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_matrixd(k,b1,b2)

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'

Output

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

M1: When the transition matrix consists of rational numbers (i.e., base 2 is p), we can specifiy two output arguments. In that case, both M and M1 are int64 matrices, and the transition matrix can be computed by using sym(M)./sym(M1)

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.