length(W,w0)
6
julia&gt; map(w-&gt;word(W,w),refls(W,1:nref(W)))
6-element Vector{Vector{Int64}}:
 [1]
 [2]
 [3]
 [1, 2, 1]
 [2, 3, 2]
 [1, 2, 3, 2, 1]
julia&gt; [length(elements(W,i)) for i in 0:nref(W)]
7-element Vector{Int64}:
 1
 3
 5
 6
 5
 3
 1</code></pre><p>The  last list tells us that there is 1 element of length 0, there are 6 of length 3, ‚Ä¶</p><p>For  most basic functions the convention is that the input is an element of the  group, rather than a  Coxeter word. The reason  for this is that 