For linear systems we have general methods (i.e. Gauss elimination). Is there a general method for solving systems of quadratic equations with many variables? I heard about Groebner bases; is there another methods? Can you advise me some books or papers?
2026-04-05 17:13:49.1775409229
A general method for solving systems of quadratic equations
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Buchberger's algorithm is the most important method, I think. This amounts to computing a Gröbner basis. In some cases, however, one can do better (the complexity of Buchberger's algorithm is double exponential, hence very bad). A standard reference is the book of Bernd Sturmfels, Solving Systems of Polynomial Equations. Here are several other methods given, i.e.,from tropical algebraic geometry.
Remark: The restriction that all polynomial are quadratic is not really a simplification.