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Results tagged with real-algebraic-geometry
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user 8846
Real algebraic geometry is the study of real solutions to algebraic equations with real coefficients. Its methods are rather different from classical algebraic geometry, which is typically done over an algebraically closed field (like the complex numbers).
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Polynomial degree comparison of Nullstellensatz and Positivstellensatz over real algebraic sets
Suppose we have a (finite) system of polynomials $P = \{ p_i \} \subseteq \mathbb{R}[x_1, \ldots, x_n]$. Then it is well known by the Nullstellensatz that either $P$ has a simultaneous zero over $\mat …
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