Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Effective Framework for Constructing Exponent Lattice Basis of
  Nonzero Algebraic Numbers   Computing a basis for the exponent lattice of algebraic numbers is a basic
problem in the field of computational number theory with applications to many
other areas. The main cost of a well-known algorithm
\cite{ge1993algorithms,kauers2005algorithms} solving the problem is on
computing the primitive element of the extended field generated by the given
algebraic numbers. When the extended field is of large degree, the problem
seems intractable by the tool implementing the algorithm. In this paper, a
special kind of exponent lattice basis is introduced. An important feature of
the basis is that it can be inductively constructed, which allows us to deal
with the given algebraic numbers one by one when computing the basis. Based on
this, an effective framework for constructing exponent lattice basis is
proposed. Through computing a so-called pre-basis first and then solving some
linear Diophantine equations, the basis can be efficiently constructed. A new
certificate for multiplicative independence and some techniques for decreasing
degrees of algebraic numbers are provided to speed up the computation. The new
algorithm has been implemented with Mathematica and its effectiveness is
verified by testing various examples. Moreover, the algorithm is applied to
program verification for finding invariants of linear loops.

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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom