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Podstawy mnogościowe wielomianów symetrycznych wielu zmiennych w notacji spektralnej : zarys teorii

Piwowarczyk T.

Czasopismo Techniczne. Elektrotechnika

2000

R. 97, z. 4-E

38--60

All symmetric polynomials of multiple variables, with the variables belonging to the fixed, final set, are denoted by means of some abstract symbols. They are known as spectral, or multipower symbols. This set is analysed from a point of view of a set theory. The article contains the definitions of those relations which are used for computing elements in numerous subsets, such as equivalence relation, ordering relation, quotient sets, combinatorics formulas. In other words, some set theory model is proposed for symmetric polynomials of multiple variables. Such a model provides a solid basis for the further study of symmetric polynomials, and first of all, for the study of their numerous vector subspaces. This study will be developed in a theoretically unlimited set of algebraic identities which are particularly useful when it comes to engineering applications