1. You are an unregistered user.
2. You are trying to delete an accepted answer.
3. You are trying to delete a question with an upvoted answer.

This is my experience from SE 2.0, but I believe that this feature is shared with MO and its obsolete software.

Answer by user "VA" to question http://mathoverflow.net/questions/14613 :

"This is just to add 1% to Dmitri's 99% complete answer. Change the coordinates to $w_0,\dots, w_{n-1}$ defined by the formula

$$ w_i = x_0 + \mu^i x_1 + \mu^{2i} x_2 + \dots, $$

where $\mu$ is a primitive $n$-th root of identity. Then the ring of invariants is the subring of monomials

$$ w_0^{k_0}\dots w_{n-1}^{k_{n-1}} \quad \text{such that}\quad n\ |\ k_1 + 2k_2 + \dots (n-1) k_n$$

and a set of generators can be obtained by taking minimal such monomials (i.e. not divisible by smaller such monomials). And relations between these generators are of the form (monomial in $w_i$) = (another monomial in $w_i$). That's a pretty easy presentation by any standard.

P.S. This works over $\mathbb C$ or any ring containing $1/n$ and $\mu$."

Notice that this answer, while not adding any new ideas, noticeably improves upon the exposition of Dmitri's one. It is voted +3, so I am surprised the author was able to delete it in the first place...