42.15 PowerMapping

PowerMapping( map, n )

PowerMapping returns the n-th power of the mapping map. map must be a mapping whose range is a subset of its source. n must be a nonnegative integer. map may be a multi valued mapping.

    gap> g := Group( (1,2,3,4), (2,4), (5,6,7) );;  g.name := "g";;
    gap> p4 := MappingByFunction( g, g, x -> x^4 );
    MappingByFunction( g, g, function ( x )
        return x ^ 4;
    end )
    gap> p16 := p4 ^ 2;
    CompositionMapping( CompositionMapping( IdentityMapping( g ), MappingB\
    yFunction( g, g, function ( x )
        return x ^ 4;
    end ) ), CompositionMapping( IdentityMapping( g ), MappingByFunction( \
    g, g, function ( x )
        return x ^ 4;
    end ) ) )
    gap> p16 = MappingByFunction( g, g, x -> x^16 );
    true 

PowerMapping calls map.operations.PowerMapping( map, n ) and returns this value.

The default function called this way is MappingOps.PowerMapping, which computes the power using a binary powering algorithm, IdentityMapping, and CompositionMapping. This function is seldom overlaid, because CompositionMapping does the interesting work.

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