Abstract
Bertini_real is a command line program for numerically decomposing the real portion of a one- or two-dimensional complex irreducible algebraic set in any reasonable number of variables. Using numerical homotopy continuation to solve a series of polynomial systems via regeneration from a witness set, a set of real vertices is computed, along with connection information and associated homotopy functions. The challenge of embedded singular curves is overcome using isosingular deflation. This decomposition captures the topological information and can be used for further computation and refinement.
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Brake, D.A., Bates, D.J., Hao, W., Hauenstein, J.D., Sommese, A.J., Wampler, C. (2014). Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_29
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DOI: https://doi.org/10.1007/978-3-662-44199-2_29
Publisher Name: Springer, Berlin, Heidelberg
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