Abstract.
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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Received: April 20, 1999; revised version: August 2, 2000
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Gerhard, J. Fast Modular Algorithms for Squarefree Factorization and Hermite Integration. AAECC 11, 203–226 (2001). https://doi.org/10.1007/PL00004222
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DOI: https://doi.org/10.1007/PL00004222