{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:10:02Z","timestamp":1776766202192,"version":"3.51.2"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"218","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Q left-parenthesis t 1 comma t 2 comma ellipsis comma t Subscript m Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>t<\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>t<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mo>\n                              \u2026\n                              \n                            <\/mml:mo>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>t<\/mml:mi>\n                              <mml:mi>m<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Q}(t_1,t_2,\\ldots ,t_m)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.\n                  <\/p>","DOI":"10.1090\/s0025-5718-97-00831-4","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"823-831","source":"Crossref","is-referenced-by-count":10,"title":["Computation of Galois groups over function fields"],"prefix":"10.1090","volume":"66","author":[{"given":"Thomas","family":"Mattman","sequence":"first","affiliation":[]},{"given":"John","family":"McKay","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1997]]},"reference":[{"issue":"8","key":"1","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1080\/00927878308822884","article-title":"The transitive groups of degree up to eleven","volume":"11","author":"Butler, Gregory","year":"1983","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"issue":"208","key":"2","doi-asserted-by":"publisher","first-page":"749","DOI":"10.2307\/2153295","article-title":"Symmetric functions, \ud835\udc5a-sets, and Galois groups","volume":"63","author":"Casperson, David","year":"1994","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"3","unstructured":"\\bysame, \u2018An ideal decomposition algorithm\u2019, preliminary report, AMS Abstracts 13 (1992) 405."},{"key":"4","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02945-9","volume-title":"A course in computational algebraic number theory","volume":"138","author":"Cohen, Henri","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540556400"},{"key":"5","unstructured":"J. Conway, A. Hulpke, J. McKay, \u2018 On transitive permutation groups\u2019 (to appear)."},{"key":"6","unstructured":"H. Darmon, private communication (1986)."},{"issue":"12","key":"7","doi-asserted-by":"publisher","first-page":"2941","DOI":"10.1080\/00927878908823887","article-title":"Computational verification of \ud835\udc40\u2081\u2081 and \ud835\udc40\u2081\u2082 as Galois groups over \ud835\udc44","volume":"17","author":"Darmon, Henri","year":"1989","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1016\/0022-314X(84)90080-5","article-title":"The construction of \ud835\udc46\ud835\udc3f(2,3)-polynomials","volume":"19","author":"Heider, Franz-Peter","year":"1984","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"key":"9","unstructured":"A. Hulpke, Konstruktion transitiver Permutationsgruppen. PhD. thesis, RWTH-Aachen, Aachen, Germany, 1996."},{"key":"10","unstructured":"T. W. Mattman, The computation of Galois groups over function fields. Master\u2019s thesis, McGill University, Montr\u00e9al, Qu\u00e9bec, Canada, December 1992."},{"key":"11","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1515\/crll.1984.349.179","article-title":"Konstruktion von Zahl- und Funktionenk\u00f6rpern mit vorgegebener Galoisgruppe","volume":"349","author":"Matzat, B. Heinrich","year":"1984","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"12","unstructured":"J. McKay, \u2018Advances in computational Galois theory\u2019, in Computers in algebra, (Martin C. Tangora, Ed.), Lecture notes in pure and applied mathematics., vol. 111, pp.99-101, (1988)."},{"issue":"3","key":"13","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1080\/00927878508823180","article-title":"Actions of permutation groups on \ud835\udc5f-sets","volume":"13","author":"McKay, J.","year":"1985","journal-title":"Comm. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0092-7872","issn-type":"print"},{"issue":"1","key":"14","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/0021-8693(91)90261-6","article-title":"The groups of order 256","volume":"143","author":"O\u2019Brien, E. A.","year":"1991","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"15","unstructured":"M. Olivier, Calcul des groupes de Galois de degr\u00e9 8,9,10, et 11. Universit\u00e9 Bordeaux I, 12 Oct. 1991 et 12 Fev. 1993."},{"key":"16","unstructured":"E. Skrzipczyk, Charaktertafeln von \ud835\udc5d-Gruppen. Diplomarbeit, Lehrstuhl D f\u00fcr Mathematik, Rheinisch-Westf\u00e4lische Technische Hochschule Aachen, Aachen, Germany, 1992."},{"key":"17","unstructured":"L. Soicher, The computation of Galois groups. Master\u2019s thesis, University of Concordia, Montr\u00e9al, Qu\u00e9bec, Canada, April 1981."},{"key":"18","isbn-type":"print","first-page":"297","article-title":"Practical strategies for computing Galois groups","author":"Kolesova, G.","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0120662701"},{"issue":"3","key":"19","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/0022-314X(85)90022-8","article-title":"Computing Galois groups over the rationals","volume":"20","author":"Soicher, Leonard","year":"1985","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"key":"20","unstructured":"Gene W. Smith, \u2018Some Polynomials over \u211a(\ud835\udd65) and their Galois groups.\u2019 (to appear in Math. Comp.)."},{"key":"21","unstructured":"R. P. Stauduhar, The automatic determination of Galois groups. Ph. D. Dissertation, University of California, Berkeley, 1969."},{"key":"22","doi-asserted-by":"publisher","first-page":"981","DOI":"10.2307\/2005536","article-title":"The determination of Galois groups","volume":"27","author":"Stauduhar, Richard P.","year":"1973","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"7","key":"23","doi-asserted-by":"publisher","first-page":"542","DOI":"10.2307\/2320017","article-title":"On the Routh-Hurwitz problem","volume":"84","author":"Strelitz, Sh.","year":"1977","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"key":"24","doi-asserted-by":"publisher","first-page":"783","DOI":"10.2307\/2371336","article-title":"Ring homomorphisms which are also lattice homomorphisms","volume":"61","author":"Ward, Morgan","year":"1939","journal-title":"Amer. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9327","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00831-4\/S0025-5718-97-00831-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00831-4\/S0025-5718-97-00831-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:27:35Z","timestamp":1776720455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1997-66-218\/S0025-5718-97-00831-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"references-count":24,"journal-issue":{"issue":"218","published-print":{"date-parts":[[1997,4]]}},"alternative-id":["S0025-5718-97-00831-4"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-97-00831-4","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1997]]}}}