Positive polynomial

In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively non-negative) on that set. Precisely, 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:

  • p is positive on S if p(x) > 0 for every x in S.
  • p is non-negative on S if p(x) ≥ 0 for every x in S.
This article is about positive polynomials and positivstellensatz-like theorems. For the Krivine–Stengle Positivstellensatz, see Krivine–Stengle Positivstellensatz.
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