240564","https://openalex.org/W3200012017","https://openalex.org/W2515465208","https://openalex.org/W1564656154","https://openalex.org/W4226142692","https://openalex.org/W2384324243","https://openalex.org/W2280182405"],"abstract_inverted_index":{"For":[0,25],"describing":[1],"specialized":[2,51,68,152],"mathematical":[3],"structures,":[4],"it":[5,83,129,159],"is":[6,57,62,130,137,160],"preferable":[7],"to":[8,27,35,145,148,162],"use":[9],"a":[10,15,78,119],"special":[11],"formalism":[12,154],"rather":[13,48],"than":[14,49],"general":[16],"one.":[17],"However,":[18],"tradition":[19],"often":[20,58],"prevails":[21],"in":[22,30,38,80,88,102,131,171],"this":[23,141],"case.":[24],"example,":[26],"describe":[28,36],"rotations":[29],"the":[31,39,125,166,172,175],"three-dimensional":[32],"space":[33],"or":[34,41,73],"motion":[37],"Galilean":[40],"Minkowski":[42],"spaces,":[43],"vector":[44],"(or":[45],"tensor)":[46],"formalism,":[47],"more":[50],"formalisms":[52],"of":[53,67,122,150,155,168,174],"Clifford":[54],"algebra":[55,136,170],"representations,":[56],"used.":[59],"This":[60],"approach":[61],"historically":[63],"justified.":[64],"The":[65],"application":[66],"formalisms,":[69],"such":[70,132],"as":[71],"spinors":[72],"quaternions,":[74],"has":[75,84],"not":[76],"become":[77],"mainstream":[79],"science,":[81],"but":[82],"taken":[85],"its":[86],"place":[87],"solving":[89],"practical":[90],"and":[91,112],"engineering":[92],"problems.":[93],"It":[94],"should":[95],"also":[96],"be":[97],"noted":[98],"that":[99,134],"all":[100],"operations":[101,123],"theoretical":[103],"problems":[104,133],"are":[105],"carried":[106],"out":[107],"precisely":[108],"with":[109,114,124],"symbolic":[110,176],"data,":[111],"manipulations":[113],"multidimensional":[115],"geometric":[116,156,169],"objects":[117],"require":[118],"large":[120],"number":[121],"same":[126],"objects.":[127],"And":[128],"computer":[135],"most":[138],"powerful.":[139],"In":[140],"paper,":[142],"we":[143],"want":[144],"draw":[146],"attention":[147],"one":[149],"these":[151],"formalisms\u2014the":[153],"algebra.":[157],"Namely,":[158],"proposed":[161],"consider":[163],"options":[164],"for":[165],"implementation":[167],"framework":[173],"computation":[177],"paradigm.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-04-02T13:48:15.688549","created_date":"2025-10-10T00:00:00"}
