Positive polynomial

In mathematics, a positive polynomial on a particular set is a polynomial whose values are positive on that set.

Let p be a polynomial in n variables with real coefficients and let S be a subset of the n-dimensional Euclidean space ℝⁿ. We say that:

For certain sets S, there exist algebraic descriptions of all polynomials that are positive (resp. non-negative, zero) on S. Any such description is called a positivstellensatz (resp. nichtnegativstellensatz, nullstellensatz.)

Similar results exist for trigonometric polynomials, matrix polynomials, polynomials in free variables, various quantum polynomials, etc.

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