Abstract
This chapter presents you the reader with one of the most powerful computer algebra tools, besides the polynomial resultants (discussed in the next chapter), for solving algebraic nonlinear systems of equations which you may encounter. The basic tools that you will require to develop your own algorithms for solving problems requiring closed form (exact) solutions are presented. This powerful tool is the “Gröbner basis” written in English as Groebner basis.
There are no good, general methods for solving systems of more than one nonlinear equation. Furthermore, it is not hard to see why (very likely) there never will be any good, general methods:
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For the terms appearing in this definition, refer to Appendix A.1, Definition A.5 on p. 502
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Awange, J.L., Paláncz, B. (2016). Groebner Basis. In: Geospatial Algebraic Computations. Springer, Cham. https://doi.org/10.1007/978-3-319-25465-4_4
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