Peakword condensation and submodule lattices: an application of the meat-axe
Journal of Symbolic Computation
STAR/MPI: binding a parallel library to interactive symbolic algebra systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
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
Constructing permutation representations for matrix groups
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Memory-based and disk-based algorithms for very high degree permutation groups
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
A comparative analysis of parallel disk-based Methods for enumerating implicit graphs
Proceedings of the 2007 international workshop on Parallel symbolic computation
Harnessing parallel disks to solve Rubik's cube
Journal of Symbolic Computation
Fast multiplication of large permutations for disk, flash memory and RAM
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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Through the use of a new disk-based method for enumerating very large orbits, condensation for orbits with tens of billions of elements can be performed. The algorithm is novel in that it offers efficient access to data using distributed disk-based data structures. This provides fast access to hundreds of gigabytes of data,which allows for computing without worrying about memory limitations. The new algorithm is demonstrated on one of the long-standing open problems in the Modular Atlas Project [11]: the Brauer tree of the principal 17-block the sporadic simple Fischer group Fi23 The tree is completed by computing three orbit counting matrices for the Fi23 orbit of size 11, 739, 046, 176 acting on vectors of dimension 728 over GF (2). The construction of these matrices requires 3-1/2 days on a cluster of 56 computers,and uses 8 GB of disk storage and 800 MB of memory per machine.