FUNCTION: SpScalarPol - scalar product on polynomials

CALLING SEQUENCE:

SpScalarPol(pol_1, pol_2, n)

SP[SpScalarPol](pol_1, pol_2, n)

PARAMETERS:

pol_1 = any polynomial expression

pol_2 = any polynomial expression

n = any positive integer denoting the degree of a symmetric group

SYNOPSIS:

• The SpScalarPol function computes the scalar product <pol_1, pol_2> corresponding to the symmetric group of degree n.

• <pol_1, pol_2> = <pol_1*pol_2, 1>.

• <pol, 1> is the symmetric function (in the basis of Schur functions) obtained by applying the maximal divided difference of Sn to pol.

• When called without the third argument, it assumes that n equals _Sn.

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

EXAMPLES:

> with(SP):
> SpScalarPol(x1^6*x2, x2^2*x3, 3);
 
                                  s[4, 2, 1]