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SciMax Toolbox >> mon2schur

mon2schur

Maxima Function

Calling Sequence

mon2schur (L)

Description

The list L represents the Schur function S_L: we have

L = [i_1, i_2, ..., i_q], with i_1 <= i_2 <= ... <= i_q. The Schur function S_[i_1, i_2, ..., i_q] is the minor of the infinite matrix h_[i-j], i <= 1, j <= 1, consisting of the q first rows and the columns 1 + i_1,2 + i_2, ..., q + i_q.

This Schur function can be written in terms of monomials by using treinat and kostka. The form returned is a symmetric polynomial in a contracted representation in the variables x_1,x_2,\ldots.

(%i1) mon2schur ([1, 1, 1]);
(%o1)                       x1 x2 x3
(%i2) mon2schur ([3]);
                                  2        3
(%o2)                x1 x2 x3 + x1  x2 + x1
(%i3) mon2schur ([1, 2]);
                                      2
(%o3)                  2 x1 x2 x3 + x1  x2

which means that for 3 variables this gives:

2 x1 x2 x3 + x1^2 x2 + x2^2 x1 + x1^2 x3 + x3^2 x1
 + x2^2 x3 + x3^2 x2

Other functions for changing bases: comp2ele.

moebius SciMax Toolbox mono