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gap-packages / qpa

GAP package for quivers and path algebras
https://folk.ntnu.no/oyvinso/QPA/
GNU General Public License v2.0
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Bug for RightApproximationByPerpT? #61

Closed Nakayamaalgebra closed 1 year ago

Nakayamaalgebra commented 2 years ago

Let A be the quiver algebra with the following quiver and relations over GF(3):

Quiver( ["v1","v2","v3"], [["v1","v1","a1"],["v1","v2","a2"],["v2","v1","a3"],["v2","v3","a4"],["v3","v2","a5"]] ) [ (Z(3))*a1^2+(Z(3)^0)*a2*a3, (Z(3)^0)*a3*a2, (Z(3)^0)*a5*a4, (Z(3)^0)*a1^3, (Z(3)^0)*a1^2*a2, (Z(3)^0)*a1*a2*a4, (Z(3))*a1*a2+(Z(3)^0)*a2*a4*a5, (Z(3)^0)*a3*a1^2, (Z(3)^0)*a3*a1*a2, (Z(3))*a3*a1+(Z(3)^0)*a4*a5*a3, (Z(3)^0)*a5*a3*a1 ]

Let T be the following A-module in QPA:

gap> Display(T); <Module over <GF(3)[<quiver with 3 vertices and 5 arrows>]/<two-sided ideal in <GF(3)[<quiver with 3 vertices and 5 arrows>]>, (11 generators)>> with dimension vector [ 6, 5, 3 ]> and linear maps given by for arrow a1: [ [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ] ] for arrow a2: [ [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ] ] for arrow a3: [ [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ] ] for arrow a4: [ [ 0*Z(3), 0*Z(3), 0*Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3) ] ] for arrow a5: [ [ Z(3)^0, 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), 0*Z(3), 0*Z(3), Z(3)^0 ] ]

T is a cotilting module:

CotiltingModule(T,2); [ 2, [ 0 -> 1:(3,2,1) -> 0:(3,2,1) -> 0, 0 -> 1:(2,2,1) -> 0:(2,2,1) -> 0, 0 -> 3:(1,1,1) -> 2:(2,2,1) -> 1:(2,2,1) -> 0:(1,1,1) -> 0 ] ]

G:=DecomposeModule(T);O:=G[1];OO:=DTr(O);

I get the following error using the command RightApproximationByPerpT:

f:=RightApproximationByPerpT(T,OO); Error: The two maps entered don't start in the same module. Error, List Element: must be a list (not a boolean or fail) in g := PushOut( exactsequences[n + 1 - i][1], f )[1];