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We discuss the parallelization of algorithms for solving polynomial systemssymbolically by way of triangular decomposition. Algorithms for solvingpolynomial systems combine low-level routines for performing arithmeticoperations on polynomials and high-level procedures which produce the differentcomponents (points, curves, surfaces) of the solution set. The latter"component-level" parallelization of triangular decompositions, our focus here,belongs to the class of dynamic irregular parallel applications. Possiblespeedup factors depend on geometrical properties of the solution set (number ofcomponents, their dimensions and degrees); these algorithms do not scale withthe number of processors. In this paper we combine two different concurrencyschemes, the fork-join model and producer-consumer patterns, to better captureopportunities for component-level parallelization. We report on ourimplementation with the publicly available BPAS library. Our experimentationwith 340 systems yields promising results.

On the Parallelization of Triangular Decomposition of Polynomial Systems