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Matrix SchreierSims short introduction
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When the package is loaded in GAP using "LoadPackage", a new Attribute
"StabChainMatrixGroup" is installed for finite matrix groups, which
contains a base and generating set, as well as the Schreier trees for
the orbits of the base points. The corresponding Operation has two
Methods. One is the standard deterministic SchreierSims algorithm and
the other one is the standard probabilistic SchreierSims algorithm,
possibly with verification using SchreierToddCoxeterSims algorithm
or using the Verify routine by Sims, the latter being the default. The
default main algorithm is the deterministic one, since it is the fastest one at the moment. The probabilistic algorithm can be chosen by passing an Option.
The package also installs a new Method for the "Size" Attribute for
finite matrix groups. The Method uses the above mentioned Attribute
"StabChainMatrixGroup" and computes the order of the group by
multiplying the sizes of the orbits of the base points.
The Option to define in order to select the probabilistic algorithm is
"Random". There are also a few more Options for the probabilistic
algorithm itself. If "Verify" is defined, the probabilistic algorithm
will execute the Verify routine at the end, to verify the
probabilistic computation, so that a correct result is guaranteed. If
also "STCS" is defined, the SchreierToddCoxeterSims algorithm will
be used instead for the verification. For other options, see the
manual.
