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Characterizing Algebraic Invariants by Differential Radical Invariants
[chapter]

2014
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Lecture Notes in Computer Science
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We prove that any invariant algebraic set of a given polynomial vector field can be algebraically represented by one polynomial and a finite set of its successive Lie derivatives. This so-called differential radical characterization relies on a sound abstraction of the reachable set of solutions by the smallest variety that contains it. The characterization leads to a differential radical invariant proof rule that is sound and complete, which implies that invariance of algebraic equations over

doi:10.1007/978-3-642-54862-8_19
fatcat:5fbanhbgzvbk3meu6m2luoqhg4