Tests of the formulas for the palindromic project (in Sagemath).

This page is a complement of the paper
P. Alexandersson, L. A. González-Serrano, E. A. Maximenko, M. A. Moctezuma-Salazar:
Symmetric polynomials in the symplectic alphabet and their expression via Dickson–Zhukovsky variables.
Preprint: arXiv:1912.12725 [math.CO].

Here are some programs in Sagemath that verify our formulas for small values of parameters. The maximal values of the parameters are selected in such a manner that each program runs less than 5 minutes on modern computers.

We denote by «pol» the tests in the polynomial field, i.e. with polynomial variables, by «numer» the random tests with rational numbers, and by «sym» the tests in the ring of the symmetric functions (in the Schur basis).

Auxiliary facts

Bialternant formulas with Chebyshov polynomials

Formulas for elemz, homz, powersumz, and their odd analogs

Analogs of Cauchy identities

Minors of banded symmetric Toeplitz matrices