The IsomorphismClassRepresentatives( L ) command returns a list containing one representative from each isomorphism class of the magmas in the input list L.  Thus, every magma in L is isomorphic to one of the magmas in the list returned, and no two magmas in the returned list are isomorphic.

If the magmas in L are already pairwise non-isomorphic, then L itself is returned.

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

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

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

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

$\mathrm{C2}≔\mathrm{IsomorphismClassRepresentatives}\left(C\right)$

$\mathrm{C2}≔\left[\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]\,\left[\begin{array}{cc}1& 2\\ 1& 1\end{array}\right]\,\left[\begin{array}{cc}1& 2\\ 1& 2\end{array}\right]\,\left[\begin{array}{cc}2& 2\\ 2& 2\end{array}\right]\,\left[\begin{array}{cc}2& 1\\ 2& 1\end{array}\right]\,\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]\,\left[\begin{array}{cc}1& 2\\ 2& 2\end{array}\right]\,\left[\begin{array}{cc}1& 1\\ 2& 1\end{array}\right]\,\left[\begin{array}{cc}1& 1\\ 2& 2\end{array}\right]\right]$

$\mathrm{evalb}\left(C=\mathrm{C2}\right)$

$\mathrm{true}$

The Magma[IsomorphismClassRepresentatives] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.