ode>l(sw)=l(w)+1</code> or <code>l(sw)=l(w)-1</code> and  in the latter case we say that <code>s</code> belongs to the <em>left descent set</em> of <code>w</code>. Computing a reduced word for  an  element,  and  other  word  problems,  are  easy if we know how to multiply elements and know left descent sets. In each of the Coxeter groups that we implement, the left descent set is easy to compute (see for example <a href="coxgroups.html#Chevie.CoxGroups.coxeter_symmetric_group"><code>coxeter_symmetric_group