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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: * 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. * p is zero on S if p(x) = 0 for every x in S.

Attributes	Values
rdfs:label	Polinomio positivo (es) Positive polynomial (en)
rdfs:comment	En matemáticas, un polinomio positivo en un conjunto dado es un polinomio cuyos valores son positivos en aquél conjunto. Sea p un polinomio en n variables con coeficientes reales y sea S un subconjunto del espacio vectorial n-dimensional euclidiano ℝn. Decimos que: * p es positivo en S si p(x) > 0 para toda x en S. * p es no-negativo en S si p(x) ≥ 0 para toda x en S. * p es cero en S si p(x) = 0 para toda x en S. (es) 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: * 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. * p is zero on S if p(x) = 0 for every x in S. (en)
dcterms:subject	Real algebraic geometry
Wikipage page ID	28416554 (xsd:integer)
Wikipage revision ID	1074534762 (xsd:integer)
Link from a Wikipage to another Wikipage	Semialgebraic set Real algebraic geometry Degree of a polynomial Mathematics Theodore Motzkin Matrix polynomial Farkas lemma Euclidean space Hilbert's seventeenth problem Hilbert's Nullstellensatz Coefficient Homogeneous polynomial Polynomial If and only if Integer Real number Set (mathematics) Polynomial SOS Trigonometric polynomial Stengle's Positivstellensatz Polytope Subset O-minimal structure
sameAs	Positive polynomial Positive polynomial Positive polynomial Positive polynomial
dbp:wikiPageUsesTemplate	dbt:About dbt:Citation_needed dbt:ISBN dbt:Reflist dbt:Manual
has abstract	En matemáticas, un polinomio positivo en un conjunto dado es un polinomio cuyos valores son positivos en aquél conjunto. Sea p un polinomio en n variables con coeficientes reales y sea S un subconjunto del espacio vectorial n-dimensional euclidiano ℝn. Decimos que: * p es positivo en S si p(x) > 0 para toda x en S. * p es no-negativo en S si p(x) ≥ 0 para toda x en S. * p es cero en S si p(x) = 0 para toda x en S. Para ciertos conjuntos S, hay descripciones algebraica de todos los polinomios que son positivos, no-negativos, o cero en S. Tal descripción es un positivstellensatz, nichtnegativstellensatz, o nullstellensatz. Este artículo se centrara en la primera de estas descripciones. Para la última de estas, véase Hilbert Nullstellensatz, el cual es el nullstellensatz más conocido. (es) 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: * 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. * p is zero on S if p(x) = 0 for every x in S. For certain sets S, there exist algebraic descriptions of all polynomials that are positive, non-negative, or zero on S. Such a description is a positivstellensatz, nichtnegativstellensatz, or nullstellensatz. This article will focus on the former two descriptions. For the latter, see Hilbert's Nullstellensatz for the most known nullstellensatz. (en)
gold:hypernym	Polynomial
prov:wasDerivedFrom	wikipedia-en:Positive_polynomial?oldid=1074534762&ns=0
page length (characters) of wiki page	8316 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Positive_polynomial
is Link from a Wikipage to another Wikipage of	Function of several real variables Theodore Motzkin Krivine–Stengle Positivstellensatz Bruce Reznick Nichtnegativstellensatz Global optimization Hilbert's seventeenth problem Real algebraic geometry Positivstellensatz Square (algebra) Polynomial SOS Negligible function Polynomial matrix spectral factorization Victoria Powers Positive polynomials
is Wikipage redirect of	Nichtnegativstellensatz Positivstellensatz Positive polynomials
is known for of	Bruce Reznick
is known for of	Bruce Reznick
is foaf:primaryTopic of	wikipedia-en:Positive_polynomial

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