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

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

coroot basis :
   1  -2   1
   0   1  -2
   0   0   4

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

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