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Magma

 SubMagmaClosure
 compute the closure of a set of magma members

 Calling Sequence SubMagmaClosure( gens, m )

Parameters

 gens - set of elements of m; subset of {1,2,...,n}. m - Array representing the Cayley table of a finite magma of order n

Description

 • The SubMagmaClosure( gens, m ) command returns the set of elements of the magma m generated by the set gens of elements of m. This is the smallest submagma of m containing the set gens.

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)
 > $\mathrm{SubMagmaClosure}\left(\left\{1,3\right\},m\right)$
 $\left\{{1}{,}{3}{,}{4}\right\}$ (2)

Compatibility

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