Identifier
Identifier
Values
[1,0] generating graphics... => 0
[1,0,1,0] generating graphics... => 1
[1,1,0,0] generating graphics... => 0
[1,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 0
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 1
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 0
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 0
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 0
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 0
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 0
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 0
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 0
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 1
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 0
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 1
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 0
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 0
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 0
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 0
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 0
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 0
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 0
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 0
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 1
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 0
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 0
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 0
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 0
click to show generating function       
Description
The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra.
Code
DeclareOperation("gradeofmodule",[IsList]);

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

local A,M,RegA,g,temmi,UT;

A:=LIST[1];
M:=LIST[2];
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
g:=GorensteinDimensionOfAlgebra(A,30);
temmi:=[];Append(temmi,[Size(HomOverAlgebra(M,RegA))]);
for i in [0..g-1] do Append(temmi,[Size(ExtOverAlgebra(NthSyzygy(M,i),RegA)[2])]);od;
UT:=Filtered([0..g],x->temmi[x+1]>0);
return(Minimum(UT));
end);




DeclareOperation("numberindinjwithgradeatleastk",[IsList]);

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

local A,k,simA,WW,injA;

A:=LIST[1];
k:=LIST[2];
injA:=IndecInjectiveModules(A);
WW:=Filtered(injA,x->gradeofmodule([A,x])>=k);
return(Size(WW));
end);


Created
May 11, 2018 at 23:56 by Rene Marczinzik
Updated
May 11, 2018 at 23:56 by Rene Marczinzik