ugh they  represent the same element of <code>W</code>. The reason  is that there are several reduced  words for an element of <code>W</code>. The function &#39;word&#39; calculates a lexicographically smallest word for <code>w</code>. Below are some other possible computations using the same Coxeter group:</p><pre><code class="language-julia-repl hljs">julia&gt; word(W,longest(W))  # the (unique) longest element in W
6-element Vector{Int64}:
 1
 2
 1
 3
 2
 1

julia&gt; w0=longest(W)
(1,4)(2,3)

julia&gt; 