Computer Science Department
School of Computer Science, Carnegie Mellon University
Characterizing Algebraic Invariants by
Khalil Ghorbal, André Platzer
To appear in the
We give a necessary and sufficient characterization of algebraic invariants of algebraic differential equations by a differential radical invariance criterion, i.e. an explicit equation on higher-order Lie derivatives. Differential radical invariants are computationally easy to check using polynomial arithmetic on higher-order Lie derivatives. The characterization makes it possible to generate invariants by solving for the coefficients in a parametrization by comparing coefficients. We investigate symbolic linear algebra tools based on Gaussian elimination to efficiently automate the generation of algebraic invariants. The approach can, e.g., generate non-trivial algebraic invariants capturing the exact airplane behavior during take-off or landing in longitudinal motion.