SYMF::SfMat
--
transition matrix between symmetric functions bases
SYMF::SfMat(n,b1,b2)
n | - | any positive integer |
b1, b2 | - | any names denoting known bases |
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.
>> 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)
MuPAD Combinat, an open source algebraic combinatorics package