Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational certificates of positivity on compact semialgebraic sets   Schm\"udgen's Theorem says that if a basic closed semialgebraic set K = {g_1
\geq 0, ..., g_s \geq 0} in R^n is compact, then any polynomial f which is
strictly positive on K is in the preordering generated by the g_i's. Putinar's
Theorem says that under a condition stronger than compactness, any f which is
strictly positive on K is in the quadratic module generated by the g_i's. In
this note we show that if the g_i's and the f have rational coefficients, then
there is a representation of f in the preordering with sums of squares of
polynomials over Q. We show that the same is true for Putinar's Theorem as long
as we include among the generators a polynomial N - \sum X_i^2, N a natural
number.

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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin