Pääinvariantit
Pääinvariantit, often translated as principal invariants or fundamental invariants, are a concept in mathematics, particularly in the fields of algebraic geometry and invariant theory. They represent a minimal set of algebraically independent polynomial functions that can generate all other invariant polynomials under a given group action. In essence, they are the building blocks from which all other symmetric polynomials (or more generally, polynomials invariant under a group transformation) can be constructed.
The idea originates from studying the symmetries of mathematical objects. When a group acts on a set
A classic example is the symmetric group $S_n$ acting on $n$ variables $x_1, \dots, x_n$. The elementary