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

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

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

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

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