FUNCTION: Gauss - compute a Gaussian polynomial

CALLING SEQUENCE:

Gauss(m, n, 'q')

CLG[Gauss](m, n, 'q')

PARAMETERS:

m = any non-negative integer

n = any integer

SYNOPSIS:

• The Gauss function computes the Gaussian polynomial corresponding to the parameters m and n. This is a polynomial in the variable 'q' that is the generalization of the corresponding binomial coefficient binomial(m,n).

• Gauss(m,n,q) = 0 whenever n<0 or n>m.

• Gauss(m,n,q) = 1 whenever n=0 or n=m.

• Gauss(m,n,q) = Gauss(m-1,n-1,q) + q^n * Gauss(m-1,n,q).

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

EXAMPLES:

> with(CLG):
> Gauss(4, 2, q);
 
                              4    3      2
                             q  + q  + 2 q  + q + 1
 
> q:=2:
> Gauss(4, 2, q);
 
                                       35
 
> Gauss(4, 2, 'q');
 
                              4    3      2
                             q  + q  + 2 q  + q + 1