Magma - Maple Programming Help

Home : Support : Online Help : Mathematics : Algebra : Magma : Magma/Rank

Magma

 Rank
 compute the (lexicographic) rank of a magma represented by its Cayley table

 Calling Sequence Rank( m )

Parameters

 m - Array representing the Cayley table of a finite magma

Description

 • The Rank command returns the lexicographic rank of the magma represented by the Cayley table m.

Examples

 > $\mathrm{with}\left(\mathrm{Magma}\right):$
 > $m≔⟨⟨⟨1|2|3⟩,⟨2|3|1⟩,⟨3|1|2⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccc}{1}& {2}& {3}\\ {2}& {3}& {1}\\ {3}& {1}& {2}\end{array}\right]$ (1)
 > $\mathrm{Rank}\left(m\right)$
 ${4070}$ (2)
 > $m≔⟨⟨⟨1|2|3⟩,⟨2|3|3⟩,⟨3|1|2⟩⟩⟩$
 ${m}{≔}\left[\begin{array}{ccc}{1}& {2}& {3}\\ {2}& {3}& {3}\\ {3}& {1}& {2}\end{array}\right]$ (3)
 > $\mathrm{Rank}\left(m\right)$
 ${4124}$ (4)

Compatibility

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