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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( "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 );