Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a Symbolic-Numeric Method to Compute Puiseux Series: The Modular
  Part   We have designed a new symbolic-numeric strategy to compute efficiently and
accurately floating point Puiseux series defined by a bivariate polynomial over
an algebraic number field. In essence, computations modulo a well chosen prime
$p$ are used to obtain the exact information required to guide floating point
computations. In this paper, we detail the symbolic part of our algorithm:
First of all, we study modular reduction of Puiseux series and give a good
reduction criterion to ensure that the information required by the numerical
part is preserved. To establish our results, we introduce a simple modification
of classical Newton polygons, that we call "generic Newton polygons", which
happen to be very convenient. Then, we estimate the arithmetic complexity of
computing Puiseux series over finite fields and improve known bounds. Finally,
we give bit-complexity bounds for deterministic and randomized versions of the
symbolic part. The details of the numerical part will be described in a
forthcoming paper.

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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex