GAP Manual: 4.9. IsFinite

IsFinite( D )

IsFinite returns true if the domain D is finite and false otherwise. D may also be a proper set (see Set), in which case the result is of course always true.

    gap> IsFinite( GaussianIntegers );
    false
    gap> IsFinite( D12 );
    true 

The default function DomainOps.IsFinite just signals an error, since there is no general method to determine whether a domain is finite or not. This default function is overlaid for each special domain. In fact, implementors of domains must implement this function for new domains, since it is, together with Elements (see Elements), the most basic function for domains, used by most of the default functions in the domain package.