A Bound for the Order of Characteristic Set Elements of an Ordinary Prime Differential Ideal and some Applications

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With respect to an elimination ordering, we give an upper bound for the order of characteristic set elements of an ordinary prime differential ideal. Using some results of complexity in the algebraic case, we show that computing characteristic sets of ordinary prime differential ideals, by change of ordering, is single exponential time.

Received: January 8, 1997; revised version: May 6, 1999