GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap> START_TEST("HAP library"); gap> gens:= [ [ [-1,0,0,0], [0,-1,0,0], [0,0,1,1/2], [0,0,0,1] ], [ [0,-1,0,0], [1,-1,0,0], [0,0,1,1/3], [0,0,0,1] ], [ [1,0,0,1], [0,1,0,0], [0,0,1,0], [0,0,0,1] ] ];; gap> G:=AffineCrystGroupOnLeft(gens);; gap> G:=StandardAffineCrystGroup(G);; gap> Y:=EquivariantEuclideanSpace(G,[0,0,0]); Equivariant CW-complex of dimension 3 gap> Y!.dimension(0); 2 gap> Y!.dimension(1); 5 gap> Y!.dimension(2); 4 gap> Y!.dimension(3); 1 gap> C:=ChainComplexOfQuotient(Y);; gap> Homology(C,0); [ 0 ] gap> Homology(C,1); [ 0 ] gap> Homology(C,2); [ 0 ] gap> Homology(C,3); [ 0 ] gap> STOP_TEST( "tst.tst", 1000 );