SYMF::SfMat --
transition matrix between symmetric functions bases
Call(s)
SYMF::SfMat(n,b1,b2)
Parametersn | - | 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 FunctionsMuPAD Combinat, an open source algebraic combinatorics package