Algorithmic Thomas decomposition of algebraic and differential systems
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The present paper is a revised version of Bachler et al. (2010) and includes the proofs of correctness and termination of the decomposition algorithm and illustrates the algorithm with further instructive examples and describes its Maple implementation.About:
This article is published in Journal of Symbolic Computation.The article was published on 2012-10-01 and is currently open access. It has received 73 citations till now. The article focuses on the topics: Differential algebraic geometry & Cylindrical algebraic decomposition.read more
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Differential systems: J. M. Thomas, American mathematical society publications. XXI. New York: Americ. math. soc., 1937. IX, 118 S. Preis geb. $2,-
TL;DR: In this paper, a minimal system of generators of the algebra of aane covariants from one of centro-aane invariants is given for planar quadratic diierential systems.
Book
Formal Algorithmic Elimination for PDEs
TL;DR: This tutorial discusses aspects of this correspondence between radical differential ideals and their analytic solution sets in differential algebra involving symbolic computation, and an introduction to the Thomas decomposition method is given.
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Decomposing polynomial sets into simple sets over finite fields: The positive-dimensional case
TL;DR: An algorithm for decomposing any positive-dimensional polynomial set into simple sets over an arbitrary finite field is presented, reducing the decomposition problem to the problem of computing the radicals of certain ideals.
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Noetherian quotients of the algebra of partial difference polynomials and Gröbner bases of symmetric ideals
TL;DR: In this article, a Grobner base theory for ideals of partial difference polynomials with constant or non-constant coefficients was proposed. But the finiteness of such bases was not investigated.
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The MAPLE package TDDS for computing Thomas decompositions of systems of nonlinear PDEs
TL;DR: The TDDS (Thomas Decomposition of Differential Systems) as mentioned in this paper decomposition of a polynomially nonlinear differential system, which in addition to equations may contain inequations, computes a decomposition into a finite set of differentially triangular subsystems whose subsets of equations are involutive.
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Ideals, Varieties, and Algorithms
TL;DR: In the Groebner package, the most commonly used commands are NormalForm, for doing the division algorithm, and Basis, for computing a Groebners basis as mentioned in this paper. But these commands require a large number of variables.
Book
Fundamental Problems of Algorithmic Algebra
TL;DR: Theorems of Algebraic Numbers: Thom's Lemma and the Routh-Hurwitz Theorem are presented, which state that theorems can be applied to both classical and ideal geometry.