24.11 ReducedAgWord

ReducedAgWord( b, x )

Let b and x be ag words of the same depth, then ReducedAgWord returns an ag word a such that a is an element of the coset U <b>, where U is the cyclic group generated by x, and a has a higher depth than b and x.

Note that the relative order of b and x must be a prime.

Let p be the relative order of b and x. Let beta and xi be the leading exponent of b and x respectively. Then there exits an integer i such that xi * i = beta modulo p. We can set <a> = <x>^{-i} <b>.

Typically this function is used when b and x occur in a generating set of a subgroup W. Then b can be replaced by a in the generating set of W, but a and x have different depth.

    gap> ReducedAgWord( a*b^2*c, a );
    b^2*c
    gap> ReducedAgWord( last, b );
    c 

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