FUNCTION: Free2Plax - quotient of the free algebra by plactic relations

CALLING SEQUENCE:

Free2Plax(free)

FREE[Free2Plax](free)

PARAMETERS:

free = any element of the free algebra

SYNOPSIS:

• The Free2Plax function projects the free algebra onto the plactic algebra. It sends any word to the unique tableau in its class (that is to say, to the word obtained by reading the successive rows of the tableau given by Schensted algorithm).

• Whenever there is a conflict between the function name Free2Plax and another name used in the same session, use the long form FREE['Free2Plax'].

EXAMPLES:

> with(FREE):
> Free2Plax(w[1,2,1] + w[2,1,1] + z*w[1,3,2]);
 
                         2 w[2, 1, 1] + z w[3, 1, 2]