On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations

Details On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations

2008-04-30

arxiv.org/abs/0804.4842v2

Mathematics

Commutative Algebra

Scientific paper

This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an algebraic definition of the differentiation index and prove a Jacobi-type upper bound for the sum of the order and the differentiation index. Our techniques also enable us to obtain an alternative proof of a combinatorial bound proposed by Jacobi for the order. As a consequence of our approach we deduce an upper bound for the Hilbert-Kolchin regularity and an effective ideal membership test for quasi-regular implicit systems. Finally, we prove a theorem of existence and uniqueness of solutions for implicit differential systems.

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