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

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

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

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

positive coroots :
[-1,1,2]
[0,1,4]
[-2,1,0]
[1,0,2]
[-1,2,4]
[1,1,4]
[-1,1,0]
[1,0,0]
[0,1,2]