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A Parallel Algorithm to Compute the Greatest Common Divisor of Sparse Multivariate Polynomials

机译:稀疏多元多项式最大公因数的并行算法

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Efficient algorithms for computing greatest common divisors (GCD) of multivariate polynomials have been developed over the last 40 years. Many of the general purpose computer algebra systems are using either Zippel's GCD Algorithm [5] or the EEZ-GCD [4] Algorithm or both. Both algorithms sequentially interpolate variables one at a time which limits parallel speedup. Since multi-core processors are now widely available, parallel algorithms are desirable. In this poster, we present a first multivariate GCD computation algorithm over Z which is based on the Ben-Or/Tiwari interpolation [1]. By using Ben- Or/Tiwari interpolation, we reduce the number of points needed to interpolate the GCD and improve parallelism.
机译:在过去的40年中,已经开发出了用于计算多元多项式的最大公因数(GCD)的高效算法。许多通用计算机代数系统都使用Zippel的GCD算法[5]或EEZ-GCD [4]算法或两者都使用。两种算法一次都按顺序插补变量,从而限制了并行加速。由于现在可以广泛使用多核处理器,因此需要并行算法。在此海报中,我们提出了基于Ben-Or / Tiwari插值[1]的第一个基于Z的多元GCD计算算法。通过使用Ben-Or / Tiwari插值,我们减少了对GCD进行插值和改善并行度所需的点数。

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