Abstract
To decompose solution sets of polynomial systems into irreducible components, homotopy continuation methods generate the action of a natural monodromy group which partially classifies generic points onto their respective irreducible components. As illustrated by the performance on several test examples, this new method achieves a great increase in speed and accuracy, as well as improved numerical conditioning of the multivariate interpolation problem.
The first author thanks the Duncan Chair of the University of Notre Dame for its support.
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Sommese, A.J., Verschelde, J., Wampler, C.W. (2001). Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components. In: Ciliberto, C., Hirzebruch, F., Miranda, R., Teicher, M. (eds) Applications of Algebraic Geometry to Coding Theory, Physics and Computation. NATO Science Series, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1011-5_16
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