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

  • Authors:

  • Ştefan Andrei;Wei-Ngan Chin

  • Affiliations:

  • CS Programme, National University of Singapore, Singapore-MIT Alliance, School of Computing, 3 Science Drive 2S15-03-12, Singapore 117543, Singapore and Faculty of Computer Science, 'Al.I.Cuza' Un ...;Department of Computer Science, School of Computing, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2004

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Abstract

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.