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

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

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

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

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