24.12 SiftedAgWord

SiftedAgWord( U, g )

SiftedAgWord tries to sift an ag word g, which must be an element of the parent group of an ag group U, through an induced generating system of U. SiftedAgWord returns the remainder of this shifting process.

The identity is returned if and only if g is an element of U.

Let u_1, ..., u_m be an induced generating system of U. If there exists an u_i such that u_i and g have the same depth, then g is reduced with u_i using ReducedAgWord (see ReducedAgWord). The process is repeated until no u_i can be found or the g is reduced to the identity.

Factor Groups of Ag Groups for details.

Note that SiftedAgGroup adds a record component U.shiftInfo to the ag group record of U. This entry is used by subsequent calls with the same ag group in order to speed up computation. If you ever change the component U.igs by hand, not using Normalize, you must unbind U.shiftInfo, otherwise all following results of SiftedAgWord will be corrupted.

    gap> s3 := Subgroup( s4, [ a, b ] );
    Subgroup( s4, [ a, b ] )
    gap> SiftedAgWord( s3, a * b^2 * c );
    c 

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