FUNCTION: BnGaOnPol - action of an element of the Bn-algebra

CALLING SEQUENCE:

BnGaOnPol(e_1, exp)

BnGaOnPol(e_1, exp, v)

BNA[BnGaOnPol](e_1, exp)

BNA[BnGaOnPol](e_1, exp, v)

PARAMETERS:

e_1 = any element of the Bn-algebra

exp = any expression

v = any (extra) string

SYNOPSIS:

• The BnGaOnPol function realizes the action of an element of the Bn- algebra, say e_1, on an expression exp. The signed permutation action is to permute variable indices and to change the sign as indicated by the signed permutation.

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

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

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

EXAMPLES:

> with(BNA):
> BnGaOnPol(B[1,0,3], x1^3*x2^2*x3);
 
                                     3   2
                                 - x3  x1  x2
 
> BnGaOnPol(B[1,0,3], x1^3*x2^2*x3, `y`);
 
                                     3   2
                                   x1  x2  x3