  An additive action on an irreducible algebraic variety $X$ is an effective
action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the vector group
$\mathbb{G}_a^n$. Any two additive actions on $X$ are conjugate by a birational
automorphism of $X$. We prove that, if $X$ is the projective space, the
conjugating element can be chosen in the affine Cremona group and it is given
by so-called basic polynomials of the corresponding local algebra.
