SOME NEW CANONICAL FORMS FOR POLYNOMIALS

We give some new canonical representations for forms over C. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power of a linear form. A general cubic form in (x(1). . . , x(n)) can be written uniquely as a sum of the cubes of linear forms l(ij) (xi,. . . , x(j)), 1 <= i <= j <= n. A general ternary quartic form is the sum of the square of a quadratic form and three fourth powers of linear forms. The methods are classical and elementary.