A New Definition for Passivity and Its Relation to Coherence
It is an essential step in decomposition algorithms for radical differential ideals to satisfy the so-called Rosenfeld property. Basically all approaches to achieve this step are based on one of two concepts: Coherence or passivity.
In this paper we will give a modern treatment of passivity. Our focus is on questions regarding the different definitions of passivity and their relation to coherence. The theorem by Li and Wang stating that passivity in Wu’s sense implies coherence is extended to a broader setting. A new definition for passivity is suggested and it is shown to allow for a converse statement so that coherence and passivity are seen to be equivalent.
KeywordsInduction Hypothesis Algebraic Group Decomposition Algorithm Derivative Operator Polynomial Algebra
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