{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T09:00:03Z","timestamp":1760346003483},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2008,2,1]],"date-time":"2008-02-01T00:00:00Z","timestamp":1201824000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:p>This paper presents an analysis of definitions and decidability for exponential functions on various matrix algebras. The main idea is to show that, generically, the entries of the exponential (or logarithm) of a matrix are Pfaffian functions of the entries of the matrix.<\/jats:p>","DOI":"10.1017\/s0960129508006622","type":"journal-article","created":{"date-parts":[[2008,3,5]],"date-time":"2008-03-05T14:42:14Z","timestamp":1204728134000},"page":"189-204","source":"Crossref","is-referenced-by-count":3,"title":["Model theory of exponentials on Lie algebras"],"prefix":"10.1017","volume":"18","author":[{"given":"ANGUS","family":"MACINTYRE","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,2,1]]},"reference":[{"key":"S0960129508006622_ref7","unstructured":"Macintyre A. J. (2005b) Some Observations about the Real and Imaginary Parts of Complex Pfaffian Functions. To appear in: Macpherson D. . (eds.) Proceedings of INI 2005 Model Theory meeting."},{"key":"S0960129508006622_ref9","unstructured":"Serre J. P. (1965) Lie Algebras and Lie groups, W. A. Benjamin."},{"key":"S0960129508006622_ref1","doi-asserted-by":"crossref","unstructured":"Barut A. O. , Zeni J. R. and Laufer A. (1994) The exponential map for the conformal group O(2,4). arXiv:hep-th\/9408105v3.","DOI":"10.1088\/0305-4470\/27\/15\/022"},{"key":"S0960129508006622_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-314X(02)00002-1"},{"key":"S0960129508006622_ref6","unstructured":"Macintyre A. J. (2005a) Elementary Theory of Elliptic Functions 1; The Formalism and a Special Case. In: Edmundo, M., Richardson, D. and Wilkie, A. (eds.) O-minimal Structures, Proceedings of the RAAG Summer School Lisbon 2003, Lecture Notes in Real Algebraic and Analytic Geometry, Cuvillier Verlag 104\u2013131."},{"key":"S0960129508006622_ref4","doi-asserted-by":"publisher","DOI":"10.2307\/2275634"},{"key":"S0960129508006622_ref3","unstructured":"Bianconi R. (1990) Some Results in the Model Theory of Analytic Functions, Ph.D. Thesis, Oxford."},{"key":"S0960129508006622_ref8","unstructured":"Macintyre A. J. and Wilkie A. (1996) On the decidability of the real exponential field. In: Odifreddi P. (ed.) Kreiseliana. About and Around Georg Kreisel, A. K. Peters 441\u2013467."},{"key":"S0960129508006622_ref5","first-page":"211","article-title":"Complexity of computations with Pfaffian and Noetherian functions","volume":"137","author":"Gabrielov","year":"2004","journal-title":"NATO Sci. Ser. II Math. Phys. Chem"},{"key":"S0960129508006622_ref10","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-96-00216-0"},{"key":"S0960129508006622_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2004.07.001"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129508006622","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T17:45:11Z","timestamp":1557337511000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129508006622\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["S0960129508006622"],"URL":"https:\/\/doi.org\/10.1017\/s0960129508006622","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,2]]}}}