Multivariate polynomials |

In order to write a given multivariate polynomial as a linear combination of Schubert polynomials you can useExample:scan(PERMUTATION,a); m_perm_schubert_monom_summe(a,b); m_perm_schubert_qpolynom(a,c); m_perm_schubert_dimension(a,d);In case you enter the permutation[2,4,3,5,1],then the output looks as follows:[2,4,3,5,1]

1 [1,2,1,1,0] 1 [2,1,1,1,0]

1 [6] 1 [7]

2

This means that the Schubert polynomial corresponding to the above permutation is

that we obtain (by replacingx_{1}x_{2}^{2}x_{3}x_{4}+x_{1}^{2}x_{2}x_{3}x_{4},xby_{i}q) the specialization^{i}and that the sum of all the coefficients isq^{6}+q^{7},2.

Here the output is a linear combination of permutations (=Schubert polynomials). Conversely you can input a linear combination of permutations and obtain the corresponding polynomials which is the linear combination of the Schubert polynomials associated with the permutations:t_POLYNOM_SCHUBERT

The correspondingt_SCHUBERT_POLYNOM

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001

Multivariate polynomials |