25.28 IsConsistent

IsConsistent( G )
IsConsistent( G, all )

IsConsistent returns true if the finite polycyclic presentation of a parent group G is consistent and false otherwise.

If all is true then G.inconsistencies contains a list for pairs [ w_1, w_2 ] such that the words w_1 and w_2 are equal in G but have different normal forms.

Note that IsConsistent check and sets G.isConsistent.

    gap> InfoAgGroup2 := Print;;
    gap> x := AbstractGenerator( "x" );;
    gap> y := AbstractGenerator( "y" );;
    gap> z := AbstractGenerator( "z" );;
    gap> G := AgGroupFpGroup( rec(
    >       generators := [ x, y, z ],
    >       relators   := [ x^2 / y, y^2 / z, z^2,
    >                       Comm( y, x ) / ( y * z ),
    >                       Comm( z, x ) / ( y * z )] ) );
    Group( x, y, z )
    gap> IsConsistent( G );
    #I  IsConsistent: y * ( y * x ) <> ( y * y ) * x
    false
    gap> IsConsistent( G, true );
    #I  IsConsistent: y * ( y * x ) <> ( y * y ) * x
    #I  IsConsistent: z * ( z * x ) <> ( z * z ) * x
    #I  IsConsistent: y * ( x * x ) <> ( y * x ) * x
    #I  IsConsistent: z * ( x * x ) <> ( z * x ) * x
    #I  IsConsistent: x * ( x * x ) <> ( x * x ) * x
    false
    gap> G.inconsistencies;
    [ [ x, x*y ], [ x*z, x ], [ z, y ], [ y*z, y ], [ x*y, x ] ]
    gap> InfoAgGroup2 := Ignore;; 

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