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If you liked The numerical solution of systems of polynomials arising in engineering and science by Andrew John Sommese, start with Interactions of classical and numerical algebraic geometry (2009) and Algorithms in algebraic geometry (2010). These recommendations are drawn from the same author, shared genres, and reader overlap on BookOrb.
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BookOrb recommends Interactions of classical and numerical algebraic geometry (2009) and Algorithms in algebraic geometry (2010).
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The numerical solution of systems of polynomials arising in engineering and science is by Andrew John Sommese.