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# 1 Introduction

### Sections

- Usage

This is a manual for the matrixss package, which is a package for
the GAP system for computational group theory. It contains an
implementation of Schreier-Sims algorithm for matrix groups, including
both the standard deterministic and the standard probabilistic
approach. There is also an implementation of the so-called
Schreier-Todd-Coxeter-Sims algorithm, which uses coset enumeration to
possibly speed up the process, but this algorithm is mainly used for
verifying the output of the probabilistic algorithm. An implementation
of the `Verify` routine by Sims can also be used for verification
purposes, and finally, an implementation of the nearly linear time
Schreier-Sims algorithm is also included in the package.

No theory about the Schreier-Sims algorithm will be covered in this
manual, since the theory is well-known and can easily be found elsewhere. For
example, the author of the package has written a report about it, see
baarnhielm04. Other references are butler91,
soicher98 and seress03. In this manual, we are instead only
concerned with the actual implementation, and how to use the package
in GAP.

The package can be downloaded from its homepage, which is
http://matrixss.sourceforge.net

The package author can be reached at redstar_@sourceforge.net.

Since the Schreier-Sims algorithm usually is just an initial step for
other algorithms, there is little actual user interaction. When the package is loaded, a method for `Size`

is installed for finite matrix groups, which uses the algorithms in this package to compute the order of the group.

At a lower level, the package installs an attribute `StabChainMatrixGroup`

for finite matrix groups, see StabChainMatrixGroup!general, where the base and strong generating set are stored. They can thus easily be used by anyone.

Currently, this is the only interaction between the package and the rest of GAP, but it should be sufficient.

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matrixss manual

september 2004