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SYMF::SfMat -- transition matrix between symmetric functions bases

Call(s)


SYMF::SfMat(n,b1,b2)

Parameters

n- any positive integer
b1, b2- any names denoting known bases

Introduction

The SYMF::SfMat function returns the transition matrix from the b1 basis to the b2 basis of the homogeneous component of weight n of the space of symmetric functions.

Parameters b1 and b2 are taken from the SYMF::SYMFBases global variable.

The result is a matrix indexed by partitions of n, each row giving the expansion of an element of the b1 basis in the b2 basis.

Example 1

>> muEC::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  |
                            +-               -+
array(1..5, 1..5, (1,1) = 1, (1,2) = 1, (1,3) = 1, (1,4) = 1, (1,5) = 1, (2,1) = 0, (2,2) = 1, (2,3) = 1, (2,4) = 2, (2,5) = 3, (3,1) = 0, (3,2) = 0, (3,3) = 1, (3,4) = 1, (3,5) = 2, (4,1) = 0, (4,2) = 0, (4,3) = 0, (4,4) = 1, (4,5) = 3, (5,1) = 0, (5,2) = 0, (5,3) = 0, (5,4) = 0, (5,5) = 1)

Related Functions

Sf

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MuPAD Combinat, an open source algebraic combinatorics package