 SubMagmaCayleyTable - Maple Help

Home : Support : Online Help : Mathematics : Algebra : Magma : SubMagmaCayleyTable

Magma

 SubMagmaCayleyTable
 compute the Cayley table of a submagma Calling Sequence SubMagmaCayleyTable( s, m ) Parameters

 s - subset of {1,2,...,n} m - Array representing the Cayley table of a finite magma of order n Description

 • The SubMagmaCayleyTable( s, m ) command returns a Cayley table for the submagma s of the magma represented by the Cayley table m.  The elements of s are renumbered to fall within the range 1..k, where k is the number of elements of s.
 • If the subset s of {1,2,...,n} is not a submagma of m, then an exception is raised. 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)
 > $\mathrm{SubMagmaCayleyTable}\left(\left\{1,3,4\right\},m\right)$
 $\left[\begin{array}{ccc}{2}& {2}& {3}\\ {3}& {1}& {3}\\ {2}& {1}& {1}\end{array}\right]$ (3) Compatibility

 • The Magma[SubMagmaCayleyTable] command was introduced in Maple 17.