Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials View Full Text


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Article Info

DATE

2016-09

AUTHORS

Daniel J. Bates, Jonathan D. Hauenstein, Matthew E. Niemerg, Frank Sottile

ABSTRACT

We give a Descartes’-like bound on the number of positive solutions to a system of fewnomials that holds when its exponent vectors are not in convex position and a sign condition is satisfied. This was discovered while developing algorithms and software for computing the Gale transform of a fewnomial system, which is our main goal. This software is a component of a package we are developing for Khovanskii-Rolle continuation, which is a numerical algorithm to compute the real solutions to a system of fewnomials. More... »

PAGES

281-304

References to SciGraph publications

  • 2016-02. Sign Conditions for Injectivity of Generalized Polynomial Maps with Applications to Chemical Reaction Networks and Real Algebraic Geometry in FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
  • 2011-10. Khovanskii–Rolle Continuation for Real Solutions in FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
  • 1999-05. Solving Zero-Dimensional Systems Through the Rational Univariate Representation in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • 2013-06. Numerically Computing Real Points on Algebraic Sets in ACTA APPLICANDAE MATHEMATICAE
  • 2010. Some Geometrical Aspects of Control Points for Toric Patches in MATHEMATICAL METHODS FOR CURVES AND SURFACES
  • 2008-10. Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals in FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
  • 1982-12. Factoring polynomials with rational coefficients in MATHEMATISCHE ANNALEN
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11075-015-0095-2

    DOI

    http://dx.doi.org/10.1007/s11075-015-0095-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1026617082


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