We describe the current state of a package, written in REDUCE, that is being developed to solve the following problems that arise in applications of elementary catastrophe theory. For an input unfolding of some singularity, the recognition problem is to find a set of topological invariants that fix the equivalence class of the singularity. If the modality invariant is less than 3 then normal forms for unfoldings are known. The recognition algorithm employs the Buchberger Algorithm for Gröbner bases modified to the local requirements of singularity theory. The mapping problem is to find the taylor polynomial, up to any desired degree, of the right-equivalence that transforms the given unfolding into its normal form.
- Normal Form
- Catastrophe Theory
- Taylor Polynomial
- Simple Singularity
- Finite Determinacy
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Cowell, R.G., Wright, F.J. (1989). Catfact: Computer algebraic tools for applications of catastrophe theory. In: Davenport, J.H. (eds) Eurocal '87. EUROCAL 1987. Lecture Notes in Computer Science, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51517-8_91
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