Abstract
We derive algorithms to solve a technical problem in elementary catastrophe theory: how to reduce an unfolding of a singularity in a univariate function to normal form up to any given degree in the unfolding parameters. Two algorithms that iterate a simple explicit transformation are proposed, which should be suitable for easy implementation using a computer algebra system. They are proved by deriving sufficient vonditions for a class of such algorithms. The complexity and generalization of the algorithms is discussed briefly.
Zusammenfassung
Es werden Algorithmen zur Lösung eines praktischen Problems der elementaren Katastrophentheorie hergeleitet: die Transformation der Entfaltung einer Singularität, die von einer Zustandsvariablen abhängt, auf Normalform bis zu beliebig vorgegebener Ordnung in den Entfaltungs-parametern. Das Problem wird durch zwei Algorithmen gelöst, die eine einfache explizite Transformation iterieren und daher zur Implementierung mit Hilfe eines Systems der Computer-Algebra geeignet sind. Der Beweis erfolgt durch Ableitung von hinreichenden, Bedingungen für eine Klasse solcher Algorithmen. Komplexität und potentielle Verallgemeinerungen der Algorithmen werden kurz diskutiert.
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Work supported by the Stiftung Volkswagenwerk, FRG.
Permanent address (from September 1984): School of Mathermatical Sciences Queen Mary College University of London Mile End Road London E1 4NS England.
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Wright, F.J., Dangelmayr, G. Explicit iterative algorithms to reduce a univariate catastrophe to normal form. Computing 35, 73–83 (1985). https://doi.org/10.1007/BF02240148
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DOI: https://doi.org/10.1007/BF02240148