Square-free algorithms in positive characteristic

摘要: We study the problem of computation square-free decomposition for polynomials over fields positive characteristic. For which are explicitly finitely generated perfect fields, we show how classical algorithm characteristic zero can be generalized using multiple derivations. more general one must make an additional constructive hypothesis in order to decidable. that Seidenberg'sCondition P gives a necessary and sufficient condition on fieldK computing complete square free with coefficients any finite algebraic extension ofK.