{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T23:02:41Z","timestamp":1725663761626},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540515173"},{"type":"electronic","value":"9783540482079"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1989]]},"DOI":"10.1007\/3-540-51517-8_91","type":"book-chapter","created":{"date-parts":[[2012,2,25]],"date-time":"2012-02-25T21:02:53Z","timestamp":1330203773000},"page":"71-80","source":"Crossref","is-referenced-by-count":2,"title":["Catfact: Computer algebraic tools for applications of catastrophe theory"],"prefix":"10.1007","author":[{"given":"R. G.","family":"Cowell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F. J.","family":"Wright","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,5,31]]},"reference":[{"key":"12_CR1","first-page":"11","volume":"29","author":"V.I. Arnold","year":"1974","unstructured":"Arnold, V.I., 1974 \u2018Critical points of smooth functions and their normal forms', Usp. Mat. Nauk 29 pp 11\u201349. (Translated as Russ. Math. Surveys 29 pp 10\u201350).","journal-title":"Usp. Mat. Nauk"},{"key":"12_CR2","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/BF01391830","volume":"88","author":"J. W. Bruce","year":"1987","unstructured":"Bruce, J. W., du Plessis, A. A. and Wall, C. T. C., 1987 \u2018Unipotency and Determinacy', Invent. Math. 88 pp 521\u2013554.","journal-title":"Invent. Math."},{"key":"12_CR3","volume-title":"Multidimensional systems theory: progress, directions, and open problems in multidimensional systems","author":"B. Buchberger","year":"1985","unstructured":"Buchberger, B., 1985 \u2018Gr\u00f6bner Bases: An algorithmic method in polynomial ideal theory', in Multidimensional systems theory: progress, directions, and open problems in multidimensional systems (Edited by N. K. Bose) Dordrecht, Holland: D. Reidel."},{"key":"12_CR4","unstructured":"Colvin, A. P., 1988 Private communication."},{"key":"12_CR5","unstructured":"Cowell, R. G., 1989 \u2018Application of ordered standard bases to catastrophe theory\u2019 (Submitted to Proc. LMS.)"},{"key":"12_CR6","doi-asserted-by":"crossref","unstructured":"Cowell, R. G. and Wright, F. J., 1989a \u2018Truncation criteria and algorithm for the reduction to normal form of catastrophe unfoldings I: Singularities with zero rank\u2019 (Submitted to Phil. Trans. R. Soc. Lond.)","DOI":"10.1098\/rspa.1989.0087"},{"key":"12_CR7","doi-asserted-by":"crossref","unstructured":"Cowell, R. G. and Wright, F. J., 1989b \u2018Truncation criteria and algorithm for the reduction to normal form of catastrophe unfoldings II: Singularities with non-zero rank\u2019 (Submitted to Phil. Trans. R. Soc. Lond.)","DOI":"10.1098\/rspa.1989.0088"},{"key":"12_CR8","volume-title":"Singular points of smooth mappings","author":"C. G. Gibson","year":"1979","unstructured":"Gibson, C. G., 1979 Singular points of smooth mappings, London: Pitman."},{"key":"12_CR9","unstructured":"Millington, K., 1985 \u2018Using computer algebra to determine equivalences in catastrophe theory\u2019 (Ph.D. Thesis, University of London)."},{"key":"12_CR10","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1007\/3-540-15984-3_244","volume":"204","author":"K. Millington","year":"1985","unstructured":"Millington, K. and Wright, F. J., 1985 \u2018Algebraic computations in elementary catastrophe theory,\u2019 EUROCAL'85 Lecture Notes in Computer Science 204 (Berlin, Heidelberg: Springer) pp 116\u2013125.","journal-title":"EUROCAL'85 Lecture Notes in Computer Science"},{"key":"12_CR11","volume-title":"Catastrophe Theory and its Applications","author":"T. Poston","year":"1978","unstructured":"Poston, T. and Stewart, I. N., 1978 Catastrophe Theory and its Applications, London: Pitman."},{"key":"12_CR12","first-page":"245","volume":"2D","author":"I. N. Stewart","year":"1981","unstructured":"Stewart, I. N., 1981 \u2018Applications of catastrophe theory to the physical sciences', Physica 2D, pp 245\u2013305.","journal-title":"Physica"},{"key":"12_CR13","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1088\/0034-4885\/45\/2\/002","volume":"45","author":"I. N. Stewart","year":"1982","unstructured":"Stewart, I. N., 1982 \u2018Catastrophe theory in Physics', Rep. Prog. Phys. 45 pp 185\u2013221.","journal-title":"Rep. Prog. Phys."},{"key":"12_CR14","volume-title":"Stabilit\u00e9 Structurelle et Morphog\u00e9n\u00e8se","author":"R. Thom","year":"1972","unstructured":"Thom, R., 1972 Stabilit\u00e9 Structurelle et Morphog\u00e9n\u00e8se. Reading, Mass.: Benjamin. (English translation by D. H. Fowler, 1975, Stuctural Stability and Morphogenesis. Reading, Mass.: Benjamin.)"},{"key":"12_CR15","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1007\/978-3-642-73001-6_32","volume-title":"The Physics of Structure Formation: Theory and Simulation","author":"F. J. Wright","year":"1987","unstructured":"Wright, F. J. and Cowell, R. G., 1987 \u2018Computer algebraic tools for applications of catastrophe theory', in The Physics of Structure Formation: Theory and Simulation. Eds. W. G\u00fcttinger and G. Dangelmayr. Berlin: Springer, pp 402\u2013415."},{"key":"12_CR16","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF02240148","volume":"35","author":"F. J. Wright","year":"1985","unstructured":"Wright, F. J. and Dangelmayr, G., 1985 \u2018Explicit iterative algorithms to reduce a univariate catastrophe to normal form', Computing 35 pp 73\u201383.","journal-title":"Computing"},{"key":"12_CR17","volume-title":"Catastrophe Theory","author":"E. C. Zeeman","year":"1977","unstructured":"Zeeman, E. C., 1977 Catastrophe Theory. Reading, Mass.: Addison-Wesley."}],"container-title":["Lecture Notes in Computer Science","Eurocal '87"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-51517-8_91.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T21:21:49Z","timestamp":1605648109000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-51517-8_91"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989]]},"ISBN":["9783540515173","9783540482079"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/3-540-51517-8_91","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1989]]}}}