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This paper demonstrates that it is possible to obtain good, scalable parallel performance by coordinating multiple instances of unaltered sequential computational algebra systems in order to deliver a single parallel system. The paper presents the first substantial parallel performance results for SymGrid-Par, a system that orchestrates computational algebra components into a high-performance parallel application. We show that SymGrid-Par is capable of exploiting different parallel/multicore architectures without any change to the computational algebra component. Ultimately, our intention is to extend our system so that it is capable of orchestrating heterogeneous computations across a high-performance computational grid.