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Separating the solution sets of analytical and polynomial systems

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Abstract

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system.

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Authors and Affiliations

  1. Departmento de Estadística e Investigación Operativa, Universidad de Alicante, 03080, Alicante, Spain

    Miguel Angel Goberna

  2. Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, 72500, Puebla, Mexico

    Lidia Hernández

  3. Departamento de Física y Matemáticas, Escuela de Ciencias, Universidad de las Americas, Sta. Catarina Mártir, 72820, Cholula, Puebla, Mexico

    Maxim I. Todorov

Authors
  1. Miguel Angel Goberna
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  2. Lidia Hernández
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  3. Maxim I. Todorov
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Additional information

Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01.

Research supported by CONACyT of Mexico, Grant 130036.

Research partially supported by CONACyT of Mexico, Grant 44003.

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Goberna, M.A., Hernández, L. & Todorov, M.I. Separating the solution sets of analytical and polynomial systems. Top 13, 321–329 (2005). https://doi.org/10.1007/BF02579058

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  • DOI: https://doi.org/10.1007/BF02579058

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