Symmetry of polynomials

Like flat figures or spatial bodies, polynomials can have symmetry. The type of symmetry of any object is determined by a set (group) of the transformations that preserve it. For example, the so -called symmetric polynomials are polynomials that do not change during any rearrangement of variables.
The brochure tells about how the polynomials are described with this type of symmetry, and it is explained why this may be needed. In particular, the polynomials, which have the symmetry of the correct polyhedra, are applied to the construction of effective close -minded formulas of integration on the field.
The text of the brochure is a supplemented processing of the recording of the lecture read by the author for schoolchildren in grades 9-11 on October 28, 2000 at the small Mehmate of Moscow State University.
The brochure is designed for a wide range of readers interested in mathematics: high school students, primary school students, teachers