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

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

2006-08-15

arxiv.org/abs/cs/0608064v2

Computer Science

Symbolic Computation

Scientific paper

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.

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