FUNCTION: Sf2SfA - from SYMF objects to SFA objects

CALLING SEQUENCE:

Sf2SfA(sf)

Sf2SfA(sf, A)

SFA[Sf2SfA](sf)

SFA[Sf2SfA](sf, A)

PARAMETERS:

sf = any valid expression in SYMF

A = any alphabet

SYNOPSIS:

• The Sf2SfA function transforms any symmetric function of the SYMF package into an object of SFA for a specific alphabet (by default A1).

• Valid bases for symmetric functions are 'e', 'h', 'p', 's', 'm'. Added bases and the c basis are not considered.

• Allowed alphabet expressions are linear combinations of formal alphabets A1, A2, A3, ..., for instance 3/2*A1 - A3 + 3/4 is valid.

• The inverse function is SfA2Sf.

• Whenever there is a conflict between the function name Sf2SfA and another name used in the same session, use the long form SFA['Sf2SfA'].

EXAMPLES:

> with(SFA):
> Sf2SfA(s[3,1]*p2 - e2*e1);
 
                       s[3, 1](A1) p[2](A1) - e[2, 1](A1)
 
> Sf2SfA(s[3,1]*p2 - e2*e1, A2);
 
                       s[3, 1](A2) p[2](A2) - e[2, 1](A2)
 
> Sf2SfA(s[2,2], 2*A3);
 
                                 s[2, 2](2 A3)