A speed-up of the algorithm for computing comprehensive Gröbner systems
A speed-up of the algorithm for computing comprehensive Gröbner systems
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DOI：
10.1145/1277548.1277589
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发表时间：
2007-07
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影响因子：
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通讯作者：
Katsusuke Nabeshima
中科院分区：
文献类型：
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作者：
Katsusuke Nabeshima
本文提出了一种计算广义Gröbner系统的新算法，并给出了计算广义Gröbner系统的Suzuki-Sato算法。Suzuki-Sato算法经常为综合Gröbner系统创建过多的参数空间单元。因此计算变得繁重。然而，通过使用不等式（“不等于零”），我们可以得到不同的细胞。在许多情况下，参数空间的单元数小于Suzuki-Sato的。因此，我们的新算法比Suzuki-Sato的算法更有效，并输出一个很好的全面的Gröbner系统。我们的新算法已在计算机代数系统Risa/Asir中实现。我们将我们实现的运行时间与Suzuki-Sato算法进行了比较，发现我们的算法在许多情况下具有上级优势。
We introduce a new algorithm for computing comprehensive Gröbner systems.There exists the Suzuki-Sato algorithm for computing comprehensive Gröbner systems. The Suzuki-Sato algorithm often creates overmuch cells of the parameter space for comprehensive Gröbner systems. Therefore the computation becomes heavy. However, by using inequations ("not equal zero"), we can obtain different cells. In many cases, this number of cells of parameter space is smaller than that of Suzuki-Sato's. Therefore, our new algorithm is more efficient than Suzuki-Sato's one, and outputs a nice comprehensive Gröbner system. Our new algorithm has been implemented in the computer algebra system Risa/Asir We compare the runtime of our implementation with the Suzuki-Sato algorithm and find our algorithm superior in many cases.