DeclareOperation("IsNthSyzygy",[IsList]);

InstallMethod(IsNthSyzygy, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h,W;

M:=LIST[1];

n:=LIST[2];

N:=DualOfModule(NthSyzygy(DualOfModule(M),n));

W:=NthSyzygy(N,n);

if IsDirectSummand(M,W)=true
then
return(1);
else return(0);
fi;
end);



DeclareOperation("Numberofsimple3syzygymodules",[IsList]);

InstallMethod(Numberofsimple3syzygymodules, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h,W;

L:=LIST[1];

A:=NakayamaAlgebra(L,GF(3));
simA:=SimpleModules(A);
U:=Filtered(simA,x->IsNthSyzygy([x,3])=1);
return(Size(U));


end);