We study the concept of canonical characteristic set of a characterizable
differential ideal. We propose an efficient algorithm that transforms any
characteristic set into the canonical one. We prove the basic properties of
canonical characteristic sets. In particular, we show that in the ordinary case
for any ranking the order of each element of the canonical characteristic set
of a characterizable differential ideal is bounded by the order of the ideal.
Finally, we propose a factorization-free algorithm for computing the canonical
characteristic set of a characterizable differential ideal represented as a
radical ideal by a set of generators. The algorithm is not restricted to the
ordinary case and is applicable for an arbitrary ranking.Comment: 26 page