Parametric Linear Algebra in Maple: Reduced Row Echelon Form

Name: Work Video:
Duration: 3 min 30 s
Description: Parametric Linear Algebra refers to the analysis of matrices containing elements which are symbolic. Properties such as the rank of the matrix can change depending upon possible values later assigned to the symbols. This is an example of the specialization problem. We discuss approaches to this problem and describe a package in Maple that is being developed to handle symbolic coefficients.
Siyuan Deng; Greg Reid; David J. Jeffrey
{'id': 'https://openalex.org/W4210971937', 'doi': 'https://doi.org/10.1109/synasc54541.2021.00017', 'title': 'Parametric Linear Algebra in Maple: Reduced Row Echelon Form', 'display_name': 'Parametric Linear Algebra in Maple: Reduced Row Echelon Form', 'publication_year': 2021, 'publication_date': '2021-12-01', 'ids': {'openalex': 'https://openalex.org/W4210971937', 'doi': 'https://doi.org/10.1109/synasc54541.2021.00017'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1109/synasc54541.2021.00017', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, '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': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5070270007', 'display_name': 'Siyuan Deng', 'orcid': None}, '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': 'Siyuan Deng', 'raw_affiliation_strings': ['Ontario Research Centre for Computer Algebra, The University of Western Ontario, Canada'], 'affiliations': [{'raw_affiliation_string': 'Ontario Research Centre for Computer Algebra, The University of Western Ontario, Canada', 'institution_ids': ['https://openalex.org/I125749732']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5044156631', 'display_name': 'Greg Reid', 'orcid': None}, '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': 'Greg Reid', 'raw_affiliation_strings': ['Ontario Research Centre for Computer Algebra, The University of Western Ontario, Canada'], 'affiliations': [{'raw_affiliation_string': 'Ontario Research Centre for Computer Algebra, The University of Western 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': 'D. J. Jeffrey', 'raw_affiliation_strings': ['Ontario Research Centre for Computer Algebra, The University of Western Ontario, Canada'], 'affiliations': [{'raw_affiliation_string': 'Ontario Research Centre for Computer Algebra, The University of Western Ontario, Canada', 'institution_ids': ['https://openalex.org/I125749732']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.132, 'has_fulltext': False, 'cited_by_count': 1, 'citation_normalized_percentile': {'value': 0.383608, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 57, 'max': 67}, 'biblio': {'volume': '43', 'issue': None, 'first_page': '33', 'last_page': '36'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11435', 'display_name': 'Polynomial and algebraic computation', 'score': 0.9823, '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': 0.9823, '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/T11416', 'display_name': 'Numerical methods for differential equations', 'score': 0.9272, 'subfield': {'id': 'https://openalex.org/subfields/2612', 'display_name': 'Numerical Analysis'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/rank', 'display_name': 'Rank (graph theory)', 'score': 0.7194778}, {'id': 'https://openalex.org/keywords/matrix-algebra', 'display_name': 'Matrix algebra', 'score': 0.65291834}, {'id': 'https://openalex.org/keywords/linear-algebra', 'display_name': 'Linear algebra', 'score': 0.59934336}, {'id': 'https://openalex.org/keywords/matrix', 'display_name': 'Matrix (chemical analysis)', 'score': 0.5355767}], 'concepts': [{'id': 'https://openalex.org/C2780414537', 'wikidata': 'https://www.wikidata.org/wiki/Q42292', 'display_name': 'Maple', 'level': 2, 'score': 0.9551562}, {'id': 'https://openalex.org/C110812573', 'wikidata': 'https://www.wikidata.org/wiki/Q175515', 'display_name': 'Symbolic computation', 'level': 2, 'score': 0.7500888}, {'id': 'https://openalex.org/C164226766', 'wikidata': 'https://www.wikidata.org/wiki/Q7293202', 