IsSubMagma - Maple Help

Magma

 IsSubMagma
 test whether a set is a submagma of a given magma

 Calling Sequence IsSubMagma( ss, m )

Parameters

 ss - subset of the domain of the magma m m - Array representing the Cayley table of a finite magma

Description

 • A submagma of a magma is a subset that is closed under the specified binary operation.  Note that the empty set is vacuously a submagma of any magma.  Also, every magma is a submagma of itself.
 • The IsSubMagma( ss, m ) command returns true if the set ss is a submagma of the magma m, and returns false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $m≔⟨⟨⟨3|5|3|4|3⟩,⟨2|5|2|3|3⟩,⟨4|3|1|4|2⟩,⟨3|2|1|1|1⟩,⟨5|2|4|5|4⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccccc}{3}& {5}& {3}& {4}& {3}\\ {2}& {5}& {2}& {3}& {3}\\ {4}& {3}& {1}& {4}& {2}\\ {3}& {2}& {1}& {1}& {1}\\ {5}& {2}& {4}& {5}& {4}\end{array}\right]$ (1)
 > $\mathrm{IsSubMagma}\left(\left\{1,3,4\right\},m\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{IsSubMagma}\left(\left\{1,2,3\right\},m\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{IsSubMagma}\left(\left\{1,2,3,4,5\right\},m\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsSubMagma}\left(\varnothing ,m\right)$
 ${\mathrm{true}}$ (5)

Compatibility

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