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Solving a class of higher-order equations over a group structure
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| Journal of Symbolic Computation |
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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
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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
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Higher-order equation, Symbolic computation, Mathematica
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