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

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

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

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

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