Values
=>
Cc0029;cc-rep
([(0,2),(2,1)],3)=>1
([(0,1),(0,2),(1,3),(2,3)],4)=>2
([(0,3),(2,1),(3,2)],4)=>1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>1
([(0,4),(2,3),(3,1),(4,2)],5)=>1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>2
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>1
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>1
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>1
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>1
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>2
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>2
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>1
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)=>2
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>2
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)=>2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>2
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>2
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)=>2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>2
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)=>2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)=>2
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>2
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>2
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>2
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>1
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>2
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>1
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>2
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>2
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>2
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>2
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)=>2
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>2
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>1
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>2
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>1
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>2
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>1
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Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Code
DeclareOperation("projdimsimpleminimum",[IsList]);
InstallMethod(projdimsimpleminimum, "for a representation of a quiver", [IsList],0,function(LIST)
local A,L,LL,M,B,n,T,D,injA,W,simA,S,P,projA;
A:=LIST[1];
projA:=IndecProjectiveModules(A);P:=Filtered(projA,x->IsInjectiveModule(x)=true)[1];
S:=TopOfModule(P);
return(ProjDimensionOfModule(S,33));
end);
Created
Oct 03, 2020 at 20:23 by Rene Marczinzik
Updated
Oct 03, 2020 at 20:23 by Rene Marczinzik
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