Simple roots:
[(0, 1, -1, 0), (0, 0, 1, -1), (0, 0, 0, 1), (1/2, -1/2, -1/2, -1/2)]
Fundamental weights:
[(1, 1, 0, 0), (2, 1, 1, 0), (3/2, 1/2, 1/2, 1/2), (1, 0, 0, 0)]
Rho= (11/2, 5/2, 3/2, 1/2)
s1*s2*s3*s4*s2*s3*s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 0 -1 0 0]
[-1 0 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
s2*s3*s4*s2*s3*s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 0 -1 0 0]
[ 0 0 1 0]
[-1 0 0 0]
[ 0 0 0 1]
s3*s4*s2*s3*s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 0 -1 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
[-1 0 0 0]
s4*s2*s3*s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 0 -1 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
[ 1 0 0 0]
s4*s3*s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 0 -1 0 0]
[ 0 0 1 0]
[ 1 0 0 0]
[ 0 0 0 1]
s4*s3*s2*s3*s4*s1*s2*s3*s2*s1
[ 0 -1 0 0]
[ 1 0 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
s2*s3*s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[-1/2 -1/2 1/2 -1/2]
[-1/2 -1/2 -1/2 1/2]
[ 1/2 -1/2 -1/2 -1/2]
s3*s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[-1/2 -1/2 1/2 -1/2]
[ 1/2 -1/2 -1/2 -1/2]
[-1/2 -1/2 -1/2 1/2]
s1*s2*s3*s4*s1*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[-1/2 -1/2 1/2 -1/2]
[ 1/2 -1/2 -1/2 -1/2]
[ 1/2 1/2 1/2 -1/2]
s1*s2*s3*s4*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[-1/2 -1/2 1/2 -1/2]
[ 1/2 1/2 1/2 -1/2]
[ 1/2 -1/2 -1/2 -1/2]
s3*s2*s3*s4*s1*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 -1/2 -1/2 -1/2]
[-1/2 -1/2 1/2 -1/2]
[-1/2 -1/2 -1/2 1/2]
s2*s3*s4*s1*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 -1/2 -1/2 -1/2]
[-1/2 -1/2 1/2 -1/2]
[ 1/2 1/2 1/2 -1/2]
s3*s4*s1*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 -1/2 -1/2 -1/2]
[ 1/2 1/2 1/2 -1/2]
[-1/2 -1/2 1/2 -1/2]
s4*s1*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 -1/2 -1/2 -1/2]
[ 1/2 1/2 1/2 -1/2]
[ 1/2 1/2 -1/2 1/2]
s2*s3*s4*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 1/2 1/2 -1/2]
[-1/2 -1/2 1/2 -1/2]
[ 1/2 -1/2 -1/2 -1/2]
s3*s4*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 1/2 1/2 -1/2]
[ 1/2 -1/2 -1/2 -1/2]
[-1/2 -1/2 1/2 -1/2]
s4*s2*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 1/2 1/2 -1/2]
[ 1/2 -1/2 -1/2 -1/2]
[ 1/2 1/2 -1/2 1/2]
s4*s3*s2*s1
[ 1/2 -1/2 1/2 1/2]
[ 1/2 1/2 1/2 -1/2]
[ 1/2 1/2 -1/2 1/2]
[ 1/2 -1/2 -1/2 -1/2]
s1*s2*s3*s2*s1
[ 1 0 0 0]
[ 0 -1 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
s2*s3*s2*s1
[ 1 0 0 0]
[ 0 0 1 0]
[ 0 -1 0 0]
[ 0 0 0 1]
s3*s2*s1
[ 1 0 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
[ 0 -1 0 0]
s2*s1
[1 0 0 0]
[0 0 1 0]
[0 0 0 1]
[0 1 0 0]
s1
[1 0 0 0]
[0 0 1 0]
[0 1 0 0]
[0 0 0 1]
1
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
s4*s3*s2*s3*s1*s2*s3*s4*s3*s2*s3*s1*s2*s3*s4
[-1 0 0 0]
[ 0 1 0 0]
[ 0 0 1 0]
[ 0 0 0 1]
s4*s3*s2*s3*s1*s2*s3*s4
[-1/2 1/2 1/2 1/2]
[ 1/2 1/2 1/2 -1/2]
[ 1/2 1/2 -1/2 1/2]
[ 1/2 -1/2 1/2 1/2]
s4*s3*s2*s3*s4
[0 1 0 0]
[1 0 0 0]
[0 0 1 0]
[0 0 0 1]
s4
[ 1/2 1/2 1/2 1/2]
[ 1/2 1/2 -1/2 -1/2]
[ 1/2 -1/2 1/2 -1/2]
[ 1/2 -1/2 -1/2 1/2]
1
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
Roots of M_w:
Error in lines 46-47
Traceback (most recent call last):
File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1234, in execute
flags=compile_flags), namespace, locals)
File "", line 1, in <module>
NameError: name 'SplitRoots' is not defined