IsomorphismClasses - Maple Help

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Magma

 IsomorphismClasses
 partition a list of magmas into isomorphism classes

 Calling Sequence IsomorphismClasses( L )

Parameters

 L - list; list of magmas to partition into isomorphism classes

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $L≔\left[\mathrm{seq}\right]\left(\mathrm{RandomMagma}\left(2\right),i=1..20\right):$
 > $C≔\mathrm{IsomorphismClasses}\left(L\right)$
 ${C}{≔}\left[\left[\left[\begin{array}{cc}{2}& {1}\\ {1}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {2}\\ {2}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {2}\\ {2}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {1}\\ {1}& {1}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{1}& {2}\\ {1}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {1}& {1}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{1}& {2}\\ {1}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {1}& {2}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{2}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {1}\\ {1}& {1}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {1}\\ {1}& {1}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{2}& {1}\\ {2}& {1}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{2}& {1}\\ {1}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{2}& {1}\\ {1}& {2}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{1}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {2}\\ {2}& {2}\end{array}\right]{,}\left[\begin{array}{cc}{1}& {1}\\ {1}& {2}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{1}& {1}\\ {2}& {1}\end{array}\right]\right]{,}\left[\left[\begin{array}{cc}{1}& {1}\\ {2}& {2}\end{array}\right]\right]\right]$ (1)
 > $\mathrm{map}\left(\mathrm{nops},C\right)$
 $\left[{4}{,}{2}{,}{2}{,}{3}{,}{1}{,}{2}{,}{4}{,}{1}{,}{1}\right]$ (2)

Compatibility

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