{"id":"https://openalex.org/W2136612619","doi":"https://doi.org/10.1007/978-3-540-73086-6_10","title":"Rule-Based Simplification in Vector-Product Spaces","display_name":"Rule-Based Simplification in Vector-Product Spaces","publication_year":2007,"publication_date":"2007-08-14","ids":{"openalex":"https://openalex.org/W2136612619","doi":"https://doi.org/10.1007/978-3-540-73086-6_10","mag":"2136612619"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-73086-6_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-73086-6_10","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/A5101826810","display_name":"Songxin Liang","orcid":"https://orcid.org/0000-0002-5840-6455"},"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":true,"raw_author_name":"Songxin Liang","raw_affiliation_strings":["Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051667032","display_name":"David J. Jeffrey","orcid":"https://orcid.org/0000-0002-2161-6803"},"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":"David J. Jeffrey","raw_affiliation_strings":["Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101826810"],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12093628,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"116","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11450","display_name":"Model-Driven Software Engineering Techniques","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T11450","display_name":"Model-Driven Software Engineering Techniques","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10703","display_name":"Business Process Modeling and Analysis","score":0.9711999893188477,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9697999954223633,"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/cartesian-product","display_name":"Cartesian product","score":0.6654549241065979},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6509557962417603},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6487252116203308},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.6222735047340393},{"id":"https://openalex.org/keywords/cross-product","display_name":"Cross product","score":0.5931881666183472},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.5797083377838135},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5591645240783691},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5465578436851501},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4587957561016083},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4221068024635315},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.41616880893707275},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3757946193218231},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3523721694946289},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35121652483940125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22763565182685852},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18118128180503845},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.17386823892593384},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06977933645248413}],"concepts":[{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.6654549241065979},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6509557962417603},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6487252116203308},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.6222735047340393},{"id":"https://openalex.org/C82927061","wikidata":"https://www.wikidata.org/wiki/Q178192","display_name":"Cross product","level":2,"score":0.5931881666183472},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.5797083377838135},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5591645240783691},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5465578436851501},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4587957561016083},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4221068024635315},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.41616880893707275},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3757946193218231},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3523721694946289},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35121652483940125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22763565182685852},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18118128180503845},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.17386823892593384},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06977933645248413},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-540-73086-6_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-73086-6_10","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:CiteSeerX.psu:10.1.1.70.8699","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.8699","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.apmaths.uwo.ca/~djeffrey/Offprints/LJcalculemus.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W207221367","https://openalex.org/W275570405","https://openalex.org/W607301767","https://openalex.org/W1525507633","https://openalex.org/W1545091652","https://openalex.org/W1965480470","https://openalex.org/W1991268470","https://openalex.org/W2000598800","https://openalex.org/W2066556741","https://openalex.org/W2083712296","https://openalex.org/W2486753540","https://openalex.org/W3010782316","https://openalex.org/W3023233245","https://openalex.org/W3102905031"],"related_works":["https://openalex.org/W2041479119","https://openalex.org/W4232341271","https://openalex.org/W4250540213","https://openalex.org/W3187046455","https://openalex.org/W177232795","https://openalex.org/W4244509909","https://openalex.org/W1855866920","https://openalex.org/W4386773258","https://openalex.org/W4253934820","https://openalex.org/W4248443820"],"abstract_inverted_index":null,"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
