76.2 CoxeterWord

CoxeterWord( W , w )

returns a reduced word in the standard generators of the Coxeter group W determined by the permutation w on the root vectors.

    gap> W := CoxeterGroup( "A", 3 );;
    gap> w := ( 1,11)( 3,10)( 4, 9)( 5, 7)( 6,12);; 
    gap> w in W;
    true;
    gap> CHEVIE.BrieskornNormalForm := true;;
    gap> CoxeterWord( W, w );
    [ 1, 3, 2, 1, 3 ] 
    gap> CHEVIE.BrieskornNormalForm := false;;
    gap> CoxeterWord( W, w );
    [ 1, 2, 3, 2, 1 ] 

For the definition of the Brieskorn normal form, see the introduction to this chapter. If the global variable CHEVIE.BrieskornNormalForm is set to false (which is automatically the case when you load CHEVIE), the result of CoxeterWord is the lexicographically smallest reduced word for~w.

See also PermCoxeterWord and ReducedCoxeterWord.

This function requires the package "chevie" (see RequirePackage).

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