e = extend(w,v)
For ease, we can also extend two permutations so that they are regarded as permutations on the same number of symbols. More precisely, if we have permutations $p=(p_1, \dots, p_n)$ and $q=(q_1, \dots, q_m)$, then extend(p,q) will return both $p$ and $q$ as permutations on $\text{max}(m,n)$ symbols.
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