Vandermonde Polynomial - Discriminant

Discriminant

Its square is widely called the discriminant, though some sources call the Vandermonde polynomial itself the discriminant.

The discriminant (the square of the Vandermonde polynomial: ) does not depend on the order of terms, as, and is thus an invariant of the unordered set of points.

If one adjoins the Vandermonde polynomial to the ring of symmetric polynomials in n variables, one obtains the quadratic extension, which is the ring of alternating polynomials.