# A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.

Laureano González-Vega; Henri Lombardi

Extracta Mathematicae (1992)

- Volume: 7, Issue: 1, page 53-58
- ISSN: 0213-8743

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topGonzález-Vega, Laureano, and Lombardi, Henri. "A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.." Extracta Mathematicae 7.1 (1992): 53-58. <http://eudml.org/doc/39965>.

@article{González1992,

abstract = {Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning the semipolynomial expressions.},

author = {González-Vega, Laureano, Lombardi, Henri},

journal = {Extracta Mathematicae},

keywords = {Geometría algebraica; Campos ordenados; Problema 17 de Hilbert; Variedad algebraica; real Nullstellensatz; real closed field; positive semidefinite polynomial; sums of squares; totally ordered field; sup-inf-polynomially definable continuous functions; piecewise polynomial functions; Positivstellensatz},

language = {eng},

number = {1},

pages = {53-58},

title = {A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.},

url = {http://eudml.org/doc/39965},

volume = {7},

year = {1992},

}

TY - JOUR

AU - González-Vega, Laureano

AU - Lombardi, Henri

TI - A real nullstellensatz and positivstellensatz for the semipolynomials over an ordered field.

JO - Extracta Mathematicae

PY - 1992

VL - 7

IS - 1

SP - 53

EP - 58

AB - Let K be an ordered field and R its real closure. A semipolynomial will be defined as a function from Rn to R obtained by composition of polynomial functions and the absolute value. Every semipolynomial can be defined as a straight-line program containing only instructions with the following type: polynomial, absolute value, sup and inf and such a program will be called a semipolynomial expression. It will be proved, using the ordinary real positivstellensatz, a general real positivstellensatz concerning the semipolynomial expressions.

LA - eng

KW - Geometría algebraica; Campos ordenados; Problema 17 de Hilbert; Variedad algebraica; real Nullstellensatz; real closed field; positive semidefinite polynomial; sums of squares; totally ordered field; sup-inf-polynomially definable continuous functions; piecewise polynomial functions; Positivstellensatz

UR - http://eudml.org/doc/39965

ER -

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