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

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Read( "homalg.g" );

W := M;

## compute a free resolution of W
P := Resolution( W );
## apply the inner functor G := Hom(-,R) to the resolution
GP := Hom( P );
## tensor with P again
FGP := GP * P;
## the bicomplex associated to FGP
BC := HomalgBicomplex( FGP );
## the total complex of BC
Tot := TotalComplex( BC );
## the associated spectral sequence
I_E := HomalgSpectralSequence( BC );
## the transposed bicomplex associated to FGP
tBC := TransposedBicomplex( BC );
## the associated spectral sequence
II_E := HomalgSpectralSequence( 2, tBC );