24.10 DifferenceAgWord

DifferenceAgWord( u, v )

DifferenceAgWord returns an ag word s representing the difference of the exponent vectors of u and v.

Let G be the parent group of u and v. Let (g_1, ..., g_n) be the AG system of G and o_i be the relative order or g_i. Then u can be expressed uniquely as g_1^{u_1}* ...* g_n^{u_n} for integers u_i between 0 and o_i-1 and v can be expressed uniquely as g_1^{v_1}* ...* g_n^{v_n} for integers v_i between 0 and o_i-1. The function DifferenceAgWord returns an ag word s = g_1^{s_1}* ...* g_n^{s_n} with integer s_i such that 0 leq s_i < o_i and s_i equiv u_i - v_i mod o_i.

    gap> DifferenceAgWord( a * b, a );
    b
    gap> DifferenceAgWord( a, b );
    a*b^2 
    gap> z27 := CyclicGroup( AgWords, 27 );
    Group( c27_1, c27_2, c27_3 )
    gap> x := z27.1 * z27.2;
    c27_1*c27_2
    gap> x * x;
    c27_1^2*c27_2^2
    gap> DifferenceAgWord( x, x );
    IdAgWord 

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