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- Joachim von zur Gathen, Jürgen Gerhard
- ISSAC
- 1997

Joachim von zur Gathen Jurgen Gerhard Fachbereich 17 Mathematik-Informatik Universitat-GH Paderborn D-33095 Paderborn, Germany {gathen, jngerhar}@uni-paderborn. de http://www.uni-paderborn .de/cs/gathen .html

- Jürgen Gerhard
- Lecture Notes in Computer Science
- 2004

- Joachim von zur Gathen, Jürgen Gerhard
- ISSAC
- 1996

We describe algorithms for polynomial multiplication and polynomial factorization over the binary field IF2.and their implementation. They allow polynomials of degree up to 100,000 to be factored in about one dqy of CPU time.

- Joachim von zur Gathen, Jürgen Gerhard
- Math. Comput.
- 2002

We describe algorithms for polynomial factorization over the binary field F2, and their implementation. They allow polynomials of degree up to 250 000 to be factored in about one day of CPU time, distributing the work on two processors.

- Jürgen Gerhard, Mark Giesbrecht, Arne Storjohann, Eugene V. Zima
- ISSAC
- 2003

New algorithms are presented for computing the dispersion set of two polynomials over <b>Q</b> and for <i>shiftless</i> factorization. Together with a summability criterion by Abramov, these are applied to get a polynomial-time algorithm for indefinite rational summation, using a sparse representation of the output.

- Olaf Bonorden, Joachim von zur Gathen, Jürgen Gerhard, Olaf Müller
- ACM SIGSAM Bulletin
- 2001

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)

- Jürgen Gerhard
- Applicable Algebra in Engineering, Communication…
- 2001

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)