HELP FOR: A package for symmetric functions as operators on alphabets.

CALLING SEQUENCE:

SFA[<function>](args)

<function>(args)

SYNOPSIS:

• This package provides functions to work with symmetric functions, considered as operators acting on the ring of polynomial with real coefficients. It more precisely implements the structure of lambda-ring.

• To get more information on symmetric functions on alphabets do either ?TYP,SfA or ?TYP[SfA].

• All defined bases are stored in the global variable SFABases that is by default ['e', 'h', 's', 'p', 'm'].

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

• The available functions are:

  Pol2SfA	Sf2SfA	SfA2Sf	SfA2TableVar
  SfACollect	SfAExpand	SfAOmega	SfAVars
  ToeA	TohA	TomA	TopA
  TosA

• For help with a particular function do either ?SFA[<function>] or ?SFA,<function> where <function> is one from the above list.

EXAMPLES:

> with(SFA):
> r := TosA( e[3,2](2*A1) );
 
   r := s[1, 1, 1, 1, 1](2 A1) + s[2, 2, 1](2 A1) + s[2, 1, 1, 1](2 A1)
 
> SfAExpand(r);
 
       20 s[2, 2, 1](A1) + 22 s[2, 1, 1, 1](A1) + 12 s[1, 1, 1, 1, 1](A1)
 
            + 2 s[4, 1](A1) + 8 s[3, 2](A1) + 12 s[3, 1, 1](A1)
 
> SfAExpand( (p[3]/3 + p[2,1]/2 + p[1,1,1]/6)(p[2](6*A1^2) + k) );
 
             3        2              2
        1/6 k  + 1/2 k  + 1/3 k + 3 k  p[2, 2](A1) + 3 k p[2, 2](A1)
 
           + 3 k p[4, 4](A1) + 18 k p[2, 2, 2, 2](A1) + 2 p[6, 6](A1)
 
           + 18 p[4, 4, 2, 2](A1) + 36 p[2, 2, 2, 2, 2, 2](A1)