{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:50:59Z","timestamp":1762325459579,"version":"3.41.0"},"reference-count":6,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:p>We present the results of our recent article [4] and discuss its applications [5]. A finite group with an integer representation has a multiplicative action on the ring of Laurent polynomials, which is induced by a nonlinear action on the compact torus. We study the structure of the orbit space as the image of the fundamental invariants. For the Weyl groups associated to crystallographic root systems of types A, B, C, D, this image is a compact basic semi-algebraic set. We give the defining polynomial inequalities explicitly as the positivity-locus of a Hermite matrix polynomial.<\/jats:p>\n          <jats:p>As an application, we consider the problem of computing the optimal value of an exponential function and solve it with algebraic methods under symmetry assumptions.<\/jats:p>","DOI":"10.1145\/3572867.3572879","type":"journal-article","created":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:37:32Z","timestamp":1669250252000},"page":"72-75","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["T-orbit spaces of multiplicative actions and applications"],"prefix":"10.1145","volume":"56","author":[{"given":"Evelyne","family":"Hubert","sequence":"first","affiliation":[{"name":"Universit\u00e9 C\u00f4te d'Azur, Sophia Antipolis, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tobias","family":"Metzlaff","sequence":"additional","affiliation":[{"name":"Universit\u00e9 C\u00f4te d'Azur, Sophia Antipolis, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philippe","family":"Moustrou","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Toulouse Jean Jaures, Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cordian","family":"Riener","sequence":"additional","affiliation":[{"name":"UiT The Arctic University, Troms\u00f8, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2022,11,23]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-014-1070-7"},{"key":"e_1_2_1_2_1","volume-title":"Actualit\u00e9s Scientifiques et Industrielles, No. 1337","author":"Bourbaki","year":"1968","unstructured":"N. Bourbaki , \u00c9l\u00e9ments de math\u00e9matique. Fasc. XXXIV. Groupes et alg\u00e8bres de Lie. Chapitre IV: Groupes de Coxeter et syst\u00e8mes de Tits. Chapitre V: Groupes engendr\u00e9s par des r\u00e9flexions. Chapitre VI: syst\u00e8mes de racines , Actualit\u00e9s Scientifiques et Industrielles, No. 1337 , Hermann , Paris , 1968 N. Bourbaki, \u00c9l\u00e9ments de math\u00e9matique. Fasc. XXXIV. Groupes et alg\u00e8bres de Lie. Chapitre IV: Groupes de Coxeter et syst\u00e8mes de Tits. Chapitre V: Groupes engendr\u00e9s par des r\u00e9flexions. Chapitre VI: syst\u00e8mes de racines, Actualit\u00e9s Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.863494"},{"key":"e_1_2_1_4_1","volume-title":"Riener: Polynomial description for the T-Orbit Spaces of Multiplicative Actions, preprint https:\/\/hal.inria.fr\/hal-03590007","author":"Hubert T.","year":"2022","unstructured":"E. Hubert , T. Metzlaff , C. Riener: Polynomial description for the T-Orbit Spaces of Multiplicative Actions, preprint https:\/\/hal.inria.fr\/hal-03590007 , 2022 E. Hubert, T. Metzlaff, C. Riener: Polynomial description for the T-Orbit Spaces of Multiplicative Actions, preprint https:\/\/hal.inria.fr\/hal-03590007, 2022"},{"key":"e_1_2_1_5_1","volume-title":"Riener: Optimization of trigonometric polynomials with crystallographic symmetry and applications to spectral bounds of graphs, in preparation","author":"Hubert T.","year":"2022","unstructured":"E. Hubert , T. Metzlaff , P. Moustrou , C. Riener: Optimization of trigonometric polynomials with crystallographic symmetry and applications to spectral bounds of graphs, in preparation , 2022 E. Hubert, T. Metzlaff, P. Moustrou, C. Riener: Optimization of trigonometric polynomials with crystallographic symmetry and applications to spectral bounds of graphs, in preparation, 2022"},{"key":"e_1_2_1_6_1","volume-title":"Inventiones mathematicae 81:539--554","author":"Procesi G.","year":"1985","unstructured":"C. Procesi , G. Schwarz: Inequalities defining orbit spaces , Inventiones mathematicae 81:539--554 , 1985 C. Procesi, G. Schwarz: Inequalities defining orbit spaces, Inventiones mathematicae 81:539--554, 1985"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3572867.3572879","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3572867.3572879","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T18:08:10Z","timestamp":1750183690000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3572867.3572879"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["10.1145\/3572867.3572879"],"URL":"https:\/\/doi.org\/10.1145\/3572867.3572879","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2022,6]]},"assertion":[{"value":"2022-11-23","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}