{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T19:13:31Z","timestamp":1687893211721},"reference-count":18,"publisher":"Elsevier BV","issue":"6","license":[{"start":{"date-parts":[[1991,12,1]],"date-time":"1991-12-01T00:00:00Z","timestamp":691545600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":7899,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[1991,12]]},"DOI":"10.1016\/s0747-7171(08)80148-4","type":"journal-article","created":{"date-parts":[[2008,7,22]],"date-time":"2008-07-22T09:12:18Z","timestamp":1216717938000},"page":"673-693","source":"Crossref","is-referenced-by-count":6,"title":["Group-classified polynomials of phase space in higher-order aberration expansions"],"prefix":"10.1016","volume":"12","author":[{"given":"Kurt Bernardo","family":"Wolf","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillermo","family":"Kr\u00f6tzsch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0747-7171(08)80148-4_bib1","volume":"8","author":"Biedenharn","year":"1981"},{"key":"10.1016\/S0747-7171(08)80148-4_bib2","doi-asserted-by":"crossref","first-page":"2215","DOI":"10.1063\/1.522868","article-title":"Lie series and invariant functions for analytic symplectic maps","volume":"17","author":"Dragt","year":"1976","journal-title":"J. Math. Phys."},{"key":"10.1016\/S0747-7171(08)80148-4_bib3","article-title":"Foundations of a Lie algebraic theory of geometrical optics","volume":"250","author":"Dragt","year":"1986"},{"key":"10.1016\/S0747-7171(08)80148-4_bib4","article-title":"Canonical integration with non-standard analysis","volume":"352","author":"Forest","year":"1989"},{"key":"10.1016\/S0747-7171(08)80148-4_bib5","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1063\/1.527333","article-title":"The metaplectic group within the Heisenberg-Weyl ring","volume":"27","author":"Garc\u00eda-Bull\u00e9","year":"1986","journal-title":"J. Math. Phys."},{"key":"10.1016\/S0747-7171(08)80148-4_bib6","series-title":"Lie Groups, Lie Algebras, and Some of their Applications","author":"Gilmore","year":"1978"},{"key":"10.1016\/S0747-7171(08)80148-4_bib7","series-title":"Classical Mechanics","author":"Goldstein","year":"1963"},{"key":"10.1016\/S0747-7171(08)80148-4_bib8","article-title":"Concatenation of Lie algebraic maps","volume":"352","author":"Healy","year":"1989"},{"key":"10.1016\/S0747-7171(08)80148-4_bib9","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/S0747-7171(85)80017-1","article-title":"Applications of a factorisation theorem for ninth-order aberration optics","volume":"1","author":"Navarro-Saad","year":"1985","journal-title":"J. Symb. Comp."},{"key":"10.1016\/S0747-7171(08)80148-4_bib10","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1063\/1.527103","article-title":"The group-theoretical treatment of aberrating systems. I. Aligned lens systems in third aberration order","volume":"27","author":"Navarro-Saad","year":"1986","journal-title":"J. Math. Phys."},{"key":"10.1016\/S0747-7171(08)80148-4_bib11","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1364\/JOSAA.3.000340","article-title":"Factorisation of the phase-space transformation produced by an arbitrary refracting surface","volume":"3","author":"Navarro-Saad","year":"1986","journal-title":"J. Opt. Soc. Am. A"},{"key":"10.1016\/S0747-7171(08)80148-4_bib12","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1119\/1.14999","article-title":"The Hamiltonian formulation of optics","volume":"55","author":"Sekiguchi","year":"1987","journal-title":"Am. J. Phys."},{"key":"10.1016\/S0747-7171(08)80148-4_bib13","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1137\/0515006","article-title":"Factored product expansions of nonlinear differential equations","volume":"15","author":"Steinberg","year":"1984","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/S0747-7171(08)80148-4_bib14","article-title":"Lie series, Lie transformations, and their applications","volume":"250","author":"Steinberg","year":"1986"},{"key":"10.1016\/S0747-7171(08)80148-4_bib15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0003-4916(86)90017-5","article-title":"Symmetry in Lie optics","volume":"172","author":"Wolf","year":"1986","journal-title":"Annals of Physics"},{"key":"10.1016\/S0747-7171(08)80148-4_bib16","doi-asserted-by":"crossref","first-page":"2498","DOI":"10.1063\/1.527739","article-title":"The group-theoretical treatment of aberrating systems. III. The classification of asymmetric aberrations","volume":"28","author":"Wolf","year":"1987","journal-title":"J. Math. Phys."},{"key":"10.1016\/S0747-7171(08)80148-4_bib17","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1364\/JOSAA.5.001226","article-title":"Symmetry-adapted classification of aberrations","volume":"5","author":"Wolf","year":"1988","journal-title":"J. Opt. Soc. Am. A"},{"key":"10.1016\/S0747-7171(08)80148-4_bib18","series-title":"Symmetries and Nonlinear Phenomena","article-title":"Nonlinearity in Aberration Optics","author":"Wolf","year":"1988"}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717108801484?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717108801484?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T03:52:33Z","timestamp":1545882753000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717108801484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,12]]},"references-count":18,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1991,12]]}},"alternative-id":["S0747717108801484"],"URL":"https:\/\/doi.org\/10.1016\/s0747-7171(08)80148-4","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[1991,12]]}}}