Differentiation index of generic DAE systems

LISI D'ALFONSO; GABRIELA JERONIMO; PABLO SOLERNÓ

Newark, NJ, USA

Workshop; Second International Workshop on Differential Algebra and Related Topics; 2007

The notion of the differentiation index for DAE systems of arbitrary order with generic second members is discussed. We prove an upper bound for the differentiation index in terms of the order of the input equations and we exhibit a probabilistic polynomial-time algorithm for the computation of this index. In addition, we obtain upper bounds for the regularity of the Hilbert-Kolchin function and the order of the ideal associated to the systems under consideration and we show how to compute an equivalent implicit ODE system.