Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The binomial ideal of the intersection axiom for conditional
  probabilities   The binomial ideal associated with the intersection axiom of conditional
probability is shown to be radical and is expressed as intersection of toric
prime ideals. This resolves a conjecture in algebraic statistics due to
Cartwright and Engstr\"om.

12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin