h3=CoxeterGroup(['H',3])

"""
Coxeter Matrix for H4 in Coxeter 3 is

[1 5 2] 
[5 1 3] 
[2 3 1] 

while the matrix for Sage is

[1 3 2]
[3 1 5]
[2 5 1].
"""


"""
The set of all elements that are fully-commutative but not subregular form one
single 2-sided cell. The following has been converted to the Sage convention. 
"""

fcsage=[31,312,231,3231,3123,2312,32312,31232,23231,23123,323123,312321,232312,231232,123231,3231232,2323123,2312321,1232312,32312321,23231232,12323123,232312321,123231232,1232312321]




"""
It splits into 5 left cells. 
"""
l1sage = [31,231,3231,23231,123231]
l2sage = [312,2312,32312,232312,1232312]
l3sage = [3123,23123,323123,2323123,12323123]
l4sage = [32323,312323,2312323,32312323,232312323]
l5sage = [31232,231232,3231232,23231232,123231232]



