Abstract
In Borodin-von zur Gathen-Hopcroft[82] the following program is laid out: obtain a “theory package for parallel algebraic computations”, i.e. fast parallel computations for the widely used problems of symbolic manipulation in an algebraic context. In that paper, two basic problems were considered: solving systems of linear equations and computing the gcd of two polynomials, both over arbitrary ground fields. The present paper continues this program, and fast parallel solutions to the following algebraic problems are given: computing all entries of the Extended Euclidean Scheme of two polynomials over an arbitrary field, gcd and lcm of many polynomials, factoring polynomials over finite fields, and the squarefree decomposition of polynomials over fields of characteristic zero and over finite fields.
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