{"id":"https://openalex.org/W2133406104","doi":"https://doi.org/10.1090/s0025-5718-97-00831-4","title":"Computation of Galois groups over function fields","display_name":"Computation of Galois groups over function fields","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2133406104","doi":"https://doi.org/10.1090/s0025-5718-97-00831-4","mag":"2133406104"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-97-00831-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00831-4","pdf_url":"https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00831-4/S0025-5718-97-00831-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00831-4/S0025-5718-97-00831-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073524329","display_name":"Thomas W. Mattman","orcid":"https://orcid.org/0000-0002-4900-6783"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Thomas Mattman","raw_affiliation_strings":["Mathematics Department, McGill University, Montr\u00c3\u00a9al, H3A 2K6, Canada","Mathematics Department, McGill University, Montr\u00e9al, H3A 2K6, Canada"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, McGill University, Montr\u00c3\u00a9al, H3A 2K6, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Mathematics Department, McGill University, Montr\u00e9al, H3A 2K6, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063250125","display_name":"John McKay","orcid":"https://orcid.org/0000-0003-4311-5513"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"John McKay","raw_affiliation_strings":["Centre Interuniversitaire en Calcul Math\u00c3\u00a9matique Alg\u00c3\u00a9brique  Concordia University  Montr\u00c3\u00a9al, H3G 1M8, Canada","Centre Interuniversitaire en Calcul Math\u00e9matique Alg\u00e9brique  Concordia University  Montr\u00e9al, H3G 1M8, Canada"],"affiliations":[{"raw_affiliation_string":"Centre Interuniversitaire en Calcul Math\u00c3\u00a9matique Alg\u00c3\u00a9brique  Concordia University  Montr\u00c3\u00a9al, H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]},{"raw_affiliation_string":"Centre Interuniversitaire en Calcul Math\u00e9matique Alg\u00e9brique  Concordia University  Montr\u00e9al, H3G 1M8, Canada","institution_ids":["https://openalex.org/I60158472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073524329"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":2.6284,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.89906782,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"66","issue":"218","first_page":"823","last_page":"831"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9921000003814697,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9815000295639038,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/algorithm","display_name":"Algorithm","score":0.648593544960022},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37932586669921875},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3760966658592224},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3403496742248535}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.648593544960022},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37932586669921875},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3760966658592224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3403496742248535}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-97-00831-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00831-4","pdf_url":"https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00831-4/S0025-5718-97-00831-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00831-4/S0025-5718-97-00831-4.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.93.2958","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.2958","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csuchico.edu/~tm108/thesis.pdf","raw_type":"text"},{"id":"pmh:oai:collectionscanada.gc.ca:QMM.56944","is_oa":false,"landing_page_url":"http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&amp;object_id=56944","pdf_url":null,"source":{"id":"https://openalex.org/S4306402307","display_name":"Library and Archives Canada (Government of Canada)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802286613","host_organization_name":"Government of Canada","host_organization_lineage":["https://openalex.org/I2802286613"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Electronic Thesis or Dissertation"},{"id":"pmh:oai:escholarship.mcgill.ca:gb19f7138","is_oa":false,"landing_page_url":"https://escholarship.mcgill.ca/concern/theses/gb19f7138","pdf_url":null,"source":{"id":"https://openalex.org/S4306401568","display_name":"eScholarship@McGill (McGill)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5023651","host_organization_name":"McGill University","host_organization_lineage":["https://openalex.org/I5023651"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-97-00831-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-97-00831-4","pdf_url":"https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00831-4/S0025-5718-97-00831-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2133406104.pdf","grobid_xml":"https://content.openalex.org/works/W2133406104.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W63192323","https://openalex.org/W1496801598","https://openalex.org/W1543220654","https://openalex.org/W1564741631","https://openalex.org/W1981653490","https://openalex.org/W1982581232","https://openalex.org/W1983607075","https://openalex.org/W1990893049","https://openalex.org/W1997236224","https://openalex.org/W2003573719","https://openalex.org/W2007439323","https://openalex.org/W2040685037","https://openalex.org/W2042510712","https://openalex.org/W2051170661","https://openalex.org/W2080980486","https://openalex.org/W2112408095","https://openalex.org/W2134984950","https://openalex.org/W2141040012","https://openalex.org/W2164227002","https://openalex.org/W2170509623","https://openalex.org/W2321049813","https://openalex.org/W2329964106","https://openalex.org/W2592324496","https://openalex.org/W4230715179","https://openalex.org/W4239003228","https://openalex.org/W4256175715","https://openalex.org/W6684962527"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W1974891317","https://openalex.org/W3107474891","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506","https://openalex.org/W2333698505"],"abstract_inverted_index":{"Symmetric":[0],"function":[1],"theory":[2],"provides":[3],"a":[4,103],"basis":[5],"for":[6,85],"computing":[7],"Galois":[8,104],"groups":[9],"which":[10],"is":[11,109],"largely":[12],"independent":[13],"of":[14,92,99],"the":[15,107],"coefficient":[16],"ring.":[17],"An":[18],"exact":[19],"algorithm":[20],"has":[21],"been":[22],"implemented":[23],"over":[24,106],"<inline-formula":[25],"content-type=\"math/mathml\">":[26],"<mml:math":[27],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[28],"alttext=\"double-struck":[29],"upper":[30],"Q":[31],"left-parenthesis":[32],"t":[33,36,41],"1":[34],"comma":[35,38,40],"2":[37],"ellipsis":[39],"Subscript":[42],"m":[43],"Baseline":[44],"right-parenthesis\">":[45],"<mml:semantics>":[46],"<mml:mrow>":[47],"<mml:mrow":[48],"class=\"MJX-TeXAtom-ORD\">":[49],"<mml:mi":[50],"mathvariant=\"double-struck\">Q</mml:mi>":[51],"</mml:mrow>":[52,75],"<mml:mo":[53,73],"stretchy=\"false\">(</mml:mo>":[54],"<mml:msub>":[55,60,69],"<mml:mi>t</mml:mi>":[56,61,70],"<mml:mn>1</mml:mn>":[57],"</mml:msub>":[58,63,72],"<mml:mo>,</mml:mo>":[59,64,68],"<mml:mn>2</mml:mn>":[62],"<mml:mo>":[65],"\u2026":[66],"</mml:mo>":[67],"<mml:mi>m</mml:mi>":[71],"stretchy=\"false\">)</mml:mo>":[74],"<mml:annotation":[76],"encoding=\"application/x-tex\">\\mathbb":[77],"{Q}(t_1,t_2,\\ldots":[78],",t_m)</mml:annotation>":[79],"</mml:semantics>":[80],"</mml:math>":[81],"</inline-formula>":[82],"in":[83],"Maple":[84],"degree":[86,100],"up":[87],"to":[88],"8.":[89],"A":[90],"table":[91],"polynomials":[93],"realizing":[94],"each":[95],"transitive":[96],"permutation":[97],"group":[98,105],"8":[101],"as":[102],"rationals":[108],"included.":[110]},"counts_by_year":[{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
