cartan matrix :
   2   0  -1   0   0   0
   0   2   0  -1   0   0
  -1   0   2  -1   0   0
   0  -1  -1   2  -1   0
   0   0   0  -1   2  -1
   0   0   0   0  -1   2

root basis :
   2   0  -1   0   0   0
   0   2   0  -1   0   0
  -2   3   0   0  -1   0
  -4   4   0   0   0  -1
   3  -2   0   0   0   0
  -1   1   0   0   0   0

coroot basis :
   1   0  -2   1   0   0
   0   1   1  -2   1   0
   0   0   0   1  -2   1
   0   0   0   0   1  -2
   0   0   1   0   0  -1
   0   0   0   0   0   3

positive roots :
[-1,-1,-1,-1,0,0]
[-1,-1,-1,0,0,0]
[-1,-1,0,0,0,0]
[-1,0,0,0,0,0]
[-1,0,1,3,-2,1]
[-1,0,2,3,-2,1]
[-1,0,2,4,-2,1]
[-1,1,2,3,-2,1]
[-1,1,2,4,-2,1]
[-1,1,3,4,-2,1]
[0,-1,-1,-1,0,0]
[0,-1,-1,-1,1,0]
[0,-1,-1,0,0,0]
[0,-1,0,0,0,0]
[0,0,-1,-1,0,0]
[0,0,-1,-1,1,0]
[0,0,-1,0,0,0]
[0,0,0,-1,0,0]
[0,0,0,-1,1,0]
[0,0,0,0,1,0]
[0,1,2,3,-2,1]
[0,1,2,3,-1,1]
[0,1,2,4,-2,1]
[0,1,3,4,-2,1]
[0,2,3,4,-2,1]
[1,-1,-3,-5,3,-1]
[1,-1,-3,-4,3,-1]
[1,-1,-2,-4,3,-1]
[1,0,-2,-4,3,-1]
[1,0,-1,-1,1,0]
[1,0,0,-1,1,0]
[1,0,0,0,1,0]
[1,1,0,-1,1,0]
[1,1,0,0,1,0]
[1,1,1,0,1,0]
[2,0,-2,-4,3,-1]

positive coroots :
[-1,0,0,-1,0,3]
[-1,0,-1,1,1,0]
[-1,-1,1,0,1,0]
[-2,1,0,0,1,0]
[0,0,-1,0,0,3]
[0,-1,1,-1,0,3]
[0,-1,0,1,1,0]
[-1,1,0,-1,0,3]
[-1,1,-1,1,1,0]
[-1,0,1,0,1,0]
[1,-1,0,-1,-1,3]
[0,-1,0,0,1,3]
[1,-1,-1,1,0,0]
[1,-2,1,0,0,0]
[0,1,-1,-1,-1,3]
[-1,1,-1,0,1,3]
[0,1,-2,1,0,0]
[0,0,1,-2,-1,3]
[-1,0,1,-1,1,3]
[-1,0,0,1,2,0]
[1,0,0,-1,-1,3]
[0,0,0,0,1,3]
[1,0,-1,1,0,0]
[1,-1,1,0,0,0]
[0,1,0,0,0,0]
[0,0,0,-1,0,3]
[0,0,-1,1,1,0]
[0,-1,1,0,1,0]
[-1,1,0,0,1,0]
[1,0,-1,0,0,3]
[1,-1,1,-1,0,3]
[1,-1,0,1,1,0]
[0,1,0,-1,0,3]
[0,1,-1,1,1,0]
[0,0,1,0,1,0]
[1,0,0,0,0,0]