Open AccessJournal Article10.1007/S11786-010-0060-3

A Normal Form Algorithm for Regular Differential Chains

- 09 Nov 2010

- Vol. 4, Iss: 2, pp 185-201

TL;DR: A new algorithm for computing the normal form of a differential rational fraction modulo differential ideals presented by regular differential chains is presented and illustrated with the new DifferentialAlgebra MAPLE package.

Abstract: This paper presents a new algorithm for computing the normal form of a differential rational fraction modulo differential ideals presented by regular differential chains. An application to the computation of power series solutions is presented and illustrated with the new DifferentialAlgebra MAPLE package.

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This paper presents a new algorithm for computing the normal form of a differential rational fraction modulo differential ideals presented by regular differential chains.. An application to the computation of power series solutions is presented and illustrated with the new DifferentialAlgebra MAPLE package.

FIGURE 5. The ExtendedEuclideanAlgorithm function

FIGURE 4. The AlgebraicInverseNonZero function

Citations

•Journal Article•10.1007/S11786-011-0093-2

Model Reduction of Chemical Reaction Systems using Elimination

François Boulier, +3 more

- 12 Nov 2011

- Mathematics in Computer Science

TL;DR: This paper focuses on some schemes of model reduction for parametric ordinary differential systems arising from chemical reaction systems which rely on quasi-steady states approximations and shows that they can be formulated by means of differential and algebraic elimination.

...read moreread less

•Book Chapter•10.1007/978-3-030-38356-5_6

On Symbolic Approaches to Integro-Differential Equations

François Boulier, +4 more

- 01 Jan 2017

TL;DR: In this article, the authors recall the origin of integro-differential equations and present new opportunities in nonlinear control theory by means of integration of input-output equations (IoE).

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•Book Chapter•10.1007/978-3-319-24021-3_8

Finding First Integrals Using Normal Forms Modulo Differential Regular Chains

François Boulier, +1 more

- 14 Sep 2015

TL;DR: The definition of polynomial first integrals in the differential algebra context and an algorithm for computing them are introduced and the method amounts to finding linear dependences of rational fractions, which is solved by evaluation techniques.

...read moreread less

•Book Chapter•10.1007/978-3-319-99639-4_6

Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling

François Boulier, +7 more

- 17 Sep 2018

TL;DR: A proof of concept for symbolic and numeric methods dedicated to the parameter estimation problem for models formulated by means of nonlinear integro-differential equations (IDE).

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•Book Chapter•10.1007/978-3-642-23568-9_6

On the regularity property of differential polynomials modulo regular differential chains

François Boulier, +2 more

- 05 Sep 2011

TL;DR: An algorithm which computes the normal form of a rational differential fraction modulo a regular differential chain if, and only if, this normal form exists is provided.

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References

The Art in Computer Programming

Andrew Hunt, +1 more

- 01 Jan 2001

TL;DR: Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.

...read moreread less

8.4K

•Book

Differential Algebra and Algebraic Groups

E. R. Kolchin

- 01 Jan 2012

1.5K

Commutative Algebra I

Craig Huneke

- 01 Jan 2012

TL;DR: A compilation of two sets of notes at the University of Kansas was published in the Spring of 2002 by?? and the other in the spring of 2007 by Branden Stone.

...read moreread less

1.2K

•Journal Article•10.1006/JSCO.1993.1051

Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering

Jean-Charles Faugère, +3 more

- 01 Oct 1993

- Journal of Symbolic Computation

TL;DR: The lexicographical GroBner basis can be obtained by applying this algorithm after a total degree Grobner basis computation: it is usually much faster to compute the basis this way than with a direct application of Buchberger's algorithm.

...read moreread less

785

•Book

The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information

Donald Ervin Knuth

- 01 Apr 1978

527

...

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A Normal Form Algorithm for Regular Differential Chains

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Citations

Model Reduction of Chemical Reaction Systems using Elimination

On Symbolic Approaches to Integro-Differential Equations

Finding First Integrals Using Normal Forms Modulo Differential Regular Chains

Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling

On the regularity property of differential polynomials modulo regular differential chains

References

The Art in Computer Programming

Differential Algebra and Algebraic Groups

Commutative Algebra I

Efficient Computation of Zero-dimensional Gröbner Bases by Change of Ordering

The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information

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