Carette, Jacques; Sexton, Alan P.; Sorge, Volker; Watt, Stephen M. Symbolic domain decomposition. (English) Zbl 1286.68515 Autexier, Serge (ed.) et al., Intelligent computer mathematics. 10th international conference, AISC 2010, 17th symposium, Calculemus 2010, and 9th international conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-14127-0/pbk). Lecture Notes in Computer Science 6167. Lecture Notes in Artificial Intelligence, 172-188 (2010). Summary: 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.For the entire collection see [Zbl 1194.68011]. Cited in 1 Document MSC: 68W30 Symbolic computation and algebraic computation PDFBibTeX XMLCite \textit{J. Carette} et al., Lect. Notes Comput. Sci. 6167, 172--188 (2010; Zbl 1286.68515) Full Text: DOI arXiv