Transition Matrices between Symmetric Polynomials

A set of Matlab programs that computes the transition matrix between different bases of symmetric polynomials

This Matlab program produces the transition matrix between six different bases of symmetric polynomials. The six bases are

e: elementary symmetric function

h: complete homogeneous symmetric function

m: monomial symmetric function

f: forgotten symmetric function

s: Schur function

p: power-sum symmetric function

Syntax:

M = trans_matrix(k,b1,b2, mode)

Input:

k: order of symmetric polynomials

b1: base 1

b2: base 2

bases 1 and 2 are either 'e', 'h', 'm', 'f', 's' or 'p'

mode = 'double' (default)

Every transition matrix except those with b2 = 'p' has integer entries; those are returned as int64 and are EXACT whenever they

fit in an int64 (|entry| < 2^63). The matrices with b2 = 'p' are rational; they are returned as double, each entry formed as one

correctly rounded quotient of two exactly computed integers.

mode = 'exact'

The same matrices as sym, exactly. Requires the Symbolic Math

Toolbox. The work is NOT done in sym.

Output

M: transition matrix that expresses symmetric polynomials in base 1 in terms of linear combination of symmetric polynomials in base 2.

Read manual.pdf for more information. I also had written a program to compute transition matrix between Jack polynomials and other symmetric polynomials. E-mail me if you need that.