The following filters and operations indicate capabilities of GAP.
They can be used in the method selection or algorithms to check whether
it is feasible to compute certain operations for a given group.
In general, they return true if good algorithms for the given arguments
are available in GAP.
An answer false indicates that no method for this group may exist,
or that the existing methods might run into problems.
Typical examples when this might happen is with finitely presented groups, for which many of the methods cannot be guaranteed to succeed in all situations.
The willingness of GAP to perform certain operations may change, depending on which further information is known about the arguments. Therefore the filters used are not implemented as properties but as ``other filters'' (see Properties and Other Filters).
CanEasilyTestMembership( grp ) F
This filter indicates whether a group can test membership of
elements in grp (via the operation in) in reasonable time.
It is used by the method selection to decide whether an algorithm
that relies on membership tests may be used.
CanComputeSize( dom ) F
This filter indicates whether the size of the domain dom (which might
be infinity) can be computed.
CanComputeSizeAnySubgroup( grp ) F
This filter indicates whether grp can easily compute the size of any subgroup. (This is for example advantageous if one can test that a stabilizer index equals the length of the orbit computed so far to stop early.)
CanComputeIndex( G, H ) F
This filter indicates whether the index [G:H] (which might
be infinity) can be computed. It assumes that H £ G. (see
CanComputeIsSubset)
CanComputeIsSubset( A, B ) O
This filter indicates that GAP can test (via IsSubset) whether B
is a subset of A.
KnowsHowToDecompose( G ) P
KnowsHowToDecompose( G, gens ) O
Tests whether the group G can decompose elements in the generators
gens. If gens is not given it tests, whether it can decompose in the
generators given in GeneratorsOfGroup.
This property can be used for example to check whether a
GroupHomomorphismByImages can be reasonably defined from this group.
GAP 4 manual