'display_name': 'Rank (graph theory)', 'level': 2, 'score': 0.7194778}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.6719105}, {'id': 'https://openalex.org/C2988995629', 'wikidata': 'https://www.wikidata.org/wiki/Q2915729', 'display_name': 'Matrix algebra', 'level': 3, 'score': 0.65291834}, {'id': 'https://openalex.org/C117251300', 'wikidata': 'https://www.wikidata.org/wiki/Q1849855', 'display_name': 'Parametric statistics', 'level': 2, 'score': 0.6383363}, {'id': 'https://openalex.org/C139352143', 'wikidata': 'https://www.wikidata.org/wiki/Q82571', 'display_name': 'Linear algebra', 'level': 2, 'score': 0.59934336}, {'id': 'https://openalex.org/C106487976', 'wikidata': 'https://www.wikidata.org/wiki/Q685816', 'display_name': 'Matrix (chemical analysis)', 'level': 2, 'score': 0.5355767}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.43926245}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.39499265}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.21535411}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.1559946}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.063165724}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.053450584}, {'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/C158693339', 'wikidata': 'https://www.wikidata.org/wiki/Q190524', 'display_name': 'Eigenvalues and eigenvectors', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C59822182', 'wikidata': 'https://www.wikidata.org/wiki/Q441', 'display_name': 'Botany', 'level': 1, '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/C192562407', 'wikidata': 'https://www.wikidata.org/wiki/Q228736', 'display_name': 'Materials science', 'level': 0, '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/C159985019', 'wikidata': 'https://www.wikidata.org/wiki/Q181790', 'display_name': 'Composite material', '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}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1109/synasc54541.2021.00017', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 14, 'referenced_works': ['https://openalex.org/W1519900778', 'https://openalex.org/W1536271794', 'https://openalex.org/W2026612342', 'https://openalex.org/W2041109929', 'https://openalex.org/W2070679587', 'https://openalex.org/W2087700323', 'https://openalex.org/W2163740240', 'https://openalex.org/W2167838416', 'https://openalex.org/W2168645231', 'https://openalex.org/W22319829', 'https://openalex.org/W2777059928', 'https://openalex.org/W3011711392', 'https://openalex.org/W3096229878', 'https://openalex.org/W3097052597'], 'related_works': ['https://openalex.org/W851952888', 'https://openalex.org/W622366405', 'https://openalex.org/W4386225212', 'https://openalex.org/W4210971937', 'https://openalex.org/W2187413387', 'https://openalex.org/W2140907685', 'https://openalex.org/W2118921095', 'https://openalex.org/W2050090934', 'https://openalex.org/W2041511182', 'https://openalex.org/W1541593858'], 'abstract_inverted_index': {'Parametric': [0], 'Linear': [1], 'Algebra': [2], 'refers': [3], 'to': [4, 30, 44, 57], 'the': [5, 17, 20, 31, 38], 'analysis': [6], 'of': [7, 19, 37], 'matrices': [8], 'containing': [9], 'elements': [10], 'which': [11], 'are': [12], 'symbolic.': [13], 'Properties': [14], 'such': [15], 'as': [16], 'rank': [18], 'matrix': [21], 'can': [22], 'change': [23], 'depending': [24], 'upon': [25], 'possible': [26], 'values': [27], 'later': [28], 'assigned': [29], 'symbols.': [32], 'This': [33], 'is': [34, 54], 'an': [35], 'example': [36], 'specialization': [39], 'problem.': [40], 'We': [41], 'discuss': [42], 'approaches': [43], 'this': [45], 'problem': [46], 'and': [47], 'describe': [48], 'a': [49], 'package': [50], 'in': [51], 'Maple': [52], 'that': [53], 'being': [55], 'developed': [56], 'handle': [58], 'symbolic': [59], 'coefficients.': [60]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4210971937', 'counts_by_year': [{'year': 2023, 'cited_by_count': 1}], 'updated_date': '2024-12-14T05:20:19.166315', 'created_date': '2022-02-13'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
