FUNCTION: BnIdcaOnPol - action of an element of the Bn-idCoxeter algebra

CALLING SEQUENCE:

BnIdcaOnPol(e_1, exp)

BnIdcaOnPol(e_1, exp, v)

BNA[BnIdcaOnPol](e_1, exp)

BNA[BnIdcaOnPol](e_1, exp, v)

PARAMETERS:

e_1 = any element of the Bn-idCoxeter algebra

exp = any expression

v = any (extra) string

SYNOPSIS:

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

• The action of the i-th elementary generator is: (exp - exp') exp -> --------------- x_{i+1}, i<>0 x_i - x_{i+1} (x1*exp - 1/x1*exp'') exp -> -----------------------, i=0 1/x1 - x1 where exp' is the image of exp under the exchange of x_i and x_{i+1} and exp'' is the image of exp under the exchange of x1 and 1/x1.

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

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

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

EXAMPLES:

> with(BNA):
> BnIdcaOnPol(B[1,0,1], x1^3*x2^2*y3^2);
 
                        6     4     2                  2
                     (x1  + x1  + x1  + 1) (x2 + x3) y3  x3
                   - --------------------------------------
                                         3
                                       x1
 
> BnIdcaOnPol(B[1,0,1], x1^3*x2^2*y3^2, `y`);
 
                                         2   3
                             (y3 + y2) x2  x1  y3