The IsomorphismClasses( L ) command partitions a list L of magmas into isomorphism classes.  The result is a list of lists, where each component list consists of pairwise isomorphic magmas, and such that no magma in one list is isomorphic to any magma in another (distinct) list.

Note that if, in the input list L, the magmas are already pairwise isomorphic, then the result will be a list of one-element lists.

$\mathrm{with}\left(\mathrm{Magma}\right)\:$

$L≔\left[\mathrm{seq}\right]\left(\mathrm{RandomMagma}\left(2\right)\,i=1..20\right)\:$

$C≔\mathrm{IsomorphismClasses}\left(L\right)$

$C≔\left[\left[\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]\,\left[\begin{array}{cc}2& 2\\ 2& 1\end{array}\right]\,\left[\begin{array}{cc}2& 2\\ 2& 1\end{array}\right]\,\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]\right]\,\left[\left[\begin{array}{cc}1& 2\\ 1& 1\end{array}\right]\,\left[\begin{array}{cc}1& 2\\ 1& 1\end{array}\right]\right]\,\left[\left[\begin{array}{cc}1& 2\\ 1& 2\end{array}\right]\,\left[\begin{array}{cc}1& 2\\ 1& 2\end{array}\right]\right]\,\left[\left[\begin{array}{cc}2& 2\\ 2& 2\end{array}\right]\,\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]\,\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]\right]\,\left[\left[\begin{array}{cc}2& 1\\ 2& 1\end{array}\right]\right]\,\left[\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]\,\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]\right]\,\left[\left[\begin{array}{cc}1& 2\\ 2& 2\end{array}\right]\,\left[\begin{array}{cc}1& 2\\ 2& 2\end{array}\right]\,\left[\begin{array}{cc}1& 2\\ 2& 2\end{array}\right]\,\left[\begin{array}{cc}1& 1\\ 1& 2\end{array}\right]\right]\,\left[\left[\begin{array}{cc}1& 1\\ 2& 1\end{array}\right]\right]\,\left[\left[\begin{array}{cc}1& 1\\ 2& 2\end{array}\right]\right]\right]$

$\mathrm{map}\left(\mathrm{nops}\,C\right)$

$\left[4\,2\,2\,3\,1\,2\,4\,1\,1\right]$

The Magma[IsomorphismClasses] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.