Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unique decomposition for a polynomial of low rank   Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined
over an algebraically closed field of characteristic 0 and suppose that $F$
belongs to the $s$-th secant variety of the $d$-uple Veronese embedding of
$\mathbb{P}^m$ into $ \PP {{m+d\choose d}-1}$ but that its minimal
decomposition as a sum of $d$-th powers of linear forms requires more than $s$
addenda. We show that if $s\leq d$ then $F$ can be uniquely written as
$F=M_1^d+\cdots + M_t^d+Q$, where $M_1, \ldots, M_t$ are linear forms with
$t\leq (d-1)/2$, and $Q$ a binary form such that $Q=\sum_{i=1}^q
l_i^{d-d_i}m_i$ with $l_i$'s linear forms and $m_i$'s forms of degree $d_i$
such that $\sum (d_i+1)=s-t$.

37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys