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

Abstract

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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.

How to cite

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González-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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