File: 4.1.1

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G:=SymmetricGroup(5);;
R:=ResolutionFiniteGroup(G,4);;
Print(Homology(TensorWithIntegers(R),2),"\n");
Print(Homology(TensorWithIntegers(R),3),"\n");
Print(R!.dimension(3),"\n");
M:=CocycleCondition(R,3);;
Mod4:=NullspaceModQ(TransposedMat(M),4);;
Mod3:=NullspaceModQ(TransposedMat(M),3);;
v:=Random(Mod4)+Random(Mod3);;
f:=StandardCocycle(R,v,3,12);
Print(f((1,2,3),(1,5,3),(2,3,4)),"\n");