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

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

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

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

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