FUNCTION: Free2NilFree - inverse plaxification map

CALLING SEQUENCE:

Free2NilFree(free)

FREE[Free2NilFree](free)

PARAMETERS:

free = any element of the free algebra

SYNOPSIS:

• The Free2NilFree is the inverse plaxification map which transforms a word into a reduced decomposition. This map is defined recursively by: invplaxify(w[i,j,...]) = w[i, invplaxify(SgaOnFree(s_i, w[j,...]))] where s_i is the simple transposition (i,i+1).

• The inverse plaxification map has the property to send a plactic class onto a nil plactic class.

• Whenever there is a conflict between the function name Free2NilFree and another name used in the same session, use the long form FREE['Free2NilFree'].

EXAMPLES:

> with(FREE):
> Free2NilFree(w[3,2,2,1,1,1]);
 
                             w[3, 2, 3, 1, 2, 3]
 
> Free2NilFree(w[1,2,1] + w[2,1,1]);
 
                           w[1, 2, 1] + w[2, 1, 2]