Advanced Programming Guide

3.6 Interfaces and Implementations • 153proc() option remember; ’procname(args)’ end procUse A, B and h to construct the homomorphism object.> hom := Homomorphism( A, B, h );hom := module()export domain, codomain, genmap;option record ;end module> type( hom, ’Homomorphism’ );trueUse the machinery developed earlier in this example to compute theorder of the image of this homomorphism.> GroupOrder( HomImage( hom ) );2Thus, the homomorphism is surjective (as expected). You can computethe elements explicitly.> GroupElements( B );[ ] [ ]0 1 1 0{ , }1 0 0 1> GroupElements( HomImage( hom ) );[ ] [ ]1 0 0 1{ , }0 1 1 0Exercises1. An automorphism α of a group G is called inner if there is anelement a in G for which α(g) = a −1 ga, for all g in G. Write aconstructor for inner automorphisms of groups.