POSITIVITY OF POLYNOMIAL IN THE CONTEXT OF CZECH EDUCATION

摘要

Decomposition of a polynomial as a Sum of squares of polynomials (SOS) is one of the classical methods how to prove that certain polynomial f is a positive semidefinite polynomial. At present, this is a technique that is not usually taught at Czech high schools or in (Computer) Algebra courses in the preparation of mathematics and/or computer science teachers at the faculties of education. In the case of polynomials of one variable, sum of squares decomposition could be a simple problem and this technique could be used by mathematical olympics solvers. The opposite case represents higher degree polynomials in multiple variables. Here we cannot solve the problem without computer technology and mathematical software. Thanks to this software, it is possible to look at the classical problems in an innovative way through the optics of computer technologies, and it is possible to solve problems which were almost impossible to solve in the past. Through the cognitive technologies, we can also bring near the more difficult parts of this issue and more abstract concepts to high school students and teachers at elementary and high schools.