Some new canonical forms for polynomials

Details Some new canonical forms for polynomials Some new canonical forms for polynomials

2012-03-26

arxiv.org/abs/1203.5722v1

Mathematics

Algebraic Geometry

I have spoken about this material under the title "steampunk canonical forms"

Scientific paper

We give some new canonical representations for forms over $\cc$. 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 $\ell_{ij}(x_i,...,x_j)$, $1 \le i \le j \le n$. 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.

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