FUNCTION: Word2Key - left or right key

CALLING SEQUENCE:

Word2Key(w)

TAB[Word2Key](w)

PARAMETERS:

w = any word

SYNOPSIS:

• The Word2Key function returns the left or the right key of a given word. By default, it returns the left key.

• When called with the optionnal parameter 'right', it returns the right key corresponding to the word w. Using 'left' as option, is equivalent to Word2Key(w).

• The left key of a word w is the set of left columns in the orbit of: PermOnCTab(perm, Word2CTab(w))

• The right key of a word w is the set of right columns in the orbit of: PermOnCTab(perm, Word2CTab(w))

• When called an extra 'nil' argument, the Word2Key returns the nilplactic corresponding key (either left or right). By default, it returns the left nilplactic key. Whenever the word is not a reduced decomposition, it returns [].

• Whenever there is a conflict between the function name Word2Key and another name used in the same session, use the long form TAB['Word2Key'].

EXAMPLES:

> with(TAB):
> Word2Key(w[5,6,2,4,3,7,1]);
 
                        [[5], [5, 2], [5, 4, 2, 1]]
 
> Word2Key(w[5,6,2,4,3,7,1], 'right');
 
                         [[7, 4, 3, 1], [7, 3], [7]]
 
> Word2Key(w[3,2,1,3,2]);
 
                             [[3, 2], [3, 2, 1]]
 
> Word2Key(w[3,2,1,3,2], 'left', 'nil');
 
                             [[2, 1], [3, 2, 1]]