FUNCTION: SgaOnPol - action of an element of the algebra on an expression

CALLING SEQUENCE:

SgaOnPol(e_1, exp)

SgaOnPol(e_1, exp, v)

SGA[SgaOnPol](e_1, exp)

SGA[SgaOnPol](e_1, exp, v)

PARAMETERS:

e_1 = any element of the symmetric group algebra

exp = any expression

v = any (extra) string

SYNOPSIS:

• The SgaOnPol function realizes the action of an element of the symmetric algebra, say e_1, on an expression exp. Each permutation acts by permuting the indices of the variables.

• By default the algebra acts on the variables x1, x2, x3, ...

• A simple transposition, say [1,2,4,3,5,6], exchanges the variables x3 and x4.

• When called with a third argument v, being, say `y`, the SgaOnPol function acts on the variables y1, y2, y3, ...

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

EXAMPLES:

> with(SGA):
> SgaOnPol(A[2,1], x1+x3);
 
                                    x2 + x3
 
> SgaOnPol(A[2,1], x1+x3, `y`);
 
                                    x1 + x3
 
> SgaOnPol(A[2,1] - x3*A[3,1,2], x1+x3);
 
                            - x3 (x2 + x3) + x2 + x3