As already mentioned in the introduction of the chapter, ag groups are
domains. Thus all set theoretic functions, for example
Size, can be applied to ag groups. This and the following sections
give further comments on the definition and implementations of those
functions for ag groups. All set theoretic functions not mentioned here
not treated special for ag groups.
Elements( G )
The elements of a group G are constructed using a canonical generating system. See Elements for Ag Groups.
g in G
Membership is tested using
SiftedAgWord (see SiftedAgWord), if g
lies in the parent group of G. Otherwise
false is returned.
IsSubset( G, H )
If G and H are groups then
IsSubset tests if the generators of H
are elements of G. Otherwise
DomainOps.IsSubset is used.
Intersection( G, H )
The intersection of ag groups G and H is computed using Glasby's algorithm. See Intersection for Ag Groups.
Size( G )
The size of G is computed using a canonical generating system of G. See Size for Ag Groups.
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