GAP Manual: 24.5. Depth

Depth( g )

Depth returns the depth of an ag word g with respect to the AG-series of its parent group as integer.

Let G be the parent group of g and G=G_0 > ... > G_n={1} the AG-series of G. Let delta be the maximal positive integer such that g is an element of G_(delta-1). Then delta is the depth of g.

Note that Depth allows record that mimic ag words as arguments.

    gap> Depth( a );
    1
    gap> Depth( d );
    4
    gap> Depth( a^0 );
    5