A data structure for a uniform approach to computations with finite groups
A data structure for a uniform approach to computations with finite groups
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用于有限群计算的统一方法的数据结构
DOI：
10.1145/1145768.1145811
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Á. Seress
中科院分区：
文献类型：
--
作者：
Max Neunhöffer;Á. Seress
我们描述了一个递归的数据结构的统一处理的置换群和矩阵群。这种数据结构允许在输入组的段的置换和矩阵表示之间切换，并且具有广泛的应用。它提供了一个框架来处理理论算法，这些算法被认为过于复杂，无法实现，例如用于基本处理大基置换群和任意置换群中的Sylow子群计算的渐近最快算法。它还有助于矩阵组的基本处理。数据结构足够通用，可以轻松地合并任何矩阵群或置换群算法代码;特别是，差距计算机代数系统处理置换群和矩阵群的库函数只需最小的修改即可工作。
We describe a recursive data structure for the uniform handling of permutation groups and matrix groups. This data structure allows the switching between permutation and matrix representations of segments of the input group, and has wide-ranging applications. It provides a framework to process theoretical algorithms which were considered too complicated for implementation such as the asymptotically fastest algorithms for the basic handling of large-base permutation groups and for Sylow subgroup computations in arbitrary permutation groups. It also facilitates the basic handling of matrix groups. The data structure is general enough for the easy incorporation of any matrix group or permutation group algorithm code; in particular, the library functions of the GAP computer algebra system dealing with permutation groups and matrix groups work with a minimal modification.