FUNCTION: Pol2Free - from polynomials to words

CALLING SEQUENCE:

Pol2Free(pol)

FREE[Pol2Free](pol)

PARAMETERS:

pol = any polynomial

SYNOPSIS:

• The Pol2Free function converts a polynomial into an element of the free algebra. The polynomial is first expressed in the basis of ordered products of elementary symmetric functions in different alphabets {x1, ..., xk}. Then the elementary symmetric functions are replaced by sums of all strictly decreasing words and their product is taken in the free algebra.

• Whenever there is a conflict between the function name Pol2Free and another name used in the same session, use the long form FREE['Pol2Free'].

EXAMPLES:

> with(FREE):
> Pol2Free(x1*x2+x1*x3+x2*x3 + aa*x2^2);
 
      aa w[1, 2] + aa w[2, 2] + (1 - aa) w[2, 1] + w[3, 1] + w[3, 2]