FUNCTION: BnNcaOnPol - action of an element of the Bn-nilCoxeter algebra

CALLING SEQUENCE:

BnNcaOnPol(e_1, exp)

BnNcaOnPol(e_1, exp, v)

BNA[BnNcaOnPol](e_1, exp)

BNA[BnNcaOnPol](e_1, exp, v)

PARAMETERS:

e_1 = any element of the Bn-nilCoxeter algebra

exp = any expression

v = any (extra) string

SYNOPSIS:

• The BnNcaOnPol function realizes the action of an element of the Bn- nilCoxeter algebra, say e_1, on an expression exp.

• Simple divided differences Di are the operators: f(..., x_i, x_{i+1}, ...) - f(..., x_{i+1}, x_i, ...) f --> -----------------------------------------------------, i<>0 x_i - x_{i+1} f(..., x_i, ...) - f(..., -x_{i}, ...) f --> --------------------------------------, i=0 2*x_i

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

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

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

EXAMPLES:

> with(BNA):
> BnNcaOnPol(B[1,0,1], x1^3*x2^2*y3^2);
 
                                          2   2
                              (x3 + x2) x1  y3
 
> BnNcaOnPol(B[1,0,1], x1^3*x2^2*y3^2, `y`);
 
                                      0