GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
LoadPackage( "RingsForHomalg" ); LoadPackage( "Modules" ); ZX := HomalgRingOfIntegersInDefaultCAS( ) * "x,y,a,X,Y,A"; ZZ3 := ZX / [ "x*X-1", "y*Y-1", "a*A-1" ]; zz := HomalgMatrix( "[ x - 1, y - 1, a - 1 ]", 3, 1, ZZ3 ); ZZ := LeftPresentation( zz ); ext := Ext( 5, ZZ, ZZ, "a" ); ByASmallerPresentation( ext );