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

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SetAssertionLevel( 1 );
LoadPackage( "GradedRingForHomalg" );

Qxyzt := HomalgFieldOfRationalsInDefaultCAS( ) * "x,y,z,t";
S := GradedRing( Qxyzt );

wmat := HomalgMatrix( "[ \
x*y,  y*z,    z*t,        0,           0,          0,\
x^3*z,x^2*z^2,0,          x*z^2*t,     -z^2*t^2,   0,\
x^4,  x^3*z,  0,          x^2*z*t,     -x*z*t^2,   0,\
0,    0,      x*y,        -y^2,        x^2-t^2,    0,\
0,    0,      x^2*z,      -x*y*z,      y*z*t,      0,\
0,    0,      x^2*y-x^2*t,-x*y^2+x*y*t,y^2*t-y*t^2,0,\
0,    0,      0,          0,           -1,         1 \
]", 7, 6, Qxyzt );

LoadPackage( "GradedModules" );

wmor := GradedMap( wmat, "free", "free", "left", S );
W := LeftPresentationWithDegrees( wmat, S );
Hom(W,W);
WW := UnderlyingModule( W );
Res := Resolution( W );
Res2 := ShortenResolution( W );
Resolution( W );
BasisOfModule( W );
ByASmallerPresentation( W );
syz := SyzygiesGenerators( W );
wmor := GradedMap( wmat, "left", S);
ker := Kernel( wmor );
Y := Hom( S^0, W );
iota := TorsionObjectEmb( W );
pi := TorsionFreeFactorEpi( W );
C := HomalgComplex( pi, 0 );
Add( C, iota );
T := TorsionObject( W );
F := TorsionFreeFactor( W );
O := HomalgCocomplex( iota, -1 );
Add( O, pi );
W2 := TensorProduct( W, W );
WW2 := TensorProduct( WW, WW );