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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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LoadPackage( "ModulePresentationsForCAP" );
LoadPackage( "RingsForHomalg" );
QQ := HomalgFieldOfRationalsInSingular( );
R := QQ * "x,y";
S := FreeLeftPresentation( 1, R );
S2 := FreeLeftPresentation( 2, R );
alpha := PresentationMorphism( S, HomalgMatrix( [ [ 1, 2 ] ], R ), S2 );
id := IdentityMorphism( S );
p := PreCompose( id, alpha );
IsIdenticalObj( p, alpha );