IsSubset( D, E )
true if the domain E is a subset of the domain D
E is considered a subset of D if and only if the set of elements of
E is as a set a subset of the set of elements of D (see Elements
and Set Functions for Sets). That is
IsSubset behaves as if
IsSubsetSet( Elements(D), Elements(E) ), except that
it will also sometimes, but not always, work for infinite domains, and
that it will usually work much faster than the above definition. Either
argument may also be a proper set.
gap> IsSubset( GaussianIntegers, [1,E(4)] ); true gap> IsSubset( GaussianIntegers, Rationals ); Error, sorry, cannot compare the infinite domains <D> and <E> gap> IsSubset( Group( (1,2), (1,2,3,4,5,6) ), D12 ); true gap> IsSubset( D12, [ (), (1,2)(3,4)(5,6) ] ); false
The default function
DomainOps.IsSubset checks whether both domains are
infinite. If they are it signals an error. Otherwise if the E is
infinite it returns
false. Otherwise if D is infinite it tests if
each element of E is in D (see Membership Test for Domains).
Otherwise it tests whether the proper set of elements of E is a subset
Set Functions for Sets).
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