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Solving a class of higher-order equations over a group structure

Stefan Andrei
Wei-Hgan Chin
Journal / Anthology

Journal of Symbolic Computation
Year: 2004
Volume: 37
Issue: 3
Page range: 329-341

1. Introduction 2. Mathematical preliminaries 3. Our proposed method 4. Implementation in Mathematica 5. Constructing functional groups 6. Case study on groups of order 3 7. Conclusions Acknowledgements References

This paper proposes a new symbolic method for solving a class of higher-order equations with an unknown function over the complex domain. Our method exploits the closure property of group structure (for functions) in order to allow an equivalent system of equations to be expressed and solved in the first-order setting.

Our work is an initial step towards the relatively unexplored realm of higher-order constraint solving, in general; and higher-order equational solving, in particular. We shall provide some theoretical background for the proposed method, and also prototype an implementation under Mathematica

*Mathematics > Algebra > Group Theory

Higher-order equation, Symbolic computation, Mathematica