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

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

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

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

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