GAP Manual: 28.9. Set Functions for Sets

As was already mentioned in the introduction to this chapter all domain functions also accept sets as arguments. Thus all functions described in the chapter Domains are applicable to sets. This section describes those functions where it might be helpful to know the implementation of those functions for sets.

IsSubset( set1, set2 )

This is implemented by IsSubsetSet, which you can call directly to save a little bit of time. Either argument to IsSubsetSet may also be a list that is not a proper set, in which case IsSubset silently applies Set (see Set) to it first.

Union( set1, set2 )

This is implemented by UnionSet, which you can call directly to save a little bit of time. Note that UnionSet only accepts two sets, unlike Union, which accepts several sets or a list of sets. The result of UnionSet is a new set, represented as a sorted list without holes or duplicates. Each argument to UnionSet may also be a list that is not a proper set, in which case UnionSet silently applies Set (see Set) to this argument. UnionSet is implemented in terms of its destructive counterpart UniteSet (see UniteSet).

Intersection( set1, set2 )

This is implemented by IntersectionSet, which you can call directly to save a little bit of time. Note that IntersectionSet only accepts two sets, unlike Intersection, which accepts several sets or a list of sets. The result of IntersectionSet is a new set, represented as a sorted list without holes or duplicates. Each argument to IntersectionSet may also be a list that is not a proper set, in which case IntersectionSet silently applies Set (see Set) to this argument. IntersectionSet is implemented in terms of its destructive counterpart IntersectSet (see IntersectSet).

The result of IntersectionSet and UnionSet is always a new list, that is not identical to any other list. The elements of that list however are identical to the corresponding elements of set1. If set1 is not a proper list it is not specified to which of a number of equal elements in set1 the element in the result is identical (see Identical Lists).