Symbolic Domain Decomposition

  • Jacques Carette
  • Alan P. Sexton
  • Volker Sorge
  • Stephen M. Watt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)

Abstract

Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any particular problem the domain can be given explicitly, but when dealing with a family of problems given in terms of symbolic parameters, matters become more difficult. This article shows how hybrid sets, that is multisets allowing negative multiplicity, may be used to express symbolic domain decompositions in an efficient, elegant and uniform way, simplifying both computation and reasoning. We apply this theory to the arithmetic of piecewise functions and symbolic matrices and show how certain operations may be reduced from exponential to linear complexity.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jacques Carette
    • 1
  • Alan P. Sexton
    • 2
  • Volker Sorge
    • 2
  • Stephen M. Watt
    • 3
  1. 1.Department of Computing and SoftwareMcMaster University 
  2. 2.School of Computer ScienceUniversity of Birmingham 
  3. 3.Department of Computer ScienceUniversity of Western Ontario 

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