Computer Algebra and Parallelism

This book contains papers presented at a workshop on the useof parallel techniques in symbolic and algebraic computationheld at Cornell University in May 1990. The eight papers inthe book fall into three groups.The first three papers discuss particular programmingsubstrates for parallel symbolic computation, especially fordistributed memory machines. The next three papers discussnovel ways of computing with elements of finite fields andwith algebraic numbers. The finite field technique isespecially interesting since it uses the Connection Machine,a SIMD machine, to achievesurprising amounts ofparallelism. One of the parallel computing substrates isalso used to implement a real root isolation technique.One of the crucial algorithms in modern algebraiccomputation is computing the standard, or Gr|bner, basis ofan ideal. The final two papers discuss two differentapproaches to speeding their computation. One uses vectorprocessing on the Cray and achieves significant speed-ups.The other uses a distributed memory multiprocessor andeffectively explores the trade-offs involved with differentinterconnect topologies of the multiprocessors.