A linear algebra approach to the differentiation index of generic DAE systems

The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper bounds for the regularity of the Hilbert–Kolchin function a...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing communication and computing, 2008-12, Vol.19 (6), p.441-473
Main Authors: D’Alfonso, Lisi, Jeronimo, Gabriela, Solernó, Pablo
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computer Hardware
Computer Science
Symbolic and Algebraic Manipulation
Theory of Computation
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Summary:The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper bounds for the regularity of the Hilbert–Kolchin function and the order of the ideal associated to the DAE systems under consideration, not depending on characteristic sets. Some quantitative and algorithmic results concerning differential transcendence bases and induced equivalent explicit ODE systems are also established.
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-008-0083-z