IsSimple - Maple Help

Magma

 IsSimple
 test whether a magma is simple

 Calling Sequence IsSimple( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • A magma is simple if it has no homomorphic images other than itself and the single magma.
 • The function IsSimple( m ) returns true if the magma m is simple and returns false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $m≔⟨⟨⟨1|1|3⟩,⟨3|3|1⟩,⟨1|1|2⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccc}{1}& {1}& {3}\\ {3}& {3}& {1}\\ {1}& {1}& {2}\end{array}\right]$ (1)
 > $\mathrm{IsSimple}\left(m\right)$
 ${\mathrm{true}}$ (2)
 > $m≔⟨⟨⟨1|1|3⟩,⟨3|1|1⟩,⟨3|1|1⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccc}{1}& {1}& {3}\\ {3}& {1}& {1}\\ {3}& {1}& {1}\end{array}\right]$ (3)
 > $\mathrm{IsSimple}\left(m\right)$
 ${\mathrm{false}}$ (4)

Compatibility

 • The Magma[IsSimple] command was introduced in Maple 16.