Fast Modular Algorithms for Squarefree Factorization and Hermite Integration
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We present new modular algorithms for the squarefree factorization of a primitive polynomial in ℤ[x] and for computing the rational part of the integral of a rational function in ℚ(x). We analyze both algorithms with respect to classical and fast arithmetic and argue that the latter variants are – up to logarithmic factors – asymptotically optimal. Even for classical arithmetic, the integration algorithm is faster than previously known methods.
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