IsomorphismClassRepresentatives - Maple Help

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Magma

 IsomorphismClassRepresentatives
 return a list of isomorphism class representatives for a list of finite magmas

 Calling Sequence IsomorphismClassRepresentatives( L )

Parameters

 L - list; list of magmas whose isomorphism class representatives are to be computed

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $L≔\left[\mathrm{seq}\right]\left(\mathrm{RandomMagma}\left(2\right),i=1..20\right):$
 > $C≔\mathrm{IsomorphismClassRepresentatives}\left(L\right)$
 ${C}{≔}\left[\left[\begin{array}{cc}{2}& {1}\\ {1}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {1}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {1}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {1}\\ {2}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {1}\\ {1}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {1}\\ {2}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {1}\\ {2}& {2}\end{array}\right]\right]$ (1)
 > $\mathrm{C2}≔\mathrm{IsomorphismClassRepresentatives}\left(C\right)$
 ${\mathrm{C2}}{≔}\left[\left[\begin{array}{cc}{2}& {1}\\ {1}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {1}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {1}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {1}\\ {2}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {1}\\ {1}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {1}\\ {2}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {1}\\ {2}& {2}\end{array}\right]\right]$ (2)
 > $\mathrm{evalb}\left(C=\mathrm{C2}\right)$
 ${\mathrm{true}}$ (3)

Compatibility

 • The Magma[IsomorphismClassRepresentatives] command was introduced in Maple 16.
 • For more information on Maple 16 changes, see Updates in Maple 16.