Jürgen Gerhard

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On 22 May 2000, the factorization of a pseudorandom polynomial of degree 1 048 543 over the binary field Z<sub>2</sub> was completed on a 4-processor Linux PC, using roughly 100 CPU-hours. The basic approach is a combination of the factorization software BIPOLAR and a parallel version of Cantor's multiplication algorithm. The PUB-library (Paderborn(More)
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(More)
We present a high-level modeling formulation based on a conserved quantities approach, with the goal of making the physical modeling process reliable and repeatable. The system of equations generated as a result of this formulation will, in general, be non-linear differential algebraic equations (DAEs). We make use of symbolic reduction techniques in order(More)