Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The MAPLE package TDDS for computing Thomas decompositions of systems of
  nonlinear PDEs   We present the Maple package TDDS (Thomas Decomposition of Differential
Systems). Given a polynomially nonlinear differential system, which in addition
to equations may contain inequations, this package computes a decomposition of
it into a finite set of differentially triangular and algebraically simple
subsystems whose subsets of equations are involutive. Usually the decomposed
system is substantially easier to investigate and solve both analytically and
numerically. The distinctive property of a Thomas decomposition is disjointness
of the solution sets of the output subsystems. Thereby, a solution of a
well-posed initial problem belongs to one and only one output subsystem. The
Thomas decomposition is fully algorithmic. It allows to perform important
elements of algebraic analysis of an input differential system such as:
verifying consistency, i.e., the existence of solutions; detecting the
arbitrariness in the general analytic solution; given an additional equation,
checking whether this equation is satisfied by all common solutions of the
input system; eliminating a part of dependent variables from the system if such
elimination is possible; revealing hidden constraints on dependent variables,
etc. Examples illustrating the use of the package are given.

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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph