On square-free decomposition algorithms
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
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The concept of polynomial squarefree decomposition is an important one in algebraic computation. The squarefree decomposition process has many uses in computer symbolic computation. A recent survey by D. Yun [3] describes many useful algorithms for this purpose. All of these methods depend on computing the greatest common divisior (gcd) of the polynomial to be decomposed and its first derivative (with respect to some variable). In the multivariate case, this gcd computation is non-trivial and dominates the cost for the squarefree decomposition.