BuildSequencesLNak:=function(n)

local all,range,len,new,seq,i,sel;

all:=[[1]];

range:=[2..n];

for len in [1..n-1] do
	new:=[];
	for seq in all do
		sel:=Filtered(range, x->x<=1+seq[1]);
		for i in sel do
			Add(new,Concatenation([i],seq));
		od;
	od;
all:=new;
od;

return all;

end; 


DeclareOperation("ProjToInjNak", [IsList]);

InstallMethod(ProjToInjNak, "for a representation of a quiver", [IsList],0,function(L)


local list, n, temp1, Liste_d, j, i, k, r, kk;


list:=L;

n:=Size(L);

temp1:=[];

Liste_d:=[];

for j in [1..n] do
		for k in L do
			r:=(j-k) mod n;
			if r=0 then r:=n; fi;
			if k>=L[r] then
			Append(temp1,[k]);
			fi;
		od;
	kk:=Minimum(temp1);
	temp1:=[];
	Append(Liste_d,[kk]);
od;

return(Liste_d);

end
);

DeclareOperation("domdimlist", [IsList]);

InstallMethod(domdimlist, "for a representation of a quiver", [IsList],0,function(L)


local list, n, Liste_d, i, Expr1, Expr2, Expr3, r, s, List1, List2, List_not_in_List2, m, f, g, x, y, j, List_for_dom, temp2, dd, z;

list:=L;

n:=Size(L);

Liste_d:=ProjToInjNak(L);

List1:=[];

List2:=[];


for i in [1..n] do
	r:=i mod n; if r =0 then r:=n; fi;
	s:=(i+1) mod n; if s = 0 then s:=n; fi;
	if Liste_d[s]<=Liste_d[r] then
		Append(List1,[i-1]);
	fi;
od;



for i in [1..n] do
	r:=i mod n; if r =0 then r:=n; fi;
	s:=(i-1) mod n; if s = 0 then s:=n; fi;
	if L[s]<=L[r] then
		Append(List2,[i-1]);
	fi;
od;





List_not_in_List2:=[];

for i in [0..n-1] do
	if (i in List2)=false then
		Append(List_not_in_List2,[i]);
	fi;
od;


List_for_dom:=[];

m:=Size(List_not_in_List2);


for j in List_not_in_List2 do
	Append(List_for_dom,[[[j+L[j+1]-1,L[j+1]]]]);
od;




f := function (x,y)
	local c;
	c:=(x-y) mod n; if c=0 then c:=n; fi;
	z:=(x+1) mod n; if z=0 then z:=n; fi;
	return([c,Liste_d[z]-y]);
	end;


for r in [1..m] do
	s:=Size(List_for_dom[r]);
	while (f(List_for_dom[r][s][1],List_for_dom[r][s][2])[1] mod n in List1) = true do
		Append(List_for_dom[r],[f(List_for_dom[r][s][1],List_for_dom[r][s][2])]);
		s:=Size(List_for_dom[r]);
	od;
	s:=0;
od;

temp2:=[];

for i in [1..Size(List_for_dom)] do
	Append(temp2,[Size(List_for_dom[i])]);
od;

dd:=Minimum(temp2);


return(dd);

end
);

 
DeclareOperation("gldim", [IsList]);

InstallMethod(gldim, "for a representation of a quiver", [IsList],0,function(L)


local list, n, i, j, f, temp, temp2, temp3, u;

list:=L;

n:=Size(L);

f := function (x,y)
	local c, z;
	c:=(x+y) mod n; if c=0 then c:=n; fi;
	z:=(x+1) mod n; if z=0 then z:=n; fi;
	return([c,list[z]-y]);
	end;

temp2:=[];
for i in [0..n-1] do
	Append(temp2,[[i,1]]);
od;


temp:=[];
for i in [0..n-1] do
	u:=temp2[i+1];
	Append(temp,[[u]]);
od;




for i in [0..n-1] do
	j:=1;
	while j<(2*n+3) do
		Append(temp[i+1],[f(temp[i+1][j][1],temp[i+1][j][2])]);
		j:=j+1;
	od;
od;



temp3:=[];
for i in [1..n] do
	temp2:=[];
	for j in [1..(2*n+3)] do
		if temp[i][j][2]=0 then Append(temp2,[j]); fi;
	od;
	if Size(temp2)>0 then
		u:=Minimum(temp2);
		Append(temp3,[u]);
	else 
		temp3:="inf"; break; 
	fi;
od;

if IsString(temp3)=false then
	temp3:=(Maximum(temp3))-2;
fi;

return(temp3);



end
);