Abstract
A core computation in numerical algebraic geometry is the decomposition of the solution set of a system of polynomial equations into irreducible components, called the numerical irreducible decomposition. One approach to validate a decomposition is what has come to be known as the “trace test.” This test, described by Sommese, Verschelde, and Wampler in 2002, relies upon path tracking and hence could be called the “tracking trace test.” We present a new approach which replaces path tracking with local computations involving derivatives, called a “local trace test.” We conclude by demonstrating this local approach with examples from kinematics and tensor decomposition.
All authors supported in part by NSF ACI 1460032, Sloan Research Fellowship, and Army Young Investigator Program (YIP).
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Brake, D.A., Hauenstein, J.D., Liddell, A.C. (2016). Decomposing Solution Sets of Polynomial Systems Using Derivatives. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_16
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DOI: https://doi.org/10.1007/978-3-319-42432-3_16
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