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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