FUNCTION: Pol2SfA - from the basis of monomials to SFA

CALLING SEQUENCE:

Pol2SfA(pol, vlist)

SFA[Pol2SfA](pol, vlist)

PARAMETERS:

pol = any polynomial symmetric in vlist

vlist = a list of variables

SYNOPSIS:

• The Pol2SfA function transforms any polynomial symmetric in the list of variables vlist into a linear combination of monomial symmetric functions of SFA.

• Whenever there is a conflict between the function name Pol2SfA and another name used in the same session, use the long form SFA['Pol2SfA'].

EXAMPLES:

> with(SFA):
> SfAVars( {{x}, u, v} );
 
                                  {v, u, {x}}
 
> r := SfAExpand( m[3,2](x1+u+v) - q*s[2,2](x1+u+v) );
 
       2  3     2  3     3  2     3  2    2  3    3  2      2  2      2
r := x1  u  + x1  v  + x1  v  + x1  u  + u  v  + u  v  - q v  u  - q v  x1
 
           2   2           2         2         2  2
      - q v  x1  - q v x1 u  - q v x1  u - q x1  u
 
> Pol2SfA(r, [x1,u,v]);
 
   m[3, 2](x1 + u + v) - q m[2, 1, 1](x1 + u + v) - q m[2, 2](x1 + u + v)