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Summary form only given. As part of a major EU infrastructure project (SCIEnce: Symbolic Computing Infrastructure in Europe), we are developing SymGrid, a new framework that will, for the first time, allow multiple invocations of symbolic computing applications to interact via the Grid. SymGrid is designed to support the specific needs of symbolic computation, including computational steering (greater interactivity), complex data structures, and domain-specifc computational patterns (for irregular parallelism). A key issue for the SymGrid design is heterogeneity: SymGrid is designed to orchestrate legacy components from different symbolic systems into a single coherent (possibly parallel) Grid application, building on the OpenMath standard for data exchange between mathematically-oriented applications.