Timeline for Polynomials of low degree that clone polynomials of higher degree

13 events

when toggle format	what		by	license	comment
Dec 17, 2014 at 1:10	vote	accept	Turbo
Dec 16, 2014 at 22:41	comment	added	Pietro Majer		I think so.$\phantom{}$
Dec 16, 2014 at 18:48	vote	accept	Turbo
Dec 17, 2014 at 0:33
Dec 16, 2014 at 9:30	comment	added	Pietro Majer		Here $\deg_k$ is the degree w.r.to $x_k$. For any (non-zero) polynomial $q$, one has $\deg_k(q)=0$ if and only if $q$ does not depend on $x_k$. Then of course $\delta_kq=0$ . So e.g. $p_1\in\mathbb{R}\mathbb[x_2,x_3,\dots,x_{16}]$.
Dec 16, 2014 at 8:55	comment	added	Pietro Majer		Yes, in other words the sum is over all $\epsilon=\sum_{j\in R}e_j$, and $R$ varies among the $2^4$ subsets of $S$
Dec 16, 2014 at 8:49	history	edited	Pietro Majer	CC BY-SA 3.0	deleted 7 characters in body
Dec 16, 2014 at 8:42	history	edited	Pietro Majer	CC BY-SA 3.0	deleted 7 characters in body
Dec 16, 2014 at 8:38	comment	added	Turbo		nice answer I like it.
Dec 16, 2014 at 8:35	comment	added	Pietro Majer		Here $e_k$ is the k-th element of the standard basis, so $x+e_k=(x_1,x_2,\dots,x_k+1,\dots,x_{16})$
Dec 16, 2014 at 8:34	history	edited	Pietro Majer	CC BY-SA 3.0	added 34 characters in body
Dec 16, 2014 at 8:32	comment	added	Pietro Majer		Yes, I used the same notation as in your post, $x:=(x_1,\dots,x_{16})$
Dec 16, 2014 at 8:30	comment	added	Pietro Majer		(I only now realize there is another answer; sorry)
Dec 16, 2014 at 8:28	history	answered	Pietro Majer	CC BY-SA 3.0