STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Computing the order of a solvablepermutation group
Journal of Symbolic Computation
Nearly linear time algorithms for permutation groups with a small base
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Fast Monte Carlo algorithms for permutation groups
Selected papers of the 23rd annual ACM symposium on Theory of computing
Fast Management of Permutation Groups I
SIAM Journal on Computing
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Hi-index | 0.00 |
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.