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• W2182451272 abstract "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 real-closed fields is decidable. Furthermore, the problem of generating invariant varieties is shown to be as hard as minimizing the rank of a symbolic matrix, and is therefore NP-hard. We investigate symbolic linear algebra tools based on Gaussian elimination to efficiently automate the generation. The approach can, e.g., generate nontrivial algebraic invariant equations capturing the airplane behavior during take-off or landing in longitudinal motion." @default.
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• W2182451272 date "2014-01-01" @default.
• W2182451272 modified "2023-10-10" @default.
• W2182451272 title "Characterizing Algebraic Invariants by Differential Radical Invariants" @default.
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• W2182451272 doi "https://doi.org/10.1007/978-3-642-54862-8_19" @default.
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