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We discuss a parallel implementation of a fast algorithm for the discrete poly-nomial Legendre transform. We give an introduction to the Driscoll-Healy algorithm using polynomial arithmetic, and present experimental results on the eciency and accuracy of our implementation. The algorithms were implemented in ANSI C using the BSPlib communications library. Further-more, we present a new algorithm for computing the Chebyshev transform of two vectors at the same time. 1