Computation schemes for splitting fields of polynomials
Computation schemes for splitting fields of polynomials
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DOI：
10.1145/1576702.1576741
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
S. Orange;G. Renault;K. Yokoyama
中科院分区：
文献类型：
--
作者：
S. Orange;G. Renault;K. Yokoyama
本文给出了用Galois群G的置换表示生成不可约多项式的分裂理想的三角基的一般形状的计算的新结果，并在研究置换群的非冗余基的基础上给出了一些理论结果和一个新的通用算法。这些新结果大大提高了多项式分裂域的计算效率。
In this article, we present new results about the computation of a general shape of a triangular basis generating the splitting ideal of an irreducible polynomial given with the permutation representation of its Galois group G. We provide some theoretical results and a new general algorithm based on the study of the non redundant bases of permutation groups. These new results deeply increase the efficiency of the computation of the splitting field of a polynomial.