gap&gt; as := AffineSpace(3,5);
AG(3, 5)
gap&gt; map := ProjectiveCompletion(as);
&lt;geometry morphism from &lt;Elements of AG(3, 
5)&gt; to &lt;All elements of ProjectiveSpace(3, 5)&gt;&gt;
gap&gt; p := Random( Points(as) );
&lt;a point in AG(3, 5)&gt;
gap&gt; p^map;
&lt;a point in ProjectiveSpace(3, 5)&gt;
