Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average-case complexity of the Euclidean algorithm with a fixed
  polynomial over a finite field   We analyze the behavior of the Euclidean algorithm applied to pairs (g,f) of
univariate nonconstant polynomials over a finite field F_q of q elements when
the highest-degree polynomial g is fixed. Considering all the elements f of
fixed degree, we establish asymptotically optimal bounds in terms of q for the
number of elements f which are relatively prime with g and for the average
degree of gcd(g,f). The accuracy of our estimates is confirmed by practical
experiments. We also exhibit asymptotically optimal bounds for the average-case
complexity of the Euclidean algorithm applied to pairs (g,f) as above.

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The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio