<div id="comment:0"></div> The method `pi.binary_factorizations` silently returned wrong results for elements in `Permutations(n)`, because the order of multiplication was wrong. I also add some tests. CC: @tscrim Component: **categories** Author: **Martin Rubey** Branch/Commit: **[`37d60d4`](https://github.com/sagemath/sagetrac-mirror/commit/37d60d4b87569ed4524fc76c5aeeb2984e683c92)** Reviewer: **Travis Scrimshaw** _Issue created by migration from https://trac.sagemath.org/ticket/34799_