Numerically Solving Polynomial Systems with Bertini

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Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations (2014, positive): “The algorithm is restricted to diﬀerential equations with polynomial nonlinearities: it solves the polynomial systems arising from subdomains with sophisticated numerical algebraic geometry software [8], and then employs continuation in an attempt to ﬁnd solutions of the original discretised system.”
Homotopy techniques for tensor decomposition and perfect identifiability (2014, methodology): “Recent progress is described in [3], which gives a semialgebraic description of tensors of format (n, n, n) of rank n and multilinear rank (n, n, n).”
Learning algebraic varieties from samples (2018, methodology): “(f), TrackType = 1, bertini_path = p1) Here p1 is the path to the Bertini binary.”
Global Identifiability of Differential Models (2018, background): “It turns out that, in practice, Gröbner bases computations are efficient enough for moderate-size problems that we encountered and significantly outperformed (unexpectedly!), for example, such numerical algebraic geometry software as Bertini [3] in several examples that we considered.”
Computational Design of Stephenson II Six-Bar Function Generators for 11 Accuracy Points (2016, methodology): “These synthesis equations were solved by the polynomial homotopy solver BERTINI [7, 8], which implemented a regeneration module that ran for 311 hours on 256×2.”