{"id":"https://openalex.org/W1982184845","doi":"https://doi.org/10.1145/1576702.1576747","title":"Computing with abstract matrix structures","display_name":"Computing with abstract matrix structures","publication_year":2009,"publication_date":"2009-07-28","ids":{"openalex":"https://openalex.org/W1982184845","doi":"https://doi.org/10.1145/1576702.1576747","mag":"1982184845"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576747","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-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/A5111170475","display_name":"Alan P. Sexton","orcid":null},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alan P. Sexton","raw_affiliation_strings":["University of Birmingham, Birmingham, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Birmingham, Birmingham, United Kingdom","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043436240","display_name":"Volker Sorge","orcid":"https://orcid.org/0000-0003-2796-1488"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Volker Sorge","raw_affiliation_strings":["University of Birmingham, Birmingham, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Birmingham, Birmingham, United Kingdom","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082854012","display_name":"Stephen M. Watt","orcid":"https://orcid.org/0000-0001-8303-4983"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Stephen M. Watt","raw_affiliation_strings":["University of Western Ontario, London, Canada"],"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.529,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.784283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":84,"max":85},"biblio":{"volume":null,"issue":null,"first_page":"325","last_page":"332"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9993,"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":0.9993,"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/T10142","display_name":"Formal Methods in Verification","score":0.9936,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9931,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/matrix","display_name":"Matrix (chemical analysis)","score":0.6448797},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.53566825}],"concepts":[{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6448797},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6441073},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6210762},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5723582},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5502057},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.541965},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.53566825},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5251448},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4943273},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46760005},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.43895924},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43730882},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.43575355},{"id":"https://openalex.org/C149488123","wikidata":"https://www.wikidata.org/wiki/Q17098730","display_name":"Matrix analysis","level":3,"score":0.42538935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4128725},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.41260204},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26673707},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17899442},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17208335},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.109880984},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08539587},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1145/1576702.1576747","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":10,"referenced_works":["https://openalex.org/W1583295953","https://openalex.org/W2000606360","https://openalex.org/W2017906382","https://openalex.org/W2019932310","https://openalex.org/W2069389193","https://openalex.org/W2093397547","https://openalex.org/W2097120215","https://openalex.org/W2137356570","https://openalex.org/W3010782316","https://openalex.org/W4230919050"],"related_works":["https://openalex.org/W752783541","https://openalex.org/W4287593139","https://openalex.org/W4206811032","https://openalex.org/W3212757063","https://openalex.org/W3099313426","https://openalex.org/W2995605830","https://openalex.org/W2596457687","https://openalex.org/W2093666864","https://openalex.org/W2086123442","https://openalex.org/W1506547947"],"abstract_inverted_index":{"Classes":[0],"of":[1,12,27,43,48,68,84,92,108],"matrices":[2,28,45,105],"are":[3],"often":[4],"presented":[5],"with":[6,24],"symbolic":[7],"dimensions":[8],"using":[9,114],"a":[10,115],"mixture":[11],"terms":[13,47],"and":[14,51,56],"ellipsis":[15],"symbols":[16],"to":[17,63,99],"describe":[18,39],"their":[19],"internal":[20],"structure.":[21],"While":[22],"working":[23],"such":[25,44],"classes":[26],"is":[29],"everyday":[30],"mathematical":[31],"practice,":[32],"it":[33],"has":[34],"little":[35],"automated":[36],"support.":[37],"We":[38,75],"an":[40,78,82],"algebraic":[41],"encoding":[42,83],"in":[46],"support":[49,85,111],"functions":[50],"define":[52,77,100],"the":[53,65,69,93],"corresponding":[54],"addition":[55],"multiplication":[57],"algorithms.":[58],"It":[59],"is,":[60],"however,":[61],"non-trivial":[62],"retrieve":[64],"structural":[66,94],"description":[67],"matrix":[70,80],"resulting":[71],"from":[72],"these":[73],"operations.":[74],"therefore":[76],"abstract":[79,104],"as":[81,106],"function":[86,112],"combinations":[87,113],"that":[88],"enables":[89],"simple":[90],"recovery":[91],"properties.":[95],"This":[96],"allows":[97],"us":[98],"arithmetic":[101],"algorithms":[102],"for":[103,110],"extensions":[107],"those":[109],"normalising":[116],"term":[117],"rewrite":[118],"system.":[119]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1982184845","counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2024-12-10T07:06:32.327482","created_date":"2016-06-24"}