24.14 ExponentAgWord

ExponentAgWord( g, k )

ExponentAgWord returns the exponent of the k.th generator in an ag word g as integer, where k refers to the numbering of generators of the parent group of g.

Let G be the parent group of g and (g_1, ..., g_n) the AG system of G and let o_i be the relative order of g_i. Then the element g can be expressed uniquely in the form g_1^{nu_1}* ...* g_n^{nu_n} for integers nu_i between 0 and o_i-1. The exponent of the k.th generator is nu_{<k>}.

See also ExponentsAgWord and Exponents.

    gap> ExponentAgWord( a * b^2 * c^2 * d, 2 );
    2
    gap> ExponentAgWord( a * b^2 * c^2 * d, 4 );
    1
    gap> ExponentAgWord( a * b^2 * c^2 * d, 3 );
    0
    gap> a * b^2 * c^2 * d;
    a*b^2*d 

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