On the generalized Ritt problem as a computational problem |
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Authors: | O D Golubitsky M V Kondratieva A I Ovchinnikov |
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Institution: | 1.University of Western Ontario, Department of Computer Science,London,Canada;2.Moscow State University, Department of Mechanics and Mathematics,Moscow,Russia;3.University of Illinois at Chicago, Department of Mathematics, Statistics, and Computer Science,Chicago,USA |
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Abstract: | The Ritt problem asks if there is an algorithm that decides whether one prime differential ideal is contained in another one
if both are given by their characteristic sets. We give several equivalent formulations of this problem. In particular, we
show that it is equivalent to testing whether a differential polynomial is a zero divisor modulo a radical differential ideal.
The technique used in the proof of this equivalence yields algorithms for computing a canonical decomposition of a radical
differential ideal into prime components and a canonical generating set of a radical differential ideal. Both proposed representations
of a radical differential ideal are independent of the given set of generators and can be made independent of the ranking. |
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