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GroupTheory

 PresentationComplexity
 return a measure of the complexity of a presentation of a finitely presented group

 Calling Sequence PresentationComplexity( G )

Parameters

 G - a finitely presented group

Description

 • The PresentationComplexity( G ) command returns a triple of the form (m, n, k), where m is the number of generators currently defined for G, n is the number of relators currently defined for G, and k is the total length of the relators.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔⟨⟨a,b⟩|⟨{a}^{2},{b}^{3},{\left(a·b\right)}^{5}=1⟩⟩$
 ${G}{≔}⟨{}{a}{,}{b}{}{\mid }{}{{a}}^{{2}}{,}{{b}}^{{3}}{,}{a}{}{b}{}{a}{}{b}{}{a}{}{b}{}{a}{}{b}{}{a}{}{b}{}⟩$ (1)
 > $\mathrm{PresentationComplexity}\left(G\right)$
 ${2}{,}{3}{,}{15}$ (2)

Compatibility

 • The GroupTheory[PresentationComplexity] command was introduced in Maple 18.