FUNCTION: SfMat - transition matrix between symmetric functions bases

CALLING SEQUENCE:

SfMat(n, b_1, b_2)

SYMF[SfMat](n, b_1, b_2)

PARAMETERS:

n = any positive integer

b_1, b_2 = any names denoting known bases

SYNOPSIS:

• The SfMat function returns the transition matrix from the b_1 basis to the b_2 basis of the homogeneous component of weight n of the space of symmetric functions.

• Parameters b_1 and b_2 are taken from the SYMFBases global variable.

• The result is a matrix indexed by partitions of n, each row giving the expansion of an element of the b_1 basis in the b_2 basis.

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

EXAMPLES:

> with(SYMF):
> SfMat(4, 's', 'm');
 
                            [ 1  1  1  1  1 ]
                            [               ]
                            [ 0  1  1  2  3 ]
                            [               ]
                            [ 0  0  1  1  2 ]
                            [               ]
                            [ 0  0  0  1  3 ]
                            [               ]
                            [ 0  0  0  0  1 ]