Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A novel necessary and sufficient condition for the positivity of a
  binary quartic form   In this paper, by considering the common points of two conics instead of the
roots of the binary quartic form, we propose a novel necessary and sufficient
condition for the positivity of a binary quartic form using the theory of the
pencil of conics. First, we show the degenerate members of the pencil of conics
according to the distinct natures of the common points of two base conics.
Then, the inequalities about the parameters of the degenerate members are
obtained according to the properties of the degenerate conics. Last, from the
inequalities we derive a novel criterion for determining the positivity of a
binary quartic form without the discriminant.

36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin